UGS2011 Application of The Hardening Soil Model in Deep Excavation Analysis [PDF]

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Underground Singapore 2011



Application of the hardening soil model in deep excavation analysis1 P.L. Teo & K. S. Wong WKS Geotechnical Consultants, Singapore



ABSTRACT: The Mohr-Coulomb model (MC) is commonly used in deep excavation analysis for its simplicity. However, it has shortcomings that may produce unrealistic soil behavior. The Hardening Soil model (HS) is an advanced soil model that is able to generate more realistic soil response in terms of non-linearity, stress dependency and inelasticity. This paper highlights some of the shortcomings of the MC model and presents a simplified approach to determine the HS parameters for drained and undrained analysis of deep excavations. Three case studies were back-analyzed to validate the application of the HS model for practical excavation analysis. The HS model suffers the same problems as the MC model in using effective stress parameters c and  to determine the undrained shear strength. 1 INTRODUCTION The Mohr-Coulomb model (MC) is commonly used in practice despite of its many shortcomings. (Wong 2011). The Hardening Soil model (HS) is an advanced soil model that can better simulate real soil behaviour. It is a big improvement over the MC model in several aspects. This paper presents an overview of the HS model and highlights its strengths over the MC model in excavation analysis. Back-analysis of deep excavation case records in Singapore are presented to compare the predicted wall and ground movements between both soil models and against measured data. The paper also discusses shortcomings of the HS model.



2 THE HARDENING SOIL MODEL 2.1 An overview The HS model is an elastic-plastic soil model based on the classical plasticity theory (Brinkgreve, 2004). For every stress increment, there is a corresponding incremental elastic and plastic strain if the soil is undergoing primary loading or only the elastic strain if it is unloading-reloading. The main attraction of this model is its ability to simulate the nonlinear, inelastic and stress dependent behaviour of soil. The model adopts the Mohr-Coulomb failure criteria. (1) 1



This paper is adapted from a paper submitted for the Hulme Prize Award of the Tunnelling and Underground Construction Society (Singapore).



59



Underground Singapore 2011 It has two yield surfaces as shown in Figure 1(a). The first one deals with yielding due to shear stress. The second one handles the expansion of the cap due to changes in mean effective stress p’. Figure 1(b) shows the yield surfaces in three-dimensional principle stress space.



q



1



E50 & Eoed combined hardening E50 shear hardening Eur elastic



(a)



Eoed cap hardening 3



p’p



p’



2



(b)



Figure 1. (a) Illustration of double yield surface of HS model; and (b) Yield surfaces of HS model in 3-D.



The hardening law for shear is given in Equation 2. For a given shear stress increment, the plastic shear strain increment can be computed from this equation and the corresponding plastic volumetric strain increment can be computed from the flow rule in Equation 3. The hardening law for the cap is given in Equation 4. For a given increment in mean stress, the plastic volumetric strain increment can be computed using this equation with no shear strain generated. (2)



(3) (4) where Kc is related to the compression index Cc and Ks is related to the recompression index Cr . 2.2 Parameters of the Hardening Soil Model The required soil parameters are summarised in Table 1. Most of the soil parameters can be determined from consolidated drained triaxial compression test (CD) and consolidation test. In the absence of consolidation test, the parameter Eoedref can be set equal to E50ref. If the unloading-reloading cycle is not carried out in the CD test, the parameter Eurref can be set equal to 3E50ref. Table 1. Parameters for the HS model. Parameter c







E50ref Eoedref Eurref m ur Ψ Ko,nc



60



Description Effective apparent cohesion Effective peak friction angle Effective secant modulus (50% stress level) at confining pressure of 100 kPa Effective 1-D compression modulus at a vertical stress of 100 kPa. Typically set equal to E50ref in the absence of test data. Effective unloading-reloading modulus at a confining pressure of 100 kPa. Typically set equal to 3E50ref in the absence of test data. Modulus exponent controlling the stress-dependency of the modulus with values typically varying between 0 and 1. Unloading-reloading Poisson’s ratio. Typically set equal to 0.2. Angle of dilation. Typical set equal to zero for undrained analysis and (  - 30o) for drained analysis. Coefficient of earth pressure at-rest. Typically set equal to (1-sin ).



