Research on Application of FEM Analysis to Braced Excavation
Mingfei Li1, Atsushi Nakamura1, Fei Cai2 and Keizo Ugai2
1FORUM8 Co., Ltd., 2-1-1, Nakameguro GT Tower 15F, Kamimeguro, Meguro-ku Tokyo, Japan
2 Department of Civil and Environmental Engineering, Gunma University, Kiryu, Gunma, 376-8515, Japan
Abstract: 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 element
method (FEM). However, the mechanical behavior of braced excavation has not been clarified fully both intheory and in experience. Therefore, improving the prediction accuracy during the prior design is very
important for making the observational method of braced excavation more effective. In this paper, FEM
analyses were performed for a model of braced excavation by using Geotechnical Finite element Elastoplastic
Analysis Software GeoFEAS(2D). As the constitutive law of ground, MC-DP model and Duncan-Chang model
were applied. The results were compared and discussed with that of a site measurement, and the effects of theconstitutive law of ground on the analyzed result were verified. For the difference between the results, thereason was investigated by the analyses adjusting the elastic modulus of ground, and the appropriate
application of the constitutive law was researched.
Keywords: numerical analysis，retaining wall，FEM，constitutive law

1 Introduction
In recent years, It is becoming possible to do detailed
numerical analyses for the various mechanical behaviorof braced excavation by researching and developing
the numerical analysis technique such as the finite
element method (FEM). The observational method
connecting mechanical behavior measured in theprocess of construction is becoming an effective designand construction technique.
However, it must be paid attentions when applying
the observational method that the mechanical behaviorof braced excavation has not been clarified fully bothin theory and in experience and the prediction accuracy
during the prior design is not quite enough.
Therefore, improving the prediction accuracy during
the prior design is very important for making theobservational method of braced excavation moreeffective. In this research, in order to improve theprediction accuracy during the prior design, FEM
analyses were performed and the results werecompared and discussed with the result of a sitemeasurement.

2 Outline of Braced excavation CaseThe plan view and cross-sectional view[1] are shown inFigure 1. The horizontal range of excavation is66×51(m) and the depth of final excavation is 8m.

3 Outline of FEM Analysis
For the A-A' section shown in Figure 1 (a), thesimulation analyses were performed by plane strain
FEM
utilizing
GeotechnicalFinite
element[2]
Elastoplastic Analysis Software GeoFEAS(2D) . The
finite element meshes are shown in Figure 2. Due tosymmetry, the half of configuration section wasmodeled and the width and back range were assumed
to 30m and 117m respectively. The retaining wall andthe strut were modeled by beam elements.
As boundary conditions, the lateral surface was fixedin the horizontal direction and was treated as roller
contact in the vertical direction. The bottom surface
was fixed in both horizontal and vertical direction. The
analysis was divided into five processes as listed inTable 1. The finish time of each process is also listed
in Table 1. The MC-DP model and Duncan-Changmodel were applied. For all the cases, the total stressanalyses were performed.
First-stage beam(GL-0.5m)

GLFirst-stage excavation (GL-1.5m)
Second-stage beam(GL-4.0m)

A'

Third-stage excavation (GL-8.0m)

1m

66m

13.5m

A51m

Second-stage excavation (GL-5.0m)(a) Plan view(b) Cross-sectional viewFig. 1 Configurations of braced excavation

33m

Second-stage excavation
Third-stage excavation

B Layer(GL0 -3.0m)

Ac1 Layer(GL-3.0 -5.0m)
Ac2-1 Layer(GL-5.0 -13.4m)

Ac2-2 Layer(GL-13.4 -19.9m)

As Layer(GL-25.0 -26.0m)

30m

8m

First-stage excavation

117m
Retaining wall

Ac2-3 Layer(GL-19.9 -25.0m)
Dc Layer(GL-26.0 -30.0m)

150m

Fig. 2 Finite element meshes

Table 1 Analysis processNo.

Analysis process

Finish time

1First-stage excavation

2

Preloading first-stage strut

3

Second-stage excavation

4

Preloading second-stage strut

5

Third-stage excavation

12th day13th day35th day36th day55th day

3.1 MC-DP model
For MC-DP model, Mohr-Coulomb equation is used toyield criterion and Drucker-Prager equation is used toplastic potential. Soil is considered as frictional
materials and the failure is induced primarily by shear
deformation.
In this paper, MC-DP model was first applied andthe material parameters are given in Table 2. The
analyses with dilatancy angle of ψ = φ and ψ = 0
were performed. Then, in order to make the analyzed
results approach to the measured results in eachexcavation stage, the elastic modulus of ground wereadjusted and the analyses were performed.
3.2 Duncan-Chang model
In Duncan-Chang Model[3], the relationship between
principal stress and tangential elastic modulus isdefined as Equation 1 and 2, in which the stress-strain
relationship modeled by hyperbola and the effect ofconfining pressure on the change of rigidity areconsidered.

