Research Article Characteristics of Braced Excavation ...downloads.hindawi.com/journals/mpe/2013/452534.pdf · Research Article Characteristics of Braced Excavation under Asymmetrical

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 452534 12 pageshttpdxdoiorg1011552013452534

Research ArticleCharacteristics of Braced Excavation under Asymmetrical Loads

Changjie Xu Yuanlei Xu Honglei Sun and Qizhi Chen

Research Center of Coastal and Urban Geotechnical Engineering College of Civil Engineering and Architecture Zhejiang UniversityHangzhou 310058 China

Correspondence should be addressed to Honglei Sun saitholygmailcom

Received 16 May 2013 Accepted 29 May 2013

Academic Editor Xu Zhang

Copyright copy 2013 Changjie Xu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Numerous excavation practices have shown that large discrepancies exist between field monitoring data and calculated resultswhen the conventional symmetry-plane method (with half-width) is used to design the retaining structure under asymmetricalloads To examine the characteristics of a retaining structure under asymmetrical loads we use the finite element method (FEM)to simulate the excavation process under four different groups of asymmetrical loads and create an integrated model to tacklethis problem The effects of strut stiffness and wall length are also investigated The results of numerical analysis clearly implythat the deformation and bending moment of diaphragm walls are distinct on different sides indicating the need for differentrebar arrangements when the excavation is subjected to asymmetrical loads This study provides a practical approach to designingexcavations under asymmetrical loads We analyze and compare the monitoring and calculation data at different excavation stagesand find some general trends Several guidelines on excavation design under asymmetrical loads are drawn

1 Introduction

The development of urban construction and the exploitationof underground space have intensified the complexity ofexcavation projects such as deep excavation different depthexcavation and excavation under asymmetric external loadsMost deep excavations in coastal areas are supported by aretaining strutting system which has been extensively inves-tigated Li et al [1] simplified the excavation as a plane issueusing displacement iteration to analyze the internal force anddeformation of the retaining structure Chen et al [2] andLiu and Zeng [3] used FLAC3D to simulate the excavationprocess and drew useful conclusions on the service abilityof the retaining structure Gharti et al [4] developed anumerical procedure based on the spectral element methodemploying the linear elastic constitutivemodel for excavationsimulations A drawback of these studies whether usingthe conventional design methods or the FEM approachesis that they all neglected the integrated work of the wholeretaining strutting system Moreover the excavation designis based on beams on elastic foundation method and aconventionally simplified plane-strain excavationmodel withone side assuming equal loads on both sides of the excavatedpit that is 119875

1= 1198752 as schematically shown in Figure 1

where 1198751and 119875

2are two design loads acting on different

sides of the ground surfaceWidely used in practice althoughthis method (ie symmetrical semiplane method) is simplebut satisfies most excavation designs When 119875

1= 1198752 the axial

forces in the supporting struts become different that is1198651= 1198652 and it is contradictory to the assumption of symmetry

condition Designing excavations by conventional methodsresults in two extreme consequences (a) reduced safetyfactor when the pit side with smaller loads is selected or (b)conservative and wasteful results when the larger load sideis selected The latter is satisfied only from the perspectiveof integral stability but this method inaccurately predicts thedeflection of retaining structures

Given the diversity of geological conditions in the soilstrata the complication of excavation surroundings and theuncertainty of construction factors asymmetrical loads ontwo sides of an excavation site have become increasinglycommon Asymmetrical loads especially those of sites indowntown areas are easily brought about by buildings andtraffic loads nearby These loads have created challengesto the conventional symmetry-plane design method whichcannot consider the integral work of foundation pits underasymmetrical loads Lv et al [5] introduced the geotechnicaland tunnel analysis system (GTS) program to analyze the

2 Mathematical Problems in Engineering

Strut

Retainingstructure

Soil

Waterpressure

Waterpressure

pressure Soilpressure

P1

F1 F2

P1 P2P2

+=

Figure 1 Schematic diagram for the calculation of conventional design method

behavior of deep foundation pits under asymmetrical loadwhich was a part of Suzhou Metro Line 1 and drew con-clusions from the simulated construction Xu [6] and Wu[7] used the Winkler model to analyze the properties ofthe retaining structure of foundation pits with asymmetricalloads nearby but oversimplified analysis and the limitation ofbeams on elastic foundationmethod prevented their findingsfrom being widely used in engineering practice

In the present work a numerical investigation by PLAXISis carried out to simulate the deformation and internalforce of retaining structures under four different groups ofasymmetrical loads (119875

1on the left and119875

2on the right119875

1= 1198752

= 15 kPa 1198751= 2119875

2= 30 kPa 119875

1= 3119875

2= 45 kPa 119875

1=

41198752= 60 kPa) The effects of strut stiffness and diaphragm

wall length are also investigated Data comparisons betweenthe monitoring and asymmetry integrated method and theconventional symmetry method confirm that the proposedasymmetry integrated method is a reliable and economicalmethod for designing asymmetrical load excavations becauseit accounts for the connections between the diaphragm walland strut under the asymmetrical loads Several generalconclusions are drawn regarding the design of excavationsunder asymmetrical loads

2 Simulation of the Excavation Process underAsymmetrical Loads

21 Introduction to FE Analysis The hardening soil (HS)[8 9] model first proposed by Schanz et al [10] is appliedto the numerical analyses by PLAXIS The HS model is anelastoplastic hyperbolic model formulated in the frameworkof friction hardening plasticity that accounts for soil dilata-tion [11] This second-order model also involves compressionhardening to simulate the irreversible compaction of soilunder primary compression The HS model can be used tosimulate the behavior of sand gravel and soft soils such asclay and silt The application of this model to engineeringis also extensive it can be used for dam filling bearingcapacity of ground slope stability analysis and foundation pitexcavation [12 13] In this model the cap type yield surface isemployed and defined as

119891119888=1199022

1205722minus 1199012minus 1199012

119901 (1)

where 120572 is the factor of cap characteristic and 119901119901is the pre-

consolidation stress

119902 = 1205901015840

1+ (120575 minus 1) 120590

1015840

2+ 1205751205901015840

3

120575 =3 + sin1205933 minus sin120593

1199011015840=1

3(1205901015840

1+ 1205901015840

2+ 1205901015840

3)