Type of Test CD or CU CD or CU CD Oedometer CD CD CD CD -



Underground Singapore 2011 Once these parameters are known, the modulus of a soil under any stress condition can be computed using the following equations in Table 2. Table 2. Equations for stiffness parameters.



*pref = reference pressure of 100 kPa.



The parameter E50ref can be determined from the CD test. Assuming that the test is carried out on three samples under different confining pressures, the secant modulus E50 can be determined from each sample. By plotting ln (E50) versus ln on a natural scale and fitting a straight line through the data, the y-intercept gives the value of ln(E50ref) and the slope is the parameter m. An illustration is shown in Figure 2(a). The parameter Eoedref can be determined from consolidation test. From the stress-strain curve, the tangent modulus at 100 kPa is Eoedref as illustrated in Figure 2(b). 1‘



ln E50



ln (a) (b) Figure 2. Illustration on how (a) E50ref and m; and (b) Eoedref are determined.



2.3 Proposed correlations for analysis of deep excavations In the absence of CD test or consolidation test data, the following approach is proposed to determine the parameters. 2.3.1



Sand



Based on the data from Wong and Duncan (1974), the parameters E50ref and m were determined for several sands. Results of the E50ref and m are plotted against the relative density Dr in Figures 3 and 4, respectively. The proposed HS parameters for sand are summarised in Table 3. 0.9



1000



0.8



E50ref (MPa) = 6 e (0.025 Dr)



m = 0.45 + 0.003 Dr



0.7 0.6



E50ref (MPa)



100



0.5



m



0.4



10



Sacramento River Sand



0.3



Port Allen Lock Sand



Port Allen Lock Sand



0.2



Fine Silica Sand



Fine Silica Sand



0.1



Monterey No. 0 Sand 0



20



40



60



Relative Density (%)



80



Monterey No. 0 Sand



0



1 100



Figure 3. Plot of E50ref against relative density.



0



20



40



60



80



100



Relative Density (%)



Figure 4. Plot of m against relative density.



61



Underground Singapore 2011 2.3.2



Clay



For analysis involving undrained behaviour in clay, it is proposed to adopt the parameters shown in Table 3. By setting m = 0, the stress dependency of the soil modulus is eliminated which is valid for undrained behaviour of clay. The HS model still captures the nonlinear and inelastic response. Table 3: Proposed relationships to determine HS parameters for sand and clay. Proposed Value / Correlation



Parameter



Sand



Clay



0



cu



c' (kPa) o



'()



28 + 0.15 Dr (%)



0



E50ref (MPa)



6 e0.025 Dr (%)



0.8 Eu (Eu based on Eu / cu ratio)



Eoedref (MPa)



E50ref



E50ref



Eurref (MPa)



3 E50ref



3 E50ref



m



0.45 + 0.003 Dr (%)



0



ur



0.2



0.2



o



o



() Ko



3







' – 30



Ko = (1 - sin ' )



Ko = (1 - sin ' )



LIMITATIONS OF THE MC MODEL AND IMPROVEMENTS BY THE HS MODEL



A comparison between the stress-strain behaviour of real soil, MC and HS models is illustrated in Figure 5. The MC soil is elastic before failure and only switches to plastic upon reaching failure. In contrast, real soil response is nonlinear even before failure. The HS model captures this nonlinear behaviour and also uses different modulus for primary loading and unloading-reloading to capture the inelastic response whereas the MC model uses the same modulus. In the CD tests on sand or clay, the modulus is stress-dependent. This stress-dependency is captured by the HS but not by the MC model.



Plastic



UU Test on Clay cu > 0 u=0



Elasticplastic



Elastic



Elasticplastic e



e



e Plastic



CD Test on Clay or Sand c' ≥ 0 ' > 0



Inelastic



Real Soil



Inelastic



Elastic e



e



e



Mohr-Coulomb Soil



Hardening Soil



Figure 5. Stress-strain behaviour of real soil, MC soil and HS.



