Application of FEM Analysis to Braced Excavation

TSINGHUA SCIENCE AND TECHNOLOGYISSN 1007-0214 07/67 pp40-45Volume 13, Number S1, October 2008Application of FEM Analysis to Braced ExcavationLI Mingfei (李明飞)", Atsushi Nakamura, CAI Fei (蔡飞)y， Keizo UgaitFORUM8 Co., Ltd, 2-1-1, Nakameguro GT Tower 15F, Kamimeguro, Meguro-ku, Tokyo, 153-0051, Japan;↑Department of Civil and Environmental Engineering, Gunma University, Kiryu, Gunma 376 8515, JapanAbstract: It is becoming possible to do detailed numerical analyses for the various mechanical behavior ofbraced excavation by researching and developing the numerical analysis technique such as the finite ele-ment method (FEM). However, the mechanical behavior of braced excavation has not been carified fullyboth in theory and in experience. Therefore, improving the prediction accuracy during the prior design is veryimportant for making the observational method of braced excavation more effective. In this paper, FEManalyses were perfomed for a model of braced excavation by using Geotechnical Finite Element Elasto-plastic Analysis Sofware, GeoFEAS (2D). As the constitutive law of ground, MC-DP model, and Dun-can-Chang model were applied. The results were compared and discussed with that of a site measurement,and the effects of the constitutive law of ground on the analyzed result were verified. For the diference be-tween the results, the reason was investigated by the analyses adjusting the elastic modulus of ground, andthe appropriate application of the constitutive law was researched.Key words: numerical analysis; retaining wall; fnite element method (FEM); constutive lawIntroductionservational method of braced excavation more effec-tive. In this research, in order to improve the predictionIn recent years, it is becoming possible to do detailedaccuracy during the prior design, FEM analyses werenumerical analyses for the various mechanical behav-.. performed and the results were compared and dis-ior of braced excavation by researching and developingcussed with the result of a site measurement.the numerical analysis technique such as the finiteelement method (FEM). The observational method1 Outline of Braced Excavation Caseconnecting mechanical behavior measured in the proc-The plan view and cross-sectional viewll are shown iness of construction is becoming an effective design andFig. 1. The horizontal range of excavation is 66mxconstruction technique.51 m and the depth of the final excavation is 8 m.However, it must be paid attentions when applyingthe observational method that the mechanical behavior2 Outline of FEM Analysisof braced excavation has not been clarified fully bothin theory and in experience and the prediction accuracyFor the A-A' section shown in Fig. la, the simulationduring the prior design is not quite enough.analyses were performed by plane strain FEM utilizingTherefore, improving the prediction accuracy duringGeotechnical Finite element Elastoplastic Analysisthe prior design is very important for making theSoftware GeoFFAS (?n)(21 The finite element meshesare sh中国煤化工y, the half of con-Received: 2008-05-30figura|YHCNMHGthewidthandback** To whom corespondence should be adressed.range were assumed to be 30 m and 117 m, with theE-mail: m-ri@forum8 cojpretaining wall and the stnut modeled by beam elements.LI Mingfei (李明飞) et al: Application OfFEMAralysis t0 Braced Excavation41iLFinst-stage beam (GL 0.5 m)Firsi-suge CXGvatii (GL-I.5 m)I Scond-sage excvaiono (GL-S.0m)十Tird-stage exeavtion (GL-8.0m)66m(a) Plan view(b) Coss-sectional viewFig. 1 Configurations of braced excavation33m117mRetaining wa3B Layer(GL0- 3.0年ESecond-stage excavation ;EAcl Layer (GL-3.0~ -5.0哇Third-stge xavatioArc2-1 Layer(GL-5.0~ 13.40- Ac2-2 Layer (GL-13.4-- 19.9 )As Layer(GL -25.0-- 26.0 m)= Ac2-3 Layer (GL-19.9~ -25.0时- De Layer(GL -26.0~ -30.0m)Fig. 2 Finite element meshesAs boundary conditions, the lateral surface wasmaterials and the failure is induced primarily by shearfixed in the horizontal direction and was treated asdeformation.roller contact in the vertical direction. The bottom sur-In this paper, MC-DP model was first applied andface was fixed in both horizontal and vertical direction.he material parameters are listed in Table 2. TheThe analysis was divided into five processes as listedanalyses with dilatancy angles of ψ=φ and ψ=0°in Table 1. The finish time of each process is alsowere performed. Then, in order to make the analyzedlisted in Table 1. The MC-DP