deep excavation-induced ground sdeep excavation-induced ground surface move men turf ace movement

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Computers and Geotechnics 35 (2008) 231–252

Deep excavation-induced ground surface movementcharacteristics – A numerical investigation

Chungsik Yoo, Dongyeob Lee *

Department of Civil and Environmental Engineering, Sungkyunkwan University, 300 Chun-Chun Dong, Jan-An Gu, Suwon,

Kyong-Gi Do 440-746, Republic of Korea

Received 13 August 2006; received in revised form 5 May 2007; accepted 6 May 2007Available online 28 June 2007

Abstract

This paper concerns the characterization of deep excavation-induced ground surface movements, using the results of numerical inves-tigation. A calibrated 2D finite element model using the Lade’s double hardening constitutive model for soil was used to form a databaseof the wall and ground surface movements associated with deep excavation. The results indicated that the cantilever and the lateral bulg-ing excavation stages produce distinctive patterns of ground surface movement profiles, and that final ground surface movement profilescan be constructed by combining the cantilever and the lateral bulging components with a reasonable degree of accuracy. A two-stepapproach for use in the prediction of ground surface movement profiles is proposed.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Deep excavation; Ground movement; Finite element analysis; Building damage; Double hardening model

1. Introduction

Rapid urban developments have resulted in many deepexcavation projects for constructions of high-rise buildingsand subways. During deep excavation, changes in the stateof stress in the ground mass around the excavation andsubsequent ground losses inevitably occur. These changesand ground losses affect the surrounding ground in theform of ground movements, which eventually impose directstrains onto nearby structures. The magnitude and distri-bution of ground movements for a given excavationdepend largely on soil properties, excavation geometryincluding depth, width, and length, and types of wall andsupport system, and more importantly construction proce-dures. Because of the increased public concern of the effectsof construction-induced ground movements on their prop-erties, the prediction of ground movements and assessmentof the damage risk have become an essential part of the

0266-352X/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compgeo.2007.05.002

* Corresponding author. Tel.: +82 31 290 7644; fax: +82 31 290 7549.E-mail address: [email protected] (D. Lee).

planning, design, and construction of deep excavations inurban environments.

Over the years, there have been a number of studies onthe subject of wall and ground movements associated withdeep excavation. Clough and O’Rourke [5] extended thework by Peck [20] and developed empirical settlement enve-lopes. Cording [7] provided a means of estimating the dis-tribution of ground movements behind an excavation wallon the basis of volume relationships based on field observa-tions. Ou et al. [19] compiled and analyzed field dataregarding wall movement associated with deep excavationand defined the apparent influence range (AIR) for damageassessment of adjacent structures. More recently, Yoo [25]collected field data on lateral wall movement for walls con-structed in soils overlying rock from more than 60 differentexcavation sites and analyzed the data with respect to walland support types.

The finite element method of analysis has also beenextensively used in studies concerning wall and groundmovements associated with deep excavation. The studiesby Clough et al. [4], Mana and Clough [17], Wong and

mailto:[email protected]

Fig. 1. Finite element mesh and modeling of interface element forparametric study.

Table 1Conditions analyzed

F Es (aver)(MPa)

L (m) Hun

(m)K (MN/m)

15, 50, 74.2, 120, 150, 176,220, 400

26.2, 53.2 3, 4, 5,6

1, 2, 3,4

15

Note: EIw, wall flexural rigidity; K, effective axial stiffness.

232 C. Yoo, D. Lee / Computers and Geotechnics 35 (2008) 231–252

Broms [23], and Hashash and Whittle [10] were directedtoward the prediction of wall movement for excavationsin soft clay. Cording and O’Rourke [6] and later Cording[7] developed a scaling relationship based on an elasticassumption and investigated the effect of relative stiffnessof the wall system with respect to soil on lateral wallmovement.

Most of the aforementioned previous studies focused onthe maximum wall movement. Studies concerning groundsurface movement characterization have been scarce duein large part to difficulties in obtaining complete sets ofdata either from field instrumentation or numerical analy-sis. Available information on the magnitude and distribu-tion of ground surface movement associated with deepexcavation is somewhat outdated and provides limitedinformation required for building damage assessment.

This study is directed toward the development of predic-tion method for deep excavation-induced ground surfacemovement profiles that can be used in the framework ofcurrently available building damage assessment procedures(Boscardin and Cording [2] and Burland [3]). In order tocorrectly simulate the deep excavation-induced groundmovement characteristics, the Lade’s double hardeningconstitutive model [14–16] was used to describe thestress–strain-strength behavior of the model ground. Thefinite element model adopted was validated by availabledata [24] before conducting the parametric study.

A parametric study on deep excavation problemsencountered in Korea was performed using the validatedfinite element model to form a database for use in thedevelopment of a prediction method associated with deepexcavation-induced wall and ground surface movements.The results of the parametric study were carefully analyzedso that the ground surface movement characteristics couldbe related to the sources of wall movements. A systematicapproach for prediction deep excavation-induced groundmovement profiles was then developed.

2. Parametric study

A series of 2D finite element analyses were performedusing a commercial finite element program ABAQUS [1]to examine the ground surface movement characteristicsand to form a database for use in the development of aground movement profile prediction method. Subsequentsections discuss the details of the parametric study.

2.1. Problem investigated

The configuration of the problem to be analyzed isshown in Fig. 1, which represents a hypothetical case ofan excavation. For simplicity, an idealized symmetric planestrain braced excavation geometry with an excavationdepth H and a width B of 20 and 30 m, respectively, wasconsidered. The wall is a 25 m in height and has with a5 m toe penetration depth at the final excavation stage.Because of symmetry about the excavation centerline, only

one-half of the excavation was considered in the finite ele-ment model.

The excavation ground considered was assumed to becomposed of a weathered granite soil overlying a weath-ered rock stratum. The weathered granite soil is the repre-sentative soil in urban excavation sites in Korea and thistype of ground formation is a typical soil profile frequentlyencountered in Korea. The excavation platform corre-sponds to the top of the weathered rock stratum.

