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Three-dimensional pile-soil interaction insoldier-piled excavations

S.H. Honga,*, F.H. Leeb, K.Y. Yongc

aST Architects and Engineers Pte Ltd, 60 Admiralty Road West #03-01, Singapore 759947, SingaporebDepartment of Civil Engineering, 1 Engineering Drive 2, Singapore 119260, SingaporecDepartment of Civil Engineering, 1 Engineering Drive 2, Singapore 117576, Singapore

Received 14 June 2001; received in revised form 29 March 2002; accepted 27 April 2002

Abstract

Strutted excavations, including soldier-piled excavations, are often analysed using two-

dimensional (2D) finite element (FE) analyses with properties which are averaged over a cer-tain span of the wall. In this paper, the effects of ‘‘smearing’’ the stiffness of the soldier pilesand timber laggings into an equivalent uniform stiffness are examined, based on comparisonbetween the results of 2D and 3D analyses. The ability of the 3D analyses to model the flex-

ural behaviour of the soldier piles and timber laggings is established by comparing the flexuralbehaviour of various FE beam representations to the corresponding theoretical solutions,followed by a reality check with an actual case study. Finally, the results of 2D and 3D ana-

lyses on an idealized soldier piled excavation are compared. The findings show that modellingerrors can arise in several ways. Firstly, a 2D analysis tends to over-represent the coupling topile to the soil below excavation level. Secondly, the deflection of the timber lagging, which is

usually larger than that of the soldier piles, is often underestimated. For this reason, theoverall volume of ground loss is, in reality, larger than that given by a 2D analysis. Thirdly, a2D analysis cannot replicate the swelling, and therefore softening, of the soil face just behind

the timber lagging. Increasing the inter-pile spacing will tend to accentuate the effects of thesemodelling errors.# 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Soldier piles; Timber lagging; Excavation; Arching; Pile deflection; Preloading

Computers and Geotechnics 30 (2003) 81–107

www.elsevier.com/locate/compgeo

0266-352X/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved.

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* Corresponding author. Tel.: +65-6765-9247; fax: +65-6769-6756.

E-mail address: [email protected] (S.H. Hong).

1. Introduction

Soldier piles with timber lags have been used extensively as an excavation supportsystem, particularly in stiff soil conditions and where ground water ingress into theexcavated area is not problematic [1–3]. The main advantage of using soldier piles istheir relatively low cost and ease of installation, compared to other forms of supportsystems such as diaphragm walls and bored piles. Furthermore, since the soldierpiles are not contiguous, much fewer soldier piles often need to be driven incomparison to sheet piles, thereby yielding significant savings in time and cost ofinstallation and thus allowing excavation to commence with a minimum of leadtime.Soldier piles are often designed and analysed as contiguous wall systems even

though they are, in reality, not so [4]. Nonetheless, designers have long recognizedthat the soldier pile retaining system is not only often more flexible than other sys-tems but the stiffness of the system is non-uniform in that the piles are much stifferthan the timber lags. To address this characteristic, Trada [5] and BS8002 [6]recommended a 20–25% reduction of Peck’s earth pressure for the soldier piles and50% reduction for the timber lagging. Armento [7] also proposed a similar reductionbased on measurements from the excavations for the 12th and 19th Street Stationsof the BART system. Empirical guidelines for the passive earth pressure mobilizedin the soil in front of the soldier piles have also been suggested. For instance, Broms[8], Teng [9], NAVFAC [10] and the CGS [11] proposed that a soldier pile of width Bcan be assumed to mobilize the passive earth pressure imposed by a lateral extent ofground of span 3B (i.e. 1.5B on both sides of the pile).The fact that the soldier piles and timber laggings are of vastly different con-

struction and have very different stiffnesses means that the interaction between theretaining system and the soil is three-dimensional (3D) in nature. However, most ofthe finite element (FE) analyses on soldier pile walls to date are two-dimensional(2D) and based on the assumption of plane strain [3,12–14]. The differences in pileand timber lagging stiffnesses cannot be modelled by these analyses, which necessa-rily assumes a ‘‘smeared’’ uniform stiffness for the entire span of the retaining wall.Briaud and Lim [15] used 3D FE analyses to study tieback soldier pile walls. How-ever, their study focuses more on the parameters of the tiebacks and depth of soldierpile embedment rather the effects of different types of analyses. Furthermore, Briaudand Lim [15] modelled the soldier piles with beam elements. As will be discussedlater, beam elements may not realistically represent the interaction between the sol-dier piles and surrounding soil, owing to their inability to replicate the finite cross-sectional dimensions of real soldier piles.In this paper, the effects of ‘‘smearing’’ the stiffness of the soldier piles and timber

