DFI JOURNAL - Deep Foundations Institute “simplified procedure” for evaluating earthquake-induced (cyclic) liquefaction. The simplified procedure evaluates the potential for liquefaction

Vol. 7, No. 1 August 2013

DFI JOURNALThe Journal of the Deep Foundations Institute

PAPERS:Commentary on the Selection, Design and Specifi cation of Ground Improvement for Mitigation of Earthquake-Induced Liquefaction – Ground Improvement Committee of DFI [3]

Liquefaction Mitigation Synthesis Report prepared for the Ground Improvement Committee of the DFI – Timothy C. Siegel [13]

Grouted Micropiles for Foundation Remediation in Expansive Soil (8th Michael W. O’Neill Lecture) – John D. Nelson, Kuo-Chieh Chao, Daniel D. Overton,

Zachary P. Fox, Jesse S. Dunham-Friel [32]

Relationship between Installation Torque and Axial Capacities of Helical Piles in Cohesive Soils – Mohammed Sakr [44]

Ultimate Lateral Resistance of Piles in Cohesive Soil – Lassad Hazzar, Mourad Karray, Mounir Bouassida, Mahmoud N. Hussien [59]

TECHNICAL NOTE: Direct Solution of the Brinch-Hansen 90% Pile Ultimate Failure Load – Don W. Dotson [69]

Deep Foundations Institute is the Industry Association of Individuals and Organizations Dedicated to Quality and Economy in the Design and Construction of Deep Foundations.

DFI JOURNAL Vol. 7 No. 1 August 2013 [1]

From the Editors and Publisher 2013 DFI Board of TrusteesPresident:Robert B. BittnerBittner-Shen ConsultingEngineers, Inc.Portland, OR USAVice President:Patrick BerminghamBermingham Foundation SolutionsHamilton, ON CanadaSecretary:Matthew JanesIsherwood AssociatesBurnaby, BC CanadaTreasurer:John R. WolosickHayward Baker Inc. Alpharetta, GA USAImmediate Past President:James A. MorrisonKiewit Infrastructure Engineers Omaha, NE USAOther Trustees:David BorgerSkyline Steel LLCParsippany, NJ USAMaurice BottiauFranki Foundations BelgiumSaintes, BelgiumDan BrownDan Brown and Associates, PLLCSequatchie, TN USAGianfranco Di CiccoGDConsulting LLCLake Worth, FL USARudolph P FrizziLangan Engineering &Environmental Services Elmwood Park, NJ USABernard H. HertleinGEI Consultants Inc. Libertyville, IL USAJames O. JohnsonCondon-Johnson & Associates, Inc.Oakland, CA USADouglas KellerRichard Goettle, Inc.Cincinnati, OH USASamuel J. KosaMonotube Pile CorporationCanton, OH USAKirk A. McIntoshAMEC Environment & Infrastructure, Inc.Jacksonville, FL USARaymond J. PolettoMueser Rutledge Consulting EngineersNew York, NY USAArturo L. Ressi di CerviaKiewit Infrastructure GroupWoodcliff Lake, NJ USAMichael H. WysockeyThatcher Engineering Corp.Chicago, IL USA

Journal PublisherManuel A. Fine, B.A.Sc, P.Eng

Journal EditorsAli Porbaha, Ph.D., P.E. Central Valley Flood Protection Board Sacramento, CA, USADan A. Brown, Ph.D. Dan Brown and Associates, Sequatchie, TN, USAZia Zafir, Ph.D., P.E. Kleinfelder Sacramento, CA, USA

Associate EditorsLance A. Roberts, Ph.D., P.E.RESPEC Consulting & ServicesRapid City, SD USAThomas Weaver, Ph.D., P.E.Nuclear Regulatory CommissionRockville, MD USA

Published By Deep Foundations Institute

Copyright © 2013 Deep Foundations Institute. AII rights reserved. Written permission must be obtained from DFI to reprint journal contents, in whole or in part.

ContactDFI Headquarters326 Lafayette AvenueHawthorne, NJ 07506staff@dfi .orgwww.dfi .org

DFI, its directors and offi cers, and journal editors assume no responsibility for the statements expressed by the journal’s authors. International Standard Serial Number (ISSN): 1937-5247

Mission/Scope The Journal of the Deep Foundations Institute publishes practice-oriented, high quality papers related to the broad area of “Deep Foundations Engineering”. Papers are welcome on topics of interest to the geo-professional community related to, all systems designed and constructed for the support of heavy structures and excavations, but not limited to, different piling systems, drilled shafts, ground improvement geosystems, soil nailing and anchors. Authors are also encouraged to submit papers on new and emerging topics related to innovative construction technologies, marine foundations, innovative retaining systems, cutoff wall systems, and seismic retrofit. Case histories, state of the practice reviews, and innovative applications are particularly welcomed and encouraged.

DFI JOURNAL

The DFI Journal has been encouraging the Technical Committees of the DFI to produce committee authored papers describing state-of-the-art subjects within the realm of their committee’s special interests. We are pleased to include in this edition the first such paper, “Commentary on the Selection, Design and Specification of Ground Improvement for Mitigation of Earthquake-Induced Liquefaction, authored by the Ground Improvement Committee. A companion paper which reports" the results of a DFI Committee Project Fund program follows, in the form of a report authored by Timothy C. Siegel entitled "Liquefaction Mitigation Synthesis Report". We are hopeful that will set a precedent, to be followed by other committee authored papers.

This edition includes a paper authored by John D. Nelson et al, “Grouted Micropiles for Foundation Remediation in Expansive Soil”, which was the subject of the 8th Michael W. O’Neill Memorial Lecture. There is also another paper from Mohammed Sakr, who has been a prolific contributor to the DFI Journal on the subject of Helical Piles, which discusses the relationship between installation torque and axial capacity of helical piles in cohesive soils.

We wish to thank our dedicated reviewers for their attention to detail and service to the authors, the DFI Journal publication, and the industry in providing input to enhance quality of the papers. We are pleased to report that new names are popping up as well as repeat services by some very responsive reviewers.

We continue to encourage submission of case history papers in particular. We are also open to publishing another themed edition and again request that any Technical Committee desiring to have their topic as the focus of a future themed edition contact the Publisher.

Other comments, suggestions, and submissions are welcome and may be submitted via the DFI website at www.dfi.org.


Commentary on the Selection, Design and Specifi cation of Ground Improvement for Mitigation of Earthquake-Induced LiquefactionBy the Ground Improvement Committee of The Deep Foundations Institute

ABSTRACTThe evaluation of earthquake-induced liquefaction has become a routine part of geotechnical engineering design. For a given project, if an analysis identifies a potential for liquefaction and the consequences of liquefaction are deemed unacceptable, then some form of hazard mitigation is required. Mitigation efforts may consist of removing the liquefiable soils, bypassing the liquefiable soils with deep foundations, structurally accommodating the deformations or strength loss caused by liquefaction, or preventing the onset of liquefaction through ground improvement. The fundamental ground improvement mechanisms for liquefaction mitigation include densification, drainage, and reinforcement. When evaluating, recommending and specifying various ground improvement methods for liquefaction mitigation, practitioners should understand the fundamental mechanics involved and applicability and limitations of the various methods. The DFI Ground Improvement Committee offers a review of the fundamental mechanics and commentary on the applicability and limitations of each method to provide clarity and guidance on the issues related to ground improvement for liquefaction mitigation.

INTRODUCTIONLiquefaction and its effect on engineered structures was recognized as an earthquake hazard in the 1960s after the widespread liquefaction-induced damage caused by the 1964 Niigata (Japan) and Alaskan earthquakes (Seed and Lee, 1966; Seed and Idriss, 1967). Independently and concurrently, Whitman (1971) and Seed and Idriss (1971) proposed a “simplified procedure” for evaluating earthquake-induced (cyclic) liquefaction. The simplified procedure evaluates the potential for liquefaction based on the relationship between earthquake-generated cyclic shear stresses and empirically-based liquefaction resistance as a function of field testing (e.g., Standard Penetration Test N-values, Cone Penetration Test tip resistance, etc.). Alternative methods for the evaluation of cyclic liquefaction have been proposed by others (e.g., Arulmoli et al, 1985; Poulos et al, 1985; Kayen and Mitchell, 1997; Andrus and Stokoe, 2000) but the simplified procedure remains the most commonly used liquefaction evaluation methodology. Although liquefaction analysis and the design of liquefaction mitigation have been part of engineering practice in the western United States for at least 40 years and guidelines are in place (CGS, 2008; Martin and Lew, 1999), only with the widespread adoption

of the International Building Code (IBC) in 2000 did earthquake hazards become an important design consideration in the central and eastern U.S.

As a result of the increased seismic demand presented in the IBC, many sites throughout the U.S. are classified as liquefiable under the design earthquake parameters. In the case of the IBC, engineers are instructed to “address” liquefaction. Options for addressing liquefaction include the following: 1) move the project to a different site that is not liquefiable, 2) design the structure to withstand liquefied conditions, or 3) use ground improvement to reduce the risk of liquefaction to an acceptable level. Because moving the project or designing for the consequences of liquefaction is often technically or financially unfeasible, liquefaction mitigation by ground improvement is frequently a preferred option.

The membership of the Deep Foundations Institute (DFI) includes government agency engineers, private consultants, and contractors; all of which have significant roles in the design, construction, and evaluation of ground improvement methods for the mitigation of liquefaction. As such, the DFI has a vested interest in examining the state-of-practice for the benefit of its members and their clients. This paper describes the fundamental

[4] DFI JOURNAL Vol. 7 No. 1 August 2013

mechanics of the most common mitigation methods, and provides brief commentary on the state-of-the-practice.

LIQUEFACTION EVALUATION Workshops were held in 1996 and 1998 by the National Center for Earthquake Engineering and Research (NCEER) in an effort to develop a consensus on the evaluation of liquefaction potential. These workshops led to the publication of a summary report (Youd et al., 2001) which, for a short time, served as a consensus document on the evaluation of liquefaction triggering.

Numerous modifications and additions to the simplified procedure have been proposed in the last decade resulting in a diminished consensus on liquefaction evaluation procedures. Additionally, following the 1999 Kocaeli earthquake and the 1999 Chi-Chi earthquake, various researchers expanded the range of potentially liquefiable materials to include some fine-grained soils that would previously not have been considered in a liquefaction evaluation. Various screening procedures have been proposed (e.g., the “Chinese” Criteria summarized in Youd et al, 2001; Bray and Sancio, 2006; Boulanger and Idriss, 2006; Idriss and Boulanger, 2008). The “Chinese” Criteria has been generally disregarded as a valid design method; however a general consensus on the alternate methods has not been achieved. This paper offers no guidance on the evaluation and screening procedures, but as subsequently presented the selected evaluation procedures must be clearly identified and communicated in the project documents related to liquefaction mitigation.

FUNDAMENTAL MECHANISMS OF GROUND IMPROVEMENT FOR LIQUEFACTION MITIGATIONA survey of the available ground improvement liquefaction mitigation techniques by the National Research Council (NRC, 1985) determined that three fundamental mechanisms are usually involved: 1) densification, 2) drainage, and/or, 3) reinforcement. These three methods are discussed in the following sections:

Densification. For sands below the groundwater table, the resistance to liquefaction is largely a function of relative density (Seed and Lee,

1966). It rationally follows that a substantial number of liquefaction mitigation techniques (e.g., vibro-compaction, vibro-stone columns, dynamic compaction, compaction grouting, etc.) are intended to sufficiently densify the soil so that liquefaction will not occur, or its consequences may be controlled, during the design earthquake. When compared to other methods, densification is attractive because improvement can be verified using the properties of the improved soil (e.g. post-improvement Standard Penetration Test N-values or Cone Penetration Test tip resistances). Baez, 1995 developed design densification models that allow an estimation of approximate improvement levels when using vibro-stone columns. Design and construction considerations of densification include (but are not limited to) the following:

• Fines Content: As the fines content of a granular soil increases, the effectiveness of all densification methods will decrease. Figs 1 and 2 illustrate this trend. Additionally, whether the fines are plastic or non-plastic and/or silt-sized or clay-sized is also important. Even a small clay fraction may limit the ability of a soil to be effectively densified (Mackiewicz & Camp, 2007). Therefore, densification methods may not be able to mitigate liquefaction in silty and clayey soils. However, it has been possible, in some cases, to increase densification of silty sands and silts when wick drains are pre-installed in combination with vibro-stone columns (Luehring et al., 2001; Seed et al., 2003, ). Micaceous sands may also present a challenge to densify. This is because the mica portion

sand silt claygravel

[FIG. 1] - Gradation curves that lie to the left of the transition zone are more easily densifi able. Soil gradation

curves within the transition zone require additional engineering judgment and test programs.


is typically retained on the No 200 sieve and is therefore not included in the fines content. However, the flat sheet particles are not easily re-arranged into a denser configuration via vibratory and cavity expansion ground treatments.

• The densification process (via vibratory energy or undrained cavity expansion) elevates pore pressures and will temporarily destroy ageing-related bonding, cementation, micro-structure, etc. As a result, penetration testing (e.g., SPT N-value or cone tip resistance) performed soon after densification may not be representative of the true degree of improvement, and the post-improvement penetration resistances may be expected to increase over time (Mitchell and Solymar, 1984; Schmertmann, 1987; Mesri et al., 1990; Charlie et al., 1992). In practice, a minimum 7 day “rest” period is often necessary to evaluate densification effects. For many projects, it is not feasible to delay the project in order to confirm the effectiveness of the ground improvement. Consequently, the analysis of the field data may consider the effects of time on penetration resistance using published relationships (Joshi, et al., 1995; Leon et al., 2006).

• There will be variation in the degree of soil improvement between the point of application of the vibroflot, point of impact,

compaction grout, etc. Degan (1997) reports a 20% variation in CPT tip resistance over a lateral distance of 20 inches (500 mm). While it would be ideal that the design computations and post-improvement testing include consideration of the lateral variation of the improvement, it is conservative to perform the post-improvement testing at the maximum distance between adjacent application points.

Drainage. By definition, cyclic liquefaction is the state of essentially zero effective stress that results when the ratio of excess pore pressure to the initial vertical effective stress (also called the pore water pressure ratio) is essentially 1. Liquefaction can be mitigated in sands if the development of high excess pore water pressure can be prevented using drains. Seed and Booker (1977) published design charts for vertical gravel drains based on the soil properties, the liquefaction susceptibility, and the earthquake conditions. More recently, Pestana et al. (1997) developed the finite element computer program FEQDrain to assist in the design of prefabricated drains consisting of a corrugated perforated plastic pipe with a geosynthetic covering (known commercially as EQ drains). As illustrated in Fig. 3, the compressibility of sand increases dramatically once the pore pressure ratio exceeds 0.6. Therefore, the objective of the design of an earthquake drain liquefaction mitigation program is to determine the spacing such that the pore pressure ratio is maintained below 0.6 to minimize deformation.

[FIG. 2] – Relationship of compactibility to CPT friction ratio (after Massarsch 1991) A larger friction ratio is

typically indicative of a higher fi nes content.

[FIG. 3] - Relationship of compressibility to peak pore pressure ratio (Seed and Booker 1977).

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

0.00 0.20 0.40 0.60 0.80 1.00

Peak Pore Pressure Ratio

Nor

mal

ized

Coe

ffic

ient

of

Vol

um

etri

c C

ompr

essi

bilit

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Dr = 30%

Dr = 40%

Dr = 50%

Dr = 60%

Dr = 70%

Dr = 80%

Dr = 90%


Design and construction considerations for the use of enhanced drainage as a liquefaction mitigation method include (but are not limited to) the following:

• Aggregate drains have been used with success in Japan. These drains are constructed using aggregate gradations that consider filter requirements for the soils in which they are being installed. Additionally, the drains are installed using low-energy methods that do not cause crushing of the aggregate or mixing of the aggregate and surrounding soil.

• Conventional stone column or aggregate pier construction in the US may not create an element that is capable of effectively functioning as a drain for purposes of liquefaction mitigation (Green, 2012). Even with the typical highly permeable aggregate that such columns or piers use, mixing/infiltration of the surrounding soils into the stone and/or crushing of the aggregate during the compaction process results in an in situ matrix with measured soil intrusions of about 20% by weight and permeability values on the order of 1E-02 cm/sec (Baez and Martin, 1995). If stone columns or aggregate piers are intended to enhance drainage, consideration must be given to the gradation and hardness of the backfill stone, the potential for mixing during the installation process, and the process used to construct the columns.

• The spacing of drains is dependent on the permeability of the soil that is to be mitigated. The spacing will become impractical for silts or sands with significant fines content. Oftentimes, soils that are most appropriate for mitigation through drainage are also appropriate for densification (high permeability sands).

• Although drains can successfully mitigate liquefaction and the associated substantial loss of soil strength, the potential for volumetric compression may remain after drain installation and consideration must be given to allowable deformations. Large shaking table test research in Japan (Iai, 1988) has demonstrated that the volume of water drained during the seismic event is approximately equal to the amount of settlement observed at the surface of the drain treated ground. This suggests that

the drains effectively facilitate, rather than prevent volume change, which is not a desired consequence for an effective liquefaction countermeasure designed to reduce seismic settlements.

• When using drainage as the sole liquefaction countermeasure (i.e., no densification or reinforcement), the designer is also cautioned to take into account the variability of the brief high seismic pulses from large earthquakes and their effect on a temporary clogging of the drain which may render it ineffective. Seed et al., 2003 refer to a drainage countermeasure as a “brittle” solution which may only be effective if it promotes the rapid pore pressure dissipation during the few critical seconds of the earthquake.

• The effectiveness of an earthquake drain installation cannot be verified through field testing. Therefore, designers must rely on the analytical design method.

Reinforcement. Liquefaction mitigation by shear reinforcement relies on the installation of stiffer elements within a soil mass to reduce the cyclic shear stress applied to liquefiable soils. Soil reinforcement options include: full soil treatment (via permeation grouting, jet grouting, or mass soil mixing), cellular or panel reinforcement (using jet grouting, soil mixing, or slurry wall systems), or individual column elements (using jet grout columns, mechanically mixed columns, stone columns, aggregate piers, grout columns, etc.). Post-earthquake observations suggest that reinforcement also reduces the earthquake-related settlement by providing an improved axial stiffness.

Baez (1995) presented a design methodology based on fundamental principles of strain compatibility between reinforcing elements and soil, and force equilibrium to calculate the reduction in cyclic shear stress on a soil mass as a function of the soil shear modulus, reinforcement shear modulus, and the amount of treatment. This methodology has been used in practice to design reinforcement-based ground improvement programs for liquefaction mitigation. However, numerous researchers have evaluated the Baez procedure and concluded that, for columnar reinforcement, it significantly overestimates the effectiveness of reinforcement in terms of shear stress reduction (Goughnour and Pestana, 1998;


Martin and Olgun, 2006, Olgun and Martin, 2008, Rayamajhi et al., 2012, Nguyen et al., 2012, Boulanger, 2012). More specifically, the research findings indicate that there is a lack of strain compatibility between the soil and the reinforcement element (stone column, aggregate pier, soilcrete column, etc.) and significant benefits of the stiffer element in terms of shear reinforcement are not realized. In contrast, research shows that wall panels arranged to form a cellular pattern maintain shear strain compatibility between the soil and the reinforcement and contribute significantly to shear stress reduction. In summary, if shear stress reduction is the design objective, as might be the case for a soil that is not easily densified or drained, current research and models indicate that wall panels or a cellular pattern of reinforcement can be effective, whereas discrete columns are not. Cellular and panel reinforcement geometries have been widely and successfully implemented in Japan and an increasing use of these geometries for non-densifiable soils will likely occur in the U.S.

Numerous researchers have evaluated the performance of improved sites after they have been subjected to earthquakes and sites with ground improvement have out-performed (i.e., settled less, suffered less foundation damage, etc.) similar nearby sites without ground improvement (Iai et al, 1994; Mitchell et al, 1995; Yasuda et al, 1996; Mitchell and Wentz, 1998; Mitchell et al, 2000; Hausler, 2002; Martin and Olgun, 2006). In particular, some sites with column reinforcement (e.g., stone columns, soilcrete columns, jet grout columns) out-performed sites without any improvement indicating that even if the column reinforcement does not provide a shear stress reduction benefit as initially assumed (i.e., does not prevent the onset of liquefaction), it may still be effective in limiting the consequences of liquefaction. Not all of the possible mechanisms for the improved performance are fully understood but a likely component is a reduction in vertical deformation due to the increased axial stiffness provided by the elements (Martin and Olgun, 2006). Additionally, the increase in the effective lateral stress that is produced by some improvement methods (e.g., aggregate piers, stone columns) may reduce shear strains during shaking, thereby reducing the potential or

extent of liquefaction. Confinement pressures and the engagement of discrete columns via caps and mats that connect the columns are another possible contributing factor to improved performance, as compared to free field conditions. Current analytical models have not evaluated such conditions, but experimental centrifuge tests (Adalier et al. 2003) show improved liquefaction consequence results for discrete columns subjected to building pressures and confinement. Most discrete column applications include a building or structure slab or mat atop the discrete columns.

With respect to the mechanism of reinforcement for liquefaction mitigation, a number of issues remain for consideration:

• The shear stress reduction potential for individual reinforcing elements (e.g., stone columns, aggregate piers, grout columns, soilcrete columns) appears to be very small. The stress reduction potential decreases as the diameter of the element decreases and the efficiency of the system decreases as the modulus of the element increases (Boulanger, 2012) but it does increase as the confining stress increases (Green et al 2008). Discrete column designs based on the Baez (1995) concept may be significantly unconservative.

• Panel or cellular reinforcement can effectively reduce the shear stresses within a soil mass and the recent work by Nguyen et al. (2012) provides a design methodology that is applicable for all sites. This methodology generally matches the Baez (1995) methodology when panel coverage is in excess of about 25%.

• Individual reinforcing elements may be effective in reducing vertical displacements following ground shaking. A rational analytical approach for the use of individual elements to reduce seismic settlement (while not eliminating liquefaction potential) has not been developed.

• Much like drainage for mitigation, the effectiveness of reinforcement cannot be field verified post-treatment. Engineers must rely on theoretical analysis for their design, the methods for which have not reached an industry-wide consensus.


SPECIFICATION CONSIDERATIONSDevelopment of appropriate specifications for liquefaction mitigation is not a trivial matter and is an area of practice that needs improvement. The means and methods for ground improvement are extremely diverse and, as a result, ground improvement programs are frequently contracted using a performance or design-build specification. When compared to a detailed design-bid-build approach, these contracting methods offer many benefits to both owners and specialty geo-constructors, but the following items should be addressed when developing the specifications:

• The design earthquake criteria should be thoroughly described in the project specifications. If the specialty geo-constructor is allowed to develop the design criteria, the owner’s representative should be of sufficient sophistication to confirm that the methodology used in developing the design criteria is consistent with the state-of-practice.

• Because there is no consensus on liquefaction evaluation and screening procedures and different methods will yield different results, the acceptable evaluation and screening method(s) should be specifically defined in the project specifications. The definition should include the required procedures for evaluating the efficacy of the ground improvement. If post-improvement in situ testing is required, the interpretation and correction (e.g., corrections to N-values for energy, rod length, overburden stress, etc.) procedures should be specified.

• A “seismic” or post-earthquake settlement tolerance is frequently specified. The selection of the settlement tolerance should reflect the performance objectives (i.e., collapse prevention in accordance with the International Building Code or a more stringent serviceability requirement). With respect to collapse prevention, post-earthquake reconnaissance routinely shows that structures tolerate very large liquefaction-induced settlement (e.g., 0.1 to 1 m or 0.33 to 3.3 ft) without collapse. Examples from the 2010-2011 Christchurch Earthquakes are shown in Figs. 4 and 5. With respect to serviceability requirements, it should be recognized that deformations

associated with liquefaction can only be crudely estimated. The expectation of a guaranteed maximum settlement with little or no tolerance is unrealistic.

• As noted above, ground improvement programs that rely on densification are particularly attractive since the effectiveness of the densification can be evaluated using post-improvement in situ testing. For such programs, a post-improvement criteria (e.g., cone penetrometer tip resistance, Standard Penetration Test N-value, dilatometer horizontal stress index, etc.) is frequently specified. The criteria should reflect the values needed in accordance with the specified evaluation procedure and design hazard. Additionally, it must be recognized that some soils (e.g., silty sands, slightly

[FIG. 4] Six story structure that experienced 0.26m of liquefaction-induced differential settlement (after

Cubrinovski and McCahon, 2011)

[FIG. 5] Two story structure that experienced 0.1 to 0.25m of liquefaction-induced settlement (after

Cubrinovski and McCahon, 2011)


clayey sands, silts) will not be able to be densified and the post-improvement criteria must make allowances for such strata. The criteria should also reflect the time-dependency of the post-improvement test results.

