Term Paper on CPT

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Advanced Foundation Design

CIVE 683

Antoine Letendre

110237568

Cone Penetration Testing and the Design of

Shallow and Deep Pile Foundations

Profs. M. Meguid and M. Sakr

McGill Faculty of Engineering

March 18th 2015

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Table of Contents 1. Abstract ................................................................................................................................................. 5

2. Introduction ........................................................................................................................................... 5

2.1. Purpose and scope ......................................................................................................................... 5

2.2. Historic and Present Use of CPT .................................................................................................. 5

3. CPT – Description and Use ................................................................................................................... 6

3.1. General Description of CPT and CPTu ......................................................................................... 6

3.2. CPT in site investigation ............................................................................................................... 8

3.3. Additional sensors ......................................................................................................................... 9

3.4. Testing standards ........................................................................................................................ 10

4. Data Correction ................................................................................................................................... 11

4.1. Porewater pressure correction ..................................................................................................... 11

4.2. Temperature Correction .............................................................................................................. 12

4.3. Other data corrections ................................................................................................................. 12

5. Data Interpretation .............................................................................................................................. 13

5.1. Soil Profiling/Soil Type Interpretation ....................................................................................... 13

5.1.1. Un-normalized SBT ............................................................................................................ 13

5.1.2. Normalized SBT ................................................................................................................. 14

5.1.3. Probabilistic Methods ......................................................................................................... 16

5.1.4. Other methods ..................................................................................................................... 17

5.2. Estimation of soil parameters ...................................................................................................... 17

5.2.1. Soil Unit Weight ................................................................................................................. 17

5.2.2. Undrained Shear Strength ................................................................................................... 18

5.2.3. Friction Angle ..................................................................................................................... 19

5.2.4. Shear waver velocity (Vs) ................................................................................................... 19

5.2.5. Constrained Modulus (M) ................................................................................................... 20

5.2.6. Small strain Shear Modulus (G) .......................................................................................... 20

5.2.7. Young’s Modulus ................................................................................................................ 20

5.2.8. Relative Density of Sands ................................................................................................... 21

5.2.9. OCR .................................................................................................................................... 21

6. Shallow Foundation Design ................................................................................................................ 21

6.1. Indirect methods for calculating bearing capacity ...................................................................... 22

6.2. Indirect methods for calculating settlement ................................................................................ 23

6.2.1. Elastic Displacement Methods ............................................................................................ 23

6.2.2. One-dimensional Oedometric method ................................................................................ 24

6.2.3. Schmertmann et al. (1978) .................................................................................................. 24

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6.3. Direct Ultimate Bearing Capacity Methods ................................................................................ 25

6.3.1. Meyerhof (1956) direct method .......................................................................................... 26

6.3.2. Tand et al. (1995) direct method ......................................................................................... 26

6.3.3. Tand et al. (1986) direct method ......................................................................................... 26

6.3.4. Schmertmann (1978) direct method .................................................................................... 27

6.3.5. Bowles (1996) ..................................................................................................................... 27

6.3.6. Eslaamizaad & Robertson (1996) ....................................................................................... 28

6.4. Direct settlement calculation methods ........................................................................................ 28

6.4.1. Meyerhof (1974) ................................................................................................................. 28

6.4.2. Burland et al. (1977) ........................................................................................................... 29

6.4.3. Mayne and Illingsworth (2010) ........................................................................................... 29

7. Deep Foundation Design ..................................................................................................................... 29

7.1. Indirect Bearing Capacity Methods ............................................................................................ 30

7.1.1. Total stress method (alpha method) .................................................................................... 31

7.1.2. Effective stress methods (beta methods) ............................................................................. 32

7.2. Direct Bearing Capacity Methods ............................................................................................... 33

7.2.1. LCPC method (1982) .......................................................................................................... 33

7.2.2. Norwegian Geotechnical Institute Building Research Establishment ................................. 35

7.2.3. Unicone method .................................................................................................................. 35

7.3. Settlement Estimation ................................................................................................................. 35

7.3.1. Elastic Continuum Solutions ............................................................................................... 36

7.3.2. Vesic (1977) ........................................................................................................................ 37

7.3.3. Das’ (1995) ......................................................................................................................... 38

7.3.4. Fleming et al. (2008) ........................................................................................................... 38

7.3.5. Artificial Neural Network Methods .................................................................................... 38

7.3.6. Approximate non-linear approximations using sCPTu ....................................................... 39

8. Design Example .................................................................................................................................. 40

8.1. Soil Classification ....................................................................................................................... 40

8.2. Soil Properties ............................................................................................................................. 40

8.3. Bearing capacity for shallow foundations ................................................................................... 40

8.4. Bearing capacity of a single pile ................................................................................................. 41

8.5. Settlement ................................................................................................................................... 41

8.6. Summary ..................................................................................................................................... 41

9. Conclusion .......................................................................................................................................... 41

10. Bibliography ................................................................................................................................... 42

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List of Figures Figure 1: Terminology of Cone Penetrometers (Lunne, Robertson, & Powell, 1997) ...................................................................... 7 Figure 2: Typical internal workings of a piezocone penetrometer (Lunne, Robertson, & Powell, 1997) ......................................... 7 Figure 3: Range of CPT sizes (from left to right: 2 cm2, 10 cm2, 15 cm2, 40 cm2,) (Robertson & Cabal, 2010) .............................. 8 Figure 4: Schematic diagrams of the use of an sCPT probe (left: (Robertson & Cabal, 2010); right: (Mayne P. W., 2007)) ......... 10 Figure 5: Applicability of in-situ testing for the determination of soil parameters (Lunne, Robertson, & Powell, 1997)............... 10 Figure 6: Schematic diagram of a piston sampler (Robertson & Cabal, 2010) ............................................................................... 11 Figure 7: Diagram showing corrections to tip resistance and sleeve friction due to porewater pressure (Jamiolkowski, Ladd,

Germaine, & Lancellotta, 1985) ..................................................................................................................................................... 11 Figure 8: BPT classification chart based on Robertson et al., 1986, updated by Robertson, 2010 (Robertson & Cabal, 2010). ..... 14 Figure 9: BPT classification chart based on Douglas and Olsen, 1981 (Lunne, Robertson, & Powell, 1997). ............................... 14 Figure 10: Normalized BPT and 𝑩𝒒 classification charts based on Robertson et al., 1986 (Lunne, Robertson, & Powell, 1997). 15 Figure 11: Normalized BPT classification chart based on Robertson et al., 1986, updated by Robertson, 2010 (Robertson &

Cabal, 2010). ................................................................................................................................................................................... 16 Figure 12: SBT classification table based on Jefferies and Davies ∗ 𝑰𝒄 (Mayne P. W., 2007) ....................................................... 16 Figure 13: Approximate unit weight of soils based on SBT as defined in Figure 10 (Lunne, Robertson, & Powell, 1997) ........... 18 Figure 14: Dimensionless unit weight based on CPT (Robertson & Cabal, 2010) ......................................................................... 18 Figure 15: Robertson and Campanella (1983) empirical graph for determining friction angle (Kulhawy & Mayne, 1990) ........... 19 Figure 16: Summary of simple bearing capacity methods from Terzaghi, Meyerhof, Hansen and Vesic (Bowles, 1996) ............. 22 Figure 17: Summary of shape and depth factors for Meyerhof (Left), Hansen and Vesic (center and right) (Bowles, 1996) ........ 23 Figure 19: Influence factor for Schmertmann (1978) method (CFEM, 2006) ................................................................................ 24 Figure 20: Modulus Correction for Schmertmann (1978) (Mohamed, 2014) ................................................................................. 25 Figure 21: 𝑹𝒌 for Tand et al. (1986) foundations on clay from (Mayne P. W., 2007).................................................................... 27 Figure 22: 𝑲 from Eslaamizaad & Robertson (1996) foundations on sand (Lunne, Robertson, & Powell, 1997) .......................... 28 Figure 23: Burland et al., 1977 Graph for approximate settlement of footings on sand (CFEM, 2006) ......................................... 29 Figure 24: Modifications made to the beta method over the years (Niazi & Mayne (2013)) .......................................................... 30 Figure 25: Modifications made to the alpha method over the years (Niazi & Mayne (2013)) ........................................................ 31 Figure 26: Adhesions as a function of undrained shear strength (CFEM, 2006)............................................................................. 32 Figure 27: Range of 𝜷 coefficients (left) and 𝑵𝒕 coefficients (right) (CFEM, 2006) ..................................................................... 33 Figure 28: Range of 𝒌𝒄 coefficients for the LCPC method (CFEM, 2006) .................................................................................... 34 Figure 29: Range of 𝜶 coefficients for the LCPC method (CFEM, 2006) ...................................................................................... 34 Figure 30: Soil classification and 𝑪𝒔𝑬 value for Unicone method (Mayne P. W., 2007) ............................................................... 35 Figure 31: 𝑰𝟎 influence factor from Poulos and Davis (1980) (CFEM, 2006) ................................................................................ 36 Figure 32: 𝑹𝒌 𝒂𝒏𝒅 𝑹𝒗 values from Poulos and Davis (1980) for pile settlement (CFEM, 2006) ................................................. 37 Figure 33: 𝑪𝒕 values from Vesic (1977) for pile settlement (CFEM, 2006) ................................................................................... 37 Figure 34: Basic structure of a neural network (Baziar, Azizkandi, & Kashkooli, 2015) ............................................................... 39 Figure 35: Concept using sCPTu for evaluating approximate non-linear settlement (Mayne P. W., 2007) .................................... 39

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1. Abstract

CPT/CPTu is an extremely practical site investigation method that has been employed with good results

for designing shallow and deep foundations. Many empirical relationships have been developed over the

years to allow for direct and indirect estimation of soil parameters as well as bearing capacities from the

CPT results. Additionally, many supplementary sensors can be joined to the CPT probe so as to improve

results and allow for direct measurements of geotechnical parameters. While these sensors and empirical

relationships are frequently used, many researchers are constantly working to improve these methods and

incorporate computer systems into their development. Presently, this method is underutilized in North

America typically as a result of a lack of knowledge and expertise in its application by North American

engineers.