3.1 Importance of modelling non-linear behaviour before failure A case study to illustrate the importance of the nonlinearity attribute is shown in Figure 6(a). A surcharge of 13 kPa was applied on the steel plates behind the shallow excavation. In the zone nearer to the excavation, the soil was sheared to a higher stress level but not to failure. Since there were no failures, the MC soil behaved elastically and produced a near symmetrical ground settlement response as shown in Figure 6(b). The HS model, on the other hand, captured the reduction in stiffness in this



62



Underground Singapore 2011 zone and yielded a non-symmetrical response as shown in Figure 6(c). The nonlinearity attribute can be important in many practical problems. 0



50



100



0



150



0



0



35



35



50



100



150



Fill



Soft Marine Clay



e



e



(a) (b) (c) Figure 6. (a) Case study to illustrate the importance of nonlinearity attribute; (b) response computed by MC model; and (c) response computed by HS model.



3.2 MC model cannot model stress-dependent stiffness Under drained condition, the stiffness of real soil is stress-dependent; while the stiffness of a MC soil is stress independent as illustrated in Figure 5. Figure 7 illustrates the settlement of a rigid footing on sand with modulus increasing with depth. Figure 7(a) shows that the MC model generated large ground surface settlement because the sand modulus near the surface was small and remained constant. Consequently, Figure 7b shows a zone of large settlement immediately below the footing. The stress-dependent stiffness is not captured in the MC model but is captured in the HS model. When the applied load and stresses below the footing increased, the HS model responded with an increase in soil stiffness and hence resulted in smaller settlement. In excavations, Figure 8 illustrates that due to stress-dependency, the stiffness of soil inside the excavation decreases as the excavation depth increases. The modulus of a soil element is initially 20 MPa and decreases to 3 MPa at the end of excavation. This change in modulus is captured by HS model but not by the MC model.



Footing Settlement



HS Model



MC Model



Load on Footing



Zone of large settlement



MC Model



HS Model



(a) (b) (c) Figure 7. Rigid footing in sand (a) load-settlement curves; and (b) stress contours of vertical displacement.



63



Underground Singapore 2011 Mohr-Coulomb Model



Hardening Soil Model



e Figure 8. Stress-dependent behaviour of soil under drained condition. 3.3 MC model cannot properly model unloading-reloading behaviour Figure 9 presents a case study of a hypothetical excavation in sand. In the MC analysis, the sand was divided into layers to simulate the increase in initial modulus with depth. During excavation, the modulus remained unchanged. The modulus of a HS soil however, changed continuously according to the change in stress and the stress-path involved. While the MC model produced larger wall deflection, toe movement, bottom heave and ground settlement, the HS model produced a more reasonable response.



0



10



Deflection (mm) 30 40



20



50



60



70



0 HS - excav to 1.5m HS - excav to 5m HS - excav to 7.5m HS - excav to 10.5m MC - excav to 1.5m MC - excav to 5m MC - excav to 7.5m MC - excav to 10.5m



Depth (m)



-5 -10



-15 -20 -25 -30



(a)



110 100 90 80 70 60 50 40 30 20 10 0



0



Distance (m) 5 10



15



20 HS - excav to 1.5m HS - excav to 5m HS - excav to 7.5 HS - excav to 10.5 MC - excav to 1.5m



MC - excav to 5m MC - excav to 7.5m MC - excav to 10.5



0



25



Heave / Settlement (mm)



Heave (mm)



-5



(b) 20



Distance (m) 40 60



25 20 15 10 5



80



100



120



HS - excav to 1.5m HS - excav to 5m HS - excav to 7.5m HS - excav to 10.5m MC - excav to 1.5m MC - excav to 5m MC - excav to 7.5m MC - excav to 10.5m



0



-5 -10 -15



(c) (d) Figure 9. Case study of excavation in Sand (a) finite element model; (b) wall deflection; (c) ground settlement; and (d) ground heave.



3.4 MC model cannot generate the correct 1-D compression behaviour The non-linear stiffness of real soil is evident from consolidation test. The stiffness increases with stress as the soil becomes more compact. The MC model produces a linear response as shown in Figure 10. The HS model is able to capture the non-linear behaviour because of the cap yield surface.