• Use of Cone Penetration Test (CPT) is widely accepted as an economical way to evaluate improvement based on tip resistance. A boundary for what may be considered non-liquefiable, and therefore not in need of improvement, is typically the use of the calculated parameter, Ic (soil behavior type index). However, the designer must recognize that this index was originally defined for non-disturbed and often normally consolidated conditions. Ground treatments with vibratory energy and cavity displacement countermeasures work by remolding and reconstituting the soil structure. Therefore, pre-treatment Ic soil type definitions do not necessarily match post treatment Ic calculations (Baez, 2005). A calibration of this parameter may need to be taken into account for the proper interpretation of post treatment CPT results.

• For soils that cannot be densified and/or for ground improvement methods that cannot be evaluated via post-improvement testing, the efficacy of the program must be based on construction observation and the fundamental mechanics and empirical observations. The tools available to researchers and practitioners have advanced significantly, but continuing research has illustrated limitations on using past practices (such as the lack of strain compatibility). Liquefaction mitigation solutions should be based on sound soil mechanics, particularly when designing mitigation programs that are not field verifiable.

CONCLUSIONS AND RECOMMENDATIONS This document presented a brief overview of the three mechanisms - densification, drainage and reinforcement - currently used for liquefaction mitigation within the geotechnical construction industry. The summaries provided describe the basic mechanics and potential concerns related to each method. Significant concerns include the following:

• When used in appropriate soils, densification allows for improvement verification, unlike drainage and reinforcement. However, densification is only applicable in cohesionless soils with less than 20% fines (and a significantly lower clay content). In cases where wick drains have been pre-installed, densification may be possible for soils with fines content up to 65% and small clay fractions. Note that successful cases using wick drains and stone columns generally require area replacement ratios in excess of 20-30% as well as wick drains that are close to the densification point. Engineers are encouraged to consider the soil characteristics and drainage properties when writing specifications that require post-treatment verification of densification.

• Because ground improvement methods that apply drainage and/or reinforcement are not amenable to post-treatment verification, the analysis used to design these types of ground improvement methods must be based on fundamental mechanical principles and empirical observations.

• Although post-earthquake observations indicate that reinforcement can effectively mitigate the effects of liquefaction, consensus has not been reached for developing a state-of-the-practice design methodology for liquefaction mitigation using soil reinforcement. Furthermore, recent research indicates that columnar reinforcement is not as effective in reducing the soil shear stress as previously believed. This is resulting in an inconsistent and potentially unconservative range of designs for this method. Engineers and agencies must be conscious of this inconsistency when evaluating reinforcement proposals and designs and continue to rely on fundamental mechanics and the most current research findings.

The geotechnical engineering community will be well served by a continued focus on the mechanics, effectiveness, and limitations of all liquefaction mitigation methods. With each new earthquake, the engineering knowledge base expands, and the engineering practice will evolve.


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17. Hausler, E.A., (2002). “Influence of ground improvement on settlement and liquefaction: a study based on field case history evidence and dynamic geotechnical centrifuge tests”, Ph.D. Dissertation, Department of Civil and Environmental Engineering, University of California, Berkeley.

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19. Iai, S., Matsunaga, Y., Morita, T., Miyata, M., Sakurai, H., Oishi, H., Ogura, H., Ando, Y., Tanaka, Y., and Kato, M. (1994). “Effects of remedial measures against liquefaction at 1993 Kishiro-Oki Earthquake”, Proceedings 5th U.S.-Japan Workshop on Earthquake Resistant Design of Lifeline Facilities and Countermeasures Against Soil Liquefaction, NCEER-94-0026, Nov, pp. 135-152.


20. Idriss, I.M. and Boulanger, R.W. (2008) Soil Liquefaction During Earthquakes, Monograph MNO-12, Earthquake Engineering Research Institute.

21. Joshi, R.C., Achari, G., Shenbaga, R.K., and Wijeweera, H. (1995). “Effect of aging on the penetration resistance of sands”, Canandian Geotechnical Journal, Vol 32, pp. 767-782.

22. Kayen, R.E. and Mitchell, J.K. (1997) “Assessment of Liquefaction Potential During Earthquakes by Arias Intensity”, Journal of Geotechnical and Geoenvironmental Engineering, 123(12), pp. 1162-1174.

23. Leon, E., Gassman, S.L., and Talwani, P. (2006). “Accounting for soil aging when assessing liquefaction potential”, Journal of Geotechnical and Geoenvironmental Engineering, 132(3), pp. 363-377.

24. Luehring, R., Snorteland N., Stevens, M., and Mejia, L. (2001) “Liquefaction Mitigation of a Silty Dam Foundation Using Vibro-Stone Columns and Drainage Wicks: A case History at Salmon Lake Dam”, 21st USSD Annual Meeting and Lecture Proceedings, Denver, Colorado, July 30 – August 03, 2001.

25. Mackiewicz, S. M., and Camp, W. M. (2007). “Ground Modification: How Much Improvement?”, Proceedings Geo-Denver, ASCE GSP 172, Denver, CO.

26. Martin G.R., and Lew M. (Editors) (1999). “Recommended Procedures for Implementation of DMG Special Publication 117 – Guidelines for Analyzing and Mitigating Liquefaction in California”, Southern California Earthquake Center, University of Southern California, March.

27. Martin, J.R., II, and Olgun, C.G. (2006). “Liquefaction mitigation using jet-grout columns – 1999 Kocaeli earthquake case history”, Ground Modification and Seismic Mitigation, ASCE GSP 152, pp. 349-358.

28. Massarsch, K.R., (1991). “Deep Soil Compaction Using Vibratory Probes”, ASTM Symposium on Design, Construction, and Testing of Deep Foundation Improvement: Stone Columns and Related Techniques, Robert C. Bachus, Ed. ASTM Special Technical Publication, STP 1089, Philadelphia, pp. 297-319.

29. Mesri, G., Feng, T.W. and Benak, J.M. (1990). “Postdensification penetration resistance in clean sands”, Journal of Geotechnical Engineering, 116(7), pp. 1095-1115.

30. Mitchell, J.K., Baxter, C.D.P., and Munson, T.C. (1995). “Performance of improved ground during earthquakes”, Soil Improvement for Earthquake Hazard Mitigation, ASCE GSP No. 49, pp. 1-36.

31. Mitchell, J. K., Martin, J. R., Olgun, C. G., Emrem, C., Durgunoglu, H. T., Cetin, K. O., and Karadayilar, T. (2000). "Performance of Improved Ground and Earth Structures”, Earthquake Spectra, 16(Supplement "A"), pp. 191-225

32. Mitchell, J.K. and Solymar, Z.V. (1984). “Time-dependent strength gain in freshly deposited or densified sand”, Journal of Geotechnical Engineering, 110(11), pp. 1559-1576.

33. Mitchell, J.K., and Wentz, F.J., Jr., (1998). “Improved-ground performance during the earthquake”, The Loma Prieta, California, earthquake of October 17, 1989 - Liquefaction, Holzer, T.L., Ed., U. S. Geological Survey Professional Paper 1551-B, pp. B241-B272.

34. Moseley, M.P. and Kirsch, K. (2004) “Ground Improvement, 2nd Edition”, Spon Press, New York, NY.

35. National Research Council (1985) “Liquefaction of Soils During Earthquakes”, National Research Council, Committee on Earthquake Engineering, Washington, District of Columbia.

36. Nguyen, T.V., Rayamajhi, D., Boulanger, R.W., Ashford, S.A., Lu, J., Elgamal, A., and Shao, L. (2012) “Effect of DSM grids on shear stress distribution in liquefiable soil”, Proceedings GeoCongress 2012, State of the Art and Practice in Geotechnical Engineering, ASCE GSP 255, Oakland, CA, pp. 1948-1957.

37. Olgun, C.G. and Martin, J.R., II, (2008) “Numerical modeling of the seismic response of columnar reinforced ground”, Proceedings Geotechnical Earthquake Engineering and Soil Dynamics IV, ASCE GSP 181, Sacramento, CA.


38. Pestana, J.M., Hunt, C.E. and Goughnour, R.R. (1997) “FEQDrain: A Finite Element Computer Program for the Analysis of the Earthquake Generation and Dissipation of Pore Water Pressure in Layered Sand Deposits with Vertical Drains”, Report No. UCB/EERC-97/15, University of California, Berkeley, 88 p.

39. Poulos, S.J., Castro, G., and France, J.W. (1985) “Liquefaction Evaluation Procedure”, Journal of Geotechnical Engineering, 111(6), pp. 772-792.

40. Rayamajhi, D., Nguyen, T.V., Ashford, S.A., Boulanger, R.W., Lu, J., Elgamal, A., and Shao, L. (2012) “Effect of discrete columns on shear stress distribution in liquefiable soil”, Proceedings GeoCongress 2012, State of the Art and Practice in Geotechnical Engineering, ASCE GSP 255, Oakland, CA, pp. 1918-1927.

41. Seed, H.B. and Lee, K.L. (1966) “Liquefaction of Saturated Sands During Cyclic Loading”, Journal Soil Mechanics and Foundation Division, ASCE, Vol. 92, No. SM6, pp. 105-134.

42. Seed, H.B. and Idriss, I.M. (1967) “Analysis of Soil Liquefaction: Niigata Earthquake”, Journal Soil Mechanics and Foundation Division, ASCE, Vol. 93, No. SM3, pp. 83-108.

43. Seed, H.B. and Idriss, I.M. (1971) “Simplified Procedure for Evaluating Soil Liquefaction Potential”, Journal Soil Mechanics and Foundation Division, ASCE, Vol. 97, No. SM9.

44. Seed, H.B. and Booker, J.R. (1977) “Stabilization of Potentially Liquefiable Sand Deposits Using Gravel Drains”, Journal Soil Mechanics and Foundation Division, ASCE, Vol. 103, No. GT7, pp. 757-768.

45. Seed, R.B., Cetin, K.O., Moss, R.E.S., Kammerer, A.M., Wu, J., Pestana, J.M., Riemer, M.F., Sancio, R.B., Bray, J.D., Kayen, R.E., and Faris, A. (2003) “Recent Advances in Soil Liquefaction Engineering: A Unified and Consistent Framework”, 26th Annual ASCE Los Angeles Geotechnical Spring Seminar, Keynote Presentation, H.M.S Queen Mary, Long Beach, California.

46. Schmertmann, J.H. (1987) Discussion on “Time-dependent strength gain in freshly deposited or densified sand by J.K. Mitchell and Z.V. Solymar", Journal of Geotechnical Engineering, pp. 117(9), pp. 171-176.

47. Whitman, R.V. (1971) “Resistance of Soil to Liquefaction and Settlement”, Japanese Society of Soil Mechanics and Foundation Engineering. Vol. 11, No. 4. December.

48. Yasuda, S., Ishihara, K., Harada, K. and Shinkawa, N. (1996). “Effect of improvement on ground subsidence due to liquefaction”, Soils and Foundations, JSSMFE, Special Issue, January, pp. 99-107.

49. Youd, T.L., Idriss, I.M., Andrus, R.D., Arango, I., Castro, G., Christian, J.T., Dobry, R., Finn, W.D.L., Harder, L.F., Jr., Hynes, M.E., Ishihara, K., Koester, J.P., Liao, S.S.C., Marcuson, W.F., III, Martin, G.R., Mitchell, J.K., Moriwaki, Y., Power, M.S., Robertson, P.K., Seed, R.B., Stokoe, K.H., II. (2001) “Liquefaction resistance of soils: Summary report from the 1996 NCEER and 1998 NCEER/NSF workshop on evaluation of liquefaction resistance of soils”, Journal of Geotechnical and Geoenvironmental Engineering, 127(10), pp. 817-833.


Liquefaction Mitigation Synthesis ReportPrepared for: The Ground Improvement Committee of the Deep Foundations Institute

By: Timothy C. Siegel, P.E., G.E., D.GE, Dan Brown and Associates PC, Knoxville; (865) 357-1715;[email protected]

PROLOGUE

This report presents the results of a synthesis on the design and analysis of ground improvement for

liquefaction mitigation. The synthesis included an industry survey concerning the practice of ground

improvement for liquefaction mitigation. Participation in the survey was solicited by advertisements

in several trade magazines and by e-mail for the DFI membership. The survey participants numbered

150. Their professional roles include consulting engineers, specialty contractors, design engineers,

government engineers, and academicians. They represent a variety of geographical areas including

North/Central/South America, United Kingdom, Middle East, Caribbean, Hawaii, Japan, India, Egypt,

France, Australia and New Zealand. Upon completion of the survey, several professionals in the fi eld

of liquefaction and ground improvement were interviewed for them to elaborate on the survey results.

The interviews are included in the Appendix of this report. Financial support for the project was

provided by DFI and Dan Brown and Associates PC.

The concept of the liquefaction mitigation synthesis was developed by DFI’s Ground Improvement

Committee in recognition that:

(a) The results of recent research and post-earthquake reconnaissance have challenged previously long-

held beliefs about liquefaction and associated mitigation techniques, and;

(b) The DFI membership and the engineering/construction industry are interested to know if and how

engineers and designers are subsequently adjusting their practice in consideration of recent research

and post-earthquake reconnaissance.

For more detailed information on recent research and post-earthquake reconnaissance, presentations

are available from the State-of-the-Art Forum: Liquefaction Consequences and Mitigation that

was held in St. Louis in 2012. A commentary of the state-of-practice in ground improvement for

liquefaction mitigation (prepared by DFI’s Ground Improvement Committee) is included in this

issue of the DFI Journal.

The author would like to thank the participants of the survey and especially Mr. Mike Jeffries, Dr. Les

Youd, and Dr. Ikuo Towhata for their willingness to share their expertise in interviews. The author also

acknowledges Mary Ellen Bruce of DFI, Billy Camp of S&ME, Inc., and Marty Taube of DGI Menard

(and Chair of DFI’s Ground Improvement Committee) for their signifi cant contributions.

INTRODUCTIONCyclic liquefaction is a phenomenon where high excess pore-water pressure develops in saturated soil as a result of cyclic loading (Seed and Lee, 1965 and 1966). When the ratio of pore-water pressure to the total vertical stress is essentially 1 (i.e., the state of zero effective stress), the soil is considered “liquefied” and loses a large portion of its shear resistance. At lower relative densities (less than approximately 70%), soils may contract resulting in large ground settlements. Soils with higher relative densities (greater than approximately 70%) are dilative, preventing a substantial loss of

shear strength and large ground settlements. Liquefaction and its impact on engineering structures came to the engineering forefront in the 1960s due, in part, to the widespread liquefaction-induced damage (primarily settlement, tilting and lateral displacement of buildings) that occurred as a result of the 1964 Niigata (Japan) and 1964 Good Friday Alaska earthquakes (Grantz, et al., 1964; Japan National Committee on Earthquake Engineering, 1965; Seed and Idriss, 1967). Liquefaction also caused severe damage in the 1959 Jaltipan (Mexico) earthquake (Marsal, 1961) and the 1960 Chilean earthquake (Duke


and Leeds, 1963). In 1971, the “simplified procedure” (Seed and Idriss, 1971; Whitman, 1971) for anticipating liquefaction was developed based on the soil conditions and the design earthquake. Seed and Booker (1977) proposed the installation of columnar gravel drains in soil of high liquefaction potential to prevent the development of excessively high pore-water pressure. In this way, a routine framework was established. First, the liquefaction potential is evaluated using a rational method involving either field or laboratory testing. Second, if a potential for liquefaction is present and the effects of liquefaction are determined to present unacceptable risk to the performance of the structure, then ground improvement can be designed to mitigate the risk.

Over the past 40 years, the evaluation of liquefaction and the methods for mitigation design has continued to rapidly evolve. The evolution process is not without difficulties. Due, in part, to the use of the research community as the primary technical source serving practicing engineers and contractors, new insights are continuously being delivered. Practicing engineers and contractors are challenged to implement the conclusions of the most recent findings in a coherent and rational manner. However, considerable controversy and an absence of consensus exist regarding several aspects related to liquefaction including the subject of the efficacy of various mitigation techniques. The resulting negative impacts may include over-conservatism (and increased cost) by the designers and consultants, conflicts within the design team, and confusion among owners and their representatives.

The dichotomy between research and practice on the subject liquefaction is not new. In his technical note from 1979, Ralph Peck advised that engineers and those that depend on engineers would be well served to distinguish between research (or science) and practice:

In short, engineering science and engineering practice are not identical. Advances in science may temporarily appear to run counter to good practice. When this occurs, the implications should be evaluated carefully, but it should by no means be assumed that the latest scientific advancement is always the right direction. Science has its own ways of making progress, as evidence accumulates it corrects

its errors and improves its predictions. In the end, it is certain to improve practice as well. But science may temporarily mislead the unwary, and it should not intimidate either the experienced engineer or the overburdened regulatory agency.

Another way of saying this is that engineering practice should be careful not to assume that the most recent opinion on the subject of liquefaction must be correct to the extent that it automatically invalidates those that precede it.

LIQUEFACTION MITIGATION SYNTHESISAs primarily an effort to support the Deep Foundations Institute (DFI) membership, this synthesis attempts to help define the current state-of-practice in liquefaction mitigation by surveying practicing engineers and specialty contractors involved in the selection and implementation of ground improvement techniques for liquefaction. The survey was divided into four sections: (1) general practice, (2) liquefaction analysis, (3) mitigation design, and (4) verification. This report summarizes the results of the survey and presents the conclusions that may be made from the survey results.

General Practice

These questions are intended to provide a profile of the participant. Taken as a summary, this information will characterize the population involved in the survey. The questions and the answers (in terms of percentages) are:

1. What best describes your position in the liquefaction mitigation industry?

• Consulting Engineer (58%)

• Design Engineer (16%)

• Specialty Contractor (14%)

• Other (12%)

Commentary: The ground improvement industry, especially for liquefaction mitigation, is different from most other geotechnical/foundation designs. The design engineer for liquefaction mitigation is typically employed directly by the specialty contractor performing the installation. Because the owner and the owner’s consultants often do not have the technical expertise to prepare or review the liquefaction mitigation design, they provide


the performance requirements (which can be very stringent). Such an environment has its problems ranging from performance requirements that are unrealistic to significant differences between competing designs.

2. What area of the US are most of your

projects involving liquefaction

(check all that apply)?

• California (29%)

• Western US (ID, UT, NE, MT, WY) (6%)

• Pacifi c Northwest (OR, WA) (19%)

• Midwest (New Madrid) (10%)

• Southeast (Charleston) (10%)

• Other (26%)

Commentary: Earthquake and liquefaction

concerns have been an essential part of

engineering design in California and other parts

of the Western United States since the 1960s.

Because of the adoption of the International

Building Code and the associated increase in

seismic demand since the mid to late 1990s,

liquefaction analysis and mitigation have become

part of engineering design in parts of the eastern

United States.

3. How many projects involving liquefaction

analysis, mitigation design and/or

construction do you participate in over a one

year period?

• less than 5 (39%)

• between 5 and 10 (38%)

• between 10 and 40 (18%)

• over 40 (5%)

4. How standardized do you believe the state-

of-practice in liquefaction mitigation using

ground improvement techniques is?

• very consistent and uniform (3%)

• somewhat consistent and uniform (33%)

• somewhat non-uniform (46%)

• highly non-uniform (18%)

Commentary: As recently as the last few years,

research and post-earthquake reconnaissance

have provided results that contradict previously

held beliefs on liquefaction and the effectiveness

of some mitigation efforts. This is one reason

why it has been particularly diffi cult to establish

a more uniform and standardized state-of-

practice in ground improvement for liquefaction

mitigation and that it is not unexpected that over

half of the participants believe that state-of-

practice is “somewhat” or “highly non-uniform”.

5. How signifi cant have recent considerations

of liquefaction of fi ne-grained soil (i.e., >

30% passing No.200 sieve) been to your

projects?

• very signifi cant (24%)

• signifi cant (39.5%)

• marginally signifi cant (24.5%)

• not signifi cant (12%)

Commentary: Results of recent research

(Boulanger and Idriss, 2006; Bray and Sancio,

2006) and earthquake reconnaissance (Martin

and Olgun, 2008) support that fi ne-grained soils

can be susceptible to liquefaction. Engineering

practice has, in many areas, incorporated fi ne-

grained soils into the triggering analysis and

design of mitigation by adapting the procedures

developed for sands.

Liquefaction Analysis

These questions relate to liquefaction analysis in engineering practice. The questions and the answers (in terms of percentages) are:

Test 1 2 3 4 5

Standard penetration test (SPT) 58% 27% 8% 3% 4%

Cone penetration test (CPT) 32% 43% 16% 5% 3%

Shear-wave velocity test 3% 15% 43% 30% 9%

Cyclic lab test 1% 5% 11% 35% 49%

Liquefaction maps 6% 10% 22% 27% 35%


6. How often are the following techniques used for site characterization associated with liquefaction analysis on your projects? 1 is most often…..5 is least often.

Commentary: The standard penetration test

(SPT) (Seed et al., 1983 and 1985) can involve

signifi cant error due to the variation in energy

delivered by the hammer during the test. In this

regard, the more controlled in situ tests – cone

penetration test (Robertson and Wride, 1998)

and shear-wave velocity test (Andrus and Stokoe,

2000) – provide more repeatable and reliable

results. However, there can be limitations

with any test. For example, Dr. Brady Cox of

the University of Texas at Austin showed that

calcareous sands experienced liquefaction during

the 2010 Haiti earthquake even though the

shear-wave velocity profi le would have indicated

otherwise (DFI Presentation, 2012).

7. What presumptive analytical maximum

depth do you consider in your liquefaction

analysis?

• 30 ft (9 m) or less (8%)

• between 30 ft and 40 ft (9 m and 12 m)

(4%)


(25%)


(25%)

• No presumptive analytical maximum

depth (38%)

Commentary: The recently published FHWA

reference manual entitled LRFD Seismic

Analysis and Design of Transportation

Geotechnical Features and Structural

Foundations (2011) recommends that

liquefaction be evaluated over the greatest of

the following depths: (a) at least 20 ft (6 m)

below the lowest expected foundation level for

deep foundations, or (b) 80 ft (24 m) below

the existing ground surface or lowest proposed

fi nished grade. It should be noted that the

geologic and hydrogeologic setting of the site

should also be part of the basis for determining

the required depth of analysis.

8. What water level do you use in the

liquefaction analysis for level sites?

• water level observed during fi eld

exploration (43%)

• an assumed elevated water level for

earthquake (48%)

• ground surface (9%)

Commentary: Selection of the water level

determines the minimum depth of potential

liquefaction and an emphasis on identifi cation

of the water level during site exploration is

well placed. A signifi cant amount of published

research exists (e.g., Okamura and Soga, 2006;

Hossain et al, 2013) that supports the conclusion

that partially saturated soils (even those soils near

saturation) have a signifi cantly greater resistance

to liquefaction than fully saturated soil. It is

understood that the water table can fl uctuate, but

trapped air is typically present for short term high

water table events. It may be overly conservative

to select a high water table for liquefaction

analysis, especially where the high water table is

a temporary condition.

9. What water level do you use in the

liquefaction analysis for slopes?

• water level observed during fi eld

exploration (40%)

• an assumed elevated water level for

earthquake (53%)

• ground surface (7%)

10. What is the minimum thickness of soil layer

that you consider to be signifi cant with

respect to liquefaction potential?

• no minimum thickness (31%)

• 6 to 12 inches (150 to 300 mm) (20%)

• 12 to 24 inches (300 to 600 mm) (23%)

• greater than 24 inches (600 mm) (26%)

Commentary: Whether or not to exclude thin

zones that may be categorized as liquefi able

can have a dramatic effect on code-related

design decisions. For example, the 2012

International Building Code requirements for steel

reinforcement for cast-in-place deep foundations

can be controlled by the location of “strata that

are liquefi able”. To illustrate an extreme but not

unrealistic scenario, a long reinforcing cage length

could be interpreted to be a code requirement based

on a few data point(s) within a very detailed CPT

sounding. Judgment should be applied as there are

typically other important considerations, such as

constructability and quality.


11. What screening criteria do you primarily

use to differentiate between “sand-like” and

“clay-like” cyclic behavior of soils?

• Chinese criteria (9%)

• Idriss and Boulanger (69%)

• Bray and Sancio (13%)

• Other (9%)

Commentary: The Chinese criteria are no longer

considered to provide a suitable indication of

“clay-like” cyclic behavior.

12. What reference in published literature do you

primarily use for estimating liquefaction-

induced settlement for sands?

• Tokimatsu and Seed, 1987 (45%)

• Ishihara and Yoshimine, 1990 (30%)

• Zhang, Robertson and Brachman,

2002 (16%)

• Other (9%)

Commentary: In his 2012 H. Bolton Seed

lecture in Oakland, California, Dr. Geoffrey

Martin presented laboratory test results

supporting that sands may experience

different degrees of liquefaction-induced

compression depending on their gradation,

shape, etc. Shamoto et al. (1996) showed that

the liquefaction-induced compression can be

uniquely related to the relative compression

defi ned by Δe/(ei – e

min).