laggings into an equivalent uniform stiffness are examined, based on comparisonbetween the results of 2D and 3D analyses. ‘‘Smeared’’ uniform stiffness is used forthe retaining systems in the 2D analyses. On the other hand, in the 3D analyses,different elements and material types represent the soldier piles and timber laggings.In the first part of the paper, the ability of the 3D analyses to model the flexuralbehaviour of the soldier piles and timber laggings is examined. This is accomplished

82 S.H. Hong et al. / Computers and Geotechnics 30 (2003) 81–107

by comparing the flexural behaviour of various FE beam representations to thecorresponding theoretical solutions. A reality check is then conducted usingO’Rourke’s study on the G Street test section as a reference. Finally, the results of acomparative study between 2D and 3D analyses on an idealized soldier piled exca-vation will be discussed to highlight the effects of using ‘‘smeared’’ uniform stiff-nesses in 2D analyses. All of the analyses reported herein were conducted using anin-house version of CRISP (Britto and Gunn [16]), with 3D beam and reduced-integration brick elements incorporated.

2. Modelling of soldier piles in 2D and 3D analyses

In this section, the modelling of soldier piles in 2D and 3D analyses is firstaddressed. Soldier piles act essentially in flexure, and it is well-known that 4-nodedquadrilaterals do not model flexural behaviour well, owing to the use of incompletepolynomials as shape functions, which causes shear-locking [17,18]. The 8-nodedquadrilateral element suffers from the same problem, albeit to a lesser extent [18]. Ithas been shown [19,20] that, by using reduced-integration eight-nodedquadrilaterals, behaviour in 2D can be readily modelled. The same may pre-sumably be true for the 20-noded brick element. In order to assess the ability ofvarious elements to represent the soldier pile, the idealized problem of a longcantilever beam subjected to a triangular load distribution, the latter representingan idealized earth pressure profile, was studied using various 2D and 3D

Fig. 1. Comparison of deflection profiles under distributed load for 2-D 43 m-cantilever beam. (a) 32-bit

precision. (b) 64-bit precision.

S.H. Hong et al. / Computers and Geotechnics 30 (2003) 81–107 83

Fig. 2. Comparison of bending moments under distributed load for 2-D 43 m-cantilever beam. (a) 32-bit


Fig. 3. Effect of aspect ratios for 2-D 43 m-cantilever beam in 64-bit precision using RIQUAD elements.

(a) Deflection. (b) Bending moment.


Fig. 4. Comparison of deflection profiles under distributed load for 3-D 43 m-cantilever beam. (a) 32-bit


Fig. 5. Comparison of bending moments under distributed load for 3-D 43 m-cantilever beam. (a) 32-bit



representations, as shown in Figs. 1–5. The 2D representations were achieved usingbeam element as well as full- and reduced-integration 8-noded quadrilateral ele-ments, hereafter termed FIQUAD and RIQUAD, respectively. The 3D representa-tions were achieved using beam element as well as full- and reduced-integration 20-noded brick elements, hereafter termed FIBRICK and RIBRICK, respectively. Foreach type of element, two different cases were studied. In the first case, one elementwas used to model the whole length of cantilever beam. In the second, the cantileverwas modelled using 18 elements of equal length. For the quadrilateral elements, theelement aspect ratios for the 1- and 18-element representations are 1:70.5 and 1:3.9,respectively.Fig. 1a compares the deflected shape computed using 32-bit precision with the

theoretical value from Euler–Bernoulli beam theory. As can be seen, all of the 8-noded quadrilateral representations show significantly smaller deflection than thetheoretical value. The only representations that come close to the theoretical valueare predictably, those using beam elements. Fig. 2a shows the correspondingbending moment profiles obtained from the various representations. For beam ele-ments, the bending moment profile was interpolated from the integration pointvalues using a spline function. For quadrilateral elements, the bending momentswere evaluated using the method suggested by Rahim and Gunn [21]. As can beseen, the discrepancy in the deflection is also reflected in the bending momentprofiles.Figs. 1b and 2b show the corresponding deflected shapes and bending moment