64



Underground Singapore 2011



Vertical Strain



p



Mohr-Coulomb Model depending depending on E’ Hardening Soil Model Vertical Stress (kPa)



Figure 10. Stress-strain curves for one-dimensional consolidation



3.5 MC model may produce an incorrect response under certain stress paths There are certain stress paths where an elastic soil will produce an incorrect response. Figure 11 illustrates one of them where a soil sample is subjected to a simultaneous reduction in 3 and ( 13). An elastic MC soil sample rebounded upwards whereas the real soil actually moved downwards. The elastic-plastic HS model is able to simulate the correct response. 3.6 MC model under-estimates the horizontal stress in certain stress paths. Consolidation tests were simulated to compare the horizontal stresses generated by the MC and HS models and the empirical relationship Ko,OC = Ko,nc OCR0.5. Figure 12 shows that the MC underestimated the horizontal stress during loading and unloading. The HS gave a better agreement with the empirical relationship.   1- 3



2.5



(kg/cm2) MohrCoulomb Soil



(kg/cm2)



500



Measured HS MC



Hardening Soil



2.0



MC



Horizontal Stress (kPa)



1.5 -0.1



0



ev(%)



0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9



e1 (%)



1



1.0



-0.1



HS



Emiprical



400



2.0



1.5



-0.2



  1- 3



2.5



300



200



100



0 0



0



-0.1



0



0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9



1



 3 3 (kg/cm )



0.5 0



0.3



0.6



200



400



600



800



Vertical Stress (kPa) 0.9



1.2



Figure 11. Behaviour in a drained triaxial test subjected to reduction in 3 and ( 1- 3).



1.5



Figure 12. Comparison of horizontal stresses computed using empirical relationship, the MC and the HS model.



3.7 MC model results may be sensitive to Poisson’s Ratio in a drained analysis For some problems, results can become very sensitive to the Poisson’s Ratio when using the MC model. Figure 13 shows an example of excavation in sand. By varying the Poisson’s Ratio from 0.2 to 0.4, the wall deflection doubled and strut forces increased by up to 1.5 times. The uncertainty and sensitivity of the Poisson’s Ratio is not an issue in the HS model. The Poisson’s Ratio only affects the elastic strain but not the plastic strain. The unloading-reloading Poisson’s Ratio value of real soil is typically between 0.15 and 0.25. A value of 0.2 is commonly used.



65



Underground Singapore 2011 Wall Deflection (mm) -20



0



20



40



60



=0.2



=0.4



Mmax ,kNm/m



298



477



Strut 1, kN/m



77



114



Strut 2, kN/m



226



335



Strut 3, kN/m



163



178



80



0



’=35o



E’=8000 kPa H=9 m



Depth (m)



c’=5 kPa



5



=0.4



10



=0.2



15 20 25 30



Figure 13. Stress-path and Strain behaviour under drained triaxial test.



CASE STUDIES



4



Back-analysis of three case studies of deep excavations in Singapore was carried out using the finite element (FE) program Plaxis version 9.02. They were the Rocher Complex, the Lavender MRT Station and the Hougang-Buangkok cut-and-cover tunnel. Results of analysis using the MC and the HS model were compared with the measured data. The HS parameters were determined according to Section 2. The total stress approach was used in the MC analyses. 4.1



The Rochor Complex



The Rochor Complex excavation was 95 m wide and 6.3 m deep. The excavation was retained using sheetpiles and three levels of preloaded struts. The ground water level was at 1.5 m below ground level. A cross-section of the excavation and the soil profile are shown in Figure 14. (Lim et al 2003; Halim and Wong 2005). Undrained Shear Strength, Cu (kPa) 0



10



30



20



40 0.6m Preload=28kN/m 1.5m Preload=104.3kN/m



0.0 SAND SAND



= 20 20kN/m kN/m3 3 ’’ == 30 30oo



1.5m



3.8m Preload=175.1kN/m



Depth, z (m)



5.05



6.3m



UPPER MARINE CLAY = 16 kN/m3 Cu = 15 to 30 kPa PI = 45/%



24m



FSP IIIA Sheetpile



18.5 FIRM CLAY



= 17kNm3



Cu = 100 kPa



PI = 20%



21.25 LOWER MARINE CLAY



= 16kN/m3



Cu = 33.1 to 36.1 kPa



PI = 40% 40%



Width of excavation = 95m



24 VERY STIFF SILTY CLAY Cu = 200 kPa PI = 20%



Figure 14. Cross-section of excavation at the Rochor Complex (Halim & Wong, 2005; Lim et al, 2003).



