Prediction and Interpretation of the Performance of a Deep ......plex elastoplastic soils (MIT-E3: Whittle and Kavvadas 1994; MIT-S1: Pestana and Whittle 1999) and have demonstrated

Prediction and Interpretation of the Performance of a DeepExcavation in Berlin Sand

Maria A. Nikolinakou, M.ASCE1; Andrew J. Whittle, M.ASCE2; Stavros Savidis3; and Ute Schran4

Abstract: This paper describes the application of a generalized effective stress soil model, MIT-S1, within a commercial finite-elementprogram, for simulating the performance of the support system for the 20-m-deep excavation of the M1 pit adjacent to the primary station“Hauptbahnhof” in Berlin. The M1 pit was excavated underwater and supported by a perimeter diaphragm wall with a single row ofprestressed anchors. Parameters for the soil model were derived from an extensive program of laboratory tests on the local Berlin sands.This calibration process highlights the practical difficulties both in the measurements of critical state soil properties and in the selection ofmodel parameters. The predictions for excavation performance are strongly affected by the vertical profiles of two key state parameters: theinitial earth pressure ratio, K0; and the in situ void ratio, e0. These parameters were estimated from field dynamic penetration test data andgeological history. The results showed good agreement between computed and measured wall deflections and tieback forces for threeinstrumented sections. Much larger wall deflections were measured at a fourth section and may be attributable to the spatial variabilityin sand properties that was not considered in the current analyses. The results of this study highlight the importance of basic state parameterinformation for the successful application of advanced soil models. DOI: 10.1061/(ASCE)GT.1943-5606.0000518. © 2011 AmericanSociety of Civil Engineers.

CE Database subject headings: Excavation; Germany; Constitutive models; Deformation; Finite element method; Diaphragm wall;Instrumentation.

Author keywords: Constitutive model; Deformation properties; Finite element analysis; Diaphragm wall; Field instrumentation.

Introduction

Although finite-element analyses are routinely used in the design ofexcavation support systems and the interpretation of measured fieldperformance, their predictive accuracy is often quite limited (e.g.,Carter et al. 2000). In many cases, the analyses use simplified soilmodels or measurements from which to calibrate model parametersare unavailable. The geotechnical group at the MassachusettsInstitute of Technology (MIT) developed a series of relatively com-plex elastoplastic soils (MIT-E3: Whittle and Kavvadas 1994;MIT-S1: Pestana and Whittle 1999) and have demonstrated theirapplication for a number of well-instrumented excavation projectsin clays (e.g., Whittle et al. 1993; Hashash and Whittle 1996, 2002;Jen 1997). In each of those projects, the numerical analyses weresupported by site investigation and laboratory testing programssuch that model parameters were well-calibrated and the role ofthe soil model clearly identified.

This paper follows a similar approach for simulating the perfor-mance of a deep excavation in sand. The effective stress-strain-strength properties of the sand were simulated by using the MIT-S1model that had been integrated within the commercial finite-element program Plaxis. The MIT-S1 model incorporates a voidratio as a separate state variable, in addition to the state of stress,to simulate characteristic transitions from a dilative to a contractiveresponse associated with increases in the formation void ratio and/or confining stress. The model also uses a new framework for de-scribing the compression behavior of soils on the basis of the exist-ence of the limiting compression curve (LCC) (Pestana and Whittle1995), which provides the means for unifying the behavior of claysand sands within a single constitutive framework.

Model input parameters were calibrated through an extensiveprogram of laboratory compression and triaxial shear tests on spec-imens of sand (Glasenapp 2002; Becker 2002) that were obtainedfrom an excavation site in central Berlin (Savidis and Rackwitz2004). The M1 site is one of a series of excavation pits that wereused for the underground construction of a new multimodal trans-portation corridor through the center of Berlin, collectively referredto as the VZB project—Verkehrsanlagen im Zentralen Bereich.Fig. 1 shows that the M1 excavation pit is located to the northof the recently completed Lehrter Bahnhof station (Mönnich andErdmann 1997). The Berlin sands were found to be very differentfrom the sands on which MIT-S1 was initially applied. This paperdescribes the challenges encountered in an independent modelcalibration for the Berlin sands and documents calibration ap-proaches different than those initially established by Pestana(1994; Pastana et al. 2002). The model predictions were then com-pared directly with the field monitoring data, and parametric cal-culations were performed to understand the factors influencing walldeflections and tieback forces.

1Research Associate, Bureau of Economic Geology, The Univ. ofTexas, Austin, TX 78713; formerly, Postdoctoral Associate, Civil andEnvironmental Engineering, Massachusetts Institute of Technology,Cambridge, MA 02139 (corresponding author). E-mail: [email protected]

2Dept. Head, Professor of Civil and Environmental Engineering,Massachusetts Institute of Technology, Cambridge, MA 02139.

3Professor and Director, Geotechnical Institute, Technical Univ. ofBerlin, Sek. TIB1-B7, Gustav-Meyer-Allee 25, 13355 Berlin, Germany.

4CDM Geotechnical Services Div., Cambridge, MA 02139.Note. This manuscript was submitted on June 16, 2009; approved on

February 2, 2011; published online on February 3, 2011. Discussion periodopen until April 1, 2012; separate discussions must be submitted for indi-vidual papers. This paper is part of the Journal of Geotechnical andGeoenvironmental Engineering, Vol. 137, No. 11, November 1, 2011.©ASCE, ISSN 1090-0241/2011/11-1047–1061/$25.00.