profiles computed using 64-bit precision. As can be seen, a dramatic improvement inaccuracy is now achieved in deflection and bending moment in the 18-elementquadrilateral representations. On the other hand, both 1-element quadrilateralrepresentations show little or no improvement in accuracy. In summary, flexuralbehaviour of the cantilever is well represented by single and multiple beam elements,in both 32- and 64-bit precision. The 18-element quadrilateral representations ade-quately represent the cantilever behaviour if they are used with 64-bit precision. Inpractice, this is unlikely to be a major constraint since 64-bit precision may be nee-ded, in any case, to capture the large difference in stiffness between soil and pile [16].Between the two 18-element quadrilateral representations tested, the RIQUADrepresentation produces a smoother bending moment profile whereas the FIQUADrepresentation produces a rather jagged bending moment profile. The 1-elementquadrilateral representations are unable to adequately replicate the deflection andbending moment profiles, regardless of whether 32- or 64-bit precision is used. Inother words, the representations which model cantilever flexure well are the beamelement and the RIQUAD element with 64-bit precision. Fig. 3 shows the effect ofusing different number of RIQUAD elements, and therefore aspect ratios. As can beseen, reasonably good bending moment representation can be achieved for aspectratio less than about 14. Figs. 4 and 5 shows the corresponding deflection andbending moment plots for the 3D representations. As can be seen, the performancetrends of the various 3D representations closely mirror those of their 2D counter-parts, with the beam elements being the most reliable and the FIBRICK elementbeing the least.


In soldier-piled excavations, the soldier piles not only act in flexure but also attractearth pressures from the retained soil. Although this phenomenon is not modelled,and thus irrelevant, in 2D analyses, it is relevant to a 3D analysis wherein soldierpiles and timber laggings are modelled explicitly. In this section, the ability of thebeam and brick representations of the soldier piles to capture the interactionbetween pile and soil in a 3D analysis will be studied using a typical section of anidealized unstrutted, soldier-piled excavation shown in Fig. 6. As can be seen, thechosen section consists of one half-soldier pile and the ground in front of and behindit. The soldier piles are modelled using 64-bit precision and are spaced at an intervalof six times the width of the soldier pile, center-to-center. In this analysis, the outercross-sectional dimensions and flexural rigidity EI of the soldier are based on theproperties of the 610 mm�305 mm�149 kg/m H-pile [22]. The outer cross-sectionaldimensions are only simulated in the RIBRICK elements, not beam element. Nodeson the four vertical faces of the mesh are only allowed to move in-plane. The bottomface is fixed in all directions. Timber laggings are not modelled, as the objective ofthis exercise is to study the ability of various soldier pile representation to model thepile-soil interaction. Soil Layer 1 is underlain by Layer 2 at 22.5 m depth to modelthe increasing stiffness of real ground. Each soil layer is assumed to be elastic anduniform. The soldier pile is socketed 1.5 m deep into Layer 2. A Poisson’s ratio of0.02 is used for RIBRICK soldier pile elements as pure bending behaviour is only

Fig. 6. Locations of beams and linear strain bricks for modelling soldier piles in the finite element model

of an idealistic excavation. (a) Plan view of beam element as soldier pile in section A–A. (b) Plan view of

RIBRICK element as soldier pile in section A–A. (c) Cross-sectional view in x–y plane of the FEM model.

(d) Soil layers, struts and excavation levels.


achieved if Poisson’s ratio is zero [23]. The properties of the soldier piles and soil areshown in Table 1.The soldier pile is assumed in-place at the start of the analysis. The excavation pro-

cess is assumed to occur in three lifts with pore pressure dissipation being modelledusing the Biot’s [24] consolidation formulation. The final depth of excavation is 11.5 m.As shown in Fig. 7a, the solid and beam elements give similar results and the dif-

ferences appear to be minor. The differences are more clearly reflected in Fig. 7b,where the bending moment of the solid elements is clearly larger than that of thebeam element, although the differences are still not substantial. This can be attrib-uted to the finite cross-sectional dimensions of the RIBRICK element, whichenables it to attract a larger proportion of the earth pressure through the archingprocess than the beam elements.Fig. 8 shows the local deflection of soldier pile and soil face, in plan view, at 9 m

depth below ground surface. As can be seen, the differential movement between pileand soil is clearly larger with the beam representation than the RIBRICK repre-sentation of the soldier pile. Furthermore, as shown in Figs. 9a and b, although thedevelopment of stress arch in the soil is evident in both representations, the localstress distribution is very different. The brick representation results in a much higherconcentration of stresses in the vicinity of the soldier pile than the beam repre-sentation, owing to its finite dimensions. In addition, the stress arch spans over ashorter distance but extends deeper into the retained soil in the case of the brickrepresentation. This allows the soil movement to be better coupled to the pile

