estimationofinfluencescopeoflateraldisplacementofsoft...

Research ArticleEstimation of Influence Scope of Lateral Displacement of SoftGround under Vacuum Pressure with PVD

Jingyun Liu1 Hongtao Fu1 Jun Wang 2 Yuanqiang Cai3 and Xiuqing Hu4

1College of Architecture and Civil Engineering Wenzhou University Wenzhou 325035 China2e Key Laboratory of Engineering and Technology for Soft Soil Foundation and Tideland Reclamation of Zhejiang ProvinceWenzhou University Wenzhou 325035 China3Zhejiang University of Technology Hangzhou 310014 China4Innovation Centre of Tideland Reclamation and Ecological Protection Wenzhou University Wenzhou 325035 China

Correspondence should be addressed to Jun Wang sunnystar1980163com

Received 8 June 2018 Accepted 26 July 2018 Published 19 August 2018

Academic Editor Yongfeng Deng

Copyright copy 2018 Jingyun Liu 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

e application of vacuum pressure to a treated area not only induces vertical settlement and inward lateral displacement but alsocauses the formation of tension cracks near the ground surface In general the strain method is applied to calculate the lateraldisplacement at the boundary of a treated area however the influence scope of lateral displacement has not yet been presentedBased on the in situ data of soft clayey soil foundation treated by vacuum consolidation lateral displacement was estimated in theinfluence scope in this study To calculate the influence scope of lateral displacement induced by vacuum pressure the ratio of thelateral displacement within the influence scope to the ground surface settlement under the centre of the treated area is defined asthe maximum value of the lateral displacement (ELD) within the influence scope is paper proposes a direct relationshipbetween ELD and the distance from the treated area boundary (Lx) considering the length of the prefabricated vertical drain Inaddition the FEA (finite-element analysis) is used to simulate the process of vacuum preloading to reinforce soft soil foundatione influence scope simulated is almost close to the calculated value Lx Accordingly the safety distance between the boundary ofthe treated area and the surrounding building can be estimated when the soft soil foundation is consolidated by using a vacuumpreloading method

1 Introduction

e preloading of a soft clayey deposit through vacuum orembankment loading is commonly used as a soft groundimprovement method With several advantages over em-bankment loading vacuum pressure applied to the pro-cessing of soft clay has a higher practicability such as no fillmaterial shorter construction periods and nonrequirementfor heavy machinery In addition the vacuum preloadingmethod does not add any chemical admixtures into theground and is consequently an environmental-friendlyground improvement method [1 2] However owing tothe principle effect of the vacuum preloading method thetreated area will not only induce vertical settlement andinward (toward the centre of the loading area) lateral

displacement of the ground but also cause crack adjacent tothe treated area Especially lateral displacement of soil atreclaimed coastal regions is more obvious because of thepoor engineering properties of soft soil as shown in Figure 1In most preloading projects the prediction of the consoli-dation settlement and lateral displacement of the ground isan essential design requirement In particular the predictionof ground lateral displacement induced by geotechnicalengineering activities in an urban environment maysometimes be a crucial design consideration [3]

e current methods for calculating lateral displacementof soil consist of the strain method (the horizontal displace-ment at the boundary is calculated based on the strain of thesoil in the treated area) [1] and the method of determining theratio of the settlement and lateral displacement [4] It is

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 8248049 11 pageshttpsdoiorg10115520188248049

noteworthy that the above methods are not used to solve thedeformation of the soil influenced by the different lengths ofa prefabricated vertical drain (PVD) Generally the afore-mentioned methods can be used to calculate or analyse thelateral deformation of soil at the boundary of the treated areaAs shown in Figure 1 in spite of the lateral displacement soilcrevices at the affected area are often induced by vacuumpressure Till now there is no practical easy-to-use method toevaluate the effect of the scope induced by vacuum pressure toadjacent engineering structures

