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Deep excavation-induced ground surface movement characteristics – A numerical investigation
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Computers and Geotechnics 35 (2008) 231–252 www.elsevier.com/locate/compgeo
Deep excavation-induced ground surface movement characteristics – 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 2007 Available online 28 June 2007
Abstract This paper concerns the characterization of deep excavation-induced ground surface movements, using the results of numerical investigation. A calibrated 2D finite element model using the Lade’s double hardening constitutive model for soil was used to form a database of the wall and ground surface movements associated with deep excavation. The results indicated that the cantilever and the lateral bulging excavation stages produce distinctive patterns of ground surface movement profiles, and that final ground surface movement profiles can be constructed by combining the cantilever and the lateral bulging components with a reasonable degree of accuracy. A two-step approach 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 deep excavation projects for constructions of high-rise buildings and subways. During deep excavation, changes in the state of stress in the ground mass around the excavation and subsequent ground losses inevitably occur. These changes and ground losses affect the surrounding ground in the form of ground movements, which eventually impose direct strains onto nearby structures. The magnitude and distribution of ground movements for a given excavation depend largely on soil properties, excavation geometry including depth, width, and length, and types of wall and support system, and more importantly construction procedures. Because of the increased public concern of the effects of construction-induced ground movements on their properties, the prediction of ground movements and assessment of the damage risk have become an essential part of the *
Corresponding author. Tel.: +82 31 290 7644; fax: +82 31 290 7549. E-mail address: [email protected] (D. Lee).
0266-352X/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compgeo.2007.05.002
planning, design, and construction of deep excavations in urban environments. Over the years, there have been a number of studies on the subject of wall and ground movements associated with deep excavation. Clough and O’Rourke [5] extended the work by Peck [20] and developed empirical settlement envelopes. Cording [7] provided a means of estimating the distribution of ground movements behind an excavation wall on the basis of volume relationships based on field observations. Ou et al. [19] compiled and analyzed field data regarding wall movement associated with deep excavation and defined the apparent influence range (AIR) for damage assessment of adjacent structures. More recently, Yoo [25] collected field data on lateral wall movement for walls constructed in soils overlying rock from more than 60 different excavation sites and analyzed the data with respect to wall and support types. The finite element method of analysis has also been extensively used in studies concerning wall and ground movements associated with deep excavation. The studies by Clough et al. [4], Mana and Clough [17], Wong and
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Broms [23], and Hashash and Whittle [10] were directed toward the prediction of wall movement for excavations in soft clay. Cording and O’Rourke [6] and later Cording [7] developed a scaling relationship based on an elastic assumption and investigated the effect of relative stiffness of the wall system with respect to soil on lateral wall movement. Most of the aforementioned previous studies focused on the maximum wall movement. Studies concerning ground surface movement characterization have been scarce due in large part to difficulties in obtaining complete sets of data either from field instrumentation or numerical analysis. Available information on the magnitude and distribution of ground surface movement associated with deep excavation is somewhat outdated and provides limited information required for building damage assessment. This study is directed toward the development of prediction method for deep excavation-induced ground surface movement profiles that can be used in the framework of currently available building damage assessment procedures (Boscardin and Cording [2] and Burland [3]). In order to correctly simulate the deep excavation-induced ground movement characteristics, the Lade’s double hardening constitutive model [14–16] was used to describe the stress–strain-strength behavior of the model ground. The finite element model adopted was validated by available data [24] before conducting the parametric study. A parametric study on deep excavation problems encountered in Korea was performed using the validated finite element model to form a database for use in the development of a prediction method associated with deep excavation-induced wall and ground surface movements. The results of the parametric study were carefully analyzed so that the ground surface movement characteristics could be related to the sources of wall movements. A systematic approach for prediction deep excavation-induced ground movement profiles was then developed. 2. Parametric study A series of 2D finite element analyses were performed using a commercial finite element program ABAQUS [1] to examine the ground surface movement characteristics and to form a database for use in the development of a ground movement profile prediction method. Subsequent sections discuss the details of the parametric study. 2.1. Problem investigated The configuration of the problem to be analyzed is shown in Fig. 1, which represents a hypothetical case of an excavation. For simplicity, an idealized symmetric plane strain braced excavation geometry with an excavation depth H and a width B of 20 and 30 m, respectively, was considered. The wall is a 25 m in height and has with a 5 m toe penetration depth at the final excavation stage. Because of symmetry about the excavation centerline, only
Fig. 1. Finite element mesh and modeling of interface element for parametric study.
one-half of the excavation was considered in the finite element model. The excavation ground considered was assumed to be composed of a weathered granite soil overlying a weathered rock stratum. The weathered granite soil is the representative soil in urban excavation sites in Korea and this type of ground formation is a typical soil profile frequently encountered in Korea. The excavation platform corresponds to the top of the weathered rock stratum. Primary variables included the wall bending stiffness (EI)w, the cantilever excavation depth Hun, the unsupported span length L below the lower-most support, and soil stiffness Es. Combinations of (EI)w and L generated the range of F shown in Table 1. In addition, a wide range of conditions was analyzed by varying the primary variables mentioned above. The parameter F in Table 1 is the flexibility ratio, defined by the following equation: F
Es L3 ðEIÞw
ð1Þ
where Es is the soil stiffness, L is the unsupported excavation length, and (EI)w is the wall flexural rigidity. The flexibility ratio was originally introduced by Cording and O’Rourke [6]. The range in wall flexibility ratio considered in this study is approximately from 15 to 400, which is consistent with the range for slurry, cast-in-place pile, sheet pile, and soldier pile walls. 2.2. Finite element analysis 2.2.1. Finite element model In the finite element modeling, the ground and the wall were discretized by using eight-noded plane strain eleTable 1 Conditions analyzed F
Es (aver) (MPa)
L (m)
15, 50, 74.2, 120, 150, 176, 220, 400
26.2, 53.2
3, 4, 5, 1, 2, 3, 15 6 4
Hun (m)
Note: EIw, wall flexural rigidity; K, effective axial stiffness.
K (MN/ m)
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ments, while the struts were modeled by using one-node spring elements with an effective axial stiffness of 15 MN/ m considering the excavation width. As shown in Fig. 1, a refined finite element mesh extended to a depth of 1.0H below the final excavation platform and laterally to a distance of 3.8H from the excavation centerline to minimize the effect of the artificial boundaries on the ground surface movement characteristics. For the material modeling, the weathered rock stratum was assumed to be an elasto-plastic material conforming to the Mohr–Coulomb failure criterion [1]. On the basis of the extensive surveys of urban excavation sites in Korea, the mechanical properties for the weathered rock in Table 2 were used in the parametric study. On the other hand, the weathered soil was assumed to follow the Lade’s double hardening model. Brief discussions on the double hardening model and the model parameters used in the analysis are given in Section 2.2.2. A series of preliminary analyses indicated that the interface modeling of the excavation side is crucial for obtaining realistic ground surface movement profiles associated with deep excavation. Although ABAQUS provides a surfacebased interface modeling option using ‘contact pair’, the contact pair was not adopted in modeling the interface in this study as significant numerical instabilities were encountered during the excavation modeling. For that reason, the Desai-type thin-layer interface model [9] shown the inset in Fig. 1 was implemented in ABAQUS using UMAT [1] to model the interface behavior between the wall facing and the soil. Details of the Desai-type thin-layer interface model can be found in [9]. The stiffness matrix of thin-layer element is the same as general solid element assuming a linear elastic behavior. Therefore, the elastic constitutive matrix of the thin-layer element is expressed as: ½C nn i ½C ns i ½Ci ¼ ð2Þ ½C sn i ½C ss i where [Cnn] and [Css] are related to normal and shear components, respectively, and [Cns], [Csn] represent coupling effects. However, the coupling effects are not included for simplification in this study. For isotropic linear elastic behavior, [C]i can be written in matrix form as: 3 2 M k k 0 0 0 6 k M k 0 0 07 7 6 7 6 6 k k M 0 0 07 7 6 ð3Þ ½Ci ¼ 6 7 6 0 0 0 G 0 07 7 6 4 0 0 0 0 G 05 0
0
0
0
0
G
Table 2 Typical mechanical properties for weathered rock in Korea Material
C (kPa)
/ ()
w ()
m
Es (MPa)
Weathered rock
100
46
6
0.3
500
233
Eð1mÞ Em and k ¼ ð1þmÞð12mÞ where, M ¼ ð1þmÞð12mÞ
Under the two-dimensional plane strain condition, Eq. (3) can be reduced to the following equation: 2 3 M k 0 6 7 ð4Þ ½Ci ¼ 4 k M 0 5 0
0
G
Based on the results of a series of preliminary analyses for model calibration, a relatively low shear modulus of 50 kPa with high bulk modulus was assigned to the interface elements. In simulating the step-by-step excavation process, the initial vertical state of stress was first created by turning on the gravity with the assumption of wished-in-placed wall. The lateral stress state was then created by multiplying the vertical stresses by the lateral earth pressure coefficient K0 = 0.5. The excavation process was then modeled by adding and removing elements at corresponding steps. Although the ground water lowering due to excavation generally affects the ground movement characteristics, the ground water was not considered for simplification and the free-draining characteristics of typical weathered soils in Korea. 2.2.2. Constitutive modeling of weathered soil It has been shown that a traditional elasto-perfectlyplastic model such as Mohr–Coulomb model does not yield satisfactory results in estimating deep excavationinduced ground movement, especially for ground surface settlements [21]. The double hardening model, which has been proven to be applicable for the weathered soil frequently encountered in Korea [13], was selected and implemented in ABAQUS using the user subroutine capability to represent the soil behavior in this study. In this section, the brief descriptions of the double hardening model based on 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 total strains are assumed to be divisible into elastic strains, plastic collapse strains, and plastic expansive strains. The elastic strains are calculated from Hooke’s law using the unloading–reloading modulus defined as: Eur ¼ K ur P a ðr3 =P a Þn