Primary variables included the wall bending stiffness(EI)w, the cantilever excavation depth Hun, the unsup-ported span length L below the lower-most support, andsoil stiffness Es. Combinations of (EI)w and L generatedthe range of F shown in Table 1. In addition, a wide rangeof conditions was analyzed by varying the primary vari-ables mentioned above. The parameter F in Table 1 is theflexibility ratio, defined by the following equation:

F � EsL3

ðEIÞwð1Þ

where Es is the soil stiffness, L is the unsupported excava-tion length, and (EI)w is the wall flexural rigidity. The flex-ibility ratio was originally introduced by Cording andO’Rourke [6]. The range in wall flexibility ratio consideredin this study is approximately from 15 to 400, which is con-sistent with the range for slurry, cast-in-place pile, sheetpile, and soldier pile walls.

2.2. Finite element analysis

2.2.1. Finite element model

In the finite element modeling, the ground and the wallwere discretized by using eight-noded plane strain ele-

C. Yoo, D. Lee / Computers and Geotechnics 35 (2008) 231–252 233

ments, while the struts were modeled by using one-nodespring elements with an effective axial stiffness of 15 MN/m considering the excavation width.

As shown in Fig. 1, a refined finite element mesh extendedto a depth of 1.0H below the final excavation platform andlaterally to a distance of 3.8H from the excavation centerlineto minimize the effect of the artificial boundaries on theground surface movement characteristics.

For the material modeling, the weathered rock stratumwas assumed to be an elasto-plastic material conformingto the Mohr–Coulomb failure criterion [1]. On the basisof the extensive surveys of urban excavation sites in Korea,the mechanical properties for the weathered rock in Table 2were used in the parametric study. On the other hand, theweathered soil was assumed to follow the Lade’s doublehardening model. Brief discussions on the double harden-ing model and the model parameters used in the analysisare given in Section 2.2.2.

A series of preliminary analyses indicated that the inter-face modeling of the excavation side is crucial for obtainingrealistic ground surface movement profiles associated withdeep excavation. Although ABAQUS provides a surface-based interface modeling option using ‘contact pair’, thecontact pair was not adopted in modeling the interface inthis study as significant numerical instabilities wereencountered during the excavation modeling. For that rea-son, the Desai-type thin-layer interface model [9] shown theinset in Fig. 1 was implemented in ABAQUS using UMAT[1] to model the interface behavior between the wall facingand the soil. Details of the Desai-type thin-layer interfacemodel can be found in [9].

The stiffness matrix of thin-layer element is the same asgeneral solid element assuming a linear elastic behavior.Therefore, the elastic constitutive matrix of the thin-layerelement is expressed as:

½C�i ¼½Cnn�i ½Cns�i½Csn�i ½Css�i

� �ð2Þ

where [Cnn] and [Css] are related to normal and shear com-ponents, respectively, and [Cns], [Csn] represent coupling ef-fects. However, the coupling effects are not included forsimplification in this study.

For isotropic linear elastic behavior, [C]i can be writtenin matrix form as:

½C�i ¼

M k k 0 0 0

k M k 0 0 0

k k M 0 0 0

0 0 0 G 0 0

0 0 0 0 G 0

0 0 0 0 0 G

2666666664

3777777775

ð3Þ

Table 2Typical mechanical properties for weathered rock in Korea

Material C (kPa) / (�) w (�) m Es (MPa)

Weathered rock 100 46 6 0.3 500

where, M ¼ Eð1�mÞð1þmÞð1�2mÞ and k ¼ Em

ð1þmÞð1�2mÞ

Under the two-dimensional plane strain condition, Eq.(3) can be reduced to the following equation:

½C�i ¼M k 0

k M 0

0 0 G

264

375 ð4Þ

Based on the results of a series of preliminary analysesfor model calibration, a relatively low shear modulus of50 kPa with high bulk modulus was assigned to the inter-face elements.

In simulating the step-by-step excavation process, theinitial vertical state of stress was first created by turningon the gravity with the assumption of wished-in-placedwall. The lateral stress state was then created by multiply-ing the vertical stresses by the lateral earth pressure coeffi-cient K0 = 0.5. The excavation process was then modeledby adding and removing elements at corresponding steps.

Although the ground water lowering due to excavationgenerally affects the ground movement characteristics, theground water was not considered for simplification andthe free-draining characteristics of typical weathered soilsin Korea.

2.2.2. Constitutive modeling of weathered soil

It has been shown that a traditional elasto-perfectly-plastic model such as Mohr–Coulomb model does notyield satisfactory results in estimating deep excavation-induced ground movement, especially for ground surfacesettlements [21]. The double hardening model, which hasbeen proven to be applicable for the weathered soil fre-quently encountered in Korea [13], was selected and imple-mented in ABAQUS using the user subroutine capabilityto represent the soil behavior in this study. In this section,the brief descriptions of the double hardening model basedon the nonlinear elasto-plastic model are given as below.Details of the double hardening model can be found in[14–16].

In the double hardening model, the incremental totalstrains are assumed to be divisible into elastic strains, plas-tic collapse strains, and plastic expansive strains. The elas-tic strains are calculated from Hooke’s law using theunloading–reloading modulus defined as:

Eur ¼ Kur � P a � ðr3=P aÞn ð5Þ

where Kur and n are dimensionless model parameters andPa is atmospheric pressure to make conversion from onesystem of units to another more convenient. Thus, the unitsof Eur and r3 are the same as units of Pa.