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The German Society for Geotechnics has used another of therecent excavation projects in Berlin as the basis for a benchmarkstudy to evaluate the accuracy of numerical analyses (Schweiger2002). In contrast to the current study, the benchmark program pro-vided minimal information on site-specific soil conditions or prop-erties and found a large scatter in numerical predictions accordingto the selection of constitutive models and stiffness parameters. In-deed, many of the 17 predictors used the same soil models, such asthe elastic-perfectly plastic, Mohr-Coulomb or Hardening Soil,integrated in the Plaxis software, but obtained widely varyingpredictions because of differences in the selection of model param-eters. The study highlighted that more refined experimental in-vestigations, including the measurement of stiffness at very smallstrains, should be employed to provide more reliable data fornumerical analysis (Schweiger 2002). This paper offers such acomplementary approach, providing a valuable database on Berlinsands and building the numerical model from laboratory measure-ments of the soil properties.

Site Characterization

The geology of the central area of Berlin is characterized by satu-rated deposits of quaternary age, reflecting three different glacialperiods (Savidis and Rackwitz 2004). The glacial sediments arehighly irregular in their horizontal and vertical distributions andalso vary widely in their composition, which consists of tills, sands,gravel, and boulder clays. The typical vertical profile at the M1 pit,Fig. 2(b), includes 3–4 m of fill overlying three primary sandy tillunits: (1) S0, upper Holocene sand, approximately 6 m with a lower1-m-thick organic soil unit, O; (2) S1 glacial sands from the latePleistocene period (Weichsel glaciation) that are typically 10 m

thick; and (3) S2 glacial sands from the early Pleistocene(Saale glaciation) that are encountered approximately 22 m belowthe ground surface. The characteristic engineering properties ofthese sand units have been reported by ArbeitsgemeinschaftUmweltgeologie und Geotechnik (GuD/DMT) (1994) and Borchertand Richter (1994), principally on the basis of empirical cor-relations from dynamic probing tests [DPH; after DeutscheForschungsgesellschaft für Bodenmechanik (Degebo) 1993].These correlations suggest design friction angles, ϕ0 ¼ 31, 34,and 37:5° for the S0, S1, and S2 units, respectively.

The local ground water table is located 2 m below the groundsurface. Given the high permeability of the surrounding sandy soils(i.e., in the range 10�3–10�4 m=s), underwater excavation wasconsidered the only practical construction method because dewa-tering would affect a large area, have a significant environmentalimpact, produce significant settlements, and potentially cause dam-age to historical buildings (Savidis and Rackwitz 2004). The M1excavation pit, shown in Fig. 2(a), is supported by a 1.2–1.5-m-thick, reinforced-concrete diaphragm wall that extends aroundthe perimeter of the site, measuring approximately 300 m longand 25 m wide. The wall panels extend to depths ranging from25 to 31 m, corresponding to toe embedments of 6.8–7.8 m belowformation level. The wall is supported by a single row of pre-stressed tieback anchors located 2–3 m below the ground surfacewith spacing ranging between 1.0 and 1.5 m. These are installedwith dip angles ranging from 25–35° and 8 m fixed (i.e., grouted)anchor lengths within the S1 or S2 sand units (free lengths rangefrom 26–40 m). Each tieback typically has eight or nine strands of ahigh-strength steel (i.e., grade 270) tendon.

After installing the diaphragm wall and tieback anchors, exca-vation was performed underwater by using a pontoon-mounted

Fig. 1. Partial plan of excavation pits for VZB project in Berlin showing area north of Spree River

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crane to an average final formation grade 20.2 m below the initialground surface. Before dewatering, the base of the excavation wassealed by a 1.5-m-thick underwater concrete slab supported by anarray of tension piles. The design for the M1 pit used a system of

H-piles installed by a vibratory driver and grouted to ensure a goodconnection with the surrounding sand (RI system). The installationof the RI piles produced significant additional movements of thediaphragm walls. Schran (2003) attributed this behavior, in part,to the presence of light cementation within the deeper S2 sand unit.This study focuses on the performance of the support system dur-ing the underwater excavation phase and does not deal directly withthe subsequent construction of the anchor piles or base slab. In ad-dition, the current analyses use properties of reconstituted sandsand therefore, do not resolve the possible role of cementationon wall movements. The performance of the excavation was moni-tored through a series of inclinometers installed within the dia-phragm walls [Fig. 2(a)] and the load cell measurements offorces in the tieback anchors. The uplift of the base slab waslater monitored with horizontal inclinometer tubes [Savidis andRackwitz 2004; Fig. 2(a)].

Soil Properties and Model Parameters

The effective stress-strain-strength properties for the three sandytill units were modeled by using the MIT-S1 model (Pestana andWhittle 1999) under the assumption that all three units had similarmaterial properties but differed principally in their in situ state (i.e.,stress conditions, void ratio, and stress history). The MIT-S1 for-mulation was built on the incrementally linearized theory of rate-independent elastoplasticity (e.g., Prévost 1978) and incorporatesvoid ratio as a separate state variable to describe peak frictionangles and dilation rates as functions of the in situ void ratioand effective stress state. The primary features of the model canbe summarized as follows:• Large-strain shearing is controlled by an isotropic, critical state

frictional failure criterion.• Shear behavior is described by a single anisotropic bounding

surface that is a function of the effective stresses and currentvoid ratio.

• The density hardening of the bounding surface is controlled bythe compression behavior of freshly deposited soils representedby the LCC (Pestana and Whittle 1995), whereas rotationalhardening accounts for the evolution of anisotropic properties.

• The small strain nonlinearity in shear and stress-strain res-ponses in unload-reload cycles is described through a perfectlyhysteretic formulation.The MIT-S1 model requires 13 material parameters to charac-

terize the behavior of freshly deposited, uncemented clean sands.Pestana et al. (2002) detailed the selection of these parameters forToyoura sand, a standard test material whose behavior has beenextensively documented in the literature over the last 25 years.For this material, model parameter selection was greatly facilitatedby the availability of high-quality laboratory test data includinghigh-pressure consolidation tests and extensive programs of triaxialshear tests.