In the FE model, the Upper Marine Clay and Lower Marine Clay layers were divided into sub-layers with increasing undrained shear strength and stiffness. The HS stiffness parameters E50ref, Eoedref and Eurref were determined for each Eu /cu ratio. Results shown in Figure 15 indicate that the Eu /cu ratio of 250 for the HS model and 300 for the MC model produced a reasonable match with the measured deflection. The MC model produced larger ground settlement and bottom heave. It is interesting that the MC model also produced more plastic points (Figure 16), which indicated more soil reaching failure.



66



Underground Singapore 2011



100



150



200



0



0



-2



-2



-4



-4



-6



-6



-8



-8



-10



-10



-12 -14



50



100



Distance from wall (m) 0 150



200



HS model - Eu/Cu = 200 HS model - Eu/Cu = 250 HS model - Eu/Cu = 300



-20 -22 -24



40



50



60



-20 -40 -60 HS model. Eu/Cu = 250 MC model. Eu/Cu = 300



-120



(c)



-12



Distance from wall (m) 0



-14



10



20



30



40



50



100 HS model. Eu/Cu = 250



-18



Measured final excav



-20



MC model. Total stress. Eu/Cu = 250 MC model. Total stress. Eu/Cu = 300 MC model. Total stress. Eu/Cu = 350



-22 -24 -26



-26



30



-80



Heave (mm)



Measured final excav



-18



20



-100



-16



-16



10



0



Settlement (mm)



50



Mohr-Coulomb Model Deflection (mm)



0



Depth (m)



Depth (m)



0



Hardening Soil Model Deflection (mm)



80



MC model. Eu/Cu = 300



60 40 20 0



(a) (b) (d) Figure 15. Comparison of results from analysis using the MC and HS models at the final excavation of Rochor Complex (a) & (b) wall deflection; (c) ground settlement; and (d) bottom heave.



Plastic points zone



Plastic points zone



(a) (b) Figure 16. Comparison of plastic points at the Rochor Complex final excavation for (a) HS model; and (b) MC model.



4.2



The Lavender Station



The excavation at Lavender Station was 15.7 m deep and 23 m wide. It was supported using 1 m thick diaphragm wall at 28 m penetration depth and 6 levels of preloaded struts. The ground water level is at 1.5 m below the ground level (Halim and Wong 2005). The analysis wall deflection was compared with measured deflection profile 3, which applied to the excavation section and soil profile presented in Figure 17 (Halim and Wong 2005). The other two measured deflections were reported for another excavation section and soil profile (Lim et al. 2003) and are presented to show the similarity in the deflection profile. Half excavation width 11.5 m 0m Fill



-1.5 m



= 18 kN/m3



Preload = 190kN/m -0.5 m Preload = 390kN/m



-3.6 m



Preload = 327kN/m



Upper Marine Clay



1000 mm Diaphragm Wall



= 16 kN/m3 -13 m



-6.53 m



Preload = 260kN/m -9.4 m Preload = 233kN/m -11.31 m Preload = 220kN/m



-13.21 m



Lower Marine Clay



= 16 kN/m3



-15.66 m



-17.5 m Medium Dense Silty Course Sand



kN/m3



= 20(N = 27) (N = 27)



-22.6 m



-22.6 m Dense Silty Coarse Sand



= 20 kN/m3



(N = 83)



-26.6 m



-26.6 m



Very Dense Clayey Silt



-40 m



-3.6 m



= 20 kN/m3



(N > 100)



-40 m



Figure 17. Soil profile and cross section of excavation at the Lavender Station.



67



Underground Singapore 2011 Table 4: Parameters used in the Lavender Station excavation case study. Both Models HS Model MC Model Unit Weight cu c' E50ref = Eoedref Eurref ' E  m Eu (MPa) (kN/m3) (kPa) (deg) (kPa) (MPa) (MPa) (MPa) Fill 18 80 0.8 Eu Upper Marine Clay 25 0 - 300 cu; 400 cu Eu = 250 cu; 300 cu 16 Lower Marine Clay 35 ref 3 E50 Medium dense silty sand 38 1 37 0.67 40 Dense silty sand 42 1 73 0.75 95 20 0.8 Eu Very dense clayey silt 500 0 - 300 cu; 400 cu Eu = 250 cu; 300 cu Soil Type



Figure 18(a) shows that the HS gave a close prediction of the wall deflection profile using Eu /cu ratio of 250 and 300. Similar agreement was also achieved using the MC model at Eu /cu ratio of 300 and 400. Compared with the MC model, the HS model predicted larger settlement but lesser ground heave. The MC analysis produced more plastic points, i.e. more extensive yielding of the soil mass.



