Evaluation of Constitutive Soil Models for Predicting Movements Caused by a Deep Excavation in Sands

Transcription

1 Evaluation of Constitutive Soil Models for Predicting Movements Caused by a Deep Excavation in Sands Bin-Chen Benson Hsiung and Sy-Dan Dao* Department of Civil Engineering, National Kaohsiung University of Applied Sciences, 415Chien-Kung Road, Kaohsiung City, 87, Taiwan *Corresponding author; sydandao@gmail.com ABSTRACT The objective of this paper is to evaluate the performance of three constitutive soil models, i.e. Morh-Coulomb model (MC model), Hardening soil model (HS model) and Hardening soil model with small strain stiffness (HSS model), implanted in PLAXIS software, for predicting movements induced by a deep excavation in sands. A case history of deep excavation in thick layers of sand, which is well documented in Kaohsiung city, Taiwan, was adopted as a basic for the numerical analyses in this study. The back analysis method was used to determine input parameters that cannot be directly obtained from tests or reliably empirical equations. In addition, parametric studies were also conducted to evaluate the sensitivity of important input parameters of the MC, HS and HSS models, which were obtained by the back analysis method. Results pointed out that the HSS model yields the best predictions of the wall deflections and ground surface settlements, and the MC model gives the worst results. This study can be helpful to engineers and researches to perform numerical analyses using the constitutive soil models more confidently. KEYWORDS: Deep excavation; constitutive soil models; sand; back analysis; parametric study. INTRODUCTION Deep excavations are often located very close to existing buildings in urban areas. As a result, they usually cause uncomfortable movements, which can influence safety of the adjacent buildings. Movements of the retaining wall and ground induced by deep excavations have been studied by many researches, for example Peck (1969), Clough and O'Rourke (199), Ou et al. (1993), Hsieh and Ou (1998), Hsieh et al. (23), Ou (26), Kung et al. (29), Hsiung (29), Lim et al. (21), Likitlersuang et al. (213) and Khoiri and Ou (213). However, these researches mainly analyzed excavations in clays rather than excavations in sands. Nowadays, commercial FEM programs, written mainly for geotechnical problems such as Plaxis, Flac and Misdas GTS, have been commonly used to analyze the behaviors caused by deep excavations. Many constitutive soil models, from a linear elastic model to non-linear elastoplastic models, have been developed in the last decades. However, it is still a problem with predicting movements induced by deep excavations using numerical analyses. The accuracy of a

2 Vol. 19 [214], Bund. Z numerical analysis depends on the appropriate selections of many factors such as the simplicity of geometry and boundary conditions, mesh generation, constitutive models, and input parameters. The input parameters of soil can be measured from the laboratory or field tests or be estimated from empirical equations. To find proper results from numerical analysis, understanding of engineers about the numerical methods and constitutive models of soil is very essential. This paper aims to evaluate the performance of constitutive soil models, i.e. Morh-Coulomb model (MC model), Hardening soil model (HS model) and Hardening soil model with small strain stiffness (HSS model), implanted in PLAXIS software, for predicting movements caused by a deep excavation in sands. A case history of deep excavation in sands, which is well documented in Kaohsiung city, Taiwan, will be used as a basic for the numerical analyses in this paper. The results of this study can be useful for engineers and researchers to perform numerical analyses using the constitutive soil models more confidently. A CASE HISTORY OF DEEP EXCAVATION A case history of deep excavation in Kaohsiung city, Taiwan, namely Case A, was adopted as a basic for numerical analyses in this paper. Case A was next to the O7 Station, which is on the orange line of Kaohsiung MRT system. As shown in Figure 1, Case A was in the central area of Kaohsiung city and about 3. km to the east of Kaohsiung harbor. Case A Figure 1: Location of Case A The shape of Case A was rectangular with 7 m in length and 2 m in width. The excavation was carried out by the bottom-up construction method and was retained by a diaphragm wall that is.9 m thick and 32 m deep. It was excavated in five stages with the maximum excavation depth of 16.8 m. The retaining wall was propped by steel struts at four levels, and the horizontal spacing of the struts was average about 5.5 m. Figure 2 below shows the cross section and ground condition of Case A. According to the site investigation, the excavation of Case A was in the coastal plain of Kaohsiung city, Taiwan. As shown in Figure 2, because three clay layers (CL type) are very thin, their influences on the excavation behavior are not significant. It can be thus concluded that the excavation of Case A is a typical case of deep excavations in sands.