(2)

The basic feature of the HS model is that the soil stiffnessdepends on the stress The relation of stress and strain in theHS model is expressed as

119864oed = 119864refoed(120590

119901ref)

119898

(3)

The HS model has 11 parameters three strength parame-ters of Mohr-Coulomb (effective cohesion 119888 effective angleof internal fraction 120593ur and angle of dilatation 120595) threebasic stiffness parameters (reference secant stiffness of triaxialdrained test 119864ref

50 reference secant stiffness of consolidation

test 119864refoed and correlation exponent 119898) and five advancedparameters (modulus of unloading and loading119864refur Poissonrsquosratio of unloading and reloading 120583 reference stress 119901ref fail-ure ratio119877

119891 and the lateral pressure coefficient under normal

consolidation 1198700) All these parameters can be measured via

the conventional triaxial and consolidation tests Howeverin the current study we select the model parameters byfollowing the procedures recommended by Schanz et al [10]and Brinkgreve [11] 119864ref

50can be obtained as follows

11986450= 119864

ref50(119888 cos120593 minus 1205901015840

3sin120593

119888 cos120593 + 119901ref sin120593)

119898

(4)

in which 11986450= 119864ref the middle stiffness of every soil layer

adopted in Mohr-Coulomb model 119901ref = 100 kPa 119898 = 10for clay and sim05 for sands and silt soil [14 15] 1205901015840

3is negative

for compression and 119864refoed = 119864ref50 119864refur = 3119864

ref50 Zhong [16]

conducted triaxial consolidation tests and found that forsandy soil 119864refur = 3 sim 5119864

ref50 and for cohesive soil 119864refur =

4 sim 6119864ref50 The model parameters used in the simulations are

described in detail in Table 1

Mathematical Problems in Engineering 3

Table 1 Soil properties at the construction site

Soil layers Depth (m) 120574 (kNm3) 119864ref50

(Mpa) 119864refoed (Mpa) 119864refur (Mpa) Poissonrsquos ratio c (kPa)Angle ofinternal

fraction (∘)

Angle ofdilatation (∘)

Plane fill 3 181 8 8 24 030 1 307 0Clay 8 20 4 4 18 032 4 25 0Sandy silt 32 21 10 10 35 030 1 32 3Silty clay with sand 2 207 35 35 165 033 3 26 1Sandy silt mdash 20 14 14 52 030 1 34 4

Soil element

NodeStress point

(a) Six-node soil element

Soil element

NodeStress point

(b) 15-node soil element

Figure 2 Connection between interface and soil elements

The calculation model adopted in this study is a two-dimensionmodelThe 15-node element with 12 Gauss pointsplate element and anchor element are used to simulate thesoil retaining structure and strut respectively Accordingto the Mohr-Coulomb elastoplastic model plate elementsare connected to surrounding soil elements with interfaceelements The interface element stiffness matrix is obtainedthrough Newton Cotes integration The node number of theinterface element is related to that of the soil element

As shown in Figure 2 the interface element has finitethickness but the coordinates of each node group are equalin the finite element formula indicating that the elementthickness is zero

22 A Brief Introduction of Excavation Red Stone CentralPark is located near the crossing of Hushu South Road andChaowang Road The main properties of the soil layers ofthe construction site are shown in Table 1 The shape of thefoundation pit of the park is an approximate rectangle 95mlong and 35m wide The average excavation depth is 9mThe excavation is supported by 800mm diaphragm wall andtwo steel struts at 1m and 5m below the ground surfacerespectively The elastic modules of the diaphragm wall andsteel strut are 30 times 104 and 21 times 105MPa respectivelyThe ground water level is at 2m below ground surface anddewatering is not considered Typical cross section of theretaining strutting system is shown in Figure 3

23 Description of FE Model Simplification Adopted Thecalculation model instead of the symmetry semi plane isintegrated to consider the interaction of both walls causedby the struts and passive soil area The model is 80m wideand 35m deep The horizontal displacement is restrained at

the left and right boundaries and the vertical and horizontaldisplacements are fixed at the bottom (Figure 4) Theseboundary conditions are consistent with the initial self-weighting deformation condition of the soil

24 Simulation of Excavation Stages The numerical simula-tion is conducted according to the following steps

Step 1 A model of the whole site together with the strutstructure is establishedStep 2 Primary geostress is balanced to establish the initialstate of stress (119870

0stress conditions) and eliminate the stiffness

of the strut structure Thus the strut structure element losesits activity and becomes uninvolved with the settlementcaused by soil weightStep 3 Displacements of the initial stress field are set to zeroStep 4 Strut structure elements are activated and loads nearthe pit are appliedStep 5 Stage-by-stage excavation is conducted and therelevant strut is activated Soil excavation is simulated bycausing soil elements to lose their activity

Excavation process is simulated in three the stages asfollows (ldquo-rdquo denotes the level below the ground surface)Stage 1 Excavation up to minus2m is performedStage 2 One steel strut is constructed at minus1m and excavationis conducted up to minus6m The first strut reaches its designstrength and starts to functionStage 3The other steel strut is constructed at minus5m and exca-vation continues up tominus9m the bottomof the foundation pit


Strut

Strut

Concrete cushion (200 mm)

35 m

minus210m

minus90m

minus50mminus10m

21 m

plusmn00 m

Figure 3 Cross section of retaining strutting system

Diaphragm wall Diaphragm wall

Strut

Strut

minus210m

minus90m

minus50m

minus10m

80 m

35 m

P2P1

Plane fill 3 m

Clay 8 m

Sandy silt 32 m

Sandy silt 138 m

Silty clay with sand 2 m

plusmn00 m

Figure 4 Model simplifications

25 Numerical Results under Four Groups of Loads

251 Horizontal Displacement In Stage 1 the calculated dataon the left and right walls under four groups of asymmetricalloads are shown in Figure 5