0



80



-20



100



-4



Measured final excav 2



-12 -14 -16



Measured final excav 3



Measured final excav 1



-4



Measured final excav 2



-6



Measured final excav 3



-8



Hs model. Eu/Cu = 250



-10



HS model. Eu/Cu = 300



-12



MC model, Eu/Cu = 300 MC model, Eu/Cu = 400



20



-20



-20



-22



-22



-24



-24



-26



-26



-28



-28 -30



100



0 -10 HS model. Eu/Cu = 250



-20



MC model. Eu/Cu = 300



-30



(c)



-16 -18



Distance from wall (m) 40 60 80



10



-14



-18



-30



0



-2



Depth (m)



Depth (m)



-10



100



Settlement (mm)



-2



Measured final excav 1



-8



80



0



0



-6



0



MC Model Deflection (mm) 20 40 60



0



2



4



Distance from wall (m) 6 8 10 12 14 16



18



20



50



Heave (mm)



-20



HS Model Deflection (mm) 20 40 60



40 30 20 10



HS model. Eu/Cu = 250 MC model. Eu/Cu = 300



0



(a) (b) (d) Figure 18. Comparison of results from analysis using the MC and HS models at the final excavation of Lavender Station: (a) wall deflection; (b) ground settlement; and (c) bottom heave.



4.3



The Hougang-Buangkok Cut-and-Cover Tunnel



The Hougang-Buangkok Cut-and-Cover Tunnel was a 16m-wide, 13.3m-deep excavation retained using sheetpile wall and four levels of struts. The ground water level was 1.5 m below ground level (Li 2001). Strut preloading was not modelled in the back-analysis.



68



Underground Singapore 2011 Half Excavation Width = 8 m GL 104.5 m Fill



=19 kN/m 3



Loose Silty Sand



N=4



E Organic Silt



=13 kN/m3 N = 0~1



F1 Loose Clayey Sand



=19 kN/m3 N=4



OA1 Loose Silty Sand



OA2 Very Stiff Clayey Silt



=20 kN/m N = 27



2W24, 610 X229X101 kg/m



3.95 m 4.6 m



2W24, 610X229X125 kg/m



6.4 m 7.0 m



2W24, 610X324X155 kg/m



9.45 m



2W24, 610 X229X101 kg/m



3m



6.5 m 8m



=20 kN/m3 N=5



1m 2m



11.5 m



13.3 m



3



16 m =20 kN/m3 OA3 Very Dense Silty Sand N = 80 18 m =20 kN/m3 OA4 Very Dense Silty Sand N = 120



11.5 m



Sheetpile Wall, LX32



21 m



=20 kN/m 3 OA5 Very Stiff Clayey Sand N = 150



Figure 19. Soil profile and cross-section of excavation at the Hougang-Buangkok Cut-and-Cover Tunnel Table 5: Parameters used in the Hougang-Buangkok Cut-and-Cover excavation case study. Both Models HS Model MC Model Unit Soil Type Weight cu c' E50ref = Eoedref Eurref ' m E (MPa) Eu (MPa) (kN/m3) (kPa) (deg) (kPa) (MPa) (MPa) Fill 19 33 0.1 14.4 0.555 15.6 0.8 cu 300 cu; E 13 15 Eu = 250 cu; 0 350 cu; 400 cu 300 cu F1 19 31 0.1 9.9 0.510 10.7 3 E50ref 0.525 12.1 OA1 20 31.5 0.1 11.2 OA2 20 135 0.8 cu 300 cu; OA3 20 400 Eu = 250 cu; 0 350 cu; OA4 20 600 300 cu 400 cu OA5 20 900



Figure 20(a) shows that at the final excavation level, both the HS and the MC models gave reasonable agreement with the measured deflection. The larger predicted than measured deflection at the lower wall portion could be due to underestimation of the soil stiffness. For the HS model, Eu/cu ratios of both 250 and 300 yielded good agreement with the measurement. Using the MC model with Eu /cu of 400 appeared to work well. As for ground settlement and bottom heave, the HS model seemed to generate more reasonable results.