The plastic collapse strains are associated with volumet-ric strains and mean effective stress. They are computedusing a cap type yield surface conforming associated flowrule and a work-hardening relationship which can be deter-mined from an isotropic compression test. The yield crite-rion, fc, and the plastic potential function, gc, are expressedin terms of the first and second invariants, I1, I2, as follows:

Table 3Parameters for the weathered soil

Parameters Weathered soil Strain component

Kur 2:57 Elastic componentn 0.865Poisson’s ratio 0.25

Collapse const. (C) 0.0086 Plastic collapse componentCollapse expo. (p) 0.789

Yield const. (g1) 38 Plastic expansive componentYield expo. (m) 0.113P1. potent. const. (R) �1.406P1. potent. const. (t) 0.488P1. potent. const. (S) 0.406Work-hard. const. (a) 1.254Work-hard. const. (b) �0.072Work-hard. const. (P) 0.52Work-hard. expo. (I) 0.653


fc ¼ gc ¼ I21 þ 2I2 ð6Þ

where I1 and I2 are first and second stress invariants.An empirical relationship for the collapse work-harden-

ing as a function of fc is defined as:

W c ¼ C � P a �fc

P 2a

� �p

ð7Þ

where C and p are material parameters and the incrementalplastic collapse work (dWc) can be determined from thederivative of Wc with regard to fc:

dW c ¼CpP a

P 2a

fc

� �1�p

dfc ð8Þ

The plastic expansive strains are related to the deviatoricstresses and they are computed using a conical yield surfaceand conform non-associated flow rule. The conical yieldsurface is described in terms of the first and third stressinvariants, I1 and I3:

fp ¼I3

1

I3

� 27

� �I1

P a

� �m

6 g1 ð9Þ

where m is a model parameter describing the curvature ofthe failure surface, and g1 is a work-hardening parameterswhich defines the size of the failure surface. The plastic po-tential function is modeled on the yield function as follows:

gp ¼ I31 � 27þ g2 �

P a

I1

� �m� �� I3 ð10Þ

where g2 can be modeled by the following simpleexpression:

g2 ¼ Sfp þ t þ R � r3

P a

� �1=2

ð11Þ

where S, t, and R are model parameters.An empirical relationship between the plastic expansive

work done (Wp) and fp is defined by the followingexpression:

fp ¼ a e�bW pW p

P a

� �1=q

ð12Þ

with a ¼ g1e P a

W ppeak

� �1=qand b ¼ 1

qW ppeak

where Wppeak and q are constants for a given value of r3

and e is the base for natural logarithms. Wppeak is the valueof Wp at the peak point and its variation with r3 can beapproximately expressed by the following empiricalrelationship:

W ppeak

P a

¼ Pr3

P a

� �l

ð13Þ

where P is the value of Wppeak/Pa when Pa = 1. The varia-tion of the parameter q with r3 can be represented by a sim-ple expression as follows:

q ¼ aþ br3

P a

� �ð14Þ

where a and b represent the intercept and slope of astraight line, respectively.

From Eq. (12), the increment in plastic expansive workcan be expressed as follows:

dW p ¼dfp

fp

1

1qW p� b

� � ð15Þ

In implementing the double hardening model using theuser subroutine capability the soil is assumed to followan elastic behavior and then the stress invariants are calcu-lated to estimate the current collapsive yield stress andexpansive yield stress. The current collapsive yield stressand expansive yield stress are then compared to the maxi-mum past collapsive yield stress and the maximum pastexpansive yield stress to determine the loading conditions.After comparing the present and the past yield stresses, themaximum past yield stresses are replaced with larger oneand then they are stored in the solution-dependent statevariables array. Four different conditions may exist: (1)only elastic strains occur, (2) only plastic collapsive surfaceis activated, (3) only plastic expansive surface is activatedand (4) both plastic collapsive and expansive surfaces areactivated. After determining the loading conditions, thestresses are calculated by using stiffness matrix suitablefor each yielding condition and then they are updatedand stored to the stress array.

A total of 14 parameters are required in the doublehardening model to define soil behavior: three parameters(Kur, n, and m) define the elastic behavior, two parameters(p, c) define the collapsive plastic strains, two parameters(g1, m) define failure surface, and three parameters (S, R,and t) define the direction strain increment but the requiredparameters can be entirely derived from the conventionaltriaxial test with volume change measurement. Table 3 pre-sents the double hardening model parameters of the weath-ered soil used in the model ground. Note that the values arebased on the previous study [13] which reports ranges of

Table 5Material properties for an urban excavation site in Korea

Material C (aver)(kPa)

/(aver)(�)

w(aver)(�)

m(aver)

Es (aver)(MPa)

USCS

Fill 10 30 8 0.3 17 SMWeathered

soil25 40 6 0.3 30 SM

Weatheredrock

300 41 6 0.3 110 None


the double hardening model parameters for weathered soilsencountered in Korea.

2.2.3. Model validation

The finite element model adopted in this study was vali-dated to a limited extent against measured data for anurban excavation site in Korea [24]. The same modelingapproach for parametric study given in Section 2.2.1 wasemployed in the finite element modeling. Fig. 2 presentsthe standard cross-section and soil profile for the site. Thewall of 26 m in height with an embedment depth of approx-imately 2 m consisted of soldier pile was supported by strutsand detailed descriptions of the site are given in Table 4 [24].

As shown in Fig. 2, the vertical spacing of the struts andthe unsupported span length were varied by the construc-tion sequences for simulating the field conditions in detail.The average of the vertical spacing of the struts and theunsupported excavation length are 2.5 m and 2–3 m respec-tively. Cantilever excavation depth of 3–4.5 m, excavationdepth 23.7 m, and the over excavation depth of 2.5–3 mare applied to the analysis.

As illustrated in the figure, the ground consists of a fillmaterial, a weathered soil, and a weathered rock. Mostof the excavation took place within the weathered soil.Table 5 summarizes the mechanical properties of the site

Fig. 2. Cross-section and soil profile for an urban excavation site inKorea.

Table 4Descriptions of an urban excavation site in Korea

Excavation depth, H (m) 23.7Wall type Soldier pile (I = 1.26 · 10�4 m4) and lagging

wallSoil type Fill + weathered soilSupport type and average

spacingStrut (A = 0.0053 m2), horizontalspacing = 4.0 m, vertical spacing = 2.5 m

Flexibility ratio (F) 150–250

in terms of the Mohr–Coulomb shear strength parametersand the elastic stiffness reported in [24] to give generalinformation of the soils layer and the rock layer. In mate-rial modeling, although the fill layer and the weathered soilin the site have a bit different shear strength parameters asshown in Table 5, these soils were considered to have thesame double hardening model parameters. This is justifiedsince the fill layer and the weathered soil are reported to besimilar in nature, i.e., classified as SM according to USCS[24] and the thickness of the fill layer was less than 1.5 m.Such an approach was adopted due to the limited informa-tion available and therefore the validation given in this sec-tion should thus be viewed as qualitative. The rock layer isassumed to follow the Mohr–Coulomb yield criterion withthe material properties in Table 5. Thus, the site wasassumed to be composed of a weathered soil overlying aweathered rock.