3 Vol. 19 [214], Bund. Z Ground level:. m SID 1 CL, N = m 2 SM, N = m 3 CL, N = m 4 SM, N = m 1.5 m (1H4x4x13x21) 6.3 m (2H4x4x13x21) 9.65 m (2H4x4x13x21) 13. m (2H4x4x13x21) m m m m m m m m SM, N = 5-17 SM, N = 5-17 CL, N = m diaphram wall 32. m m SM, N = m SM, N = Mudstone Figure 2: Cross section and ground condition of Case A The field observation also reported that the groundwater level before excavation was about 2. m deep below the ground surface. The groundwater level inside the pit was lowered to a depth of 1. m below each excavation level before each stage of excavation to make a convenient space for construction process of excavation. The wall deflections and surface settlements were monitored by inclinometers and settlement observation sections during construction process of the excavation, respectively. Figure 3 below shows the wall deflections and ground surface settlements measured at the central section of long side of Case A, in which the wall deflections were corrected to take into account the toe movements of inclinometers (see Hwang et al., 27 and Hsiung and Hwang, 29). It can be assumed that the movements of the wall and ground at the central section of long side are in the plane strain condition because this section is far away from the excavation corners, and the ratio of the excavation width to length (B/L) is less than.3.

4 Vol. 19 [214], Bund. Z Displacement (mm) Distance from the wall (m) The 1st strut: 2 1.5m Depth (m) The 5th stage: 16.8m Ground surface settlement (mm) Stage 1 Stage 2 Stage Stage 4 Stage 5 Figure 3: Wall deflections and ground surface settlements measured at the central section of long side of Case A As can be noted from Figure 3, the wall is to behave as a cantilever at the first stage of excavation because the steel struts at the first level have not yet installed and preloaded. The wall then displays the deep inward movements at subsequent stages of excavation. The maximum wall deflection at the final excavation stage is near the excavation level and equal to.39%h e (H e is the excavation depth). This value is thus consistent with the range of.2%h e to.5%h e found in the study of Ou et al. (1993). The range of observed settlements behind the retaining wall was quite limited because there was a crowed traffic road near the excavation, which causes the difficulty for full observation of settlement. The maximum surface settlement (δ vm ) varies from 21 mm to 3 mm at the final stage of excavation, or the ratio δ vm /H e is equal to from.12% to.18%. According to the study of Clough and O'Rourke (199), the maximum surface settlement was average about.15%h e for excavations in stiff clays and sands. Theore, the ratio δ vm /H e in this study is similar to the study of Clough and O'Rourke (199). NUMERICAL ANALYSES AND RESULTS The commercial software PLAXIS 2D, version 9 (29), was selected as a tool for 2D numerical analyses in this study. PLAXIS 2D is a two-dimensional finite element program, which is developed at Deft University of Technology in the Netherlands and is made commercially available by PLAXIS Bv, Amsterdam, the Netherlands.