2. Introduction

2.1. Purpose and scope

Cone penetration testing (or CPT) is one of the more versatile in situ tests for use in geotechnical studies,

in part, due to the possibility of adding additional sensors to a cone penetrometer such as pressure sensors,

lateral stress measurements (strain gauges), cone pressure meters (incorporated pressuremeter),

geophones (seismic CPT), electric resistivity sensors, heat flow sensors, radioisotope sensors and acoustic

noise sensors. These additional sensors can allow for the accumulation of a wealth of information

pertaining to the mechanical and physical properties of the soil matrix in a mostly continuous manner.

This report aims to present all the required information so as to enable the reader to perform basic

foundation design (both deep and shallow), as well as identify references that can be used. In order to do

so, it will outline the various sensors that can be added to an electric CPT and their uses in shallow and

deep foundation designs. It will also outline the process of data analysis which must be undertaken in

order to obtain such information from the results, as well as summarize commonly used CPT calculation

methods employed for the determination of bearing capacities and designs of shallow and deep

foundations. This will focus primarily on the methods recommended by the CFEM, Eurocode 7 and the

Transportation Research Board. It should be noted that this report is formulated as design guide as

opposed to a journal paper due to the extremely large quantity of information required in order to design

foundations based on CPT results, and does not delve into the accuracy of these methods. Finally, while

many case studies and design examples are available, due to the volume of material to be covered by this

report, these will not be covered in depth but will instead be glossed over in section 2.2 and referenced in

the bibliography.

2.2. Historic and Present Use of CPT

CPT testing was developed in the 1950s in order to provide a quicker and more reliable soil testing

method than conventional drilling methods (Lunne, Robertson, & Powell, 1997). The original design

involved the use of a mechanical probe with pneumatic sensors. At that time, simple empirical methods

were developed to determine bearing capacities, soil classifications and soil parameters. Over the years,

these probes have been vastly updated through the addition of additional sensors and state of the art

electronics (Lunne, Robertson, & Powell, 1997) (Mayne P. W., 2007).

Many empirical and analytical relationships between CPT results, soil parameters and bearing capacities

have been developed over the years and research into these topics are continuously being developed

(Baziar, Azizkandi, & Kashkooli, 2015) (Mayne & Illingworth, 2010) (Niazi & Mayne, 2013) (Schnaid,

2010) (Ardalan, Eslami, & Nariman-Zadeh, 2008) (Gholami & Eslami, 2006) (Lee & Salagado, 2005).

Additionally, the existing methods are constantly being re-evaluated, often in the form of case studies, so

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as to assess the quality of the results obtained from these tests (Cai, Liu, & Puppala, 2012) (Cai, Liu,

Tong, & Du, 2009) (Cherubini & Vessia, 2007) (Eslami, Aflaki, & Hosseini, 2011) (Ibrahim, Malik, &

Omar, 2013) (Monzon A., 2006) (Niazi & Mayne, 2013) (Niazi, Mayne, & Woeller, 2010) (Thomassen,

Andersen, & Ibsen, 2012) (Togliani, 2010) (Togliani & Reuter, 2010) (White & Bolton, 2005) (Cunha &

Stewart, 2010) (Ryul, Gyo, Dung, & Fellenius, 2012) (Eslami & Gholami, 2006) (Togliani, 2010). To

date, the results have been reasonably accurate, with older methods generally shown to be more

conservative and the newer ones more accurate (Niazi & Mayne, 2013).

While research on CPT and case studies on the results of its use continues to be investigated, a recent

survey of North American Transportation Bureaus has shown that the North American geotechnical

engineering community does not feel competent or comfortable using this site investigation method in

their design (Robertson P. , 2006) (Robertson & Cabal, 2010) (Mayne P. W., 2007). The author would

surmise that one factor that may contribute to this is the lack of the incorporation of these new methods

into standards such as CFEM (2006), Eurocode-7 (2004), and Mayne (2007), which show a reliance on

older methods. As a result only CPT experts are familiar with the more recent and accurate methods for

these calculations.

One solution to the lack of expertise with the newer more complex and accurate CPT analyses methods is

the development of software packages to perform these comprehensive analyses (Mayne P. W., 2007).

While these are in development (Mayne P. W., 2007) (Baziar, Azizkandi, & Kashkooli, 2015) (Ardalan,

Eslami, & Nariman-Zadeh, 2008), they are still not at the point where they can supplement a lack of

experience and expertise on CPT methods (Mayne P. W., 2007).

3. CPT – Description and Use

3.1. General Description of CPT and CPTu

In cone penetration testing (CPT), a cone penetrometer (probe) consisting of a cone is connected to a thin

sleeve around an instrumented rod section. The sleeve is connected to a load cell in order to allow the

recording of the frictional force exerted on the outside of the sleeve by the soil, and the cone is connected

to a force sensor to allow the measurements of the axial force (CFEM, 2006) (Eurocode-7, 2004) (Mayne

P. W., 2007). The penetrometer contains various sensors and is connected to the end of a series of rods

and pushed through the soil at a constant rate. During the process sensors in the probe record the

penetration resistance and sleeve friction resistance at either continuous or intermittent rates. A piezocone

penetrometer (or CPTu) is a cone penetrometer that also records the pore water pressure. Figure 1 (Lunne,

Robertson, & Powell, 1997) shows the terminology used for cone penetrometers.

An axial load sensor inside the penetrometer records the total force acting on the cone (Qs). This force is

divided by the projected area of the cone (Ac) to provide the penetration end resistance (qc).

Simultaneously a second force sensor records the force experienced by the friction sleeve (Fs) which is

divided by the total area of the friction sleeve (As) to obtain what is commonly referred to as the sleeve

friction (fs). In the case of a piezocone penetrometer, the porewater pressure is recorded in the cone (u1

on Figure 1), behind the cone (u2) or behind the sleeve (u3). Figure 2 shows a typical design of the internal

workings of a CPT probe (CFEM, 2006) (Eurocode-7, 2004) (Mayne P. W., 2007).

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Figure 1: Terminology of Cone Penetrometers (Lunne, Robertson, & Powell, 1997)

Figure 2: Typical internal workings of a piezocone penetrometer (Lunne, Robertson, & Powell, 1997)

In many references, three categories of CPT probes exist depending on the type of sensors incorporated:

mechanical, electric and piezocone penetrometers. More recently many additional specific types are

considered depending on the type of sensors incorporated. These include seismic CPT, pressuremeter

CPT, soil resistivity CPT and various others.

It should be noted that the ASTM discontinued their standards pertaining to mechanical CPTs in 2014,

and as such this report will not cover mechanical CPTs. Should further information be required on

mechanical CPTs, Mayne (2007) and Robertson and Cabal (2010) can be consulted.

The most common cone penetrometer dimensions are a cone of 10 cm2 and 15 cm

2 area with an apex

angle of 60o and are specified in most codes (Robertson & Cabal, 2010) (ISSMFE) (ISSMGE) (ASTM,

D-5778). The 10 cm2 CPT is typically considered the international standard (Lunne, Robertson, & Powell,

1997). Other sizes available vary from a miniature CPT with an area of 2 cm2 to oversized CPTs with

surface areas of 40 cm2 penetrometers (Mayne & Illingworth, 2010) (Robertson & Cabal, 2010) (Baziar,

Azizkandi, & Kashkooli, 2015). The smaller CPT probes have recently been used for soil testing at

shallow depths. Referred to as miniature cone penetrometers (Mini-CPT), these relatively new probes

provide the advantages of decreasing the applied load, and the ability to mount them into smaller trucks

(Mayne P. W., 2007) (Robertson & Cabal, 2010). Mini-CPT has been shown to have comparable results

to those obtained from standard CPT and more accurate results than standard CPTs for relative soil

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densities (Nikudel, Mousavi, Khamehchiyan, & Jamshidi, 2012). A range of CPT sizes can be seen in

Figure 3.

Figure 3: Range of CPT sizes (from left to right: 2 cm2, 10 cm2, 15 cm2, 40 cm2,) (Robertson & Cabal, 2010)

3.2. CPT in site investigation

The objective of initial site investigations is to obtain information about the site (CFEM, 2006)

(Eurocode-7, 2004) (Mayne P. W., 2007). This includes:

The soil nature and stratigraphy of the site

The groundwater elevation and variations

Physical and mechanical properties of the subsurface

Distribution and composition of contaminants in the case of geo-environmental studies.