Fig. 3 presents the comparisons between the measuredand predicted ground surface settlements. The solid linesrepresent the predictions from the double hardening modeland the points represent the measured results. Note thatdue to the general practice of not measuring horizontalground surface settlements during excavation, only the ver-tical ground settlement data were used for validation. Asshown in the figure, the predicted maximum settlement of

Fig. 3. Comparison between results of proposed method and measureddata.


0.16%H agrees well with the measured one. The extent ofthe settlement zone is also well predicted as 2.5–3.0H. Moreimportantly, the results agree fairly well in qualitativeterms suggesting that the finite element modelingapproach, including the constitutive modeling of theweathered soils using the double hardening model, is rea-sonably appropriate for use in this study.

It should however be noted that a small-strain stiffnessmodel may yield better results, especially in terms of lateralextent of the settlement profiles, such a model was notadopted in this study due to limited information availableas to the applicability of the model to typical weatheredsoils encountered in Korea. Considering that the doublehardening model is based on the nonlinear isotropic elastic-ity, the results may be comparable to those based on asmall-strain stiffness model. However, a further study con-cerning the use of a small-strain stiffness model for typicalground conditions in Korea is warranted.

3. Wall and ground movement characteristics

The results of the finite element analyses were compiledsuch that the patterns of wall and ground movements couldbe related to the parameters comprising the flexibility ratio.Important findings are discussed under the subsequentsubheadings.

3.1. Effect of wall stiffness

Fig. 4 illustrates the effect of wall bending stiffness onthe wall and ground surface movement patterns. In the plotof the ground surface displacements, two sets of curves areshown. For the horizontal displacements, the displacementtoward the excavation wall was taken as positive. Likewisethe downward movement was taken as positive for the ver-tical settlements. Note that cantilever excavation depth andthe unsupported span length during the lateral bulging

Fig. 4. Variation of wall and gro

stage were kept constant at Hun = 4 m and L = 5 m,respectively.

As expected, an increase in the wall stiffness (EI)w

resulted in the decreases in the wall and ground surfacemovements. The results are described by more of a stepfunction than a gradual change with the wall stiffness. Asseen in Fig. 4, as the wall stiffness decreases, the shape ofthe wall displacements changes from the cantilever formto the lateral bulging form for wall movements, and thehorizontal component of the ground surface settlementprofiles tend to become convex up and also the verticalcomponent yields concave down. In terms of the maximumvalues, the location of the maximum settlement tends tomove away from the edge of excavation as the wall stiffnessincreases. This trend indicates that for a given excavationcondition, the wall bending stiffness influences not onlythe magnitudes of ground surface movements but alsothe pattern of the movements. In addition, the locationof maximum settlement greatly varies at the flexibility ratioof F = 120.

Moreover, as seen in Fig. 4b, significant horizontalground surface displacements are developed, as great as100–127% of the vertical settlements in terms of maximumvalues. These results demonstrate the need for consideringhorizontal ground surface displacements when assessingthe risk of damage especially for buildings with small resis-tance to lateral ground displacements, as noted by Cordinget al. [8], although the lateral building strains are signifi-cantly less than the lateral ground strains.

Presented in Figs. 5 and 6 are the results of four caseshaving the same flexibility ratio of F = 120 but differentcombinations of (EI)w and L and different Hun, one withHun = 1 m and the other with Hun = 4 m. The differencesin the wall and ground surface movements between thecases thus represent the combined effect of (EI)w and L.As seen in these figures, the wall and ground surface dis-placement profiles tend to significantly vary in shape

und movements with (EI)w.

Fig. 5. Variation of wall and ground movements according to combination of (EI)w and L (Hun = 4 m, F = 120 and Es = 26.2 MPa).

Fig. 6. Variation of wall and ground movements according to combination of (EI)w and L (Hun = 1 m, F = 120 and Es = 26.2 MPa).


depending on the combination of (EI)w and L despite thesame F.

For the wall deformations, the maximum displacementsof the wall do not vary in direct proportion to the bendingstiffness. Furthermore, the curve 2 with the larger L and(EI)w yields greater wall and ground surface movementsthan the curve 1 with the smaller L and (EI)w due to theover excavation. A similar trend is shown in curves 3 and4, suggesting that L and over excavation have a greaterinfluence on the performance of a given excavation than(EI)w. For each unsupported excavation depth L (=3, 4,5, 6 m), the depth of over excavation is 0.5, 1.5, 0, and1.0 m, respectively. The trends shown in these figures illus-trate the dependency of the wall and ground movements onthe combined effect of (EI)w and L and suggest that the

wall flexibility ratio F alone cannot correctly capture thewall and ground responses to a given excavation.

3.2. Effect of unsupported excavation depth

During an excavation, unsupported excavation is inevi-tably carried out both in the cantilever and the lateral bulg-ing stages. The effect of cantilever excavation depth Hun onthe wall and ground movements is illustrated in Fig. 7. Thecantilever excavation depth Hun was controlled in the anal-yses by varying the maximum depth of excavation beforeinstalling the top most support but keeping the other vari-ables constant. Therefore, the differences in the wall andground movements between the different cases solely reflectthe effect of Hun.

Fig. 7. Variation of wall and ground movements with Hun (F = 120 and Es = 26.2 MPa).


As seen in Fig. 7, it appears that the wall movementsduring the cantilever stage became significant when allow-ing Hun greater than 3 m, resulting in the ground surfacedisplacement profiles with large volume losses in closeproximity to the edge of the excavation. A strict provisionon Hun should be placed during the early stages of excava-tion for cases in which buildings and buried utilities arelocated in close proximity to the edge of excavation.

In addition, the wall deformations are almost constantwith the increase of Hun, and similar results are shownfor the vertical components. Hence, it is seen that maxi-mum wall deformation and the vertical displacement ofground settlements are more dependent on the wall bend-ing stiffness and the unsupported length L than the cantile-ver excavation depth Hun.

Fig. 8. Variation of wall and ground

Examples with different Hun used to show the influencesof the unsupported span length L for a given wall stiffnessare illustrated in Figs. 8 and 9. As shown in these figures,an increase in L from 3 to 6 m results in substantialincreases in the wall and ground surface movements byapproximately an order of magnitude.