In his 2013 Ralph B. Peck lecture in San Diego,

California, Dr. Jonathan Bray presented the

results of post-earthquake reconnaissance and

concluded that the procedures described above

are not applicable for building settlements.

While the procedures may be applicable to

free-fi eld conditions, they do not represent

the conditions within the zone of infl uence of

foundations. In general, these procedures are

expected to under-predict building settlement,

particularly for thinner liquefi able strata.

13. Do you estimate liquefaction-induced

settlement of liquefi able fi ne-grained soils

using the published charts for sands?

• Yes (45%)

• No (55%)

Commentary: Considering the recent

developments that show that fi ne-grained

soils are liquefi able, the absence of research

concerning liquefaction-induced compression

for these soils is understandable. Dr. Ed

Kavazanjian at the Arizona State University

stated that limited research suggests that

published literature for estimating liquefaction-

induced settlement for sands provides reasonable

results for non-plastic silts (DFI Seminar, 2012).

14. What approach do you primarily use for

estimating lateral spread in liquefi able sand?

• Empirical correlations (53%)

• Laboratory-based methods (13%)

• Newmark sliding block analysis (15%)

• Numerical modeling/analyses (10%)

• Other (9%)

15. What approach do you primarily use for

estimating lateral spread in liquefi able fi ne-

grained soil?

• Empirical correlations (47%)

• Laboratory-based methods (13%)

• Newmark sliding block analysis (18%)

• Numerical modeling/analyses (11%)

• Other (11%)

16. How much confi dence do you put in the

calculated lateral spread displacement?

• 0 to 10% (12%)

• 10 to 50% (64%)

• 50 to 90% (21%)

• greater than 90% (3%)

Commentary: Dr. Scott M. Olson of the

University of Illinois presented the results of

his research indicating that actual lateral spread

displacements are within one-half to 2 times

the predictions made based on the accepted

estimation approaches (DFI Seminar, 2012)

Mitigation Design

These questions relate to liquefaction mitigation

design in engineering practice. The questions

and the answers (in terms of percentages) are:


17. How do you rank the following engineering

tools for liquefaction mitigation designs?

Engineering Tool

Very important

Less important

Least Important

theory/analysis/modeling

49% 33% 19%

local precedence

25% 34% 41%

published reconnaissance of earthquake damage

26% 33% 40%

Commentary: While it is recognized that analysis should be validated by field performance, this is problematic in the practice of earthquake design where the opportunities for first-hand observations are rare. The implementation of liquefaction mitigation techniques solely on precedence does not explicitly consider the variation in soil and seismic conditions; however, numerical modeling without calibration and validation can provide misleading results.

18. How often do you use the following fundamental approaches to mitigate liquefaction on your projects?

Fundamental Approach

Most often

Less oftenLeast often

densification 51% 35% 14%

reinforcement 40% 46% 14%

drainage 9% 19% 72%

19. How often do you use the following densification methods to mitigate liquefaction on your projects?

Densification method

Most often

Less often

Least often

vibrocompaction 66% 27% 8%

dynamic compaction

18% 41% 41%

compaction grouting 16% 32% 51%

20. What technical resources (literature,

software, etc.) do you primarily use in

designing against liquefaction using

densifi cation?

Commentary: There was a wide variety

of responses to this question. Specialty

contractor’s typically responded that their design

approaches were proprietary. For the remaining

respondents, the results to this question may be

broadly categorized as follows:

• The criteria are established by the consultant

but the design, implementation and

verifi cation are made the responsibilities of

the specialty contractor;

• Spreadsheets and commercial software, and;

• Numerical models (e.g., Plaxis and FLAC)

21. How often do you use the following

reinforcement methods to mitigate

liquefaction on your projects?

Reinforcement method

Most often

Often Less often

Least often

vibro-stone columns

55% 28% 11% 6.5%

rammed aggregate piers

19% 28% 17% 35%

grout columns 11% 20% 42% 26.5%

deep soil mixing cells

15% 24% 30% 32%




reinforcement?

Commentary: The results to this question may

be broadly categorized as follows:

• No analysis is typically performed but

rely on precedence and judgment with the

recognition that reinforcement may not fully

mitigate the liquefaction;

• Use of methodology proposed by Baez and

Martin (1993)

• Use of numerical models (e.g., Plaxis and

FLAC)

23. How often do you use the following drainage

methods to mitigate liquefaction on your

projects?

Drainagemethod

Most often

Less often

Least often

EQ drains 22% 20% 57%

gravel drains 41% 44% 15%

pre-fabricated vertical drains

37% 36% 28%


Commentary: Vertical gravel drains were

described by Seed and Booker (1972). However,

they are not widely used in the United States.

One reason is a concern about their effectiveness

and reliability. It is recognized that vertical

gravel drains need to reliably provide a high

ratio of permeability between the drain material

and the adjacent soil to prevent the buildup of

high excess pore water pressure. Dr. Russell

Green with Virginia Tech (DFI Seminar, 2012)

presented research results showing that high

degree of control during installation is required

to maintain an effective gradation in order to

achieve the target permeability.

From the comments provided by participants, it

may be concluded that the use of drains is rarely

relied upon as the primary or sole mechanism for

mitigating liquefaction in the U.S. The use of

EQ drains is focused on parts of the US, namely

Charleston, SC.




drainage?

Commentary: FEQDrain (Pestana et al., 1997)

was recognized as a technical resource for the

design of EQ drains. Gravel drains, which have

been more popular in Japan (Towhata, 2008),

can be designed by using the charts presented

by Onoue (1988).

25. What is the typical liquefaction-induced

settlement tolerance or design criteria used

on your foundation projects?

• No liquefaction as determined by a

required post-improvement SPT or

CPT resistances (23%)

• 1 inch (25 mm) (27%)

• 3 inches (76 mm) (21%)

• Greater than 3 inches (76 mm) (6%)

• No maximum settlement so long as there

is an adequate factor-of-safety against

bearing capacity failure (23%)

Commentary: Participants commented that the

type of structure and that whether the design

is to be determined based on life safety or

serviceability were important considerations

regarding selection of the tolerable settlement.

Assuming that most foundations can tolerate

about one inch of settlement with only cosmetic

damage, the results indicate that about half of

the participants of the participants typically

design for serviceability. Considering that

we often use the one inch as the tolerable

foundation settlement for non-seismic conditions

as well, it is very conservative to use either one

inch of liquefaction-induced settlement or no

liquefaction even for serviceability.

26. Is the typical liquefaction-induced settlement

tolerance or design criteria used on

your foundation projects reasonable and

achievable?

• Yes (82%)

• No (18%)

27. What is the typical lateral spread tolerance

used on your foundation projects?

• less than 1 foot (0.3 m) (55%)

• 1 to 3 ft (0.3 to 0.9 m) (35%)

• greater than 3 ft (0.9 m) (10%)

28. Is the typical lateral spread tolerance or

design criteria used on your foundation

projects reasonable and achievable?

• Yes (87%)

• No (13%)

29. What primary reference do you use in

estimating residual strength of liquefi ed

soils?

• Seed and Harder, 1990 (23%)

• Olson and Stark, 2002 (17%)

• Idriss and Boulanger, 2008 (50%)

• Other (10%)

30. Would you be in favor of performance-

based design where the tolerable ground

movements were more closely related to the

design of the structure?

• Yes (96%)

• No (4%)


Verification

These questions relate to verifi cation of

liquefaction mitigation efforts in engineering

practice. The questions and the answers (in

terms of percentages) are:

31. For mitigation dependent on densifi cation,

what approximate percentage of your

projects includes post-improvement

verifi cation testing?

Commentary: The responses ranged from 0

to 100%. Approximately ½ of the participants

responded that 100% of their projects included

post-improvement verifi cation testing and the

majority of the remaining participants responded

with values that were between 25% and 50%.

32. How often do you use the following

techniques for post-improvement verifi cation

testing?

Verification test technique

Most often

Less often

Least often

Standard Penetration Test

40% 42% 18%

Cone Penetration Test 55% 38% 6%

Shear-Wave Velocity Test 5% 20% 76%

33. When evaluating the densifi cation by the

CPT, do you use the fi nes content estimated

from the pre-improvement or

post-improvement?

• Pre-Improvement (61%)

• Post-Improvement (39%)

Commentary: The fi nes content interpreted

from CPT data can change between the pre-

improvement testing and post-improvement

testing. This emphasizes that a good practice

is to validate CPT data with the fi nes content

determined from laboratory gradation testing

performed on samples collected in the fi eld.

34. For sites improved by densifi cation, does

your post-improvement liquefaction analysis

consider ageing effects?

• Yes (29%)

• No (71%)

Commentary: Research supports that dynamic

compaction, blasting and vibro-compaction can

temporarily destroy inter-particle structure and

bonds associated with aging. Therefore, the

cone tip resistance is expected to increase with

time after improvement using these techniques

(Mitchell and Solymar, 1984; Schmertmann,

1986; Mesri et al., 1990; Charlie et al., 1992).

Other densifi cation methods such as compaction

grouting, displacement piles, or compaction piles

may also have the same effect although it has

not been documented. Lunne et al. (1997) states

the recommended procedure is to perform fi eld

trials at the start of the project by performing

CPT at different time intervals after compaction

to evaluate the signifi cance of any time effect.

There are fi nancial drawbacks to such fi eld trials

including extending the construction schedule

and requiring a greater amount of CPT services.



consider lateral stress relaxation?

• Yes (27%)

• No (73%)

Commentary: Mejia and Boulanger (1995)

performed SPT and CPT to evaluate the

effects of compaction grouting in silt and sand.

The study observed a large increase in the

penetration resistance one week after treatment.

A loss of approximately 30% of the average

increase was subsequently observed within the

following 18 months.



consider lateral variation in the degree of

densifi cation?

• Yes (48%)

• No (52%)

Commentary: Degen (1998) reports that the

practice of testing at the mid-point between

three vibro-compaction improvement points

(assuming an equilateral triangular spacing)

introduces “a rather large additional factor of

safety into the design”. Field data suggest that

the CPT resistance is about 20% higher, only

500 mm (20 in) away from the midpoint.


37. How do you model the response of

liquefi ed soil when evaluating lateral loading

on a deep foundation?

• use a p-multiplier of 0.1 for loose sand

and 0.25 for dense sand (16%)

• use the equivalent fl uid pressure of the

liquefi ed sand (19%)

• use a p-y curve for soft clay based on

the residual strength (26%)

• use the Rollins et al. (2005) liquefi ed

sand p-y curves (27%)

• other (12%)

CONCLUSIONS

On the basis of the subject survey, the following

conclusions are presented:

1. The state-of-practice is perceived to be

“somewhat” to “highly” non-uniform by a

majority of the survey respondents. This

illustrates the need for continued efforts to

develop greater consensus within engineering

practice for many of the issues included in this

synthesis.

2. The SPT and CPT are the two primary tools

for evaluating the site conditions for the design

and verifi cation for ground improvement for

liquefaction mitigation.

3. A majority of the survey respondents use

an elevated ground water level or a ground

water level at the ground surface for their

liquefaction analysis. Such a practice is

expected to introduce conservatism because

unsaturated soil (even soil near saturation)

has a higher resistance to liquefaction than

saturated soil.

4. Almost one-third of the survey respondents

do not apply a minimum liquefi ed thickness

when performing liquefaction analysis. Such a

practice may introduce conservatism, especially

where liquefaction is isolated to one or a few

thin zones within the subsurface profi le.

5. A performance-based design where the design

criteria are determined based on the tolerance(s)

of the proposed structure, is overwhelmingly

preferred. While two levels of design

performance were recognized (serviceability

and life safety), it was not clear which level

provides the basis of most designs.

6. Densifi cation is the most implemented

primary mechanism for liquefaction mitigation

and is followed by reinforcement. Post-

improvement testing for densifi cation projects

may involve signifi cant judgment to consider

the effects of cementation associated with

aging, stress relaxation and lateral variation in

improvement.

7. While the owner’s consulting engineers

typically defi ne the densifi cation requirements,

it is the specialty contractor (and/or their

subconsultant) that is given the responsibilities

of design, implementation and verifi cation of

the means and methods.

8. The application of reinforcement for

liquefaction mitigation relies on precedence

and judgment, as well as, the results of

numerical modeling. Research is in progress

to better defi ne the effi cacy of reinforcement

and to develop simplifi ed design methods

(Nguyen et al., 2012; Rayamajhi et al., 2012.)

9. Drainage as the primary mechanism does not

appear to be widely implemented in the U.S.

Towhata (2008) reports that the installation

of drains for liquefaction mitigation has

experienced a decrease in Japan.

REFERENCES

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“Liquefaction resistance of soils from shear-

wave velocity”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE,

126(11), pp. 1015-1025.

2. Arulmoli, K., Arulanandan, K., and Seed,

H.B. (1985) “New method for evaluating

liquefaction potential”, Journal of Geotechnical Engineering, ASCE, 111

(1), pp. 95-114.

3. Baez, J.I. and Martin, G.R. (1993) “Advances

in the design of vibro systems for the

improvement of liquefaction resistance”, Proceedings of the Symposium on Ground Improvement, Vancouver Geotechnical

Society, B.C. Canada.


4. Boulanger, R.W. and Idriss, I.M. (2006)

“Liquefaction susceptibility criteria for silts

and clays”, Journal of Geotechnical and Geoenvironmental Engineering, 132(11), pp.

1413-1426.

5. Bray, J.D. and Sancio, R.B. (2006)

“Assessment of the liquefaction

susceptibility of fi ne-grained soils”, Journal of Geotechnical and Geoenvironmental Engineering, 132(9), pp. 1165-1177.

6. Charlie, W.A., Rwebyogo, M.F.J. and

Doehring, D.O. (1992) “Time-dependent

cone penetration resistance due to blasting”

7. Cox, B.R. (2012) Liquefaction lessons

learned from recent post-earthquake

reconnaissance, DFI State-of-the-Art Forum:

Liquefaction Consequences and Mitigation,

St. Louis, MO.

8. Degen, W.S. (1998) Vibration Ground Improvement, Vibrofl otation AG,

Altendorf, 194 p.

9. Duke, C.M. and Leeds, D.J. (1963)

“Response of soils, foundations and earth

structures to the Chilean earthquake of

1960”, Bulletin Seismological Society of America, 63(2).

10. Grantz, A., Plafker, G. and Kacherdoorian,

R. (1964) “Alaska’s Good Friday

Earthquake, March 27, 1964”, Geologic Survey Circular 491, Department of the

Interior, Washington.

11. Hossain, M.A., Andrus, R.D. and Camp,

W.M. (2013) “Correcting liquefaction

resistance of unsaturated soil using wave

velocity”, Journal of Geotechnical and Geoenvironmental Engineering, in press.

12. Idriss, I.M. and Boulanger, R.W. (2008)

“Soil liquefaction during earthquakes”,

Monograph MNO-12, EERI.

13. Ishihara, K. and Yoshimine, M. (1992)

“Evaluation of settlements in sand deposits

following liquefaction during earthquakes",

Soils and Foundations, 32(1), pp. 173-188.

14. International Code Council (2012)

International Building Code, 690 p.

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Engineering (1965) “Niigata Earthquake of

1964”, Proceedings, 3rd World Conference on Earthquake Engineering.

16. Kavazanjian, E. Jr. (2012) Evaluation and

mitigation of liquefaction impacts: an

overview, DFI State-of-the-Art Forum:


St. Louis, MO.

17. Kavazanjian, E. Jr., Wang, J-W., Martin,

G.R., Shamsabadi, A., Lam, P., Dickenson,

S.E., and Hung, C.J. (2011) LRFD Seismic Analysis and Design of Transportation Geotechnical Features and Structural Foundations, Report No. FHWA-NHI-11-032, 592 p.

18. Kayen, R.E. and Mitchell, J.K.

(1997) “Assessment of liquefaction

potential during earthquakes by Arias

Intensity”, Journal of Geotechnical and Geoenvironmental Engineering, 123(12),

pp. 1162-1174.

19. Lunne, T., Robertson, P.K. and Powell,

J.J.M (1997) Cone Penetration Testing in Geotechnical Practice, Spon Press, 312 p.

20. Marsal, R.J. (1961) “Behavior of a sandy

uniform soil during the Jaltipan Earthquake,

Mexico”, Proceedings, 5th International Conference on Soil Mechanics and Foundation Engineering, Paris.

21. Martin, J.R. II and Olgun, C.G. (2008)

“Soil improvement for damage mitigation

along Izmit Bay during the 1999 Kocaeli

earthquake”, Geotechnical Engineering for Disaster Mitigation and Rehabilitation.

22. Mejia, L.H. and Boulanger, R.W. (1995)

“A long term test of compaction grouting

for liquefaction mitigation”, Earthquake-Induced Movements and Seismic Remediation of Existing Foundations and Abutments, ASCE, GSP No.55, 94-109.

23. Mesri, G., Feng, T.W. and Benak, J.M.

(1990) “Post-densifi cation penetration

of clean sands”, Journal of Geotechnical Engineering, ASCE, 116(7), pp. 1095-1115.


24. Mitchell, J.K. and Solymar, Z.V. (1984)

“Time-dependent strength gain in freshly

deposited or densifi ed sand”, Journal of the Geotechnical Engineering, ASCE,

104(GT7), pp. 995-1012.

25. Nguyen, T.V., Rayamajhi, D., Boulanger,

R.W., Ashford, S.A., Lu, J., Elgamal, A. and

Shao, L. (2012) “Effect of DSM grids on

shear stress distribution in liquefi able soil”,

Proceedings, Geo-Institute GeoCongress,

Oakland, pp. 1948-1957.

26. Okamura, M. and Soga, Y. (2006) “Effects

of pore fl uid compressibility on liquefaction

resistance of partially saturated sand”, Soils and Foundations, 46(5), pp. 695-700.

27. Olson, S.M. (2012) Lateral spreading during

liquefaction, DFI State-of-the-Art Forum:


St. Louis, MO.

28. Olson, S.M. and Stark, T.D. (2002)

“Liquefi ed strength ratio from liquefaction

fl ow case histories”, Canadian Geotechnical Journal, 39, pp. 629-647.

29. Onoue, A. (1988) “Diagrams considering

well resistance for designing spacing ratio of

gravel drains”, Soils and Foundations, 28(3),

160-168.

30. Pestana, J.M., Hunt, C.E. and Goughnour,

R.R. (1997) “FEQDrain: A fi nite element

computer program for the analysis of the

earthquake generation and dissipation of

pore water pressure in layered sand deposits

with vertical drains”, Report No. UCB/EERC-97/15, Earthquake Engineering

Research Center, College of Engineering,

University of California at Berkeley.

31. Peck, R.B. (1979) “Liquefaction potential:

science versus practice”, Journal of Geotechnical Engineering Division, ASCE,

105(GT3), pp. 393-398.

32. Rayamajhi, D., Nguyen, T.V., Ashford,

S.A., Boulanger, R.W., Lu, J., Elgamal,

A. and Shao, L. (2012) “Effect of discrete

columns on shear stress distribution in

liquefi able soil”, Proceedings, Geo-Institute GeoCongress, Oakland, pp. 1948-1957.

33. Robertson, P.K. and Wride, C.E. (1998)

“Evaluating cyclic liquefaction potential

using the cone penetration test”, Canadian Geotechnical Journal, 35, 442-459.

34. Rollins, K.M., Gerber, T.M., Lane, J.D. and

Ashford, S.A. (2005) “Lateral resistance

of a full-scale pile group in liquefi ed

sand”, Journal of Geotechnical and Geoenvironmental Engineering, 131(1), pp.

115-125.

35. Schmertmann, J.H. (1986) “CPT/DMT

QC of ground modifi cation at a power

plant”, Proceedings of the ASCE Specialty Conference, In Situ ’86: Use of In Situ Tests

in Geotechnical Engineering, Blacksburg,

pp. 985-1001.

36. Seed, H.B. and Booker, J.R. (1977)

"Stabilization of Potentially Liquefi able Sand

Deposits Using Gravel Drains", Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 103, No. GT7, pp. 757-

768

37. Seed, R.B. and Harder, L.F., Jr. (1990)

“SPT-based analysis of cyclic pore pressure

generation and undrained residual strength”

in H.B. Seed Memorial Symposium, J.M.

Duncan, Editor, Bi-Tech Publishers Ltd,

Vancouver, Canada, Vol.2, pp. 351-376.

38. Seed, H.B. and Idriss, I.M. (1967) “Analysis

of soil liquefaction: Niigata Earthquake”,

Journal of the Soil Mechanics and Foundations Division, ASCE, 93(SM3),

pp. 83-108.

39. Seed, H.B. and Idriss, I.M. (1971)

“Simplifi ed procedure for evaluating soil

liquefaction potential”, Journal of Soil Mechanics and Foundations Division, ASCE,

97(SM9), pp. 1249-1273.

40. Seed, H.B., Idriss, I.M., and Arango, I.

(1983) “Evaluation of liquefaction potential

using fi eld performance data”, Journal of Geotechnical Engineering, 109(3), pp. 458-

482.


41. Seed, H.B. and Lee, K.L. (1965) “Studies

of the liquefaction of sands under cyclic

loading conditions”, Report No. TE-65-5 to the State of California Department of Water Resources, University of California at

Berkeley, 46 p.

42. Seed, H.B. and Lee, K.L. (1966)

“Liquefaction of saturated sands during

cyclic loading”, Journal of the Soil Mechanics and Foundations Division, ASCE,

92(SM6), pp. 105-134.

43. Shamato, Y., Sato, M. and Zhang, J-M.

(1996) “Simplifi ed estimation of earthquake-

induced settlements in saturated sand

deposits”, Soils and Foundations, 36(1), pp.

39-50.

44. Tokimatsu, K. and Seed, H.B. (1987)

“Evaluation of settlements in sands due

to earthquake shaking”, Journal of the Geotechnical Engineering Division, ASCE,

113(8), pp. 861-878.

45. Towhata, I. (2008) Geotechnical Earthquake Engineering, Springer Series in Geomechanics and Geoengineering,

46. Whitman, R.V. (1971) “Resistance of soil

to liquefaction and settlement”, Soil and Foundations, 11(4).

47. Youd, T.L. (2011) “Evaluation and

mitigation of liquefaction hazard”,

Geostrata, ASCE, 15(5), pp. 53-54.

48. Youd, T.L., Hansen, C.M. and Bartlett, S.F.

(2002). “Revised multilinear regression

equations for prediction of lateral spread

displacement”, Journal of Geotechnical and Geoenvironmental Engineering, 128(12), pp.

1007-1017.

49. Zhang, G., Robertson, P.K. and Brachman,

R.W.I. (2002) “Estimating liquefaction-

induced ground settlements from CPT for

level ground", Canadian Geotechnical Journal, 39, pp. 1168-1180.

APPENDIX: INTERVIEWS

Interview with Mike Jefferies with Golder Associates who co-authored with Ken Been the book entitled “Soil Liquefaction: A critical state approach” (2006) from CRC Press.

(1) What are your reservations regarding the use of numerical modeling in the design of ground improvement for liquefaction mitigation? Please elaborate.

The biggest reservation is the generic

classifi cation “numerical modeling”, which

would seem to allow anybody to pick up a

standard package (Plaxis, Flac) with some

standard properties lifted from the user manual

to generate a result… “Garage In, Garbage

Out”.

In principle I am a great fan of numerical

modeling and think it will become the way

forward. But, when specifying “modeling”

it is also essential to add the following:

a) an appropriate stress strain model. you

can do a lot with standard Mohr Coulomb

provided that an appropriate dilation angle

is chosen and G = Gmax/3, but for many

ground improvement projects we will need

to go further and adopt a “good” stress

strain model that predicts how the proposed

improvement changes the soil stiffness and

strength. And the problem that you then run

into is that none of the standard numerical

codes used by engineers in practice have

such models as one of their “menu” choices.

So, you wind up with a decent numerical

model that actually requires a user defi ned

model where you code one of the “good”

models for yourself – predictably, rarely

done! Things will improve in the future

as the software developers pre-pack good

models into commercial codes, but even

then users will need to be aware of how

their, seemingly innocent, choice of model

impacts their results.

b) Relevant and reliable soil properties.

Too many times I have seen people

(both clients and fellow engineers) ask

for sophisticated fi nite element analysis

using SPT blowcounts as the basis of

soil properties; this is complete nonsense

and simply produces delusions about

adequacy. The very minimum is that

anything using numerical analysis must

have measured Gmax data as the starting

point for the analysis (at least we get the


elastic response right, and Gmax/3 is not a

bad approximation for the secant modulus

to mobilized strength for many soils at

usual FS). This is actually not a big $$$

requirement, as geophysical methods to

assess Gmax are cheap and easy to do in

situ and ‘bender elements’ are becoming

readily available in commercial testing labs.