5 Vol. 19 [214], Bund. Z Because the clay layers are very thin, their influences on excavation behavior are not significant. In contrast, the excavation behavior is mainly influenced from sand layers. Three constitutive soil models, i.e. MC model, HS model, HSS model, were adopted to simulate the sand layers for evaluating their performances in predicting the wall deflections and surface settlements induced by the excavation of Case A in numerical analyses herein. In these different models, strength parameters are the same, but stiffness parameters are different. The stiffness parameters are constant in the MC model, but they are stress dependent in the HS model and HSS model and are strain dependent in the HSS model. All sand layers were assumed to be drained materials in the numerical analyses. To obtain a consistent evaluation, the clay layers were all modeled with the MC model in a total stress undrained analysis in the analyses above. For the total stress undrained analysis of the clay layers, parameters of undrained Young's modulus E u,undrained internal friction angle φ u = and undrained shear strength S u were used. Undrained Young's modulus E u can be computed by the empirical equation E u = 5S u as suggested in researches of Bowles (1996), Lim et al. (21), Likitlersuang et al. (213), and Khoiri and Ou (213). Poisson's ratio ν u =.495 (.5) was adopted to simulate the incompressibale behavior of water and to avoid numerical problems caused by an extremely low compressibility (singularity of the stiffness matrix). Table 1 shows the input parameters of clay layers used for analyses. Layer Depth (m) Table 1: Input parameters of clay layers Soil Type g t S u (kpa) E u (kpa) ν u Analysis Type (kn/m 3 ) CL Undrained CL Undrained CL Undrained The diaphragm wall was simulated by plate elements, and the steel struts were simulated by elements of fixed-end anchor. The linear elastic model was adopted to model both the diaphragm wall and steel struts. This model requires two input parameters, i.e. Poisson's ratio and Young's modulus. The Poisson's ratio was taken to be.2 for both the diaphragm wall and steel struts. The Young's modulus of the diaphragm wall was calculated by the formula of ACI Committee 318 (1995) as follows:, E = 47 f ( MPa) (1) c, in which f c ( MPa) is the standard compressive strength of the diaphragm wall concrete. The Young s modulus of steel struts was taken to be 2.1x1 5 (MPa). The stiffnesses of the diaphragm wall and the steel struts were reduced by 3% and 4%, respectively, from their nominal values to consider the cracks in the diaphragm wall due to bending moments and to consider the repeated uses as well as improper installation of steel struts as suggested by Ou (26). Tables 2 and 3 below show input parameters of the diaphragm wall and steel struts used for numerical analyses. The weight of plate is obtained by multiplying the unit weight of plate by thickness of plate. It is noted that the unit weight of plate was subtracted a value of soil unit weight because the wall was modeled as non-volume elements. Interface elements were also simulated to represent the friction between soil and the diaphragm wall. As proposed by PLAXIS 2D (29) and Khoiri and Ou (213), the stiffness of interface elements could be taken as.67 to simulate the disturbance of ground between the wall and soil.

6 Vol. 19 [214], Bund. Z Table 2: Input parameters of diaphragm wall Parameter Name Value Unit Compressive strength of concrete f' c 28 MPa Young's modulus E 24.8x1 6 kpa Thickness d.9 m Axial stiffness x 7% 7%EA 15.66x1 6 kpa/m Flexural stiffness x 7% 7%EI 1.57x1 6 kpa/m Weight w 4.95 kn/m/m Poisson's ratio ν.2 Table 3: Input parameters of steel struts Strut Preload Section EA 6%EA Strut level level (kn) area (m 2 ) (kn) (kn) Level 1 1H4x4x13x x x1 6 Level 2 2H4x4x13x x x1 6 Level 3 2H4x4x13x x x1 6 Level 4 2H4x4x13x x x1 6 Figure 4 below presents the finite element model adopted for the numerical analyses of Case A. Only a half of the excavation of Case A was modeled because of its symmetrical geometry. The base of the finite element model was placed at the top of mudstone layer, i.e. at a depth of 6 m below the ground surface. The distance from the lateral boundary of the model to the retaining wall was taken to be 12 m, which is appropriately seven times excavation depth as suggested by Khoiri and Ou (213). The horizontal movement was restrained for the lateral boundaries, and both the vertical and horizontal movements were restrained for the bottom boundary of the model. 1 m 12 m 6 m Figure 4: Finite element model adopted in numerical analyses Mohr-Coulomb model (MC model) The MC model assumes the stress-strain relation to be linear elastic-perfectly plastic, and its failure criterion is Mohr-Coulomb's failure criterion. The slope of linear elastic section of stressstrain curve is defined as Young's modulus of soil (E'), and the perfectly plastic section is