ð5Þ
where Kur and n are dimensionless model parameters and Pa is atmospheric pressure to make conversion from one system of units to another more convenient. Thus, the units of Eur and r3 are the same as units of Pa. The plastic collapse strains are associated with volumetric strains and mean effective stress. They are computed using a cap type yield surface conforming associated flow rule and a work-hardening relationship which can be determined from an isotropic compression test. The yield criterion, fc, and the plastic potential function, gc, are expressed in terms of the first and second invariants, I1, I2, as follows:
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fc ¼ gc ¼ I 21 þ 2I 2
ð6Þ
where I1 and I2 are first and second stress invariants. An empirical relationship for the collapse work-hardening as a function of fc is defined as: p fc ð7Þ W c ¼ C Pa 2 Pa where C and p are material parameters and the incremental plastic collapse work (dWc) can be determined from the derivative of Wc with regard to fc: 1p Cp P 2a dW c ¼ dfc ð8Þ P a fc The plastic expansive strains are related to the deviatoric stresses and they are computed using a conical yield surface and conform non-associated flow rule. The conical yield surface is described in terms of the first and third stress invariants, I1 and I3: 3 m I I1 fp ¼ 1 27 6 g1 ð9Þ I3 Pa where m is a model parameter describing the curvature of the failure surface, and g1 is a work-hardening parameters which defines the size of the failure surface. The plastic potential function is modeled on the yield function as follows: m Pa ð10Þ gp ¼ I 31 27 þ g2 I3 I1 where g2 can be modeled by the following simple expression: 1=2 r3 g2 ¼ Sfp þ t þ R ð11Þ Pa where S, t, and R are model parameters. An empirical relationship between the plastic expansive work done (Wp) and fp is defined by the following expression: 1=q Wp fp ¼ a ebW p ð12Þ Pa 1=q Pa with a ¼ g1 Weppeak and b ¼ qW 1 ppeak
where Wppeak and q are constants for a given value of r3 and e is the base for natural logarithms. Wppeak is the value of Wp at the peak point and its variation with r3 can be approximately expressed by the following empirical relationship: l W ppeak r3 ¼P ð13Þ Pa Pa where P is the value of Wppeak/Pa when Pa = 1. The variation of the parameter q with r3 can be represented by a simple expression as follows: r3 q¼aþb ð14Þ Pa
where a and b represent the intercept and slope of a straight line, respectively. From Eq. (12), the increment in plastic expansive work can be expressed as follows: dW p ¼
dfp fp
1 qW p
1 b
ð15Þ
In implementing the double hardening model using the user subroutine capability the soil is assumed to follow an elastic behavior and then the stress invariants are calculated to estimate the current collapsive yield stress and expansive yield stress. The current collapsive yield stress and expansive yield stress are then compared to the maximum past collapsive yield stress and the maximum past expansive yield stress to determine the loading conditions. After comparing the present and the past yield stresses, the maximum past yield stresses are replaced with larger one and then they are stored in the solution-dependent state variables array. Four different conditions may exist: (1) only elastic strains occur, (2) only plastic collapsive surface is activated, (3) only plastic expansive surface is activated and (4) both plastic collapsive and expansive surfaces are activated. After determining the loading conditions, the stresses are calculated by using stiffness matrix suitable for each yielding condition and then they are updated and stored to the stress array. A total of 14 parameters are required in the double hardening 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 required parameters can be entirely derived from the conventional triaxial test with volume change measurement. Table 3 presents the double hardening model parameters of the weathered soil used in the model ground. Note that the values are based on the previous study [13] which reports ranges of
Table 3 Parameters for the weathered soil Parameters
Weathered soil
Strain component
Kur n Poisson’s ratio
2:57 0.865 0.25
Elastic component
Collapse const. (C) Collapse expo. (p)
0.0086 0.789
Plastic collapse component
Yield const. (g1) Yield expo. (m) P1. potent. const. (R) P1. potent. const. (t) P1. potent. const. (S) Work-hard. const. (a) Work-hard. const. (b) Work-hard. const. (P) Work-hard. expo. (I)
38 0.113 1.406 0.488 0.406 1.254 0.072 0.52 0.653
Plastic expansive component
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the double hardening model parameters for weathered soils encountered in Korea.
Table 5 Material properties for an urban excavation site in Korea Material
2.2.3. Model validation The finite element model adopted in this study was validated to a limited extent against measured data for an urban excavation site in Korea [24]. The same modeling approach for parametric study given in Section 2.2.1 was employed in the finite element modeling. Fig. 2 presents the standard cross-section and soil profile for the site. The wall of 26 m in height with an embedment depth of approximately 2 m consisted of soldier pile was supported by struts and detailed descriptions of the site are given in Table 4 [24]. As shown in Fig. 2, the vertical spacing of the struts and the unsupported span length were varied by the construction sequences for simulating the field conditions in detail. The average of the vertical spacing of the struts and the unsupported excavation length are 2.5 m and 2–3 m respectively. Cantilever excavation depth of 3–4.5 m, excavation depth 23.7 m, and the over excavation depth of 2.5–3 m are applied to the analysis. As illustrated in the figure, the ground consists of a fill material, a weathered soil, and a weathered rock. Most of the excavation took place within the weathered soil. Table 5 summarizes the mechanical properties of the site
235
Fill Weathered soil Weathered rock
C (aver) (kPa)
Es (aver) (MPa)
/ (aver) ()
w (aver) ()
m (aver)
10 25
30 40
8 6
0.3 0.3
17 30
300
41
6
0.3
110
USCS
SM SM None
in terms of the Mohr–Coulomb shear strength parameters and the elastic stiffness reported in [24] to give general information of the soils layer and the rock layer. In material modeling, although the fill layer and the weathered soil in the site have a bit different shear strength parameters as shown in Table 5, these soils were considered to have the same double hardening model parameters. This is justified since the fill layer and the weathered soil are reported to be similar 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 information available and therefore the validation given in this section should thus be viewed as qualitative. The rock layer is assumed to follow the Mohr–Coulomb yield criterion with the material properties in Table 5. Thus, the site was assumed to be composed of a weathered soil overlying a weathered rock. Fig. 3 presents the comparisons between the measured and predicted ground surface settlements. The solid lines represent the predictions from the double hardening model and the points represent the measured results. Note that due to the general practice of not measuring horizontal ground surface settlements during excavation, only the vertical ground settlement data were used for validation. As shown in the figure, the predicted maximum settlement of
Fig. 2. Cross-section and soil profile for an urban excavation site in Korea. Table 4 Descriptions of an urban excavation site in Korea Excavation depth, H (m) Wall type Soil type Support type and average spacing Flexibility ratio (F)
23.7 Soldier pile (I = 1.26 · 104 m4) and lagging wall Fill + weathered soil Strut (A = 0.0053 m2), horizontal spacing = 4.0 m, vertical spacing = 2.5 m 150–250
Fig. 3. Comparison between results of proposed method and measured data.
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0.16%H agrees well with the measured one. The extent of the settlement zone is also well predicted as 2.5–3.0H. More importantly, the results agree fairly well in qualitative terms suggesting that the finite element modeling approach, including the constitutive modeling of the weathered soils using the double hardening model, is reasonably appropriate for use in this study. It should however be noted that a small-strain stiffness model may yield better results, especially in terms of lateral extent of the settlement profiles, such a model was not adopted in this study due to limited information available as to the applicability of the model to typical weathered soils encountered in Korea. Considering that the double hardening model is based on the nonlinear isotropic elasticity, the results may be comparable to those based on a small-strain stiffness model. However, a further study concerning the use of a small-strain stiffness model for typical ground conditions in Korea is warranted. 3. Wall and ground movement characteristics The results of the finite element analyses were compiled such that the patterns of wall and ground movements could be related to the parameters comprising the flexibility ratio. Important findings are discussed under the subsequent subheadings. 3.1. Effect of wall stiffness Fig. 4 illustrates the effect of wall bending stiffness on the wall and ground surface movement patterns. In the plot of the ground surface displacements, two sets of curves are shown. For the horizontal displacements, the displacement toward the excavation wall was taken as positive. Likewise the downward movement was taken as positive for the vertical settlements. Note that cantilever excavation depth and the unsupported span length during the lateral bulging
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 surface movements. The results are described by more of a step function than a gradual change with the wall stiffness. As seen in Fig. 4, as the wall stiffness decreases, the shape of the wall displacements changes from the cantilever form to the lateral bulging form for wall movements, and the horizontal component of the ground surface settlement profiles tend to become convex up and also the vertical component yields concave down. In terms of the maximum values, the location of the maximum settlement tends to move away from the edge of excavation as the wall stiffness increases. This trend indicates that for a given excavation condition, the wall bending stiffness influences not only the magnitudes of ground surface movements but also the pattern of the movements. In addition, the location of maximum settlement greatly varies at the flexibility ratio of F = 120. Moreover, as seen in Fig. 4b, significant horizontal ground surface displacements are developed, as great as 100–127% of the vertical settlements in terms of maximum values. These results demonstrate the need for considering horizontal ground surface displacements when assessing the risk of damage especially for buildings with small resistance to lateral ground displacements, as noted by Cording et al. [8], although the lateral building strains are significantly less than the lateral ground strains. Presented in Figs. 5 and 6 are the results of four cases having the same flexibility ratio of F = 120 but different combinations of (EI)w and L and different Hun, one with Hun = 1 m and the other with Hun = 4 m. The differences in the wall and ground surface movements between the cases thus represent the combined effect of (EI)w and L. As seen in these figures, the wall and ground surface displacement profiles tend to significantly vary in shape
Fig. 4. Variation of wall and ground movements with (EI)w.