No comparable test database was available for the Berlin sands;and hence, the authors initiated a laboratory test program on recon-stituted test specimens (Glasenapp 2002; Becker 2002). Sampleswere obtained from the VZB excavation pit M1 and were blendedand mixed to obtain an average set of physical properties (Table 1).

Berlin sand is a poorly graded, fine-medium sand with roundedparticles, which are associated with fluvio-glacial deposition.When compared with other natural sands of similar particle size,shape, and grading (e.g., Pestana and Whittle 1995) it is apparentthat Berlin sand exhibits very low formation void ratios (i.e., emax ¼0:59 and emin ¼ 0:39) and has a small range of formation condi-tions (Δe ¼ 0:20, Table 1).

Fig. 2. Site conditions and excavation support system at M1 pit: (a) siteplan with instrumentation and borehole locations; (b) typical verticalsection with lateral earth support system; particular details for eachcross section are summarized in Table 3 and are shown to scale incorresponding Figs. 13–19



The test program performed by Glasenapp (2002) included aseries of four one-dimensional (1D) consolidation tests that werecarried to high confining stresses to identify the parameters asso-ciated with the LCC used in the MIT-S1 model. Nineteen triaxialtests were also conducted on specimens formed at void ratiose0 ¼ 0:43–0:60 that were hydrostatically consolidated to effectivestresses σ0

c ¼ 100, 500, and 800 kPa and sheared in both undrainedand standard drained compression modes (CIUC and CIDC,respectively). A subsequent program of 16 triaxial shear tests,performed by Becker (2002), with e0 ¼ 0:43–0:57, σ0

c ¼ 100,800 kPa, used more refined testing procedures including reduced-friction end-platens and local strain measurements to enable themore reliable interpretation of large-strain, critical state conditionsand nonlinear stiffness properties at small shear strains.

Table 2 summarizes the input parameters used by the MIT-S1model together with their physical meaning and the values ulti-mately selected for Berlin sand. The following section provideadditional details about the parameter selection.

Compression Behavior

The MIT-S1 model assumes that sand specimens compressed fromdifferent initial formation densities approach a unique response at

high stress levels, referred to as the limiting compression curve. For1D compression tests, the behavior in the LCC regime is charac-terized by a linear relationship in the log½e� � log½σ0

v� space:

logðeÞ ¼ �ρc log�σ0v

σ0vr

�ð1Þ

where ρc = slope of the LCC curve; and σ0vr = vertical effective

stress at a reference void ratio, e ¼ 1:0.Fig. 3 shows data from four 1D compression tests on Berlin

sand, each from a different formation void ratio. The data clearlysupport the LCC concept, with slope ρc ¼ 0:34 and σ0

vr=pa ¼ 25:5,where pa is the atmospheric pressure. The reference pressure forBerlin sand is substantially smaller than expected from empiricalcorrelations on the basis of the mean particle size, d50, and angu-larity. For d50 ≈ 0:4 mm, the data compiled by Pestana and Whittle(1995) show σ0

vr=pa increasing from 30 for angular particles (e.g.,ground quartz) to 80 for rounded particles (e.g., Ottawa sand). Thisvery interesting observation echoes earlier findings of De Beer(1965) who suggested that Berlin sand is more sensitive to particlesplitting than those of other similar sand deposits, such as Molsand, and attributed this behavior to impurities in the particles.

The MIT-S1 model assumes that the compressibility parameter,ρc, is independent of the lateral earth pressure ratio, σ0

h=σ0v. How-

ever, a fixed spacing exists between the LCC regimes measured in1D (i.e., K0-LCC) and hydrostatic (i.e., I-LCC) compression. Themodel (Table 2) actually uses the reference mean effective stress,σ0r, corresponding to hydrostatic compression as an input param-

eter. Following Pestana and Whittle (1999), this can be obtainedfrom

σ0r

σ0vr¼

�1þ 2KONC

3

��1þ

�6α2

��1� KONC

1þ 2KONC

�2�

ð2Þ

where α2 ¼ 24sin2ϕ0cs=ð3� sin2ϕ0

csÞ2 ≤ 1.No direct measurements of the earth pressure coefficient

exist for compression of Berlin sand in the high-pressure LCCregime. Instead, the current analyses assumes K0NC ¼ 0:5, whichis consistent with empirical correlations (Jaky 1944), assuming a

Table 1. Physical Properties of Berlin Sand

PropertyTest

materialAverage Lehrter

Bahnhofa

Mineralogy Quartz and feldspar

Grain shape Rounded

Specific gravity of solids, Gs 2.65

Mean particle size, d50 (mm) 0.38 0.42

Coefficient of uniformity, Cuð¼ d60=d10Þ 3.0 3.1

Coefficient of curvature, Czð¼ d230=d10d60Þ 1.2 —Maximum void ratiob, emax 0.590 0.59

Minimum void ratiob, emin 0.389 0.40

Range of formation void ratios, Δe 0.201 0.19aTest data reported by Rackwitz (2003).bTests performed according to Deutsches Institut für Normung e.V. (DIN)18124 (1997).