In this study according to a practical application of thevacuum preloading method to engineering practice thestrain method was generalised to calculate the lateral dis-placement of soil at the affected area Furthermore based onthe observed results of the case history and the strainmethod an empirical equation is proposed for calculatingthe influence scope of vacuum preloading method con-sidering the different lengths of PVD Finally the FEA wasapplied to compare the simulated range of influence with thecalculated value Lx to evaluate the feasibility of the empiricalequation

2 Site and Soil Conditions

Wenzhou Vocational Secondary School is located in the newdistrict of Oujiang estuary China e site of this project isshown in Figure 2 e treated area covers approximately157820m2

e field is located in a reclamation area with differentthicknesses of dredger fill at the ground surface For theconvenience of construction the test site should be reinforcedusing the vacuum preloading method for preliminary shallowlayer treatment During this process the strengthened depth is

approximately 3ndash5m Figure 3 shows the physical propertiesof the soil after shallow treatment where the moisture contentis still greater than 62 and the compression index is ap-proximately 11ese characteristics cause the soil to producea large postconstruction settlement [5 6] which can onlysatisfy the bearing capacity for the smooth functioning of thelight-weight machine but cannot meet the requirements of thefoundation treatment us the test site should be furtherreinforced using a vacuum preloading method again becauseof the poor engineering properties of soft soil

3 In Situ Instrumentation

According to different reinforcement requirements twoPVD lengths (01m wide and 40mm thick) were applied tothis project To prevent the pile of buildings from slopinginto the construction a 6m PVD was adopted at Section 1Similarly a 15m PVD was adopted at Section 2 to preventthe cracking of the pavement and playground in use Boththe PVDs were arranged in a winter sweet shape witha spacing of 08m

Vacuum pressure was applied using the air-sealing sheetmethod [7] and the sheet used for this project was a 05mmthick polyvinyl chloride (PVC) membrane Before placingthe sealing membrane three layers of geotextiles were laiddown and a sealing membrane was placed around in thesealing groove In addition the groundwater level at the sitewas approximately 048m from the ground surface To avoidair leakage through the top unsaturated zone the edges ofthe sealing sheet were embedded in a 15m deep trench

After installing the PVDs 13 surface settlement plates53 multilevel settlement gauges and 11 inclinometers wereinstalled to monitor the performance of the treated groundFigures 4(a) and 4(b) present the general plan views of thetest sites and Table 1 tabulates the installed depths of thelayered settlement gauges

e measured vacuum pressure applied under the air-sealing sheet was over 80 kPa At the time of stopping thevacuumpump themeasured ground surface average settlementfrom Sections 1 and 2 was approximately 908 and 1197mmrespectively e curve of the settlement over time in eachtreated area is shown in Figures 5(a) and 5(b)

4 Lateral Displacement

41 At the Boundary of Treated Area For the soft soilfoundation the soil can be considered in the K0 consoli-dation state If only the vacuum pressure is larger than thelateral stress required for a no horizontal strain condition aninward lateral displacement is observed Based on a series oftest results Chai et al [1] reported an approximate methodfor calculating the ground lateral displacement induced byvacuum pressure eir method was used in the currentstudy to calculate the lateral displacement of soil at boundaryof the treated area e dimensions of Sections 1 and 2 were230mtimes 101m and 185mtimes 140m (lengthtimeswidth) re-spectively Table 2 lists the information needed to calculatethe lateral displacement induced by vacuum consolidationby using the approximate method

Figure 1 Deformation of the soil under vacuum consolidation

Figure 2 Location of the test

2 Advances in Civil Engineering

ndash27

ndash24

ndash21

ndash18

ndash15

ndash12

ndash9

ndash6

ndash3

0

3

20 40 60 1 2 3 0 2 4

Muddysilt

Mud-1

Dredgerfill

Horizontal hydraulicconductivity Kh

(10ndash6cms)

Elevation(m)

Vertical hydraulicconductivity Kv

(10ndash6cms)

Water contentatterberg limits

()

ndash30

ndash27

ndash24

ndash21

ndash18

ndash15

ndash12

ndash9

ndash6

ndash3

0

GL(m)