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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 the same F. For the wall deformations, the maximum displacements of the wall do not vary in direct proportion to the bending stiffness. Furthermore, the curve 2 with the larger L and (EI)w yields greater wall and ground surface movements than the curve 1 with the smaller L and (EI)w due to the over excavation. A similar trend is shown in curves 3 and 4, suggesting that L and over excavation have a greater influence 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, and 1.0 m, respectively. The trends shown in these figures illustrate the dependency of the wall and ground movements on the combined effect of (EI)w and L and suggest that the
wall flexibility ratio F alone cannot correctly capture the wall and ground responses to a given excavation. 3.2. Effect of unsupported excavation depth During an excavation, unsupported excavation is inevitably carried out both in the cantilever and the lateral bulging stages. The effect of cantilever excavation depth Hun on the wall and ground movements is illustrated in Fig. 7. The cantilever excavation depth Hun was controlled in the analyses by varying the maximum depth of excavation before installing the top most support but keeping the other variables constant. Therefore, the differences in the wall and ground movements between the different cases solely reflect the effect of Hun.
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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 movements during the cantilever stage became significant when allowing Hun greater than 3 m, resulting in the ground surface displacement profiles with large volume losses in close proximity to the edge of the excavation. A strict provision on Hun should be placed during the early stages of excavation for cases in which buildings and buried utilities are located in close proximity to the edge of excavation. In addition, the wall deformations are almost constant with the increase of Hun, and similar results are shown for the vertical components. Hence, it is seen that maximum wall deformation and the vertical displacement of ground settlements are more dependent on the wall bending stiffness and the unsupported length L than the cantilever excavation depth Hun.
Examples with different Hun used to show the influences of the unsupported span length L for a given wall stiffness are illustrated in Figs. 8 and 9. As shown in these figures, an increase in L from 3 to 6 m results in substantial increases in the wall and ground surface movements by approximately an order of magnitude. An important observation is that an increase in the unsupported span length L results in increases in the magnitude of ground surface settlements and tends to modify the settlement profiles to more a concave downward shape because of the increased deep-seated movements. Although the flexibility due to the increase of the unsupported length L is increased, the wall and ground movements are severely varied by over excavation. Such results shown in these figures demonstrate that the excavation procedure during
Fig. 8. Variation of wall and ground movements with L (Hun = 4 m).
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239
Fig. 9. Variation of wall and ground movements with L (Hun = 1 m).
construction significantly affects the patterns of ground surface displacement profiles and the wall deformations. 3.3. Effect of soil stiffness The relative stiffness between the excavation wall and the soil has a significant influence on the magnitude and distribution of wall and ground movements for a given excavation. With respect to ground movement prediction, it would be more convenient if cases having the same flexibility ratio but different combinations of (EI)w and Es would yield similar ground surface movement profiles. Figs. 10–15 represent the ground surface movement profiles at the cantilever, lateral bulging, and final stages for cases having F = 50 and 150 but different combinations of (EI)w (=21.8, 44.4, 65.4, 133.1 MN m2/m) and Es
(=26.2, 53.2 MPa) and different Hun. In all cases, the unsupported depth during the lateral bulging stage was kept constant at L = 5 m. Note that Es represents the average soil modulus of the excavation ground calculated using the hyperbolic relationship given by Janbu [12] in the following equation: Es ¼ K P a ðr3 =P a Þ
n
ð16Þ
According to Wong and Duncan [22], the parameter Kur in Eq. (5), which is the modulus parameter determining Eur, is generally 1.2–3 times greater than K, which is the modulus parameter for Es. Considering this, the average value of Es was back-calculated from Eur. As seen in these figures, it appears that the cases with a same F would yield similar settlement profiles in terms of magnitude and slope despite the differences in the
Fig. 10. Ground movements profiles with soil stiffness (Hun = 4 m): (a) F = 50 and (b) F = 150.
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Fig. 11. Ground movements profiles with soil stiffness (Hun = 4 m): (a) F = 50 and (b) F = 150.
Fig. 12. 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 horizontal displacement profiles for a given F are similar, and the case with less rigid ground and wall tends to yield larger movements. An important conclusion is that as long as L is the same, the flexibility ratio F can be used as a common index for the prediction of ground surface settlement profiles for 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 settlement (dv,max) is usually taken as a fraction of the maximum lateral wall movement (dw,max). The results of the finite element analyses are compiled such that the maximum 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 maximum values for each component, i.e., the cantilever and the lateral bulging, are separately analyzed, and that the results are only relevant to the cases with ground conditions similar 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 cantilever as well as the lateral bulging components in a semilog plot. The case with the unsupported length L = 5 m was chosen to eliminate the effect of over excavation. As seen in Fig. 16a, the dv,max/dw,max ratio tends to linearly decrease with increasing F because of the increase of dw,max at an approximately same rate, regardless of the soil stiffness in the cantilever stage. The range of decrease
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241
Fig. 13. Ground movements profiles with soil stiffness (Hun = 1 m): (a) F = 50 and (b) F = 150.
Fig. 14. Ground movements profiles with soil stiffness (Hun = 1 m): (a) F = 50 and (b) F = 150.
is within 20%. In the lateral bulging stage, as the result of the decrease of the wall bending stiffness, dv,max/dw,max ratio tends to linearly increase with F, and the rate of increase for the soil stiffness remains almost constant within 10%. The dh,max/dw,max ratio shown in Fig. 17 appears to significantly vary with F in the cantilever stage, in the range of about 30%. This result suggests that even for a rigid wall system, a large amount of volume loss can be led in the cantilever stage. For a flexible wall system, as a result of the increase of wall deformation, dh,max/dw,max ratio tends to decrease and the effect of soil stiffness is insignificant like dv,max/dw,max. As seen in Fig. 17b, the dh,max/dw,max ratio does not appear to significantly vary with F in the lateral bulging stage, exhibiting similar results displayed by
dv,max/dw,max ratio. The difference in soil stiffness results from the lateral expansion of the retained soil. As illustrated in Fig. 18, the change of the vertical component lies within 5% because of the decrease in Hun and the immediate installation of struts after excavation. In the lateral bulging stage, the effect of the flexibility is also insignificant, and only the change associated to the soil stiffness appears. As seen in Fig. 19, dh,max/dw,max ratio also displays an almost similar trend for the case of Hun = 4 m. However, the range of variation is within 15%, and the effect related to the wall and the soil stiffness decreases. This result, as previously mentioned, reflects the influence of Hun. Therefore, dv,max/dw,max is dependent on Hun and F, regardless of the soil stiffness in the cantilever stage, and the lateral bulging stage is affected by Es, F, and
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Fig. 15. Ground movements profiles with soil stiffness (Hun = 1 m): (a) F = 50 and (b) F = 150.
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 horizontal component of ground settlement is greatly affected by the cantilever excavation depth. A constant value for dh,max/dw,max can be assumed for the lateral bulging stage without introducing a significant error, at least, within the limits of the F considered. Fig. 20 represents the ratio of settlement volume to wall displacement volume (Vs/VL). As seen in Fig. 20, the ratio of settlement volume to wall displacement volume almost linearly increases with increasing F in the semi-log plot. These results are a direct consequence of the increase in the ground settlement volume relative to the volume of wall displacement as the wall stiffness decreases. Fig. 21 illustrates the relationship between the normalized maximum ground displacements and wall movements.
As seen in the figure, the range of dv,max/dw,max ratio lies within 0.5–1.0. This trend is similar to the field data [24] in Fig. 21c and strongly supports the trends observed in the results of the finite element analyses, in which the wall flexibility increased due to the increase in L as the excavation proceeded. A similar trend has been reported by O’Rourke [18], in which the ratio of the volume of ground settlement increased, to as great as 1.0, as the wall flexibility increased by the increase in L. This similarity indicates that the way in which the ground loss at the wall is reflected to the ground surface depends not only on the dilatancy characteristics of the ground but also on the wall flexibility. The wall flexibility should therefore be taken into consideration when inferring the maximum ground surface settlement from the maximum lateral wall movement for a given excavation.
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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 movement profiles for the conditions analyzed are decomposed into cantilever and lateral bulging components, and the characteristics of each component are discussed. 4.1. Components of ground surface movement profiles Illustrated in Figs. 22 and 23 are the ground surface movement profiles for two cases, both of which have the same wall and excavation conditions but different Hun. Each figure shows three curves; one for the final, and the other two for the cantilever and the lateral bulging components, respectively. Note that the lateral bulging component of a given movement profile is obtained by subtracting the
cantilever component from the final profile. Comparisons between the two cases thus provide insights into the general characteristics of the cantilever and the lateral bulging components of ground surface movement profiles. As seen in Fig. 22a for the case of Hun = 1 m, it is evident that the cantilever components are negligibly small, and that the final profiles and the lateral bulging components are practically the same. For the case of Hun = 4 m shown in Fig. 22b, in which significant cantilever-type wall movements are allowed to develop, both the cantilever and the lateral bulging components are apparent. A salient feature observed in Fig. 22 is that the final settlements of the two cases are practically identical, regardless of Hun, illustrating that the cantilever excavation depth Hun has a transitional effect on the final settlements of a given excavation.
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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 combinations of (EI)w and Es exhibit the same trend. The results illustrated in these figures have significant practical implications on the prediction of ground movement profiles, as they imply that the cantilever and the lateral bulging components are separable and independent of each other. Therefore, any deep excavation-induced ground movement profiles can be conveniently constructed by simply adding the cantilever and the lateral bulging components. This is discussed further later in this paper. 4.2. Cantilever component Cantilever-type movements develop during excavation to upper levels of supports. The magnitude and distribution of ground movement due to cantilever wall move-
ments for a given excavation depend basically on the depth of cantilever excavation Hun and the relative wall stiffness with respect to soil stiffness. A survey conducted on deep excavation practice in Korea as part of this study indicated that the depth of cantilever excavation was approximately 4–5 m with wall flexibility F = 10–250. For this reason, the results for cases having four levels of flexibility ratio, i.e., F = 15, 74.2, 120, and 220 with the soil stiffness of Es = 26.2 MPa are presented in Fig. 24 associated with the cantilever-type lateral wall movements. As noticed, the vertical settlement profiles are essentially bilinear in shape with the maximum values occurring near the edge of excavation. The horizontal displacement profiles change from parabolic to bilinear in shape as the wall bending stiffness decreases. In addition, significant horizon-
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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 within 0.2H from the edge of excavation. Buildings and utilities located in close proximity to a deep excavation with a flexible wall, therefore, can experience significant levels of angular as well as lateral distortions even in the early stages of excavation. 4.3. Lateral bulging component The lateral bulging components of the ground surface movement profiles are illustrated in Figs. 25 and 26 for cases having two levels of flexibility ratio, i.e., F = 15 and 220 with different Hun. For each flexibility ratio, a number of profiles having different combinations of (EI)w and L are presented.