It is a matter of appropriate understanding

and attitude. How often do you see the

analyst reporting calibration of their

model to the soil behavior they are

trying to capture?

c) Validation studies have been done.

Although one might like to think (and

hope) that numerical modeling would be

formally correct, in reality there are ways of

setting up the problems, sorting out initial

conditions, and dealing with the loading

conditions that all affect the results. As

well as modeling in 2D when the works

are 3D… All of which means that the

procedures used need to be validated

against ‘case histories’. This validation

of modeling procedures is actually a

requirement in the European standard EN

1997 (Eurocode 7), but not often done by

the consulting fi rms I know.

If you put (a) – (c) together, you wind up with

my fear that simply giving numerical methods

as an allowable/desirable design approach

will allow all sort of bogus work to be put in

front of clients as good engineering. Done

well, numerical methods are a brilliant

technology to help us in what we do. But, they

are done badly 95% of the time (in my view)

and it would be better to not do them at all in

this situation.

(2) What future improvements do you consider most important regarding the different technical aspects related to ground improvement for liquefaction mitigation - liquefaction analysis, design, verifi cation? Please elaborate.

“None of the above”; the biggest problem I

see is intellectual dishonesty/incompetence in

academia where we have largely outsourced

all development – possibly a surprising view,

but it is detailed in my book! In reality,

liquefaction is not diffi cult to analyze, but

what is acceptable has been hijacked by one

faction (lets us be charitable and call them the

‘engineering geology view’) and they have the

support of the regulators. As engineers, we

can do much better than present practice but it

simply is not allowed.

On the bright side, I think the survey results

show a super-majority consensus on post-

treatment validation, and it would be easy to

pull an ASTM standard together on this issue.

The only real issue seems to be the degree of

post-treatment aging we include and how that is

assessed.

(3) What practices (either technical or non-technical) by those involved - consultant, designer, specialty contractor, owner - do you consider problematic to the consistency within the practice? Please elaborate.

a) Continued use of the SPT. The test, and

its correction factors, are so variable that

even a single organization is challenged

in producing a uniform standard between

projects if they base their work on the SPT.

b) Uncertainty and/or lack of understanding

of how “fi nes content” affect liquefaction

susceptibility, leading to wildly inconsistent

engineering in anything other than clean

sand. And it is not the contractors or

owners who are the problem; academia is at

a loss and consultants seemingly take little

interest in challenging them.

c) Lack of best-practice guides. I’ve just been

part of a consensus guide to compaction

grouting, and really similar guides are

needed for dynamic compaction and vibro-

densifi cation (in its various forms).

(4) Are you satisfi ed with the current approach for considering liquefaction-induced settlement and lateral spread?Do you consider these estimates as relative measures of liquefaction severity or actual/accurate values? Please elaborate.

No! None of the approaches to settlement

are properly based on soil behavior (post


liquefaction settlement is a consolidation

problem requiring Cc as a basic input

parameter; any method without Cc as a soil

property is bogus mechanics). Similar

comments follow about lateral spreads with the

exception of Newmark’s method.

(5) Do you have any other comments that haven't been covered by the survey or this interview?

Could I suggest the compaction grout guide as

a prototype of what is needed across other areas

of the ground improvement industry?

Interview with Dr. Les Youd, Professor Emeritus of Civil Engineering at Brigham Young University.

(1) Do you have any reservations regarding the use of numerical modeling in the design of ground improvement for liquefaction mitigation? Please elaborate.

I have major reservations on this issue.

Numerical modeling is only one of several

tools that should be applied by designers.

Over reliance on numerical modeling can lead

to nonsensical results because of imperfect

or inadequate models. With the present state

of practice, it is generally impossible to

construct accurate models of (1) subsurface soil

stratigraphy, (2) lateral and vertical variances

in stratigraphy, (3) soil properties, (4) variances

in soil properties in space and time, and (5)

imposed seismic loads in both space and time.

Numerical analyses are generally useful to

gain a rough perspective of expected results

and to perform parametric analyses to estimate

how the results might change with variations

in stratigraphy, soil properties, loading

assumptions, etc., but not as the sole basis

for design.

A more important tool, in my opinion,

is assessment of case histories of past

performance compiled from post-earthquake

investigations and successful or unsuccessful

similar projects. Empirical procedures

are generally applied in present practice;

these procedures were primarily developed

from analysis of case histories, and thus are

grounded on observed actual performance.

Although past performance and empirical

techniques may not allow exact duplication of

site conditions and constraints for each project,

they usually provide realistic estimates as a

guide to the design engineer.

The third tool that should be applied is

engineering judgment. Expert guidance from

those with past earthquake experience and

from analysis and design should be sought

after to assure that sound engineering judgment

is applied on all critical ground modifi cation

projects. Conversely, design of critical ground

modifi cation projects should not be entrusted

to inexperienced engineers, although they may

have attained expert computer skills but with

little practical experience.


I believe that much money has been wasted in

the past on mitigation to prevent liquefaction

from occurring, when the occurrence of

liquefaction would not lead to signifi cant

damage. To avoid such waste, education

of the profession is needed to increase

understanding of the following key points

(extracted from a short paper I prepared for

the ASCE publication Geo-Strata (Youd,

September-October 2011, p. 53-54)). This

paper was written to increase this needed

understanding. “In analyzing liquefaction

the following fundamental questions should

be asked and appropriate answers and actions

determined: 1. Will liquefaction occur? If the

answer to this question is “no,” mitigation is

obviously not required. If the answer is “yes,”

the analysis proceeds to the second question: 2.

Will liquefaction lead to potentially damaging

ground deformations, displacements or ground

failure? If the answer is “no,” liquefaction will

not cause signifi cant damage and the hazard

can be safely accepted without mitigation. If

the answer is “yes,” the analysis proceeds to the

third question: 3. What mitigative measures are


required to reduce the hazard to an acceptable

risk?” Only when this level of understanding

has been gained should the analysis proceed to

design of mitigation measures.

Verifi cation of the effectiveness of ground

modifi cations has been a major issue for

several projects I have encountered. Additional

research, discussion and consensus building is

required to improve verifi cation procedures for

use in engineering practice.


Procedures for liquefaction hazard evaluation

and mitigation relies heavily upon empirical

procedures, which are generally based on

analyses of collected case histories and

performance assessments. Development

of empirical procedures usually occurs

through research and analyses by individual

investigators or teams of investigators; these

investigators or teams do not always (or seldom)

agree; thus development of empirical procedures

tends to be a messy and often chaotic process;

disagreements and disputes are common and

to be expected. Most of this chaos occurs at

the researcher and consultant levels. Because

of this chaos, practitioners and designers often

are confused or uncertain as to which expert

they should rely on or which procedure they

should follow. With time the chaos usually

calms as procedures are vetted or tested and

consensus builds. Sometimes professional

societies or other professional groups can

speed the process through workshops or expert

panels to develop consensus guidelines for

engineering practice. Such was the case with

the NCEER/NSF workshop I chaired in 1996

on evaluation of liquefaction resistance, which

developed consensus guidelines that calmed the

atmosphere for triggering evaluations for about

10 years. Groups such as DFI may assist by

organizing or supporting workshops or panels

of this type to build consensus and reduce chaos

and develop improved and more consistent

usage within the profession.

(4) Are you satisfi ed with the current approach for considering liquefaction-induced settlement and lateral spread? Do you consider these estimates as relative measures of liquefaction severity or actual/accurate values? Please elaborate.

a) Lateral Spread: As an author of the

empirical MLR procedure, one of the more

widely used procedures for evaluating

lateral spread displacement, I feel that the

MLR procedure is a valid procedure if

applied within the limitations specifi ed by

the authors (Youd et al 2002 from Journ

of Geotech and Geoenviron Engr, v. 128,

no 12, p. 1007-1017). This procedure

provides mean predicted values that are

demonstrated to be accurate within a factor

of plus or minus two if applied within the

specifi ed limits. Extension beyond the

stated limits leads to greater uncertainty

of results. Because the MLR procedure is

empirical, it is not valid for all conditions

that may be encountered. In some instances

extrapolation using numerical procedures

may allow reasonable, but still uncertain,

results for a wider range of site conditions.

For example, inclusion of a deep foundation

for a bridge in a sediment cross-section to

be analyzed creates a condition beyond that

in the empirical database. The additional

infl uence of this bridge foundation could

be analyzed through numerical procedures.

An accuracy of plus or minus 2 may seem

too uncertain for engineering applications,

however, such uncertainties are common in

other geotechnical engineering calculations.

For example, similar uncertainty is

inherent in calculations of bearing capacity

and foundations settlement under static

conditions.

One of the greater sources of erroneous

results that I have encountered reviewing the

work of others using the MLR procedure is

insuffi cient geotechnical information. Often

analyses are made on the basis of one or

a few boreholes or soundings exacerbated

by an improper assumption that penetrated

soil layers are laterally homogeneous


and continuous across and beyond site

boundaries. If critical layers thin or pinch

out or important facies changes occur

within the layer, inaccurate to nonsensical

predicted displacements may be calculated.

Thus, I feel that adequately accurate tools

are available for calculation of lateral

spread displacements for many applications.

However, MLR and other empirical

procedures need to be verifi ed and updated

as additional earthquakes occur and new

case histories are developed.

b) Ground Settlement: The same general

limitations apply to empirical procedures

for calculation of liquefaction-induced

ground settlement as for lateral spread.

However, the limitations for ground

settlement do not seem to be as well

defined as for lateral spread. For example,

most empirical settlement procedures

appear to be based on relatively clean sand

conditions. Limits on the procedure with

respect to silt and gravel contents do not

seem to be clearly defined. Thus, the

user must evaluate soil conditions at a site

in question, compare those conditions

against those implicit in the development

of the empirical procedure, and then

make an unspecified adjustment for

incompatible soil conditions. Such

adjustments increase the uncertainty of

the calculated settlements.


From reading the survey text and these

questions, diffi culties faced by design engineers

appear to stem from one or more of the

following issues:

(1) lack of adequate communication between

researchers, expert consultants, analysts, and

designers;

(2) confusion within these same groups with

respect to which procedures should be

recommended for application in practice,

and;

(3) lack of adequate research and verifi cation

of procedures to answer many fundamental

questions.

DFI and other professional organizations

could play a major role in fostering

communication, supporting studies to

develop and verify procedures, education of

professionals at all levels, assisting profession

to identify unresolved issues, and assisting

in the development of support for research,

workshops and other means to resolve

important issues.

Interview with Ikuo Towhata, Professor of Geotechnical Engineering at the University of Tokyo and author of the “Geotechnical Earthquake Engineering” from Springer Series.

(1) Do you have any reservations regarding the use of numerical modeling in the design of ground improvement for liquefaction mitigation? Please elaborate.

Everybody points out the shortcomings of the

use of numerical analysis in design. Those

shortcomings are caused by the complex stress-

strain-dilative behavior of soils, heterogeneous

subsoil conditions that cannot be fully

recorded by current soil investigations and

many others. Although those critical attitudes

are understandable, I feel that some critics

use those shortcomings as an excuse for not

challenging advanced (numerical) studies.

Recent desires towards seismic performance

design require approaches that can calculate

residual deformation of structures in place of

the conventional factor of safety. I would ask a

question whether or not the traditional

non-numerical approaches are more reliable and

more useful than the numerical approaches. The

traditional approaches often rely on empirical

knowledge and their use is certainly limited

within the range of available knowledge. It is

risky to apply them to totally new soil and load

conditions. Moreover, the traditional methods

cannot be applied to the behavior of complicated

underground structures that are subject to

liquefaction of soils around. In this regard, we

should not discriminate numerical methods.

They should be considered to be tools which


give us indices that help us assess the seismic

performance of structures to be designed.

Do not misunderstand that I am trying to

favor numerical methods. Good numerical

methods have to be associated with elaborate

but costly fi eld / laboratory investigations. I

feel that many current projects do not allocate

reasonable budget to investigations, resulting

in unexpected diffi culty during the later

construction stages. A small investigation

budget results in a great loss of money and time

during construction.

The attitudes of numerical people are also a

problem. They do not go to the site. They prefer

to stay in a comfortable offi ce and 100% trust

documented data. They do not imagine that the

reality is more complicated than information

in paper.

Because my most interested fi eld of study is

the assessment of liquefaction-induced large

displacement, I should make one more point

about numerical approaches. To my knowledge,

the constitutive models that are employed

in major computer codes were developed in

1970s and 80s when nobody cared that the

liquefaction-induced large deformation of

subsoil. Also, even today laboratory devices

cannot reproduce such large shear deformation

as 30%, 50%, or more. Laboratory tests after

the onset of liquefaction are not possible

because of segregation of water and sand grains

within a tested specimen. Therefore, those

constitutive models are not fully supported by

laboratory test data after onset of liquefaction

and development of large shear deformation.

In summary, I would propose to use both

simple traditional approaches and numerical

approaches and compare them prior to drawing

the fi nal conclusion.


After the M=9 gigantic earthquake in 2011,

I encountered a very diffi cult problem of soil

improvement. It was how to improve soil

(reduction of liquefaction vulnerability) under

existing houses with relatively low fi nancial

burden to house owners.

The current solution is two-fold. For a frequent

design earthquake (return period being about 50

years), public and private funds are combined.

Liquefaction vulnerability is mitigated by either

constructing underground rigid walls under

streets and house-lot borders to constrain cyclic

shear deformation of soil, or pumping ground

water to lower the ground water level and to

create an unliquefi able soil crust. The former

has a limitation that the spacing of walls cannot

be very small because of existing houses at the

surface. The latter has a problem of possibly

triggering consolidation settlement in the

underlying thick soft clay.

Note further that house owners have to spend

their own money on soil improvement, if

they wish to do it, against a stronger design

earthquake with a return period of hundreds

of years. This is diffi cult and costly because

the ground surface is occupied by a house

and compaction or other traditional soil

improvement is not possible.

Soil improvement under existing structures

is further important for big industries as

well. This is because the intensity of design

earthquake tends to be increased and existing

old structures cannot satisfy the safety

requirement under newer regulations.

I suppose that the following kinds of soil

improvement are feasible under existing

structures; installation of drainage, compaction

grouting by good technicians, injection

of colloidal silica, and construction of

underground walls around the foundation

of houses. Noteworthy is that some

improvement methods cannot prevent the

onset of liquefaction but reduce the residual

deformation. Thus, methodology is necessary

to assess the residual deformation of subsoil

and surface structures (possibly by a numerical

method) and also to determine the allowable

extent of deformation.


Gravel drains became less popular after the

1995 Kobe earthquake. This is because the

intensity of design earthquake was increased

and design calculation could not prove that

gravel drains under the stronger design

earthquake can still maintain the development

of excess pore water pressure less than 50%

of the full liquefaction. However, it is possible

that the columns of gravel drain maintain

some rigidity during a strong earthquake and

reinforce the stability and integrity of subsoil.

Further study is needed in this direction.


Owners try not to spend suffi cient money

on subsoil investigation. Hence all the input

data for analysis have to be determined by

SPT-N only. Although liquefaction of fi ne-

grained soil is important, plasticity index is

hardly measured. Owners should understand

that they should allocate more money on

soil investigation so that they can avoid

unnecessary big expenditures on construction

and unnecessary liquefaction damage during

future earthquakes.

Some consultants do not want to visit sites.

They prefer to stay in the offi ce and analyze

the supplied borehole data. For them, the

data on paper is the reality and they do not

want to experience the reality on site. One

reason for this situation is found in the

owners who do not pay suffi cient money for

fi eld activities. To accurately interpret bore

hole data, it is important for consultants to

have good knowledge of local soils and local

geological history as well as history of human

action on soils such as land reclamation and

consolidation settlement. Hence, it is possible

that a local experienced consultant is better

than an international famous consultant.

(4) Are you satisfi ed with the current approach for considering liquefaction-induced settlement and lateral spread? Do you consider these estimates as relative

measures of liquefaction severity or actual/accurate values? Please elaborate.

My attitude towards numerical methods was

described already in (1). I do not think that

numerical methods are worse than simplifi ed

and traditional factor-of-safety approach. All

the methods give us an index to assess the

performance of a designed structure.

Numerical methods can assess the lateral

displacement of liquefi ed subsoil with an

error of +- 50%. This is not too bad. The error

of non-numerical methods is most probably

similar.

Some people state that the Newmark rigid

block analogy is better than other methods

to assess the liquefaction-induced lateral

displacement. I would say that the use of the

Newmark method in liquefaction problem

is beyond the applicability of this method,

because Newmark intended to calculate the

movement of a "rigid block" subjected to

seismic action. Liquefi ed soil is never a rigid

block.


There are several methods of subsoil

investigation. In publications, I often encounter

such an article in which the author insists that

his device is able to determine all the required

soil data accurately. In reality, this is diffi cult.

Every method has good points and bad points.

I suggest that we should combine different

methods and get the best subsoil data. It is good

to interpolate a big spacing among SPT by

means of less expensive CPT or other device.

It is often stated that engineering judgment is

extremely important and that less experienced

engineers should not be trusted. Then it

becomes important how to produce the next

generation of experienced engineers. If a

young engineer is not trusted, he will never

become an experienced one. Moreover, the

engineering judgment is a kind of empiricism.

During the medieval time, technology relied

totally on empiricism. There was no systematic

education. Hence, the power of technology was


poor. This situation was changed drastically

during the time of modern technology and

education because the problems were analyzed,

interpreted, understood, and solved. Long

patience behind a “meister” is not necessary

any more. It should be borne in mind that too

much emphasis on empiricism will push things

back to the medieval time.


Grouted Micropiles for Foundation Remediation in Expansive Soil (8th Michael W. O’Neill Lecture)John D. Nelson, Ph.D., P.E., D.GE., CEO and Principal Geotechnical Engineer, Engineering Analytics, Inc., and Professor Emeritus, Colorado State University, Fort Collins, Colorado, USA: 970-488-3111, [email protected]

Kuo-Chieh Chao, Ph.D., P.E., Vice President and Senior Geotechnical Engineer, Engineering Analytics, Inc., Fort Collins, Colorado, USA; 970-488-3111, [email protected]

Daniel D. Overton, M.S., P.E., President and Principal Geotechnical Engineering, Engineering Analytics, Inc., Fort Collins, Colorado, USA

Zachary P. Fox, M.S., Geotechnical Engineer, Engineering Analytics, Inc., Fort Collins, Colorado, USA

Jesse S. Dunham-Friel, M.S., P.E., Geotechnical Engineer, Engineering Analytics, Inc., Fort Collins, Colorado, USA

ABSTRACTFoundation underpinning is a common component of remediation schemes for distressed foundations on expansive soils. For many applications in expansive soil, micropiles have distinct advantages over other techniques. This paper will concentrate on the design and construction of micropiles in expansive soil. It discusses the nature of building distress and the relationship between foundation movement and soil heave. It presents methods for determining the factors that are required for the design of micropiles. Such factors include calculation of expected free-field heave, depth of soil wetting, and prediction of pier movement. A finite element program developed by the authors and others to determine pier heave and internal forces is presented. The input parameters that are required for pier analysis are discussed, and the nature of the output and the sensitivity of the results to the output are described. A case example illustrates the advantages of micropiles over other methods.

INTRODUCTIONHeave of expansive soils is a common cause of differential movement of building foundations resulting in structural distress. For foundations constructed on soils consisting of highly expansive clay, underpinning of the foundation is the most reliable method of remediation. Recently, micropiles have found increasing use for underpinning, particularly in the Front Range of Colorado because of the reliability of the method and its ease of installation. The drilling equipment for micropiles is easily attached to existing foundations utilizing the weight of the structure for reaction. This makes the use of micropiles advantageous in places such as crawlspaces, garages, basements, and other confined areas.

Appropriate design of the micropiles involves careful site investigation, calculation of anticipated free-field heave, and then analysis of the required micropile length. The successful

performance of the micropiles also involves careful attention to detail during construction.

The following sections present examples of the nature of distress caused by heave of expansive soil and typical foundation types that have been underpinned. They outline the geotechnical engineering parameters that are necessary for design and present methods for analysis of the micropiles. The input parameters required and methods of determination of these parameters are discussed. Important aspects of the construction are also discussed. A case example is used to demonstrate the advantages of micropiles in terms of ease of installation and reliability.

FOUNDATION TYPES AND NATURE OF DISTRESS When highly expansive soils are encountered on a given site, the most reliable foundation type is a deep foundation consisting of drilled


pier and grade beam systems. Drilled pier and grade beam foundations isolate the structure from the expansive soils by creating a void space beneath the superstructure such that only the shaft of the drilled pier is in contact with the problematic soil. As will be discussed in greater detail later, uplift forces acting on the upper portion of a pier due to soil heave in the active zone are resisted by the embedment or anchorage zone below. Distress in pier and grade beam foundations caused by expansive soils is typically the result of differential pier heave and manifests itself through cracking of the pier and/or grade beam causing distortion of the superstructure above. Fig. 1 shows a grade beam that experienced diagonal cracking due to pier heave. Fig. 2 shows a diagonal crack in a 30 inch (762 mm) diameter drilled pier near the intersection with the grade beam. In this case lateral forces were also imposed on the pier due to soil heave.

[FIG. 1] - Grade beam crack due to pier heave

[FIG. 2] - Diagonal crack in a 30 inch drilled pier

Associated with the pier and grade beam foun-dation is a structural floor to isolate the floor slab from the soil. Slab-on-grade basement floors can experience large amounts of heave that can also be transmitted to the superstruc-ture above. Fig. 3 shows a scenario where sig-nificant slab heave has necessitated the cutting of the interior wall studs in the basement of a residence to avoid lifting the first floor. Fig. 4 shows a “center lift” condition in a basement slab-on-grade.

[FIG. 3] - Wall studs sawed off due to slab heave

[FIG. 4] - Differential heave of basement slab

Regardless of the foundation type, distress as-sociated with expansive soils typically results in significantly increased maintenance and repair costs throughout the life cycle of the structure. Additionally, differential movements result in racked doors and windows which in addition to inconvenience, may result in loss of emer-gency egress. To remediate such distress and losses of functionality, foundations are often underpinned with structural elements such as micropiles.


DESIGN OF MICROPILES IN EXPANSIVE SOILSMicropiles have been used to underpin foundations since the early 1950s and they are increasingly being used for underpinning foundations experiencing heave due to expansive soils. Despite their increasing usage, there is a lack of published literature regarding micropile design, installation, or performance in expansive soils. The following offers a method for analysis of the behavior of micropiles installed in expansive soils.

Heave Prediction

Free-field heave is defined as the amount of heave the ground surface will experience without any applied surface load. The distribution of heave with depth is the primary data on which pier heave is calculated. Therefore, a review of free-field heave calculations is presented below.

Various heave prediction methods have been developed based on results of one-dimensional oedometer tests (Fredlund et al. 1980; U.S. Army Corps of Engineers, 1983; Nelson and Miller, 1992; Fredlund and Rahardjo, 1993; Fredlund et al. 2012). These methods utilize the net mechanical stress, σ’ = (σ – u

a), and

the matric suction, h = (ua - u

w) as the stress

state variables. In these variables, σ is the total stress and u

a and u

w are the pore air and pore

water pressures. The soil heave takes place as the suction is decreased. These methods are commonly referred to as “oedometer” methods. The oedometer methods all use the same basic equation for calculation of heave. The equation for heave of a soil layer of thickness, ∆z

i,

subjected to an applied stress, ∆σ’v, is

DESIGN OF MICROPILES IN EXPANSIVE SOILS

icv

vvoiHi zC Δ+Δ= ⋅ '

''

logσ

σσρ [1]

and the heave of the entire soil column is,

DESIGN OF MICROPILES IN EXPANSIVE SOILS

=

=n

i 1iρρ [2]

where: ρ = free-field heave; ∆zi = thickness of

each soil layer; σ’vo

= overburden stress; ∆σ’v =

applied stress; σ’cv

= constant-volume swelling pressure, and C

H = constitutive parameter.

The parameter CH defines the amount by which

a soil sample will swell when it becomes wetted. The method presented here is characterized

by the manner in which the CH parameter is

determined. It considers both the change in suction due to wetting and the applied stress that is acting on the soil when it is wetted.

The determination of CH is depicted in Fig. 5

which is a three dimensional plot of the stress paths followed during the inundation and heave of a soil. In a conventional consolidation-swell oedometer test, a sample of soil is consolidated under an inundation stress, labelled as σ’

i in

Fig. 5. The initial state of the soil under the inundation stress, σ’

i, is represented by the

point labeled K. At that point the soil suction is equal to some value labelled as h

c1. The initial

percent swell, εs%

, at point K (and H) is equal to zero. When the sample is inundated, the suction is reduced to h

o and the soil swells along the

path KB. The projection of that stress path on the plane defined by the axes for ε

s% and log σ’

is the line GB. The sample is then loaded back to its original height along the path BA. The value of stress corresponding to point A is the “consolidation-swell swelling pressure”, σ’

cs.

