study on model and tests of sheet pile wall with a relieving...

Research ArticleStudy on Model and Tests of Sheet Pile Wall with aRelieving Platform

Ming Zhang1 Wei Wang 2 Ronghua Hu3 and Ziyi Wang4

1Institute of Civil Engineering Henan University of Engineering Xianghe Rd 1 Zhengzhou 451191 China2College of Architecture and Urban Planning Beijing University of Technology Pingleyuan Rd 100 Beijing 100124 China3Amer International Group Co Ltd West Hongli Rd 8133 Shenzhen 518040 China4College of Architecture and Civil Engineering Beijing University of Technology Pingleyuan Rd 100 Beijing 100124 China

Correspondence should be addressed to Wei Wang ieewwbjuteducn

Received 4 June 2020 Revised 23 August 2020 Accepted 6 September 2020 Published 18 September 2020

Academic Editor Hui Yao

Copyright copy 2020 Ming Zhang et al +is 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

A new type of retaining wall the sheet pile wall with a relieving platform is introduced in this paper Based on the prototyperetaining wall with a height of 12 meters the model tests with a geometric similarity ratio of 7 are designed and we focus on themodel production and analysis on the test results Some comparative analyses between the measured values and the calculationvalues by using the theoretical calculation method and finite difference method are carried out including Earth pressure behindthe wall prepile resistance force the bending moment and the deformation of rib pillars in the retaining wall +e results showthat Earth pressure behind the wall has a linear increase with the depth and lies between Rankine Earth pressure and Earthpressure at rest Moreover the prepile resistance force can be approximated by the m method and the bending moment can bealso used for approximate calculation by the mmethod and is larger than the results calculated by the finite differencemethod It isalso observed that there is a zero-displacement point on the pile bottom and the Earth pressure above the point behind the piledevelops from Earth pressure at rest to the active Earth pressure the Earth pressure under the point behind the pile develops fromEarth pressure at rest to the passive Earth pressure +erefore the Earth pressure behind the bottom wall is larger than thecalculated value by the Rankine theory Finally the displacement of the rib pillars is greater than the calculated results using thefinite differencemethod and exceeds the standard requirements owing to the failure of the retaining wall and the unloading boardneeds to be constructed to improve the retaining wallrsquos behaviour +ese findings verify the modelrsquos credibility and provide anunderpinning for studying the behavior of the retaining wall

1 Introduction

Currently the standard methods that have been used to in-vestigate and analyze the interaction between retaining structureand soil include model tests centrifugal tests field tests ana-lytical methods and numerical analysis Compared with theother tests such as centrifugal tests and field tests the modeltests have the advantages of excellent repeatability strong op-erability and unconstrained field conditions +us they aresuitable for studying the various influencing factors on theretaining structure and their complex mechanisms In additionthe model tests can adjust test parameters or change testconditions and investigate one or several factors intensively toreveal the nature of the problem of retaining structural

engineering +erefore model testing is considered as the mostimportant means to study complex engineering problemsparticularly in the areas of the new retaining structure [1 2]

With regard to the reinforced soil retaining wall (RSW) ithas become one of the Earthrsquos retaining structures that can beseen in geotechnical engineering since 1963 +e RSW securesstructural stability through the frictional force between thefoundation and the reinforcement by installing reinforcementsand walls simultaneously with the foundations [3] A series ofmodel tests have been conducted to investigate the failurephenomenon [4ndash7] the deformation behavior [3 7ndash9] andEarth pressure distributions [9 10] of the RSW Inclined Earthretaining (IER) structure is developed in order to improve themechanical properties of the existing Earth retaining method

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 8894601 16 pageshttpsdoiorg10115520208894601

IER consists of three main structures front support backsupport and head binding and the back support is very effectivefor the reduction of the Earth pressure acting on the frontsupport and the lateral displacement of IER which has beenconfirmed by model tests [11 12] Assembled Earth Retainingwall (AER-wall) using back pile has been developed at PusanNational University Both cost and time have been significantlyreduced because AER-wall can be fabricated in a shop Also itsstability has been improved with a back-supporting beam re-ducing Earth pressure which has been confirmed by laboratorymodel tests and the lateral displacement of AER-wall signifi-cantly decreases with both inclined wall and back-supportingbeams [13] +e field model tests of AER-wall have beenperformed to confirm that the Earth pressure is considerablyreduced compared with the L-shaped retaining wall [14] Aprecast concrete double wall (PCDW) system is developed toimprove the productivity of conventional retaining wall [15]+e ARE-wall is composed of the PCDW system and retainingwall system which can contribute to securing integrity re-ducing the delay in construction and improving quality Anoverall process for themember design and construction stage ofthe ARE-wall system has been proposed and its improvementeffects are examined regarding various aspects in comparison tothe reinforced concrete method However no experimentalmethod has been used to determine the performance of theARE-wall

+e distribution of Earth pressure behind the cantileverretaining walls subjected to line loads has been predicted by acomparison between the conventional theories of Earthpressure and the finite element method [16] +e magnitudeand distribution of lateral Earth pressure of the cantileverretaining walls resting on clayey soil are studied by a series oftwo-dimensional plane-strain analyses and the finite ele-ment method [17] However the cantilever retaining wallcan be the most economical solution by adding relievingplatforms on the backfill side of the wall +e relievingplatforms have advantages of decreasing the lateral Earthpressure and increasing the overall stability of the retainingwall +e retaining wall is not a new type of construction incountries such as China Korea India and Russia Modeltests have been performed to determine the distribution ofthe Earth pressure and confirm the effect of decreasing thelateral Earth pressure on the retaining wall with relievingplatform [18ndash20] From the model tests comparisons be-tween the retaining wall with relieving platform and thecantilever retaining wall show that the reduction of thelateral Earth pressure and deformation of wall are indicatedclearly on the retaining wall with a relieving platform andthe overall stability is increased by the relieving platform[21] +e length and the location of the platform are the keyfactors influencing the lateral Earth pressure A sheet pileretaining wall is composed of a pile a retaining plate and arib pillar Its advantages include a small space for ar-rangement and no limitation on bearing capacity of thefoundation structure +e behavior of the contiguous boredpile retaining wall supporting system has been investigatedusing a physical model [22] and a series of plane-strainsmall-scale model tests on a piled retaining wall embeddedin sand under axial loads are performed in the laboratory

and the influence of the penetration depth pile stiffness andsand relative density on both ultimate axial capacity anddeformation behavior of the piled system has been evaluated[23]

Combining the advantages of the retaining wall withrelieving platforms and the sheet pile retaining wall thesheet pile wall with a relieving platform (shown in Figure 1)has been successfully used in various slope managementprojects in China +e retaining wall has the followingadvantages

(1) It has the advantages of the sheet pile retaining wallincluding a small space for arrangement good safetyand reliability and good durability

(2) +e Earth pressure behind the wall under theunloading board is reduced through the unloadingeffect of the unloading board

(3) +e unloading board provides a reverse bendingmoment to the rib pillars and piles therefore theinternal force distribution of the retaining wall tendsto be reasonable and the mechanical deformationcharacteristics of the retaining wall are optimized

(4) Due to the unloading effect of the unloading boardand its inverse bending moment to the wall theretaining wall is applicable to higher slope than thecantilever sheet pile retaining wall

(5) Compared with the reinforced soil retaining wall(RSW) the excavation space behind the wall is re-duced which has good adaptability to the site andhigh safety for long-term use

Currently both Chinese and international scholars andengineers have used simplified theoretical calculationmethods and numerical analysis to determine some pa-rameters and analyze the mechanical deformation prop-erties of the retaining structure+eoretical analysis has beenused to obtain the ratio between the reasonable unloadingboard buried depth and board width as well as the ratio ofheight between the upper wall and lower wall [24] Hu et al[25] developed the computational formula of the range valuefor unloading board width and computational formula of theminimum pile length Meanwhile the validity and credi-bility of computational formula for the minimum pile lengthwere verified through the data and example analysis Huet al [26] divided the sheet pile wall with a relieving platforminto loaded segment and anchored segment and developed aFEM numerical model to calculate the inner force anddeformation of the sheet pile with relieving platform and theeffectiveness of the calculation model was confirmed byusing FEM model and fielding monitoring data Hu et al[27] deduced the analytical formula for the deformation ofthe retaining wall based on elastic foundation beam methodand analyzed the influence of the diameter and length of pilethe proportional coefficient of foundation soil resistancecoefficient and the internal friction angle of the backfill onthe structural deformation +eir studies show that thelength of the unloading board has significant effective lowerand upper limit value

2 Advances in Civil Engineering

However there is no comprehensive and accurate cal-culation theory or method for the retaining wall structure+us this research conducted a model test study on the sheetpile wall with a relieving platform and provided a basis forthe design principles and calculation method of the retainingwall In this study the model pile box and the modelstructure of the sheet pile wall with a relieving platform weremade A test scheme was developed after determining themodel material model structure and size model loadingequipment and measurement system +is study found aseries of test results such as the Earth pressure behind thewall prepile resistance force the bending moment and thedeformation of rib pillars in the retaining wall +e analysisof the findings verified the credibility of the test model testdata and the test instrument A credibility test method wasthus provided for studying the mechanical and deformationcharacteristics of the sheet pile wall with a relieving platform

2 General Structure of Sheet Pile Wall with aRelieving Platform

Currently in China the sheet pile walls with the relievingplatform are generally used for retaining engineering andthey are ranging between 80m and 150m Figure 2 showsthe sheet pile wall structure with a relieving platform used inthe project with 12m support +is wall structure is used asthe prototype of the model testing +e mechanical pa-rameters of the retaining wall and characteristic parametersof the retaining wall structure are shown in Tables 1 and 2respectively