Table 1

Idealised soil and soldier pile properties for beam and brick soldier piles study

Soil layer 1 (depth: 0–22.5 m) �s=19.5 kN/m3

Elastic E=50 000 kN/m2

�=0.3

K0=0.94

kx=1.0�10�9 m/s

ky=1.0�10�9 m/s

Soil layer (depth: 22.5–37 m) �s=19.5 kN/m3


�=0.3

kx=1.0�10�9 m/s

ky=1.0�10�9 m/s

Half soldier pile modelled with beam at 6B pile spacing E=1�108 kN/m2

Ixx=1.259�10�3 mm4

Iyy=9.308�10�5 mm4

�=0.29

A=0.019 m2

Half-soldier pile modelled with RIBRICKs at 6B pile spacing (610�152.5 mm) E=4.36�107 kN/m2

�=0.02

G=2.14�107 kN/m2


movement than the beam representation. Thus, although a beam element is slightlymore accurate in replicating the flexural behaviour of the soldier pile, local pile-soilinteraction is better represented using solid elements. For this reason, subsequent3D analyses discussed herein will model the soldier piles using reduced-integration20-noded bricks with 64-bit precision, unless otherwise stated.

3. Comparison with case history

In this section, a comparison is made with O’Rourke’s [3] field measurement of a18.3 m-deep braced excavation in the G Street test section (Panel 158). Fig. 10 shows

Fig. 8. Plan view of lateral deflection retaining system 9 m depth after final excavation stage.

Fig. 7. (a) Deflection profile of soldier pile and soil at the center between adjacent piles. (b) Bending

moment profile of soldier piles.


Fig. 9. Lateral stress contours for at 9.3 m below ground level for excavation to 11.5 m. (a) Beam soldier

pile elements. (b) RIBRICK soldier pile elements.

Fig. 10. Plan view of retaining system after O’Rourke (1975).


the plan view of the retaining system. The modelled geometry and excavationsequence follows closely that of O’Rourke’s. Fig. 11 shows the 2D and 3D FEmeshes used in the current analyses. The 2D mesh follows that of O’Rourke’s, whilstthe 3D mesh is merely an ‘‘extrusion’’ of the 2D mesh in the third dimension.Fig. 11 shows the soil parameters from O’Rourke [3], which were adopted in this

comparative study. Since O’Rourke only presented total stress parameters, only atotal stress analysis was performed. Furthermore, following O’Rourke, theDrucker–Prager soil model is used for all soil layers.In the 2D analysis, the soldier pile wall was modelled using beam elements with a

‘‘smeared’’ wall stiffness derived by scaling the bending stiffness of individual soldierpiles over the distance separating them and neglecting the effects of the timber lags;this also follows O’Rourke’s [3] procedure. In the 3D analyses, the soldier piles andtimber lags are modelled using RIBRICK elements, the properties of which areshown in Table 2. The soldier pile properties were derived from the section proper-ties of the 24 WF 100 H-piles used in the excavation. Less is known about the timberlags apart from the fact that they were made from oak wood. Back-calculation usingBS8002 [6] guidelines and AITC [25] suggest that the required thickness of the tim-ber lags is likely to be about 100 mm, which falls within the common range of timberlagging thickness [2]. Because of the uncertainty over the thickness of the timberlagging, the analysis was repeated with timber lagging thickness of 50 and 100 mm.Since timber lagging is normally installed in the form of long, narrow planks slotted

Fig. 11. Finite element mesh used for reality check with O’Rourke (1975).


horizontally in between the flanges of the soldier piles [2,6], the flexural rigidity ofthe timber lagging to bending in the vertical direction is likely to be very small. Tomodel this behaviour, an anisotropic elastic material model is used for the timberlagging, with the Young’s modulus in the vertical direction being set much lowerthan that in the horizontal direction, Table 2. This differs from Briaud and Lim’s[15] analyses which used isotropic shell elements to model the timber lagging. The

Fig. 12. Comparison of a series of 2-D and 3-D analyses from O’Rourke (1975). (a) Soldier pile deflec-

tion. (b) Bending moments.