Mud-2

nWWlWp

Figure 3 Soil profile and some physical properties at the test site

LD5

LD4LD1

LD2

LD3

S5 S1

S6 S4 S2

230m

101m

Layered settlement gauge (S)Inclinometer casing (LD)

S3

(a)

LD1

LD2

LD4

LD3

LD5

LD6S5 S3 S1

S6 S4 S2

S7

140m

1845m


(b)

Figure 4 Plan layout of instrumentation points (a) Section 1 and (b) Section 2

Advances in Civil Engineering 3

Table 1 Installed depth of layered settlement gauges

Monitoring points Installed depth (m)Section 1 S1 S2 S3 S4 S5 S6 15 45 75Section 2 S1 S2 S3 S4 S5 S6 S7 15 45 75 105 150

0 30 60 90 120 150ndash1000

ndash800

ndash600

ndash400

ndash200

0

Pumpstopped

Ground surfaceS1 (GL-15m)

S2 (GL-45m)S3 (GL-75m)

Elasped time (day)

Settl

emen

t (m

m)

(a)


S2 (GL-45m)S3 (GL-75m)

0 30 60 90 120 150ndash1400

ndash1200

ndash1000

ndash800

ndash600

ndash400

ndash200

0

Pumpstopped

Settl

emen

t (m

m)

Elapsed time (day)

(b)

Figure 5 Settlement versus elapsed time curve (a) Section 1 and (b) Section 2


emethod proposed by Chai et al [1] for calculating lateraldisplacement of the soil at the treated area boundary as a result ofthe vacuum-drain consolidation can be summarized as follows

(1) horizontal earth pressure coefficient calculation

Ka0 βKa +(1minus β)K0 (1)

where Ka is the active earth pressure coefficient K0 isthe at-rest earth pressure and β is an empiricalfactor It is suggested that β should normally beassigned a value in the range from 067 to 1

(2) e maximum depth (z1) calculation of soil withlateral displacement is as follows

Zc 2cprime

ctKa

1113968 for zc lt zw (2a)

Zc 1

ct minus cw

2cprimeKa

1113968 minus cwzw1113888 1113889 for zc gt zw (2b)

σprimeav ltzprimecprimeKa0 ge0 for zlt zc

Ka0zprimecprime for zl gt zgt zc1113896 (3)

Δσvac K0 middot σprimev0 minus σprimeav

1minusK0 (4)

where ct is total unit weight of soil cw is the unit weightof pore water cprime is the effective stress cohesion zc is thedepth of cracking zw is the groundwater level and thedepth belowwhich no lateral displacement occurs in thesoil is given as zl zc + zprime

(3) e variation of the model parameter (α) with depthis given as

α αmin +1minus αmin

ΔσvacK0σprimev0 minus σprimeav

1minusK01113888 1113889 for zc ge zge zl

(5)

(4) e calculations for volumetric and horizontalstrains are given as

εvol λ

1 + eln 1 +Δσvacσprimev0

1113888 1113889 (6a)

εh 12(1minus α)

λ1 + e

ln 1 +Δσvacσprimev0

1113888 1113889 (6b)

where λ is the virgin compression index in aneminus lnpprime plot e is the voids ratio Δσvac is the

incremental vacuum pressure of the treated area σprimea0is the in situ vertical effective stress in the treatedarea and σprimeav is the horizontal effective stress Pa-rameters εh and εvol are the horizontal and volu-metric strains under vacuum consolidationrespectively

(5) Lateral displacement of the soil at the treated areaboundary is given as

δh εhB (7)

where B is the half width of the treated area

It is suggested that for triaxial stress conditions themodel parameter αmin 08 where α has the minimumvalue (αmin) at the ground surface Moreover the parameterreaches a unit value when zgt zl In this case the initialeffective stress applied to the field is zero or at least close tozero e lateral displacements of the boundaries of twotreatment sections are shown in Figures 6(a) and 6(b)