Fig. 3. Comparison of predicted and measured 1D compressionbehavior of Berlin sand (measured data from Glasenapp 2002)

Table 2. Input Parameters for MIT-S1 Model

Parameter/symbol Physical contribution/meaning

Berlinsand

ρc Compressibility of sands at large stresses (LCC

regime)

0.34

σ0r=pa Reference stress at unit void ratio for conditions

of hydrostatic compression in the LCC regime

23.5

θ First loading curve in the transitional stress regime 0.25

h Irrecoverable plastic strain, OCa —K0NC K0 in the LCC regime 0.50

μ00 Poisson’s ratio at load reversal 0.28

ω Nonlinear Poisson’s ratio; 1D unloading stress path 1.00

ϕ0cs Critical state friction angle in triaxial compression 31:0°

ϕ0mr

p

Control the maximum friction angle as a function of

formation density at low effective stresses

12:5°

2.7

m Controls the cap geometry of the bounding surface 0.42

ωs Small strain (< 0:1%) nonlinearity in shear 4.0

ψ Rate of evolution of anisotropy; stress-strain curves 10

Cb Small strain stiffness at load reversal 950aParameter not needed in current study.



friction angle ϕ0cs ¼ 31° for shear strength at high confining

pressures (Table 2). Substituting into Eq. (2), σ0r=σ0

vr ≈ 0:92 andσ0r=pa ¼ 23:5.The MIT-S1 model introduces a parameter, θ, to describe the

progressive breakage of particles as specimens are compressed.Larger values of θ cause a more gradual transition to the LCCregime; whereas low values of θ represent materials with well-defined yield points associated with particle breakage (typically ob-served in tests on very uniform materials such as glass ballotini).Fig. 3 shows that the measured compression behavior of Berlinsand is well represented by θ ¼ 0:25. This is consistent with theexpected behavior from empirical correlations between θ and theuniformity coefficient; θ≈ 0:1 Cu ≈ 0:3 for rounded particles, pre-sented by Pestana and Whittle (1995, 1999).

Small Strain Stiffness Properties

The model parameters μ00 and Cb define the elastic Poisson’s ratio

and bulk modulus that control the stiffness of sand immediatelyupon load reversal (Pestana 1994):

Cb ¼Kmax

pa

�e

1þ e

��σ0

pa

��1=3ð3a Þ

where e = void ratio; σ0 = mean effective stress; and Kmax = smallstrain elastic bulk modulus. The small strain elastic shear modulus,Gmax, can then be derived from Cb and μ0

0:

2Gmax

Kmax¼ 3ð1� 2μ0

0Þ1þ μ0

0ð3b Þ

The model parameters Cb and μ00 were derived from local

strain measurements in the triaxial shear tests performed byBecker (2002).

The tangential elastic moduli and, hence, Poisson’s ratio duringunloading, are updated as a function of stress variations and aparameter, ω. This parameter captures the nonlinearity in the effec-tive stress paths during unloading (ω ¼ 0 would yield a linear re-lationship between K0 and OCR). In principle, ω can be interpretedfrom the unloading effective stress path in a rigid-walled, 1D com-pression device, requiring very precise measurements of lateralstresses, or through very accurate small strain measurements inboth vertical and radial directions during unloading in a triaxialcell. No such measurements were recorded for Berlin sand, andinstead, ω ¼ 1:0 was selected on the basis of the recommendationsof Pestana from typical data reported in the literature (Pestana et al.2005). This value yields nonlinearity in the effective stress patheven for OCR≈ 1:5. Nonlinear behavior at relatively small shearstrain levels (i.e., less than 0.1%) is controlled by a second param-eter ωs that, in principle, can be fitted to local strain data on modu-lus degradation.

Shear Behavior

In the previous formulation of MIT-S1 for Toyoura sand, Pestanaet al. (2002) tried to develop procedures that could provide theunambiguous estimate of the remaining six model input parametersas follows: (1) the large strain friction angle, ϕ0

cs, measured in eitherdrained or undrained shear tests; (2) the peak friction angle mea-sured in drained shear tests on dense specimens to enable theselection of parameters ϕ0

mr and p (Table 2); (3) the effective stresspaths in undrained shearing to enable the selection of parameters mand ψ; and (4) the small strain nonlinear stiffness used to define ωs.This approach also minimizes the need to measure critical stateconditions in the laboratory tests.

For Berlin sand, it has proven difficult to follow such a simpleprocedure because of the uncertainties in the critical state and thevariability in the peak friction angles, as shown in Figs. 4–6.

Fig. 4 shows typical drained shear tests on Berlin sand at threedifferent confining pressures and formation void ratio, e0 ¼ 0:51.As expected, the measured peak friction angle decreases with thelevel of confining pressure, and the three tests converge to a uniquestress ratio at large shear strains, corresponding to a friction angleof approximately 31°. This angle is assumed to be the critical statefriction angle in the MIT-S1 model (ϕ0

cs, Table 2), although it is notclear from the volumetric strain data if the samples have actually

Fig. 4. Effect of confining pressure on drained shear behavior of Berlinsand (measured data from Glasenapp 2002)

Fig. 5. Comparison of predicted and measured peak friction anglesin CIDC tests on Berlin sand (measured data from Glasenapp 2002;Becker 2002)



achieved critical state conditions (i.e., a zero rate of volumetricstrain) at the end of each test with shear strains exceeding 20%.

A relatively small range in peak friction angles was measured inthe CIDC shear tests (Fig. 5) (i.e., ϕ0

peak ¼ 32–40°), and significantvariability, up to 2°, among tests performed under nominally iden-tical formation conditions. The peak friction angles are lower thanwould be expected for other quartzitic sands, at a similar range ofconfining pressures and void ratios, as noted by De Beer (1965).Preliminary estimates indicated that the observed maximum fric-tion angles can be simulated by combinations of two model inputparameters, p ¼ 2–3 and ϕ0

mr ¼ 8–16°. Although values for p wereconsistent with previous data for other quartzitic sands, the rangefor ϕ0

mr was much lower than expected from previous studies (e.g.,Pestana et al. 2002).