σEi = K ⋅ Pa ⎛⎜ 3 ⎞⎟⎝ Pa ⎠n⎧ R f (1 − sin φ )(σ 1 − σ 3 ) ⎫Et = ⎨1 −⋅ Ei
2c ⋅ cos φ + 2σ 3 sin φ ⎬⎭⎩

(1)
(2)

where, E i is initial elastic modulus; Et is tangential
elastic modulus; Pa is atmospheric pressure; c iscohesion coefficient; φ is friction angle; σ 1 andσ 3 are maximum and minimum principal stress; Kand n are experimentally determined constants;

R f is failure ratio. The material parameters are given

in Table 3.

Table 2 Material parameters of ground(MC-DP model)
LayersDepthPoisson's
Unit weightratio
ν(m)γ (kN/m3)

Elasticmodulus
E (MPa)Cohesionc (kPa)Friction
angle
φ (°)

16.8
3.8
7.7
11.1
15.4
56.0
388.5

0
1632
49
720
185

25
9.90
9.8
1.2
350K

RfnCohesionc (kPa)Friction angle
φ (°)

7520
934
211120290
1716
10646

1.0
1.0
1.01.01.0
1.0
1.0

0.5
0.5
1.0
1.0
1.0
0.5
0.5

0
1632
49
72
0
185

25
9.90
9.8
1.2
350

Filling soilSilt(Ac1)
Silt(Ac2-1)
Silt(Ac2-2)
Silt(Ac2-3)
Fine sand(As)Mud stone(Dc)

0.0～3.0
3.0～5.050～13.4
13.4～19.9
19.9～25.0
25.0～26.0
26.0～30.0

15.0
15.7
14.5
14.0
14.7
18.0
19.5

0.33
0.45
0.45
0.45
0.45
0.33
0.45

Table 3 Material parameters of ground(Duncan-Chang model)
Layers
Depth
Unit weight Poisson's ratioν(m)γ (kN/m3)
Filling soilSilt(Ac1)
Silt(Ac2-1)
Silt(Ac2-2)
Silt(Ac2-3)
Fine sand(As)Mud stone(Dc)

0.0～3.0
3.0～5.050～13.4
13.4～19.9
19.9～25.0
25.0～26.0
26.0～30.0

15.0
15.7
14.5
14.0
14.7
18.0
19.5

0.33
0.45
0.45
0.45
0.45
0.33
0.45

4. Analysis Result and Discussion
4.1 Displacement of retaining wall(1)MC-DP model
Figure 3 shows the displacements of retaining wallwith MC-DP model for each excavation stage. For theresults before adjusting the elastic modulus of ground,the deformation shapes of all excavation stages areconsistent in general. The analyzed results with
ψ = φ and ψ = 0 are almost identical. The
difference between the measured and analyzed
maximum displacements is 11mm for the first-stage
excavation, 15mm for the second-stage excavation and5mm for the third-stage excavation. For eachexcavation stage, the analyzed values are greater thanmeasured value. For the results after adjusting theelastic modulus of ground, the ratio of the adjusted
elastic modulus to the original elastic modulus for thelayer with maximum displacement is 1.84 for thefirst-stage excavation, 1.26 for the second-stageexcavation and 1.01 for the third-stage excavation.
(2)Duncan-Chang model
Figure 4 shows the displacements of retaining wallwith Duncan-Chang model for each excavation stage.
The deformation shapes of all excavation stages areDilatancy angle ψ(°)ψ =φ

ψ =0259.90
9.8
1.2
3500000000

consistent in general and the analyzed values agreewith the measured values. The differences between themeasured and analyzed maximum displacement are-1mm, -3mm and -8mm respectively for the three
excavation stages and the analyzed values are smaller
than the measured value for each excavation stage. For
this case, it can be said that Duncan-Change model isappropriate.
4.2 Variation of displacement of retaining wall(1)MC-DP model
For MC-DP model, the analyzed and measured
displacements of retaining wall at the point with 5m
and 10m depths (GL-5.0m and GL-10.0m) are shownin Figure 5. It can be seen that there is a difference
between the measured and analyzed value for both
before and after adjusting the elastic modulus ofground. The analyzed results with ψ = φand
ψ = 0 are almost identical. As the results ofdisplacement of retaining wall, the analyzed values
before the adjustment have a large difference from themeasured values. The analyzed values after theadjustment became close to the measured values, but
the value with GL-5.0m for the third-stage excavationis large relatively.
(2)Duncan-Chang model
For Duncan-Chang model, the results are shown inFigure 6. There are differences between the calculated
and measured value but they are in range of small error.

-20020 40 60 80-2000-2020 40 60 80-5-10-10-10-20

Depth (m)-5-15-15-2020 40 60 80-15-20-25-25-25-30-30-30-3500-5Depth (m)Depth (m)0The value with GL-5.0m for the third-stage excavationis large relatively.