As seen in these figures, the vertical and the horizontal settlement profiles follow predominantly concave upward and downward shapes with the maximum values occurring approximately at 0.3–0.4H and 0.5–0.6H away from the edge 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 profiles tend to vary depending on the combination of (EI)w and L with this trend being more pronounced as the wall flexibility increases. This trend supports the results presented earlier that L and the depth of the over excavation are by far a more important controlling factor of ground movement than the wall stiffness (EI)w for excavation cases. Secondly, although not as apparent, the locations of the maximum horizontal displacement and vertical settlement
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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 excavation as L increases, due primarily to the deep-seated movements associated with increasing L. 4.4. Normalized ground surface displacement profiles With respect to the ground surface movement prediction, it would be desirable if normalized relationships can be established among different cases. Figs. 27 and 28 present the lateral bulging components of the ground surface movement profiles normalized with their respective maximum values for cases having F = 15 and 220. Interestingly, the normalized profiles for a given F but different combinations of (EI)w and L tend to collapse more or less into one curve. This trend indicates that although dif-
ferent in magnitude, normalization holds for the ground surface movement profiles for cases having the same flexibility ratio. The variation in the region beyond the maximum values is of little practical importance on account of the relatively small magnitudes. Although not included here, other cases exhibited the same trend. Fig. 29 presents normalized profiles for the case of Hun = 4 m with their respective maximum values at the final excavation stage for the cantilever as well as the lateral bulging components, which can be readily used to make the prediction of deep excavation-induced ground movements for cases with similar excavation conditions considered in this study. The normalized profiles for the cantilever component shown in Fig. 29a represent cases with a cantilever excava-
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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 normalized lateral bulging components for various flexibility ratios. The flexibility ratios covered in this figure bracket a wide range of cases frequently encountered in practice, and therefore, these profiles can be used to make a prediction of ground movement profiles for a given excavation with a reasonable degree of accuracy. A two-step approach is proposed for prediction of deep-excavation-induced ground movement profiles, in which the normalized cantilever and lateral bulging components of ground surface movements are first systematically determined from Fig. 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 then obtained by multiplying the normalized profiles with their
respective maximum values obtained either from Fig. 29 or local experience. Complete ground surface movement profiles can then be constructed by simply adding the cantilever and the lateral bulging components of profiles. 4.5. Estimation of settlement influence zone The influence zone of ground settlements should be reasonably established to evaluate the damage of adjacent buildings caused by deep excavation. In this study, the influence zone of ground movement obtained by FE analysis is compared with that of a previous study by Hsieh and Ou [11]. Figs. 30–33 show the normalized ground surface profiles with their maximum horizontal and vertical ground settlements for cases having various flexibility
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Fig. 26. Lateral bulging components of ground movements profiles (Hun = 4 m).
Fig. 27. Normalized lateral bulging components of ground movement profiles (Hun = 4 m).
ratios, different cantilever excavation depths, and soil stiffness. In these cases, the unsupported excavation span length is held constant at L = 5 m. In these figures, the dotted line represents the influence zone of ground surface settlements obtained by Hsieh and Ou [11] and the solid lines represent the results from this study. As indicated in Fig 30a, the ratio of dv/dv,max is approximately equal to 0.5 and agrees well with the results of Hsieh and Ou [11]. The primary influence zone and the secondary influence zone are about to 1.7H and 3H, respectively. These results are smaller than those proposed by Hsieh and Ou [11] but agree with the results obtained by the method of Clough and O’Rourke [5] as well as the field measurements [24] as presented in this study. According to the 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, approximately 0.28–0.36H. In the relationship between dw,max and dv,max, the ratio of the distance where dv,max occurs to the depth where dw,max occurs increases to approximately 0.51–0.86 for the rigid wall as L increases. This trend indicates that the distances where dv,max and dw,max occur vary with the unsupported excavation length L. For the flexible wall, the ratio increases approximately to 0.47–0.62 with increasing L. The influence zone of the horizontal ground settlements is examined in this study. In most previous studies, there is no guideline for the prediction of the horizontal settlement profiles because of the difficulty in measuring horizontal
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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 the influence zone for the vertical ground surface profiles has been proposed. Presented in Fig. 30b is the ratio of dh to dw,max at the wall, being a range of 0.7–1.0. This range decreases with increasing F. For the rigid wall system, the horizontal ground movements at the wall is directly associated with the wall displacement but the maximum horizontal ground displacement occurs away from the wall for the flexible wall system due to the lateral bulging. The maximum value of dh/dh,max occurs at 0.5H except for rigid wall system, and the primary influence and secondary influence zones for the horizontal ground surface movements are approximately equal to 1.7H and 3.0H, respectively. Such results are similar to the cases for the vertical ground surface movements.
As shown in Fig. 31 for the case with Hun = 1 m, the results exhibit the same trend as the case with Hun = 4 m except that the displacements at the wall greatly decrease due to the installation of the top most support. As seen in Figs. 32 and 33, the results yield similar settlement profiles in terms of the magnitudes and the slope despite of the differences in Es. Based on the finite analyses, it can be concluded that the primary influence and the secondary influence zones are approximately equal to 2H and 3H, respectively. These results 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 movement can be estimated by using the double hardening model implemented in this study with a reasonable degree
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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 be applied to the damage assessment of adjacent buildings induced by deep excavation in urban areas. 5. Conclusions This paper presents the results of numerical investigation on deep excavation-induced ground surface movement characteristics under the ground conditions encountered in Korea. In order to realistically model ground movements associated with deep excavation, Lade’s double hardening model was incorporated into ABAQUS and used to simulate stress–strain behavior of the weathered soil. The appropriateness of the Lade’s dou-
ble hardening model and the finite element model adopted in this study was validated using available field instrumentation data. The finite element model was then employed for a parametric study on deep excavations with emphasis on ground movements. On the basis of the parametric study, a method for predicting deep excavation-induced ground movement profiles is proposed, which is of prime importance in damage assessment of adjacent structures. Based on the results of the present study, the following conclusions can be drawn: (1) The general shape of a ground surface settlement profile is closely related to the sources of wall movements, and that the unsupported span length has a
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Fig. 32. Estimation of settlement influence zone (Hun = 4 m, L = 5 m and Es = 53.2 MPa): (a) vertical component and (b) horizontal component.
Fig. 33. Estimation of settlement influence zone (Hun = 1 m, L = 5 m and Es = 53.2 MPa): (a) vertical component and (b) horizontal component.
significant influence on the magnitude and distribution of wall and ground movement characteristics. (2) For a given ground condition, the ratio of the maximum ground surface settlement to the maximum wall movement decreases with increasing wall flexibility for the cantilever component but increase with increasing wall flexibility for the lateral bulging components. (3) The cantilever and the lateral bulging stages of excavation produce distinctive ground surface displacement profiles, which are separable and independent of each other. Deep excavation-induced ground surface movement profiles for a given excavation can be predicted with a reasonable degree of accuracy
by combining the cantilever and the lateral bulging components. (4) The primary influence and the secondary influence zones are approximately equal to 2H and 3H for vertical ground movements, respectively. The results agree with the previous studies by Clough and O’Rourke and Hsieh and Ou. (5) The proposed method for predicting ground surface movement profiles captures the fundamental characteristics of ground surface movement profiles, and therefore can be used with a reasonable degree of accuracy to make an estimate of ground surface movement profiles.
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References [1] ABAQUS (ver. 5.8) User’s Manual. Hibbitt, Karlsson & Sorensen Inc.; 1999. [2] Boscardin MD, Cording EJ. Building response to excavation-induced settlement. J Geotech Eng, ASCE 1989;115(1):1–21. [3] Burland JB. Assessment of risk of damage to buildings due to tunneling and excavations. In: Invited special lecture to IS-ToKyo ’95: proceedings of the first international conference on earthquake geotechnical engineering; 1995. [4] Clough GW, Hansen LA, Mana AI. Prediction of supported excavation movements under marginal stability conditions in clay. In: Proceedings of the third international conference on numerical methods in geomechanics; 1979. p. 1485–502. [5] Clough GW, O’Rourke TD. Construction induced movements of insitu walls. In: Proceedings of the design and performance of earth retaining structures, ASCE special conference; 1990. p. 439–70. [6] Cording EJ, O’Rouke TD. Excavation, ground movements, and their influence on buildings, protection of structures adjacent to braced excavation. In: Proceedings of the ASCE annual convention; 1977 [preprint]. [7] Cording EJ. Evaluation and control of ground movements around tunnels and excavations in soil. In: Proceedings of the XII international conference on soil mechanics and foundation engineering; 1985. p. 106–31. [8] Cording EJ, Long JH, Son M, Laefer DF. Modeling and analysis of excavation-induced building distortion and damage using a strainbased damage criterion. In: Proceedings of the international conference response of buildings to excavation-induced ground movements, CIRIA; 2000. [9] Desai CS, Zaman MM, Lightner JG, Siriwardance HJ. Thin-layer elements for interfaces and joints. Int J Numer Anal Method Geomech 1984;8(1):19–43. [10] Hashash YM, Whittle AJ. Ground movement prediction for deep excavations in soft clay. J Geotech Eng, ASCE 1996;122(6): 474–86. [11] Hsieh PO, Ou CY. Shape of ground surface settlement profiles caused by excavation. Can Geotech J 1998;35:1004–17.