Table 2

Idealised soil and soldier pile properties for O’Rourke’s case study

Soldier piles E (kPa) � Ghv (kPa)

5.09�107 0.02 2.5�107

Struts E (kPa) Ixx (m4) Iyy (m

4) Area (m2)

Level 1 (36 WF 260) 1�108 0.0072 4.54�10�4 0.0623

Level 2 1�108 1.19�10�6 1.19�10�6 0.0296

Level 3 1�108 0.55�10�6 0.55�10�6 0.0238

Level 4 1�108 1.19�10�6 1.19�10�6 0.0296

Level 5 1�108 1.19�10�6 1.19�10�6 0.0296

Timber lagging Eh (kPa) Ev (kPa) �hh ��h Gh� (kPa)

12�103 1 0.02 3�10�13 0.3676


braces and walers were modelled using beam elements, with properties adjusted toreplicate those in the field.Fig. 12a compares the computed wall deflection to the O’Rourke’s measured final

deflection. As can be seen, all the computed deflections agree reasonably well withone another and with the field measurements. The same can be said of the bendingmoment diagrams in Fig. 12b. This indicates that the results of the FE analyses arereasonably realistic. Nonetheless, it is interesting to note that the 3D FE analysispredicts a slightly larger maximum soldier pile deflection than the 2D analyses; inspite of the fact that the ‘‘smeared’’ stiffness of the soldier pile wall in the 2D ana-lysis does not take into account the contribution from the timber lagging. In otherwords, if the 3D analysis is taken as a reasonably accurate representation of reality,then the wall deflection from the 2D analysis represents an optimistic, rather thanaverage, estimate of the soldier pile and timber lagging deflection. The reason forthis will be examined in greater detail later.Fig. 13a–c show the deflection profiles leading to at various excavation levels. As

can be seen, more substantial differences between measured and predicted walldeflection are present in the earlier stages. This may be attributed to the fact that soilbehaviour is not truly linearly elastic prior to yielding. The lower strain levels whichare incurred in the early stages could have allowed higher soil stiffness to be mobi-lised than in the final stages. The timber lagging thickness of 50 and 100 mm leads tonearly the same result, thus indicating that the results are not heavily contingentupon the assumed thickness of timber lagging. In both cases, the computed deflec-tion of the timber lagging is significantly larger that that of the soldier piledeflection. This is to be expected, since the timber lagging is much more flexible than

Fig. 13. Deflection of soldier pile and soil at midspan with respect to excavation sequence. (a) Excavation

depth at 6.1 m. (b) Excavation depth at 11.9 m. (c) Excavation depth at 18.3 m.


the soldier piles and thus expected to deflect more. In other words, significantdifferences can arise between the soldier pile deflection and that of the interveningsoil.Fig. 13 also shows that, just below excavation level, there is a short segment of the

soldier pile which moves ahead of the soil. This is to be expected; the soldier pilewall is not a continuous wall below excavation level. The presence of soil betweenadjacent soldier piles allows the piles to move relative to the intervening soil; thismovement being accentuated if the soil yields. In 2D analysis, the discontinuousnature of the wall cannot be modelled since a uniform wall with a reduced‘‘smeared’’ stiffness is assumed instead. This suppresses the relative pile-soil move-ment, thus exaggerating the degree of rotational fixity afforded by the pile embed-ment. As shown in Fig. 14, using a ‘‘smeared’’ stiffness for the soldier pile and theintervening soil in a 3D analysis leads to a deflection profile that is virtually identicalwith that from a 2D analysis, thus indicating that the difference in deflectionbetween 2D and 3D analyses noted earlier arises from the representation of the non-uniform stiffness of the soldier pile and intervening soil.It is interesting to note that the S-profile present in O’Rourke’s field data was not

predicted in the FE analyses. One possible reason for this is the high values ofcohesion and friction angle prescribed by O’Rourke [3] for the top layers of soil.O’Rourke reported significant variation in the modulus of the Upper Brown sand

Fig. 14. Effect of ‘smearing’ on rotational fixity below excavation level.


from about 41 to about 97 MPa. This is suggestive of significant variation in soilproperties with location, which is not considered in the analysis wherein uniform soilproperties are assumed. As shown in Fig. 15, progressive reduction in c and � valuesdoes lead to an S-shape soldier pile deflection profile.