While site investigations may include test-pits, conventional borehole drilling, pressuremeter, dilatometer

testing, soil sampling and lab testing, CPT provides many advantages and several disadvantages.

CPT testing is faster than conventional borehole testing and provides more information of the mechanical

soil properties without additional tests. The primary advantages of CPT/CPTu testing over conventional

borehole testing are the following (CFEM, 2006) (Eurocode-7, 2004) (Mayne P. W., 2007) (Lunne,

Robertson, & Powell, 1997):

1. Fast and continuous profiling

2. Improved repeatability of testing data (data is not operator dependent)

3. Cost savings due to high productivity

4. Strong theoretical basis for data interpretation

Despite the positives of CPT testing, it also has several disadvantages over conventional borehole testing

(CFEM, 2006) (Eurocode-7, 2004) (Mayne P. W., 2007) (Lunne, Robertson, & Powell, 1997):

1. High capital investment

2. Cone penetrometers can be damaged by dense layers, or fail to penetrate them

3. No information of bedrock depth and properties can be obtained

4. No soil samples can be obtained from CPT testing

5. Requires skilled operators to obtain quality results

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Due to the high capital investment in performing CPT testing, CPT tends to be more applicable for large

projects as supplementary information to a borehole campaign or in an area where the soil stratigraphy is

well known to begin with. This is primarily due to the need in most studies to obtain confirmation of

bedrock depth, and pass through dense soils (Mayne P. W., 2007).

While no soil samples are obtained during CPT testing, CPT pushing equipment can be used to obtain

samples using a CPT based sampler as shown in Figure 6. The Robertson and Cabal CPT guide

(Robertson & Cabal, 2010) therefore recommends that many CPT tests be performed to define the

stratigraphy and material properties prior to sampling soils and specific depths and locations. Figure 5

shows the applicability of various in situ testing in site properties.

3.3. Additional sensors

One advantage of the electric CPT is that the additional sensors can be incorporated into the hollow tube

in order to obtain additional information. Presently the following additional sensors are available for use

in CPT testing (Mayne P. W., 2007) (Lunne, Robertson, & Powell, 1997) (Robertson & Cabal, 2010):

Piezometric sensors (CPTu)

Inclinometer

Geophones (seismic wave velocity) (sCPT)

Pressuremeter

Temperature

Lateral stress sensors

Acoustic noise sensors

Camera (visible light sensors)

Radioisotope detector (gamma ray and neutron detector)

Electrical resistivity and conductivity

Dielectric

pH

Oxygen exchange (redox)

Laser/ultraviolet induced fluorescence (LIF/UVOST)

Membrane interface probe (MIP)

Of these the first five are often used for geotechnical purposes, whereas the others are primarily used for

geo-environmental studies (Robertson & Cabal, 2010). Of these two of the most common ones are the

piezometric sensors (CPTu) and the geophones (SCPTu) which allow for the reading of seismic waves

(Lunne, Robertson, & Powell, 1997) (Mayne P. W., 2007). Knowing the location of the seismic source

and the geophone, the seismic wave velocities can be calculated. Figure 4 shows a schematic diagram of

the use of an SCPTu probe.

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Figure 4: Schematic diagrams of the use of an sCPT probe (left: (Robertson & Cabal, 2010); right: (Mayne P. W., 2007))

3.4. Testing standards

The primary standards applicable to CPT testing are the following:

1) ASTM D6067 - Standard Practice for Using the Electronic Piezocone Penetrometer Tests for

Environmental Site Characterization.

2) ASTM D-5778 "Standard Test Method for Performing Electronic Friction Cone and Piezocone

Penetration Testing of Soils".

3) ASTM, 2004, "Standard Method of Deep Quasi-Static Cone and Friction-Cone Penetration Tests

of Soil"

4) International Reference Test Procedure for CPT and CPTU - International Society of Soil

Mechanics and Geotechnical Engineering (ISSMGE).

5) ISSMFE International Reference Test Procedure for Cone Penetration Test (CPT) 39

6) Swedish Geotechnical Society (SGF): Recommended Standard for Cone Penetration Tests (1993)

39

7) Norwegian Geotechnical Society (NGF): Guidelines for Cone Penetration Tests (1994) 43 8) Dutch Standard: Determination of the Cone Resistance and Sleeve Friction of Soil. NEN5140

(1996) 43

Figure 5: Applicability of in-situ testing for the determination of soil parameters (Lunne, Robertson, & Powell, 1997)

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Figure 6: Schematic diagram of a piston sampler (Robertson & Cabal, 2010)

4. Data Correction

Electric CPT testing relies on electronic sensors to provide information on soil properties. As such the

data obtained is subject to the same issues as all electronic sensor readings. In order to ensure that

analysis of the data is accurate, the data must be representative. This means performing several

corrections to the data prior to its interpretation. This section discusses several reasons for which data

must be corrected, and expands on the primary employed data corrections for CPT data.

4.1. Porewater pressure correction

Porewater pressure acts on the edges of the friction sleeve and on the end of the cone as shown in Figure

7 resulting in a systematic error on recorded tip resistance and sleeve friction. As such the tip resistance

and sleeve friction must be corrected.

Figure 7: Diagram showing corrections to tip resistance and sleeve friction due to porewater pressure (Jamiolkowski,

Ladd, Germaine, & Lancellotta, 1985)

The sleeve friction measurements can be corrected by simply summing up the difference in forces

induced by the pressure differences. Summing these forces yields the following:

𝑓𝑡 = 𝑓𝑠 −(𝜋𝑑2𝑡2𝑢2 + 𝜋𝑑3𝑡3𝑢3)

𝜋𝑑𝑐ℎ𝑠

(1)

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While equation 1 may provide the complete solution for the for the corrected sleeve friction, Lunne,

Robertson and Powell (1997) showed that since 𝑢2 ≈ 𝑢3, and the rest of the terms in the equation are

physical properties of the probe, the equation can be approximated by equation 2:

𝑓𝑡 ≈ 𝑓𝑠 − 𝑏𝑛𝑢2 (2)

Where 𝑏𝑛 is a constant determined from triaxial testing. It should be noted that triaxial testing shows that

this method is reasonably accurate (Mayne P. W., 2007).

Similarly, the tip resistance correction can be corrected using equation 3 (Lunne, Robertson, & Powell,

1997):

𝑞𝑡 = 𝑞𝑐 −(𝜋𝑑2𝑡2𝑢2 −

𝜋𝑑𝑐2𝑢14 )

𝜋𝑑𝑐2

4

(3)

Since 𝑢2 ≈ 𝑢3, equation 3 can be simplified to give equation 4 in which the area ratio can similarly be

determined from triaxial testing (Mayne P. W., 2007):

𝑞𝑡 ≈ 𝑞𝑐 −(𝜋𝑑2𝑡2𝑢2)

𝜋𝑑𝑐2

4

+(𝜋𝑑𝑐

2𝑢24 )

𝜋𝑑𝑐2

4

= 𝑞𝑐 +(1 −(𝜋𝑑2𝑡2)

𝜋𝑑𝑐2

4

)𝑢2 = 𝑞𝑐 + (1 − 𝑎𝑛)𝑢2

(4)

4.2. Temperature Correction

As with all electronics sensors, the data obtained from the sensors contained within a cone penetrometer

are subject to variations with temperature. While various methods for correcting for temperature have

been employed over the years, the cost of temperature sensors has significantly decreased (Lunne,

Robertson, & Powell, 1997) (Robertson & Cabal, 2010). As such, it is commonplace to incorporate

temperature sensors into load cells and other sorts of electronic sensor devices.

While details on the methods of these corrections are discussed in depth in Lunne, Robertson and Powell

(1997), the details are not pertinent to this paper and are not discussed in detail.

4.3. Other data corrections

A myriad of other corrections should be considered specific to the type of sensors and testing being

conducted. These include but are not limited to (Lunne, Robertson and Powell, 1997):

Filter location,

Effect of axial load on pore water pressure readings,

Inclination,

Calibration and resolution of errors,

Effect of wear,

Correction for CPTU zeroed at the bottom of a borehole.

While these are all items to take into account, they are not pertinent to this report and will not explored in

detail. Should more information on these be required, Lunne, Robertson and Powell (1997) can be

consulted.

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5. Data Interpretation

CPT testing provides nearly continuous data (Mohamed, 2014). As such the data analysis can be rather

extensive. While the majority of the data analysis is performed using computational software packages,

many analysis methods are not commonly available in premade software packages and it is important to

understand the process so as to ensure that the limitations of the methods and to ensure that manually

programmed analysis programs are properly coded (Mayne P. W., 2007).

The methods used to interpret the data can provide two major groups of information: soil parameters and

soil classification (Schnaid, 2010). This section covers the most common methods employed for data

analysis.