[12] Janbu N. Soil compressibility as determined by oedometer and triaxial tests. In: Proceedings of the European conference on soil mechanics and foundation engineering, vol. 1; 1963. p. 19–25. [13] Kang Byung Sun, Yang Jae Hyouk. Adoptability of double hardening 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 with curved-yield surfaces. Int J Soild Struct 1977;13:1019–35. [15] Lade PV, Nelson RB. Incrementalization procedure for elasto-plastic constitutive model with multiple, intersecting yield surfaces. Int J Numer Anal Method Geomech 1984;8:311–23. [16] Lade PV. Three-dimensional behavior and parameter evaluation of an elastoplastic soil model. Geomech Model Eng Pract 1986:297–311. [17] Mana AI, Clough GW. Prediction of movement for braced cuts in clay. J Geotech Eng, ASCE 1981;107(6):759–77. [18] O’Rourke TD. A study of two braced excavation in sands and interbedded stiff clay. PhD thesis, University of Illinois at UrbanaChampaign; 1975. [19] Ou CY, Hsieh PO, Chiou DC. Characteristics of ground surface settlement during excavation. Can Geotech J 1993;30(5):758–67. [20] Peck RB. Deep excavations and tunneling in soft ground. state-ofthe-art report. In: Proceedings of the seventh international conference on soil mech. and found. engineering, state-of-the-art volume; 1969. p. 225–90. [21] Viggiani Gioacchino, Tamagnini Claudio. Ground movements around excavations in granular soils: a few remarks on the influence of the constitutive assumptions on FE predictions. Mech Cohes Frict Mater 2000;5:399–423. [22] Wong KS, Duncan JM. Hyperbolic stress–strain parameters for nonlinear finite element analyses of stresses and movements in soil mass. Geotechnical engineering research report no. TE/74-3, University of California, Berkeley; 1974. [23] Wong KS, Broms BB. Lateral wall deflections of braced excavations in clay. J Geotech Eng, ASCE 1989;15(6):853–70. [24] Yang G. Analysis of adjacent ground movements for deep excavations 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.
Computers and Geotechnics 35 (2008) 231–252 www.elsevier.com/locate/compgeo
Deep excavation-induced ground surface movement characteristics – 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 2007 Available online 28 June 2007
Abstract This paper concerns the characterization of deep excavation-induced ground surface movements, using the results of numerical investigation. A calibrated 2D finite element model using the Lade’s double hardening constitutive model for soil was used to form a database of the wall and ground surface movements associated with deep excavation. The results indicated that the cantilever and the lateral bulging excavation stages produce distinctive patterns of ground surface movement profiles, and that final ground surface movement profiles can be constructed by combining the cantilever and the lateral bulging components with a reasonable degree of accuracy. A two-step approach 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 deep excavation projects for constructions of high-rise buildings and subways. During deep excavation, changes in the state of stress in the ground mass around the excavation and subsequent ground losses inevitably occur. These changes and ground losses affect the surrounding ground in the form of ground movements, which eventually impose direct strains onto nearby structures. The magnitude and distribution of ground movements for a given excavation depend largely on soil properties, excavation geometry including depth, width, and length, and types of wall and support system, and more importantly construction procedures. Because of the increased public concern of the effects of construction-induced ground movements on their properties, the prediction of ground movements and assessment of the damage risk have become an essential part of the *
Corresponding author. Tel.: +82 31 290 7644; fax: +82 31 290 7549. E-mail address: [email protected] (D. Lee).
0266-352X/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compgeo.2007.05.002
planning, design, and construction of deep excavations in urban environments. Over the years, there have been a number of studies on the subject of wall and ground movements associated with deep excavation. Clough and O’Rourke [5] extended the work by Peck [20] and developed empirical settlement envelopes. Cording [7] provided a means of estimating the distribution of ground movements behind an excavation wall on the basis of volume relationships based on field observations. Ou et al. [19] compiled and analyzed field data regarding wall movement associated with deep excavation and defined the apparent influence range (AIR) for damage assessment of adjacent structures. More recently, Yoo [25] collected field data on lateral wall movement for walls constructed in soils overlying rock from more than 60 different excavation sites and analyzed the data with respect to wall and support types. The finite element method of analysis has also been extensively used in studies concerning wall and ground movements associated with deep excavation. The studies by Clough et al. [4], Mana and Clough [17], Wong and
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Broms [23], and Hashash and Whittle [10] were directed toward the prediction of wall movement for excavations in soft clay. Cording and O’Rourke [6] and later Cording [7] developed a scaling relationship based on an elastic assumption and investigated the effect of relative stiffness of the wall system with respect to soil on lateral wall movement. Most of the aforementioned previous studies focused on the maximum wall movement. Studies concerning ground surface movement characterization have been scarce due in large part to difficulties in obtaining complete sets of data either from field instrumentation or numerical analysis. Available information on the magnitude and distribution of ground surface movement associated with deep excavation is somewhat outdated and provides limited information required for building damage assessment. This study is directed toward the development of prediction method for deep excavation-induced ground surface movement profiles that can be used in the framework of currently available building damage assessment procedures (Boscardin and Cording [2] and Burland [3]). In order to correctly simulate the deep excavation-induced ground movement characteristics, the Lade’s double hardening constitutive model [14–16] was used to describe the stress–strain-strength behavior of the model ground. The finite element model adopted was validated by available data [24] before conducting the parametric study. A parametric study on deep excavation problems encountered in Korea was performed using the validated finite element model to form a database for use in the development of a prediction method associated with deep excavation-induced wall and ground surface movements. The results of the parametric study were carefully analyzed so that the ground surface movement characteristics could be related to the sources of wall movements. A systematic approach for prediction deep excavation-induced ground movement profiles was then developed. 2. Parametric study A series of 2D finite element analyses were performed using a commercial finite element program ABAQUS [1] to examine the ground surface movement characteristics and to form a database for use in the development of a ground movement profile prediction method. Subsequent sections discuss the details of the parametric study. 2.1. Problem investigated The configuration of the problem to be analyzed is shown in Fig. 1, which represents a hypothetical case of an excavation. For simplicity, an idealized symmetric plane strain braced excavation geometry with an excavation depth H and a width B of 20 and 30 m, respectively, was considered. The wall is a 25 m in height and has with a 5 m toe penetration depth at the final excavation stage. Because of symmetry about the excavation centerline, only
Fig. 1. Finite element mesh and modeling of interface element for parametric study.
one-half of the excavation was considered in the finite element model. The excavation ground considered was assumed to be composed of a weathered granite soil overlying a weathered rock stratum. The weathered granite soil is the representative soil in urban excavation sites in Korea and this type of ground formation is a typical soil profile frequently encountered in Korea. The excavation platform corresponds to the top of the weathered rock stratum. Primary variables included the wall bending stiffness (EI)w, the cantilever excavation depth Hun, the unsupported span length L below the lower-most support, and soil stiffness Es. Combinations of (EI)w and L generated the range of F shown in Table 1. In addition, a wide range of conditions was analyzed by varying the primary variables mentioned above. The parameter F in Table 1 is the flexibility ratio, defined by the following equation: F
Es L3 ðEIÞw
ð1Þ
where Es is the soil stiffness, L is the unsupported excavation length, and (EI)w is the wall flexural rigidity. The flexibility ratio was originally introduced by Cording and O’Rourke [6]. The range in wall flexibility ratio considered in this study is approximately from 15 to 400, which is consistent with the range for slurry, cast-in-place pile, sheet pile, and soldier pile walls. 2.2. Finite element analysis 2.2.1. Finite element model In the finite element modeling, the ground and the wall were discretized by using eight-noded plane strain eleTable 1 Conditions analyzed F
Es (aver) (MPa)
L (m)
15, 50, 74.2, 120, 150, 176, 220, 400
26.2, 53.2
3, 4, 5, 1, 2, 3, 15 6 4
Hun (m)
Note: EIw, wall flexural rigidity; K, effective axial stiffness.