4. 3D and 2D comparisons

4.1. Idealised excavation

The complexity of the soil profile and multi-level bracing at the G Street excava-tion renders an in-depth study of pile-soil interaction difficult. For this reason, theidealized excavation involving two levels of bracing in a single soil type is studied, asshown in Fig. 6. To enhance the long-term stability of the soil face, 3-inch thicktimber laggings were modelled. As can be seen, the two levels of bracing were pre-scribed at 4.5 and 7.5 m below the original ground level. Boundary conditions aresimilar to those used in the back-analysis of the G Street excavation. Initialgroundwater table is assumed to be 2 m below original ground level, this being atypical groundwater table depth in Singapore conditions. The corresponding 2Dmesh is not shown since it is merely a vertical section of the 3D mesh.

Fig. 15. Modelling the S-shaped deflection profile of the soldier pile in 3D.


Table 3

Idealised soil and soldier pile properties for idealised study

Soil layer 1 (depth: 0–22.5 m) �S=19.5 kN/m3

Modified Cam-clay cc=0.1

cS=0.01

M=1.2

ecs=1.47

�=0.3

K0=0.94

Soil layer 2 (depth: 22.5–37 m) �S=19.5 kN/m3


�=0.3

Timber lagging at 3 in thickness Eh=16.3�103 kN/m2

Elastic E�=1 kN/m2

�hh=0.02

�vh=2.2�10�5

Ghv=0.37 kN/m2

Soldier pile modelled with 2D beam element E=1.09�108 kN/m2

Ixx=1.259�10�3 mm4

�=0.29

A=0.019 m2

Half soldier pile modelled with RIBRICK at E=2.18�107 kN/m2

3B pile spacing (610�152.5 mm) �=0.02

G=1.07�107 kN/m2

Half soldier pile modelled with RIBRICK at E=4.36�107 kN/m2

6B pile spacing (610�152.5 mm) �=0.02

G=2.14�107 kN/m2

Strut at 3.75 m spacing modelled with beams E=2.67�107 kN/m2

Level 1 at 165.0 kN/m Ixx=1.259�10�3 mm4

Level 2 at 441.1 kN/m �=0.29

A=0.019 m2

Half strut with stiffness equivalent to 3.75 m E=1.22�107 kN/m2

spacing modelled with beams for cases of Ixx=1.259�10�3 mm4

3B pile spacing Iyy=9.308�10�5 mm4

Level 1 at 75.5 kN �=0.29

Level 2 at 201.8 kN A=0.019 m2

Half strut with stiffness equivalent to 3.75 m E=2.44�107 kN/m2

spacing modelled with beams for cases of 6B pile spacing Ixx=1.259�10�3 mm4

Level 1 at 151.0 kN (30–60%) Iyy=9.308�10�5 mm4

Level 2 at 403.6 kN (40–70%) �=0.29

A=0.019 m2

Note: Walers are assumed to be sufficiently stiff and able to distribute the load evenly to all soldier piles

and thus not modelled in the idealized analyses.


Table 3 shows the properties of soil and structural components used in the ana-lyses. The analyses conducted are effective stress analyses and the soil propertiesprescribed are representative of granitic sapprolites. Such geologic material occurswidely in Singapore [26] and can be described as a silt of intermediate or high plas-ticity [27]. Soldier piles have been used as a retaining system in such soils [28]. Themodified Cam Clay model is used to describe the behaviour of the soil skeleton sinceit allows soils with different over-consolidation ratios (OCRs) to be modelled whilerequiring relatively few parameters compared to other, more complex models. Thelack of detailed information about the soil to be modelled does not justify the use ofmore sophisticated models in such an idealized study.Fig. 16 shows the excavation and wall installation sequences of the idealized

excavation. For the non-preloaded cases, the preloading stage is simply omitted inthe analyses. As shown in Table 4, the effects of preloading and centre-to-centreinter-pile spacing on the discrepancy between 2D and 3D analyses are examined.

Fig. 16. Construction sequence for idealized excavation from stage A through G.

Table 4

Summary of effective stress analyses for the idealised excavation at OCR=3 and k=1�10�8 m/s

Analysis Geometric representation Preloading

2D-1 Plane strain No

2D-2 Plane strain Yes

3D-1 3B No

3D-2 6B No

3D-3 3B Yes

3D-4 6B Yes

Note: B is the width of the soldier pile.