[FIG. 5] - Stress Paths for Soil Expansion

In a conventional constant-volume oedometer test, the sample is constrained from swelling during inundation and the stress required to prevent swell is determined. The initial point for this test is also point K but because it is constrained from swelling it develops a confining stress as the suction decreases to h

o and the stress path would be along a line

such as KE. The value of stress corresponding to point E is the “constant volume swelling pressure”, σ’

cv. Due to hysteretic effects, the

value of σ’cv

is generally less than that of σ’cs.

The reason for this is somewhat intuitive in that it should be easier to prevent water molecules


from entering into the soil lattice than to force the water out once it has entered into the soil.

For an element of soil at some depth in the ground, the initial stress conditions could be at some point such as J. When that sample is inundated it will swell along a stress path such as JD. Point D will fall between points B and E. Our experience and data has shown that the line BDE is close to being a straight line (Justo et al. 1984; Reichler, 1997; Nelson et al. 2006; Fredlund et al. 2012). Thus, the slope of the line BDE defines the constitutive relationship between the percent swell, ε

s%, that a soil will

undergo, and the applied stress when it is wetted. The slope of that line is C

H.

It is important to note that, as shown in Fig. 5, the line BDE which defines C

H represents the

expansion, or heave, that will occur due to suction changes under different values of applied stress. Thus, it is a constitutive relationship that incorporates both of the independent stress state variables, σ’ and (u

a –

uw), for use in computing heave.

Fig. 6 shows the projection of the stress paths shown in Fig. 5 onto the ε

s% and log σ’ plane.

The results of both consolidation-swell test and constant-volume test are shown as the lines GBA and GFE, respectively.

The heave index, CH, is the slope of the line BDE

in Fig. 6 and is equal to:

[FIG. 5] Stress Paths for Soil Expansion

s%CH 'cv100 log 'i

ε=

×

[3]

where εs%

is the percent swell corresponding to σ’

i expressed as a percent, and σ’

i is the vertical

stress at which the sample is inundated.

[FIG. 6] - Determination of Heave Index, CH

The value of CH can be determined from the

results of a consolidation-swell test and a constant volume test using identical samples of the same soil. However, in practice it is virtually impossible to obtain two identical samples from the field. Therefore, it is convenient to utilize a relationship between σ’

cs and σ’

cv so that C

H

can be determined from a single consolidation-swell test. On the basis of data that has been assembled from a number of different sources, it was found that experimental data corresponded well to Equations 4a and 4b. The authors have found that for use in the Front Range area of Colorado a value of λ

l of

0.6 is reasonable when Equation 4a is used or a value of λ

a of 0.3 is reasonable when

Equation 4b is used. However, for application of these equations to other soil types, it would be prudent to perform tests to determine an appropriate value for the soil being considered (Nelson et al. 2012a).

[FIG. 6] Determination of Heave Index, CH

)(logloglog '

''i

'cv

i

csl σ

σλσ +=

[4a]

[FIG. 6] Determination of Heave Index, CH

)( '''i

'cv icsa σσλσ −+=

[4b]

Zone of Soil Contributing to Heave

The depth of soil that is contributing to heave at a particular point in time depends on two factors. These are the depth to which water contents in the soil have increased since the time of construction, and the expansion potential of the various soil strata. As water migrates through a soil profile different strata become wetted, some of which may have more swell potential than others. Consequently, the zone of soil that is contributing to heave varies with time.

The amount of heave that will occur at a particular time depends on the manner in which the groundwater migrates in the soil and the expansion potential of the soil at depth. Movement of the soil surface will begin almost immediately after construction, whereas some time will be required for the soil at deeper depths to become wetted. Thus, the surface of the soil will begin to heave almost immediately, but movement of piers will be delayed, sometimes by several years.

The term “active zone” has been in common usage in the field of expansive soils. However, the usage of that term has taken different


meanings at different times and in different places. Therefore, for purposes of clarity and consistency, the following definitions have been put forth (Nelson et al. 2001).

Active Zone, ZA, is that zone of soil that is

contributing to heave due to soil expansion at a particular point in time.

Zone of Seasonal Moisture Fluctuation, Zs, is

that zone of soil in which water contents change seasonally due to climate changes.

Zone of Wetting, Zw, is that zone in which

water contents have increased beyond the pre-construction conditions.

Depth of Potential Heave, Zp, is the depth to

which the overburden vertical stress equals or exceeds the swelling pressure of the soil. This represents the maximum depth of Active Zone that could occur.

Design Active Zone, ZAD

, is the zone of soil that is expected to become wetted during the design life of the structure. It may be less than the depth of potential heave if the entire depth of potential heave is not expected to become wetted. If water migration analyses are not performed and if the depth of potential heave is of reasonable value for design, it is prudent to assume the depth of the design active zone is equal to the depth of potential heave.

Construction of buildings and pavements in arid regions typically results in a reduction of evapotranspiration from the soil. Additionally, the introduction of irrigation typically exceeds the evapotranspiration of the vegetation. These factors as well as others result in the development of a wetting front that progresses downward in the soil. Above the wetting front, the soil may be saturated or unsaturated. The difference in soil suction between the wetter and drier zones will result in downward flow of water, and the wetting front will continue to move downward until an impermeable boundary or a water table is reached (McWhorter and Nelson, 1979). Once a low permeability boundary is reached by the wetting front, a perched water table will be formed. Full wetting of the soil profile would be expected to occur if the soil above the wetting front is saturated and the wetting front advances to below the depth of potential heave. If full wetting is not expected to occur, analyses should be conducted to determine the water content profile at the end of the design life.

Pier Heave Calculations

The simplest method used to design piers in expansive soil is termed the “Rigid Pier” method. This method assumes that the pier will not move and determines a required pier length by equating the negative, or downward, skin friction below the depth of the design active zone, plus the dead load, to the uplift pressures exerted on the pier by the swelling soil. Chen (1965), O’Neill (1988), and Nelson and Miller (1992) present methods for rigid pier analysis in expansive soil. Rigid pier design generally produces conservative pier lengths for a light structure founded on a deep deposit of highly expansive soil. The rigid pier design works well if the stratum of expansive soil is not thick and is underlain by a stable non-expansive stratum. However, in a deep deposit of expansive soil, the design rigid pier length is generally not practical for a light structure.

In reality almost all structures are able to tolerate some amount of pier heave. The amount of tolerable heave to be used for design depends on the nature of the structure. Methods of analysis of pier heave were developed by Poulos and Davis (1980) and were adapted by Nelson and Miller (1992) to develop design charts for calculating pier heave. This method is termed the “Elastic Pier” method. The elastic pier method calculates the pier heave assuming the pier is a stiff inclusion in an elastic half space. The elastic pier method presented in Nelson and Miller (1992) was developed for piers with uniform properties installed in a uniform soil profile. Additionally, the elastic pier analysis formulation breaks down when the length to diameter ratio becomes too great. Micropiles typically have non-uniform properties with depth, are often installed in non-uniform soil profiles, and have large length to diameter ratios. Therefore, the elastic pier method is not well suited for their analysis.

Finite element approaches to pier analyses provide versatility to consider such details as non-uniform soil or pier interface properties with depth and large length to diameter ratios. Nelson et al. (2012b) presents one such finite element based numerical analysis approach termed APEX for Analysis of Piers in EXpansive Soils. This finite element based approach is discussed below.


APEX Formulation

The APEX formulation is discussed in detail in Nelson et al. (2012b) and is briefly summarized below. Swell is assumed to be isotropic and it is simulated using conventional analyses of thermal strains in solids. The constitutive equations are as follows:

( )1rr rr zz isoE θθε σ ν σ σ ε= − + + [5]

( )1zz rr isoEθθ θθε σ ν σ σ ε= − + + [6]

( )1zz zz rr isoE θθε σ ν σ σ ε= − + + [7]

where: εiso

= isotropic swelling strain; and εrr,

εθθ, εzz = components of stress and strain in

cylindrical coordinates. The pier-soil interface is accounted for with a mixed boundary condition. The mixed boundary condition is shown in Fig. 7 and can be written as follows:

( )t p tF k H U= − [8]

where: Ft = nodal force tangent to pier; H

p =

pier heave; Ut = nodal displacement tangent to

pier; and k = parameter used to adjust shear stress, which serve a purpose similar to a spring constant.

Fig. 8 depicts the manner in which APEX calculates pier heave. The pier is modeled as a rigid body connected to an elastic, expansive medium by springs with a spring constant k. Fig. 8a illustrates the conditions before swell takes place when there are no uplift forces on the pier. Fig. 8b illustrates the conditions after swelling takes place but before any pier heave, when the shear forces exerted on the pier result in an upward force on the pier. At this point the pier is not in equilibrium, and the pier is then allowed to move up until forces are balanced. Fig. 8c illustrates the condition after forces are balanced and the pier is in equilibrium.

The APEX formulation allows for movement between the pier and the expansive soil mass by either slip between the pier-to-soil interface or failure of the soil adjacent to the pier. The slip and soil failure mechanisms are calculated at each iteration to evaluate which condition governs.

[FIG. 7] - Boundary Conditions: (a) Soil Boundary, (b) Mixed Boundary (after Nelson et al. 2012b)

[FIG. 8] - Schematic of pier and soil interface: (a) initial-no force on pier, (b) soil heave-upward force on pier, (c)

pier heave-resultant force on pier is zero (after Nelson et al. 2012b)

Input Parameters for APEX

The soil and heave profiles are the primary input parameters used in the APEX analysis. Detailed and accurate characterization of the soil profile to the full depth to which the soil will influence the behavior of the piers is a critical element of pier design. If the depth of exploration is too shallow, or if an insufficient number of samples are collected and tested, variations in the soil profile will not be detected. Fig. 9 shows two examples of soil profiles.

Fig. 9a illustrates a simplified soil profile where one relatively uniform expansive soil such as clay or claystone is encountered to the full depth of exploration. In this case the incremental heave is high at the surface and decreases exponentially with depth to the depth of potential heave. Relatively uniform soil


profiles such as that shown in Fig. 9a are rarely encountered in the field. Instead it is typical to encounter multiple soil layers with varying expansion potential such as in the profile shown in Fig. 9b. Fig. 9b illustrates a complex soil profile which is typical of many expansive soil sites in the Front Range Area of Colorado. The soil profile shown in Fig. 9b has multiple layers with varying expansion potential. Accurate analysis of pier heave constructed in complex soil profiles such as that requires a detailed analysis which can account for the variations in heave with depth. Incremental free-field heave computed for such profiles is the most important input parameter in the APEX analysis. The free-field heave profile can be determined by predicting heave versus depth as discussed in the above sections.

The primary elastic input properties used in APEX analysis are the Young’s modulus (E), Poisson’s ratio (ν), and coefficient of lateral stress (K

o). The sensitivity of the analysis to

those parameters is discussed in detail in Nelson et al. (2012b).

Example calculations performed by Nelson et al. (2012b) have demonstrated that changes to the interface friction parameters, α, do not substantially affect the calculated pier heave but do have a significant impact on the tensile force in the pier when the frictional interface is uniform with depth. However, if

the upper portion of the micropiles installed in expansive soils is sleeved with PVC, the frictional properties for each part require accurate determination of the value for α with depth along the micropile. The APEX analysis developed by the authors and others allows for α to be changed with depth in order to allow for accurate representation of the frictional properties at all locations along the micropile.

The frictional interfaces that typically occur during the construction of micropiles in expansive soils are soil to grout, grout to PVC, and PVC to soil as is discussed in Schaut et al. (2011). The values of α presented in the literature for a concrete to soil interface generally range from 0.1 to 0.25 (Chen, 1988; O’Neill, 1988; Sorochan, 1991; Nelson and Miller, 1992). However, field test results presented by Benvenga (2005) indicate that α generally ranges from about 0.4 to 0.6 and can be as high as 0.9. Schaut et al. (2011) completed testing on the soil to grout interface as well as the grout to PVC and PVC to soil interfaces using typical micropile construction materials and claystone soil from the Front Range Area of Colorado. The results of this research indicate that the value of α depends on the method of testing, whether the soil is remolded and what the water content of the soil is during testing. It was shown that PVC casing reduces the frictional resistance along the cased section of the micropile.

[FIG. 9] - Examples of soil and heave profi les: (a) uniform expansive soil and (b) complex soil profi le


Output Results from APEXTypical APEX input and output for a soil profile is presented on Fig. 10. Fig. 10a shows the heave profile input into the APEX program. Fig. 10b shows the distribution of slip along the pier. This figure indicates that for this case, slip was the failure mechanism along the entire length of the pier and therefore soil failure was not experienced. Fig. 10c shows the distribution of shear stress along the pier with positive shear stresses in the anchorage zone and negative shear stresses in the uplift zone. Fig. 10d shows the axial force in the pier with the maximum value occuring at the interface between the uplift and anchorage zones.

[FIG. 10] - Typical output from APEX Program: (a) cumulative heave used as input, (b) variation of slip along pier, (c) shear stress distribution along pier, (d) axial force distribution (after Nelson et al. 2012a)

portion of the micropile is cased with a PVC sleeve while the bottom portion has grout in direct contact with the soil. Depending on the method of construction and the fit between the PVC casing and the drilled hole, grout can flow up in the annulus between the PVC and the side of the hole as shown on Fig. 12. An all thread bar is typically used to reinforce the micropile and provide a means for attachment to the foundation.

[FIG. 12] - Schematic of typical micropile in expansive soil (after Schaut et al. 2011)

Pier Design Chart

An example of a pier design chart that was derived using the results of APEX analyses is shown in Fig. 11. Design charts of this nature can be developed using APEX and can be used to design micropiles. E

A is the modulus of

elasticity of the soil in bars.

[FIG. 11] - Pier heave versus pier length - nonlinear free-fi eld heave (after Nelson et al. 2012a)

MICROPILE TYPES AND TYPICAL CONSTRUCTION IN EXPANSIVE SOIL Micropiles have been classified into different types based on construction technique (FHWA, 2005 and AASHTO, 2012). A typical micropile installed in expansive soil has a configuration similar to that shown in Fig. 12. The upper


Micropiles used in expansive soils typically consist of drilling a 4 to 6 inch (102 to 152 mm) hole using a hydraulic drill rig that mounts to the foundation as shown in Fig. 13. After drilling, casing made of rigid PVC pipe or other material is placed in the open hole in order to reduce the friction between the micropile and the surrounding expansive soil. Fig. 14 shows PVC casing placed in the drilled hole prior to grout placement. Micropiles are typically tremie grouted from the bottom of the hole which often allows the grout to flow up the inside of the PVC casing as well as into the annulus between the side of the hole and casing as discussed in Schaut et al. (2011). Soil swelling or worn cutting teeth on the auger bit may restrict flow of grout into the annulus between the soil and the casing. Fig. 15 shows a micropile during tremie grouting. After curing of the grout, the micropile is then connected to the bracket.

[FIG. 13] - Micropile drill rig bolted to grade beam foundation

[FIG. 14] - Micropile prior to grouting with annulus around the outside of casing

[FIG. 15] - Micropile during grouting. Note that the grout is tremied into the hole

CASE EXAMPLEAn interesting case example regarding the use of grouted micropiles in the remediation of distressed structures is the case of a single family home originally constructed on spread footings in Loveland, Colorado during the summer of 1995. After the original homeowners reported evidence of structural distress, local geotechnical and structural engineering firms were hired to investigate potential causes. Results of their investigations indicated that differential movement of the expansive soils beneath the residence had resulted in the basement and garage slabs being up to 7.0 in (178 mm) out of level, respectively. The respective reports recommended underpinning of the residence and a number of alternative underpinning methods were proposed including helical piers, push-pins, straight shaft piers and micropiles. A combination of steel push pins and helical piers were ultimately used to underpin the residence during the winter of 2001. The push pins and helical piers were recommended to be installed to a minimum depth of 30 ft (9 m). In 2010, continuing structural distress was observed by the homeowners and measured by performing inverted joist level surveys of the basement and garage. Figs. 16 and 17 illustrate some of the observed distress to the residence in 2010 after the initial underpinning.


[FIG. 16] - Diagonal Brick Cracking

[FIG. 17] - Diagonal Drywall Cracking

The lack of as-built information regarding the installation of the steel push-pins and the nature of the distress caused suspicion that the push-pins may not have been installed to the depths specified. To investigate, a geophysical survey was conducted by Zonge International, Inc. using a magnetic difference meter and a conductivity meter. In order to conduct the survey, a micropile drill rig was used to drill 4-in (102 mm) diameter holes to a depth of 35 ft (10.7 m) adjacent to three existing push-pins and one helical pier. The boreholes were cased with PVC pipe and the geophysical meters were inserted into the boreholes allowing data collection along the entire length of the boreholes. Fig. 18 shows the magnetometer/conductivity probe with the PVC-cased borehole in the background. Results of the geophysical survey clearly showed that the depth of the push-pin piers and helical piers ranged from 9 to 21 ft (2.7 to 6.4 m), significantly less than the depth specified. Due to the very hard state of the claystone beneath the residence it was

not possible to install the push-pins and helical piers to the depths specified. The micropile drill rig used in this investigation was secured to the foundation in order to drill in the hard claystone. The fact that the exploratory holes for the geophysical testing were drilled to a depth of 35 ft (10.7 m) using micropile technology shows that grouted micropiles could have been drilled and installed to the depths specified in the underpinning plans. In contrast, push pins and helical piers had not been able to be successfully installed to the depths specified, thereby significantly reducing their ability to resist uplift caused by heave of the expansive soils. This case study demonstrates the advantage of micropiles as compared to other underpinning options for use in hard expansive soil conditions.

[FIG. 18] - Magnetic Gradiometer, Testing Apparatus and Cased Hole

CONCLUSIONS The authors offer the following conclusions regarding the use of grouted micropiles for underpinning of foundations on expansive soils.

• Grouted micropiles began to find substantial use in the United States as far back as the 1970s. Since that time they have been used for a wide variety of applications including use as a structural element to underpin foundations constructed on expansive soils.

• The design of grouted micropiles in expansive soils is complex due to the use of low friction casing, large length to diameter ratios and typically complex soil and wetting profiles. The use of finite element based solutions can be used to model pier heave and tensile force if the free field


heave and other input parameters are determined accurately.

• The depth and degree of wetting must be accurately determined for use in a formulation such as APEX to predict pier heave and tensile force in micropiles installed in expansive soil.

• Micropiles have distinct advantages as compared to alternative methods for underpinning of foundations on expansive soils. These advantages include ease of construction, ability to use the foundation as a reaction block on which to secure drilling equipment, ability to be installed in confined spaces and ability to be advanced to a specified design depth in stiff expansive soil.

REFERENCES1. American Association of State Highway and

Transportation Officials (AASHTO), 2012. Design specifications customary U.S. units. Publication Code LRFDUS-6.

2. Benvenga, M. M., 2005. "Pier-soil adhesion factor for drilled shaft piers in expansive soil", Master’s Thesis, Colorado State University, Fort Collins, Colorado.

3. Chen, F. H., 1965. "The use of piers to prevent the uplift of lightly loaded structures founded on expansive soils", Proceedings of the International Conference on Expansive Soils, College Station, Texas.

4. Chen, F. H., 1988. Foundations on expansive soils. Elsevier. New York, NY.

5. Federal Highway Administration (FHWA), 2005. Micropile design and construction reference manual. Publication No. NHI-05-039, NHI Course No. 132078, U.S. Dept. of Transportation. December.

6. Fredlund, D. G. and Rahardjo, H., 1993. Soil mechanics for unsaturated soils. John Wiley & Sons, New York, NY.

7. Fredlund, D. G., Hasan, J. U., and Filson, H., 1980. "The prediction of total heave", Proceedings 4th International Conference on Expansive Soils, Denver, Colorado, June 16-18, pp. 1-11.

8. Fredlund, D. G., Rahardjo, H., and Fredlund, M. D., 2012. Unsaturated soil mechanics in engineering practice. John Wiley & Sons, Hoboken, NJ.

9. Justo, J. L., Saura, J., Rodriguez, J. E., Delgado, A., and Jaramillo, A., 1984. "A finite element method to design and calculate pier foundations in expansive-collapsing soils", Proceedings of the 5th International Conference on Expansive Soils, Adelaide, Australia, pp. 199-123.

10. McWhorter, D. B. and Nelson, J. D., 1979. "Unsaturated flow beneath tailings impoundments", Journal. Geotechnical and Engineering Division, ASCE, November, Vol. 105(GT11), pp. 1317-1334.

11. Nelson, J. D. and Miller, D. J., 1992. Expansive soils: problems and practice in foundation and pavement design. John Wiley and Sons, New York, NY.

12. Nelson, J. D., Chao, K. C., Overton, D. D., and Schaut, R. W., 2012a. "Calculation of heave of deep pier foundations", Geotechnical Engineering Journal of the Southeast Asian Geotechnical Society and Association of Geotechnical Societies in Southeast Asia, Vol. 43, No. 1, pp. 12-25.

13. Nelson, J. D., Overton, D. D., and Durkee, D. B., 2001. "Depth of wetting and the active zone", Proceedings of the Geo-Institute Shallow Foundation and Soil Properties Committee Sessions at the ASCE Civil Engineering Conference 2001, Houston, Texas, October 10-13, in “Expansive Clay Soils and Vegetative Influence on Shallow Foundations” ed. C. Vipulanandan, M.B. Addison, and M. Hansen, GSP115, pp. 95-109.

14. Nelson, J. D., Reichler, D. K., and Cumbers, J. M., 2006. "Parameters for heave prediction by oedometer tests", Proceedings of the 4th International Conference on Unsaturated Soils. Carefree, Arizona. April, GSP 147, pp. 951-961.

15. Nelson, J. D., Thompson, E. G., Schaut, R. W., Chao, K. C., Overton, D. D., and Dunham-Friel, J. S., 2012b. "Design considerations for piers in expansive soils", Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 138, No. 8, pp. 945-956.


16. O’Neill, M. W., 1988. "Special topics in foundations", Proceedings of the Geotechnical Engineering Division National Convention, ASCE, Nashville, Tennessee, pp. 1-22.

17. Poulos, H. G. and Davis, E. H., 1980. Pile foundation analysis and design. John Wiley, New York, NY.

18. Reichler, D. K., 1997. "Investigation of variation in swelling pressure values for an expansive soil", Master’s Thesis, Colorado State University, Fort Collins, Colorado.

19. Schaut, R. W., Nelson, J. D., Overton, D. D., Carraro, J. A. H., and Fox, Z. P., 2011. "Interface testing for the design of micropiles in expansive soils", Proceedings of the 36th Annual Conference on Deep Foundations, Boston, MA, Oct 18-21, Deep Foundations Institute.

20. Sorochan, E. A., 1991. Construction of buildings on expansive soils. A.A. Balkema Publishers, Brookfield, VT.

21. U.S. Army Corps of Engineers, 1983. Technical manual TM 5-818-7, foundations in expansive soils. Washington, DC., September 1.


Relationship between Installation Torque and Axial Capacities of Helical Piles in Cohesive SoilsMohammed Sakr, PhD., P.Eng, Manager, Geotechnical Engineering, Vertex, Sherwood Park, AB Canada; Ph: (780) 920-0652; [email protected]

ABSTRACTThe empirical relationship between torque measured during installation and pile capacity has gained a wide acceptance in the helical pile industry in the last few decades. This paper presents a theoretical model developed to estimate torsional resistance of cohesive soils to helical pile installation. The proposed torsional resistance model was then used to establish torque factor, K

t, a factor that is widely

used in the industry. The results of the study indicated that the Kt factor is a function of the load path

(i.e. tension or compression), pile geometry and soil properties. The assessed Kt factors in tension

and compression were validated by the results of 74 installation records and full-scale helical pile load tests. A parametric study was also performed to qualitatively assess the relative importance of different parameters that affect the K

t factors.

INTRODUCTIONEmpirical relationship between measured torque during installation and helical pile capacity is widely used in the industry in North America especially for small-size helical piles. The empirical relationship can be expressed as (Hoyt and Clemence, 1989; Canadian Foundation Engineering Manual (CFEM) 2006, Perko 2009).

Qt = K

tT [1]

where

Qt = ultimate capacity of screw pile;

Kt = empirical factor; and

T = average installation torque.