The MIT-S1 model assumes that a unique critical state conditionexists for homogeneous shearing to large strains in the triaxial com-pression shear mode. The critical state in the triaxial modes ofshearing can be estimated in a closed-form (see Pestana et al. 2005)as a function of the three input parameters, p, ϕ0

mr , and m (i.e., thesame parameters affecting predictions of the peak friction angle). Inpractice, critical state conditions are rarely achieved in laboratoryshear tests on sands. Shear banding or strain localization commonlyoccurs in drained shear tests in which post-peak strain softeningoccurs concurrently with dilative volumetric strains, whereas un-drained shear tests often cavitate before reaching a steady state ofdeformation. The testing of Berlin sand was no exception, as shownin Fig. 6. The figure provides a symbolic interpretation of the endpoints measured in the triaxial shear tests. The arrowhead directionsindicate the proximity of the critical state in each test on the basis ofa subjective interpretation of the data. The size of these symbolsgives an indication of test quality. The results show a broad bandof possible locations for the critical state line defined from combi-nations of drained tests that either contract or dilate toward criticalstate, and undrained tests that generate positive or negative shearinduced pore pressures.

Fig. 6 also illustrates the role of the model input parameters inpredictions of the critical state for Berlin sand. The parameter mcontrols the location of the critical state at high pressures, nomi-nally for σ0 > 1 MPa, whereas p and ϕ0

mr both affect predictionsin the lower stress range. The final parameter set reported in Table 2(i.e., p ¼ 2:7, m ¼ 0:42, and ϕ0

mr ¼ 12:5°) provided the most con-sistent prediction of both the critical state conditions and the peakfriction angles in CIDC shear tests, as shown in Fig. 5. The modeltended to underestimate the measured peak friction angles at lowconfining pressures (i.e., σ0

c ¼ 100 kPa) but was in good agreement

with data for σ0c ¼ 500, 800 kPa. The computed critical state line

had a critical void ratio ecrit ¼ 0:6 (i.e., ecrit ≈ emax) at a loweffective stress (Fig. 6). According to Ishihara (1993), sands witha state index Isð¼ ½ecrit � e�=½ecrit � ecs�Þ < 0 will collapse duringundrained shearing with zero residual strength.

The final model input parameter, ψ, controls the rotationalhardening of the yield surface in MIT-S1 and, hence, characterizesthe evolution of anisotropic deformation and strength properties. Inprevious studies, ψ has been calibrated from the stress-strain re-sponse measured during undrained shearing to large strains. Forexample, Fig. 7 illustrates the selection of ψ for one undrained sheartest. The parameter has minimal effect on the predicted responseuntil the mobilized friction exceeds ϕ0

cs. For Berlin sand, a strongcross-coupled effect of ψ with ωs exists, which was not previouslyfound for Toyoura sand. Fig. 8 shows that ωs has a very similareffect as ψ on the undrained stress-strain response at large shearstrains and also influences the initial effective stress path.

Fig. 9 compares the model predictions for ψ ¼ 10 and 25with the measured shear stress-strain behavior from CIDC testson Berlin sand consolidated to σ0

c ¼ 800 kPa from different forma-tion void ratios. Although the results show that the model tends tounderestimate the initial shear stiffness and peak shear resistance ofthe densest specimens (i.e., e0 ¼ 0:462, 0.491), the general trendsin behavior were well described by the model with ψ ¼ 10 andother input parameters listed in Table 2.

Initial Soil State Parameters

To apply MIT-S1 for simulations of excavation performance for theM1 pit, it is first necessary to establish the ranges of two key statevariables, e0, the in situ void ratio; and K0, the lateral earth pressurecoefficient at rest. No direct measurements of these parametersexist. The only in situ data are from dynamic probing (DPH) testsperformed in conjunction with the boreholes shown in Fig. 2(a).The DPH N10 blowcount data can be correlated with relativedensity, Dr:

Dr ¼ 0:23þ 0:38 logðN10Þ ð4ÞEq. (4) follows DIN 4094-3 (2002) and uses the laboratory val-

ues of emax and emin for Berlin sands (Table 1). Fig. 10 summarizesthe resulting profiles of the estimated void ratio from four typicallocations around the M1 pit [Fig. 2(a)]. Although the results doshow a trend of increased density with depth, considerable scatteris present in the estimated void ratio at any selected depth. The datasuggest that the upper sand unit, S0, is in a loose state with e0 ≈ 0:6(i.e., the upper 8 m), whereas the lowest unit, S2, is very dense withe0 ≈ 0:3–0:4; the intermediate unit, S1, has e0 ≈ 0:5–0:6. The au-thors have not found any clear spatial pattern in the data and, hence,assume the same void ratio profile in the analyses at each of theinstrumented sections.

The in situ K0 values should be strongly influenced by the geo-logical history. In principle, the heavily precompressed Pleistoceneunits (i.e., S1 and S2) can be expected to have higher values of K0than the recent Holocene unit, S0. On the basis of this reasoning,and in the absence of any direct measurements, the authors haveassumed default values K0 ¼ 0:5 and 1.0 for the S0 and S1/S2units, respectively.

An alternative method for estimating the void ratio is throughthe empirical correlations used for the mobilized friction angles ineach of the three sand units. According to GuD/DMT (1994),ϕ0 ¼ 31, 34, and 37:5° for the S0, S1, and S2 units, respectively.Assuming that these friction angles are to be correctly representedby the MIT-S1 model, a consistent set of in situ void ratios can be

Fig. 6. Interpretation of critical state conditions from triaxial shear testson Berlin sand



obtained from the model predictions relating the peak friction to thevoid ratio and effective confining stress (cf. Fig. 5). This procedureis illustrated in Fig. 11. The soil profile is approximated by the threesand units, ignoring secondary details such as the fill and organiclayers, as shown in Fig. 11(a). For the upper S0 sand, ϕ0 ¼ ϕ0

cs and,hence, e0 ≥ 0:6. For S1, the in situ stress ranges from 135 to265 kPa and, hence, e0 ¼ 0:51–0:53 is consistent with ϕ0 ¼ 34°.By a similar procedure, e0 ¼ 0:40–0:45 in S2. These results sug-gest higher in situ void ratios than those derived directly from DPHcorrelations (Fig. 10).