The following observations are summarized as follows

(a) The maximum horizontal displacements on bothsides occur on top of the walls

(b) The horizontal displacement of the left wall growswith 119875

1 When 119875

1increases from 15 kPa to 60 kPa the

maximum horizontal displacement of the left wall 1198781

is growing from 405mm to 1503mm(c) On the right side 119875

2is kept constant at 15 kPa The

deformation of the right wall is far less severe thanthat of the left wall With increased 119875

1 the passive

earth pressure transferred to the right wall rises effec-tively restraining the deformation of the right walltoward the excavationWhen119875

1increases from 15 kPa

to 60 kPa the maximum horizontal displacement ofthe right wall 119878

2decreases from 405mm to 236mm

The displacements for Stage 2 are shown in Figure 6

The following observations are summarized as follows(a) As the first strut starts to function the horizontal dis-

placement is restrained The initial cantilever move-ments of the wall represent a very large component ofthe lateral displacement of the wall for shallow cuts

(b) With increase in 1198751 the ability of the brace system

to constrain deformation is weakened When 1198751=

15 kPa 1198781is 742mm and appears 2m above the

excavation surfaceWhen 1198751= 60 kPa 119878

1is 2050mm

and occurs on top of the wall(c) 1198782is smaller than 119878

1due to the restraint function of

the strut The larger the 1198751 the smaller the defor-

mation of the right wall toward the excavation Thegeneral increased deformation of the right wall inStage 2 is smaller than that in Stage 1 Moreoverwhen 119875

1= 60 kPa a 226mm reversed horizontal

displacement (outwards the excavation) appears ontop of the right wall

By Stage 3 excavation is completed The horizontaldisplacements are given in Figure 7



0 5 10 15Horizontal displacement (mm)

Dep

th (m

)

0

5

10

15

20

P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(a) Left wall

Dep

th (m

)

0

5

10

15

20

minus4 minus3 minus2 minus1 0Horizontal displacement (mm)

P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(b) Right wall

Figure 5 Horizontal displacement of diaphragm wall under different load groups (stage 1)

0 5 10 15 20Horizontal displacement (mm)

Dep

th (m

)

0

5

10

15

20

P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(a) Left wall

Dep

th (m

)

0

5

10

15

20


P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(b) Right wall




Dep

th (m

)0

5

10

15

20

P1 = P2

P1 = 2P2

P1 = 3P2

P1 = 4P2

(a) Left wall

Dep

th (m

)

0

5

10

15

20

minus8 minus6 minus4 minus2 2 4 6 80Horizontal displacement (mm)

P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(b) Right wall


(a) Themaximumhorizontal displacements of bothwallsmove to the bottom of the pit except the group of 119875

1

= 60 kPa and 1198752= 15 kPa The maximum values of 119878

1

and 1198782of this group are achieved on top of the wall In

general the deformation caused by Stage 3 is smallerthan those in previous stages illustrating the effectiverestriction of the two-strut retaining system

(b) In the left wall as 1198751increases from 15 kPa to 60 kPa

1198781increases from 847mm to 2463mm whereas1198752remains constant Given the increased excava-

tion depth reverse horizontal displacement appearsearlier (when 119875

1= 45 kPa) than Stage 1 (when 119875

1

= 60 kPa) At 1198751= 60 kPa reversed displacement

reaches 683mm

252 Bending Moment Themaximum bending moments ofthe different stages are shown in Figure 8

Some observations can be summarized as follows(a) In Stage 1 with increased 119875

1on the left side

the magnitude of the bending moment increasesfrom 5765 kNsdotmm to 12100 kNsdotmm The bendingmoment on the right side varies slightly regardless ofthe variation in 119875

1 With the increasing gap between

1198751and 119875

2 the difference of the bending moment of

the two sides becomes more obvious(b) In Stage 2 as 119875

1on the left wall rises from 15 kPa

to 60 kPa the maximum bending moment changesfrom 20074 kNsdotm to 36135 kNsdotm signifying an 80increase The maximum bending moment of the

1 2 3 40

100

200

300

400

500

Bend

ing

mom

ent (

kNmiddotm

m)

S-1 (L)S-1 (R)S-2 (L)

S-2 (R)S-3 (L)S-3 (R)

P1P2

Figure 8 Maximum bending moment of multiple stages (S stageL left R right)

right wall changes from 20074 kNsdotm to 26625 kNsdotmindicating a 326 growing Compared with that inStage 1 the gap between the left and right wallsnarrows as excavation depth increases

(c) In Stage 3 with increased 1198751 the magnitudes of the

left and right walls increasingly vary During excava-tion the discrepancy between the bending momentof the left wall and that of the right first increases and


10

5

0

15

20

25

1 2 3 4

Max

imum

Ux

(mm

)

LR

EA (times106 kN)

(a) Maximum horizontal displacement

1 2 3 4200

250

300

350

400

450

LR

Max

imum

ben

ding

mom

ent (

kNmiddotm

m)

EA (times106 kN)

(b) Maximum bending moment

Figure 9 Relationship between diaphragm wall characteristics and strut stiffness (L left R right)

0

5

10

15

20

17 19 21 23

LR

Wall length (m)

Max

imum

Ux

(mm

)


17 19 21 23

LR

250

300

350

400

450

Wall length (m)

Max

imum

ben

ding

mom

ent (

kNmiddotm

m)


Figure 10 Relationship between diaphragm wall characteristics and wall length (L left R right)

then decreasesThe asymmetrical characteristic of theretaining structure is not proportional to excavationdepth

26 Effect of Strut Stiffness Strut stiffness is directly relatedto wall deflection and bending moment distribution Thecharacteristics of wall deflection and maximum bendingmoment are investigated under the asymmetrical loads 119875

1=

31198752= 45 kPa with strut stiffness (EA) varying from 1 times

106 kN to 4times106 kNThemaximum horizontal displacement

and bending moment of the diaphragm walls in Stage 3 areplotted in Figure 9

With increased strut stiffness the discrepancy betweenthe left and right walls narrows When EA increases from 1 times106 kN to 2times106 kN themaximumhorizontal displacements

of the left and right walls are reduced by 1023 and 1059respectively The increasing EA does not have a significanteffect Based on the inner force appropriately increasing strutstiffness reduces diaphragm wall rebar and saves cost