Torque-load correlation factors, Kt, were

statistically established based on a large database, and the method has been used successfully in the installation of thousands of piles and anchors over the past two decades, as indicated by Hoyt et al. (1995). However, the obtained K

t values did not differentiate between

compression and tension loading. For example, Hoyt and Clemence proposed a K

t factor equal

to 9.8 m-1 (32.2 ft-1) for 89 mm (3.5 in) diameter round shaft helical piles regardless of load path (i.e. compression or tension). The K

t

values published in literature and adapted in the Canadian Engineering Foundation Manual (CFEM; 2006) were mainly based on the results of pullout (tension) tests for small diameter piles. Therefore, the available K

t values may be

not suitable for estimating the axial capacities

of helical piles under compressive loads or for large diameter helical piles.

Perko (2001) proposed a correlation between installation torque and pile capacity based on an energy model similar to that model for driven piles. However, the main limitation to the energy model is that it requires numerous parameters, some of which are not easily measurable during pile installation.

Perko (2009) proposed another empirical relationship between K

t and effective

shaft diameter (deff

) based on exponential regression analysis of over 300 load tests in both compression and tension. The empirical equation can be expressed as:

92.0eff

kt dK

λ= [2]

where

kλ = fitting factor equal to 1433 mm0.92/m

deff

= shaft diameter for round shaft, mm.

It should be noted that in Eqn. 2, torque factor is inversely proportional to pile shaft diameter. However, the main limitations to Eqn. 2 are the lack of explanation of the physical meaning of fitting factor and the estimated K

t values in

compression and tension were identical.

Despite the effort over decades to empirically correlate between installation torque and pile capacity, a comprehensive relationship has not been attainable. Moreover, some practitioners


have misgivings about determining the capacity of helical piles using only torque measurements, without taking into consideration geotechnical parameters (Cannon, 2000). There are a number of factors that affect installation torque such as pile configuration, soil conditions, operator skill level, and accuracy of measurements. Pile configuration such as shaft size and shape, number of helices, diameter of helix, and pitch size are some parameters that affect torque measurements. The presence of cobbles or boulders during installation results in a sharp rise in torque values, which is not necessarily an indication of better soil conditions. The use of empirical torque correlations is viewed with reservation by some engineers, who see the dependency of the procedure adopted by the installer on the results (Beim and Luna, 2012). Installation procedures such as applying down-pressure (crowd) on the pile, use of predrilling process and speed of rotary head are other factors that impact torque measurements. Methods of measuring torque using either a differential hydraulic pressure measured using mechanical devices or using an electronic load cell attached to the pile head may also impact the torque measurements. The frequency of calibrating torque measurement devices is another parameter that affects the quality and reliability of torque measurements.

The main objective of the paper is to propose a comprehensive theoretical model to estimate torque factors for helical piles installed into cohesive soils. The proposed torque factors can be used to assess torque requirements for selecting the suitable equipment for installation. They can be also used as a quality control measure for production piles to accept or reject installed piles. Moreover, the proposed torque factors can be used to approximately assess axial pile capacities in tension and compression. Other objectives of the study are to evaluate the effect of different parameters on torque factors, K

t and to assess their relative importance.

THEORETICAL MODELHelical piles are typically installed through the use of mechanical torque applied at the pile head with a rotary hydraulic head. Fig. 1 shows a typical installation of helical piles. Torque measured during pile installation is a function of numerous factors that includes pile configuration, soil conditions, method of

[FIG. 1] Typical Helical Pile Installation

installation, operator experience, and accuracy of measurements. Pile configuration such as shaft diameter, shape of pile shaft, number of helices, diameter of the helices, and pitch are measurable values and can be included in the theoretical torque model. Soil conditions and groundwater level have a considerable effect on pile installation and can be reasonably evaluated at the geotechnical investigation stage. However, there are other non-measurable parameters that affect measured torque values such as installation procedure, method of torque measurements, and accuracy of torque measuring devices. Methods of installation are highly dependent on the manufacturer’s installation specifications, availability of equipment, operators’ experience, and speed of installation. The accuracy of measuring torque devices depends on the method used for torque reading, such as differential pressures or using strain gauges at pile head. The reliability of torque measurements depends on the frequency of equipment calibration. These factors are difficult to quantify and do not affect the torsional resistance of soils to pile installation, but they adversely affect the measurements of torque values. Therefore, installation procedures and quality of measurements will not be considered for the development of a theoretical torque model.


The theoretical model assumes that the exerted torque during helical pile installation into cohesive soils is resisted by torsional shear along the pile shaft and torsional shear along the helices, as shown in Fig. 2. The main assumptions that are considered for the development of the proposed torque model include the following:

1. Down pressure force (crowd) applied on the pile during installation is neglected.

2. Torsional shear along the pile shaft is equal to axial unit shaft friction.

3. The soil layer is assumed to be a homogenous layer that extends to infinite depth.

4. Resisting torque during pile installation is independent of the speed of the robust hydraulic head.

5. The pile is advanced into the soil at a constant penetration rate equal to the pitch, and soil disturbance is minimal.

6. Helices are a true spiral shape, and their projected area is equal to the size of a disk with a diameter equal to the helix diameter.

Therefore, the exerted torque during pile installation may be given by the following expression:

∑+=N

his TTT1

[3]

where:

Ts = torsional moment acting on pile shaft,

(kN.m)

Thi = torsional moment acting on helix i, (kN.m)

N = number of helices

In the present model, the torsional resisting moment of the pile shaft is a function of the shaft resistance and can be given by the following equation:

2dQ

T ss =

[4]

where:

d = shaft diameter, (m) for round shaft piles and equivalent diameter for square shaft piles.

Assuming a homogenous soil layer, the shaft friction resistance of the helical pile may be given by:

ss LfdQ π= [5]

[FIG. 2] Torsional Moments during Pile Installation

where:

L = embedded pile length, (m)

fs = unit shaft friction, (kPa).

Therefore, the torsional resistance of pile shaft to installation can be given by:

2

2s

sLfd

Tπ

= [6]

Eqn. 6 assumes that the torsional stress on the pile-soil interface reaches a limiting value equal to the pile-soil unit shaft friction (Basile, 2010). The unit shaft friction for piles installed in cohesive soils can be given from the following equation (CFEM 2006):

urs Cf α= [7]

where:

α = adhesion factor, (m)

Cur

= remoulded undrained shear strength, (kPa).

Adhesion factor, α is given by:

u

a

Cp26.0

21.0 +=α ≤ 1 [8]

where:

pa = atmospheric pressure, (101 kPa).

Therefore Eqn. [6] can be rewritten as:

Ts=πd 2Lα

jC

uj

2 [9]


The torsional resisting moment on a helix during pile installation, as indicated in Fig. 3, is analogous to a giant vane shear test with a height equal to the pitch of helix, p, and diameter equal to the diameter of helix, D. Therefore, the torque required to shear the soil surrounding the helix can be estimated as the torque required to shear a cylinder of soil with height equal to the pitch of helix, p, and diameter equal to the diameter of the helix, D (Fig. 3). The torque required to separate the cylinder of soil is proportional to the undrained shear strength of the clay (C

u). The model

assumes that installation is consistent with minimal soil disturbance and that the pile is advanced into the soil at a constant rate equal to pitch per full revolution of drive head.

The torque required to separate a helix i is the sum of the torsional moment at the upper surface of the helix, T

ti; torsional moment due

to the resistance of the separated cylinder, Tci;

and the moment at the bottom of helix, Tbi; as

shown on the following equation:

bicitihi TTTT ++= [10]

Torque due to shearing the cylinder of soil around a helix i can be expressed as:

uiiii

uici CpD

daD

CT22

2

π== ∫ [11]

where

Cui = undrained shear strength at helix level i, (kPa).

D = helix diameter, m.

Torque due to shearing resistance at the top of the soil cylinder can be expressed as:

utiii

D

d utiti CdD

rdaCTi

12)( 33

2

2

−== ∫ π [12]

whereC

uti = undrained shear strength at top of helix

level i, (kPa).

Di = helix i diameter, m.

Torque due to shearing resistance at the bottom of the soil cylinder can be expressed as:

ubiii

D

d ubibi CdD

rdaCTi

12)( 33

2

2

−== ∫ π [13]

where

Cubi

= undrained shear strength at bottom surface of helix i, (kPa).

[FIG. 3] Torsional Resistance Model of a Helix during Pile Installation

Therefore, resisting moment acting on helix i can be expressed as:

2/)(12

)( 233

uiiiubiutiii

i CpDCCdD

T ππ ++−

= [14]

Assuming that soil around the helix i is homogenous, (i.e. C

ui = C

uti = C

ubi), Equation [14]

can be rewritten as:

⎟⎟⎠

⎞⎜⎜⎝

⎛ −+=

6)(

2

332iiii

uiidDpD

CT π [15]

It should be noted that, since the installation of a helical pile typically requires a relatively large number of revolutions to install the pile to final depth, remoulded undrained shear strength values are suggested for use in Equation [15]. However, for the bottom helix, the intact undrained shear strength values (peak values) are suggested for use. For the bottom helix, the resisting torsional moment can be expressed as:

⎟⎟⎠

⎞⎜⎜⎝

⎛ −++=

12)(

122

31

31

311

21

11dDDpD

CT uπ [16]


MODEL VERIFICATIONIn order to verify the proposed theoretical torque model, the measured torque values versus depth for a helical pile with double helices, ST72, reported by Sakr (2012b) are presented in Fig, 4. Pile ST72 had a shaft diameter of 406 mm (16 in), with two helices, 813 mm (32 in) in diameter spaced at 1.63 m (5.35 ft) (i.e. two times helix diameter). The pitch for both helices was 152 mm (6 in). The side friction from Cone Test Penetration Test (CPT) sounding at the test location is also presented in Fig. 4. The main advantage of a CPT test is that it provides a near-continuous soil profile and, therefore, the data is of great importance for verification of the proposed torque model.

Soil properties at the test site location, as interpreted from CPT data and summarized in Table 1, consisted of surficial sandy silt, to a depth of about 1.9 m (6.2 ft) below existing grade, over a stiff to very stiff silty clay layer, to a depth of about 13.7 m (45 ft) , underlain by a hard silty clay layer that extended to the end of sounding at 16.4 m (53.8 ft). The estimated undrained shear strength, Cu, for the stiff and very stiff silt clay were 80 kPa and 115 kPa (11.6 psi and 16.7 psi), respectively. The estimated undrained shear strength of the lower hard silty clay layer was 180 kPa (26 psi). Based on the results of the CPT sounding, soil properties for each soil layer were relatively consistent with the exception of few peaks, such as at a depth of about 14.6 m (48 ft), where an abrupt increase in sleeve friction was observed.

The measured torque values during pile ST72 installation are also presented in Fig. 4. The torque values were measured using differential pressures displayed on mechanical gauges. The estimated torque values using equations [3], [9]; [15] and [16] at different depths for pile ST72 are also presented in Fig. 4. The following observations were made based on comparing between measured torque values at pile head and estimated torsional resistance of pile ST72:

1. Measured torque at the pile head increased considerably as the upper helix advanced into the ground. The estimated torsional resistance of the soil followed a similar trend to the measured values. As expected when the bottom helix travels through different soil layers, the torque value shows an abrupt change to reflect the properties of the soil layer at the bottom helix level.

2. When both helices travel through the same soil layer, torsional resistance increases

0 100 200 300 400 500 600 700

0

2

4

6

8

10

12

14

16

18

50.00 100.00 150.00 200.00 250.00 300.00 350.00

Cone side shear, kPa

Dep

th, m

Torque, kN-m

ST72 Torque estimated CPT Sleeve Frictiion

Dense sand φd 33°, γ=19 kN/m3

Avg Torque 88 kN-m

Hard silty clay, cu 180kPa, γ=19 kN/m3

Avg Torque 296 kN-m

Very stiff silty clay,cu 115kPa, γ=18 kN/m3

Avg Torque 233 kN-m

Stiff silty clay, cu 80kPa, γ=18 kN/m3

Avg Torque 160 kN-m6.9

13.7

10.8

1.9

[FIG. 4] Comparison between Measured Torque and Estimated Torsional Resistance of Pile ST72 during Installation

[TABLE 1] Summary of Soil Properties

Depth

mSoil description

Total unit weight, kN/m3

Undrained Shear Strength, kPa

Frictional resistance angle,

φ (o)

0 – 1.9 Sand, compact 18.5 - 33

1.9 – 6.9 Glacial Till, stiff 18 80 0

6.9 – 13.7 Glacial Till, very stiff 18 115 0

13.7 – 16.4 Glacial Till, very stiff to hard 19 180 0


linearly due to the increase of resisting moment of the shaft.

3. Torque measured up to a depth of about 8 m (26.2 ft) was considerably higher than the estimated torque.

4. The slope of the measured and estimated torque between depths of about 9 m and 13 m (29.5 ft and 42.7 ft) was similar.

5. In general, the measured and estimated installation torque values both agreed reasonably.

6. The estimated torsional resistance at the end of pile installation agreed reasonably with the measured values.

7. Spikes were observed from the CPT data (sleeve friction) indicating that the soil layers were not truly homogenous.

The comparison between measured and estimated torque values at different levels indicated that both estimated and measured values generally followed similar trend and agreed reasonably. It should be noted that remoulded undrained shear strength values were used for the torque estimate. The estimated lower torque values up to depth of 9 m (29.5 ft) could be as a result of using remoulded shear strength as opposed to intact undrained shear strength of native materials.

COMPARISON BETWEEN MEASURED AND ESTIMATED TORQUE VALUESAs indicated in Eqns. [3]; [9] and [15], the estimated torsional soil resistance values at the end of installation are a function of shaft size (i.e. either diameter or width of square shaft helical piles); helix diameter; pitch; and number of helices. The estimated torsional resistance is also a function of soil strength parameters, including undrained shear strength, adhesion and soil sensitivity. Moreover, as indicated on the model assumption, it is assumed that the pile is advanced into the soil at a constant rate equivalent to the pitch. Therefore, operator experience and pile installation consistency affect the measured torque values during pile installation. Auguring effect, where the pile is advanced at a smaller rate less than pitch size, may cause additional soil disturbance and reduce the measured torque during installation. Sensitivity of the torque reader and accuracy and frequency of calibrating the

device are other factors that affect the quality of measurements.

In order to compare between measured and estimated torque values, a total of 74 installation tests were considered in the present study. Pile configuration and a summary of soil parameters are presented elsewhere (Zhang 1999; Tappenden 2007; Livneh and El Nagger 2008; Cerato and Victor 2009; Sakr 2008, 2011, 2012a and 2012b; Beim and Luna 2012). The selected installation cases were selected to satisfy the following conditions:

1. Pile configuration, including shaft sizes and helix diameters, cover a wide range. For example, shaft sizes varied between square shafts 44 mm (1.73 in) in width to round shafts with diameters up to 508 mm (20 in). Helix diameters varied between 203 mm (8 in) and 1016 mm (40 in). The number of helices varied between 1 and 4. Pitch was either 76 mm or 152 mm (3 in or 6 in).

2. Selected piles were also installed by different operators so that the data reflect the variability in installation procedures for different contractors.

3. Installation technique included standard installation and use of predrilled pilot holes.

4. Soils considered for the study varied between soft clays to clay shale with undrained shear strength, C

u, that varied

between 5 kPa and 400 kPa (0.73 psi and 58 psi) (very soft to very hard clay materials).

The measured and estimated torque values for different piles were compared in Fig. 5. The prediction ratio, which is the ratio between estimated and measured torque values, varied between 0.78 and 1.29. The data were also linearly fitted with a standard deviation of 0.96. Therefore, the proposed torque model reasonably estimated installation torque for helical piles considered in the study.

RELATIONSHIP BETWEEN AXIAL TENSILE CAPACITY AND INSTALLATION TORQUEThe empirical torque-capacity relationship, expressed in Eqn. [1], assumes a proportional relationship between measured torque at the end of installation and axial pile capacity by torque factor. To separate different torque factors (i.e. compression versus tension); torque factor in tension, K

t, is defined as the ratio


between axial tensile capacity of the pile and the measured torque at the end of installation. Therefore, K

t, can be expressed as:

thtshst

t KKTQ

TQ

TQ

K +=+== [17]

Eqn. [17] suggests that the torque factor in tension, K

t, can be uncoupled into two

components including torque factor due to shaft, K

ts, and torque factor due to helices, K

th.

For predicting the ultimate uplift resistance of a helix i installed into cohesive soils considering the individual helix capacity method (i.e. neglecting the interaction factors between different helices), the following expression may be used (Das and Seeley, 1975):

D + NC = D + Q =Q 11ui

N

111

N

1hih hHuiHihH AAA γγ ′′ ∑∑ [18]

9)(2.1 ≤=DDN h

U [19]

where:

γ’ = Average effective unit weight of soil above the top helix, (kN/m3);

Qhi = ultimate helix i resistance, (kN);

Cui = undrained shear strength of soil layer at

helix i, kPa

Dhi = depth to helix i, (m);

Di = diameter of helix i, (m);

Nui = Dimensionless uplift bearing capacity

factor for helix i;

0

40

80

120

160

200

240

280

320

360

0 40 80 120 160 200 240 280 320 360

Est

imat

ed T

orqu

e (k

N.m

)

Measured Torque (kN.m)

CompressionTension

Equity Line

[FIG. 5] Comparison between Measured and Estimated Torque Values

AHi

= net surface area of bearing helix (helix area – shaft area), m2; and

N is the number of helices.

For round shaft piles, the net surface area of

helix i, )4

(22 dD

A hiHi

−=π where d = shaft

diameter, (m). Therefore the torque factor due to shaft, K

ts can be estimated as:

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ −+++⎟⎟

⎠

⎞⎜⎜⎝

⎛ −++

==

∑ = 12)(

1226)(

22

131

31

311

21

12

332 dDDpDC

dDpDC

QdT

QK

uN

iiiii

uis

sts

π [20]

It should be noted that neglecting the interaction between different helices is a reasonable assumption for most cases where the spacing between helices is equal to or greater than three times the helix diameter. However, for the cases where spacing between helices is less reduction of helix capacities due to interaction should be considered. Therefore, the torque factor due to helices can be expressed as following:

( )

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ −+++⎟

⎟⎠

⎞⎜⎜⎝

⎛ −++

+==

∑

∑

=

=

12)(

1226)(

22

31

31

311

21

12

332

11

/

dDDpDC

dDpDC

dQ

DNCA

TQ

K

uN

iiiii

uis

N

nhuiuiHi

hth

ππ

γ

[21]

RELATIONSHIP BETWEEN AXIAL COMPRESSIVE CAPACITY AND INSTALLATION TORQUESimilar to torque-factor in tension, torque factor in compression K

c, defined as the ratio between

the axial compressive capacity and measured torque at the completion of pile installation can be expressed as the sum of torque factor due to the shaft, K

cs and torque factor due to helices, K

ch.

For simplicity, the frictional resistance of pile shaft in tension may be assumed similar to that value in compression. Hence, Eqn. [20] can be used to estimate torque factor due to shaft resistance, K

cs.

For the case of compressive loading for helical piles founded in cohesive soils, the axial compressive resistance of a helix i can be estimated as follows:

Qchi

= AHi

Cui N

ci [22]

where

Nci = dimensionless bearing capacity factor for

helix i;

(Nc = 9 for helices smaller than 0.5m; N

c = 7 for

helices between 0.5 m (20 in); and Nc = 6 for

helixes larger than 1 m (40 in) in diameter)


Tables 2 and 3. The measured torque factors were based on the results of full-scale axial compressive and tension tests reported in literature. A total of twenty-one axial tensile load tests and fifty-three axial compression tests were used to assess the tension and compression torque factors (K

t and K

c). The

theoretical torque factors in tension and compression were estimated using Eqns. [20], [21] and [25].

The comparison between measured and estimated torque factors in tension and compression are also presented in Figs. 6 and 7. It can be seen that there is a reasonable agreement between measured and estimated torque factors both in tension and compression. However measured K

c values for square

shaft piles were generally lower than the estimated values. Possible reason for that is that for square shaft piles, soil disturbance is considerably higher compared to round shaft piles due to the rotation of the square shaft

For round shaft piles, the ultimate compressive resistance for helix i can be expressed as:

ciuihichi NCdDQ )(4

22 −=π

[23]

For round shaft piles, the ultimate compressive resistance of the bottom helix 1 can be expressed as:

11211 4 cubhch NCDQ π

= [24]

The torque factor in compression for helices can be expressed as:

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ −+++⎟⎟

⎠

⎞⎜⎜⎝

⎛ −++

⎟⎠

⎞⎜⎝

⎛−+

==

∑

∑

=

=

12)(

1226)(

22

)(41

31

31

311

21

12

332

2

2211

21

dDDpDC

dDpDC

dQ

NCdDNCD

TQ

K

uN

iiiii

uis

N

nciuihicubh

chch

π

[25]

COMPARISON BETWEEN THEORETICAL AND MEASURED TORQUE FACTORSMeasured and estimated torque factors in tension and compression are presented in

[TABLE 2] Comparison between Measured and Estimated Torque Factors in Tension, Kt.

Pile ID Soil TypeShaft

Diameter

m

No of helices

Theoretical K

t

m-1

Measured K

t

m-1

Reference Notes

T1 Silty Clay 0.089 1 18.2 12.7 Sakr (2011)

ST62 Clay Till 0.406 2 4.8 4.8 Sakr (2012a) predrilled holeST72 0.406 2 5.8 6.2

ST14 Clay Shale 0.406 1 4.4 5 Sakr (2012a) predrilled holeST5 0.324 2 6.3 5.7

TL Clay Till 0.219 3 8.4 9.9 Zhang (1999)TS 0.219 3 9.3 7.6

Tprod 0.219 2 9.8 9.2

T7 Clay Till 0.273 1 8.8 9.8 Tappenden (2007)T8 Clay Till 0.273 2 9.3 10.9

7 Clay Till 0.0445 3 25.6 21.3Livneh and El Naggar

(2008)8 0.0445 3 26 26.5

16 0.0445 3 25.5 23.6

20 0.0445 3 24.7 29.2

10 0.0445 3 23.9 24.7

T1 Clay 0.219 3 7.7 7 Sakr (2008)

T2 Clay Till 0.273 2 7.7 10.7

T1 0.273 1 8.5 9.9

Clay Till 0.508 1 4.9 2.6 Sakr (2012b)

Clay Till 0.508 2 3.8 1.9

Clay Till 0.508 2 4.4 5.2


[TABLE 3] Comparison between Measured and Estimated Torque Factors in Compression


Diameter

m

No of helices

Theoretical K

t

m-1

Measured K

t

m-1

Reference Notes

Silty Clay 0.089 1 19.2 19.8 Sakr (2011)

ST61 Clay Till 0.406 2 6.1 5.5 Sakr (2012a) predrilled holeST15 Clay Shale 0.508 1 5.2 7.1

ST14 Clay Shale 0.406 1 6.3 6.8

ST7 Clay Shale 0.406 1 7.7 7.3

Clay Till 0.219 3 14.4 9.2 Zhang (1999)0.219 3 10.9 7.6

0.219 2 10.9 10.8

C7 Clay 0.178 1 9.5 11.8 Tappenden (2007)C8 Clay 0.219 1 9 9.9

C9 Clay 0.178 2 9.7 12.8

C10 Clay Shale 0.24 2 9.8 14.1

C11 Clay Till 0.273 1 12.1 8.9

C12 Clay Till 0.273 2 10.1 8

C15 Clay 0.14 3 13.7 13.7

C16 Clay 0.114 2 15.4 18.1

C17 Clay 0.114 1 15.9 21.1

2 Clay Till 0.0445 3 28.6 42.6 Livneh and El Naggar

(2008)

Square shaft

6 0.0445 3 25.5 37.8

Clay 0.324 1 6.3 5.6 Sakr (2012b)

Clay 0.324 1 6.3 5.3

Clay 0.324 1 6.3 6

Clay 0.324 3 7.8 7.1

Clay 0.324 2 7.7 7.9

Clay 0.324 2 8.3 9.3

Clay Till 0.324 4 6.5 6.1

Clay Till 0.324 3 6.3 6.1

Clay Till 0.324 2 7.6 7.8

Clay Till 0.324 2 7.3 6.8

C1 Clay 0.324 3 5.9 7.1 Sakr (2008)

C2 0.324 4 6.9 7.6

C2 Clay Till 0.273 2 8 14.1 Sakr (2012b)

C1 0.273 1 8.1 12.1

0.324 1 6.7 5.5

0.406 1 5.4 5.6

0.508 1 4.4 4.2

0.508 1 4.6 4.4

0.508 2 5 5.3

0.508 3 5.5 6

0.508 2 6.2 6


and causing void around pile shaft during installation. The mean prediction ratio for K

c is 1.06 with a coefficient of variation of

17.8%, while the mean prediction ratio for Kt

is 0.98 with a coefficient of variation of 17.2%. Generally, torque factors in tension were more predictable than torque factors in compression. This can be explained by the fact that during helical pile installation, torque measured at the end of installation can be considered to be representing average soil conditions within pile embedment depth. However, for the case of torque factor in compression, there are no torque measurements within the soil layer immediately below the bottom helix (which considerably affects the performance of helical

piles in compression), and therefore torque factor in compression may not be accurate.