The MIT-S1 model simulates nonlinear stress-strain behaviorfrom small levels of shear strain. Fig. 12 illustrates the profileof the small strain shear modulus, Gmax, computed for the M1 siteon the basis of laboratory stiffness parameters and the assumedprofiles for K0 and e0 [Eqs. (3a) and (3b); Table 2]. These resultsare in very good agreement with well-known empirical correlationsfor Gmax of sands such as those proposed by Hardin and Richart(1963), which are also included in the recommendations of theGerman Society for Geotechnical Engineering (DGGT). In princi-ple, these results should match closely the values of Gmax from

Fig. 7. Calibration of parameter ψ from undrained shear test; ωs ¼ 4:0; Table 2 (measured data from Glasenapp 2002)

Fig. 8. Influence of parameter ωs on predicted undrained shear behavior; ψ ¼ 10; Table 2 (measured data from Glasenapp 2002)



measurements of the cross-hole shear wave velocity, vs, reportedin the preliminary site investigation work by GuD/DMT (1994).However, Fig. 12 shows that the cross-hole Gmax data are muchlower than expected. Indeed, the cross-hole values of Gmax wereactually lower than empirical estimates of the “reload modulus”used in the original wall design methods for the VZB pits. Thesource of this discrepancy is not known but the small strain stiffnessused by MIT-S1 is higher than the modulus values from the pre-vious empirical correlations in Berlin.

Numerical Model for M1 Excavation

The two-dimensional finite-element analyses of the M1 excavationpit were performed by using the commercial finite-element soft-ware, Plaxis. The MIT-S1 model was integrated within this codethrough a “user-defined” constitutive model interface. The analysesfocus on four half-sections through the excavation pit [all similar toFig. 2(b)] that correspond to the locations of inclinometers MQ2–MQ5 [Fig. 2(a)]. The characteristics of the cross sections are sum-marized in Table 3. The ground surface on the west side of the M1pit is 1.5 m lower than on the east side, and the excavation pro-gressed northwards. The final depth in MQ2 was reached more thana month after MQ4. The soil is represented by six-node plane strainelements, the tiebacks by using a combination of node-to-nodeanchor and “geotextile” elements for the free and fixed anchorlengths, respectively, and the diaphragm wall by using elasticMindlin-beam elements. The analyses assumed that the wall was“wished-in-place” and hence, did not consider local changes instresses or soil properties associated with trench excavation andconcreting. The analyses simulated the initial excavation to 30.5 m,followed by tieback installation and prestress, then by four stages ofunderwater excavation to the final formation level (no quantitativedata about the underwater excavation stages were available).

Results

Initial parametric analyses were performed assuming a uniform soilprofile (single sand unit) at a reference section, MQ3, to investigatethe effects of the in situ state parameters e0 and K0. Fig. 13 sum-marizes the measured wall deflections and tieback loads immedi-ately after prestress and at the final formation stage. The measureddata were compared with finite-element simulations for a constantvoid ratio (i.e., e0 ¼ 0:5) and three possible values of K0 ¼ 0:5,0.75, and 1.0. The results showed that higher K0 values generatedlarger wall deflections and anchor loads at the end of excavation.The measured data were within the midrange of the computedmaximum wall deflections (i.e., 1.5–2.8 cm) whereas the tiebackforce was in close agreement with results for K0 ¼ 1:0. However,the analyses generally underestimated the wall pull-back upon theinitial application of the prestress and overestimated deflections atthe top of the wall during excavation.

Fig. 14 shows a further set of calculations for a constant K0 ¼0:5 and three possible values of e0 ¼ 0:4, 0.5, and 0.6. The in situvoid ratio had a minimal effect on the wall deflections at prestressor on the values of the tieback force at the end of excavation. How-ever, wall deflections during excavation were very strongly influ-enced by e0. The maximum wall deflection increased from 1.0 to4.0 cm as e0 increased from 0.4 to 0.6. The movements at the topand toe of the wall were little affected by changes in e0 between 0.4and 0.5 and were generally in close agreement with the measureddata.

The parametric analyses highlighted the need to subdividethe vertical profile and corroborate the variation of state variables

Fig. 9. Effect of parameter ψ on MIT-S1 model predictions of CIDCtests on Berlin sand

Fig. 10. Estimated void ratio profile for M1 excavation; relativedensity (DIN 2002): Dr ¼ 0:23þ 0:38 logðN10Þ; N10 = DPHblowcount per 10 cm; and e� obtained from ðemin; emaxÞ in Table 1



discussed previously. A third set of analyses for MQ3, Fig. 15,considered a more realistic profile represented by three sand unitswith e0 ¼ 0:60, 0.53, and 0.40 and K0 ¼ 0:5, 1.0, and 1.0 in S0,S1, and S2, respectively. The overall pattern of predictions wasmuch improved for this case. The numerical analyses were in ex-cellent agreement with the movements at the top and toe of the wallat the final formation grade but underestimated the maximum walldeflection by 0.5 cm. The bending of the wall was much betterdescribed than in either of the two preceding sets of analyses withhomogeneous state variables. The model predicted very small sur-face settlements (i.e., up to 0.2 cm) in the retained soil, and 1.5 cmof heave below the base of excavation. Unfortunately no data wasavailable to evaluate those results.