7 Vol. 19 [214], Bund. Z obtained when the stress states reach the Mohr-Coulomb's failure criterion. The MC model is a basic model of soil, and it represents a first-order approximation of soil behavior. It is thus recommended to use this model for preliminary analyses of the considered problem. Because each soil layer is estimated by a constant average stiffness, computations with the MC model are relatively fast. The MC model involves six input parameters as summarized in Table 4. MC model Input parameters HS model HSS model Table 4: Input parameters of soil models Explanation of parameters φ' Internal friction angle c' Cohesion E' Young's modulus for elasticity ν' Poisson' ratio for elasticity Initial estimates Slope of failure line from Morh- Coulomb's failure criterion y-intercept of failure line from Morh-Coulomb's failure criterion E or E 5 or E ur depends on considered problem From.3 to.4 as suggested by Plaxis 2D (29) ψ Dilatancy angle Function of φ' peak and φ' critical state K Coefficient of earth pressure at 1 - sinφ' (default setting) rest ( σ1 σ 3) f /(( σ1 σ 3) R f Failure ratio ult =.9 (default setting) E 5 E oed E ur m Reference secant stiffness from drained triaxial test Reference tangent stiffness for oedometer primary loading Reference unloading/reloading stiffness Power for stress-level dependency of stiffness ν ur Unloading/reloading Poisson's ratio Reference small strain shear G modulus g.7 Shear strain magnitude at.722g y-intercept in log(σ' 3 /p ) - log(e 5 ) curve y-intercept in log(σ' 1 /p ) - log(e oed ) curve y-intercept in log(σ' 3 /p ) - log(e ur ) curve Slope of trend-line in log(σ' 3 /p ) - log(e 5 ) curve.2 (default setting) y-intercept in log(σ' 3 /p ) - log(g ) curve Modulus degradation curve between G/G and logg Remarks: σ' 1 is major principal stress (kpa); σ' 3 is minor principal stress (kpa); p is erence pressure (1 kpa). The effective friction angle (φ') for each sand layer was directly obtained from laboratory tests. Values of effective cohesion (c') for sand layers were assumed to be zero, but to avoid complication for calculation of PLAXIS software, a very small value c' =.5 kpa was set for sand layers. The drained Poisson' ratio was assumed to be.3 for sand layers as suggested by PLAXIS 2D (29), Khoiri and Ou (213). As proposed by Bolton (1986), the dilatancy angle could be obtained as follows: For sands with φ' 3 : ψ '= (2) For sands with φ' > 3 : ψ (3) ' = φ' 3

8 Vol. 19 [214], Bund. Z The coefficient of lateral earth pressure at rest can be determined by the following formula of Jaky (1944): K = 1 sin ' (4) φ A common problem of sandy soils is that the field samples are easily disturbed. Thus, the strength parameter of sand, i.e. φ', can be directly obtained from the laboratory tests, but it is difficult to get an accurate value of stiffness parameter (E') from the laboratory tests for sands. This is because the φ' is related to the surface roughness, compaction and shape of the sand particles that are little influenced by the sample disturbance. In contrast, the Young's modulus of sand E' depends on physical properties and intergranular force between the sand gains that are much affected from the sample disturbance. As a result, the E' is often obtained from the empirical equations, which are often found by either calibration studies or back analyses (inverse analyses) from the full-scale load test data obtained from the field or the case histories of deep excavation. The standard penetration test is recently the most popular and economical means to provide the geotechnical engineering properties of soil. The standard penetration test values (SPT or N values) are in situ field measurements, and they are little influenced from the sample disturbance. Theore, the use of correlations between N values and soil properties has become common practice in many countries. Consequently, the empirical relations between the E' and N for sands have proposed by many researchers, for example Schertmann (197), Poulos (1975), Bowles (1996), Ou et al. (2), Hsiung (29). However, these correlations are significantly various because they were established from various ground conditions. Alternatively, the E' of sand layers in this study can be evaluated by back analysis method, in which E' is evaluated by minimizing the deviation or difference between the field measurements and numerically calculated results (see Calvello and Finno, 24). Because almost previously empirical equations between E' and N are in form of E' = AxN, in which A is a correlation ratio, this study also used this form in the back analysis to evaluate the Young's modulus of sands. In addition, the back analysis was based on the observed wall deflections at the final excavation stage at the central section of long side because the wall deflections are the largest, which are easier for comparing the numerically calculated wall deflections with the field measurements. The back analysis found that the best-fit correlation between the E' and N for the sand layers of Case A is: E ' = 2N( kpa) (5) This equation is identical to the equation used by Hsiung (29) for sands of the excavation at O6 station, which is about.6 km away from the excavation of Case A, as shown in Figure 1. Table 5 lists the input parameters of sand layers for the MC model used for analysis. Layer Depth (m) Table 5: Input parameters of sand layers for the MC model Soil type g t N value φ' ( o ) c' (kpa) E' (kpa) (kn/m 3 ) SM SM SM SM SM SM ν' ψ ( o ) K