3 Similarity Coefficient of the Model

Using three similar theorems to calculate the similaritycoefficient λx of the same physical quantity in the prototypeand the model of the sheet pile wall with a relieving platform[28ndash32]

λx Xp

Xm (1)

In equation (1) x is any physical quantity the subscriptsldquoprdquo and ldquomrdquo represent the prototype and the model

respectively According to the catalogue of scaling laws [33]the theory of elasticity the theory of soil strength and a loadof sheet pile wall with a relieving platform and the similarrelationship of the main physical quantities are shown inTable 3 (the results are derived from Iai [34]) +e geometricsimilarity coefficient λ is 7 in this test Iai [34] studied thesimilarity relationship of each physical quantity in modeltest and the results showed that only the geometric simi-larity coefficient λ density similarity coefficient λρ andstrain similarity coefficient λε were independent in thephysical quantities in Table 3

4 Construction of the Test Model

41 Model Materials When soil materials are being se-lected the similarity coefficient λc of the soil specificgravity is made close to 1 in the prototype that is the

Counterfort

Pile foundation

Unloading board

Wall surface plate

Top beam

Figure 1 3D schematic diagram of the sheet pile wall with arelieving platform

Wall top or groundUpper wall plate

Lower wall column (plate)

39m

50m

70m

08m

90m

-12

0m

14m

Pile

Ground

Unloading board

Figure 2 +e cross section of sheet pile wall with a relievingplatform in a project

Table 1 Mechanical parameters of the sheet pile wall with therelieving platform

Items E (MPa) Μ ρ (kgm3) c (kPa) φ (deg)Pile foundation 280000 020 25000 mdash mdashTop beam 280000 020 25000 mdash mdashRib pillar 280000 020 25000 mdash mdashWall surface plate 280000 020 25000 mdash mdashUnloading board 280000 020 25000 mdash mdashFill soil (stone powder) 800 028 24000 10 350Soil between piles 300 030 18000 280 160

Advances in Civil Engineering 3

similarity coefficient λE of the elastic modulus is madeclose to 7 and the medium-coarse sand is selected as thefill soil and soil between piles in the model test A series ofphysical and mechanical tests including specific gravitytest the maximum and minimum dry density test directshear test particle separation test and water content testare completed in the geotechnical laboratory of CivilEngineering Department of Shenzhen University inChina +e physical and mechanical parameters of themedium-coarse sand are as shown in Table 4 +e gradingcurve is shown in Figure 3

Steel polymethyl methacrylate (PMMA) gypsum andfine-aggregate reinforced concrete are considered when themodel material for the retaining wall is selected +estructural material of the prototype retaining wall is thereinforced concrete as it is in an elastic state under normalworking conditions Owing to its characteristic of being easyto produce and simulate a steel is chosen as the modelmaterial for the retaining wall Corresponding to each part ofthe prototype structure the circular steel pipe pile is usedwhile the square steel pipe is applied in the pillar ribs +echannel steel and steel plates are applied in the unloadingboard

42 Model Structure Size

421 Size and Construction of the Model Test Box +eprototype retaining wall is 12m high the piles have 3m

spacing and the filling height is 12m +e horizontal widthof the prototype retaining wall is 125m Accordingly themodel test box is 20m wide and 4 piles are simulated +elongitudinal length of the test box is determined by thespatial dimension calculated using the sliding plane of theactive Earth pressure and the passive Earth pressure +erelationship between the prototype size and model size isshown in Table 5 and Figure 4

In this study the size of the model test box is 65m(length) times 20m (width) times 40m (height) +e real figure ofthe model test box is shown in Figure 5 Due to the highstructural model of the retaining wall the model box is fixedfirmly into the ground for easy testing and operation Fouranchor fixing bolts are prescrewed into the top of the modeltest box to secure the reaction frame

422 Size of Model Structure and Production According tothe characteristic parameters of the retaining wall in Table 2and the similarity relationship in Table 3 the characteristicparameters of the retaining wall structure are shown inTable 6

In the equivalent calculation several aspects should bestated [35]

(1) Assume that (EI)p and (EI)m are the actual stiffnessesof the prototype structure and model structure re-spectively while (EI)acutep and (EI)acutem are the stiffnessesof unit width in the prototype structure and model

Table 2 Characteristic parameters of the sheet pile wall with the relieving platform

Components Concreteno

Sectiondimension

(m)

Sectionmoment ofinertia (m4)

Stiffness(Nmiddotm2) (E)

Stiffness inunit width(Nmiddotm2m)

Calculativewidth (m) Remarks

Pilefoundation C25 Pile diameter

14 021 499 163E9 3Reinforcement ratio is

considered as the calculatingmoment of inertia

Rib pillar C25 08times11 005 149 467E8 3Upper base multiplied by thelower base for equivalent

calculationUnloadingboard C25 05times 30 003125 8758 292E8 3 +ickness multiplied by the

width

Top beam C25 16times 08 00683 1919 mdash mdash Rectangle length multipliedby the height

Wall surfaceplate C25 12times 03 00027 7568 252E8 3 Rectangle height multiplied

by the thickness

Table 3 +e similar relationship of the main physical quantities

Symbols Physical quantity Similarity relation (prototype model) Test valuel Length (geometry size) Λe 7ρ Density λρ 1q Load (area force) λλρ 7ε Strain λε 1σ Stress λλρ 7s Displacement λλε 7EI Flexural rigidity with unit width λ4λρλε 2401M Bending moment with unit width λ3λρ 343φ Internal friction angle of soil λφ 1


structure respectively +e following equation isshown in Table 3

(EI)primem (EI)primep

ρconcreteρsteel( 1113857λ41113872 1113873 (2)

(2) +e unit width of the model is 17 of the prototypewidth that is 3m7asymp 043m In order to expand themeasurement displacement and facilitate the

generating of the structural model the pile spacing inthe model is 06 meters

(3) +e unit width stiffness of a 5mm thick steel plate isnegligible compared to the unit width stiffness of thechannel steel

(4) In the equivalent calculation of the retainingplate the parameters of the wooden board are asfollows [36] Eboard 275 GPa and ρboard 600 kgm3

0

10

20

30

40

50

60

70

80

90

100

000100100100100010000Particle size (mm)

Soil

part

icle

qua

lity

perc

enta

gepa

ssin

g a p

artic

le si

ze

Sample ASample BSample C

Figure 3 Grading curve

Table 4 Physical and mechanical parameters of the medium-coarse sand

Items E (MPa) Μ ρd (kgm3) φ (deg) Specificgravity

Moisturecontent ()

Coefficient ofuniformity Cu Coefficient of curvature Cc

Medium-coarse sand 15 030 15910 358 2653 12 286 092

Table 5 +e relationship between the prototype size and model size

ItemsPile

length(m)

Height of theretaining wall

(m)

Horizontalwidth (m)

Longitudinal length(m)

RemarksLengthbeforethe pile

Lengthafter thepile

Prototype 120 120 125 (width of 4piles) mdash mdash +e longitudinal length of the model is calculated and

determined by the sand parametersModel 170 170 20 (width of 4piles) 375 275


+e front elevation drawing and profile drawing of themodel structure are shown in Figure 6 while the realfigure of the model structure is illustrated in Figure 7

43 Loading Equipment and MeasurementSystem of the Test Model

431 Loading Equipment of the Test Model In the modeltests the air pressure load is used to simulate the load on thetop of the wall +e loading equipment is shown in Figure 8+e test is undertaken among five levels from 10 kPa to50 kPa with each level increasing by 10 kPa

It is found that the air pressure load has two advantages(1) When the load is unloaded the load transmission isconsistent and continuous without impact (2) Its airpressure valve can be adjusted to maintain the load stabilityof each stage load +e magnitude of the change can becontrolled within the range of plusmn01 kPa

432 Measurement System +e layout of the selected Earthpressure measuring equipment is shown in Figure 9

+e test data present the Earth pressure in the upper andlower walls It is found that the measured Earth pressurebefore and after the pile foundation is the Earth pressure onthe pile not the average Earth pressure in the two piles +e

Wall height 4000

300

2000

300

300 3003750 2750

Wall height 2000

(a)

300

2000

1700

Top of sandfilling

P

Sand filling

Active failure surface

Top of sand fillingModel channel boundary

Passive failure surface

ψ = 358deg

45deg + ψ2

45deg ndash ψ2Model channel boundary

2000 17

0030

0

Model channel boundary42791 332209

D le 200189339 85661-D

3750 2750

ψ = 358deg

(b)

Figure 4 +e dimension of model test box (a) Planar graph (b) Profile drawing (the unit of the dimension is mm)

Anchor fixing bolts Anchor fixing bolts

Figure 5 +e real figure of model test box


conversion equation (3) is used to transform the measuredvalue

P1 P0d

b (3)

In equation (3) P0 is the measured Earth pressure beforeand after the pile P1 is the average Earth pressure in the twopiles d is the pile diameter and b is the pile spacing

+e strain gauges are set up in the maximal internal forceside of the pile and rib pillar in the retaining wall+e layoutsof strain gauges are shown in Figure 10 After measuring thestrain the moment at each measurement point of the pile iscalculated [37]

Mxz EIεy

(d2) (4)

In equation (4) εy is the compressive (tensile) strain atthe measurement point E is the elastic modulus of the pileand I is the moment of inertia of the cross section of the pile+e directions represented by x y and z are shown inFigure 11

By using the displacement measurement the dial indicatorwith a range of 30mm and an accuracy of 001mm is selectedWith the finite element method the maximum displacement ofthe top of the retaining wall is 208mm when it is in the mostunsafe environment (without the unloading board) Assumingthat the pile bottom is fixed the maximum displacement at the

Table 6 Characteristic parameters of retaining wall model structure

Components

Required flexuralrigidity with unitwidth (Nmiddotm2m)