27 Effect of DiaphragmWall Length Figure 10 compares themaximum horizontal displacement and bending moment ofthe Stage 3 walls which has diaphragm wall lengths of 17 1921 and 23m and embedded lengths of 8 10 12 and 14mrespectively The asymmetrical loads are 119875

1= 31198752= 45 kPa

The strut conditions remain the sameThe extension of wall length significantly affects the mag-

nitude of the bending moment and the maximum bendingmoment of both walls decreases The left diaphragm wall


Chaowang Road

Sout

h H

ushu

Roa

d

Residential building

(under construction Stage 1)

Red stone central parkF21

N

Axial force meterDewatering wellGroundwater table pipe

Inclinometer pipeBuilding settlement

No 6

No 7

No 8No 9No 10No 11No 12

No 13

No 14

No 1 No 2 No 3 No 4 No 5

80 m

80 m

110

m9

0 m

Excavation depth 10 m

Figure 11 Layout of field monitoring

is reduced by 392 and the right wall by 112 Howevermaximum horizontal displacement is only slightly affected

3 Comparison of Integrated Method andObservation Data

General information is described in A brief introduction ofexcavation Strut stiffness is 2 times 106 kN and diaphragm walllength is 21m Given the limitation of the construction sitethe raw materials and construction machineries are stackednear the edge of the pit As a result the load on the left side is45 kPa and on the right 15 kPa approximately To highlight theadvantage of the asymmetry integrated method we presentthe results of the symmetry semiplane calculation below (119875

1

= 45 kPa for left diaphragm wall 1198752= 15 kPa for right)

31 Comparisons of Horizontal Displacement To verify theapplicability of the asymmetrical integrated design we mea-sure the horizontal displacement of the walls every 1m alongthe depth at the end of each stage One portion of thefield monitoring locations is shown in Figure 11 and themeasurements from inclinometer pipes of No 3 and No 10are compared with numerical data

Shown in Figure 12 is comparison of horizontal displace-ments

It is seen that with an excavation depth of 2m (Stage 1)the calculation data of the symmetry semiplane method (15

or 45 kPa) are not much different from the monitoring dataThrough the asymmetry integrated method the calculationand monitoring data are generally consistent from Stage 1to Stage 3 The magnitude of 119878

1is larger than the symmetry

semiplane calculation results in all stages (however the loadis 15 or 45 kPa)This discrepancy illustrates that the symmetryloads on both sides facilitate the deformation control of sideswith larger loads In practice the horizontal deformation ofthe right wall is well restrained

The deformation of soil surrounding the excavationsignificantly affects buildings and pipes nearby This defor-mation is closely related to the horizontal deformation of thediaphragmwallTherefore the horizontal deformation of thewall should be predicted as accurately as possible Thus theasymmetry integrated method is recommended

32 Comparisons of Bending Moment To obtain the bendingmoment rebar stress gauges are deployed by being connectedwith the main rebar every two meters along the depth beforewall construction The positions of the gauges on the northand southwalls are shown in Figure 13 Such gauges are placedon both wall interior and exterior tomeasure the positive andnegative bending moment Seventy-two rebar stress gaugesare deployed The stresses are recorded at the end of eachstage

Figure 14 shows the comparison graphs of stresses Ingeneral the calculated data match the monitoring datain Stage 1 with the semiplane method As the excavation



0

5

10

15

20

Dep

th (m

)

Symmetry semiplane method (45 kPa)Asymmetrical integrated methodMonitoring data

(a) Left wall (Stage 1)

Horizontal displacement (mm)

0

5

10

15

20

Dep

th (m

)

minus5 minus4 minus3 minus2 minus1 0


(b) Right wall (Stage 1)

0 2 4 6 8 10 12 14 16Horizontal displacement (mm)

0

5

10

15

20

Dep

th (m

)


(c) Left wall (Stage 2)

0

5

10

15

20

Dep

th (m

)minus8 minus6 minus4 minus2 2 40



(d) Right wall (Stage 2)

Horizontal displacement (mm)0 5 10 15 20

0

5

10

15

20

Dep

th (m

)


(e) Left wall (Stage 3)

minus8minus10 minus6 minus4 minus2 2 4 6 80Horizontal displacement (mm)

0

5

10

15

20

Dep

th (m

)


(f) Right wall (Stage 3)

Figure 12 Horizontal displacement of diaphragm wall with different methods and monitoring data


Excavationbottom

08 m

Rebar stressgauges

Diaphragm wall

Rebar

Strut

Strut

minus210mminus210m

210

m

minus90m

30 m

20 m

plusmn00 mplusmn00 m

Figure 13 Layout of rebar stress gauges

progresses the semiplane method becomes too conservativefor the left wall and a little risky for the right althoughthe discrepancy of the right wall is small The results of theasymmetry integrated method are only marginally smallerthan measured data a difference of roughly 20 The resultsare consistent probably because the locations of the stressgauges are not the exact places where the maximum bendingmoment occurs

The results of rebar arrangement are shown in Table 2With foundation pit safety still ensured the asymmetrical

integrated design reduces the rebar requirement of the leftwall by 148 a remarkable economic benefit

These results confirm the reliability of the parametersselected and the feasibility of the proposed method in termsof horizontal displacement and bending moment

4 Conclusions

The following conclusions can be drawn from this study

(1) Increased load on one side positively affects the defor-mation control of the other side When the load gapof two sides is enlarged the side with a smaller loadexperiences reverse displacement on top of the wallwhich is not observed with the semiplane methodThe horizontal displacement of the diaphragm wallof excavations near important structures should beaccurately predicted and strictly controlled becausethese pits have strict deformation requirementsThusthe displacement caused by the symmetry semiplanemethod should not be used to forecast the horizontaldisplacement of the wall

(2) When the load of one side increases the bendingmoment of this side becomes significantly differentwhereas changes in the other side are marginal Thepositions of maximum value change as excavationdepth increases In both cases when the larger loadis more than two times the smaller load the gapof the maximum bending moment between them isover 20 Then the asymmetry integrated method isnecessary In situations with no strict requirementson deformation the semiplane method is still usedfor the angle of the bending moment for convenientconstruction