9 Vol. 19 [214], Bund. Z Figure 5 below presents the comparison of measured and predicted wall deflections and ground surface settlements for the excavation of Case A using the MC model. Displacement (mm) Distance from the wall (m) The 1st strut: 2 1.5m Depth (m) The 5th stage: 16.8m Ground surface settlement (mm) Stage 1-Measurement Stage 3-Measurement Stage 5-Measurement Stage 2-Analysis Stage 4-Analysis Stage 2-Measurement Stage 4-Measurement Stage 1-Analysis Stage 3-Analysis Stage 5-Analysis Figure 5: Wall deflections and ground surface settlements measured and predicted for the excavation of Case A using the MC model As shown in Figure 5, the predicted wall deflections at the earlier stages of excavation (Stages 1, 2 and 3) in general are all larger than the field measurements, respectively. It is because the MC model dose not consider the strain-dependent stiffness behavior or the small train characteristics that invole high stiffness modulus at small strain levels of soil. It is thus concluded that the Young's modulus of sands adopted in the MC model was underestimated at the earlier stages of excavation due to the wider range of small strain soil area at these stages. The predicted wall deflections at the later stages of excavation (Stages 4 and 5) are very close to the field measuremetns at the upper wall parts but are significantly larger than the field measurements at the lower wall parts, respectively. The the largest wall displacements of observation and prediction are equal to each other and near the excavation level. The main reason can be related to the fact that the MC model only uses a single Young's modulus and dose not also distinguish between loading and unloading stiffnesses. These features of the MC model cause over-prediction of heave of excavation bottom becauce the higher stiffness of ground below the excavation level that is unloaded during excavation process is not considered. The overprediction of the heave of excavation bottom then causes the larger wall deflections at the lower wall parts. From Figure 5, it is obviously seen that the predicted settlements for all stages of excavation are very different from the field measurements. The unrealistic heaving of the ground surface

10 Vol. 19 [214], Bund. Z near the retaining wall and under-prediction of the maximum ground surface settlements are also seen herein. These can be explained that the so large heave of the excavation bottom, as mentioned above, pushes the wall and surrounding ground up, which then causes the unrealistic heave of the ground surface and under-prediction of the maximum settlements. On the contrary, the settlements in the secondary influence zone (SIZ), which are far away from the retaining wall (see Hsieh and Ou, 1998), are higher and wider than those reported in the previous studies of excavations in sands such as Peck (1969), Clough and O'Rourke (199), Ou et al. (1993), Bowles (1996). This is because the MC model dose not take into account the strain-depent stiffness behavior. It can be thus concluded that the single Young's modulus used in the MC model was underestimated in the SIZ whose strains are mainly in small strain levels. The same profiles of the ground surface settlement predicted from MC model can be also found in the previous researches of Brinkgreve et al. (26), Schweiger (29), and Khoiri and Ou (213) for excavations in sands. Hardening soil model (HS model) The HS model is an advanced model for simulation of soil behavior (see Schanz et al., 1999), and it uses the same failure criterion as the MC model. Before reaching the failure surface, the HS model adopts a hyperbolic stress-strain ralation between the vertical strain and deviatoric stress for primary loading, which is the well-known model proposed by Duncan and Chang (197). In the HS model, soil stiffness is calculated much more accurately by using three different stiffnesses, i.e. triaxial loading secant stiffness E 5, triaxial unloading/reloading stiffness E and oedometer loading tangent stiffness E at the erence pressure p that is usually taken as 1 oed kpa (1 bar). The MC model represents Young's modulus of soil in the in situ stress state. On the other hand, the HS model represents its three moduli at the erence pressure, and these moduli at the in situ stress state are automatically calculated as a function of the current stress state, for example: For sands: E m c' cosf' + s ' 3 sinf' s ' 3 5 = E5 = E 5 c'cosf' + p sinf' in which σ ' is the minor effective principal stress, a positive value for compression; m is the 3 power determining the rate of variation of E with 5 σ ' 3 (see PLAXIS 2D, 29). There are 1 input parameters for the HS model as listed in Table 4. The parameters of φ', c', ψ and K were completely the same as those used in the MC model. The parameters of m and ν ur were taken as.5 and.2 for sands, respectively, as suggested by Schanz et al. (1999), PLAXIS 2D (29) and Khoiri and Ou (213). The failure ratio R f was taken to be.9 as a default value in the PLAXIS program. For stiffness parameters, the E and ur E were set equal to oed 3E 5 and E 5 for sands, respectively, as suggested by Schanz and Vermeer (1998), Schanz et al. (1999), Schweiger (29) and PLAXIS 2D (29). It is similar to the E' of the MC model, the E 5 of the HS model was also evaluated by back analysis method with the same form of E', and the back analysis was also based on the monitoring wall deflections at the final stage of excavation at the central section of long side of Case A. The best-fit relation found from the back analysis between the E 5 and N for sand layers of Case A is: p E 5 = 12N( kpa) (7) m ur (6)