69



Underground Singapore 2011 Final Excavation Deflection (mm) -5 0 5 10 15 20 25 30 35 40 45 50 55 60



0



Heave (mm)



0 -2 -4 -6



2



Distance from wall (m) 4 5 6



3



22 20 18 16 14 12 10 8 6



7



8



9



10



HS model. Eu/Cu = 250 HS model. Eu/Cu = 300 MC model. Eu/Cu = 300 MC model. Eu/Cu = 350 MC model. Eu/Cu = 400



(c)



-10 0



-12



Settlement (mm)



Depth (m)



-8



1



-14 -16 Measured final excav HS model. Eu/Cu = 250 HS model. Eu/Cu = 300 MC model. Eu/Cu = 300 MC model. Eu/Cu = 350 MC model. Eu/Cu = 400



-18 -20 -22



Distance from wall (m) 40 60



20



4 0 -4 -8 -12 -16 -20 -24 -28 -32



80



100



Measured HS model. Eu/Cu = 250 HS model. Eu/Cu = 300 MC model. Eu/Cu = 300 MC model. Eu/Cu = 350 MC model. Eu/Cu = 400



(a) (d) Figure 20. Comparison of results from analysis using the MC and HS models at the final excavation of Hougang-Buangkok Cut-and-Cover Tunnel (a) deflection at final excavation level; (b) ground settlement; and (c) bottom heave.



Figure 21 shows the wall deflection at the different stages of excavation. The differences in wall deflection generated by both models were not significant and comparisons with measured deflection for both models were reasonable. Figure 20(c) shows the comparison of strut force. The HS model gave slightly better agreement with the measured strut forces. Hardening Soil Model. Eu/cu = 250 Deflection (mm) -5 0 5 10 15 20 25 30 35 40 45 50 55 60 0



Measured 1st excav Measured 2nd excav Measured 3rd excav Measured 4th excav Measured final excav Analysis 1st excav Analysis 2nd excav Analysis 3rd excav Analysis 4th excav Analysis final excav



Depth (m)



-4 -6 -8 -10 -12 -14



-16 -18 -20 -22



0



Measured 1st excav Measured 2nd excav Measured 3rd excav Measured 4th excav Measured final excav Analysis 1st excav



-2



-4 -6



Depth (m)



-2



-5 0



Mohr-Coulomb Model. Eu/cu = 400 Deflection (mm) 5 10 15 20 25 30 35 40 45 50 55 60



-8



-10 -12 -16



Analysis 2nd excav Analysis 3rd excav



-18



Analysis 4th excav



-20



Analysis final excav



-14



-22



(a) 0



50



100



150



Depth (m)



0 -2 -4 -6 -8 -10 -12



(b) Strut Force (kPa)



Measured Strut Force



HS model. Eu/Cu = 250



MC model. Eu/Cu = 300



(c)



Figure 21. Comparison of wall deflections from analyses using MC and HS models (a) & (b) deflection; and (c) strut force.



70



Underground Singapore 2011 5



SHORTCOMINGS OF THE HARDENING SOIL



The HS model is a great improvement over the MC model. However, it has its own set of short comings. Some of them are listed below. a. b. c. d. e. f.



Over-estimation of undrained shear strength, cu of soft clay Under-estimation of pore pressure of soft clay Over-estimation of cu/p ratio for normally consolidated clay Under-estimation of cu/p ratio for over-consolidated clay Over-estimation of undrained shear strength cu under simple shear and triaxial extension condition For stress paths below yield surface, the HS soil becomes elastic and has all the shortcomings associated with an elastic soil.