5.1. Soil Profiling/Soil Type Interpretation

After data correction, the first analysis conducted is soil profiling. This is one of the major advantages of

CPT is the determination of changes in soil strata can be ascertained to high precision. However, since no

soil samples are taken, empirical relationships have been developed in order to determine soil type and

profiles. While these relationships do not provide accurate information pertaining to physical properties

such as grain size distribution, they have been shown to provide accurate mechanical properties (stiffness

and strength) as well as soil behavior type typically referred to as SBT (Robertson & Cabal, 2010)

(Lunne, Robertson, & Powell, 1997) (Mayne P. W., 2007). Several methods for performing this

classification including but not limited to:

Un-normalized SBT based on end resistance and friction ratio,

Normalized SBT based on normalized end resistance and friction ratio,

Probabilistic methods

This section briefly describes these methods and presents interpretation graphs from accepted literature.

5.1.1. Un-normalized SBT

The most common method for classifying a soil SBT from CPT data is the use of the standard SBT chart.

This method uses the friction ratio (𝑅𝑓 =𝑓𝑠𝑞𝑡⁄ ) and cone resistance (𝑞𝑡) and empirical graphs

developed by Robertson et al., 1986, and updated by Robertson, 2010 to classify the soil (Robertson &

Cabal, 2010). This graph is presented in Figure 8. This method is accepted as valid for CPT tests of up to

20 m in depth (Lunne, Robertson, & Powell, 1997) (Robertson & Cabal, 2010). Additionally a chart was

produced by Douglas and Olsen, 1981 (Lunne, Robertson, & Powell, 1997), to determine soil behavior

type. This second graph is presented in Figure 9.

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Figure 8: BPT classification chart based on Robertson et al., 1986, updated by Robertson, 2010 (Robertson & Cabal,

2010).

Figure 9: BPT classification chart based on Douglas and Olsen, 1981 (Lunne, Robertson, & Powell, 1997).

5.1.2. Normalized SBT

Since the sleeve-resistance and end resistance are a function of the depth of the sounding, a series of

normalized charts were developed by Robertson (Robertson & Cabal, 2010) in order to account for this.

15

In addition to normalising the parameters, an additional figure was presented by Robertson to account for

porewater pressure based on a new parameter defined as 𝐵𝑞. These normalised parameters are defined as:

Normalized friction ratio: 𝐹𝑟 =𝑓𝑠

𝑞𝑡−𝜎𝑣𝑜 (5)

Normalized end resistance ratio: 𝑄𝑡 =𝑞𝑡−𝜎𝑣𝑜

𝜎𝑣𝑜′ (6)

Normalized pore pressure ratio: 𝐵𝑞 =u2−𝑢0

𝑞𝑡−𝜎𝑣𝑜 (7)

And the applicable graphs are presented in Figure 11 and Figure 10.

To further simplify the application of this method, a soil behavior type index was developed by Robertson

and Cabal (2010) corresponding to the boundary curves between the zones. The definition of this index,

𝐼𝑐 is presented in equation 8. It can be used to classify the soil type based on the table included in Figure

11.

Soil Behaviour Type Index: 𝐼𝑐 = √(3.47 − log𝑄𝑡)2 + (log𝐹𝑟 + 1.22)

2 (𝐹𝑟 in percentage) (8)

Figure 10: Normalized BPT and 𝑩𝒒 classification charts based on Robertson et al., 1986 (Lunne, Robertson, & Powell,

1997).

16

Figure 11: Normalized BPT classification chart based on Robertson et al., 1986, updated by Robertson, 2010 (Robertson

& Cabal, 2010).

An alternative BPT index approach was developed by Jeffries and Davies assuming

𝐵𝑞 < 1 (Mayne P.W. , 2007)�. This approach defined an index of ∗ 𝐼𝑐 as given by equation 9. The

results can be used in conjunction with the table presented in Figure 12.

Soil Behaviour Type Index: ∗ 𝐼𝑐 = √(3 − log (𝑄𝑡(1 − 𝐵𝑞)))2+ (1.5 + 1.3 log𝐹𝑟)

2 (9)

Figure 12: SBT classification table based on Jefferies and Davies ∗ 𝑰𝒄 (Mayne P. W., 2007)

5.1.3. Probabilistic Methods

Recently Zhang and Tumay (1999) developed a probabilistic method for assessing percentages of clay,

silt and sand based on CPT results. The method has been coined the P-Class method and uses cone tip

resistance and sleeve resistance to compute a probability of soil type. The method is available in a fully

17

automated piece of software provided for free from the Louisiana Transportation Research Center

(LTRC) website and has been shown to provide good results (Mayne P. W., 2007).

5.1.4. Other methods

Various other methods have been developed including other methods for computing normalized friction

ratios and cone resistances, methods for calculating equivalent SPT values and various methods

developed based on SCPT methods (Lunne, Robertson, & Powell, 1997). However, these methods are

less common and will not be discussed in this report.

5.2. Estimation of soil parameters

Similar to soil classification, soil parameters can be estimated from CPT testing. These parameters

include but are not limited to (Robertson & Cabal, 2010) (Lunne, Robertson, & Powell, 1997) (Mayne P.

W., 2007) (Gavin & Tolooiyan, 2012):

Soil unit weight,

Shear wave velocity,

Shear and elastic moduli,

Friction angle,

Sensitivity,

OCR,

Relative density,

Consolidation coefficients,

Earth pressure coefficients,

Soil permeabilities.

The following section will elaborate methods for the evaluation of several of parameters required in

foundation design using simple methods. While more complicated methods exist, and the other

parameters can also be evaluated, this is considered beyond the scope of this report. While it is not

elaborated in this report, the use of additional sensors in the CPT can allow for improved accuracy of the

measured parameters and permit for almost all desired parameters to be measured to a reasonable level of

precision.

5.2.1. Soil Unit Weight

Several methods for obtaining the soil’s unit weight from CPT data have been developed over the years.

Two of the simpler methods are to use existing correlations between SBT results and typical soil densities

(Lunne, Robertson and Powell, 1997). Figure 10 shows the correlated values proposed in (Lunne,

Robertson, & Powell, 1997).

18

Figure 13: Approximate unit weight of soils based on SBT as defined in Figure 10 (Lunne, Robertson, & Powell, 1997)

A second simple method was proposed by Robertson in 2010 (Robertson & Cabal, 2010). This method

uses equation 10 to compute the relative density of the soils where 𝑝𝑎 is atmospheric pressure.

𝛾

𝛾𝑤= 0.27 log𝑅𝑓 + 0.36 log

𝑞𝑡𝑝𝑎⁄ + 1.236

(10)

Figure 14: Dimensionless unit weight based on CPT (Robertson & Cabal, 2010)

5.2.2. Undrained Shear Strength

Extensive research has been conducted on the evaluation of the undrained shear strength of clay materials

based on CPT results and to date no consensus has been reached on which method should be used (Mayne

P. W., 2007). The majority of the research has shown that the best method for computing this parameter is

of the form given in equation 11 (Robertson & Cabal, 2010).

19

𝑠𝑢 =𝑞𝑡 − 𝜎𝑣𝑁𝑘𝑡

(11)

𝑁𝑘𝑡 typically varies from 10 to 18 and has been shown to increase with plasticity and decrease with

sensitivity. Additionally, Lunne, Robertson and Powell (1997) showed that 𝑁𝑘𝑡 varies with 𝐵𝑞 and can be

as low as 6 when 𝐵𝑞 = 1.

5.2.3. Friction Angle

The soil friction angle is a parameter necessary for many design calculation. As such, several empirical

relationships have been developed in order to obtain the friction angle based on CPT results.

For sandy soils, Robertson and Campanella proposed an empirical relationship between the friction angle

and cone penetration resistance (Kulhawy & Mayne, 1990). This relationship has classically been

presented as a graph which can be seen in Figure 15.

Figure 15: Robertson and Campanella (1983) empirical graph for determining friction angle (Kulhawy & Mayne, 1990)

For fine grained soils, the relationship proposed by Mayne (2006) is recommended in his CPT guide

(Mayne P. W., 2007) and is given as follows:

𝜙′ = 29.5𝐵𝑞0.121(0.256 + 0.336𝐵𝑞 + log𝑄𝑡) (12)

5.2.4. Shear waver velocity (Vs)

While shear wave velocity can be measured directly using SCPTu testing, several empirical correlations

are available for times when seismic testing is not available. While many of these relationships apply

uniquely to clays or sandy materials, one of the more recent ones applying to all soil types is presented by

Hegazy and Mayne (Hegazy & Mayne, 1995) (Mayne P. W., 2007) and is as follows:

20

𝑉𝑠 = [10.1 log 𝑞𝑡]1.67 [100

𝑓𝑠𝑞𝑡]0.3

(13)

5.2.5. Constrained Modulus (M)

For computing one dimensional settlement in clay below shallow foundations, one popular method

involves using the constrained modulus. A popular relationship for estimating this parameter is given by:

𝑀 = 𝛼𝑀(𝑞𝑡 − 𝜎𝑣𝑜) (14)

Recently 𝛼𝑀 has been suggested by Robertson (Robertson P. K., 2009) based on SBT Ic values as

(Robertson & Cabal, 2010):

For Ic>2.2 𝛼𝑀 = min(𝑄𝑡 , 14), For Ic<2.2 𝛼𝑀 = 0.0188(100.55𝐼𝑐+1.68).