(E)

Calculationwidth (m)

Sectionproperty ofmaterials

Sectiondimension ofmaterials (mm)

Selected flexuralrigidity with unit

width (Nmiddotm2m) (E)Remarks

Pile 6795 06 Circular steelpipe 159times 5 7205 Outer

diametertimes thickness

Rib pillar 1945 06 Square steelpipe 100times 25 2155 Outer


Unloadingboard 1225 06

Channel steeland steelplate

Channel10 + 5mm steel

plate1025 Small stiffness of channel

steel

Top beam 8195 mdash Square steelpipe 250times 5 9815 mdash

Retainingplate 1055 06 Wooden

board +ickness 36 1155+ickness 18mmoverlapped wooden

board

Square steel pipe100 times 25

10

Slot

Steel plate thickness 5

Wooden board thickness 18

Welding plate thickness 10

Continuous connectionSquare steel pipe 250 times 5

Steel pipe 159 times 5

530

300

300

350

300

300

1650

250

1500

100 600 600 600 1002000

(a)

700

100

850

250

150017

5034

0016

50

Support baseboardthickness 5


2M16

Steel pipe159 times 5

Square steel pipe 250 times 5 Continuous connection

Support baseboard thickness 8Wooden board thickness 18

Welding plate


10Equal leg angle steel 100 times 5

(b)

Figure 6 Front elevation drawing and profile drawing of model structure (a) Front elevation drawing (b) Profile drawing (the unit of thedimension mm)


top of the retaining wall is calculated as 144mm It is consistentwithin an environment with only one supported beam+erefore the meter of the dial gauge has a full scale of 30mm+e dial indicator is fixed by using the magnetic gauge seat andensuring that the extendable rods are tipped on the square steeltubular It is found that the retaining wall is deflected with theincreasing thickness of the sand layer Moreover the dial in-dicator can be used tomeasure the displacement of the retainingwall simultaneously At the time of testing there are ten hor-izontal displacement measuring points on the rib pillar Ten dialindicators are installed to measure the horizontal displacementof the retaining wall +e layout and number of displacementmeasurement points are shown in Figure 12

433 Data Acquisition and Processing System Earth pres-sure and strain data acquisition are equipped with the au-tomatic acquisition of artificial guards Moreover theautomatic collection box is equipped with an accumulatorand a module that automatically controls the measurementof the sensor within a specified time +e measurementresults are first saved in the vibrating wire sensor (as shownin Figure 13) which is connected to an external data col-lection box +en the automatic dynamic monitoring of thenetwork is implemented Finally the data acquisition system

software is used to aggregate data collected in various modesinto a database and further display and process taskswitching Measurement data is saved in an Excel spread-sheet for subsequent analysis and processing +e schematicdiagram of data transmission collection and processingswitching work is shown in Figure 14

5 Test Scheme

A total of 28 grouping model tests are conducted one grouptest without the unloading board 18 group comparison testswithout external loading and 9 group external load com-parison tests +e combination of tests is shown in Table 7and the parameters are shown in Figure 15

A retaining wall model test without the unloading boardis performed firstly +e test has four purposes First it isused to verify the validity and reliability of the test instru-ment Second it is known that the structure of the retainingwall without the unloading board is relatively simple +usthe accuracy of the measurement data of the retaining wallmodel is verified by comparing them with the results fromother theories +ird in comparison with the results of thetest model of the unloading board retaining wall theunloading effect of the unloading board is analyzed that is

Rib pillar

Top beam

Pile

(a)

Unloading board(channel steel + steel plate)

(b)

Figure 7 Real figure of model structure (a) Real figure 1 (b) Real figure 2

Reducingvalve

Inlet valve

PipeSnuffle valve

Air pressure gauge

Pressurized air bags

Airpressure

gauge

Reactionwoodenboard

Anchor fixing boltReaction frame (channel steel)

Aircompressor

Figure 8 Schematic diagram of air pressure loading


the unloading effect is established +e effect of theunloading board has mechanical and deformation charac-teristics +e retaining wall is analyzed at the end of the testFourth by analyzing all the issues involved in the test theexperience of conducting the test is reflected and summa-rized Based upon these the subsequent tests are completed+e test process is shown in Figure 16

6 Test Results and Discussion

61 Distribution of Earth Pressure +e Earth pressure be-hind the retaining wall and prepile resistance force withoutthe unloading board25 are shown in Figures 17 and 18Figure 17 shows that there is a linear increasing tendencywith the depth in the measured Earth pressure behind the

A bus (six cores)

ty08

ty09ty10

ty11ty12

ty13ty01ty02

ty03ty04ty05ty06

ty07

ty14ty15

ty16

Sand filling

ty17 ty18

1650

1750

90 310

380

450

120

250

250

250

150

310

160

160

200

170

500

1150

3400

250

250

440

130

630

50

Sand filling

Earth pressure cellData processor

Automatic collecting system

Computer

Data line

Data bus

Statements1 When the length of plate changes the layout of earth pressure cell position is not affected on some

plates (ty17 ty18)When the plate position changes earth pressure cell position change didnrsquot affect the upper lowerand pile bottom unloading boarde dimension unit in the figure is mm

2

3

50

Figure 9 +e layout of Earth pressure cell

Strain gauge before pileStrain gauge aer pileData processor

Automatic collectingsystemComputer

Data lineData bus

1650

1750

220

280 50

011

5025

034

0015

00

980

240

280

300

350

500

250

420

220

360

500

yb06

yb09yb10

yb07

yb08

yb01yb02

yb03

yb04

500yb05

yb01

yb06 yb16yb17yb09yb18yb10

yb19yb20

yb07

yb08

100 600 6002000

600 100

yb02

yb03

yb04

yb11yb12

yb13

yb14 Sandfilling

1650

1500

250

Statements1 Strain gauge position layout when plate length changed didnrsquot affect the plate (yb05)

Strain gauge position change when the plate position changed didnrsquot affect the upperlower and pile bottom unloading boarde dimension unit in the figure is mm

2

3

Figure 10 Strain gauge layout


retaining wall Moreover the measured Earth pressure be-hind the wall lies between Rankine Earth pressure and Earthpressure at rest showing that the soil behind the wall is keptin the progressive active failure state +e measured Earthpressure at the bottom of retaining wall is 133 times thecalculation value by Rankine theory and 082 times Earthpressure at rest

Figure 18 shows that the measured prepile resistanceforce tends to increase first and then decrease afterwardswith the depth It is found that the measured prepile re-sistance force at the bottom of retaining wall is close to zero(this is much less than theoretical calculation value byRankinersquos theory) +e measured prepile resistance force ofthe upper wall (above 06m depth) is close to CoulombrsquosEarth pressure +is indicates that the upper wall remains ina progressive passive limit state +e measured prepile re-sistance force of the lower wall (below 06m depth) is foundto be much less than the calculation value by Rankine Earthpressure +e measured prepile resistance force is close tothe calculation value by m method in ldquoJGJ 120ndash2012 J1412ndash2012 Technical Specifications for Retaining andProtection of Building Foundation Excavationsrdquo (Ministryof Housing and Urban-Rural Development of the PeoplersquosRepublic of China 2010) It indicates that the prepile re-sistance force can be approximated by using the m method

oprime

o y

x

z

Strain gaugeMxz

Figure 11 +e directions represented by x y and z

400

400

400

400

50

bf01

bf02

bf03

bf04

bf05

Sand filling

Sand filling

γ

γ

γ

γ

γ

Dial indicator

(a)

bf01bf02

bf03

bf04bf05

bf06bf07

bf08

bf09

bf10

Sandfilling

Sandfilling

1650

250

1500

100 600 6002000

600 100

(b)

Figure 12 External displacement measurement point layout of retaining wall (unit mm) (a) Side view drawing (b) Front elevationdrawing

Figure 13 +e vibrating wire sensor


+e present study found that the Earth pressure distri-bution measured before and behind the wall has a certainregularity+e reason is shown in Figure 19 In Figure 19 It isfound that there is a turning point on the position of thebottom of retaining wallrsquos pile foundation that is a zero-displacement point With the development of deformationwith the retaining wall structure the Earth pressure above thezero-displacement point behind the pile develops from thestatic Earth pressure to the active Earth pressure showing agradual active limit state Moreover the Earth pressure underthe zero-displacement point behind the pile develops fromstatic Earth pressure to passive Earth pressure +erefore the

Earth pressure measured by the Earth pressure cell H is thepassive Earth pressure and the Earth pressure measured bythe Earth pressure cell H is larger than the calculated value bythe Rankine theory +e Earth pressure above the zero-dis-placement point before the pile develops from static Earthpressure to passive Earth pressure showing a progressivelypassive limit state +e Earth pressure under the zero-dis-placement point before the pile changes from static Earthpressure to active Earth pressure In addition during theprocess of the turning of the pile it is found that the de-formation of the right sand at the bottom of the pile is smallor the deformation of the right sand cannot grasp the turning

Collection sowareprocessing data

Automaticcollection box Data processor

Surface concrete strain gauge (n)Earth pressure cell (n)

Figure 14 Schematic diagram of data transmission collection and processing switching work

Hprime = 175

H = 17

L

h

B

Sand filling

20

20

Air bag reservation

Square steel pipeLock beam

275375

Circular steel pipePile

Channel steelUnloading board

Square steel pipeColumn

Statement the dimension in the figure is m

Top of sand filling

Top of model box

Sand filling

Figure 15 Parameters figure for the combination of tests


deformation of the pile In other words there is a loosecontact between the pile and the sand resulting in a smallmeasurement of the Earth pressure unit N