11 Vol. 19 [214], Bund. Z Equation (7) compared with Equation (5) shows that the E 5 6%E' of the MC model for sand layers. A similar relation between E' and of the HS model is equal to E 5 is also seen in the study of Schweiger (29) for sand. Table 6 below presents the input parameters of sand layers for the HS model used for analysis. Table 6: Input parameters of sand layers for the HS model Layer Depth g t N φ' c' ψ E 5 E (m) (kn/m 3 ) value ( o oed E ur ) (kpa) ( o ) (kpa) (kpa) (kpa) ν' ur m R f K Figure 6 shows the comparison of measured and predicted wall deflections and ground surface settlements for the excavation of Case A using the HS model. It is clearly seen from Figure 6 that the results of the HS model are much more improved in comparison with the MC model, especially the prediction of surface settlements. Because the unloading stiffness is calculated in the HS model, the large movements of the wall toe and unrealistic heaving of the ground surface near the retaining wall are not seen in the results of this model. The maximum ground surface settlement estimated from the HS model is located in range of.6h e to 1.H e away from the wall, and its value is equal to about.3%h e. However, the predicted wall displacements at the earlier stages of excavation are still larger than the field measurements, respectively, and the estimated settlements in the SIZ are still larger and wider than those found from the previous researches. It is because the HS model dose not still compute the strain-dependent stiffness behavior or the small strain characteristics of soil. Hardening soil model with small strain stiffness (HSS model) The HSS model is modified from the HS model with considering the small strain characteristics of soil, which is based on the research of Benz (26). At very small and small strain levels, most soils show a higher stiffness than that at engineering strain levels. The HSS model uses a modified hyperbolic law for the stiffness degradation curve, which was proposed by Hardin and Drnevich (1972) and Santos and Correia (21). In addition to the same parameters as the HS model, the HSS model requires two additional parameters. These two parameters are the erence shear modulus at very small strain ( G ) and shear strain (g.7 ) at which the secant shear modulus is equal to about 7% its initial value ( G s =.722G =. 722G ). Thus, there are total 12 max input parameters for the HSS model as shown in Table 4. All input parameters for the HS model were kept completely the same for the HSS model. There are 21 empirical equations for determining the shear wave velocity (V s ) of sand soils at different places in over the world as reported in the study of Marto et al. (213). All of these B equations were in a power-law relationship between V s and N, i.e. V s = AN, in which A and B are regression parameters. For estimating the V s more generally, a power-law relationship between V s and N value was established by the regression method based on the 21 empirical

12 Vol. 19 [214], Bund. Z equations mentioned above. As can be noted from Figure 7, a newly found correlation between V s and N value, which is shown in Equation (8), is quite reliable because its coefficient of determination is quite high, R 2 = V s = 71.48N (8) Displacement (mm) Distance from the wall (m) The 1st strut: 2 1.5m -4-3 Depth (m) The 5th stage: 16.8m Ground surface settlement (mm) Stage 1-Measurement Stage 3-Measurement Stage 5-Measurement Stage 2-Analysis Stage 4-Analysis Stage 2-Measurement Stage 4-Measurement Stage 1-Analysis Stage 3-Analysis Stage 5-Analysis Figure 6: Wall deflections and ground surface settlements measured and predicted for the excavation of Case A using the HS model 5 Shear wave velocity (m/s) V s = 71.48N.391 R² = N value Figure 7: Found correlation between V s and N based on earlier correlations for sandy soils