5.2.6. Small strain Shear Modulus (G)

The small strain shear modulus is commonly estimated as (Lunne, Robertson, & Powell, 1997)

(Robertson & Cabal, 2010) (Mayne P. W., 2007):

𝐺𝑚𝑎𝑥 =𝛾

𝑔𝑉𝑠2

(15)

Where 𝛾 is the bulk unit weight of the soil and g is the gravitational constant 9.81 m/s2.

5.2.7. Young’s Modulus

The drained and undrained elastic moduli of soils are extremely useful in predicting soil settlement under

foundations. Several methods have been suggested in order to estimate these parameters. Mayne (2007)

suggests that 𝐸 = (1 + 𝜈)2𝐺𝑚𝑎𝑥 where 𝜈 = 0.5 for undrained conditions and 𝜈 = 0.2 for drained

conditions.

Another method is suggested by Robertson and Cabal (2010) in which the following relationship is

employed for estimating drained modulus of uncemeted sands:

𝐸′ = 𝛼𝐸(𝑞𝑡 − 𝜎𝑣𝑜) (16)

Where 𝛼𝑀 = 0.015(100.55𝐼𝑐+1.68).

21

5.2.8. Relative Density of Sands

For sands a commonly estimated parameter is the relative density (Dr). One of the more recent methods

for estimating this parameter was presented by Jamiolkowski et al. (2001) (Mayne P. W., 2007) and is

given as follows:

𝐷𝑟 = 100

(

0.268 ln

(

𝑞𝑡𝜎𝑎𝑡𝑚

√𝜎𝑣𝑜′

𝜎𝑎𝑡𝑚)

− 0.675

)

(17)

5.2.9. OCR

Several empirical relationships have been developed for the estimation of the over consolidation ratios of

sands and clays. One of the simpler ones for clays was suggested by Robertson (2009) as follows:

𝑂𝐶𝑅 = 0.25(𝑄𝑡)1.25 (18)

Alternative methods involve the estimation of the pre-consolidation pressure from CPTu testing. The

MAyne (2007) recommends the following relationships for estimating these values for:

Sands:

𝜎𝑝′ = 0.101𝜎0.102𝐺𝑜

0.478𝜎𝑣𝑜′ 0.420 (19)

Clays:

𝜎𝑝′ = 0.6(𝑞𝑡 − 𝑢2) (20)

6. Shallow Foundation Design

Several methods have been developed for the design of shallow foundations based on CPT testing. They

can be grouped into two categories (Mayne & Illingworth, 2010):

Indirect methods,

Direct methods.

Indirect methods involve the use of the CPT results to determine the soil strength and settlement

parameters, which are then utilized to establish the bearing capacity and settlement. Section 3 of this

report provides methods for evaluating the majority of the required parameters for conventional bearing

capacity calculations. Section 4.1 lists some of the more commonly used traditional methods to evaluate

bearing capacity, and 4.2 list some of the more commonly used methods for predicting settlement.

Direct methods involve using the CPT results to directly estimate bearing capacity and settlements for

shallow foundations. Several direct methods for computing bearing capacity are detailed in section 4.3 of

22

this report while several direct methods for evaluating settlement are presented in section 4.4 of this

report.

6.1. Indirect methods for calculating bearing capacity

Indirect methods for computing bearing capacity of shallow foundations involve the determination of soil

strength parameters (𝑠𝑢, 𝜙′, 𝑐′, 𝛾). These parameters are then used in conjunction with traditional methods

for computing bearing capacity. These traditional methods include, but are not limited to, the following:

Terzaghi and Peck (Bowles, 1996),

Meyerhoff, Hansen and Vesic (Bowles, 1996) (CFEM, 2006) (Eurocode-7, 2004),

The following figures show the equations proposed by these authors as well as the shape factors required

to use them.

Figure 16: Summary of simple bearing capacity methods from Terzaghi, Meyerhof, Hansen and Vesic (Bowles, 1996)

23

Figure 17: Summary of shape and depth factors for Meyerhof (Left), Hansen and Vesic (center and right) (Bowles, 1996)

6.2. Indirect methods for calculating settlement

Indirect methods for computing bearing settlement of shallow foundations involve the determination of

soil elasticity parameters (𝐸𝑢, 𝐸′, 𝑉, 𝐺,𝑀). These parameters are then used in conjunction with traditional

methods for computing settlement. These traditional methods include, but are not limited to, the

following:

Elastic displacement methods (CFEM)

One-dimensional Oedometric method (CFEM, Bowles)

Schmertmann et al. (1978) indirect method (CFEM)

These methods are included in most text books and design codes.

6.2.1. Elastic Displacement Methods

Many elastic displacement methods are available and can be used to estimate settlement. This can be

performed by estimating the required parameters from CPT results as presented in section 3. While many

methods derived from this theory are available including Skempton and Bjerrum (1957), Poulos and

Davis (1974), etc. these methods are generally of the form given in the following equation, although

additional terms may appear for changes in the media and foundation geometry.

𝑆 =𝑞𝐵𝐼

𝐸

(22)

Where q is the applied stress, B is the footing width and 𝐼 is an influence factor based on the foundation

and soil geometry, E is the modulus (drained or undrained) (CFEM, 2006) (Mayne P. W., 2007).

The Young’s modulus and shear modulus of the soils can be estimated as outlined in section 3, and the

influence factors can be obtained from the (CFEM, 2006) or (Mayne P. W., 2007).

More generally, elastic strain integration can be used with the results from CPT testing using the

following equation:

24

𝑆 =∑1

𝐸(Δ𝜎𝑧

′ − 𝜈′(Δ𝜎𝑥′ + Δ𝜎𝑦

′)) 𝛿ℎ

𝑛

𝑖=1

(23)

Where the changes in stress can all be obtained from stress distribution theories such as that presented in

Poulos and Davis (1974) which can be found in the CFEM as well as many textbooks and other standards.

6.2.2. One-dimensional Oedometric method

Since the one-dimensional constrained modulus can be estimated from CPT results as shown in section 3,

the one-dimensional oedometric method can be applied to estimate consolidation settlements. This

method can be computed using the following equation (CFEM, 2006) (Bowles, 1996) and an accepted

stress incrementation method (ie trapezoidal, Bousinesque, etc.):

𝑆𝑜𝑒𝑑 =∑[𝑚𝑣Δ𝜎𝑧′𝛿ℎ]𝑖

𝑛

𝑖=1

(24)

Where 𝑚𝑣 =1

𝑀 where M is the constrained modulus, Δ𝜎𝑧

′ is the change in effective stress at the midpoint

of the layer and 𝛿ℎ is the layer thickness.

6.2.3. Schmertmann et al. (1978)

Schmertmann et al. (1978) is the most commonly used method for computing settlement based on CPT

testing. In order to perform this calculation, the Young’s modulus of the soil is estimated using the CPT

results, and the settlement is computed using the following:

𝑆 = 𝐶1𝐶2𝐶3Δ𝑞∑Δ𝑧𝑖𝐸𝑖′ 𝐼𝑧

𝑛

𝑖=1

(25)

Where 𝐶1 = 1 − 0.5𝑞𝑠′

Δ𝑞 , 𝐶2 = 1 + 0.2 log10 10𝑡, 𝐶3 = 1.03 − 0.03 (

𝐿

𝐵), Δ𝑞 = 𝑞𝑎 − 𝜎𝑣𝑜

′ , t is the time of

load application in years, 𝐼𝑧 is the strain influence factor obtained from figure , Δ𝑧𝑖 is the thickness of

the ith layer, 𝐸𝑖

′ is the modulus of the ith layer of sand.

While the CFEM suggests using 𝐸′ = 3.5𝑞𝑐 for L/B<10 and 𝐸′ = 2.5𝑞𝑐 for L/B=1, any of the accepted

methods for estimating 𝐸′ can be used.

Figure 18: Influence factor for Schmertmann (1978) method (CFEM, 2006)

25

This method has generally been found to overestimate the settlement of soils beneath foundations. As

such, Fathi (2014) proposed that the flowchart presented in Figure 19 be used to estimate Young’s

modulus prior to using the Schmertmann method based on the relative density of the soil.

It should be noted, however, that the relative density used by Mohamed (2014) were obtained through

laboratory testing, and as such using CPT estimated relative densities may not provide any significant

improvement to the Schmertmann method.

Figure 19: Modulus Correction for Schmertmann (1978) (Mohamed, 2014)

6.3. Direct Ultimate Bearing Capacity Methods

Several direct methods are available for the direct computation of the bearing capacity of shallow

foundations. This section describes four of the most commonly used ones:

Meyerhof (1956) direct method (Lunne, Robertson, & Powell, 1997),

Tand et al (1995) direct method (Lunne, Robertson, & Powell, 1997),

Tand et al (1986) direct method (Mayne P. W., 2007),

26

Schmertmann (1978) direct method (Mayne P. W., 2007),

Bowles (1996)

Eslaamizaad & Robertson (1996) (Robertson & Cabal, 2010).