62 Internal Force Distribution of the Retaining Wall +einternal force change of the retaining wall is largely reflectedin the bending moment of the retaining wall structure +ebending moment distribution curve of the retaining wall isshown in Figure 20 In Figure 20 it is found that the

measured bending moment value approximates the calcu-lated value by the m method and is larger than the bendingmoment value calculated by the finite difference methodDuring the model test the sand is layered 6 times in total Itis found that when the sand surface is flat the external loadgenerated by the human bodyrsquos own weight increasescausing the measured strain value to be greater than thestrain value calculated by the finite difference method+erefore the measuredmoment value is found to be greater

Table 7 Combination of tests

Grouping number H (m) B (m) H (m) BH hH Load at wall top q (kPa)1 170 0 170 0 mdash 02 170 04 06 024 035 03 170 04 09 024 053 04 170 04 12 024 070 05 170 05 06 030 035 06 170 05 09 030 053 07 170 05 12 030 070 08 170 06 06 035 035 09 170 06 09 035 053 010 170 06 12 035 070 011 170 08 06 047 035 012 170 08 09 047 053 013 170 08 12 047 070 014 170 10 06 059 035 015 170 10 09 059 053 016 170 10 12 059 070 017 170 12 06 070 035 018 170 12 09 070 053 019 170 12 12 070 070 020 170 04 06 024 035 102030405021 170 04 09 024 053 102030405022 170 04 12 024 070 102030405023 170 06 06 035 035 102030405024 170 06 09 035 053 102030405025 170 06 12 035 070 102030405026 170 10 06 059 035 102030405027 170 10 09 059 053 102030405028 170 10 12 059 070 1020304050Notes the meanings of B and h in the table are shown in Figure 15

Install retaining wallstructure model

Arrange the lowermeasurement instrument

Measure the initial value ofthe instrument

Instrument debugging andcalibration Fill sand to the ground

elevation

Arrange the upper measurement instrument andread the initial value of the instrument

Fill sand to the designelevation

Install unloading board andfill in sand to full load

Measure data until stabledata

Start the next test

Discharge sand and cleanthe model box

Figure 16 Flow chart of test


than the moment value calculated by the finite differencemethod

63 Deformation of the Retaining Wallrsquos Rib PillarsFigure 21 shows that the deformation measurements aremade on the two rib pillars of the retaining wall (pillar A ison the right side and pillar B is on the left side) It is foundthat the field measurement conditions limit the measure-ment resulting in the fact that only the measured values of

the left and right rib pillars are measured +e amount ofdeformation of the rib pillars on the retaining wall and thecalculated value of the finite difference method are shown inFigure 22

Figure 22 presents the following important findings

(1) +e entire retaining wall structure is externally in-clined +e ratio between the displacement of theretaining wallrsquos upper rib pillar at the top ∆x and ribpillar height H is 2512mm1650mm 152 +isvalue is greater than the value of sheet pile retaining

20 40 60 80 100 120 140 160 180Prepile resistance force (kPa)

Measured prepile resistance forceCalculated value by m methodRankine earth pressureCoulombrsquos earth pressureEarth pressure at rest

18

16

14

12

10

08

06

04

02

000

Dep

th (m

)

Figure 18+e prepile resistance force of the retaining wall withoutthe unloading board

35

30

25

20

15

10

05

00 0 5 10 15 20 25Earth pressure behind the wall (kPa)

Dep

th (m

)

Earth pressure behind the wallRankine earth pressureCoulombrsquos earth pressureEarth pressure at rest

17Ground line

Figure 17 Earth pressure behind the retaining wall without theunloading board

Earth pressure cell

Statements A B C hellip N are the number of Earth pressure cells

A

B

N H

G

F

E

D

C

IJ

LK

M

Sand filling

Wall turning point

Active Earth pressure area

Dividing line between active Earth pressure andpassive Earth pressure areas

Passive Earth pressure area



Sand filling

Figure 19 Interpretation drawing of Earth pressure distribution ofthe retaining wall

35

30

25

20

15

10

05

00

Dep

th (m

)

Moment value calculated by measured strainMoment value calculated by m methodMoment value calculated by finite difference method

Moment (kNm)0 1 2 3 4 5 6 7 8

Figure 20 Bending moment distribution curve of the retainingwall


wallrsquos displacement however it is less than 1 ofretaining wallrsquos cantilever length required by ldquoTB10025ndash2006 J 127ndash2006 Code for Design onRetaining Structures of Railway Subgraderdquo (Ministryof Railways of the Peoplersquos Republic of China 2006)namely ∆xHle 10 +is results in a failedretaining wall In summary this finding indicatesthat when the upper part of the retaining wall has nounloading board the entire retaining wall structurefails

(2) +e deformation of pillar A is slightly larger than thatof pillar B which indicates that numerous buriedinstrument wires below pillar A force the sand fillingof pillar A to be loose In addition it is found that theexternal displacement of pillar A is greater than thedisplacement of pillar B

(3) Owing to the 6 times (in total) of layers of sand in themodel test the measured deformation in the retainingwallrsquos upper rib pillar is greater than the calculatedresults using the finite difference method +e sum ofthe incremental results of the six times monitoring isconsidered as the total displacement (the external load

has to be generated by the bodyrsquos self-weight each timeand the sand surface is flattened) +is total displace-ment is then calculated by using the finite differencemethod from the start to the equilibrium increment foraccurate measurement +erefore it is found that thedisplacement is greater than the displacement calculatedby the finite difference method

7 Conclusions

Based on the studies presented in this study the credibilityand validity of the self-made model of the retaining wall thetest instrument and the test data are verified and the fol-lowing five contributions to the field can be extracted

(1) +e measured Earth pressure behind the sheet pilewall with relieving platform without the unloadingboard has a strong linear correlation with its depth+is value lies between the values of Rankine Earthpressure and Earth pressure at rest and the soil behindthe wall remains in a progressive active failure state

(2) +e measured prepile resistance force of the upperwall (above 06m depth) is close to the CoulombrsquosEarth pressure and that of the lower wall (below06m depth) is much less than the calculation valueby Rankine Earth pressure Moreover the measuredprepile resistance force can be used for approximatecalculation by the m method

(3) +ere is a zero-displacement point on the pilebottom of the retaining wall with the develop-ment of deformation with the retaining wallstructure the front and back zones of the pile aredivided into the passive Earth pressure zone andactive Earth pressure zone by the zero-displace-ment point

(4) +e measured moment value of the sheet pile wallwith relieving platform without the unloading boardis close to the value calculated by the m method andthe m method can be used for the approximatecalculation

(5) +e ratio between the displacement of the upper ribpillars in the retaining wall and its height is greaterthan the corresponding standard requirement in-dicating that the retaining wall without theunloading board has failed +us the unloadingboard should be installed to exert the unloadingeffect and improve the stress and deformationcharacteristics of the retaining wall

Nomenclature

E Elastic modulus of the material in the retainingwall structure

μ Poissonrsquos ratio of the material in the retaining wallstructure

ρ Natural density of the material in the retainingwall structure

c Cohesive force of soil

Pillar B Pillar A

Figure 21 Position of pillar A and pillar B and embedded linediagram of the instrument

20

18

16

14

12

10

08

06

04

02

00

24 22 20 18 16 14 12 10Deformation of rib pillar (mm)

Hei

ght o

f rib

pill

ar (m

)

Measured deformation value of pillar AMeasured deformation value of pillar BCalculated value by finite difference method

Figure 22 +e deformation curve of the retaining wallrsquos upper ribpillar


φ Internal friction angle of soilρd Dry density of the medium-coarse sandλ Similarity coefficient of the same physical

quantity in the prototype and model of theretaining wall

xp Any physical quantity in the prototype of theretaining wall

xm Any physical quantity in the model of theretaining wall

λε Similarity coefficient of the strain of the materialλρ Similarity coefficient of the natural density of the

materialλc Similarity coefficient of material specific gravity or

bulk densityλφ Similarity coefficient of the internal friction angle

of the materialε Strain of the structureq Area force at wall topσ Stress of the structures Displacement of the structureEI Unit flexural stiffness of the structureCu Coefficient of uniformity of the soilCc Coefficient of curvature of the soil(EI)p Actual stiffness of the prototype structure(EI)m Actual stiffness of the model structure(EI)rsquop Stiffness of unit width in the prototype structure(EI)rsquom Stiffness of unit width in the model structureρSoilρSand

Natural density of the soil and sand

ρConcrete Natural density of the concrete materialρSteel Natural density of the steel materialEboard Elastic modulus of the wooden board in themodel

structureρboard Natural density of the wooden board in the model

structureP0 Measured Earth pressure before and after the pileP1 Average Earth pressure within two pilesd Pile diameterb Pile spacingM Moment at each measurement point of the pileεy Compressive (tensile) strain at the measurement

pointI Moment of inertia of cross section of the pileH Height of the retaining wall or rib pillarh Buried depth of the unloading boardB Width of the unloading boardx Displacement of the retaining wallrsquos upper rib

pillar at the top

Data Availability

+e data and figures used to support the findings of thisstudy are included within the article

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the National Natural ScienceFoundation of China (no 51678017) the National Key RampDProgram of China (no 2018YFD1100902-1) and the KeyScientific Research Projects of Henan Provincial Collegesand Universities (no 17A560002) in China +e authorswould like to express their gratitude to these financialsupports

References

[1] G M Sabnis H G Harris R N White et al ldquoStructuralmodeling and experimental techniquesrdquo Journal of DynamicSystems Measurement and Control vol 105 no 7 Article ID307 1983

[2] J J Yang Similarity eory and Structural Modeling Exper-iment Wuhan University of Technology Press WuhanChina 2005

[3] J K Young S J Hyuk and J L Yong ldquoBehaviour analysis ofreinforced soil retaining wall according to laboratory scaletestrdquo Applied Sciences vol 10 no 3 Article ID 901 2020