13 Vol. 19 [214], Bund. Z From the shear wave velocity calculated from the correlation above, the shear modulus at very small strain level of sand layers can be determined by the following equation: 2 g 2 G = ρ Vs = Vs ( kpa) (9) g in which ρ is total density of soil; g is total unit weight of soil (kn/m 3 ); g is gravitational acceleration (m/s 2 ) and V s is shear wave velocity in soil (m/s). The erence shear modulus at very small strain level was then obtained as follows: G σ ' p 3 = G m Since the researches of the threshold shear strain g.7 is very limited, especially for sandy soils. In addition, values of g.7 are very scattered for various types of soil, as reported in studies of Vucetic and Dorbry (1991), Brinkgreve et al. (26), Schweiger (29), Lim et al. (21) and Likitlersuang et al. (213). As a result, in this study, the g.7 was evaluated by back analysis method based on the monitoring wall deflection at the final stage of excavation at the central section of long side of Case A. The best-fit value of g.7 found from the back analysis was 1-4. This found value of g.7 is consistent with previous researches mentioned above. Table 7 below shows the two additional parameters of sand layers for the HSS model used for analysis. Layer Table 7: Two additional parameters of sand layers for the HSS model Depth (m) Soil type N value V s (m/s) σ' 3 (kpa) G (kpa) G (kpa) SM SM SM SM SM SM Figure 8 shows the comparison of measured and predicted wall deflections and ground surface settlements for the excavation of Case A using the HSS model. As shown in Figure 8, the wall deflections and ground surface settlements computed from the HSS model are much more improved in comparison with the MC model and HS model. The large displacements of the wall toe at the later stages of excavation and the over-prediction of the wall deflections at the earlier stages of excavation are not seen with the HSS model. Furthermore, for settlement prediction, the larger and wider settlements in the SIZ are not also found in the HSS model. The better results above are found because the HSS model considers the unloading stiffness and the strain-dependent stiffness behavior of soil. The largest settlement of the HSS model is also located in range of.6h e to 1.H e away from the wall, and its value is equal to about.29%h e that is a little smaller than that of the HS model. g.7 (1)

14 Vol. 19 [214], Bund. Z Displacement (mm) Distance from the wall (m) The 1st strut: 2 1.5m Depth (m) The 5th stage: 16.8m Ground surface settlement (mm) Stage 1-Measurement Stage 3-Measurement Stage 5-Measurement Stage 2-Analysis Stage 4-Analysis Stage 2-Measurement Stage 4-Measurement Stage 1-Analysis Stage 3-Analysis Stage 5-Analysis Figure 8: Wall deflections and ground surface settlements measured and predicted for the excavation of Case A using the HSS model DISCUSSIONS Comparison of results from the different soil models In this section, the wall deflections and ground surface settlements predicted from the MC model, HS model and HSS model are compared with each other in each stage of excavation. Figs. 9, 1 and 11 below present the observed and computed wall displacements and surface settlements in the first stage (Stage 1), the intermediate stage (Stage 3) and the final stage (Stage 5) of excavation, respectively. As shown in Figure 9, for Stage 1 of excavation, the wall deflections estimated from the HSS model are very close to the field measurements, but the wall deflections from the MC and HS model are slightly larger than the field measurements. The surface settlements of the three models are all smaller than the observations. However, the settlements of the HS model and HSS model are similar to each other and closer to the field measurements whereas the settlement profile of the MC model is very far from the observation. For Stage 3 of excavation, the wall deflections from the HS model and HSS model are consistent with each other but slightly larger than the measurements. On the contrary, the MC model results in the significant over-prediction of the wall movements. The settlement profile of the MC model is very different from the field measurements and those of the HS model and HSS model. The maximum settlement of the MC model are much smaller than those of the HS and HSS models, and the settlements in the SIZ of the MC model are larger than those of the HSS

15 Vol. 19 [214], Bund. Z model. The maximum settlement from the HS model is close to that of the HSS model, but the settlements in the SIZ of the HS model are larger and wider than those of the HSS model. For the final stage of excavation (Stage 5), the wall movements of the HS and HSS models are the same as each other and the observation. In contrast, the MC model yields the significant over-prediction of the wall deflections at the lower depths of the wall. The trends of settlement predicted at Stage 5 of excavation are seen to be the same as those predicted at Stage 3 of excavation. Parametric studies The parameters E', E 5 and g.7 are important input parameters of the MC, HS and HSS models, respectively, which were obtained by the back analysis method. To evaluate the sensitivity of these parameters on prediction of movements induced by the excavation of Case A, parametric studies were conducted with various values of E', E 5 and g.7 in the analyses using the MC, HS and HSS models, respectively. The E' was varied in values of.5e' = 1N, 1.E' = 2N and 1.5E' = 3N; the E 5 was varied in values of.5e 5 = 6N, 1.E 5 = 12N and1.5e 5 = 18N. The g.7 was varied in values of 5x1-5, 1-4 and 5x1-4. All other input parameters of the MC, HS and HSS models were kept unchanged in the parametric studies. Results of the parametric studies are shown in Figs. 12, 13 and 14. In these figures, d htop is the deflection at the wall top, d hm is the maximum wall deflection, d htoe is the deflection at the wall toe, d vw is the surface settlement at the wall, d vm is the maximum surface settlement, and d vb is the surface settlement at the model boundary. Displacement (mm) Distance from the wall (m) Stage Depth (m) Ground surface settlement (mm) Measurement The HS model The MC model The HSS model 32 Figure 9: Wall deflections and ground surface settlements measured and predicted at Stage 1 of excavation from the MC model, HS model and HSS model