6.3.1. Meyerhof (1956) direct method

In 1965 Meyerhof suggested a direct method for computing bearing capacities on sand based on CPT

results. He defined 𝑞𝑢𝑙𝑡 as:

𝑞𝑢𝑙𝑡 =�̅�𝑐𝐵

𝐶(1 + 𝐷 𝐵⁄ )

(26)

Where B is the width of the footing, �̅�𝑐 is the average cone resistance over a depth equal to the width of

the footing, D is the depth of the footing below the ground surface and C is a constant equal to 12.2 m

(Lunne, Robertson, & Powell, 1997). A factor of safety of 3 is recommended for determining the

allowable bearing capacity using this method.

6.3.2. Tand et al. (1995) direct method

Tand et al. (1995) (Lunne, Robertson, & Powell, 1997) proposed the use of the following method for the

determination of bearing capacity of shallow footings on medium cemented dense sand:

𝑞𝑢𝑙𝑡 = 𝑅𝑘𝑞𝑐 + 𝜎𝑣𝑜 (27)

Where 𝑅𝑘 is a constant that varies between 0.14 to 0.2 and and 𝜎𝑣𝑜 is the initial vertical stress at the base

of the footing.

6.3.3. Tand et al. (1986) direct method

Tand et al. (1986) proposed the use of the following method for the determination of bearing capacity of

shallow footings on clay (Mayne P. W., 2007):

𝑞𝑢𝑙𝑡 = 𝑅𝑘(𝑞𝑐 − 𝜎𝑣𝑜) + 𝜎𝑣𝑜 (28)

Where 𝑅𝑘 is a constant that can be obtained from Figure 20 and 𝜎𝑣𝑜 is the initial vertical stress at the base

of the footing. It should be noted that 𝑅𝑘 is dependent on 𝐻𝑒 (the embedded depth of the footing) and B

(the footing width).

27

Figure 20: 𝑹𝒌 for Tand et al. (1986) foundations on clay from (Mayne P. W., 2007)

6.3.4. Schmertmann (1978) direct method

Schmertmann (1978) presented the following direct method (Mayne P. W., 2007) for calculating 𝑞𝑢𝑙𝑡 when 𝐵 > 0.9 𝑚 embedded to a depth of 𝑧𝑒 ≥ 1.2 𝑚 and when 𝐵 ≤ 0.9 𝑚 embedded to a depth of

𝑧𝑒 ≥ 0.45 𝑚 +𝐵

2:

Square footings: 𝑞𝑢𝑙𝑡 = 0.55𝜎𝑎𝑡𝑚 (𝑞𝑐

𝜎𝑎𝑡𝑚)0.785

Strip foorings: 𝑞𝑢𝑙𝑡 = 0.36𝜎𝑎𝑡𝑚 (𝑞𝑐

𝜎𝑎𝑡𝑚)0.785

(29)

(30)

Where 𝜎𝑎𝑡𝑚 is one atmosphere of pressure.

6.3.5. Bowles (1996)

Bowles (1996) presents a similar method based on charts provided in Schmertmann (1978) and credited

to an unpublished reference by Awakti (Bowles, 1996). This method contains the following solutions:

Strip footings:

On sand: 𝑞𝑢𝑙𝑡 = 28 − 0.0052(300 − 𝑞𝑐)1.5

On clay: 𝑞𝑢𝑙𝑡 = 2 + 0.25𝑞𝑐

(31)

(32)

Square footings:

On sand: 𝑞𝑢𝑙𝑡 = 48 − 0.009(300 − 𝑞𝑐)1.5

On clay: 𝑞𝑢𝑙𝑡 = 5 + 0.34𝑞𝑐

(33)

(34)

Where 𝑞𝑢𝑙𝑡 and 𝑞𝑐 are in kg/cm2 and 𝑞𝑐 is the average penetration resistance from B/2 above the footing

to a depth of 1.1B below the footing.

28

6.3.6. Eslaamizaad & Robertson (1996)

Eslaamizaad & Robertson (1996) proposed the following relationship for direct computation of 𝑞𝑢𝑙𝑡 for

shallow foundations on sand (Lunne, Robertson, & Powell, 1997):

𝑞𝑢𝑙𝑡 = 𝐾�̅�𝑐 (35)

Where �̅�𝑐 is the average cone penetration resistance over a depth equal to the width of the footing below

the footing base and K is a constant that can be obtained from

Figure 21: 𝑲 from Eslaamizaad & Robertson (1996) foundations on sand (Lunne, Robertson, & Powell, 1997)

6.4. Direct settlement calculation methods

Several direct methods are available for the direct computation of the settlement of shallow foundations.

This section describes some of the most commonly used ones:

Meyerhof (1974)

Burland et al (1977)

Mayne and Illingworth (2010)

While these methods exist, for settlement calculations, it is generally recommended that indirect methods

be used by estimating the modulus of elasticity of the soil with depth, and then employing the

Schmertmann (1978) method (CFEM, 2006) or other geoelasticity based methods. It should additionally

be mentioned that the direct computation methods included in this report are all applicable only to

foundations on sands.

6.4.1. Meyerhof (1974)

Meyerhof (1974) suggested an empirical method (using equation 17) to estimate a conservative value for

the settlement of shallow foundations on sand from the CPT results (Lunne, Robertson, & Powell, 1997).

𝑆 =𝑞𝑎𝐵

2�̅�𝑐

(36)

Where B is the footing width, 𝑞𝑎 is the applied pressure from the footing and �̅�𝑐 is the average cone

penetration resistance over a depth of B below the footing.

29

6.4.2. Burland et al. (1977)

Burland et al. (1977) presented a graph showing predicted settlements based on the cone penetration

resistance obtained from the CPT testing (CFEM, 2006). This graph can be seen in Figure 22.

Figure 22: Burland et al., 1977 Graph for approximate settlement of footings on sand (CFEM, 2006)

6.4.3. Mayne and Illingsworth (2010)

Mayne and Illingsworth (2010) recently conducted an analysis of a database of existing footings on sand

varying in footing width from 0.5 m to 6 m. They then proposed an empirical method for estimating the

settlement of shallow foundations on sand directly from CPT results:

𝑆 =25𝐵𝑞𝑎

2

9�̅�𝑐2

(37)

Where B is the footing width, 𝑞𝑎 is the applied pressure from the footing and �̅�𝑐 is the average cone

penetration resistance over a depth of 1.5B below the footing (Mayne & Illingworth, 2010).

7. Deep Foundation Design

Several methods have been developed for the design of deep foundations based on CPT testing. The

common trait of all methods is that the bearing capacity of a single pile is calculated in two parts:

𝑞𝑢 = 𝑞𝑡 + 𝑞𝑠 (38)

Where 𝑞𝑡 is the end bearing resistance and 𝑞𝑠 is the friction resistance of the pile.

In terms of methods for calculating these capacities, they can be separated into two types of method

(Robertson & Cabal, 2010) (Titi & Abu-Farsakh, 1999):

Indirect methods,

Direct methods.

30

Indirect methods involve the use of the CPT results to determine the soil strength and settlement

parameters and use them to determine the bearing capacity and settlement. Section 3 of this report

provides methods for evaluating the majority of the required parameters for conventional bearing capacity

calculations. Section 5.1 lists some of the more commonly used methods to evaluate bearing capacity.

Direct methods involve using the CPT results to directly estimate bearing capacity and settlements for

shallow foundations. Several direct methods for computing bearing capacity are detailed in section 5.2 of

this report (Mayne P. W., 2007).

A brief discussion of settlement calculations for piles is included in section 5.3.

7.1. Indirect Bearing Capacity Methods

Indirect methods for computing bearing capacity of deep foundations involve the determination of soil

strength parameters. These parameters are then used in conjunction with traditional methods for

computing bearing capacity. Two basic categories of indirect methods exist:

Total stress methods (𝛼 methods) (Bowles, 1996, CFEM, Eurocode 7, Niazi and Mayne, 2013),

Effective stress methods (𝛽 methods) (Bowles, 1996, CFEM, Eurocode 7, Niazi and Mayne,

2013).

While the general formulation of these methods has remained the same, various scientists have modified

them over the years so as to account for various parameters. Figure show the modifications made to these

methods by scientists over the years as summarized by Niazi and Mayne (2013).

Figure 23: Modifications made to the beta method over the years (Niazi & Mayne (2013))

31

Figure 24: Modifications made to the alpha method over the years (Niazi & Mayne (2013))

Due to the numerous iterations of these methods, this report will outline the basic methods as covered by

the CFEM. A comprehensive explanation of each of the modifications made to these methods can be

found in Niazi and Mayne (2013), should other iterations be desired.

7.1.1. Total stress method (𝛼 method)

The total stress method for determining single pile bearing capacity involves use of total stress to compute

the bearing capacity of piles in cohesive soils.

For cohesive soils the skin friction is calculated using the following equation (CFEM, 2006):

𝑞𝑠 = 𝛼𝑠𝑢 (39)

Where 𝑠𝑢 is the undrained shear strength and 𝛼 can be obtained from Figure 25.

32

Figure 25: Adhesions as a function of undrained shear strength (CFEM, 2006)

End resistance can be obtained from the following equation (CFEM, 2006):

𝑅𝑡 = 𝑁𝑡𝑠𝑢𝐴𝑡 (40)

Where 𝑁𝑡 = 9 for pile diameter D < 0.5 m, 𝑁𝑡 = 7 for 0.5 m < D < 1 m, 𝑁𝑡 = 6 for D > 1 m. 𝐴𝑡 is the cross

section area of the pile at the toe.