K (MN/ m)
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ments, while the struts were modeled by using one-node spring elements with an effective axial stiffness of 15 MN/ m considering the excavation width. As shown in Fig. 1, a refined finite element mesh extended to a depth of 1.0H below the final excavation platform and laterally to a distance of 3.8H from the excavation centerline to minimize the effect of the artificial boundaries on the ground surface movement characteristics. For the material modeling, the weathered rock stratum was assumed to be an elasto-plastic material conforming to the Mohr–Coulomb failure criterion [1]. On the basis of the extensive surveys of urban excavation sites in Korea, the mechanical properties for the weathered rock in Table 2 were used in the parametric study. On the other hand, the weathered soil was assumed to follow the Lade’s double hardening model. Brief discussions on the double hardening model and the model parameters used in the analysis are given in Section 2.2.2. A series of preliminary analyses indicated that the interface modeling of the excavation side is crucial for obtaining realistic ground surface movement profiles associated with deep excavation. Although ABAQUS provides a surfacebased interface modeling option using ‘contact pair’, the contact pair was not adopted in modeling the interface in this study as significant numerical instabilities were encountered during the excavation modeling. For that reason, the Desai-type thin-layer interface model [9] shown the inset in Fig. 1 was implemented in ABAQUS using UMAT [1] to model the interface behavior between the wall facing and the soil. Details of the Desai-type thin-layer interface model can be found in [9]. The stiffness matrix of thin-layer element is the same as general solid element assuming a linear elastic behavior. Therefore, the elastic constitutive matrix of the thin-layer element is expressed as: ½C nn i ½C ns i ½Ci ¼ ð2Þ ½C sn i ½C ss i where [Cnn] and [Css] are related to normal and shear components, respectively, and [Cns], [Csn] represent coupling effects. However, the coupling effects are not included for simplification in this study. For isotropic linear elastic behavior, [C]i can be written in matrix form as: 3 2 M k k 0 0 0 6 k M k 0 0 07 7 6 7 6 6 k k M 0 0 07 7 6 ð3Þ ½Ci ¼ 6 7 6 0 0 0 G 0 07 7 6 4 0 0 0 0 G 05 0
0
0
0
0
G
Table 2 Typical mechanical properties for weathered rock in Korea Material
C (kPa)
/ ()
w ()
m
Es (MPa)
Weathered rock
100
46
6
0.3
500
233
Eð1mÞ Em and k ¼ ð1þmÞð12mÞ where, M ¼ ð1þmÞð12mÞ
Under the two-dimensional plane strain condition, Eq. (3) can be reduced to the following equation: 2 3 M k 0 6 7 ð4Þ ½Ci ¼ 4 k M 0 5 0
0
G
Based on the results of a series of preliminary analyses for model calibration, a relatively low shear modulus of 50 kPa with high bulk modulus was assigned to the interface elements. In simulating the step-by-step excavation process, the initial vertical state of stress was first created by turning on the gravity with the assumption of wished-in-placed wall. The lateral stress state was then created by multiplying the vertical stresses by the lateral earth pressure coefficient K0 = 0.5. The excavation process was then modeled by adding and removing elements at corresponding steps. Although the ground water lowering due to excavation generally affects the ground movement characteristics, the ground water was not considered for simplification and the free-draining characteristics of typical weathered soils in Korea. 2.2.2. Constitutive modeling of weathered soil It has been shown that a traditional elasto-perfectlyplastic model such as Mohr–Coulomb model does not yield satisfactory results in estimating deep excavationinduced ground movement, especially for ground surface settlements [21]. The double hardening model, which has been proven to be applicable for the weathered soil frequently encountered in Korea [13], was selected and implemented in ABAQUS using the user subroutine capability to represent the soil behavior in this study. In this section, the brief descriptions of the double hardening model based on 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 total strains are assumed to be divisible into elastic strains, plastic collapse strains, and plastic expansive strains. The elastic strains are calculated from Hooke’s law using the unloading–reloading modulus defined as: Eur ¼ K ur P a ðr3 =P a Þn
ð5Þ
where Kur and n are dimensionless model parameters and Pa is atmospheric pressure to make conversion from one system of units to another more convenient. Thus, the units of Eur and r3 are the same as units of Pa. The plastic collapse strains are associated with volumetric strains and mean effective stress. They are computed using a cap type yield surface conforming associated flow rule and a work-hardening relationship which can be determined from an isotropic compression test. The yield criterion, fc, and the plastic potential function, gc, are expressed in terms of the first and second invariants, I1, I2, as follows:
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fc ¼ gc ¼ I 21 þ 2I 2
ð6Þ
where I1 and I2 are first and second stress invariants. An empirical relationship for the collapse work-hardening as a function of fc is defined as: p fc ð7Þ W c ¼ C Pa 2 Pa where C and p are material parameters and the incremental plastic collapse work (dWc) can be determined from the derivative of Wc with regard to fc: 1p Cp P 2a dW c ¼ dfc ð8Þ P a fc The plastic expansive strains are related to the deviatoric stresses and they are computed using a conical yield surface and conform non-associated flow rule. The conical yield surface is described in terms of the first and third stress invariants, I1 and I3: 3 m I I1 fp ¼ 1 27 6 g1 ð9Þ I3 Pa where m is a model parameter describing the curvature of the failure surface, and g1 is a work-hardening parameters which defines the size of the failure surface. The plastic potential function is modeled on the yield function as follows: m Pa ð10Þ gp ¼ I 31 27 þ g2 I3 I1 where g2 can be modeled by the following simple expression: 1=2 r3 g2 ¼ Sfp þ t þ R ð11Þ Pa where S, t, and R are model parameters. An empirical relationship between the plastic expansive work done (Wp) and fp is defined by the following expression: 1=q Wp fp ¼ a ebW p ð12Þ Pa 1=q Pa with a ¼ g1 Weppeak and b ¼ qW 1 ppeak
where Wppeak and q are constants for a given value of r3 and e is the base for natural logarithms. Wppeak is the value of Wp at the peak point and its variation with r3 can be approximately expressed by the following empirical relationship: l W ppeak r3 ¼P ð13Þ Pa Pa where P is the value of Wppeak/Pa when Pa = 1. The variation of the parameter q with r3 can be represented by a simple expression as follows: r3 q¼aþb ð14Þ Pa
where a and b represent the intercept and slope of a straight line, respectively. From Eq. (12), the increment in plastic expansive work can be expressed as follows: dW p ¼
dfp fp
1 qW p
1 b
ð15Þ
In implementing the double hardening model using the user subroutine capability the soil is assumed to follow an elastic behavior and then the stress invariants are calculated to estimate the current collapsive yield stress and expansive yield stress. The current collapsive yield stress and expansive yield stress are then compared to the maximum past collapsive yield stress and the maximum past expansive yield stress to determine the loading conditions. After comparing the present and the past yield stresses, the maximum past yield stresses are replaced with larger one and then they are stored in the solution-dependent state variables array. Four different conditions may exist: (1) only elastic strains occur, (2) only plastic collapsive surface is activated, (3) only plastic expansive surface is activated and (4) both plastic collapsive and expansive surfaces are activated. After determining the loading conditions, the stresses are calculated by using stiffness matrix suitable for each yielding condition and then they are updated and stored to the stress array. A total of 14 parameters are required in the double hardening 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 required parameters can be entirely derived from the conventional triaxial test with volume change measurement. Table 3 presents the double hardening model parameters of the weathered soil used in the model ground. Note that the values are based on the previous study [13] which reports ranges of
Table 3 Parameters for the weathered soil Parameters
Weathered soil
Strain component
Kur n Poisson’s ratio
2:57 0.865 0.25
Elastic component
Collapse const. (C) Collapse expo. (p)
0.0086 0.789
Plastic collapse component
Yield const. (g1) Yield expo. (m) P1. potent. const. (R) P1. potent. const. (t) P1. potent. const. (S) Work-hard. const. (a) Work-hard. const. (b) Work-hard. const. (P) Work-hard. expo. (I)
38 0.113 1.406 0.488 0.406 1.254 0.072 0.52 0.653
Plastic expansive component
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the double hardening model parameters for weathered soils encountered in Korea.
Table 5 Material properties for an urban excavation site in Korea Material
2.2.3. Model validation The finite element model adopted in this study was validated to a limited extent against measured data for an urban excavation site in Korea [24]. The same modeling approach for parametric study given in Section 2.2.1 was employed in the finite element modeling. Fig. 2 presents the standard cross-section and soil profile for the site. The wall of 26 m in height with an embedment depth of approximately 2 m consisted of soldier pile was supported by struts and detailed descriptions of the site are given in Table 4 [24]. As shown in Fig. 2, the vertical spacing of the struts and the unsupported span length were varied by the construction sequences for simulating the field conditions in detail. The average of the vertical spacing of the struts and the unsupported excavation length are 2.5 m and 2–3 m respectively. Cantilever excavation depth of 3–4.5 m, excavation depth 23.7 m, and the over excavation depth of 2.5–3 m are applied to the analysis. As illustrated in the figure, the ground consists of a fill material, a weathered soil, and a weathered rock. Most of the excavation took place within the weathered soil. Table 5 summarizes the mechanical properties of the site
235
Fill Weathered soil Weathered rock
C (aver) (kPa)
Es (aver) (MPa)
/ (aver) ()
w (aver) ()
m (aver)
10 25
30 40
8 6
0.3 0.3
17 30
300
41
6
0.3
110
USCS
SM SM None
in terms of the Mohr–Coulomb shear strength parameters and the elastic stiffness reported in [24] to give general information of the soils layer and the rock layer. In material modeling, although the fill layer and the weathered soil in the site have a bit different shear strength parameters as shown in Table 5, these soils were considered to have the same double hardening model parameters. This is justified since the fill layer and the weathered soil are reported to be similar 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 information available and therefore the validation given in this section should thus be viewed as qualitative. The rock layer is assumed to follow the Mohr–Coulomb yield criterion with the material properties in Table 5. Thus, the site was assumed to be composed of a weathered soil overlying a weathered rock. Fig. 3 presents the comparisons between the measured and predicted ground surface settlements. The solid lines represent the predictions from the double hardening model and the points represent the measured results. Note that due to the general practice of not measuring horizontal ground surface settlements during excavation, only the vertical ground settlement data were used for validation. As shown in the figure, the predicted maximum settlement of
Fig. 2. Cross-section and soil profile for an urban excavation site in Korea. Table 4 Descriptions of an urban excavation site in Korea Excavation depth, H (m) Wall type Soil type Support type and average spacing Flexibility ratio (F)
23.7 Soldier pile (I = 1.26 · 104 m4) and lagging wall Fill + weathered soil Strut (A = 0.0053 m2), horizontal spacing = 4.0 m, vertical spacing = 2.5 m 150–250
Fig. 3. Comparison between results of proposed method and measured data.