According to the calculation results the value of βmainly influences the lateral displacement at deeper loca-tions and the calculated depth at which the lateral dis-placement becomes insignificant e smaller the β value isthe larger the calculated lateral displacement is and the largerthe zl value (below which no lateral displacement occurs inthe soil) is In Section 1 when β 067 zl 21m β 084zl 165m and β 1 zl 14m In contrast in Section 2when β 067 zl 26m β 084 zl 20m and β 1zl 17m e comparison of the calculation results showsthat the zl value is not related to the depth of the PVD Inaddition the overall value of β 10 seems to providea better simulation of the in situ data Of course β 10corresponds to the active earth pressure state and will ob-viously underestimate the earth pressure for soil at depthsnear zl e figure shows that the longer the length of thePVD is the greater the depth of the reinforcement is and thegreater the maximum horizontal displacement is

42 In the Affected Area Although the mechanism of vac-uum preloading method is researched relatively perfectlythe influence of vacuum pressure on the consolidation anddeformation of soil adjacent to the treated area is not veryclear According to the actual situation of engineering ap-plications in this study the formula used to calculate thelateral deformation of the soil of the treated area boundary isgeneralised to calculate lateral deformation of the affectedarea

Table 2 Parameters for the soil at Wenzhou Vocational Secondary School Foundation

K0 Ka cprime (kPa) ct (kNm3) λ e Es (MPa) ϕprime (deg)Dredger fill 08246 07016 83 16 minus01717 1639 198 101Mud 1 08958 06747 79 165 minus01659 1516 134 112Muddy silt clay 06596 04921 74 17 minus02645 1267 231 154Mud 2 0847 07346 103 158 minus01063 1718 167 245Silty clay 07802 06396 145 168 minus02362 1312 248 88Note Ka is the active earth pressure coefficient Ka tan2(45minus (ϕprime2))


e following changes have been adapted in the processof calculating the lateral displacement for the expansion ofthe strain method

(1) According to a series of laboratory tests Robinson[8] proposed that lateral stresses should be consid-ered when estimating the vertical strains of the soil inthe affected area e magnitude of vertical andlateral strains also depends on the magnitude ofhorizontal stress When the horizontal stress fromthe affected area is equivalent to the active pressurea more vertical settlement is observed compared towhen the horizontal stress is equivalent to the earthpressure at rest Similarly the lateral strain is greaterwhen the horizontal stress from the affected area is atrest Assuming that the volumetric strain varies withthe magnitude of the vacuum pressure in the affectedarea the effective volumetric strain of the soil in theaffected area can be calculated according to (6a) asfollows

εvolminuse η times εvol (8)

where η is the attenuation coefficient of the volu-metric strainKondner [9] proposed a hyperbolic function todescribe the stress-strain relationship of clay soilconsolidation drainage tests

εvolminuseσ1 minus σ3

a + bεvolminuse (9)

where σ1 and σ3 are the maximum and minimumprincipal stresses respectively According to thestress-strain normalization characteristics of co-hesive soil [10] a and b can be calculated from thestress-strain values of the treated area WhenK0 065 a 00002 and b 00342 and when

K0 089 a 00007 and b 01089 According to(9) and (10) the calculated value of η is given inTable 3

(2) Under plane strain conditions the lateral strainfactor (LF) which is the ratio of lateral strain (εhminuse) tovolumetric strain (εvolminuse) can be determined by themethod of Poulos and Davis [11] as

LF εhminuseεvolminuse

χ(1minus ])minus ]

(1 + χ)(1minus 2]) (10)

where χ Δσvach(Δσvacv + σvoprime ) σv0prime is the in situvertical effective stress in the affected area and v isPoissonrsquos ratio Under k0 condition (χ k0) there isno lateral deformation such that

] K0

1 + K0 (11)

(3) e lateral displacement at distance Lx from theboundary of the affected area can be calculated by

δhminuse εhminuse times Lx (12)

where εhminuse is the horizontal strain of the soil in theaffected area and Lx is the distance from the treatedarea boundary (m)Figure 7 plots the variations in the LF where theLF 0 when χ K0 A stress ratio (k) [1] was definedas

k ΔσvacΔσvac + σprimevo

(13)

ey postulated that if kleK0 there will be no lateraldisplacement and vice versa e lateral deformations ofthe different distances of the treated area boundary areshown in Figures 8ndash11 Despite the affected area being

ndash15

ndash12

ndash9

ndash6

ndash3

0

0 150 300 450 600 750

Dep

th (m

)