From these the total bearing capacity of a pile can be combined as:

𝑄𝑢 = 𝑁𝑡𝑠𝑢𝐴𝑡 + ∑𝐿𝑖𝑃𝛼𝑖𝑠𝑢𝑖

𝑛

𝑖=1

(41)

Where 𝐿𝑖 is the length of the section of the friction pile, P is the perimeter of the pile and 𝑄𝑢 is the

ultimate load that can be held by the pile.

7.1.2. Effective stress methods (𝛽 methods)

In the case of cohesionless soils, the skin friction and end resistance of a pile are given by (CFEM, 2006)

(Eurocode-7, 2004):

𝑅𝑠 = ∑𝐿𝑖𝑃𝜎𝑣′𝐾𝑠 tan 𝛿

𝑛

𝑖=1

=∑𝐿𝑖𝑃𝛽𝜎𝑣′

𝑛

𝑖=1

(42)

𝑅𝑡 = 𝑁𝑡𝜎𝑡′ (43)

Where 𝐿𝑖 is the length of the pile section, P is the pile perimeter, 𝜎𝑣′ is the vertical effective stress at depth

of 𝐿𝑖, 𝐾𝑠 is the coefficient of lateral earth pressure.

33

Typically values of 𝛽 and 𝑁𝑡 are obtained from Figure 26.

Figure 26: Range of 𝜷 coefficients (left) and 𝑵𝒕 coefficients (right) (CFEM, 2006)

7.2. Direct Bearing Capacity Methods

To date a very large number of direct methods for relating CPT/CPTu results to pile bearing capacity

have been developed. Recently several researchers have compared many of these methods including Cai

et al. (2009) who evaluated 10 methods and Niazi and Mayne (2013) who presented 35 methods. Of these

the following methods are recommended by CFEM, Mayne (2007) and Lunne, Robertson and Powell

(1997) and are presented in this report:

LCPC method (Bustamante & Gianeselli, 1982),

Norwegian Geotechnical Institute Building Research Establishment,

Unicone (Eslami and Fellenius, 1997).

While only these three methods will be presented in this report, it should be noted that a list of the other

methods can be found in Niazi and Mayne (2013) and Cai et al. (2009).

7.2.1. LCPC method (1982)

The Laboratoire Central des Ponts et Chaussées (LCPC) method was developed by Bustamante &

Gianeselli (1982) on the results from 197 pile load tests. This method is one of the most commonly used

method and is currently recommended by the CFEM (2006).

From the LCPC method the capacities for a single pile can be calculated as follows:

𝑞𝑠 =1

𝛼𝑞𝑐

(44)

𝑅𝑡 = 𝑘𝑐𝑞𝑐𝑎𝐴𝑡 (45)

Where 𝑞𝑐 is the cone penetration resistance (varies with depth), 𝑞𝑐𝑎 is the cone penetration resistance at

the base of the pile, 𝐴𝑡 is the cross sectional area of the pile end, 𝑘𝑐 and 𝛼 are constants obtained from

Figure 27 and Figure 28.

34

Figure 27: Range of 𝒌𝒄 coefficients for the LCPC method (CFEM, 2006)

Figure 28: Range of 𝜶 coefficients for the LCPC method (CFEM, 2006)

35

7.2.2. Norwegian Geotechnical Institute Building Research Establishment

The NGI-BRC method is an updated version of Almeida et al. (1996) by Powell et al. (2001) and as such

is only applicable to clays. Based on this method the side friction and end bearing resistance of a pile are

given by the following (Mayne P. W., 2007):

𝑞𝑠 =𝑞𝑡 − 𝜎𝑣𝑜

10.5 + 13.3 log𝑄𝑡

(46)

𝑞𝑏 =𝑞𝑡 − 𝜎𝑣𝑜𝑘2

(47)

Where 𝑄𝑡 is the normalized cone penetration resistance, 𝑞𝑡 is the porewater pressure corrected cone

penetration resistance and 𝑘2 =𝑁𝑘𝑡

9⁄ , where 𝑁𝑘𝑡 is typically taken as a value of 15, but may be as high

as 25 to 35 for hard clays (Mayne P. W., 2007).

7.2.3. Unicone method

The unicone method is based on Eslami and Fellenius (1997) and requires CPTu readings to be applied.

Based on this method the side friction and end bearing resistance of a pile are given by the following

(Mayne P. W., 2007):

𝑞𝑠 = 𝐶𝑠𝐸𝑞𝐸 (48)

𝑞𝑏 = 𝐶𝑡𝐸𝑞𝐸𝑔 (49)

Where 𝑞𝐸 = 𝑞𝑡 − 𝑢2, 𝑞𝐸𝑔 is the geometric mean of 𝑞𝐸 values over the influence zone (4d below the pile

tip to 8d above the pile tip), CsE is obtained from Figure 29, and CtE is generally taken as 1, but is given as

𝐶𝑡𝐸 =1 𝑚

3𝑑⁄ 𝑓𝑜𝑟 𝑑 > 0.4 𝑚 (Niazi and Mayne, 2013).

Figure 29: Soil classification and 𝑪𝒔𝑬 value for Unicone method (Mayne P. W., 2007)

7.3. Settlement Estimation

Several methods are currently available for the estimation of settlements of pile foundations. The

following methods are elaborated in this report:

Elastic Continuum Solutions (Poulos and Davis, 1980)

Vesic (1977) (Empirical solution)

36

Das’ (1995) method

Fleming et al (2008)

ANN methods (Baziar et al. 2014)

Non-Linear sCPTu methods

7.3.1. Elastic Continuum Solutions

Poulos and Davis (1980) provided a solution using elastic continuum methods for both floating and end-

bearing piles. From their results, the settlement for a pile in a deep layer of uniform elastic material is

given by the CFEM (2006):

𝑆 =𝑄

𝐸𝑠𝑑𝐼0𝑅𝑘𝑅𝜈

(50)

Where 𝐸𝑠 is the soil modulus and 𝐼0𝑅𝑘 𝑎𝑛𝑑 𝑅𝜈 are influence factors found in Figure 29, Figure 30 and

Figure 31.

For most purposes in the case of layered soils it is adequate to use the following equation for 𝐸𝑠 (CFEM,

2006):

𝐸𝑠(𝑎𝑣𝑒) =1

𝐿∑𝐸𝑖ℎ𝑖

𝑛

𝑖=1

(51)

Figure 30: 𝑰𝟎 influence factor from Poulos and Davis (1980) (CFEM, 2006)

37

Figure 31: 𝑹𝒌 𝒂𝒏𝒅 𝑹𝒗 values from Poulos and Davis (1980) for pile settlement (CFEM, 2006)

It should be noted that Fleming et al. (1992) developed a closed form solution for 𝐼0 for piles in a soil

with a modulus that increases linearly with depth. While this solution is not included in this report, it can

be found in the CFEM (2006).

7.3.2. Vesic (1977)

Vesic (1977) proposed an empirical equation for determining pile settlement. The proposed equation is

the following (CFEM, 2006):

𝑆 = 𝑆𝑝 + 𝑆𝑠𝑠 + 𝑆𝑠𝑡 (52)

Where 𝑆𝑝 is the elastic deformation of the pile, 𝑆𝑠𝑠 is the settlement from load transmitted along the pile

shaft and 𝑆𝑠𝑡 is the settlement of the pile toe caused by load transmitted to the toe.

These terms were then defined as follows:

𝑆𝑝 = (𝑄𝑡𝑎 + 𝛼𝑠𝑄𝑆𝑎)𝐿

𝐴𝑝𝐸𝑝≈ 0.75

𝑄𝐿

𝐴𝑝𝐸𝑝

(53)

𝑆𝑠𝑠 = 𝐶𝑠𝑄𝑆𝑎𝐿𝑞𝑡

(54)

𝑆𝑠𝑡 = 𝐶𝑡𝑄𝑡𝑎𝑑𝑞𝑡

(55)

Where L is the pile length, d is the pile diameter, 𝑞𝑡 is the end bearing capacity, 𝑄𝑆𝑎 is the portion of the

pile load transmitted by the pile toe, 𝑄𝑡𝑎 is the portion of the load transmitted through skin friction, 𝛼𝑠 is

a factor dependent on skin friction, 𝐶𝑠 = 0.93 + 0.16(𝐿𝑑⁄ )0.5

and 𝐶𝑡 is found from

Figure 32: 𝑪𝒕 values from Vesic (1977) for pile settlement (CFEM, 2006)

38

7.3.3. Das’ (1995)

Das (1995) proposed a method similar to Vesic (1977) with changes to 𝑆𝑠𝑠 and 𝑆𝑠𝑡. His proposed

definitions for these two terms were as follows (Mayne P. W., 2007):

𝑆𝑠𝑠 =𝑄𝑆𝑎𝑂𝐿

(𝑑

𝐸𝑠) (1 − 𝜈2)𝐼𝜌𝑠

(56)

𝑆𝑠𝑡 =𝑄𝑡𝑎𝑑

𝐴𝑝𝐸𝑠(1 − 𝜈2)𝐼𝜌

(57)

Where O is the pile perimeter, 𝜈 is the Poisson’s ratio of the soil, 𝐼𝜌 = 0.85, and 𝐼𝜌𝑠 = 2 + 0.35√𝐿

𝑑.