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0.16%H agrees well with the measured one. The extent of the settlement zone is also well predicted as 2.5–3.0H. More importantly, the results agree fairly well in qualitative terms suggesting that the finite element modeling approach, including the constitutive modeling of the weathered soils using the double hardening model, is reasonably appropriate for use in this study. It should however be noted that a small-strain stiffness model may yield better results, especially in terms of lateral extent of the settlement profiles, such a model was not adopted in this study due to limited information available as to the applicability of the model to typical weathered soils encountered in Korea. Considering that the double hardening model is based on the nonlinear isotropic elasticity, the results may be comparable to those based on a small-strain stiffness model. However, a further study concerning the use of a small-strain stiffness model for typical ground conditions in Korea is warranted. 3. Wall and ground movement characteristics The results of the finite element analyses were compiled such that the patterns of wall and ground movements could be related to the parameters comprising the flexibility ratio. Important findings are discussed under the subsequent subheadings. 3.1. Effect of wall stiffness Fig. 4 illustrates the effect of wall bending stiffness on the wall and ground surface movement patterns. In the plot of the ground surface displacements, two sets of curves are shown. For the horizontal displacements, the displacement toward the excavation wall was taken as positive. Likewise the downward movement was taken as positive for the vertical settlements. Note that cantilever excavation depth and the unsupported span length during the lateral bulging
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 surface movements. The results are described by more of a step function than a gradual change with the wall stiffness. As seen in Fig. 4, as the wall stiffness decreases, the shape of the wall displacements changes from the cantilever form to the lateral bulging form for wall movements, and the horizontal component of the ground surface settlement profiles tend to become convex up and also the vertical component yields concave down. In terms of the maximum values, the location of the maximum settlement tends to move away from the edge of excavation as the wall stiffness increases. This trend indicates that for a given excavation condition, the wall bending stiffness influences not only the magnitudes of ground surface movements but also the pattern of the movements. In addition, the location of maximum settlement greatly varies at the flexibility ratio of F = 120. Moreover, as seen in Fig. 4b, significant horizontal ground surface displacements are developed, as great as 100–127% of the vertical settlements in terms of maximum values. These results demonstrate the need for considering horizontal ground surface displacements when assessing the risk of damage especially for buildings with small resistance to lateral ground displacements, as noted by Cording et al. [8], although the lateral building strains are significantly less than the lateral ground strains. Presented in Figs. 5 and 6 are the results of four cases having the same flexibility ratio of F = 120 but different combinations of (EI)w and L and different Hun, one with Hun = 1 m and the other with Hun = 4 m. The differences in the wall and ground surface movements between the cases thus represent the combined effect of (EI)w and L. As seen in these figures, the wall and ground surface displacement profiles tend to significantly vary in shape
Fig. 4. Variation of wall and ground movements with (EI)w.
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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 the same F. For the wall deformations, the maximum displacements of the wall do not vary in direct proportion to the bending stiffness. Furthermore, the curve 2 with the larger L and (EI)w yields greater wall and ground surface movements than the curve 1 with the smaller L and (EI)w due to the over excavation. A similar trend is shown in curves 3 and 4, suggesting that L and over excavation have a greater influence 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, and 1.0 m, respectively. The trends shown in these figures illustrate the dependency of the wall and ground movements on the combined effect of (EI)w and L and suggest that the
wall flexibility ratio F alone cannot correctly capture the wall and ground responses to a given excavation. 3.2. Effect of unsupported excavation depth During an excavation, unsupported excavation is inevitably carried out both in the cantilever and the lateral bulging stages. The effect of cantilever excavation depth Hun on the wall and ground movements is illustrated in Fig. 7. The cantilever excavation depth Hun was controlled in the analyses by varying the maximum depth of excavation before installing the top most support but keeping the other variables constant. Therefore, the differences in the wall and ground movements between the different cases solely reflect the effect of Hun.
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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 movements during the cantilever stage became significant when allowing Hun greater than 3 m, resulting in the ground surface displacement profiles with large volume losses in close proximity to the edge of the excavation. A strict provision on Hun should be placed during the early stages of excavation for cases in which buildings and buried utilities are located in close proximity to the edge of excavation. In addition, the wall deformations are almost constant with the increase of Hun, and similar results are shown for the vertical components. Hence, it is seen that maximum wall deformation and the vertical displacement of ground settlements are more dependent on the wall bending stiffness and the unsupported length L than the cantilever excavation depth Hun.
Examples with different Hun used to show the influences of the unsupported span length L for a given wall stiffness are illustrated in Figs. 8 and 9. As shown in these figures, an increase in L from 3 to 6 m results in substantial increases in the wall and ground surface movements by approximately an order of magnitude. An important observation is that an increase in the unsupported span length L results in increases in the magnitude of ground surface settlements and tends to modify the settlement profiles to more a concave downward shape because of the increased deep-seated movements. Although the flexibility due to the increase of the unsupported length L is increased, the wall and ground movements are severely varied by over excavation. Such results shown in these figures demonstrate that the excavation procedure during
Fig. 8. Variation of wall and ground movements with L (Hun = 4 m).
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Fig. 9. Variation of wall and ground movements with L (Hun = 1 m).
construction significantly affects the patterns of ground surface displacement profiles and the wall deformations. 3.3. Effect of soil stiffness The relative stiffness between the excavation wall and the soil has a significant influence on the magnitude and distribution of wall and ground movements for a given excavation. With respect to ground movement prediction, it would be more convenient if cases having the same flexibility ratio but different combinations of (EI)w and Es would yield similar ground surface movement profiles. Figs. 10–15 represent the ground surface movement profiles at the cantilever, lateral bulging, and final stages for cases having F = 50 and 150 but different combinations of (EI)w (=21.8, 44.4, 65.4, 133.1 MN m2/m) and Es
(=26.2, 53.2 MPa) and different Hun. In all cases, the unsupported depth during the lateral bulging stage was kept constant at L = 5 m. Note that Es represents the average soil modulus of the excavation ground calculated using the hyperbolic relationship given by Janbu [12] in the following equation: Es ¼ K P a ðr3 =P a Þ
n
ð16Þ
According to Wong and Duncan [22], the parameter Kur in Eq. (5), which is the modulus parameter determining Eur, is generally 1.2–3 times greater than K, which is the modulus parameter for Es. Considering this, the average value of Es was back-calculated from Eur. As seen in these figures, it appears that the cases with a same F would yield similar settlement profiles in terms of magnitude and slope despite the differences in the
Fig. 10. Ground movements profiles with soil stiffness (Hun = 4 m): (a) F = 50 and (b) F = 150.
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Fig. 11. Ground movements profiles with soil stiffness (Hun = 4 m): (a) F = 50 and (b) F = 150.
Fig. 12. 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 horizontal displacement profiles for a given F are similar, and the case with less rigid ground and wall tends to yield larger movements. An important conclusion is that as long as L is the same, the flexibility ratio F can be used as a common index for the prediction of ground surface settlement profiles for 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 settlement (dv,max) is usually taken as a fraction of the maximum lateral wall movement (dw,max). The results of the finite element analyses are compiled such that the maximum 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 maximum values for each component, i.e., the cantilever and the lateral bulging, are separately analyzed, and that the results are only relevant to the cases with ground conditions similar 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 cantilever as well as the lateral bulging components in a semilog plot. The case with the unsupported length L = 5 m was chosen to eliminate the effect of over excavation. As seen in Fig. 16a, the dv,max/dw,max ratio tends to linearly decrease with increasing F because of the increase of dw,max at an approximately same rate, regardless of the soil stiffness in the cantilever stage. The range of decrease
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Fig. 13. Ground movements profiles with soil stiffness (Hun = 1 m): (a) F = 50 and (b) F = 150.
Fig. 14. Ground movements profiles with soil stiffness (Hun = 1 m): (a) F = 50 and (b) F = 150.
is within 20%. In the lateral bulging stage, as the result of the decrease of the wall bending stiffness, dv,max/dw,max ratio tends to linearly increase with F, and the rate of increase for the soil stiffness remains almost constant within 10%. The dh,max/dw,max ratio shown in Fig. 17 appears to significantly vary with F in the cantilever stage, in the range of about 30%. This result suggests that even for a rigid wall system, a large amount of volume loss can be led in the cantilever stage. For a flexible wall system, as a result of the increase of wall deformation, dh,max/dw,max ratio tends to decrease and the effect of soil stiffness is insignificant like dv,max/dw,max. As seen in Fig. 17b, the dh,max/dw,max ratio does not appear to significantly vary with F in the lateral bulging stage, exhibiting similar results displayed by
dv,max/dw,max ratio. The difference in soil stiffness results from the lateral expansion of the retained soil. As illustrated in Fig. 18, the change of the vertical component lies within 5% because of the decrease in Hun and the immediate installation of struts after excavation. In the lateral bulging stage, the effect of the flexibility is also insignificant, and only the change associated to the soil stiffness appears. As seen in Fig. 19, dh,max/dw,max ratio also displays an almost similar trend for the case of Hun = 4 m. However, the range of variation is within 15%, and the effect related to the wall and the soil stiffness decreases. This result, as previously mentioned, reflects the influence of Hun. Therefore, dv,max/dw,max is dependent on Hun and F, regardless of the soil stiffness in the cantilever stage, and the lateral bulging stage is affected by Es, F, and
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Fig. 15. Ground movements profiles with soil stiffness (Hun = 1 m): (a) F = 50 and (b) F = 150.
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 horizontal component of ground settlement is greatly affected by the cantilever excavation depth. A constant value for dh,max/dw,max can be assumed for the lateral bulging stage without introducing a significant error, at least, within the limits of the F considered. Fig. 20 represents the ratio of settlement volume to wall displacement volume (Vs/VL). As seen in Fig. 20, the ratio of settlement volume to wall displacement volume almost linearly increases with increasing F in the semi-log plot. These results are a direct consequence of the increase in the ground settlement volume relative to the volume of wall displacement as the wall stiffness decreases. Fig. 21 illustrates the relationship between the normalized maximum ground displacements and wall movements.
As seen in the figure, the range of dv,max/dw,max ratio lies within 0.5–1.0. This trend is similar to the field data [24] in Fig. 21c and strongly supports the trends observed in the results of the finite element analyses, in which the wall flexibility increased due to the increase in L as the excavation proceeded. A similar trend has been reported by O’Rourke [18], in which the ratio of the volume of ground settlement increased, to as great as 1.0, as the wall flexibility increased by the increase in L. This similarity indicates that the way in which the ground loss at the wall is reflected to the ground surface depends not only on the dilatancy characteristics of the ground but also on the wall flexibility. The wall flexibility should therefore be taken into consideration when inferring the maximum ground surface settlement from the maximum lateral wall movement for a given excavation.