4.2. Wall deflection

Fig. 17 compares the 2D and 3D computed wall deflection profiles for the non-preloaded soldier piles at the final stage of construction. As can be seen, for inter-pile spacings of 3 and 6 times the soldier pile width B, the 3D analyses predictslightly larger maximum soldier pile deflection than the 2D analysis, this being con-sistent with the trend indicated for the G-Street excavation. The deflection profile atthe mid-span of the timber lagging is more variable. For an inter-pile spacing of 3B,the timber lagging deflection remains reasonably well coupled to the soldier piledeflection. For an inter-pile spacing of 6B, the timber lagging deflection becomesmuch larger than the soldier pile deflection. It should be noted that an inter-pilespacing of 6B is not unrealistic; in the G-Street excavation [3], the inter-pile spacingwas approximately 6.5. Comparison of the soldier pile and timber lagging deflectionprofiles shows that, above excavation level, the mid-span deflection is larger than thesoldier pile deflection, which is consistent with the fact that the soldier pile is sup-porting the soil face through the timber lagging and the soil arch spanning acrossadjacent piles. On the other hand, the reverse is the case just below excavation level.This occurs because, whereas the soil face at the mid-span can adopt rather sharp

Fig. 17. Comparison of wall deflection between 2D and different pile spacing for cases without preloading

at final stage of construction.


curvature, the soldier pile cannot, owing to its much higher flexural stiffness. Thus,soldier pile deflection can only decrease gradually below excavation level therebyresulting in higher deflection in the pile than the mid-span soil. This is similar to the3D FE results on the deflection of pile groups adjacent to surcharge, reported byBransby and Springman [29].

Fig. 18. Comparison of wall deflection between 2D and different pile spacing for cases with preloading at

final stage of construction.

Fig. 19. Comparison of effects of preloading on wall deflection for 3D-4 at 4.5 m below ground level with

stages B, C and D shown in Fig. 16.


Fig. 20. Location of stress paths plotted for soil behind first level of strut at 4.22 m below ground level in

x–z plane.

Fig. 21. Stress path plot for 2D-1 without preload. Stages A–G are shown in Fig. 16. Units of stresses in

kPa.


Fig. 18 shows the wall deflection profiles of the preloaded cases at the final stageof construction. As can be seen, preloading pushes the soldier pile backwards intothe retained soil, this combining with the excavation below strut level to produce theS-shape profile that is also present in O’Rourke’s measurement, but not in theidealised non-preloaded case discussed in the previous section. Fig. 19 compares thedifferences in deflection at the excavation face 4.5 m below ground level before andafter preloading. As shown in Fig. 16, in stage B, excavation just reaches a depth of4.5 m. At this point, the deflection of the soldier pile is larger than that of theintervening soil, owing to the large flexural stiffness of the wall, as discussed earlier.In stage C, the process of preloading pushes soldier pile and the soil rearwards, butwith the soldier pile displacing more. Subsequent excavation (stage D) allows thesoil to move forward more than the soldier pile as the latter is restrained by the strutand waler system.

4.3. Stress changes

This interaction between soil and soldier pile is illustrated in Figs. 21–26, whichshow the stress paths for two points in the retained soil at the upper strut level,

Fig. 22. Stress path plot for 2D-2 with preload. Stages A to G are shown in Fig. 16. Units of stresses

in kPa.


which is located at a depth of 4.22 m below ground surface. As shown in Fig. 20,one point (marked I) is located just behind a soldier pile whereas the other (markedII) is located just behind the mid-span of the timber lagging. Results for a corre-sponding point at the same depth from a corresponding 2D analysis are also plottedfor comparison. The deviator stress q is strictly a positive quantity. In Fig. 21, amodified quantity q̂ is instead plotted, such that

q̂ ¼�’y � �’x� �

�’y � �’x�� q ð1Þ

where �x0 and �y

0 are the horizontal and vertical effective stresses. The use of q̂ inplace of q allows an active stress state (�y

0>�x0) to be distinguished from a passive

stress state (�x0>�y

0).As Fig. 21 shows, for the 2D analysis, initial excavation leads to an increase in

mean effective stress due to the drag from the soil flow above the monitored point.However, this quickly faded away as the formation level approaches the monitoredlevel (end point B) and lateral effective stress starts to decrease. Meanwhile, q con-tinues to increase as shear stresses builds up in the retained soil. Further excavation

Fig. 23. Stress path plots for 3D-1 and 3D-2 at point I without preload. Stages A–G are shown in Fig. 16.