It can be seen from Tables 2 and 3 that torque factors in tension were generally lower than torque factors in compression. For example, pile ST61 and ST62 with similar configurations, measured torque factors in tension and compression were 4.8 and 5.5, respectively. It can be also seen from Tables 2 and 3 that torque factors for square shaft piles were considerably higher than those for cylindrical shafts. Discrepancies between measured and estimated torque factors were also higher for square shaft piles.


Diameter

m

No of helices

Theoretical K

t

m-1

Measured K

t

m-1

Reference Notes

0.406 1 5.3 4.6

0.508 2 4.4 4.6

0.508 2 4.6 5.7

HP5 Varved Clay 0.073 3 26.7 54.1 Beim and Luna (2012)HP10 0.073 3 26.7 46.6

HP15 0.073 3 26.7 44.3

HP4 0.073 3 32.1 33.3

HP7 0.073 3 32.1 31.9

HP9 0.073 3 32.1 40.4

HP12 0.073 3 32.1 43.3

HP14 0.073 3 32.1 37.7

[TABLE 3] Comparison between Measured and Estimated Torque Factors in Compression (continued)

y = 0.9955xR² = 0.9234

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

0 5 10 15 20 25 30 35 40

Est

imat

ed T

orqu

e Fa

ctor

, Kt(m

-1)

Measured Torque Factor, Kt (m-1)

Measured and Estimated TorqueEquity LineLinear (Measured and Estimated Torque)

[FIG. 6] Comparison between Measured and Estimated Torque Factors in Tension

[FIG. 7] Comparison between Measured and Estimated Torque Factors in Compression

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

45.00

50.00

55.00

0 5 10 15 20 25 30 35 40 45 50 55

Est

imate

d T

orq

ue F

act

or,

Kc

(m-1

)

Measured Torque factor, Kc (m-1)

Measured and Estimated Torque Equity Line


PARAMETERS INFLUENCING TORQUE FACTORSParameters affecting torque factors in cohesive soils can be grouped into five main groups:

1. soil properties such as undrained shear strength, adhesion and sensitivity;

2. pile configuration (i.e. shaft diameter, helix diameter, pitch, number of helices and embedment depth);

3. installation procedure;

4. reliability of torque measurements; and

5. loading path (i.e. tension or compression).

Parameters 1 to 4 are discussed in more detail in the following sections, while the last parameter has been discussed earlier.

Soil Properties

In order to evaluate the effect of undrained shear strength on torque factors, a hypothetical pile configuration was assumed, consisting of a round shaft pile, 0.324 m (12.75 in) in diameter with a single-helix diameter of 0.762 m (30 in) in diameter. Estimated torque factors in tension, K

t versus embedment depth ratio (i.e.

embedment depth divided by helix diameter) for cohesive soils with undrained shear strength are presented in Fig. 8. A homogeneous soil layer with undrained shear strengths that varied between 25 kPa (3.64 psi) ( soft clay) and 400 kPa (58 psi) (very hard clay) was assumed. It can be seen from Figure 8 that at shallow embedment depths, up to depth of about 4.5 D, the softer soils showed lower K

t factors

compared to harder soils. At deeper embedment depths, the harder clay soils showed relatively

high Kt factors. However, the increase in

torque factor Kt due to increasing undrained

shear strength was relatively insignificant. For example, the torque factor for a pile installed into very hard clay (C

u = 400 kPa or 58 psi) at

an embedment depth of about 8 helix diameters were about 7 m-1 (23 ft-1) compared to 6 m-1 (19.7 ft-1) for a pile with a similar configuration installed in soft clay (C

u = 25 kPa or 3.64 psi)

Adhesion around a pile shaft is typically proportional to the undrained shear strength, as indicated in Eqn. [7]. The adhesion factor expressed in Eqn. [8] is inversely proportional to the undrained shear strength of soils. For soft clay, the adhesion around a pile shaft is equivalent to the undrained shear strength value.

Sensitivity of soils is another factor that affects the torsional resistance of soils to installation and torque factors. For sensitive clays where the ratio between undisturbed shear strength and remolded shear strength is high, the effect of soil disturbance on pile installation is expected to be high. Therefore, the predicted torsional soil resistance to installation using undisturbed undrained shear strength is likely to be in error.

Pile Configurations

To evaluate the effect of increasing shaft diameter on torque factor in tension, K

t, Eqns.

[20] and [21] were used to estimate torque factors for helical pile with a single-helix, 0.4 m (1.3 ft) in diameter, installed into cohesive soil with undrained shear strength C

u = 50 kPa

(7.25 psi). The shaft diameters were 89 mm (3.5 in), 178 mm (7 in) and 273 mm (10.75 in) respectively. The torque factors in tension, K

t,

versus embedment depth ratios are presented in Fig. 9. It can be seen from Fig. 9 that, as expected, increasing the shaft diameter resulted in considerably reducing torque factors. For example, at an embedment depth of 7.5 D, the torque factors for piles with shaft diameters of 89 mm, 178 mm and 273 mm (3.5 in, 7.0 in and 10.75 in) were 17 m-1, 12 m-1 and 8 m-1 (55.8 ft-1, 39.4 ft-1,and 26.2 ft-1) respectively.

In order to evaluate the effect of varying helix diameters on the torque factors in tension, K

t, the torque factors were estimated for a

pile with a shaft diameter of 406 mm (16 in) equipped with a single helix installed into clay material with undrained shear strength of 50 kPa (7.25 psi). Helix diameters of 0.763 m

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

0 2 4 6 8 10 12 14 16 18 20

Estim

ated

Tor

que

Fact

or, K

t(m

-1)

Embedment Depth Ratio (H/D)

Cu = 50 kPa100 kPa200 kPa400 kPa25 kPa

[FIG, 8] Effect of Undrained Shear Strength on Torque Factors in Tension, Kt.


(30 in) and 1.2 m (48 in) were considered for the comparison, and the results are presented in Fig. 10. As seen in Fig. 10, increasing helix diameter resulted in slightly increasing K

t.

Fig. 11 shows piles with helix and shaft diameter ratios of 2, 2.5 and 3. As seen in Fig. 11, increasing the ratio between D/d resulted in considerably increasing torque factors. For example, K

t for piles with D/d ratios

of 2, 2.5 and 3 at embedment depth of 7.5 D were about 6.5, 7.5 and 9.0 respectively.

Torque factors in tension Kt for piles with a

shaft diameter of 0.324 m (12.75 in), single helix and pitch of either 76 mm or 152 mm (3 in or 6 in) are presented in Fig. 12. As seen in Fig. 12, the pitch had a minor effect on the torque factors. However, it should be noted that the pitch for piles with small shaft diameters may have more pronounced effects (Sakr 2012b).

As indicated in Figs. 8 to 12, the torque factors increased with increasing embedment depths for relatively short piles (i.e. piles with embedment depth ratios up to about 8), beyond which the torque factors were relatively independent of embedment depth.

Torque factors in tension Kt for piles with

single, double or triple helices are presented in Fig. 13. The torque factors were estimated using a pile with shaft diameter of 0.324 m (12.75 in) and helix diameter of 0.763 m (30 in), installed into clay with undrained shear strength of 50 kPa (7.25 psi). The assumed spacing between different helices is 3D, and pitch is 152 mm (6 in). As seen in Fig. 13, K

t at lower embedment

depths is inversely proportional to number of

[FIG. 10] Effect of Varying Helix Diameters on Torque Factors in Tension, Kt.

[FIG. 12] Effect of Varying Pitch Size on Torque Factors in Tension, Kt.

[FIG. 11] Effect of Varying Helix to Shaft Diameter Ratio on Torque factors in Tension, Kt.

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

0 2 4 6 8 10 12 14 16 18 20

Estim

ated

Tor

que

Fact

or, K

t(m

-1)


Undrained Shear Strength Cu = 50 kPaShaft Dia = 406 mm

Helix Dia 762 mm

Helix Dia 1200 mm

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

0 2 4 6 8 10 12 14 16 18 20

Estim

ated

Tor

que

Fact

or, K

t(m

-1)


Undrained Shear Strength = 50 kPaD/d = 3D/d = 2D/d = 2.5

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

0 2 4 6 8 10 12 14 16 18 20

Est

imat

ed T

orqu

e F

acto

r, K

t(m

-1)


Cu = 50 kPaShaft Dia = 324 mm

Single Helix 763 mm in Dia

pitch = 76 mm

pitch = 152 mm

[FIG. 9] Effect of Shaft Size on Torque Factors in Tension, Kt.

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

18.00

20.00

22.00

24.00

0 2 4 6 8 10 12 14 16 18 20

Est

imat

ed T

orqu

e Fa

ctor

, Kt(m

-1)


Undrained Shear Strength, Cu = 50 kPaHelix Dia. = 0.4 m

168 mm shaft89 mm shaft273 mm shaft


helices. However, at higher embedment depths, K

t increased with increasing the number of

helices.

The method of installation is one of the major factors that affects the quality of torque values used in practice. In general, methods of installations that cause more soil disturbance negatively impact the torque measurements and reduce the reliability of torque data. For example, the presence of cobbles or boulders during installation results in a sharp rise in torque values, which is not necessarily an indication of stronger soil conditions. Installation procedures such as applying down pressure, predrilling, or advancing the pile at a smaller rate than the pitch are other factors that impact torque measurements. An auguring effect (or spinning), where pile rotation is continued and little or no advancement into ground (usually occurs when pile hit hard soil layer or spinning on rock), is likely to considerably reduce the torque requirement during installation and cause significant soil disturbance.

Reliability of Torque Readings

Methods of measuring torque during pile installation are mainly either using a mechanical gauge that measures the differential pressure across the gear motor, or using an electronic torque transducer that consists of a series of strain gauges attached to the drive head. Theoretical torque using differential pressure may be estimated as:

( )24πη×××Δ

=PGRCIDPT [26]

where

PΔ = Differential pressure across the motor, (psi);

CID = Cubic inch displacement of the hydraulic motor;

PGR = Planetary gear ratio; and η = Combined motor and planetary gear efficiency.

It should be mentioned that, when using torque measuring method based on differential pressures, the hydraulic gear motor torque versus differential pressure curves may not reflect the manufacturer’s stated performance data. Equipment and hydraulic line size may also affect the torque versus differential pressure curve for the same motor. Deardorff (2011) advocated that installation speed and flow rate at the lower end of differential pressure curve may also affect the torque versus differential pressure curve for the same motor and same equipment line setup. Therefore, the use of torque measurement based on differential pressures may not be accurate. Electronic torque transducers may provide more reliable means of measuring torque during pile installation. Frequency of calibrating torque measurement devices is another factor that affects the reliability of torque measurements.

Moreover, a clear definition of the average torque value at the end of installation is required. For example, Hoyt and Clemence (1989) averaged the installation torque over the final distance of penetration equal to three times the largest helix diameter. Some contractors specify the use of average torque over the last 0.3 m (1 ft), while others specify that torque should be averaged over the last 1 m (3.3 ft) of installation.

CONCLUSIONSThis paper presents a theoretical model for predicting torsional resistance to helical pile installation into cohesive soils. The developed model was validated by comparing the estimated torque to the measured values at different embedment depths for a case reported in the literature. The measured and estimated

[FIG. 13] Effect of Increasing Number of Helices on Torque Factors in Tension, Kt.

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

0 2 4 6 8 10 12 14 16 18 20

Est

imat

ed T

orqu

e Fa

ctor

, Kt(m

-1)


Single helix2 helices3 helices


torque values at the end of pile installation from total of seventy four (74) field installations reported in the literature were also compared. Both measured and estimated torque values agreed reasonably. The developed torque model was then used to assess torque factors. The following general conclusions may be drawn:

1. Torque required to install piles into cohesive soils can be reasonably estimated using the theoretical model developed in this paper.

2. Based on the proposed torque model, theoretical torque factors (K

t and K

c) that

represent the ratio between ultimate capacity and installation torque were proposed.

3. Parameters required to assess theoretical torque factors include pile geometry and soil strength parameter such as undrained shear strength. The required soil parameters to assess torque factors are standard parameters and therefore it is relatively easy to obtain for the project site.

4. Pile geometry, including shaft shape, ratio of helix to shaft diameter, and embedment depth has a considerable effect on the torque factors. Other factors that influence torque factors include pitch and number of helices.

5. Torque factors in compression and tension for piles with similar configurations installed into similar cohesive soils are different. It was found that torque factors in compression are generally higher than those factors in tension.

6. Torque measurements are also influenced by other factors such as the method of installation, operator experience, and accuracy of the measurement device. Therefore, in absence of precise installation procedures and quality torque device measurements, installation torque readings should be used with caution and may only be used to qualitatively assess installation.

REFERENCES1. Basile, F. 2010. "Torsional response of

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2. Beim, J., and Luna, S.C. 2012. "Results of dynamic and static load tests on helical piles in the varved clay of Massachusetts", DFI Journal, Deep Foundations Institute, In print.

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4. Cerato, A.B., and Victor, R. 2009. "Effects of long-term loading on fluctuating water table on helical anchor performance for small wind tower foundations", Journal of Performance of Constructed Facilities, ASCE 23(4): pp. 251-261.

5. CFEM. 2006. Canadian Foundation Engineering Manual. 4th Edition. Canadian Geotechnical Society, Technical Committee on Foundations, BiTech Publishers Ltd., Richmond, BC.

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7. Deardorff, D. 2011. "A comparison of gear motor performance curves for helical pile installation", Seminar presented at DFI Helical Foundations and Tiebacks Specialty Seminar, Deep Foundations Institute, March 17, 2011, Dallas, Texas, USA.

8. Hoyt, R.M., and Clemence, S.P. 1989. "Uplift capacity of helical anchors in soil", Proceedings of the 12th International Conference on Soil Mechanics and Foundation Engineering, Rio de Janerio, Brazil, Vol. 2, pp. 1019-1022.

9. Hoyt, R., Seider, G., Reese, L. C., and Wang, S. T. 1995. "Buckling of helical anchors used for underpinning: Foundation upgrading and repair for infrastructure improvement", Edited by William F. K. and Thaney, J. M. Geotechnical Special Publication No. 50, ASCE, pp. 89-108.

10. Livneh, B., and El Naggar, M.H. 2008. "Axial testing and numerical modeling of square shaft helical piles under compressive and tensile loading", Canadian Geotechnical Journal, 45: pp. 1142–1155.


11. Perko, H.A. 2001. "Energy method for predicting the installation torque of helical foundations and anchors", New Technologies and Design Developments in Deep Foundations, Reston, VA, ASCE, pp. 342:352.

12. Perko, H. A. 2009. Helical Piles: A Practical guide to design and installation. John Wiley & Sons. New York, N.Y.

13. Sakr, M. 2008. "Helical piles for power transmission lines: Case study in Northern Manitoba, Canada", Ninth International Conference on Permafrost, Extended Abstracts, NICOP 2008, Fairbanks, Alaska, USA, pp. 261:262.

14. Sakr, M. 2011. Helical piles - "An effective foundation system for solar plants", 64th Canadian Geotechnical Conference and Pan-AM CGS, Toronto, Ontario, 2-6 October 2011, Toronto.

15. Sakr, M. 2012a. "Installation and performance characteristics of high capacity helical piles in cohesive soils", DFI Journal, 6(1): 41-57, July 2012.

16. Sakr, M. 2012b. "Torque prediction of helical piles in cohesive soils", The 65th Canadian Geotechnical Conference (CGC); at the Fairmont Hotel, Winnipeg, Manitoba, Canada from September 30 to October 3, 2012.

17. Tappenden, K.M. 2007. "Predicting the axial capacity of screw piles installed in Western Canadian soils", MSc. Thesis, The University of Alberta, Edmonton, Alberta, Canada.

18. Zhang, D.J.W. 1999. "Predicting capacity of helical screw piles in Alberta soils", MSc. Thesis, The University of Alberta, Edmonton, Alberta, Canada.


Ultimate Lateral Resistance of Piles in Cohesive SoilLassaad Hazzar, University of Sherbrook, Canada; (819) 446 5100; [email protected]

Mourad Karray, University of Sherbrook, Canada

Mounir Bouassida, University of Tunis El Manar, Tunis, Tunisia

Mahmoud N. Hussien, University of Sherbrook, Canada

ABSTRACT The ultimate lateral resistance of piles in cohesive soil is studied using the well-known finite difference code, FLAC2D. The Modified Cam Clay (MCC) constitutive relation is adopted in the analyses to model the cohesive soil behavior, whereas the structural pile model with three degree of freedoms, available in FLAC2D library, is adopted to model the piles. The reliability of Broms's method, still used in the current design practice of piles under lateral loads, is verified. Comparisons between the ultimate lateral resistances of piles and those deduced from the graphs proposed by Broms (1964) are presented in graphs. Different factors thought to affect the lateral resistance of piles in cohesive soil, not adequately considered in Broms's method, such as clay stiffness, pile length, pile diameter and axial load are parametrically studied. A special concern is devoted to elucidate the effects of over-consolidation ratio (OCR) on the ultimate lateral resistance of piles in cohesive soil.

INTRODUCTIONPile foundations have been used extensively for supporting both axial and lateral loads for a variety of structures including heavy buildings, transmission lines, power stations, and highway structures. In some cases, the lateral loads may be relatively light and there is no need to account for them in pile design; however, in other cases, lateral loads govern the design of piles. A key element in the design of pile foundations under lateral loads is the determination of the ultimate lateral resistance that can be exerted by the soil against the pile (Murff and Hamilton, 1993). For example, the ultimate lateral resistance is required for calculating the p-y curves, which have been used extensively in recent years in piles design.

Several methods have been published for predicting the ultimate lateral resistance of pile in cohesive soils (Brinch Hansen, 1961; Broms, 1964; Poulos and Davis, 1980; Fleming et al.,1992; Reese and Van Impe, 2001). However, these methods often produce significantly different predictions of the ultimate resistance. This makes it difficult for engineers to effectively select the appropriate method when designing laterally loaded piles in cohesive soils.

Because the problem of determining the ultimate resistance of a laterally loaded pile is a three dimensional (3D) and nonlinear

problem, finding a rigorous solution is very unlikely. Thus existing solutions for the ultimate lateral resistance of the pile are either of a semi-empirical nature or employ approximate analysis which often involves many simplifications (Jamiolkowski and Garassino, 1977). These approximations may account for the significantly different ultimate resistance values obtained from the different methods. This makes it difficult for practicing engineers to effectively select the appropriate method when designing laterally loaded piles in cohesive soils. In this paper an assessment of the most important method, Broms's method, still used in the current design practice of piles under lateral loads, is done. A two-dimensional (2D) finite difference code, FLAC2D (Version 6, Manual [2008]) is used to this end. The Modified Cam Clay (MCC) constitutive relation is adopted in the analyses to model the cohesive soil behaviour, whereas the structural pile model with three degrees of freedom, available in FLAC2D elements library, is adopted to model the piles. Different factors thought to affect the ultimate lateral resistance of piles in cohesive soil such as clay stiffness, pile length, pile diameter and axial load are parametrically studied. A special concern is devoted to elucidate the effects of over-consolidation ratio (OCR) on the ultimate lateral resistance of piles in cohesive soil. The investigations were carried out for single piles in a type of clay which has


been used by several studies conducted at the University of Sherbrook, Quebec, Canada.

The existing methods of predicting the ultimate lateral resistance of pile foundations under lateral loads are first reviewed, to be followed by the main part of the study with respect to the effects of clay stiffness, pile length, pile diameter, axial loads and OCR on the lateral ultimate resistance of pile foundations. The primary findings from this study are summarized as conclusions.

EXISTING METHODS OF PREDICTION OF ULTIMATE LATERAL RESISTANCEThe existing methods used to estimate the lateral resistance of vertical piles can be divided into two main categories: methods of ultimate lateral resistance and methods of acceptable deflection at a given working lateral load. First investigation by Terzaghi (1955) consisted in the use of variable passive earth coefficients for modeling the lateral reaction of soil as a function of its internal angle of friction. Adopting the method proposed by Brinch Hansen (1961), the pile is assumed to rotate with respect to its centre of rotation, the ultimate lateral load is then estimated and the shearing force and bending moment diagrams are drawn. Broms (1964) presented a method to determine the ultimate lateral load in cohesive and cohesionless soils. Kasch (1977), stated that using Rankine’s passive states will result in very conservative solutions. Reese (1977) developed a

computer program that is widely used to predict the performance of piles subjected to lateral loading. This program solves a differential equation derived on the assumption that the pile is linearly elastic and that the soil reaction may be represented as a line load. In recent years, extensive research and developments have been undertaken to predict theoretically the behavior of laterally loaded piles in clayey soils (Poulos and Davis, 1980; Brown and Shie, 1991; Fleming et al.,1992; Liang, 1998; Reese and Van Impe, 2001).

Broms's method is still used in the current design practice of piles under lateral loads to calculate the lateral bearing capacity of piles because of its simplicity. This method will be briefly reviewed in the next paragraph.

Broms’ method (1964), proposed for the prediction of lateral resistance of vertical piles, is similar to that developed by Brinch Hansen without consideration of c-φ’ soil parameters. In fact, Broms’s method is based on earth pressure for calculation of lateral resistance of vertical piles, but quite simple assumptions are made for the distribution of ultimate soil resistance over the length of the pile. These methods study two types of piles, a short-rigid and long-flexible, embedded in mono layered half space. Broms (1964) elaborated charts for determination of the ultimate lateral load for each class as illustrated in Figs. 1(a) and 1(b) respectively (FHWA, 1997). Figs. 1(a) and 1(b) show also that the ultimate lateral resistance of the piles is affected by pile head conditions.

[Fig. 1] Ultimate Lateral Load of Piles in Cohesive Soils; (a) Short Pile, (b) Long Pile (Broms, 1964)


The ultimate lateral resistance of a fixed head pile is higher than that of free-head conditions for both cases of short and long piles. In this method, the load-deflection relationships of laterally loaded piles driven into cohesive soils are similar to the stress-strain relationships as obtained from consolidated-undrained tests (Broms, 1964). In fact, Broms method calls for some comments that be discussed later. Broms’ contribution does not consider the effect of axial loading on lateral bearing capacity of piles.

In this study, the finite differences method is implemented to examine how the lateral load capacity of the pile is influenced by varying the length of the pile, its diameter and by considering the vertical component of load as well. The numerical modeling also aims to verify whether the OCR for clayey soil has a significant effect when determining the lateral capacity at failure of the loaded pile. Note that the OCR has not been taken into consideration in several previous investigations made about the ultimate lateral capacity of piles. Elsewhere, as for Broms’ method, the vertical load component was not considered in prior analyses, this study aims to clarify how the behavior of laterally loaded piles will be affected when subjected to additional vertical load.

Therefore, the main objective is to draw design charts making possible the design of laterally loaded piles in cohesive soils and to compare the numerical predictions by FLAC2D (Fast Lagrangian Analyses of Continua in 2D) program with the Broms’ solution.

STUDIED MODEL

Finite-Difference code

In this study the finite-difference code FLAC2D (Fast Lagrangian Analysis of Continua) is used to model the behavior of single piles embedded in a clay layer in non-symmetric loading plane strain condition. FLAC2D is a commercial finite difference program that adopts an explicit numerical scheme which solves the dynamic equations of motion (even for static problems) in conjunction with an incremental constitutive law over a small time step, at discrete points in space. This method is particularly well adapted for analyzing nonlinear behavior of soils.

Geometry of the model

Fig. 2 shows the general layout and meshing of the finite differences model. Side boundary displacements were fixed in the horizontal direction, while those at the bottom boundary were fixed in both the horizontal and vertical directions. The pile is modeled by means of a structural pile model, available in the FLAC2D library, with three degrees of freedom: horizontal and vertical displacements and a rotation with respect to perpendicular axis of the plan in Fig. 2. As shown in Fig. 2, the pile toe is anchored in a separate stratum (rock). The finite difference analyses were performed in two stages. In the first stage (self-weight analysis), the in-situ stresses were initialized in the soil due to the self weight of the soil. Properties of the pile were set to be zero during this stage of analysis. During the second stage

[Fig. 2] Numerical plane strain model


of analysis (lateral load analysis), the actual properties of soil and pile were assigned. The applied loading was simulated by the application of a lateral load at the top of the pile. The modeling of the pile installation process is rather complicated, so that pile is assumed to be in a stress-free state at the beginning of the analysis, and the effect of the pile installation is ignored.

Soil properties

The soil was a soft post-glacial clay of marine origin, sampled from the site of Grande Baleine River (Demers, 1980). Two specimens (COE-01 and COE-02) have been tested to identify the geotechnical characteristics of this clay.