[4] K S Wong B B Broms and B Chandrasekaran ldquoFailuremodes at model tests of a geotextile reinforced wallrdquo Geo-textiles and Geomembranes vol 13 no 6-7 pp 475ndash4931994

[5] C S Yoo H S Jung S S Jeon et al ldquoFailure mechanism ofgeosynthetic reinforced segmental retaining wall in tieredconfiguration using reduced-scale model testsrdquo Journal of theKorean Geotechnical Society vol 21 pp 65ndash77 2005

[6] R H Chen and Y M Chiu ldquoModel tests of geocell retainingstructuresrdquo Geotextiles and Geomembranes vol 26 no 1pp 56ndash70 2008

[7] C Z Xiao Q Q Chen and J Han ldquoExperimental study ofperformance of geogrid-reinforced retaining wall subjected toload from strip foundation at the top surface of wallrdquo Rockand Soil Mechanics vol 34 no 6 pp 1586ndash1592 2013

[8] J S Ki W H Rew S K Kim and B S Chun ldquoA behavior ofcurve section of reinforced retaining wall by model testrdquoJournal of e Korean Society of Civil Engineers vol 32no 6C pp 249ndash257 2012

[9] L H Li C D Yu H L Xiao et al ldquoExperimental study on thereinforced fly ash and sand retaining wall under static loadrdquoConstruction and Building Materials vol 248 no 10 ArticleID 118678 2020

[10] H Wang G Yang Z Wang and W Liu ldquoStatic structuralbehavior of geogrid reinforced soil retaining walls with adeformation buffer zonerdquo Geotextiles and Geomembranesvol 48 no 3 pp 374ndash379 2020

[11] D-U Jeong J-C Im J-W Yoo M-S Seo Y-M Koo andS-J Kim ldquoAn experimental study on the inclined earthretaining structure in clayrdquo Journal of the Korean GeotechnicalSociety vol 29 no 6 pp 63ndash75 2013

[12] M-S Seo J-C Im D-U Jeong J-W Yoo Y-M Koo andG-H Kim ldquoAn experimental study on the stability of inclinedearth retainingrdquo Journal of the Korean Geotechnical Societyvol 28 no 12 pp 99ndash110 2012

[13] J-W Yoo J-C Im S-P Hwang C-Y Kim J-H Choi andH-S Kim ldquoAn experimental study on the stability of as-sembled earth retaining wall in sandy groundrdquo Journal of theKorean Geotechnical Society vol 32 no 2 pp 43ndash52 2016

[14] H Kim J-C Im J Choi and M Seo ldquoMechanical effects ofback supporting beam of assembled earth retaining wall on


field model tests resultsrdquo Journal of the Korean Society of CivilEngineers vol 37 no 2 pp 343ndash355 2017

[15] S Kim D E Lee Y Kim et al ldquoDevelopment and applicationof precast concrete double wall system to improve produc-tivity of retaining wall constructionrdquo Sustainability vol 12no 8 Article ID 3454 2020

[16] F A Salman M Y Fattah S M Shirazi et al ldquoComparativestudy on earth pressure distribution behind retaining wallssubjected to line loadsrdquo Scientific Research and Essays vol 6pp 2228ndash2244 2011

[17] F A Salman M Y Fattah and D K Sabre ldquoLong termbehaviour of a retaining wall resting on clayey soilrdquo Inter-national Journal of the Physical Sciences vol 6 pp 730ndash7452011

[18] W-K Yoo B-I Kim I-J Moon and Y-S Park ldquoCom-parison of the lateral earth pressure on the retaining wall withthe relieving platform by model test and numerical analysisrdquoJournal of the Korea Academia-Industrial Cooperation Societyvol 13 no 5 pp 2382ndash2389 2012

[19] I-J Moon B-I Kim W-K Yoo and Y-S Park ldquoModel testsfor measurement of lateral earth pressure on retaining wallwith the relieving platform using jumoonjin sandrdquo Journal ofthe Korea Academia-Industrial Cooperation Society vol 14no 11 pp 5923ndash5929 2013

[20] H F Shehata ldquoUse of retaining walls with relief shelves as aneconomic solutionrdquo in Proceedings of the Advances in Nu-merical and Experimental Analysis of Transportation Geo-materials and Geosystems for Sustainable InfrastructureFourth Geo-China International Conference ASCE Shan-dong China pp 82ndash90 July 2016

[21] I Kim W K Yoo M R Yang et al ldquoModel test study on theearth pressure of the retaining wall with the relieving plat-formrdquo Journal of Korean Society of Civil Engineers vol 32no 1 pp 27ndash35 2012

[22] A Eslami and J Bazaz ldquoStudy of bored pile retaining wallusing physical modelingrdquo International Journal Civil Envi-ronmental Structure Construction Architecture Engineeringvol 9 no 1 pp 15ndash18 2015

[23] W R Azzam and A Z Elwakil ldquoPerformance of axiallyloaded-piled retaining wall experimental and numericalanalysisrdquo International Journal of Geomechanics vol 17no 2 Article ID 04016049 2017

[24] Y C Liu ldquo+emodel test research on pile-supported relievingretaining wallrdquo MS +esis China Academy of RailwaySciences Beijing China 2010

[25] R H Hu G N Liu and X H Pan ldquoParameters determi-nation of unloading board and pile length of sheet pile wallwith relieving platformrdquo Railway Engineering vol 11pp 74ndash77 2011

[26] Y L Hu G N Liu and Y M Zhao ldquoCalculation method ofdeformation and inner force of a sheet pile wall with relievingplatformrdquo in e Proceeding of Fourth International Con-ference on Transportation Engineering 2013 (ICTE 2013)ASCE Chengdu China pp 172ndash179 2013

[27] Y L Hu G N Liu and Y M Zhao ldquoCalculation on internalforce and deformation of sheet pile wall with relievingplatformrdquo Subgrade Engineering vol 4 pp 70ndash75 2013

[28] X H Chen Structural Modeling Experiment of Brittle Ma-terial China Water amp Power Press Beijing China 1984

[29] J H Cui Geomechanical Model Test Method and Applicationof High Arch Dam China Water amp Power Press BeijingChina 2008

[30] X S Liu Model Test and Dynamic Analysis of Large ShakingTable for Concrete Face Dam China Water amp Power PressBeijing China 2005

[31] W Z Yuan Similarity eory and Statical Mode TestSouthwest Jiaotong University Press Chengdu China 1998

[32] H Heinz Model Analysis of Structures Van NostrandReinhold Company New York NY USA 1974

[33] J Garnier C Gaudin S M Springman et al ldquoCatalogue ofscaling laws and similitude questions in geotechnical cen-trifugemodellingrdquo International Journal of Physical Modellingin Geotechnics vol 7 no 3 pp 01ndash23 2007

[34] S Iai ldquoSimilitude for shaking table tests on soil-structure-fluidmodel in 1g gravitational fieldrdquo Soils and Foundations vol 29no 1 pp 105ndash118 1989

[35] R H Hu ldquoStudy on the mechanical behavior and failuremechanism for sheet pile wall with relieving platformrdquo PhD+esis China Academy of Railway Sciences Beijing China2011

[36] G Y Li Y S He Y Q Tao et al Latest Practical HardwareManual (Revised Edition) Guangdong Science and Tech-nology Press Beijing China 2011

[37] X F Sun Material Mechanics China Science Publishing ampMedia Ltd Beijing China 2009


IER consists of three main structures front support backsupport and head binding and the back support is very effectivefor the reduction of the Earth pressure acting on the frontsupport and the lateral displacement of IER which has beenconfirmed by model tests [11 12] Assembled Earth Retainingwall (AER-wall) using back pile has been developed at PusanNational University Both cost and time have been significantlyreduced because AER-wall can be fabricated in a shop Also itsstability has been improved with a back-supporting beam re-ducing Earth pressure which has been confirmed by laboratorymodel tests and the lateral displacement of AER-wall signifi-cantly decreases with both inclined wall and back-supportingbeams [13] +e field model tests of AER-wall have beenperformed to confirm that the Earth pressure is considerablyreduced compared with the L-shaped retaining wall [14] Aprecast concrete double wall (PCDW) system is developed toimprove the productivity of conventional retaining wall [15]+e ARE-wall is composed of the PCDW system and retainingwall system which can contribute to securing integrity re-ducing the delay in construction and improving quality Anoverall process for themember design and construction stage ofthe ARE-wall system has been proposed and its improvementeffects are examined regarding various aspects in comparison tothe reinforced concrete method However no experimentalmethod has been used to determine the performance of theARE-wall

+e distribution of Earth pressure behind the cantileverretaining walls subjected to line loads has been predicted by acomparison between the conventional theories of Earthpressure and the finite element method [16] +e magnitudeand distribution of lateral Earth pressure of the cantileverretaining walls resting on clayey soil are studied by a series oftwo-dimensional plane-strain analyses and the finite ele-ment method [17] However the cantilever retaining wallcan be the most economical solution by adding relievingplatforms on the backfill side of the wall +e relievingplatforms have advantages of decreasing the lateral Earthpressure and increasing the overall stability of the retainingwall +e retaining wall is not a new type of construction incountries such as China Korea India and Russia Modeltests have been performed to determine the distribution ofthe Earth pressure and confirm the effect of decreasing thelateral Earth pressure on the retaining wall with relievingplatform [18ndash20] From the model tests comparisons be-tween the retaining wall with relieving platform and thecantilever retaining wall show that the reduction of thelateral Earth pressure and deformation of wall are indicatedclearly on the retaining wall with a relieving platform andthe overall stability is increased by the relieving platform[21] +e length and the location of the platform are the keyfactors influencing the lateral Earth pressure A sheet pileretaining wall is composed of a pile a retaining plate and arib pillar Its advantages include a small space for ar-rangement and no limitation on bearing capacity of thefoundation structure +e behavior of the contiguous boredpile retaining wall supporting system has been investigatedusing a physical model [22] and a series of plane-strainsmall-scale model tests on a piled retaining wall embeddedin sand under axial loads are performed in the laboratory

and the influence of the penetration depth pile stiffness andsand relative density on both ultimate axial capacity anddeformation behavior of the piled system has been evaluated[23]