(3) Compared with wall length strut stiffness signifi-cantly affects the asymmetrical characteristic of thewalls Given that the quantity of the strut is farsmaller than that of the diaphragm wall increasingstrut stiffness to reduce wall deflection and bendingmoment is more economical than increasing thelength of the diaphragm wall

(4) Based on the engineering case symmetry-plane cal-culation has obvious limitations compared with theproposed asymmetry integrated method which hasbetter consistency with the monitoring data of bothhorizontal displacement and bending moment Theproposedmethod reflects the realmechanical proper-ties of the retaining structure and promotes economicbenefits while ensuring safety

(5) Under asymmetric loads the characteristic differenceof walls is related to the width and length of thefoundation pit as well as the load which needs furtherinvestigation


minus100 minus50 0 50 100Bending moment (kN middotmm)

0

5

10

15

20

Dep

th (m

)



minus40 minus20 0 20Bending moment (kN middotmm)

0

5

10

15

20

Dep

th (m

)



minus200minus100 0 100 200 300 4000

5

10

15

20

Dep

th (m

)

Bending moment (kN middotmm)



0

5

10

15

20

Bending moment (kN middotmm)minus250minus200minus150minus100 minus50 0 50

Dep

th (m

)



0

5

10

15

20

Dep

th (m

)

minus200minus100 0 100 200 300 400 500Bending moment (kN middotmm)



0

5

10

15

20

Dep

th (m

)

Bending moment (kN middotmm)minus200minus300 minus100 0 100



Figure 14 Bending moment of diaphragm wall under different methods and monitoring data


Table 2 Comparison of symmetry-plane and asymmetrical integrated designs

Left wall Right wallMaximum bendingmoment (kNsdotmm) Rebar Maximum bending

moment (kNsdotmm) Rebar

Symmetry-plane design(1198751= 45 kPa) 4567 Φ 26200 mdash mdash

(1198752= 15 kPa) mdash mdash 2425 mdash

Asymmetrical integrated design(1198751= 31198752= 45 kPa) 37924 Φ 24200 27061 Φ 20200

Acknowledgments

Many people and organizations contributed to the success ofthis project and special thanks are due to Zhejiang UniversityFirst Geotechnical Investigations amp Design Institute Co Ltdfor providing the detailed information for soil conditions atthe project site and field dataThe financial supports from theNational Natural Science Foundation of China (NSFC Grantno 51278449) and Project of Zhejiang EducationDepartment(no N20110091) are gratefully acknowledged

References

[1] P Li X P Deng J H Xiang and T Li ldquoMethod of displacementiteration in numerical simulation of foundation pitrdquo Rock andSoil Mechanics vol 26 no 11 pp 1815ndash1818 2005

[2] M H Chen Z X Chen and C S Zhang ldquoApplication ofFLAC in analysis of foundation excavationrdquo Chinese Journal ofGeotechnical Engineering vol 28 pp 1437ndash1440 2006

[3] J G Liu and YW Zeng ldquoApplication of FLAC3D to simulationof foundation excavation and supportrdquoRock and SoilMechanicsvol 27 no 3 pp 505ndash508 2006

[4] H N Gharti V Oye D Komatitsch and J Tromp ldquoSimula-tion of multistage excavation based on a 3D spectral-elementmethodrdquo Computers and Structures vol 100-101 pp 54ndash692012

[5] X J Lv Q YangD L Qian and J Liu ldquoDeformation analysis onsupporting structure of deep foundation pit under the conditionof asymmetric overloadingrdquo Chinese Journal of Hefei UniversityTechnology vol 35 no 6 pp 809ndash813 2012

[6] Z B Xu Study on deformation of foundation pit under asymmet-ric load [Dissertation] Southeast University of China 2005

[7] X J Wu Deformation control research on deep foundationpit of subway transfer station paralleling with the station hall[Dissertation] Tongji University of China 2006

[8] B O Hardin and W L Black ldquoClosure to vibration modulusof normally consolidated claysrdquo Journal of Soil Mechanic andFoundations Division vol 95 no 6 pp 1531ndash1537 1969

[9] B O Hardin and V P Drnevich ldquoShear modulus and dampingin soils design equations and curvesrdquo Journal of Soil Mechanicand Foundations Division vol 98 no 7 pp 667ndash692 1972

[10] T Schanz P A Vermeer and P G Bonnier ldquoThe hardeningsoil model formulation and verificationrdquo in Beyond 2000 inComputational Geotechnics pp 281ndash296 Balkema AmsterdamThe Netherlands 1999

[11] R B J Brinkgreve ldquoSelection of soil models and parametersfor geotechnical engineering applicationrdquo in Soil ConstitutiveModels Proceedings of the Sessions of the Geo-Frontiers Congresspp 69ndash98 ASCE Austin Tex USA 2005

[12] Z H Xu andW DWang ldquoSelection of soil constitutive modelsfor numerical analysis of deep excavations in close proximity tosensitive propertiesrdquo Rock and Soil Mechanics vol 31 no 1 pp258ndash264 2010

[13] A Tolooiyan and K Gavin ldquoModelling the cone penetrationtest in sand using cavity expansion and arbitrary lagrangianeulerian finite element methodsrdquo Computers and Geotechnicsvol 38 no 4 pp 482ndash490 2011

[14] J Janbu ldquoSoil compressibility as determined by oedometer andtriaxial testsrdquo ECSMFEWiesbaden vol 1 pp 19ndash25 1963

[15] X L Liu R Ma G Q Guo T Tao and H Zhou ldquoApplicabilityof PLAXIS2D used for numerical simulation in foundation pitexcavationrdquo Chinese Journal of Ocean University vol 42 no 4pp 019ndash025 2012

[16] L ZhongThe characteristic of retaining structure of multi-stageexcavation [Dissertation] Fuzhou University of China 2007

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Strut

Retainingstructure

Soil

Waterpressure

Waterpressure

pressure Soilpressure

P1

F1 F2

P1 P2P2

+=

Figure 1 Schematic diagram for the calculation of conventional design method

behavior of deep foundation pits under asymmetrical loadwhich was a part of Suzhou Metro Line 1 and drew con-clusions from the simulated construction Xu [6] and Wu[7] used the Winkler model to analyze the properties ofthe retaining structure of foundation pits with asymmetricalloads nearby but oversimplified analysis and the limitation ofbeams on elastic foundationmethod prevented their findingsfrom being widely used in engineering practice