16 Vol. 19 [214], Bund. Z Displacement (mm) Distance from the wall (m) Depth (m) Stage 3 Ground surface settlement (mm) Measurement The HS model The MC model The HSS model 32 Figure 1: Wall deflections and ground surface settlements measured and predicted at Stage 3 of excavation from the MC model, HS model and HSS model Displacement (mm) Distance from the wall (m) Depth (m) Stage 5 Ground surface settlement (mm) Measurement The HS model The MC model The HSS model 32 Figure 11: Wall deflections and ground surface settlements measured and predicted at Stage 5 of excavation from the MC model, HS model and HSS model

17 Vol. 19 [214], Bund. Z Wall deflections and surface settlements (mm) E' 1 1.E' 1 1.5E' 2 2 Young'smodulus, E' d htop d hm d htoe d vw d vm d vb Figure 12: Effects of E' on wall deflections and surface settlements at the final stage of excavation in the analysis using the MC model Figure 13: Effects of Wall deflections and surface settlements (mm) E E E 5 1.5E 5-2 Young'smodulus, E 5 on wall deflections and surface settlements at the final stage of d htop d hm d htoe excavation in the analysis using the HS model d vw d vm d vb Wall deflections and surface settlements (mm) Shear strain, γ.7 Figure 14: Effects of g.7 on wall deflections and surface settlements at the final stage of excavation in the analysis using the HSS model d htop d hm d htoe d vw d vm d vb

18 Vol. 19 [214], Bund. Z CONCLUSIONS The following are conclusions drawn from this study: 1) The back analyses found that the Equation (5) and Equation (7) are the best-fit correlations of input parameters E' and of the sand layers for the MC model and HS model, E 5 respectively. The back analyses also found that the best-fit value of g.7 of the sand layers for the HSS model is 1-4. Furthermore, a quite reliable correlation between V s and N for sandy soils is also found as Equation (8), which is based on the previously empirical equations in the literature. 2) In general, the more advanced soil model is adopted in the numerical analyses, the better predictions of the wall deflection and surface settlement are obtained from the analyses. In order, the HSS model is better than the HS model, and the HS model is better than the MC model. 3) For the first stage of excavation (Stage 1), the wall deflections of the HSS model are very close to the field measurements, but those of the MC model and HS model are slightly larger than the field measurements. The surface settlements of the three models are all smaller than the observations. However, the settlements of the HS model and HSS model are similar to each other and closer to the field measurements whereas the settlement profile of the MC model is very far from the observations. 4) For the intermediate stage of excavation (Stage 3), the wall deflections of the HS model and HSS model are consistent with each other and slightly larger than the measurements. On the contrary, the MC model gives the significant over-prediction of the wall movements. The settlement profile of the MC model is very different from the field measurements and those of the HS model and HSS model. The maximum settlement of the MC model is much smaller than those of the HS and HSS models, but the settlements in the SIZ of the MC model are larger than those of the HSS model. The maximum settlement from the HS model is close to that of the HSS model, but the settlements in the SIZ of the HS model are larger and wider than those of the HSS model. 5) For the final stage of excavation (Stage 5), the wall movements of the HS and HSS models are the same as each other and the observations. In contrast, the MC model yields the significant over-prediction of the wall deflections at the lower depths of the wall. The trends of settlement predicted at Stage 5 of excavation are seen to be the same as those predicted at Stage 3 of excavation. 6) The variations of input parameters E', E 5 and g.7 of the MC, HS and HSS models, respectively, are significantly influence the predictions of d hm and d vm but have a little effect on results of d vb and d htop. ACKNOWLEDGGMENTS The authors would like to thank Mr. Hsin-Nan Huang and Mr. Wei-Ya Song, graduate students of Department of Civil Engineering, National Kaohsiung University of Applied and Sciences, Kaohsiung, Taiwan, for helping to collect the field data used in the study. REFERENCES 1. ACI Committee 318 (1995), "Building code requirements for structure concrete and commentary", American Concrete Institute, Farmington Hills, Mich.

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