Combining the advantages of the retaining wall withrelieving platforms and the sheet pile retaining wall thesheet pile wall with a relieving platform (shown in Figure 1)has been successfully used in various slope managementprojects in China +e retaining wall has the followingadvantages

(1) It has the advantages of the sheet pile retaining wallincluding a small space for arrangement good safetyand reliability and good durability

(2) +e Earth pressure behind the wall under theunloading board is reduced through the unloadingeffect of the unloading board

(3) +e unloading board provides a reverse bendingmoment to the rib pillars and piles therefore theinternal force distribution of the retaining wall tendsto be reasonable and the mechanical deformationcharacteristics of the retaining wall are optimized

(4) Due to the unloading effect of the unloading boardand its inverse bending moment to the wall theretaining wall is applicable to higher slope than thecantilever sheet pile retaining wall

(5) Compared with the reinforced soil retaining wall(RSW) the excavation space behind the wall is re-duced which has good adaptability to the site andhigh safety for long-term use

Currently both Chinese and international scholars andengineers have used simplified theoretical calculationmethods and numerical analysis to determine some pa-rameters and analyze the mechanical deformation prop-erties of the retaining structure+eoretical analysis has beenused to obtain the ratio between the reasonable unloadingboard buried depth and board width as well as the ratio ofheight between the upper wall and lower wall [24] Hu et al[25] developed the computational formula of the range valuefor unloading board width and computational formula of theminimum pile length Meanwhile the validity and credi-bility of computational formula for the minimum pile lengthwere verified through the data and example analysis Huet al [26] divided the sheet pile wall with a relieving platforminto loaded segment and anchored segment and developed aFEM numerical model to calculate the inner force anddeformation of the sheet pile with relieving platform and theeffectiveness of the calculation model was confirmed byusing FEM model and fielding monitoring data Hu et al[27] deduced the analytical formula for the deformation ofthe retaining wall based on elastic foundation beam methodand analyzed the influence of the diameter and length of pilethe proportional coefficient of foundation soil resistancecoefficient and the internal friction angle of the backfill onthe structural deformation +eir studies show that thelength of the unloading board has significant effective lowerand upper limit value







λx Xp

Xm (1)





Counterfort

Pile foundation

Unloading board

Wall surface plate

Top beam




39m

50m

70m

08m

90m

-12

0m

14m

Pile

Ground

Unloading board
















Sectiondimension

(m)










width



by the thickness











0

10

20

30

40

50

60

70

80

90

100

000100100100100010000Particle size (mm)

Soil

part

icle

qua

lity

perc

enta

gepa

ssin

g a p

artic

le si

ze





Moisturecontent ()




ItemsPile

length(m)


(m)

Horizontalwidth (m)



Lengthafter thepile










Wall height 4000

300

2000

300

300 3003750 2750

Wall height 2000

(a)

300

2000

1700

Top of sandfilling

P

Sand filling




ψ = 358deg

45deg + ψ2


2000 17

0030

0


D le 200189339 85661-D

3750 2750

ψ = 358deg

(b)






P1 P0d

b (3)



Mxz EIεy

(d2) (4)




Components


(E)














steel




board


10

Slot






530

300

300

350

300

300

1650

250

1500

100 600 600 600 1002000

(a)

700

100

850

250

150017

5034

0016

50



2M16




Welding plate



(b)






5 Test Scheme



Rib pillar

Top beam

Pile

(a)


(b)


Reducingvalve

Inlet valve

PipeSnuffle valve

Air pressure gauge


Airpressure

gauge

Reactionwoodenboard


Aircompressor






A bus (six cores)

ty08

ty09ty10

ty11ty12

ty13ty01ty02

ty03ty04ty05ty06

ty07

ty14ty15

ty16

Sand filling

ty17 ty18

1650

1750

90 310

380

450

120

250

250

250

150

310

160

160

200

170

500

1150

3400

250

250

440

130

630

50

Sand filling



Computer

Data line

Data bus



2

3

50




Data lineData bus

1650

1750

220

280 50

011

5025

034

0015

00

980

240

280

300

350

500

250

420

220

360

500

yb06

yb09yb10

yb07

yb08

yb01yb02

yb03

yb04

500yb05

yb01


yb19yb20

yb07

yb08

100 600 6002000

600 100

yb02

yb03

yb04

yb11yb12

yb13

yb14 Sandfilling

1650

1500

250



2

3





oprime

o y

x

z

Strain gaugeMxz


400

400

400

400

50

bf01

bf02

bf03

bf04

bf05

Sand filling

Sand filling

γ

γ

γ

γ

γ

Dial indicator

(a)

bf01bf02

bf03

bf04bf05

bf06bf07

bf08

bf09

bf10

Sandfilling

Sandfilling

1650

250

1500

100 600 6002000

600 100

(b)










Hprime = 175

H = 17

L

h

B

Sand filling

20

20

Air bag reservation


275375





Top of sand filling

Top of model box

Sand filling












elevation





Start the next test











18

16

14

12

10

08

06

04

02

000

Dep

th (m

)


35

30

25

20

15

10

05


Dep

th (m

)


17Ground line


Earth pressure cell


A

B

N H

G

F

E

D

C

IJ

LK

M

Sand filling

Wall turning point






Sand filling


35

30

25

20

15

10

05

00

Dep

th (m

)


Moment (kNm)0 1 2 3 4 5 6 7 8







7 Conclusions







Nomenclature





Pillar B Pillar A


20

18

16

14

12

10

08

06

04

02

00


Hei

ght o

f rib

pill

ar (m

)

















pillar at the top

Data Availability




Acknowledgments


References














































λx Xp

Xm (1)





Counterfort

Pile foundation

Unloading board

Wall surface plate

Top beam




39m

50m

70m

08m

90m

-12

0m

14m

Pile

Ground

Unloading board
















Sectiondimension

(m)










width



by the thickness











0

10

20

30

40

50

60

70

80

90

100

000100100100100010000Particle size (mm)

Soil

part

icle

qua

lity

perc

enta

gepa

ssin

g a p

artic

le si

ze





Moisturecontent ()




ItemsPile

length(m)


(m)

Horizontalwidth (m)



Lengthafter thepile










Wall height 4000

300

2000

300

300 3003750 2750

Wall height 2000

(a)

300

2000

1700

Top of sandfilling

P

Sand filling




ψ = 358deg

45deg + ψ2


2000 17

0030

0


D le 200189339 85661-D

3750 2750

ψ = 358deg

(b)






P1 P0d

b (3)



Mxz EIεy

(d2) (4)




Components


(E)














steel




board


10

Slot






530

300

300

350

300

300

1650

250

1500

100 600 600 600 1002000

(a)

700

100

850

250

150017

5034

0016

50



2M16




Welding plate



(b)






5 Test Scheme



Rib pillar

Top beam

Pile

(a)


(b)


Reducingvalve

Inlet valve

PipeSnuffle valve

Air pressure gauge


Airpressure

gauge

Reactionwoodenboard


Aircompressor






A bus (six cores)

ty08

ty09ty10

ty11ty12

ty13ty01ty02

ty03ty04ty05ty06

ty07

ty14ty15

ty16

Sand filling

ty17 ty18

1650

1750

90 310

380

450

120

250

250

250

150

310

160

160

200

170

500

1150

3400

250

250

440

130

630

50

Sand filling



Computer

Data line

Data bus



2

3

50




Data lineData bus

1650

1750

220

280 50

011

5025

034

0015

00

980

240

280

300

350

500

250

420

220

360

500

yb06

yb09yb10

yb07

yb08

yb01yb02

yb03

yb04

500yb05

yb01


yb19yb20

yb07

yb08

100 600 6002000

600 100

yb02

yb03

yb04

yb11yb12

yb13

yb14 Sandfilling

1650

1500

250



2

3





oprime

o y

x

z

Strain gaugeMxz


400

400

400

400

50

bf01

bf02

bf03

bf04

bf05

Sand filling

Sand filling

γ

γ

γ

γ

γ

Dial indicator

(a)

bf01bf02

bf03

bf04bf05

bf06bf07

bf08

bf09

bf10

Sandfilling

Sandfilling

1650

250

1500

100 600 6002000

600 100

(b)










Hprime = 175

H = 17

L

h

B

Sand filling

20

20

Air bag reservation


275375





Top of sand filling

Top of model box

Sand filling












elevation





Start the next test











18

16

14

12

10

08

06

04

02

000

Dep

th (m

)


35

30

25

20

15

10

05


Dep

th (m

)


17Ground line


Earth pressure cell


A

B

N H

G

F

E

D

C

IJ

LK

M

Sand filling

Wall turning point






Sand filling


35

30

25

20

15

10

05

00

Dep

th (m

)


Moment (kNm)0 1 2 3 4 5 6 7 8







7 Conclusions







Nomenclature





Pillar B Pillar A


20

18

16

14

12

10

08

06

04

02

00


Hei

ght o

f rib

pill

ar (m

)

















pillar at the top

Data Availability




Acknowledgments


References




















































Sectiondimension

(m)










width



by the thickness











0

10

20

30

40

50

60

70

80

90

100

000100100100100010000Particle size (mm)

Soil

part

icle

qua

lity

perc

enta

gepa

ssin

g a p

artic

le si

ze





Moisturecontent ()




ItemsPile

length(m)


(m)

Horizontalwidth (m)