7.3.4. Fleming et al. (2008)

Fleming et al. (2008) showed using finite element and boundary element analysis that the skin friction

load is transferred to the soil through shear stress. Solving the differential equations assuming that the

shear stress decreases with distance from the pile, he obtained the following solution for the settlement of

a pile (Fleming, Weltman, Randolph, & Elson, 2009):

𝑄𝑡𝑎𝑤𝑡𝐺𝑟0

=

2휂(1 − 𝜈𝑠)휀

+2𝜋𝜌휁2𝜋𝜌 tanh(𝜇𝐿)

𝜇𝐿𝐿𝑑

1 +8휂

𝜋𝜆(1 − 𝜈𝑠)휀tanh(𝜇𝐿)𝜇𝐿

𝐿𝑑

(58)

Where 휂 =𝑑𝑏𝑑⁄ (ratio of underream for underreamed piles), 휀 =

𝐺𝐿𝐺𝑏⁄ (ratio of end bearing for end

bearing piles), 𝜌 = �̅� 𝐺𝐿⁄ (variation of soil modulus with depth), 𝜆 =

𝐸𝑝𝐺𝐿⁄ (pile-soil stiffness ratio), 휁 =

ln (2𝑟𝑚

𝑑) (radius of influence of the pile), 𝜇𝐿 = 2√

2

𝜁𝜆

𝐿

𝑑 (measured pile compressibility).

7.3.5. Artificial Neural Network Methods

Recently, Baziar et al. (2014) proposed the use of artificial neural networks to estimate settlements for

complicated pile soil configurations in which many parameters are unknown. By developing a neural

network based on 101 pile loading tests and CPT results, it was shown that the network could predict pile

settlement more accurately than most commonly used methods (Baziar, Azizkandi, & Kashkooli, 2015).

While elaborating on this method is beyond the scope of this report, Figure shows the basic structure of

such a neural network (Baziar, Azizkandi, & Kashkooli, 2015).

39

Figure 33: Basic structure of a neural network (Baziar, Azizkandi, & Kashkooli, 2015)

7.3.6. Approximate non-linear approximations using sCPTu

As soil properties are highly non-linear, in the event that sCPTu testing is performed, Mayne (2007)

recommends the following approximation for determining pile settlement:

𝑤𝑡 =𝑄𝑡𝐼𝜌

𝑑𝐸𝑚𝑎𝑥 [1 − (𝑄𝑡𝑄𝑡𝑢)𝑔

]

(59)

Where 𝐸𝑚𝑎𝑥 is the small strain modulus, 𝑔 = 0.3 ± 0.1, 𝑄𝑡𝑢 is the ultimate bearing capacity for the pile, 𝑄𝑡

𝑄𝑡𝑢=

1

𝐹𝑆 . This method is illustrated in Figure 34.

Figure 34: Concept using sCPTu for evaluating approximate non-linear settlement (Mayne P. W., 2007)

40

8. Design Example

The previous sections of this report have presented historically and currently used methods for

interpreting CPT/CPTu results in order to design shallow and deep foundations. This section presents a

design example for foundation design using CPT results.

In order to illustrate the process for the design of a building footing, consider the following example

assuming a simplified site. Determine the bearing capacity of a 3 m wide and 2 m deep strip footing and

13 m long 0.6 m diameter end driven pile using direct methods for the following CPT results:

A cone penetration test is performed and uniform values of 𝑞𝑐 = 1.5 𝑀𝑃𝑎 and 𝑓𝑠 = 100 𝑘𝑃𝑎

over a depth of 20 m from the site surface.

A homogeneous soil profile will be assumed.

8.1. Soil Classification

The soil type must first be determined in order to assess which methods are applicable for estimating the

bearing capacity. To do so the first step is to compute the friction ratio of the site as defined in section

3.1.1: 𝑅𝑓 =100 𝑘𝑃𝑎

1500 𝑘𝑃𝑎100% = 6.7%. Since the testing was performed up to a depth of 20 m, the un-

normalized soil classification system may be used. From this value using Figure 8, the soil can be

classified as a Type 3 material or clay.

8.2. Soil Properties

As direct methods are being used, soil strength parameters are un-necessary, however a soil unit weight is

still required. Based on Figure 14, a soil unit weight of 19kPa can be estimated.

Additionally, in order to classify the clay soil, its undrained shear strength is required. This is done using

equation 11:

𝑠𝑢 =1500 − 2 ∗ 19𝑘𝑃𝑎

14= 104 𝑘𝑃𝑎

Implying that this is a stiff clay.

8.3. Bearing capacity for shallow foundations

For foundations on clay several methods are available for direct calculation. It is recommended that the

methods be compared and the lowest one be used. Additionally, a safety factor of 3 is typically used for

determining allowable bearing capacity.

Meyerhof: 𝑞𝑢𝑙𝑡 =1500∗3

12.2(1+2 3⁄ )= 220 𝑘𝑃𝑎,

Schmertmann: 𝑞𝑢𝑙𝑡 = 0.36 ∗ 100𝑘𝑃𝑎 ∗ (1500

100)0.785

= 300 𝑘𝑃𝑎

Tand et al.: 𝑞𝑢𝑙𝑡 = 0.4(1500 − 19 ∗ 2) + 19 ∗ 2 = 620 𝑘𝑃𝑎

From these, Meyerhof is the most conservative so an allowable capacity 220/3 = 70 kPa may be

employed. Should previous experience in the area be available, it may be justifiable to employ one of the

other methods.

41

8.4. Bearing capacity of a single pile

For piles in clay several methods are available for direct calculation. It is noted that the NGI and unicone

methods only apply to CPTu tests and can therefore not be used with the information provided.

LCPC: From Figure 27 and Figure 28 𝛼 = 80 and 𝑘𝑐 = 0.45. As such,

𝑞𝑠 =1

801500 𝑘𝑃𝑎 = 18.75 𝑘𝑃𝑎 , and 𝑅𝑡 = 0.45 ∗ 1500 𝑘𝑃𝑎 ∗ 𝜋 ∗ 0.3

2 = 190 𝑘𝑁

So total capacity with a safety factor of 3 is 𝑄 =18.75∗𝜋∗0.6𝑚∗12𝑚+190 𝑘𝑁

3=614 𝑘𝑁

3= 205𝑘𝑁.

8.5. Settlement

As the pile and foundation are in clay and not sand, no direct methods are available for estimating

settlement. It is therefore recommended to estimate the material elasticity parameters and use a traditional

method for their estimation. This is considered beyond the scope of this report, and examples can be

found in Mayne (2007) as well as other sources cited in this report.

8.6. Summary

Using direct bearing capacity calculation methods can be used to quickly estimate the capacities of piles

and shallow foundations using CPT results. These results can be improved through the use of SCPTu or

CPTu results. Based on these calculations, a significantly larger pile would be required to obtain a

reasonable bearing capacity, while the shallow footing provides a reasonable capacity for a small

structure.

9. Conclusion

CPT/CPTu is an extremely useful tool for investigating site properties and predicting foundation bearing

capacity and settlement. It provides a means for determining in-situ soil parameters in a quick and cost

effective manner. In fact, CPT can often outperform conventional drilling programs while providing more

complete information about the site. The primary drawbacks to this method are the lack of sampling and

the limitations to penetration through dense soils, and the inability to determine rock depth. As a result of

this, CPT/CPTu is ideally suited to be combined with conventional drilling as part of a larger

investigation campaign.

CPT/CPTu provides certain key advantages over conventional drilling for estimating foundation bearing

capacities. These advantages include the direct assessment of geostratigraphy, the identification of

interbedded lenses of material, the exact location of changes in strata and the digital nature of the data.

The digital nature of the data allows the results to be processed extremely quickly and efficiently. In

addition to the assessment of the soil stratigraphy is highly repeatable and reliable and many well defined

empirical and analytical relationships exist between CPT results and soil strength, consolidation,

permeability and elastic parameters. This allows a near continuous evaluation of soil properties and

permits the use of complex traditional methods for bearing capacity and settlement analyses with regards

to foundation design.

In addition to the use of indirect methods for the design of foundations, over the years several direct

methods have been developed in order to facilitate the design of foundations. This allows for multiple

methods to be used and a range of results to be obtained.

42

A major advantage in CPT testing is the possibility to add additional sensors to the CPT probe in order to

perform addition testing simultaneously. Two major examples of this are SCPTu and pressuremeter CPT

testing. These allow for direct measurements of shear wave velocities and elastic properties of soils

further improving the results of the testing and accuracy of foundation bearing capacity and settlement

calculations.

Unfortunately certain limitations in CPT testing present major issues in testing. These limitations include

difficulties penetrating dense layers and boulders, probe deflections and limitations in the frequency of

shear wave velocity measurements (SCPTu). As such, research and development in the field of CPT is

very active including the development of new analytical methods for analysing CPT data, new types of

CPT probes and new software packages to perform the analysis.

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