model and Dun-results approach to the measured results in each exca-can-Chang model were applied. For all the cases, thevation stage, the elastic moduli of ground were ad-total stress analyses were performed.justed and the analyses were performed.Table 1 Analysis process2.2 Duncan-Chang model_No.Analysis processFinish time_In Duncan-Chang Model), the relationship betweenFirst-stage excavation12th daythe principal stress and tangential elastic modulus isPreloading first stage strut13th daydefined as Eqs. (1) and (2), in which the stress strainSecond-stage excavation35th dayrelationship modeled by hyperbola and the effect ofPreloading second-stage strut36th dayconfining pressure on the change of rigidity areThird-stagc excavationsSth day__considered.2.1 MC-DP modelE,=KP(1](1)For MC-DP model, Mohr-Coulomb equation is used to中国煤化工,)](2)yield criterion and Drucker-Prager equation is used toMHC NMH Gnφplastic potential. Soil is considered as frictionalwhere E is the initial elastic modulus; E, is the42Tsinghua Science ard Technology, October 2008, 13(S1): 40-45tangential elastic modulus; p is the atmospheric pres-principal stresses; K and n are the experimentallysure; c is the cohesion coefficient; φ is the frictiondetermined constants; and R is the failure ratio. Theangle; σ and σ，are the maximum and minimummaterial parameters are listed in Table 3.Table 2 Material parameters of ground (MC-DP model)Unit weight, Poisson's ratio, Elastic modulus,Cohesion,Friction angle,LayersDepth (m)y (kN/m)E (MPa)c (kPa)φ(°)Filling soil0.0-3.0 .15.00.3316.825.0Silt (Acl)3.0-5.015.70.45.86).9Silt (Ac2-1)50-13.414.57.732Silt (Ac2-2)13.4-19.914.011.149Silt (Ac2-3)19.9-25.014.715.412.2Fine sand (As)25.0-26.056.0 .35.0Mud stone (Dc)26.0-30.019.5388.5185Note: Two circunstances for the dilatancy angles are considered. (1) v=φ;(2) v=0".Table 3 Material parameters of ground (Duncan-Chang model)Unit weight,Poisson's ratio,KRr n_卫 (kNm2)0.0-3.07520 1.0 0.5Silt (Ac1)934 1.0 0.5169.9211 1.0 1.00120 1.0 1.0 .199.8290 1.0 1.02Fine sand (As) 25.0-26.018.017161.0 0.5Mud stone (Dc) 26.0-30.010646 1.0 0.535_03 Results and Discussionthird-stage excavation.3.1.2 Duncan-Chang model3.1 Displacement of retaining wallFigure4 shows the displacements of retaining wallwith Duncan-Chang model for each excavation stage.3.1.1 MC-DP modelFigure3 shows the displacements of retaining wallThe deformation shapes of all excavation stages arewith MC-DP model for each excavation stage. For theconsistent in general and the analyzed values agreeresults before adjusting the elastic modulus of ground,with the measured values. The differences between thethe deformation shapes of all excavation stages aremeasured and analyzed maximum displacements areconsistent in general. The analyzed results with-1 mm, -3 mm, and -8 mm, respectively, for the threeψ=φ and ψ=0 are almost identical. The differenceexcavation stages and the analyzed values are smallerbetween the measured and analyzed maximum dis-than the measured values for each excavation stage.For this case, it can be confrmed that Duncan-Changeplacements is 11 mm for the first-stage excavation,model is appropriate.15 mm for the second-stage excavation, and 5 mm forthe third-stage excavation. For each excavation stage,3.2 Variation of displacement of retaining wallthe analyzed values are larger than the measured values.For the results after adjusting the elastic modulus of3.2.1 MC-DP modelground, the ratio of the adjusted elastic modulus to theFor中国煤化iand measured dis-original elastic modulus for the layer with maximumplacertEpoint with 5 m anddisplacement is 1.84 for the first-stage excavation, 1.2610 mHCNMHGom)areshowninfor the second-stage excavation, and 1.01 for theFig. 5. It can be seen that there is a difference betweenLI Mingfei (李明飞) et al: Application of FEM Analysis to Braced Excavation4:st-s$t~5-10}-10-E-15宜-15-8-20营-20f含-20f-25)-25--30--30|0 2040 60 800 20406080-3200204060 80Displacement (mm)(a) First-stage excavation(b) Second-stage excavation(c) Third-stage excavation- -o-MeasuredO Analyzed ψ= φ (Before adjusting) 0 Analyzed y=0 (Before adjusting)▲Analyzed y=中(After adjusting)● Analyzed V=0 (After adjusting)Fig.3 Displacement of retaining wall (MC-DP model)0r的官-15-官-1s名-20-名-20吕-20--25- -30-3202040 6-3-2025080-320020406080(C) Third-stage excavation- 0 Measured. - - AnalyzedFig 4 Displacement of retaining wall Duncan-Chang model)the measured and analyzed values for both before andvalue with