These samples were extracted from three (3) holes using a sampler developed by the University of Sherbrook (Quebec-Canada). The tool provides specimens of clay having a diameter ranging between 250 and 270 mm (9.8 and 10.6 in) and about 350 mm (14 in) in height. In the laboratory, the samples were cut into slices of 110 to 120 mm (4.3 4.7 in) in height, surrounded by paraffin and stored in a room where the humidity hovers around 97% and the temperature is maintained at about 14 °C (57 °F) . Laboratory tests such as Consolidation oedometer tests and triaxial tests CU (isotropically consolidated triaxial tests and sheared under undrained conditions) were carried out on the soil samples. In situ tests such as the Swedish cone were also carried out to measure the undrained shear strength of the clay. The obtained value of the undrained shear strength of the clay was found to vary between 40 and 80 kPa (5.8 and 11.6 psi). Table1 summarizes the recorded geotechnical characteristics of tested clays.

The Modifi ed Cam-Clay Model (CCM) (Roscoe

and Burland, 1968) was adopted as quite

appropriate, particularly for materials whose

behavior is infl uenced by volume variation.

In fact, the CCM may be used to represent

materials when the infl uence of volume change on

bulk property and resistance up to failure should

be taken into consideration, as for soft clays.

The CCM may give softening behavior

for particular stress paths. Without special

regularization techniques, this softening behavior

may lead to mesh dependency and numerical

instability. The use of the CCM in practical

applications is not recommended.

The CCM is expressed in terms of three variables:

the mean effective pressure, p; the deviator

stress, q; and the specifi c volume, v. In the FLAC

implementation of this model, principal stresses σ

1, σ

2, σ

3 are used, the out-of-plane stress, σ

zz,

being recognized as one of these. (By convention,

traction and dilation are positive.)

The generalized stress components p and q may

be expressed in terms of principal stresses, as

follows:

( )1 2 3

2

1p = − σ + σ + σ

2 21 2 2 3 3 1

31q ( ) ( ) ( )2

= σ −σ + σ −σ + σ −σ [1]

(Note that 2q 3J= , where J2 is the second

invariant of the effective stress deviator tensor).

The incremental strain variables associated with

p and q are the volumetric strain increment, Δe,

and distortional strain increment, Δeq , and we

have

1 2 3

2 2 2q 1 2 2 3 1 3

e e e e

2e ( e e ) ( e e ) ( e e )3

Δ = Δ + Δ + Δ

Δ = Δ − Δ + Δ − Δ + Δ − Δ [2]

Where Δej, j = 1, 3 are principal strain

increments. The principal strain increments may

be divided into elastic and plastic parts so that

pei i ie e e i 1,3Δ = Δ + Δ = [3]

The specifi c volume, υ, is defi ned as:

[TABLE 1] Geotechnical properties of clay studied

Test no Plasticity

index, Ip (%)

Initial void

ratio, e0 (-)

Effective

stress, σ0’

(kPa)

Pre-con-

solidation

pressure, σP’

(kPa)

Compression

index, CC (-)

Swelling

coeffi cient

CS (-)

Total unit

weight, γ

(kN/m³)

Undrained

shear

strength, cu

(kPa)

COE-01 11.7 1.59 40.7 105 0.90 0.08 16.7 16.0-39.0

COE-02 7.0 1.57 41.0 112 0.88 0.06 16.7 43.0- 62.0


s

VV

υ = [4]

Where Vs is the volume of solid particles

(assumed incompressible), contained in a volume,

V, of soil. The incremental relation between

volumetric strain, e, and specifi c volume has the

form

e ΔυΔ =υ

[5]

Starting with an initial specifi c volume, υ0,

we may thus write, for small volumetric strain

increments,( )0 1 eυ = υ + [6]

Where e is the current accumulated volumetric

strain.The incremental expression of Hooke’s law

in principal axes may be expressed in the form

)( )(( )

e e e1 1 1 2 2 3

e e e2 1 2 2 2 3

e e e3 3 3 2 2 3

e e e

e e e

e e e

Δσ =α Δ + α Δ + Δ



[7]

Where: α1 = K + 4G/3; and α

2 = K − 2G/3.

In this study, eight material parameters were

required to specify the soil model, including

either the elastic bulk modulus “K” or elastic

shear modulus “G”, mass density “ρ”, Poisson’s

ratio “µ”, slope of the normal consolidation

line “λ”, slope of the elastic swelling line“κ”,

frictional constant “M”, pressure of reference “p1”

and the specifi c volume at pressure of reference,

p1, on the normal consolidation line “υλ”.

Fig. 3 presents the oedometer curve in the

semi-logarithmic plot (υ, ln p) where p, is the

effective vertical pressure and, υ, the specifi c

volume of specimen.

The material properties adopted in the analyses

for soft, medium and hard clay are presented

in Table 2. In this table, the coeffi cient of earth

pressure (K0) is defi ned as the ratio of effective

horizontal stresses (σh) to applied effective

vertical stresses (σv) at zero stress strain

(Donath, 1981):

h 0 vKσ = ⋅σ [8]

Alpan (1967) indicated that K0 is a function of

over consolidation ratio (OCR), defi ned as the

[Fig. 3] Oedometer curves of tested clays (Demers, 1980)


ratio of initial pre-consolidation pressure to the

in situ overburden effective stress, and in over

consolidated clays:

n

0(NC)K

0(OCR) 0(NC)K K OCR= ⋅

0.15 0.233log (Ip)= +

Ip / 281n 0.54 10−= ⋅

[9]

[10]

[11]

Pile properties

The pile is modeled as a structure element

made up of concrete material characterised by a

Poisson’s ratio of 0.2, a unit mass of 2500 kg/m3

(4200 lb/ yd3) and Young’s modulus equal to

25 GPa (3.6x106 psi).

The length D and the diameter b of pile are

variable in order to investigate their infl uences

on the lateral bearing capacity of the pile.

The ultimate lateral load of the pile, Qu, is

represented by the dimensionless factor defi ned

by “Qu/cu b2” for which the infl uence of several

parameters will be studied.

Limitations of 2D analysis

A pile foundation subjected to lateral loads is

a class of problem that incorporates pile-soil

interaction in 3D. In this paper, the soil-pile

interaction in the direction perpendicular to the

loading direction is not accounted for in the used

simple 2D fi nite difference formulation. This

simplifi cation leads to overestimation of the

lateral displacement of the pile compared to

the actual behavior encountered in the fi eld.

Prediction of lateral resistance of pile

The adopted modeling of a beam element

subjected to the lateral action/reaction of soil

is derived from the well-known equilibrium

equation of beams:

4

4d yEI p(x) 0dx

+ = [12]

Fig. 4 details how the horizontal resistance of

soil p(x) can be determined by adopting the

spring equation:

(x) k(x) y= ⋅ p [13]

k(x) : modulus of the horizontal reaction of soil

(kN/m²);

y : horizontal displacement of the pile at depth x

(m);

E : young’s modulus of the pile (kPa);

I : moment of inertia of the cross section at

x (m4);

x: current depth along the length of pile.

[Fig. 4] Model of soil reaction by elastic springs

Introducing the bending moment, M (kN.m) and

the shear force, V (kN) at depth x within a current

cross section of the pile, the equilibrium equation

provides relationships between the bending

moment and shear force, and, then as illustrated in

Soil rigidity ρ (kg/m3) G (MPa) K (MPa) µ (-) λ (-) κ (-) M (-) p1 (kPa) υλ (-) K

0 (-)

Soft clay

cu = 16.0 kPa

1670 4.80 12.48 0.33 0.262 0.065 0.77 1 5.3 0.63

medium clay

cu = 39.0 kPa

1670 11.70 30.42 0.33 0.262 0.065 0.77 1 5.3 0.63

Stiff clay

cu = 64.0 kPa

1670 19.20 49.92 0.33 0.257 0.064 0.77 1 5.25 0.58

[TABLE 2] Parameters according to CCM

DFI JOURNAL Vol. 7 No. 1 August 2013 [65] [Fig. 6] Behaviour of pile under lateral load

line for p=p1, is given by:

( ) ( )ln 2λΓ = υ − λ − κ × [15]

The numerical analysis has been conducted by

adopting zero free vertical distance from the

head of pile to the soil surface (ec=0), and

varied ratio D/b, D is the embedment of pile in

the clay layer. The comparison between

numerical predictions and Broms’ results are

presented in Fig. 7. For this case, it can be seen

that Broms’ assumption greatly overestimates

the ultimate lateral resistance of pile in purely

cohesive clays that was assumed equal to 9bcu,

but numerical predictions show that the soil

will collapse much earlier.

EFFECTS OF VERTICAL LOAD AND PILE DIAMETER ON ITS LATERAL RESISTANCE

The infl uence on pile diameter has been also

investigated. Fig. 8 shows that the variation of

pile diameter, especially when D/b is less than

14, does not signifi cantly affect the normalized

ultimate lateral bearing capacity of the pile.

The infl uence of vertical load on the ultimate

lateral bearing capacity is studied. At this stage,

fi rst, the ultimate vertical bearing capacity is

obtained, and then by introducing a factor of

safety equal to 3 the allowable vertical load is

deduced. The ultimate lateral bearing capacity

of the pile is fi nally determined. Results of

Fig. 9 show that the ultimate lateral resistance

will decrease when the vertical load component

increases. Therefore special care should be

accorded when it comes to the prediction of the

ultimate lateral resistance of a pile.

Fig. 6, the lateral resistance of soil is derived from

Eqn. (9). The complete solution is obtained once

the horizontal defl ection of pile is determined.

Therefore, we concluded that the lateral soil

reaction p (x) can be determined as follows

(see Fig. 5):

[Fig. 5] Shear and lateral load

For a pile of length D = 8.0 m (26 ft) and

diameter b = 0.8m (2.6 ft), Fig. 6 displays the

diagrams for profi les of pile behavior under a

lateral load equal at 250 kN (28.1 ton).

EFFECT OF SOIL STIFFNESS ON LATERAL RESISTANCE

The undrained shear strength has been varied in

order to study the effect of the stiffness of clayey

soils on the ultimate lateral resistance of the pile.

For capped plasticity model, like the Modifi ed

Cam Clay here investigated, the undrained shear

strength, cu, is uniquely related to the specifi c

volume, υ, by the equation [14]:

1u

Mpc exp

2Γ − υ=

λ [14]

Where the specifi c volume, Γ, at the critical state


[Fig. 7] Effect of soil stiffness on lateral load capacity compared with Broms method

[Fig. 8] Effect of diameter on lateral bearing of capacity pile

[Fig. 9] Effect of vertical load, ec/b = 0


[Fig. 10] The ultimate lateral capacity vs OCR

EFFECT OF OVER-CONSOLIDATION RATIO

The infl uence of OCR on the ultimate lateral

load capacity of a single pile is presented in

this section. The same soil proprieties presented

in Table 2 were adopted with changing the

OCR values from 1 to 10 (K0 values vary

between 0.4 to 1.23).

Fig. 10 shows the effect of OCR on the ultimate

lateral capacity of the pile. When the OCR

increases from 2 to 10, the increase in the

ultimate lateral load is about 20%. The

increase of the OCR values is accompanied

by an increase in the K0 values. This increase

in the K0 values is due to the increase of

the horizontal lateral stress of the soil, the

confi ning pressure, compared to the applied

vertical stresses. The increase of the confi ning

pressure is the major deriving factor causing

the increase in the ultimate resistance of a pile

to lateral loads. Thus, it is concluded that the

role of pre-consolidation pressure cannot be

neglected in the pile design.

CONCLUSIONS

The ultimate resistance of pile foundations

embedded in cohesive soil has been studied

in this paper through a series of 2D fi nite

differences analyses. FLAC2D was employed

to this end. The Modifi ed Cam Clay (MCC)

constitutive relation was adopted in the

analyses to model the cohesive soil behavior;

whereas the structural pile model with three

degrees of freedom is adopted to model the

piles. The reliability of the well-known Broms'

method is discussed in this paper. Different

factors thought to affect the lateral resistance

of piles in cohesive soil, not adequately

considered in Broms' method, such as clay

stiffness, pile length, pile diameter and axial

load were parametrically studied.

Of the fi ndings of this study, the following

conclusions can be drawn:

- The ultimate lateral capacities of pile

foundations obtained from the current

fi nite differences analyses were found to

be smaller than that obtained by Broms'

graphs.

- The pile diameter, not considered in

Broms's method, seems to have a signifi cant

effect on the ultimate lateral capacities

- For low values of soil stiffness, Broms'

method overestimates the ultimate lateral

resistances of piles. As the soil stiffness is

increased, the ultimate lateral resistances

obtained from the current analyses

approach that obtained using Broms'

graphs.

- The axial load increases ultimate bearing

capacity and special care to choose the

ultimate bearing capacity of pile should be

taken.

- The CCM is a suitable model to describe

sensitive clays, and it is necessary to


take care of the value of OCR or pre-

consolidation pressure in the design of piles

embedded in cohesive soils.

REFERENCES

1. Alpan, I. "The Empirical Evaluation of

the Coeffi cient K0 and K

or", Soils and

Foundations, Vol.7, No.1, 1967, pp. 31-40.

2. Brinch Hansen, J. "The Ultimate Resistance

of Rigid Piles against Transversal Forces",

Geoteknish Institute Bulletin No.12, Danish

Geotechnical Institute, Copenhagen,

Denmark, 1961, pp. 5-9.

3. Britto, A. M., and Gunn, M.J. Critical

State Soil Mechanics via Finite Elements.

Chichester U.K.: Ellis Horwood Ltd, 1987.

4. Broms, B.B. "Lateral Resistance of Piles in

Cohesive Soils", Journal of Soil Mechanics Foundation Division, Vol. 90(2), 1964, pp.

27-64.

5. Brown, D.A., and Shie, C.F. "Evaluation

of the Relative Infl uence of Major

Parameters for Laterally Loaded Piles in

three Dimensional Finite Element Models",

Civil Engineering Department, Harbert

Engineering Center. Auburn University,

Alabama, 1991.

6. Demers, B. "Résistance Cyclique d’une

Argile Extra-Sensible", Thesis M.Sc., University of Sherbrook, Quebec, Canada,

1980.

7. Donath, A.D. Untersuchungen Veber den

Erddruck auf Stuetz waende. Zeitschrift

Fuer Bauwesen, 1981.

8. Federal Highway Administration.

Design and Construction of Driven Pile

Foundations. Workshop Manual – Vol. I,

Publication no13, Washington, D.C. 1997.

9. Fleming, W.G.K., Weltman, A.J., Randolph,

M.F. and Elson, W.K. Piling Engineering.

Surrey University Press, London, 1992.

10. Itasca Consulting Group. FLAC: Fast

Lagrangian Analysis of Continua User’s and

Theory Manuals, Version 6.0, Minneapolis,

USA, 2008.

11. Jamiolkowski, M. and Garassino, A. "Soil

Modulus for Laterally Loaded Piles",

Proceedings, 9th International Conference, Soil Mechanics Foundation Engineering. Tokyo, 1977, pp. 87-92.

12. Kasch, V.R. "Lateral Load test of Drilled

Shaft in Clay", Research report 211-1. Texas Transportation Institute, Texas A&M

University, 1977.

13. Liang, R. "Development and

Implementation of New Driven Piles

Technology", The Ohio Department of

Transportation and the US Department

of Transportation, Federal Highway

Administration, 1998.

14. Murff, J.D. and Hamilton, J.M. "P-Ultimate

for Undrained Analysis of Laterally

Loaded Piles", Journal of Geotechnical Engineering, Vol. 119(1), 1993, pp. 91-107.

15. Poulos, H.G. and Davis, E.H. Pile

Foundation Analysis and Design. Wiley,

New York, 1980.

16. Reese, L.C. "Laterally Loaded Piles:

Program Documentation", Journal of Geotechnical Engineering Division, ASCE.

Vol. 103(GT4), 1977, pp. 287-305.

17. Reese, L.C. and Van Impe, W.F. Single Piles

and Pile Groups Under Lateral Loading. A.

A. Balkema, Rotterdam, 2001.

18. Roscoe, K.H. and Burland, J.B. On the

Generalized Stress-Strain Behavior of ‘Wet

Clay’. Engineering Plasticity, Cambridge

University Press, New York, 1968, pp. 535-

609.

19. Terzaghi, K. "Evaluation of Coeffi cients of

Subgrade Reaction", Géotechnique. Vol.

5(4), 1955, pp. 297-236",


TECHNICAL NOTEDirect Solution of the Brinch-Hansen 90% Pile Ultimate Failure LoadDon W. Dotson, PhD., PE, DGE, Chief Designer, Geo-Structural Design Group, AMEC Environment and Infrastructure, Adj. Prof., Dept. of Civil Engineering, Tennessee State University, Nashville, TN, USA’ Ph: (615) 333-0630; [email protected]

ABSTRACTIn 1962, Kondner prepared several papers dealing with hyperbolic stress-strain response of cohesive soils. The following year, Brinch Hansen proposed 80% and 90% failure criteria for stress-strain behavior of cohesive soils. Fellenius was instrumental in popularizing these failure criteria for pile load tests and offered a direct solution equation for the failure load according to the 80% failure criterion. Since the 90% Criterion has been incorporated into the International Building Code, equations for the direct solution of the failure load at the 90% Criterion would be useful to practicing engineers. This Technical Note supplies the derivation methodology for the 80% Criterion and provides expressions to determine the load and deflection at failure for the 90% Criterion.

INTRODUCTIONRobert Kondner (1962a, 1962b) proposed that the stress-strain behavior of cohesive soils in triaxial testing could be reasonably approximated by a two-constant rectangular hyperbola (Eqn. 1) which could be algebraically transformed into a linear relationship with determinable slope and intercept (Eqn. 2):

[1]

[2]

where: σ = stress ϵ = strain

a,b = constants

In a discussion of Kondner (1963), Hansen (1963) reported equations similar to Kondner’s, especially Eqn. 3.

[3]

(Note: Hansen’s original formulation contained an erroneous minus sign which was later corrected in Kondner, 1964.) The linear transformation of Eqn. 3 is shown in Eqn. 4.

[4]

Hansen (1963) observed that when this latter form gave a good approximation to the test data, it could be used to provide a general, simple failure criterion in which failure is

represented by the stress for which the strain is equal to four times the strain at a 20% smaller stress. This became known as the Brinch Hansen 80% Failure Criterion.

Hansen (1963) compared this 80% Failure Criterion to a definition he previously proposed (source not cited) in which he defined the stress at failure as equal to two times the strain at a 10% smaller stress (i.e., the 90% Failure Criterion). Hansen (1965) further noted that these hyperbolic curves “seem to apply, not only to direct shear tests, but to almost any test, in which shear stresses play a dominant role, for example triaxial tests, plate loading tests, pile loading tests.”

Fellenius (1975) compared various failure criteria for pile load testing. Fellenius (1980) gave more detailed examples of a number of these criteria, including the 80% Criterion along with algebraic expressions used to calculate the load and deflection at failure.

Fig. 1 is a digitization of a load-movement curve for a driven concrete pile load test using the Constant Rate of Penetration method (Fellenius, 1980). Fig. 2 is a plot of 15 of the data points prior to pile plunging using the transformed ordinate axis along with a “best fit” line. (Note: any consistent set of units could be used. Fellenius multiplied the ordinate by 103 for presentation. That same format has been preserved here.)


[FIG. 1] - Pile Test Results (after Fellenius 1980)

[FIG. 2] - Brinch Hansen Transformation (after Fellenius 1980)

The equation of the line that can be fitted to the data in Fig. 2 is:

[5]

where C1 is the slope and C

2 is the y-intercept of

the fitted line. The load P can be determined at any point as:

[6]

Fellenius (1980) gives the following equation for the 80% failure load:

[7]

and the corresponding deflection:

[8]

The derivation of these expressions for the 80% Criterion were not provided, nor were similar expressions provided for the 90% Criterion. Since the 90% Criterion has been incorporated into the International Building Code (2000), and not the 80% Criterion, equations for the direct solution of the failure load at the 90% Criterion would be useful to the practicing engineer. This Technical Note supplies the derivation methodology for the 80% Criterion and provides expressions to determine the load and deflection at failure for the 90% Criterion. In practice, the results obtained from either direct solution method should be validated by comparison to the load-movement curve.

DERIVATIONFor both the 80% and 90% Failure Criteria, a plot of the pile test data is prepared in which pile head deflection (∆) is plotted along the abscissa and the square root of the deflection divided by the test load (P) is plotted along the ordinate (Fig. 2). A “best fit” linear approximation is fitted to the data and the slope and intercept are determined. The portion of the curve with the highest loads is of principal interest, thus points at lower loads may be omitted since they tend to skew the “best fit” line. Failure for the 80% Criterion corresponds to the values of P

u

and ∆ that satisfy Eqn. 6 and Eqn. 9 as a system of linear equations (equating P with P

u).

[9]

Eqn. 7 is the solution to this system of equations.

Similarly, failure for the 90% Criterion corresponds to the values of P

u and ∆ that

satisfy Eqn. 6 and Eqn. 10.

[10]

After solving and rearranging (see Appendix), an approximate solution can be written as:

[11]

with deflection [12]

As Hansen (1963) noted, the 80% and 90% failure criteria give approximately the same failure load, although the IBC code specifies the 90% Criterion.

(inches)


Using Eqn. 11 and the best-fit coefficients from Fellenius, the calculated 90% Criterion failure load is 209 tons (190 tonnes), which compares favorably with the 205 tons (186 tonnes) reported (Fellenius, 1980).

ACKNOWLEDGEMENTSI would like to thank my colleague Siphay Douangvilay for his review and comments along with the anonymous reviewers.

REFERENCES1. Fellenius, B. H. (1975). “Test loading of piles

and new proof testing procedure”, Journal of Geotechnical Engineering Division pp. 101(9), 855-869.

2. Fellenius, B. H. (1980). “The analysis of results from routine pile load tests”, Ground Engineering. 13(6), pp. 19-31.

3. Hansen, J. Brinch. (1963). “Discussion: Hyperbolic stress-strain response: cohesive soils”, Journal of Soil Mechanics, Foundations Division, 89(4), pp. 241-242.

4. Hansen, J. Brinch. (1965). “Some stress-strain relationships for soils”, The Danish Geotechnical Institute, Bulletin, No. 19, pp. 231-234.

5. International Building Code. (2000). International Code Council, Inc. Falls Church, VA 22041-3401.

6. Kondner, R. L. (1962a). “Hyperbolic Stress-Strain Relation in Direct Shear”, Technical Report, Civil Engineering Department, Northwestern University.

7. Kondner, R. L. (1962b). “Friction pile groups in cohesive soil”, Journal of Soil Mechanics, Foundations Division, 88(3), pp. 117-149.

8. Kondner, R. L. (1963). “Hyperbolic stress-strain response: cohesive soils”, Journal of Soil Mechanics, Foundations Division, 89(1), pp. 115-143.

9. Kondner, R. L. (1964). “Hyperbolic stress-strain response: cohesive soils – Closure”, Journal of Soil Mechanics, Foundations Division, 90(1), pp. 121-126.

APPENDIXSolve the following system of equations:

[A1]

[A2]

Solve Eqn. A1 for Pu

[A3]

Solve Eqn. A2 for Pu

[A4]

Set Eqn. A3 and A4 equal to each other:

[A5]

Find a common denominator

[A6]

Multiply the numerator on the left-hand side of the equal sign of Eqn. A6

[A7]

Multiply the numerator on the right-hand side of the equal sign of Eqn. A6

[A8]

Substitute the results of Eqn. A7 and Eqn. A8 into Eqn. A6 and rewrite

[A9]

Subtract the right-hand side of the equal sign from the left-hand side of Eqn. A9

[A10]

Factor √Δ out of the numerator

[A11]

Remove √Δ by dividing both sides of the equation by √Δ:

[A12]

Multiply both sides of Eqn. A12 by 9:

[A13]


To avoid trivial or undefined solutions, the constraints on Eqn. A13 are that∆ ≠ 0, (C

2 + C

1∆) ≠ 0, and (2C

2 + C

1∆) ≠ 0.

Therefore, the numerator of Eqn. A13 must be = 0 for a valid solution. Set the numerator = 0 and solve for ∆:

[A14]

Rearrange terms

[A15]

Factor Eqn. A15 [A16]

Solve for ∆

[A17]

After evaluation, the approximate solution to Eqn. A17 is:

[A18]

Substituting Eqn. A18 into Eqn. A3 gives

[A19]

Simplifying

[A20]

If desired, a more precise solution can be obtained by substituting Eqn. A17 into Eqn. A3. In the Fellenius (1980) example, the difference between approximate solution Eqn. A20 and a more precise solution determined by incorporating Eqn. A17 into Eqn. A3, is 0.004 tons (0.0036 tonnes).


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