An important observation is that an increase in theunsupported span length L results in increases in the mag-nitude of ground surface settlements and tends to modifythe settlement profiles to more a concave downward shapebecause of the increased deep-seated movements. Althoughthe flexibility due to the increase of the unsupported lengthL is increased, the wall and ground movements are severelyvaried by over excavation. Such results shown in these fig-ures demonstrate that the excavation procedure during

movements with L (Hun = 4 m).

Fig. 9. Variation of wall and ground movements with L (Hun = 1 m).


construction significantly affects the patterns of groundsurface displacement profiles and the wall deformations.

3.3. Effect of soil stiffness

The relative stiffness between the excavation wall andthe soil has a significant influence on the magnitude anddistribution of wall and ground movements for a givenexcavation. With respect to ground movement prediction,it would be more convenient if cases having the same flex-ibility ratio but different combinations of (EI)w and Es

would yield similar ground surface movement profiles.Figs. 10–15 represent the ground surface movement pro-

files at the cantilever, lateral bulging, and final stages forcases having F = 50 and 150 but different combinationsof (EI)w (=21.8, 44.4, 65.4, 133.1 MN m2/m) and Es

Fig. 10. Ground movements profiles with soil stiff

(=26.2, 53.2 MPa) and different Hun. In all cases, theunsupported depth during the lateral bulging stage waskept constant at L = 5 m. Note that Es represents the aver-age soil modulus of the excavation ground calculated usingthe hyperbolic relationship given by Janbu [12] in the fol-lowing equation:

Es ¼ K � P a � ðr3=P aÞn ð16Þ

According to Wong and Duncan [22], the parameter Kur

in Eq. (5), which is the modulus parameter determiningEur, is generally 1.2–3 times greater than K, which is themodulus parameter for Es. Considering this, the averagevalue of Es was back-calculated from Eur.

As seen in these figures, it appears that the cases witha same F would yield similar settlement profiles in termsof magnitude and slope despite the differences in the

ness (Hun = 4 m): (a) F = 50 and (b) F = 150.

Fig. 11. Ground movements profiles with soil stiffness (Hun = 4 m): (a) F = 50 and (b) F = 150.



combination of (EI)w and Es. The general shapes of the hor-izontal displacement profiles for a given F are similar, andthe case with less rigid ground and wall tends to yield largermovements. An important conclusion is that as long as L isthe same, the flexibility ratio F can be used as a commonindex for the prediction of ground surface settlement profilesfor cases having different combinations of (EI)w and Es.

3.4. Maximum wall and ground surface displacements

During a design stage, the maximum ground surface set-tlement (dv,max) is usually taken as a fraction of the maxi-mum lateral wall movement (dw,max). The results of thefinite element analyses are compiled such that the maxi-mum ground surface movements (dv,max and dh,max) can

be related to the maximum lateral wall movements (dw,max)for cases having different wall flexibilities. The maximumvalues for each component, i.e., the cantilever and the lat-eral bulging, are separately analyzed, and that the resultsare only relevant to the cases with ground conditions sim-ilar to those considered in this study.

Presented in Figs. 16–19, dv,max/dw,max and dh,max/dw,max

ratios are plotted against the flexibility ratio F for the can-tilever as well as the lateral bulging components in a semi-log plot. The case with the unsupported length L = 5 mwas chosen to eliminate the effect of over excavation.

As seen in Fig. 16a, the dv,max/dw,max ratio tends to lin-early decrease with increasing F because of the increaseof dw,max at an approximately same rate, regardless of thesoil stiffness in the cantilever stage. The range of decrease




is within 20%. In the lateral bulging stage, as the result ofthe decrease of the wall bending stiffness, dv,max/dw,max

ratio tends to linearly increase with F, and the rate ofincrease for the soil stiffness remains almost constantwithin 10%.

The dh,max/dw,max ratio shown in Fig. 17 appears to sig-nificantly vary with F in the cantilever stage, in the range ofabout 30%. This result suggests that even for a rigid wallsystem, a large amount of volume loss can be led in thecantilever stage. For a flexible wall system, as a result ofthe increase of wall deformation, dh,max/dw,max ratio tendsto decrease and the effect of soil stiffness is insignificant likedv,max/dw,max. As seen in Fig. 17b, the dh,max/dw,max ratiodoes not appear to significantly vary with F in the lateralbulging stage, exhibiting similar results displayed by

dv,max/dw,max ratio. The difference in soil stiffness resultsfrom the lateral expansion of the retained soil.

As illustrated in Fig. 18, the change of the vertical com-ponent lies within 5% because of the decrease in Hun andthe immediate installation of struts after excavation. Inthe lateral bulging stage, the effect of the flexibility is alsoinsignificant, and only the change associated to the soilstiffness appears. As seen in Fig. 19, dh,max/dw,max ratio alsodisplays an almost similar trend for the case of Hun = 4 m.However, the range of variation is within 15%, and theeffect related to the wall and the soil stiffness decreases.This result, as previously mentioned, reflects the influenceof Hun. Therefore, dv,max/dw,max is dependent on Hun andF, regardless of the soil stiffness in the cantilever stage,and the lateral bulging stage is affected by Es, F, and


Fig. 16. Variation of dv,max/dw,max with flexibility ratio (Hun = 4 m): (a) cantilever stage and (b) lateral bulging stage.


Hun. As discussed in Section 3.2, the change of the horizon-tal component of ground settlement is greatly affected bythe cantilever excavation depth. A constant value fordh,max/dw,max can be assumed for the lateral bulging stagewithout introducing a significant error, at least, withinthe limits of the F considered.

Fig. 20 represents the ratio of settlement volume to walldisplacement volume (Vs/VL). As seen in Fig. 20, the ratioof settlement volume to wall displacement volume almostlinearly increases with increasing F in the semi-log plot.These results are a direct consequence of the increase inthe ground settlement volume relative to the volume of walldisplacement as the wall stiffness decreases.

Fig. 21 illustrates the relationship between the normal-ized maximum ground displacements and wall movements.