Lengthafter thepile










Wall height 4000

300

2000

300

300 3003750 2750

Wall height 2000

(a)

300

2000

1700

Top of sandfilling

P

Sand filling




ψ = 358deg

45deg + ψ2


2000 17

0030

0


D le 200189339 85661-D

3750 2750

ψ = 358deg

(b)






P1 P0d

b (3)



Mxz EIεy

(d2) (4)




Components


(E)














steel




board


10

Slot






530

300

300

350

300

300

1650

250

1500

100 600 600 600 1002000

(a)

700

100

850

250

150017

5034

0016

50



2M16




Welding plate



(b)






5 Test Scheme



Rib pillar

Top beam

Pile

(a)


(b)


Reducingvalve

Inlet valve

PipeSnuffle valve

Air pressure gauge


Airpressure

gauge

Reactionwoodenboard


Aircompressor






A bus (six cores)

ty08

ty09ty10

ty11ty12

ty13ty01ty02

ty03ty04ty05ty06

ty07

ty14ty15

ty16

Sand filling

ty17 ty18

1650

1750

90 310

380

450

120

250

250

250

150

310

160

160

200

170

500

1150

3400

250

250

440

130

630

50

Sand filling



Computer

Data line

Data bus



2

3

50




Data lineData bus

1650

1750

220

280 50

011

5025

034

0015

00

980

240

280

300

350

500

250

420

220

360

500

yb06

yb09yb10

yb07

yb08

yb01yb02

yb03

yb04

500yb05

yb01


yb19yb20

yb07

yb08

100 600 6002000

600 100

yb02

yb03

yb04

yb11yb12

yb13

yb14 Sandfilling

1650

1500

250



2

3





oprime

o y

x

z

Strain gaugeMxz


400

400

400

400

50

bf01

bf02

bf03

bf04

bf05

Sand filling

Sand filling

γ

γ

γ

γ

γ

Dial indicator

(a)

bf01bf02

bf03

bf04bf05

bf06bf07

bf08

bf09

bf10

Sandfilling

Sandfilling

1650

250

1500

100 600 6002000

600 100

(b)










Hprime = 175

H = 17

L

h

B

Sand filling

20

20

Air bag reservation


275375





Top of sand filling

Top of model box

Sand filling












elevation





Start the next test











18

16

14

12

10

08

06

04

02

000

Dep

th (m

)


35

30

25

20

15

10

05


Dep

th (m

)


17Ground line


Earth pressure cell


A

B

N H

G

F

E

D

C

IJ

LK

M

Sand filling

Wall turning point






Sand filling


35

30

25

20

15

10

05

00

Dep

th (m

)


Moment (kNm)0 1 2 3 4 5 6 7 8







7 Conclusions







Nomenclature





Pillar B Pillar A


20

18

16

14

12

10

08

06

04

02

00


Hei

ght o

f rib

pill

ar (m

)

















pillar at the top

Data Availability




Acknowledgments


References
















































0

10

20

30

40

50

60

70

80

90

100

000100100100100010000Particle size (mm)

Soil

part

icle

qua

lity

perc

enta

gepa

ssin

g a p

artic

le si

ze





Moisturecontent ()




ItemsPile

length(m)


(m)

Horizontalwidth (m)



Lengthafter thepile










Wall height 4000

300

2000

300

300 3003750 2750

Wall height 2000

(a)

300

2000

1700

Top of sandfilling

P

Sand filling




ψ = 358deg

45deg + ψ2


2000 17

0030

0


D le 200189339 85661-D

3750 2750

ψ = 358deg

(b)






P1 P0d

b (3)



Mxz EIεy

(d2) (4)




Components


(E)














steel




board


10

Slot






530

300

300

350

300

300

1650

250

1500

100 600 600 600 1002000

(a)

700

100

850

250

150017

5034

0016

50



2M16




Welding plate



(b)






5 Test Scheme



Rib pillar

Top beam

Pile

(a)


(b)


Reducingvalve

Inlet valve

PipeSnuffle valve

Air pressure gauge


Airpressure

gauge

Reactionwoodenboard


Aircompressor






A bus (six cores)

ty08

ty09ty10

ty11ty12

ty13ty01ty02

ty03ty04ty05ty06

ty07

ty14ty15

ty16

Sand filling

ty17 ty18

1650

1750

90 310

380

450

120

250

250

250

150

310

160

160

200

170

500

1150

3400

250

250

440

130

630

50

Sand filling



Computer

Data line

Data bus



2

3

50




Data lineData bus

1650

1750

220

280 50

011

5025

034

0015

00

980

240

280

300

350

500

250

420

220

360

500

yb06

yb09yb10

yb07

yb08

yb01yb02

yb03

yb04

500yb05

yb01


yb19yb20

yb07

yb08

100 600 6002000

600 100

yb02

yb03

yb04

yb11yb12

yb13

yb14 Sandfilling

1650

1500

250



2

3





oprime

o y

x

z

Strain gaugeMxz


400

400

400

400

50

bf01

bf02

bf03

bf04

bf05

Sand filling

Sand filling

γ

γ

γ

γ

γ

Dial indicator

(a)

bf01bf02

bf03

bf04bf05

bf06bf07

bf08

bf09

bf10

Sandfilling

Sandfilling

1650

250

1500

100 600 6002000

600 100

(b)










Hprime = 175

H = 17

L

h

B

Sand filling

20

20

Air bag reservation


275375





Top of sand filling

Top of model box

Sand filling












elevation





Start the next test











18

16

14

12

10

08

06

04

02

000

Dep

th (m

)


35

30

25

20

15

10

05


Dep

th (m

)


17Ground line


Earth pressure cell


A

B

N H

G

F

E

D

C

IJ

LK

M

Sand filling

Wall turning point






Sand filling


35

30

25

20

15

10

05

00

Dep

th (m

)


Moment (kNm)0 1 2 3 4 5 6 7 8







7 Conclusions







Nomenclature





Pillar B Pillar A


20

18

16

14

12

10

08

06

04

02

00


Hei

ght o

f rib

pill

ar (m

)

















pillar at the top

Data Availability




Acknowledgments


References















































Wall height 4000

300

2000

300

300 3003750 2750

Wall height 2000

(a)

300

2000

1700

Top of sandfilling

P

Sand filling




ψ = 358deg

45deg + ψ2


2000 17

0030

0


D le 200189339 85661-D

3750 2750

ψ = 358deg

(b)






P1 P0d

b (3)



Mxz EIεy

(d2) (4)




Components


(E)














steel




board


10

Slot






530

300

300

350

300

300

1650

250

1500

100 600 600 600 1002000

(a)

700

100

850

250

150017

5034

0016

50



2M16




Welding plate



(b)






5 Test Scheme



Rib pillar

Top beam

Pile

(a)


(b)


Reducingvalve

Inlet valve

PipeSnuffle valve

Air pressure gauge


Airpressure

gauge

Reactionwoodenboard


Aircompressor






A bus (six cores)

ty08

ty09ty10

ty11ty12

ty13ty01ty02

ty03ty04ty05ty06

ty07

ty14ty15

ty16

Sand filling

ty17 ty18

1650

1750

90 310

380

450

120

250

250

250

150

310

160

160

200

170

500

1150

3400

250

250

440

130

630

50

Sand filling



Computer

Data line

Data bus



2

3

50




Data lineData bus

1650

1750

220

280 50

011

5025

034

0015

00

980

240

280

300

350

500

250

420

220

360

500

yb06

yb09yb10

yb07

yb08

yb01yb02

yb03

yb04

500yb05

yb01


yb19yb20

yb07

yb08

100 600 6002000

600 100

yb02

yb03

yb04

yb11yb12

yb13

yb14 Sandfilling

1650

1500

250



2

3





oprime

o y

x

z

Strain gaugeMxz


400

400

400

400

50

bf01

bf02

bf03

bf04

bf05

Sand filling

Sand filling

γ

γ

γ

γ

γ

Dial indicator

(a)

bf01bf02

bf03

bf04bf05

bf06bf07

bf08

bf09

bf10

Sandfilling

Sandfilling

1650

250

1500

100 600 6002000

600 100

(b)










Hprime = 175

H = 17

L

h

B

Sand filling

20

20

Air bag reservation


275375





Top of sand filling

Top of model box

Sand filling












elevation





Start the next test











18

16

14

12

10

08

06

04

02

000

Dep

th (m

)


35

30

25

20

15

10

05


Dep

th (m

)


17Ground line


Earth pressure cell


A

B

N H

G

F

E

D

C

IJ

LK

M

Sand filling

Wall turning point






Sand filling


35

30

25

20

15

10

05

00

Dep

th (m

)


Moment (kNm)0 1 2 3 4 5 6 7 8







7 Conclusions







Nomenclature





Pillar B Pillar A


20

18

16

14

12

10

08

06

04

02

00


Hei

ght o

f rib

pill

ar (m

)

















pillar at the top

Data Availability




Acknowledgments


References










































P1 P0d

b (3)



Mxz EIεy

(d2) (4)




Components


(E)














steel




board


10

Slot






530

300

300

350

300

300

1650

250

1500

100 600 600 600 1002000

(a)

700

100

850

250

150017

5034

0016

50



2M16




Welding plate



(b)






5 Test Scheme



Rib pillar

Top beam

Pile

(a)


(b)