Figure 22 shows the stress paths of a CU test. The MC model greatly over-predictes the cu. The HS model fares a little better. The over-prediction by the HS model is due to the location of the elliptical cap adopted by the model as shown in Figure 23. The Modified Cam Clay also uses an elliptical yield surface but predicts a much lower cu than the HS model. This problem could be overcome by using a lower friction angle or by setting c = cu and  =0. This method works well for excavation analysis in most cases. However, it would not be appropriate for problems involving consolidation analysis and changes in strength with time. Figure 24(a) shows that the HS model over-predicts the cu/p ratio for normally consolidated clay and under-predicts the ratio for over-consolidated clay. This issue may not be crucial for excavation analysis. However, for problems with complex stress paths involving unloading-reloading and changes in effective stress, it may be prudent to scrutinise the results carefully. The HS model also over-predicts cu tested under simple shear or triaxial extension conditions as compared to the cu from real soils as shown in Figure 24(b).



q (kPa)



It is interesting to note that from tests on real soil and simulations on HS soil, the moduli obtained from the simple shear, triaxial extension and triaxial compression tests are different. Test results also show that the strength and modulus obtained under plane strain condition are also different from those obtained from triaxial test. Therefore, it should be reminded that the parameters obtained from the conventional UU, CU, CD and consolidation tests can only be used as a crude approximation.



qD



Mohr-Coulomb Soil Hardening Soil



Real Soil



u at qD = UAB Effective Stress



u at qD = UAC



u at qD = UAD



D



C



B



A



Total Stress



p or p’ (kPa)



Figure 22. Stress paths of a CU test.



Figure 23. Effect of yield surface on cu.



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Underground Singapore 2011



0.6 0.5



cu/p'



0.4



cu/p



0.3 f'’ == 20 20o f'’ == 25 25o 30o f'’==30



0.2 0.1



0.8 0.22 OCR OCR^0.8 0.22



0 0



0.5



1



1.5



2



2.5



3



3.5



0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0



Drammen Plastic clay Vaterland Clay Studenterlunden Drammer Lean Clay HS Model φ' = 25°



Compression



OCR



(a)



Simple Shear



Extension



(b)



Figure 24. HS prediction of (a) cu/p ratio and (b) cu under different test conditions.



6 CONCLUSIONS AND RECOMMENDATIONS The HS model overcomes some of the shortcomings of the MC model. The three case studies show that the HS model can produce reasonable wall deflection and ground movement that compared well with measured data. Highlights from the back-analyses are summarised below. a. For the HS model, the application of Eu/cu ratio of 250 to the clayey soils seemed to work well for these three case studies. b. To achieve a similar agreement with the measured deflection using the MC model, it would be necessary to vary the Eu/cu ratio, as in the case of the back-analysis, to 300 or 400. c. The HS model produced a more realistic ground settlement profile. The consideration of nonlinear and inelastic stiffness in the HS model gave a better prediction of the settlement near the excavation, as shown in the Hougang-Buangkok cut-and-cover tunnel case study. d. The HS model produced a smaller toe movement than the MC model. e. The HS model predicted smaller bottom heave than the MC model. f. The HS model generated lesser plastic points because the model is able to simulate the softer soil behaviour as the soil approaches failure. The MC model generated more plastic points which gave a false impression on the extent of soil yielding.



REFERENCES Brinkgreve, R.B.J et al. 2004. Plaxis Version 8, Material Model Manual. Kulwawy, F. H. & Mayne, P. W. 1990. Manual on estimating soil properties for foundation design. Report EL6800, Electric Power Research Institute, Palp Alto, CA. Lim, K. W. et al. 2003. Comparison of results of excavation analysis using Wallap, Sage Crisp and Excav97. Proceedings of Conference on Underground Singapore 2003, Singapore, 83-94. Halim, D. & Wong K.S. 2005. Evaluation of Modified Cam Clay Parameters for Deep Excavation Analysis, Proceedings of Conference on Underground Singapore 2005, Singapore, 188-200. Li, W. 2001. Braced Excavation in Old Alluvium in Singapore, PhD Thesis, School of Civil and Environmental Engineering, Nanyang Technological University, Singapore. Wong, K.S. & Duncan, J.M. 1974. Hyperbolic stress-strain parameters for nonlinear finite element analyses of stresses and movements in soil masses. Geotechnical Engineering Report, Department of Civil Engineering, University of California, Berkeley. Wong, K.S. 2011. Things you should know about the Mohr-Coulomb Model. Seminar on Infrastructure in Soft Ground – Challenges and Solutions, Singapore.



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