As seen in the figure, the range of dv,max/dw,max ratio lieswithin 0.5–1.0. This trend is similar to the field data [24] inFig. 21c and strongly supports the trends observed in theresults of the finite element analyses, in which the wall flex-ibility increased due to the increase in L as the excavationproceeded. A similar trend has been reported by O’Rourke[18], in which the ratio of the volume of ground settlementincreased, to as great as 1.0, as the wall flexibility increasedby the increase in L. This similarity indicates that the way inwhich the ground loss at the wall is reflected to the groundsurface depends not only on the dilatancy characteristicsof the ground but also on the wall flexibility. The wall flex-ibility should therefore be taken into consideration wheninferring the maximum ground surface settlement from themaximum lateral wall movement for a given excavation.

Fig. 17. Variation of dh,max/dw,max with flexibility ratio (Hun = 4 m): (a) cantilever stage and (b) lateral bulging stage.

Fig. 18. Variation of dv,max/dw,max with flexibility ratio (Hun = 1 m): (a) cantilever stage and (b) lateral bulging stage.


4. Ground surface movements characterization

In the sections that follow, the ground surface move-ment profiles for the conditions analyzed are decomposedinto cantilever and lateral bulging components, and thecharacteristics of each component are discussed.

4.1. Components of ground surface movement profiles

Illustrated in Figs. 22 and 23 are the ground surfacemovement profiles for two cases, both of which have thesame wall and excavation conditions but different Hun.Each figure shows three curves; one for the final, and theother two for the cantilever and the lateral bulging compo-nents, respectively. Note that the lateral bulging componentof a given movement profile is obtained by subtracting the

cantilever component from the final profile. Comparisonsbetween the two cases thus provide insights into the generalcharacteristics of the cantilever and the lateral bulging com-ponents of ground surface movement profiles.

As seen in Fig. 22a for the case of Hun = 1 m, it is evi-dent that the cantilever components are negligibly small,and that the final profiles and the lateral bulging compo-nents are practically the same. For the case of Hun = 4 mshown in Fig. 22b, in which significant cantilever-type wallmovements are allowed to develop, both the cantileverand the lateral bulging components are apparent. A sali-ent feature observed in Fig. 22 is that the final settlementsof the two cases are practically identical, regardless ofHun, illustrating that the cantilever excavation depth Hun

has a transitional effect on the final settlements of a givenexcavation.

Fig. 19. Variation of dh,max/dw,max with flexibility ratio (Hun = 1 m): (a) cantilever stage and (b) lateral bulging stage.

Fig. 20. Relationship between Vs and VL (L = 5 m): (a) Hun = 4 m and (b) Hun = 1 m.


As seen in Fig. 23, cases having different combinationsof (EI)w and Es exhibit the same trend. The results illus-trated in these figures have significant practical implica-tions on the prediction of ground movement profiles, asthey imply that the cantilever and the lateral bulging com-ponents are separable and independent of each other.Therefore, any deep excavation-induced ground movementprofiles can be conveniently constructed by simply addingthe cantilever and the lateral bulging components. This isdiscussed further later in this paper.

4.2. Cantilever component

Cantilever-type movements develop during excavationto upper levels of supports. The magnitude and distribu-tion of ground movement due to cantilever wall move-

ments for a given excavation depend basically on thedepth of cantilever excavation Hun and the relative wallstiffness with respect to soil stiffness.

A survey conducted on deep excavation practice inKorea as part of this study indicated that the depth of can-tilever excavation was approximately 4–5 m with wall flex-ibility F = 10–250. For this reason, the results for caseshaving four levels of flexibility ratio, i.e., F = 15, 74.2,120, and 220 with the soil stiffness of Es = 26.2 MPa arepresented in Fig. 24 associated with the cantilever-type lat-eral wall movements.

As noticed, the vertical settlement profiles are essentiallybilinear in shape with the maximum values occurring nearthe edge of excavation. The horizontal displacement pro-files change from parabolic to bilinear in shape as the wallbending stiffness decreases. In addition, significant horizon-

Fig. 21. Relationship between dv,max and dw,max: (a) Hun = 4 m, (b) Hun = 1 m and (c) field data.


tal and vertical movements develop in the region within0.2H from the edge of excavation. Buildings and utilitieslocated in close proximity to a deep excavation with a flex-ible wall, therefore, can experience significant levels ofangular as well as lateral distortions even in the early stagesof excavation.

4.3. Lateral bulging component

The lateral bulging components of the ground surfacemovement profiles are illustrated in Figs. 25 and 26 forcases having two levels of flexibility ratio, i.e., F = 15 and220 with different Hun. For each flexibility ratio, a numberof profiles having different combinations of (EI)w and L arepresented.

As seen in these figures, the vertical and the horizontalsettlement profiles follow predominantly concave upwardand downward shapes with the maximum values occurringapproximately at 0.3–0.4H and 0.5–0.6H away from theedge of excavation for the lateral bulging stage, respectively.

Salient features shown in these figures are two-fold.First, for a given flexibility ratio, the movement profilestend to vary depending on the combination of (EI)w andL with this trend being more pronounced as the wall flexi-bility increases. This trend supports the results presentedearlier that L and the depth of the over excavation are byfar a more important controlling factor of ground move-ment than the wall stiffness (EI)w for excavation cases. Sec-ondly, although not as apparent, the locations of themaximum horizontal displacement and vertical settlement

Fig. 22. Ground surface displacement profiles (F = 120 and Es = 26.2 MPa): (a) Hun = 1 m and (b) Hun = 4 m.

Fig. 23. Ground surface displacement profiles (F = 120 and Es = 53.2 MPa): (a) Hun = 1 m and (b) Hun = 4 m.


tend to move slightly farther away from the edge of exca-vation as L increases, due primarily to the deep-seatedmovements associated with increasing L.

4.4. Normalized ground surface displacement profiles

With respect to the ground surface movement predic-tion, it would be desirable if normalized relationships canbe established among different cases. Figs. 27 and 28 pres-ent the lateral bulging components of the ground surfacemovement profiles normalized with their respective maxi-mum values for cases having F = 15 and 220.