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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 movement profiles for the conditions analyzed are decomposed into cantilever and lateral bulging components, and the characteristics of each component are discussed. 4.1. Components of ground surface movement profiles Illustrated in Figs. 22 and 23 are the ground surface movement profiles for two cases, both of which have the same wall and excavation conditions but different Hun. Each figure shows three curves; one for the final, and the other two for the cantilever and the lateral bulging components, respectively. Note that the lateral bulging component of a given movement profile is obtained by subtracting the
cantilever component from the final profile. Comparisons between the two cases thus provide insights into the general characteristics of the cantilever and the lateral bulging components of ground surface movement profiles. As seen in Fig. 22a for the case of Hun = 1 m, it is evident that the cantilever components are negligibly small, and that the final profiles and the lateral bulging components are practically the same. For the case of Hun = 4 m shown in Fig. 22b, in which significant cantilever-type wall movements are allowed to develop, both the cantilever and the lateral bulging components are apparent. A salient feature observed in Fig. 22 is that the final settlements of the two cases are practically identical, regardless of Hun, illustrating that the cantilever excavation depth Hun has a transitional effect on the final settlements of a given excavation.
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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 combinations of (EI)w and Es exhibit the same trend. The results illustrated in these figures have significant practical implications on the prediction of ground movement profiles, as they imply that the cantilever and the lateral bulging components are separable and independent of each other. Therefore, any deep excavation-induced ground movement profiles can be conveniently constructed by simply adding the cantilever and the lateral bulging components. This is discussed further later in this paper. 4.2. Cantilever component Cantilever-type movements develop during excavation to upper levels of supports. The magnitude and distribution of ground movement due to cantilever wall move-
ments for a given excavation depend basically on the depth of cantilever excavation Hun and the relative wall stiffness with respect to soil stiffness. A survey conducted on deep excavation practice in Korea as part of this study indicated that the depth of cantilever excavation was approximately 4–5 m with wall flexibility F = 10–250. For this reason, the results for cases having four levels of flexibility ratio, i.e., F = 15, 74.2, 120, and 220 with the soil stiffness of Es = 26.2 MPa are presented in Fig. 24 associated with the cantilever-type lateral wall movements. As noticed, the vertical settlement profiles are essentially bilinear in shape with the maximum values occurring near the edge of excavation. The horizontal displacement profiles change from parabolic to bilinear in shape as the wall bending stiffness decreases. In addition, significant horizon-
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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 within 0.2H from the edge of excavation. Buildings and utilities located in close proximity to a deep excavation with a flexible wall, therefore, can experience significant levels of angular as well as lateral distortions even in the early stages of excavation. 4.3. Lateral bulging component The lateral bulging components of the ground surface movement profiles are illustrated in Figs. 25 and 26 for cases having two levels of flexibility ratio, i.e., F = 15 and 220 with different Hun. For each flexibility ratio, a number of profiles having different combinations of (EI)w and L are presented.
As seen in these figures, the vertical and the horizontal settlement profiles follow predominantly concave upward and downward shapes with the maximum values occurring approximately at 0.3–0.4H and 0.5–0.6H away from the edge 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 profiles tend to vary depending on the combination of (EI)w and L with this trend being more pronounced as the wall flexibility increases. This trend supports the results presented earlier that L and the depth of the over excavation are by far a more important controlling factor of ground movement than the wall stiffness (EI)w for excavation cases. Secondly, although not as apparent, the locations of the maximum horizontal displacement and vertical settlement
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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 excavation as L increases, due primarily to the deep-seated movements associated with increasing L. 4.4. Normalized ground surface displacement profiles With respect to the ground surface movement prediction, it would be desirable if normalized relationships can be established among different cases. Figs. 27 and 28 present the lateral bulging components of the ground surface movement profiles normalized with their respective maximum values for cases having F = 15 and 220. Interestingly, the normalized profiles for a given F but different combinations of (EI)w and L tend to collapse more or less into one curve. This trend indicates that although dif-
ferent in magnitude, normalization holds for the ground surface movement profiles for cases having the same flexibility ratio. The variation in the region beyond the maximum values is of little practical importance on account of the relatively small magnitudes. Although not included here, other cases exhibited the same trend. Fig. 29 presents normalized profiles for the case of Hun = 4 m with their respective maximum values at the final excavation stage for the cantilever as well as the lateral bulging components, which can be readily used to make the prediction of deep excavation-induced ground movements for cases with similar excavation conditions considered in this study. The normalized profiles for the cantilever component shown in Fig. 29a represent cases with a cantilever excava-
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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 normalized lateral bulging components for various flexibility ratios. The flexibility ratios covered in this figure bracket a wide range of cases frequently encountered in practice, and therefore, these profiles can be used to make a prediction of ground movement profiles for a given excavation with a reasonable degree of accuracy. A two-step approach is proposed for prediction of deep-excavation-induced ground movement profiles, in which the normalized cantilever and lateral bulging components of ground surface movements are first systematically determined from Fig. 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 then obtained by multiplying the normalized profiles with their
respective maximum values obtained either from Fig. 29 or local experience. Complete ground surface movement profiles can then be constructed by simply adding the cantilever and the lateral bulging components of profiles. 4.5. Estimation of settlement influence zone The influence zone of ground settlements should be reasonably established to evaluate the damage of adjacent buildings caused by deep excavation. In this study, the influence zone of ground movement obtained by FE analysis is compared with that of a previous study by Hsieh and Ou [11]. Figs. 30–33 show the normalized ground surface profiles with their maximum horizontal and vertical ground settlements for cases having various flexibility
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Fig. 26. Lateral bulging components of ground movements profiles (Hun = 4 m).
Fig. 27. Normalized lateral bulging components of ground movement profiles (Hun = 4 m).
ratios, different cantilever excavation depths, and soil stiffness. In these cases, the unsupported excavation span length is held constant at L = 5 m. In these figures, the dotted line represents the influence zone of ground surface settlements obtained by Hsieh and Ou [11] and the solid lines represent the results from this study. As indicated in Fig 30a, the ratio of dv/dv,max is approximately equal to 0.5 and agrees well with the results of Hsieh and Ou [11]. The primary influence zone and the secondary influence zone are about to 1.7H and 3H, respectively. These results are smaller than those proposed by Hsieh and Ou [11] but agree with the results obtained by the method of Clough and O’Rourke [5] as well as the field measurements [24] as presented in this study. According to the 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, approximately 0.28–0.36H. In the relationship between dw,max and dv,max, the ratio of the distance where dv,max occurs to the depth where dw,max occurs increases to approximately 0.51–0.86 for the rigid wall as L increases. This trend indicates that the distances where dv,max and dw,max occur vary with the unsupported excavation length L. For the flexible wall, the ratio increases approximately to 0.47–0.62 with increasing L. The influence zone of the horizontal ground settlements is examined in this study. In most previous studies, there is no guideline for the prediction of the horizontal settlement profiles because of the difficulty in measuring horizontal
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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 the influence zone for the vertical ground surface profiles has been proposed. Presented in Fig. 30b is the ratio of dh to dw,max at the wall, being a range of 0.7–1.0. This range decreases with increasing F. For the rigid wall system, the horizontal ground movements at the wall is directly associated with the wall displacement but the maximum horizontal ground displacement occurs away from the wall for the flexible wall system due to the lateral bulging. The maximum value of dh/dh,max occurs at 0.5H except for rigid wall system, and the primary influence and secondary influence zones for the horizontal ground surface movements are approximately equal to 1.7H and 3.0H, respectively. Such results are similar to the cases for the vertical ground surface movements.
As shown in Fig. 31 for the case with Hun = 1 m, the results exhibit the same trend as the case with Hun = 4 m except that the displacements at the wall greatly decrease due to the installation of the top most support. As seen in Figs. 32 and 33, the results yield similar settlement profiles in terms of the magnitudes and the slope despite of the differences in Es. Based on the finite analyses, it can be concluded that the primary influence and the secondary influence zones are approximately equal to 2H and 3H, respectively. These results 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 movement can be estimated by using the double hardening model implemented in this study with a reasonable degree
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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 be applied to the damage assessment of adjacent buildings induced by deep excavation in urban areas. 5. Conclusions This paper presents the results of numerical investigation on deep excavation-induced ground surface movement characteristics under the ground conditions encountered in Korea. In order to realistically model ground movements associated with deep excavation, Lade’s double hardening model was incorporated into ABAQUS and used to simulate stress–strain behavior of the weathered soil. The appropriateness of the Lade’s dou-
ble hardening model and the finite element model adopted in this study was validated using available field instrumentation data. The finite element model was then employed for a parametric study on deep excavations with emphasis on ground movements. On the basis of the parametric study, a method for predicting deep excavation-induced ground movement profiles is proposed, which is of prime importance in damage assessment of adjacent structures. Based on the results of the present study, the following conclusions can be drawn: (1) The general shape of a ground surface settlement profile is closely related to the sources of wall movements, and that the unsupported span length has a
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Fig. 32. Estimation of settlement influence zone (Hun = 4 m, L = 5 m and Es = 53.2 MPa): (a) vertical component and (b) horizontal component.
Fig. 33. Estimation of settlement influence zone (Hun = 1 m, L = 5 m and Es = 53.2 MPa): (a) vertical component and (b) horizontal component.
significant influence on the magnitude and distribution of wall and ground movement characteristics. (2) For a given ground condition, the ratio of the maximum ground surface settlement to the maximum wall movement decreases with increasing wall flexibility for the cantilever component but increase with increasing wall flexibility for the lateral bulging components. (3) The cantilever and the lateral bulging stages of excavation produce distinctive ground surface displacement profiles, which are separable and independent of each other. Deep excavation-induced ground surface movement profiles for a given excavation can be predicted with a reasonable degree of accuracy
by combining the cantilever and the lateral bulging components. (4) The primary influence and the secondary influence zones are approximately equal to 2H and 3H for vertical ground movements, respectively. The results agree with the previous studies by Clough and O’Rourke and Hsieh and Ou. (5) The proposed method for predicting ground surface movement profiles captures the fundamental characteristics of ground surface movement profiles, and therefore can be used with a reasonable degree of accuracy to make an estimate of ground surface movement profiles.
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