Units of stresses in kPa.


below the formation level leads to a reversal in the sign of q̂ (end point D) as thelateral stress falls below the vertical stress, leading to an active stress state. Com-parison of Figs. 21 and 22 shows that preloading causes the stress state to remain ina passive, rather than active, state throughout the entire construction sequence,thereby eliminating the passive–active reversal predicted for the unpreloaded case.As Figs. 23 and 24 show, the initial stress changes behind the soldier pile (point

I) and the timber lagging (point II) are similar to that of the 2D prediction inFig. 21. At both locations, initial excavation leads to an increase in mean effectivestress and a passive stress state due to the drag from the soil flow above the mon-itored point. As excavation approaches the monitored level, the release in lateralstress due to soil removal in front of the wall leads to an active stress state (endpoints B and C). However, further excavation below the first strut level producesvery different stress paths at the two monitored locations. As shown in Fig. 23, thebuild-up of lateral stress at the base of the soil arch between adjacent soldier pilesresults in a passive stress state, which persists up to the end of the constructionsequence. On the other hand, as negative pore pressure in front of the soil arch dis-sipates, the effective stress in the soil behind the timber lagging decreases as the soilapproaches a state of incipient active failure at the end of the construction sequence.

Fig. 24. Stress path plots for 3D-1 and 3D-2 at point II without preload. Stages A–G are shown in Fig. 16.



In physical terms, this suggests significant softening of the soil behind the timberlagging. These stress path differences are accentuated as the soldier pile spacingincreases from 3B to 6B.Comparison of Figs. 25 and 26 with Figs. 23 and 24 shows that preloading does

not have the significant effect that it has on the 2D analysis. The only significancechanges that arise from preloading occur behind the soldier pile and consist of anearlier reversal back to a passive stress state (before end point C) and a slightly lar-ger mean effective stress at the end of the construction sequence. Both of these aredirectly attributable to the preload. There is no significant difference at location II.Comparison of Fig. 21 with Figs. 23 and 24 as well as Fig. 22 with Figs. 25 and 26

shows that, at any given end point, the stress state predicted by the 2D analysisappears to lie somewhere between those of locations I and II in the 3D analysis. Thisis not surprising in view of the fact the retaining effect of the soldier pile and timberlagging is ‘‘smeared’’ in a 2D analysis. The large changes in the 2D stress pathsbetween Figs. 21 and 22 appears to be due to the fact that ‘‘smeared’’ stress path ofthe 2D analysis is affected by the small variations in the strongly divergent stressstates of the two locations.

Fig. 25. Stress paths plots for 3D-3 and 3D-4 at point I with preload. Stages A–G are shown in Fig. 16.



5. Conclusions

Strutted excavations, including soldier-piled excavations, are often analysed using2D FE analyses with properties that are averaged over a certain span of the wall.The foregoing discussion shows that when such an approach is applied to soldier-piled excavations, modelling errors can arise in several ways. Firstly, by modellingthe discrete soldier piles as a wall, a 2D analysis tends to over-predict the coupling topile to the soil below excavation level. In instances where the pile is not embeddedinto stiff soil, this modelling error can give rise to discernible underestimation ofsoldier pile deflection. Secondly, the deflection of the timber lagging, which isusually larger than that of the soldier piles, is often underestimated. Thirdly, a 2Danalysis cannot replicate the differences in stress paths taken by the retained soil atdifferent locations at the same depth. In particular, it cannot model the softening ofthe soil face just behind the timber lagging. In instances where the timber lagging isinsufficient or its installation, this softening can give rise to local collapse, whichmay exacerbate the ground loss and therefore ground movement. Increasing theinter-pile spacing will tend to accentuate the effects of these modelling errors.

Fig. 26. Stress paths plots for 3D-3 and 3D-4 at point II with preload. Stages A–G are shown in Fig. 16.



Acknowledgements

The first author would like to acknowledge the research scholarship and scholar-ship augmentation provided by the National University of Singapore and Econ Pil-ing Pte. Ltd., respectively. The equipment and software support provided by theCentre for Soft Ground Engineering at the National University of Singapore is alsogratefully acknowledged.

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