Interestingly, the normalized profiles for a given F butdifferent combinations of (EI)w and L tend to collapse moreor less into one curve. This trend indicates that although dif-

ferent in magnitude, normalization holds for the groundsurface movement profiles for cases having the same flexi-bility ratio. The variation in the region beyond the maxi-mum values is of little practical importance on account ofthe relatively small magnitudes. Although not includedhere, other cases exhibited the same trend.

Fig. 29 presents normalized profiles for the case ofHun = 4 m with their respective maximum values at thefinal excavation stage for the cantilever as well as the lat-eral bulging components, which can be readily used tomake the prediction of deep excavation-induced groundmovements for cases with similar excavation conditionsconsidered in this study.

The normalized profiles for the cantilever componentshown in Fig. 29a represent cases with a cantilever excava-

Fig. 24. Cantilever components of the ground movements profiles (Es = 26.2 MPa): (a) Hun = 4 m and (b) Hun = 1 m.

Fig. 25. Lateral bulging components of ground movements profiles (Hun = 1 m).


tion depth of Hun = 4 m. Fig. 29b presents the normalizedlateral bulging components for various flexibility ratios.The flexibility ratios covered in this figure bracket a widerange of cases frequently encountered in practice, andtherefore, these profiles can be used to make a predictionof ground movement profiles for a given excavation witha reasonable degree of accuracy. A two-step approach isproposed for prediction of deep-excavation-inducedground movement profiles, in which the normalized canti-lever and lateral bulging components of ground surfacemovements are first systematically determined fromFig. 29a and b, respectively, based on the wall stiffness(EI)w and the flexibility ratio F for a given excavation.Actual cantilever and lateral bulging components are thenobtained by multiplying the normalized profiles with their

respective maximum values obtained either from Fig. 29or local experience. Complete ground surface movementprofiles can then be constructed by simply adding the can-tilever and the lateral bulging components of profiles.

4.5. Estimation of settlement influence zone

The influence zone of ground settlements should be rea-sonably established to evaluate the damage of adjacentbuildings caused by deep excavation. In this study, theinfluence zone of ground movement obtained by FE anal-ysis is compared with that of a previous study by Hsieh andOu [11]. Figs. 30–33 show the normalized ground surfaceprofiles with their maximum horizontal and verticalground settlements for cases having various flexibility

Fig. 27. Normalized lateral bulging components of ground movement profiles (Hun = 4 m).

Fig. 26. Lateral bulging components of ground movements profiles (Hun = 4 m).


ratios, different cantilever excavation depths, and soil stiff-ness. In these cases, the unsupported excavation spanlength is held constant at L = 5 m. In these figures, the dot-ted line represents the influence zone of ground surface set-tlements obtained by Hsieh and Ou [11] and the solid linesrepresent the results from this study.

As indicated in Fig 30a, the ratio of dv/dv,max is approx-imately equal to 0.5 and agrees well with the results ofHsieh and Ou [11]. The primary influence zone and the sec-ondary influence zone are about to 1.7H and 3H, respec-tively. These results are smaller than those proposed byHsieh and Ou [11] but agree with the results obtained bythe method of Clough and O’Rourke [5] as well as the fieldmeasurements [24] as presented in this study. According tothe studies by Hsieh and Ou [11], the distance from the wall

where dv,max occurs is half the final excavation depth 0.5H.Compared to the results of Hsieh and Ou [11], however,dv,max from this study occurs at a shorter distance, approx-imately 0.28–0.36H. In the relationship between dw,max anddv,max, the ratio of the distance where dv,max occurs to thedepth where dw,max occurs increases to approximately0.51–0.86 for the rigid wall as L increases. This trend indi-cates that the distances where dv,max and dw,max occur varywith the unsupported excavation length L. For the flexiblewall, the ratio increases approximately to 0.47–0.62 withincreasing L.

The influence zone of the horizontal ground settlementsis examined in this study. In most previous studies, there isno guideline for the prediction of the horizontal settlementprofiles because of the difficulty in measuring horizontal

Fig. 28. Normalized lateral bulging components of ground movement profiles (Hun = 1 m).

Fig. 29. Normalized ground movement profiles (Hun = 4 m and L = 5 m): (a) cantilever component and (b) lateral bulging component.


ground surface displacements, and consequently, only theinfluence zone for the vertical ground surface profiles hasbeen proposed.

Presented in Fig. 30b is the ratio of dh to dw,max at thewall, being a range of 0.7–1.0. This range decreases withincreasing F. For the rigid wall system, the horizontalground movements at the wall is directly associated withthe wall displacement but the maximum horizontal grounddisplacement occurs away from the wall for the flexiblewall system due to the lateral bulging. The maximum valueof dh/dh,max occurs at 0.5H except for rigid wall system, andthe primary influence and secondary influence zones for thehorizontal ground surface movements are approximatelyequal to 1.7H and 3.0H, respectively. Such results are sim-ilar to the cases for the vertical ground surface movements.

As shown in Fig. 31 for the case with Hun = 1 m, the resultsexhibit the same trend as the case with Hun = 4 m exceptthat the displacements at the wall greatly decrease due tothe installation of the top most support. As seen in Figs.32 and 33, the results yield similar settlement profiles interms of the magnitudes and the slope despite of the differ-ences in Es.

Based on the finite analyses, it can be concluded that theprimary influence and the secondary influence zones areapproximately equal to 2H and 3H, respectively. Theseresults agree with the method of Clough and O’Rourke[5] and almost coincide with the study by Hsieh and Ou[11]. Therefore, the influence zone of ground surface move-ment can be estimated by using the double hardeningmodel implemented in this study with a reasonable degree

Fig. 30. Estimation of settlement influence zone (Hun = 4 m, L = 5 m and Es = 26.2 MPa): (a) vertical component and (b) horizontal component.

Fig. 31. Estimation of settlement influence zone (Hun = 1 m, L = 5 and Es = 26.2 MPa): (a) vertical component and (b) horizontal component.


of accuracy, and the double hardening model can beapplied to the damage assessment of adjacent buildingsinduced by deep excavation in urban areas.