Figs. 16–18 summarize further computations and measurementsfor three independent cross sections [i.e., MQ5, MQ4, and MQ2,respectively, cf. Fig. 2(a)]. Table 3 summarizes the differences inthe support systems and the excavation depths for each of thesesections.

Section MQ5, Fig. 16, is immediately opposite MQ3 but issupported with a thinner diaphragm wall section (i.e., 1.2 versus1.5 m), less steeply inclined anchor (i.e., 25 versus 35° dip angle)and lower prestress load. The measured data showed slightly highermaximum wall deflections (i.e., 2.7 versus 2.1 cm at MQ3) andmovements at the top of the wall (i.e., 1.1 versus�0:2 cm at MQ3)that were consistent with these differences in support conditions.The measured toe movements were almost the same at both MQ3and MQ5 (i.e., 0.3 cm).

Fig. 11. Selection of initial void ratio values for three-layered profile that uses predicted peak friction angles from calibrated MIT-S1 model

Fig. 12. Maximum shear modulus profiles over depth; Hardin andRichart (1963): Gmax ¼ AFðeÞσ0n where A = 6.9; n = 0.5; andFðeÞ ¼ ð2:174� eÞ2=ð1þ eÞ

Table 3. Properties of Excavation Support Structures at Inclinometer Locations

LocationExcavactiondepth (m)

Wall Tieback anchors

Thickness(m)

Height(m)

Spacing(m)

Free length(m)

Dip angle(°)

Number oftendons As (cm2=m)

Prestress(kN=m)

MQ2 23.30 1.5 31.05 1.0 40.0 38 10 18.15 400

MQ3 21.40 1.5 28.70 1.0 34.5 35 8 14.52 540

MQ4 18.00 1.2 24.80 1.5 30.5 19 8 9.68 213

MQ5 20.10 1.2 27.20 1.2 26.5 25 9 13.61 292

Note: Wall: elastic properties, E ¼ 30 GPa, ν ¼ 0:15, γc ¼ 24 kN=m3; tiebacks: head at elevation þ31 m, fixed anchor length, L2 ¼ 8:0 m,15.2-mm-diameter steel tendons, modulus, E ¼ 210 GPa.



For this section, the numerical predictions were in excellentagreement with the measured top, toe, and maximum wall deflec-tions and anchor forces at the final formation level. The analysesalso predicted much larger settlements at MQ5 (i.e., 1.2 versus0.2 cm for MQ3) because of differences in anchor location and

prestress, whereas predictions of heave inside the excavation werealmost the same for both MQ5 and MQ3.

Section MQ4, Fig. 17, used the same diaphragm wall sectionas MQ5 but had a shallower dip of the tieback anchors and wasdesigned with lower anchor stiffness and prestress (Table 3).

Fig. 13. Effect of in situ K0 on lateral wall movements and tieback forces at MQ3

Fig. 14. Effect of in situ void ratio on lateral wall movements and tieback forces at MQ3



The excavation was also 1.8 m shallower at MQ4. Numerical pre-dictions for MQ4 were consistent with expected behavior on thebasis of these perturbations of support conditions. The computedmaximum wall deflection (i.e., 1.9 cm) was smaller than that foundat MQ5 (i.e., 2.5 cm), whereas computed movements at the top ofthe wall were larger (i.e., 2.0 versus 1.2 cm for MQ5). Althoughexcellent agreement existed between the computed and measured

top-of-wall deflection and anchor load, the numerical analysissignificantly underestimated the measured toe movement (i.e.,0.2 versus 0.9 cm) and, hence, underestimated the measured maxi-mum wall deflection (i.e., 2.6 cm). These discrepancies are noteasily explained from the results at the previous sections of MQ5or MQ3. Although the borehole data do indicate a thicker zoneof organic materials in the vicinity of MQ4, no evidence suggests

Fig. 15. Predicted excavation performance for MQ3 from best estimate of state parameters

Fig. 16. Predicted excavation performance for MQ5



high void ratios in the sands from DPH soundings at B1129[cf. Figs. 2(a) and 10]. However, construction problems were as-sociated with the diaphragm wall panel installation in this area (byusing a hydrofraise), and it is possible that this may be associatedwith the local loosening of the soil at the toe of the wall.

Finally, results for MQ2 in Fig. 18 are most directly comparableto the conditions at the reference section MQ3 (Fig. 15). These twoused the same diaphragm wall section (ie., 1.5 m) and had similar

anchor inclinations (38 versus 35° for MQ3), but the excavationwas almost 2 m deeper at MQ2. The wall deflection data fromMQ2 differed significantly from any of the three preceding sec-tions. It was the only section in which significant inward walldeflections were measured at the prestress stage, up to 0.7 cm atthe middepth of the wall. At the end of excavation, the maximummeasured wall deflection was approximately 5.2 versus 2.1 cmat MQ3. This difference in measured performance was certainly





not expected from the variations in support conditions but couldstill be related to unreported variations in construction activities.The numerical analyses predicted maximum wall deflections upto 2.4 cm, of which 0.7 cm occurred at the top of the wall versus2.3 cm measured, whereas there is good agreement at the toe (i.e.,0.3 cm). The predictions were consistent with the other three sec-tions; and hence, the underestimation of wall deflections is againmost likely related to the spatial variability in soil properties. In thiscase, the data appeared to reflect lower density (i.e., higher voidratio) in the S0 and S1 units and/or higher K0 in the upper S0 unit.However, again, no indication of such variability from the localDPH data was evident (B1137, Fig. 10).

Discussion

The preceding numerical analyses have shown that it is possible toobtain reasonable predictions of wall deflections and tieback forcesby using a constitutive model that is calibrated to the results oflaboratory tests on reconstituted sand specimens. The MIT-S1model was able to describe variations realistically in the shearstrength and stiffness parameters measured at different confiningstresses and void ratios by using a single set of input parameters.However, further judgment was needed in the selection of in situstate variables e0 and K0.