In the present work a numerical investigation by PLAXISis carried out to simulate the deformation and internalforce of retaining structures under four different groups ofasymmetrical loads (119875

1on the left and119875

2on the right119875

1= 1198752

= 15 kPa 1198751= 2119875

2= 30 kPa 119875

1= 3119875

2= 45 kPa 119875

1=

41198752= 60 kPa) The effects of strut stiffness and diaphragm

wall length are also investigated Data comparisons betweenthe monitoring and asymmetry integrated method and theconventional symmetry method confirm that the proposedasymmetry integrated method is a reliable and economicalmethod for designing asymmetrical load excavations becauseit accounts for the connections between the diaphragm walland strut under the asymmetrical loads Several generalconclusions are drawn regarding the design of excavationsunder asymmetrical loads

2 Simulation of the Excavation Process underAsymmetrical Loads

21 Introduction to FE Analysis The hardening soil (HS)[8 9] model first proposed by Schanz et al [10] is appliedto the numerical analyses by PLAXIS The HS model is anelastoplastic hyperbolic model formulated in the frameworkof friction hardening plasticity that accounts for soil dilata-tion [11] This second-order model also involves compressionhardening to simulate the irreversible compaction of soilunder primary compression The HS model can be used tosimulate the behavior of sand gravel and soft soils such asclay and silt The application of this model to engineeringis also extensive it can be used for dam filling bearingcapacity of ground slope stability analysis and foundation pitexcavation [12 13] In this model the cap type yield surface isemployed and defined as

119891119888=1199022

1205722minus 1199012minus 1199012

119901 (1)

where 120572 is the factor of cap characteristic and 119901119901is the pre-

consolidation stress

119902 = 1205901015840

1+ (120575 minus 1) 120590

1015840

2+ 1205751205901015840

3

120575 =3 + sin1205933 minus sin120593

1199011015840=1

3(1205901015840

1+ 1205901015840

2+ 1205901015840

3)

(2)

The basic feature of the HS model is that the soil stiffnessdepends on the stress The relation of stress and strain in theHS model is expressed as

119864oed = 119864refoed(120590

119901ref)

119898

(3)

The HS model has 11 parameters three strength parame-ters of Mohr-Coulomb (effective cohesion 119888 effective angleof internal fraction 120593ur and angle of dilatation 120595) threebasic stiffness parameters (reference secant stiffness of triaxialdrained test 119864ref

50 reference secant stiffness of consolidation

test 119864refoed and correlation exponent 119898) and five advancedparameters (modulus of unloading and loading119864refur Poissonrsquosratio of unloading and reloading 120583 reference stress 119901ref fail-ure ratio119877

119891 and the lateral pressure coefficient under normal

consolidation 1198700) All these parameters can be measured via

the conventional triaxial and consolidation tests Howeverin the current study we select the model parameters byfollowing the procedures recommended by Schanz et al [10]and Brinkgreve [11] 119864ref

50can be obtained as follows

11986450= 119864

ref50(119888 cos120593 minus 1205901015840

3sin120593

119888 cos120593 + 119901ref sin120593)

119898

(4)

in which 11986450= 119864ref the middle stiffness of every soil layer

adopted in Mohr-Coulomb model 119901ref = 100 kPa 119898 = 10for clay and sim05 for sands and silt soil [14 15] 1205901015840

3is negative

for compression and 119864refoed = 119864ref50 119864refur = 3119864

ref50 Zhong [16]

conducted triaxial consolidation tests and found that forsandy soil 119864refur = 3 sim 5119864

ref50 and for cohesive soil 119864refur =

4 sim 6119864ref50 The model parameters used in the simulations are

described in detail in Table 1





fraction (∘)



Soil element

NodeStress point


Soil element

NodeStress point














Strut

Strut


35 m

minus210m

minus90m

minus50mminus10m

21 m

plusmn00 m



Strut

Strut

minus210m

minus90m

minus50m

minus10m

80 m

35 m

P2P1

Plane fill 3 m

Clay 8 m

Sandy silt 32 m

Sandy silt 138 m


plusmn00 m







1 When 119875






1 the passive












1is 2050mm











Dep

th (m

)

0

5

10

15

20

P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(a) Left wall

Dep

th (m

)

0

5

10

15

20


P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(b) Right wall



Dep

th (m

)

0

5

10

15

20

P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(a) Left wall

Dep

th (m

)

0

5

10

15

20


P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(b) Right wall




Dep

th (m

)0

5

10

15

20

P1 = P2

P1 = 2P2

P1 = 3P2

P1 = 4P2

(a) Left wall

Dep

th (m

)

0

5

10

15

20


P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(b) Right wall



1


1







1


reaches 683mm



1on the left side



1198751and 119875





1 2 3 40

100

200

300

400

500

Bend

ing

mom

ent (

kNmiddotm

m)

S-1 (L)S-1 (R)S-2 (L)

S-2 (R)S-3 (L)S-3 (R)

P1P2






10

5

0

15

20

25

1 2 3 4

Max

imum

Ux

(mm

)

LR

EA (times106 kN)


1 2 3 4200

250

300

350

400

450

LR

Max

imum

ben

ding

mom

ent (

kNmiddotm

m)

EA (times106 kN)



0

5

10

15

20

17 19 21 23

LR

Wall length (m)

Max

imum

Ux

(mm

)


17 19 21 23

LR

250

300

350

400

450

Wall length (m)

Max

imum

ben

ding

mom

ent (

kNmiddotm

m)





1=







1= 31198752= 45 kPa




Chaowang Road

Sout

h H

ushu

Roa

d




N



No 6

No 7


No 13

No 14


80 m

80 m

110

m9

0 m






1













0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)





0

5

10

15

20

Dep

th (m

)



0

5

10

15

20

Dep

th (m






0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)