GL-5.0 m for the third-stage excavation isafter adjusting the elastic modulus of ground. The ana-large relatively.lyzed results with ψ=φ and ψ=0 are almost iden-tical. As the results of the displacement of retaining3.3 Axial force of strutwall, the analyzed values before the adjustment are3.3.1 MC-DP modelgreatly different from the measured values. The ana-The axial forces of first-stage and second-stage strutlyzed values after the adjustment became close to theanalyzed by MC-DP model are shown in Fig. 7. Formeasured values, but the value with GL -5.0 m for theboth two figures, the tendencies of variation of thethird-stage excavation is large relatively.analyzed and mpasured axial fonrces are consistent in3.2.2 Duncan-Chang modelgeneral中国煤化工e with the meas.For Duncan-Chang model, the results are shown inured v:YHCN MH Gwith ψ=φ andFig. 6. There are differences between the calculatedψ=0 are almost identical.and measured values in the range of small errors. The44Tsinghua Science and Technology, October 2008, 13(S1): 40-450p70r上。50}a10-0-30-量00gga营209020 3040 50 6010Time (day)(a) GL-5.0 m(b) GL-10.0m- -o- Measured0 Analyzed=φ (Before adjusting) 。Analyzed y=0 (Before adjusting)▲Analyzed v=φ (Afer adjusting)● Analyzed y=0 (After adjusting)Fig.5 Variations of the retaining wall displacement (MC-DP model)70p50-of400}0+20}10bo- d01020305060.o(a)GL-5.0m(b) GL-10.0 mFig.6 Variations of the retaining wall displacement Duncan-Chang model)The analyzed values before and after adjusting theadjusting the elastic modulus of ground are consistentelastic modulus of ground are consistent in general.in general.Differing from this result, the displacement of retaining3.3.2 Duncan-Chang modelwall creates a large difference when adjusting the elas-The axial forces of first-stage and second-stage struttic modulus of ground as shown in Fig.5. It can beanalyzed by Duncan-Chang model are shown in Fig. 8.considered that the axial force is created when the stnutFor both two figures, the tendencies of the variation ofis preloaded and varies with the variation of displace-the analyzed and measured axial forces are consistentment of retaining wall. As shown in Fig. 7, the ana-general and the analyzed values agree with thelyzed axial forces induced by preloading before andmeasured values.after adjusting the elastic modulus of ground are al-most identical. It can be found from Fig. 5 that the dis-4 Conclusionsplacements of retaining wall before and after adjustingIn thtich MC-DP modelthe elastic modulus of ground greatly differ, but theandI中国煤化工plied, reciveye,tendencies of variations are consistent in general. ThatwereYHC N M H Gere compared andis, the amnounts of variation of displacements are close.Therefore, the analyzed axial forces before and afterdiscussed with that of a site measurement. The mainU Mingfei (李明飞) et al: Application of FEM Analysis to Braced Excavation4:2.0p2.0rs5-.5-g 1.0f1.0f< 0.s- od对化).5|▲10230405602050 60Time (day)(a) Fiststage strut(b) Second-stage strut- 0- Measured△Analyzed y=φ (Before adjusting) 0 Analyzed v=0 (Before adjusting)▲Analyzed y=φ (Afer adjusting)● Analyzed y=0 (After adjusting)Fig. 7 Axial force of strut MC-DP model)1.55g1.040.5 '0.5150(a) First-stage strut(b) Second stage strut- 0 Measured- AnalyzedFig.8 Axial force of strut (Duncan-Chang model)conclusions are as follows.excavation by FEM analysis including the examination(1) For MC-DP model, the analyzed displacementsfor the effect on the surrounding ground will be con-of the retaining wall can be approach to the measuredducted.displacements by adjusting the elastic modulus ofReferencesground. .(2) In the analyses, for MC-DP model, adjusting the[1] Sanematsu T, Isobe T. Behavior of braced excavations andelastic modulus of ground has a lttle effect on the axialsimulation analysis of eExcavation in soft ground. In: An-force of strut.nual Report, KAJIMA Technical Research Intitute. 1998(3) For Duncan-Chang model, the analyzed values46. (in Japanese)agree with the measured values. The possibility of the[2] UC-I Geotechnical Finite element Elastoplastic Analysisapplication of Duncan-Chang model that can considerSoft~中国煤化rumcjplngithe nonlinearity was confirmed.In future, various case studies will be conducted and[3] DunTYHC N M H Galysis of stess andthe determination method of materials parameters willstrain in soils. Journal of the Soil Mech. and Found. Div,be discussed. On this basis, the design of bracedASCE, 1970, 96(SM5): 1629-1653.