It is certainly plausible to achieve comparable agreement be-tween computed and measured behavior by using simpler constit-utive soil models. However, the difficulty lies in the rationalselection of input parameters. None of the “simple models” usedin current practice can describe the full range of stiffness and shearstrength properties measured in the laboratory tests on Berlin sand.Instead, it is more effective to consider optimizing the selectionof key input parameters for these models and then to comparethe optimized parameters with the results of the laboratory tests.For example, the authors optimized the selection of shear strengthand stiffness parameters for the Hardening Soil Model (Schanz et al.1999) within the Plaxis software at section MQ3. This was accom-plished by using genetic algorithms similar to those described byLevasseur et al. (2008) and by optimizing the selection of twomodel input parameters, Eref

50 and ϕ0peak. The objective function

was set to minimize the differences in the computed and measuredtieback forces and lateral wall deflections, over the full depth of thewall, at the preload stage and at the end of excavation. Table 4 sum-marizes the input for the Hardening model, including the selectedrange for the optimizing parameters. Fig. 19 plots the predictionsobtained by the best-fit Hardening Soil Model parameters at MQ3.Good agreement exists between the computed and measured maxi-mum wall deflections at the end of excavation. However, the modeloverestimated the inward movements at the toe of the wall and,

Fig. 19. Predicted excavation performance for MQ3 by using the Hardening Soil Model; input was optimized by using genetic algorithms (Table 4)

Table 4. Input Parameters Used in Generic Algorithms for Hardening Soil Model

Eref50 (MPa) Eref

oed (MPa) Erefur (MPa) νur m pref (kPa) ϕ0

peak (°) ψ0d (°)

[20–200] bEref50 3Eref

50 0.25 0.5 100 [30–40] Calculated

Note: In Plaxis, the following relationships are used to calculate E50 and the dilation angle ψ0d:

E50 ¼ Eref50

�σ0c

pref

�m

sinψ0d ¼

ðsinϕ0peak � sinϕ0

cvÞð1� sinϕ0

peak sinϕ0cvÞ

where ϕ0cv ¼ 31°; b, and K0 vary with depth and are shown in Fig. 19.



compared with the MIT-S1 predictions, yielded larger deformationsbelow the base of excavation. Moreover, it predicted heave behindthe wall, an improbable response for the retained soil. The bench-mark study on a similar Berlin excavation (Schweiger 2002) alsoreported heave predictions, illustrating the inadequacy of some ofthe models used and the lack of calibration data for the Berlinsands. The backfitted value for the peak angle, ϕ0

peak ¼ 36:6°,was in reasonable agreement with the friction angle measured atσ0c ¼ 100 kPa (test #570, Fig. 4). The predicted dilation angle,

ψd ¼ 6:8° was at the upper limit of dilation angles measured inthe laboratory triaxial tests (cf., #570, Fig. 4). However the elasticmoduli, E50 ¼ 45–128 MPa for σ0

c ¼ 100–800 kPa were signifi-cantly lower than the stiffness values measured in the correspond-ing test (i.e., E50 ≈ 140–245 MPa, respectively). These resultssuggest the need for further refinement in the selection of the Hard-ening Soil Model parameters for the lower sand unit S2 but give noinsight into the broader applicability of the laboratory test results.

Conclusions

This paper described the application of a generalized effectivestress soil model, MIT-S1, for predicting the performance of deepexcavations in Berlin sand. The model was calibrated by using datafrom an extensive laboratory program of tests on reconstituted sandspecimens. The calibration process proved quite challenging be-cause of the variability in the peak friction angles with small per-turbations in the formation void ratio and uncertainties in theinterpretation of critical state conditions.

The model was used in finite-element simulations of the under-water excavations at a series of instrumented sections in theM1 pit near the Lehrter Bahnhof in central Berlin. Site investiga-tions for this project showed that the vertical profile included threeprimary sand units, wheras in situ density and shear strength wereestimated by using correlations to DPH N10 blowcount data. Themeasured data showed significant variability in the estimated in situvoid ratio. The current study assumed a single average profile andused the DPH correlations and background information on the geo-logical history to estimate the in situ void ratio, e0, and earth pres-sure coefficients, K0.

The numerical simulations were in very good agreement withmeasured diaphragm wall deflections and forces in the singlerow of tieback anchors for three of the four instrumented sectionsconsidered in this study. The measured data for a fourth section(i.e., MQ2) showed much larger wall movements than predictedor expected on the basis of the design of the lateral earth supportsystem, whereas unusual wall-toe movements occurred at a secondsection (i.e., MQ4). Although these deviations in behavior weremost probably caused by the spatial variations in soil properties,no supporting evidence exists from the local DPH data.

The study showed that realistic predictions of excavation perfor-mance can be achieved through the careful site-specific calibrationof sand behavior and by using a constitutive model capable of rep-resenting variations in stress-strain-strength properties as functionsof the confining stress and void ratio. This approach provides amore consistent method of model validation than generic bench-mark studies that use aggregated soil properties. However, furtherwork is needed to address the effects of spatial variability in site-specific applications.

Acknowledgments

This research was supported by collaboration grants from theNational Science Foundation (NSF) Western Europe program

(INT-0089508) and Deutscher Akademischer Austausch Dienst(DAAD). The laboratory tests were performed at the MIT geotech-nical laboratory under the expert supervision of Dr John Germaine.Special thanks are given to Ralf Glasenapp and Tim Becker fortheir meticulous experimental work, to Dr Frank Rackwitz forhis help in compiling field data, to Gonzalo Corral for performingthe inverse analyses in Plaxis, and to the reviewers for improvingthe original manuscript.

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