Excavationbottom

08 m

Rebar stressgauges

Diaphragm wall

Rebar

Strut

Strut

minus210mminus210m

210

m

minus90m

30 m

20 m







4 Conclusions









0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)



minus200minus100 0 100 200 300 4000

5

10

15

20

Dep

th (m

)




0

5

10

15

20


Dep

th (m

)



0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)












Acknowledgments


References
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













fraction (∘)



Soil element

NodeStress point


Soil element

NodeStress point














Strut

Strut


35 m

minus210m

minus90m

minus50mminus10m

21 m

plusmn00 m



Strut

Strut

minus210m

minus90m

minus50m

minus10m

80 m

35 m

P2P1

Plane fill 3 m

Clay 8 m

Sandy silt 32 m

Sandy silt 138 m


plusmn00 m







1 When 119875






1 the passive












1is 2050mm











Dep

th (m

)

0

5

10

15

20

P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(a) Left wall

Dep

th (m

)

0

5

10

15

20


P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(b) Right wall



Dep

th (m

)

0

5

10

15

20

P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(a) Left wall

Dep

th (m

)

0

5

10

15

20


P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(b) Right wall




Dep

th (m

)0

5

10

15

20

P1 = P2

P1 = 2P2

P1 = 3P2

P1 = 4P2

(a) Left wall

Dep

th (m

)

0

5

10

15

20


P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(b) Right wall



1


1







1


reaches 683mm



1on the left side



1198751and 119875





1 2 3 40

100

200

300

400

500

Bend

ing

mom

ent (

kNmiddotm

m)

S-1 (L)S-1 (R)S-2 (L)

S-2 (R)S-3 (L)S-3 (R)

P1P2






10

5

0

15

20

25

1 2 3 4

Max

imum

Ux

(mm

)

LR

EA (times106 kN)


1 2 3 4200

250

300

350

400

450

LR

Max

imum

ben

ding

mom

ent (

kNmiddotm

m)

EA (times106 kN)



0

5

10

15

20

17 19 21 23

LR

Wall length (m)

Max

imum

Ux

(mm

)


17 19 21 23

LR

250

300

350

400

450

Wall length (m)

Max

imum

ben

ding

mom

ent (

kNmiddotm

m)





1=







1= 31198752= 45 kPa




Chaowang Road

Sout

h H

ushu

Roa

d




N



No 6

No 7


No 13

No 14


80 m

80 m

110

m9

0 m






1













0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)





0

5

10

15

20

Dep

th (m

)



0

5

10

15

20

Dep

th (m






0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)





Excavationbottom

08 m

Rebar stressgauges

Diaphragm wall

Rebar

Strut

Strut

minus210mminus210m

210

m

minus90m

30 m

20 m







4 Conclusions









0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)



minus200minus100 0 100 200 300 4000

5

10

15

20

Dep

th (m

)




0

5

10

15

20


Dep

th (m

)



0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)












Acknowledgments


References
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Strut

Strut


35 m

minus210m

minus90m

minus50mminus10m

21 m

plusmn00 m



Strut

Strut

minus210m

minus90m

minus50m

minus10m

80 m

35 m

P2P1

Plane fill 3 m

Clay 8 m

Sandy silt 32 m

Sandy silt 138 m


plusmn00 m







1 When 119875






1 the passive












1is 2050mm











Dep

th (m

)

0

5

10

15

20

P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(a) Left wall

Dep

th (m

)

0

5

10

15

20


P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(b) Right wall



Dep

th (m

)

0

5

10

15

20

P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(a) Left wall

Dep

th (m

)

0

5

10

15

20


P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(b) Right wall




Dep

th (m

)0

5

10

15

20

P1 = P2

P1 = 2P2

P1 = 3P2

P1 = 4P2

(a) Left wall

Dep

th (m

)

0

5

10

15

20


P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(b) Right wall



1


1







1


reaches 683mm



1on the left side



1198751and 119875





1 2 3 40

100

200

300

400

500

Bend

ing

mom

ent (

kNmiddotm

m)

S-1 (L)S-1 (R)S-2 (L)

S-2 (R)S-3 (L)S-3 (R)

P1P2






10

5

0

15

20

25

1 2 3 4

Max

imum

Ux

(mm

)

LR

EA (times106 kN)


1 2 3 4200

250

300

350

400

450

LR

Max

imum

ben

ding

mom

ent (

kNmiddotm

m)

EA (times106 kN)



0

5

10

15

20

17 19 21 23

LR

Wall length (m)

Max

imum

Ux

(mm

)


17 19 21 23

LR

250

300

350

400

450

Wall length (m)

Max

imum

ben

ding

mom

ent (

kNmiddotm

m)





1=







1= 31198752= 45 kPa




Chaowang Road

Sout

h H

ushu

Roa

d




N



No 6

No 7


No 13

No 14


80 m

80 m

110

m9

0 m






1













0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)





0

5

10

15

20

Dep

th (m

)



0

5

10

15

20

Dep

th (m






0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)





Excavationbottom

08 m

Rebar stressgauges

Diaphragm wall

Rebar

Strut

Strut

minus210mminus210m

210

m

minus90m

30 m

20 m







4 Conclusions









0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)



minus200minus100 0 100 200 300 4000

5

10

15

20

Dep

th (m

)




0

5

10

15

20


Dep

th (m

)



0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)












Acknowledgments


References
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Dep

th (m

)

0

5

10

15

20

P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(a) Left wall

Dep

th (m

)

0

5

10

15

20


P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(b) Right wall



Dep

th (m

)

0

5

10

15

20

P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(a) Left wall

Dep

th (m

)

0

5

10

15

20


P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(b) Right wall




Dep

th (m

)0

5

10

15

20

P1 = P2

P1 = 2P2

P1 = 3P2

P1 = 4P2

(a) Left wall

Dep

th (m

)

0

5

10

15

20


P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(b) Right wall



1


1







1


reaches 683mm



1on the left side



1198751and 119875





1 2 3 40

100

200

300

400

500

Bend

ing

mom

ent (

kNmiddotm

m)

S-1 (L)S-1 (R)S-2 (L)

S-2 (R)S-3 (L)S-3 (R)