-35-35
Displacement (mm)Displacement (mm)Displacement (mm)(a)First-stage excavation(b)Second-stage excavation(c)Third-stage excavation-20020406080100
Measured
0-5-10-15Analyzed
ψ=φ (Before adjusting)-20-25-30-35
Analyzed ψ=φ (After adjusting)Analyzed ψ=0 (Before adjusting)Analyzed ψ=0 (After adjusting)Fig. 3 Displacement of retaining wall (MC-DP model)-20

020 40 60 80-200020 40 60 80-20-5-10-10-10-20

Depth (m)-5-15-15-20-20-25-25-30-30-30-35

20 40 60 80-15-25-3500-5Depth (m)Depth (m)0-35

Displacement (mm)Displacement (mm)Displacement (mm)(a)First-stage excavation(b)Second-stage excavation(c)Third-stage excavation-20020406080Measured

AnalyzedFig. 4 Displacement of retaining wall (Duncan-Chang model)

4.3 Axial force of strut(1)MC-DP model
The axial forces of first-stage and second-stage strut
analyzed by MC-DP model are shown in Figure 7. For
both two figures, the tendencies of variation of theanalyzed and measured axial forces are consistent ingeneral and the analyzed values agree with themeasured value. The analyzed results with ψ = φand ψ = 0 are almost identical.
The analyzed values before and after adjusting theelastic modulus of ground are consistent in general.
Differing from this result, the displacement of retaining
wall creates a large difference when adjusting theelastic modulus of ground as shown in Figure 5. It canbe considered that the axial force is created when thestrut is preloaded and varies with the variation ofdisplacement of retaining wall. As shown in Figure 7,

almost identical. It can be found from Figure 5 that thedisplacements of retaining wall before and after

70

70

60

60

Displacement(mm)Displacement (mm)the analyzed axial forces induced by preloading beforeand after adjusting the elastic modulus of ground are

504030204030
201010050

102030405060

100Time (day)20304050

605060Time (day)(a) GL-5.0m(b) GL-10.0m-20020406080100
Measured
0-5-10-15
Analyzed
ψ=φ (Before adjusting)-20-25-30-35
Analyzed ψ=φ (After adjusting)Analyzed ψ=0 (Before adjusting)Analyzed ψ=0 (After adjusting)70706060

Displacement (mm)Displacement (mm)Fig. 5 Variation of displacement of retaining wall (MC-DP model)

504030204030
20
1010050

10203040
Time (day)5060

10020(a) GL-5.0m

3040Time (day)(b) GL-10.0m-20020406080Measured

Analyzed

Fig. 6 Variation of displacement of retaining wall

adjusting the elastic modulus of ground have a large
difference, but the tendencies of variation are
consistent in general. That is, the amounts of variationof displacements are close. Therefore, the analyzed
axial forces before and after adjusting the elastic
modulus of ground are consistent in general.
(2)Duncan-Chang model
The axial forces of first-stage and second-stage strut
analyzed by Duncan-Chang model are shown in Figure
8. For both two figures, the tendencies of variation of
the analyzed and measured axial forces are consistent(Duncan-Chang model)

in general and the analyzed values agree with themeasured values.

5. Conclusions
In this paper, FEM analyses in which MC-DP modeland Duncan-Chang model were applied respectively
were performed and the results were compared anddiscussed with that of a site measurement. The main
conclusions are as follows.
1) For MC-DP model, the analyzed displacements ofretaining wall can be approach to the measured that byelastic modulus of ground has a little effect on the axialforce of strut.

2000

2000

1500

1500

Axial force (kN)

Axial force (kN)adjusting the elastic modulus of ground.
2) In the analyses, for MC-DP model, adjusting the1000
500
01020304050

1000
500
01060

2030Time (day)4050605060

Time (day)(a) first-stage strut(b) second-stage strut-20020406080100
Measured
0-5-10-15
Analyzed
ψ=φ (Before adjusting)-20-25-30-35
Analyzed ψ=φ (After adjusting)Analyzed ψ=0 (Before adjusting)Analyzed ψ=0 (After adjusting)

2000

2000

1500

1500

Axial force (kN)

Axial force (kN)

Fig. 7 Axial force of strut (MC-DP model)

1000
500
0102030405060

1000
500
010203040Time (day)Time (day)(a) First-stage strut-20020406080Measured(b) Second-stage strut

Analyzed

Fig. 8 Axial force of strut (Duncan-Chang model)

3) For Duncan-Chang model, the analyzed values
agree with the measured values. The possibility of theapplication of Duncan-Chang model that can consider
the nonlinearity was confirmed.
In future, various case studies will be conducted andthe determination method of materials parameters will
be discussed. On the basis of this, the design of braced
excavation by FEM analysis including the examination
for the effect on the surrounding ground will be
conducted.

References[1] Toshiaki Sanematsu, Takahisa Isobe, et al. Behavior ofBraced excavations and Simulation Analysis of Excavation
in Soft Ground, Annual Report, KAJIMA TechnicalResearch Institute, Vol.46，1998. (In Japanese)[2] UC-1 Geotechnical Finite element Elastoplastic Analysis
Software (GeoFEAS)2D(http://www.forum8.co.jp/english/uc-1/geo2d-e.htm)[3] J.M. Duncan and C.Y. Chang, Non-linear analysis of stressand strain in soils, Journal of the Soil Mech. and Found. Div.,ASCE, Vol.96, No.SM5, pp.1629-1653, 1970