Reducingvalve

Inlet valve

PipeSnuffle valve

Air pressure gauge


Airpressure

gauge

Reactionwoodenboard


Aircompressor






A bus (six cores)

ty08

ty09ty10

ty11ty12

ty13ty01ty02

ty03ty04ty05ty06

ty07

ty14ty15

ty16

Sand filling

ty17 ty18

1650

1750

90 310

380

450

120

250

250

250

150

310

160

160

200

170

500

1150

3400

250

250

440

130

630

50

Sand filling



Computer

Data line

Data bus



2

3

50




Data lineData bus

1650

1750

220

280 50

011

5025

034

0015

00

980

240

280

300

350

500

250

420

220

360

500

yb06

yb09yb10

yb07

yb08

yb01yb02

yb03

yb04

500yb05

yb01


yb19yb20

yb07

yb08

100 600 6002000

600 100

yb02

yb03

yb04

yb11yb12

yb13

yb14 Sandfilling

1650

1500

250



2

3





oprime

o y

x

z

Strain gaugeMxz


400

400

400

400

50

bf01

bf02

bf03

bf04

bf05

Sand filling

Sand filling

γ

γ

γ

γ

γ

Dial indicator

(a)

bf01bf02

bf03

bf04bf05

bf06bf07

bf08

bf09

bf10

Sandfilling

Sandfilling

1650

250

1500

100 600 6002000

600 100

(b)










Hprime = 175

H = 17

L

h

B

Sand filling

20

20

Air bag reservation


275375





Top of sand filling

Top of model box

Sand filling












elevation





Start the next test











18

16

14

12

10

08

06

04

02

000

Dep

th (m

)


35

30

25

20

15

10

05


Dep

th (m

)


17Ground line


Earth pressure cell


A

B

N H

G

F

E

D

C

IJ

LK

M

Sand filling

Wall turning point






Sand filling


35

30

25

20

15

10

05

00

Dep

th (m

)


Moment (kNm)0 1 2 3 4 5 6 7 8







7 Conclusions







Nomenclature





Pillar B Pillar A


20

18

16

14

12

10

08

06

04

02

00


Hei

ght o

f rib

pill

ar (m

)

















pillar at the top

Data Availability




Acknowledgments


References












































5 Test Scheme



Rib pillar

Top beam

Pile

(a)


(b)


Reducingvalve

Inlet valve

PipeSnuffle valve

Air pressure gauge


Airpressure

gauge

Reactionwoodenboard


Aircompressor






A bus (six cores)

ty08

ty09ty10

ty11ty12

ty13ty01ty02

ty03ty04ty05ty06

ty07

ty14ty15

ty16

Sand filling

ty17 ty18

1650

1750

90 310

380

450

120

250

250

250

150

310

160

160

200

170

500

1150

3400

250

250

440

130

630

50

Sand filling



Computer

Data line

Data bus



2

3

50




Data lineData bus

1650

1750

220

280 50

011

5025

034

0015

00

980

240

280

300

350

500

250

420

220

360

500

yb06

yb09yb10

yb07

yb08

yb01yb02

yb03

yb04

500yb05

yb01


yb19yb20

yb07

yb08

100 600 6002000

600 100

yb02

yb03

yb04

yb11yb12

yb13

yb14 Sandfilling

1650

1500

250



2

3





oprime

o y

x

z

Strain gaugeMxz


400

400

400

400

50

bf01

bf02

bf03

bf04

bf05

Sand filling

Sand filling

γ

γ

γ

γ

γ

Dial indicator

(a)

bf01bf02

bf03

bf04bf05

bf06bf07

bf08

bf09

bf10

Sandfilling

Sandfilling

1650

250

1500

100 600 6002000

600 100

(b)










Hprime = 175

H = 17

L

h

B

Sand filling

20

20

Air bag reservation


275375





Top of sand filling

Top of model box

Sand filling












elevation





Start the next test











18

16

14

12

10

08

06

04

02

000

Dep

th (m

)


35

30

25

20

15

10

05


Dep

th (m

)


17Ground line


Earth pressure cell


A

B

N H

G

F

E

D

C

IJ

LK

M

Sand filling

Wall turning point






Sand filling


35

30

25

20

15

10

05

00

Dep

th (m

)


Moment (kNm)0 1 2 3 4 5 6 7 8







7 Conclusions







Nomenclature





Pillar B Pillar A


20

18

16

14

12

10

08

06

04

02

00


Hei

ght o

f rib

pill

ar (m

)

















pillar at the top

Data Availability




Acknowledgments


References












































A bus (six cores)

ty08

ty09ty10

ty11ty12

ty13ty01ty02

ty03ty04ty05ty06

ty07

ty14ty15

ty16

Sand filling

ty17 ty18

1650

1750

90 310

380

450

120

250

250

250

150

310

160

160

200

170

500

1150

3400

250

250

440

130

630

50

Sand filling



Computer

Data line

Data bus



2

3

50




Data lineData bus

1650

1750

220

280 50

011

5025

034

0015

00

980

240

280

300

350

500

250

420

220

360

500

yb06

yb09yb10

yb07

yb08

yb01yb02

yb03

yb04

500yb05

yb01


yb19yb20

yb07

yb08

100 600 6002000

600 100

yb02

yb03

yb04

yb11yb12

yb13

yb14 Sandfilling

1650

1500

250



2

3





oprime

o y

x

z

Strain gaugeMxz


400

400

400

400

50

bf01

bf02

bf03

bf04

bf05

Sand filling

Sand filling

γ

γ

γ

γ

γ

Dial indicator

(a)

bf01bf02

bf03

bf04bf05

bf06bf07

bf08

bf09

bf10

Sandfilling

Sandfilling

1650

250

1500

100 600 6002000

600 100

(b)










Hprime = 175

H = 17

L

h

B

Sand filling

20

20

Air bag reservation


275375





Top of sand filling

Top of model box

Sand filling












elevation





Start the next test











18

16

14

12

10

08

06

04

02

000

Dep

th (m

)


35

30

25

20

15

10

05


Dep

th (m

)


17Ground line


Earth pressure cell


A

B

N H

G

F

E

D

C

IJ

LK

M

Sand filling

Wall turning point






Sand filling


35

30

25

20

15

10

05

00

Dep

th (m

)


Moment (kNm)0 1 2 3 4 5 6 7 8







7 Conclusions







Nomenclature





Pillar B Pillar A


20

18

16

14

12

10

08

06

04

02

00


Hei

ght o

f rib

pill

ar (m

)

















pillar at the top

Data Availability




Acknowledgments


References











































oprime

o y

x

z

Strain gaugeMxz


400

400

400

400

50

bf01

bf02

bf03

bf04

bf05

Sand filling

Sand filling

γ

γ

γ

γ

γ

Dial indicator

(a)

bf01bf02

bf03

bf04bf05

bf06bf07

bf08

bf09

bf10

Sandfilling

Sandfilling

1650

250

1500

100 600 6002000

600 100

(b)










Hprime = 175

H = 17

L

h

B

Sand filling

20

20

Air bag reservation


275375





Top of sand filling

Top of model box

Sand filling












elevation





Start the next test











18

16

14

12

10

08

06

04

02

000

Dep

th (m

)


35

30

25

20

15

10

05


Dep

th (m

)


17Ground line


Earth pressure cell


A

B

N H

G

F

E

D

C

IJ

LK

M

Sand filling

Wall turning point






Sand filling


35

30

25

20

15

10

05

00

Dep

th (m

)


Moment (kNm)0 1 2 3 4 5 6 7 8







7 Conclusions







Nomenclature





Pillar B Pillar A


20

18

16

14

12

10

08

06

04

02

00


Hei

ght o

f rib

pill

ar (m

)

















pillar at the top

Data Availability




Acknowledgments


References















































Hprime = 175

H = 17

L

h

B

Sand filling

20

20

Air bag reservation


275375





Top of sand filling

Top of model box

Sand filling












elevation





Start the next test











18

16

14

12

10

08

06

04

02

000

Dep

th (m

)


35

30

25

20

15

10

05


Dep

th (m

)


17Ground line


Earth pressure cell


A

B

N H

G

F

E

D

C

IJ

LK

M

Sand filling

Wall turning point






Sand filling


35

30

25

20

15

10

05

00

Dep

th (m

)


Moment (kNm)0 1 2 3 4 5 6 7 8







7 Conclusions







Nomenclature





Pillar B Pillar A


20

18

16

14

12

10

08

06

04

02

00


Hei

ght o

f rib

pill

ar (m

)

















pillar at the top

Data Availability




Acknowledgments


References


















































elevation





Start the next test











18

16

14

12

10

08

06

04

02

000

Dep

th (m

)


35

30

25

20

15

10

05


Dep

th (m

)


17Ground line


Earth pressure cell


A

B

N H

G

F

E

D

C

IJ

LK

M

Sand filling

Wall turning point






Sand filling


35

30

25

20

15

10

05

00

Dep

th (m

)


Moment (kNm)0 1 2 3 4 5 6 7 8







7 Conclusions







Nomenclature





Pillar B Pillar A


20

18

16

14

12

10

08

06

04

02

00


Hei

ght o

f rib

pill

ar (m

)

















pillar at the top

Data Availability




Acknowledgments


References
















































18

16

14

12

10

08

06

04

02

000

Dep

th (m

)


35

30

25

20

15

10

05


Dep

th (m

)


17Ground line


Earth pressure cell


A

B

N H

G

F

E

D

C

IJ

LK

M

Sand filling

Wall turning point






Sand filling


35

30

25

20

15

10

05

00

Dep

th (m

)


Moment (kNm)0 1 2 3 4 5 6 7 8







7 Conclusions







Nomenclature





Pillar B Pillar A


20

18

16

14

12

10

08

06

04

02

00


Hei

ght o

f rib

pill

ar (m

)

















pillar at the top

Data Availability




Acknowledgments


References













































7 Conclusions







Nomenclature





Pillar B Pillar A


20

18

16

14

12

10

08

06

04

02

00


Hei

ght o

f rib

pill

ar (m

)

















pillar at the top

Data Availability




Acknowledgments


References






















































pillar at the top

Data Availability




Acknowledgments


References









































study on model and tests of sheet pile wall with a relieving...

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