P1P2






10

5

0

15

20

25

1 2 3 4

Max

imum

Ux

(mm

)

LR

EA (times106 kN)


1 2 3 4200

250

300

350

400

450

LR

Max

imum

ben

ding

mom

ent (

kNmiddotm

m)

EA (times106 kN)



0

5

10

15

20

17 19 21 23

LR

Wall length (m)

Max

imum

Ux

(mm

)


17 19 21 23

LR

250

300

350

400

450

Wall length (m)

Max

imum

ben

ding

mom

ent (

kNmiddotm

m)





1=







1= 31198752= 45 kPa




Chaowang Road

Sout

h H

ushu

Roa

d




N



No 6

No 7


No 13

No 14


80 m

80 m

110

m9

0 m






1













0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)





0

5

10

15

20

Dep

th (m

)



0

5

10

15

20

Dep

th (m






0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)





Excavationbottom

08 m

Rebar stressgauges

Diaphragm wall

Rebar

Strut

Strut

minus210mminus210m

210

m

minus90m

30 m

20 m







4 Conclusions









0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)



minus200minus100 0 100 200 300 4000

5

10

15

20

Dep

th (m

)




0

5

10

15

20


Dep

th (m

)



0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)












Acknowledgments


References
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Dep

th (m

)0

5

10

15

20

P1 = P2

P1 = 2P2

P1 = 3P2

P1 = 4P2

(a) Left wall

Dep

th (m

)

0

5

10

15

20


P1 = P2P1 = 2P2

P1 = 3P2

P1 = 4P2

(b) Right wall



1


1







1


reaches 683mm



1on the left side



1198751and 119875





1 2 3 40

100

200

300

400

500

Bend

ing

mom

ent (

kNmiddotm

m)

S-1 (L)S-1 (R)S-2 (L)

S-2 (R)S-3 (L)S-3 (R)

P1P2






10

5

0

15

20

25

1 2 3 4

Max

imum

Ux

(mm

)

LR

EA (times106 kN)


1 2 3 4200

250

300

350

400

450

LR

Max

imum

ben

ding

mom

ent (

kNmiddotm

m)

EA (times106 kN)



0

5

10

15

20

17 19 21 23

LR

Wall length (m)

Max

imum

Ux

(mm

)


17 19 21 23

LR

250

300

350

400

450

Wall length (m)

Max

imum

ben

ding

mom

ent (

kNmiddotm

m)





1=







1= 31198752= 45 kPa




Chaowang Road

Sout

h H

ushu

Roa

d




N



No 6

No 7


No 13

No 14


80 m

80 m

110

m9

0 m






1













0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)





0

5

10

15

20

Dep

th (m

)



0

5

10

15

20

Dep

th (m






0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)





Excavationbottom

08 m

Rebar stressgauges

Diaphragm wall

Rebar

Strut

Strut

minus210mminus210m

210

m

minus90m

30 m

20 m







4 Conclusions









0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)



minus200minus100 0 100 200 300 4000

5

10

15

20

Dep

th (m

)




0

5

10

15

20


Dep

th (m

)



0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)












Acknowledgments


References
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










10

5

0

15

20

25

1 2 3 4

Max

imum

Ux

(mm

)

LR

EA (times106 kN)


1 2 3 4200

250

300

350

400

450

LR

Max

imum

ben

ding

mom

ent (

kNmiddotm

m)

EA (times106 kN)



0

5

10

15

20

17 19 21 23

LR

Wall length (m)

Max

imum

Ux

(mm

)


17 19 21 23

LR

250

300

350

400

450

Wall length (m)

Max

imum

ben

ding

mom

ent (

kNmiddotm

m)





1=







1= 31198752= 45 kPa




Chaowang Road

Sout

h H

ushu

Roa

d




N



No 6

No 7


No 13

No 14


80 m

80 m

110

m9

0 m






1













0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)





0

5

10

15

20

Dep

th (m

)



0

5

10

15

20

Dep

th (m






0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)





Excavationbottom

08 m

Rebar stressgauges

Diaphragm wall

Rebar

Strut

Strut

minus210mminus210m

210

m

minus90m

30 m

20 m







4 Conclusions









0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)



minus200minus100 0 100 200 300 4000

5

10

15

20

Dep

th (m

)




0

5

10

15

20


Dep

th (m

)



0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)












Acknowledgments


References
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Chaowang Road

Sout

h H

ushu

Roa

d




N



No 6

No 7


No 13

No 14


80 m

80 m

110

m9

0 m






1













0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)





0

5

10

15

20

Dep

th (m

)



0

5

10

15

20

Dep

th (m






0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)





Excavationbottom

08 m

Rebar stressgauges

Diaphragm wall

Rebar

Strut

Strut

minus210mminus210m

210

m

minus90m

30 m

20 m







4 Conclusions









0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)



minus200minus100 0 100 200 300 4000

5

10

15

20

Dep

th (m

)




0

5

10

15

20


Dep

th (m

)



0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)












Acknowledgments


References
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)





0

5

10

15

20

Dep

th (m

)



0

5

10

15

20

Dep

th (m






0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)





Excavationbottom

08 m

Rebar stressgauges

Diaphragm wall

Rebar

Strut

Strut

minus210mminus210m

210

m

minus90m

30 m

20 m







4 Conclusions









0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)



minus200minus100 0 100 200 300 4000

5

10

15

20

Dep

th (m

)




0

5

10

15

20


Dep

th (m

)



0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)












Acknowledgments


References
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Excavationbottom

08 m

Rebar stressgauges

Diaphragm wall

Rebar

Strut

Strut

minus210mminus210m

210

m

minus90m

30 m

20 m







4 Conclusions









0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)



minus200minus100 0 100 200 300 4000

5

10

15

20

Dep

th (m

)




0

5

10

15

20


Dep

th (m

)



0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)












Acknowledgments


References
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)



minus200minus100 0 100 200 300 4000

5

10

15

20

Dep

th (m

)




0

5

10

15

20


Dep

th (m

)



0

5

10

15

20

Dep

th (m

)




0

5

10

15

20

Dep

th (m

)












Acknowledgments


References
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Acknowledgments


References
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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