5. Conclusions

This paper presents the results of numerical investiga-tion on deep excavation-induced ground surface move-ment characteristics under the ground conditionsencountered in Korea. In order to realistically modelground movements associated with deep excavation,Lade’s double hardening model was incorporated intoABAQUS and used to simulate stress–strain behavior ofthe weathered soil. The appropriateness of the Lade’s dou-

ble hardening model and the finite element model adoptedin this study was validated using available field instrumen-tation data. The finite element model was then employedfor a parametric study on deep excavations with emphasison ground movements. On the basis of the parametricstudy, a method for predicting deep excavation-inducedground movement profiles is proposed, which is of primeimportance in damage assessment of adjacent structures.Based on the results of the present study, the followingconclusions can be drawn:

(1) The general shape of a ground surface settlement pro-file is closely related to the sources of wall move-ments, and that the unsupported span length has a




significant influence on the magnitude and distribu-tion of wall and ground movement characteristics.

(2) For a given ground condition, the ratio of the maxi-mum ground surface settlement to the maximum wallmovement decreases with increasing wall flexibility forthe cantilever component but increase with increasingwall flexibility for the lateral bulging components.

(3) The cantilever and the lateral bulging stages of exca-vation produce distinctive ground surface displace-ment profiles, which are separable and independentof each other. Deep excavation-induced ground sur-face movement profiles for a given excavation canbe predicted with a reasonable degree of accuracy

by combining the cantilever and the lateral bulgingcomponents.

(4) The primary influence and the secondary influencezones are approximately equal to 2H and 3H for ver-tical ground movements, respectively. The resultsagree with the previous studies by Clough andO’Rourke and Hsieh and Ou.

(5) The proposed method for predicting ground surfacemovement profiles captures the fundamental charac-teristics of ground surface movement profiles, andtherefore can be used with a reasonable degree ofaccuracy to make an estimate of ground surfacemovement profiles.


References

[1] ABAQUS (ver. 5.8) User’s Manual. Hibbitt, Karlsson & SorensenInc.; 1999.

[2] Boscardin MD, Cording EJ. Building response to excavation-inducedsettlement. J Geotech Eng, ASCE 1989;115(1):1–21.

[3] Burland JB. Assessment of risk of damage to buildings due totunneling and excavations. In: Invited special lecture to IS-ToKyo’95: proceedings of the first international conference on earthquakegeotechnical engineering; 1995.

[4] Clough GW, Hansen LA, Mana AI. Prediction of supportedexcavation movements under marginal stability conditions in clay.In: Proceedings of the third international conference on numericalmethods in geomechanics; 1979. p. 1485–502.

[5] Clough GW, O’Rourke TD. Construction induced movements ofinsitu walls. In: Proceedings of the design and performance of earthretaining structures, ASCE special conference; 1990. p. 439–70.

[6] Cording EJ, O’Rouke TD. Excavation, ground movements, and theirinfluence on buildings, protection of structures adjacent to bracedexcavation. In: Proceedings of the ASCE annual convention; 1977[preprint].

[7] Cording EJ. Evaluation and control of ground movements aroundtunnels and excavations in soil. In: Proceedings of the XII interna-tional conference on soil mechanics and foundation engineering;1985. p. 106–31.

[8] Cording EJ, Long JH, Son M, Laefer DF. Modeling and analysis ofexcavation-induced building distortion and damage using a strain-based damage criterion. In: Proceedings of the international confer-ence response of buildings to excavation-induced ground movements,CIRIA; 2000.

[9] Desai CS, Zaman MM, Lightner JG, Siriwardance HJ. Thin-layerelements for interfaces and joints. Int J Numer Anal MethodGeomech 1984;8(1):19–43.

[10] Hashash YM, Whittle AJ. Ground movement prediction fordeep excavations in soft clay. J Geotech Eng, ASCE 1996;122(6):474–86.

[11] Hsieh PO, Ou CY. Shape of ground surface settlement profiles causedby excavation. Can Geotech J 1998;35:1004–17.

[12] Janbu N. Soil compressibility as determined by oedometer andtriaxial tests. In: Proceedings of the European conference on soilmechanics and foundation engineering, vol. 1; 1963. p. 19–25.

[13] Kang Byung Sun, Yang Jae Hyouk. Adoptability of double harden-ing constitutive model for compacted decomposed granite soil,KSCE. J Civil Eng 1999;19(3):1013–20.

[14] Lade PV. Elasto-plastic stress–strain theory for cohesionless soil withcurved-yield surfaces. Int J Soild Struct 1977;13:1019–35.

[15] Lade PV, Nelson RB. Incrementalization procedure for elasto-plasticconstitutive model with multiple, intersecting yield surfaces. Int JNumer Anal Method Geomech 1984;8:311–23.

[16] Lade PV. Three-dimensional behavior and parameter evaluation ofan elastoplastic soil model. Geomech Model Eng Pract 1986:297–311.

[17] Mana AI, Clough GW. Prediction of movement for braced cuts inclay. J Geotech Eng, ASCE 1981;107(6):759–77.

[18] O’Rourke TD. A study of two braced excavation in sands andinterbedded stiff clay. PhD thesis, University of Illinois at Urbana-Champaign; 1975.

[19] Ou CY, Hsieh PO, Chiou DC. Characteristics of ground surfacesettlement during excavation. Can Geotech J 1993;30(5):758–67.

[20] Peck RB. Deep excavations and tunneling in soft ground. state-of-the-art report. In: Proceedings of the seventh international conferenceon soil mech. and found. engineering, state-of-the-art volume; 1969.p. 225–90.

[21] Viggiani Gioacchino, Tamagnini Claudio. Ground movementsaround excavations in granular soils: a few remarks on the influenceof the constitutive assumptions on FE predictions. Mech Cohes FrictMater 2000;5:399–423.

[22] Wong KS, Duncan JM. Hyperbolic stress–strain parameters fornonlinear finite element analyses of stresses and movements in soilmass. Geotechnical engineering research report no. TE/74-3, Univer-sity of California, Berkeley; 1974.

[23] Wong KS, Broms BB. Lateral wall deflections of braced excavationsin clay. J Geotech Eng, ASCE 1989;15(6):853–70.

[24] Yang G. Analysis of adjacent ground movements for deep excava-tions in urban areas. PhD thesis, Seoul National University; 1996.

[25] Yoo C. Behavior of braced and anchored walls in soils overlying rock.J Geotech Geoenviron Eng, ASCE 2001;27(3):225–33.

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