Chai β = 1Chai β = 084Chai β = 067

Measured

Lateral displacement (mm)

(a)

Dep

th (m

)


Measured

ndash20

ndash15

ndash10

ndash5

0

0 150 300 450 600 750 900 1050Lateral displacement (mm)

(b)

Figure 6 Lateral displacement of soil at treated area (a) Section 1 and (b) Section 2


without air-sealing sheet the surface or subsurface soillayer acts as an equivalent air-sealing sheet for sealing theupper soil layer is method was proposed by Chai et al[12]

As the vacuum in the affected area is less than that inthe treated area the farther it is away from the boundaryof the treated area the smaller the degree of the vacuum

is Assuming that the attenuation rate of vacuum pressureis 2 kPam in the horizontal direction the vacuumpressures at 10 and 20m distance from the treated areaboundary are 60 and 40 kPa respectively it was observedthat it mainly depended on the vacuum pressure at the

ndash10

ndash8

ndash6

ndash4

ndash2

0

0 20 40 60 80 100 120 140 160 180 200

Measured


Dep

th (m

)

Calculated k = 065Calculated k = 089

Figure 8 Lateral displacement at a distance of 10m from Section 1boundary

00 01 02 03 04 05 06 07 08 09 10ndash8

ndash7

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

Plain strain k0 = 065Plain strain k0 = 089

Late

ral s

trai

n fa

ctor

k = ∆σvach∆σvacv

Figure 7 Lateral strain factor variations

ndash7

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0


Dep

th (m

)

MeasuredCalculated k = 065Calculated k = 089


Table 3 Calculation results of the η value

Section 1 Section 2K0 065 K0 089 K0 065 K0 089

Lx 10 Lx 20 Lx 10 Lx 20 Lx 10 Lx 20 Lx 10 Lx 2001160 00502 01274 00552 01151 00500 01268 00551Note K0 is the at-rest earth pressure Lx is the distance from the treated area boundary (m)

ndash13ndash12ndash11ndash10

ndash9ndash8ndash7ndash6ndash5ndash4ndash3ndash2ndash1

0

0 30 60 90 120 150 180 210 240 270Lateral displacement (mm)

Dep

th (m

)


Figure 10 Lateral displacement at a distance of 10m from Section2 boundary


ground surface ese assumptions are attributed to thefollowing factors

(a) Owing to the surface or subsurface soil layer beingthe sealing layer the soil of the affected area could bemaintained under the influence of vacuum pressure

(b) In the range of natural sludge the attenuation rate ofvacuum pressure in horizontal direction is 6 kPamin the vertical direction [13]

(c) e attenuation of the vacuum is responsible for thepermeability coefficient of the soil the greater thepermeability coefficient is the slower the attenuationrate is [14] In this case the horizontal permeabilitycoefficient of the soil is approximately three times ofthe vertical permeability coefficient

At the affected area the vacuum pressure can be con-sidered to vary linearly from the ground surface to zl (belowwhich no lateral displacement occurs in the soil) [1] In theaffected area the coefficients of lateral earth pressure wereassumed to vary linearly from k0 at the bottom of the drainto ka at the surface [8] e calculated inward lateral earthpressures with k 065 and 089 under plane strain con-ditions are plotted in Figures 8ndash11 e figures show that atshallow depths χ 089 can predict the lateral displacementvery well whereas the measured values approach the pre-dicted values when k 065 (at-rest condition) It is notedthat the sudden change of k at the boundary of the soil layerwas attributed to a change in the parameters of soil betweeneach layer

5 Scope of Influence under Vacuum Pressure

Under vacuum consolidation the settlement and lateral dis-placement induced by the vacuum pressure were determinede effective stress increased in the treated area which willcause soil reinforcement outside of the treated area in some

way and induced the lateral displacement rough researchmany domestic scholars believe that the range of influenceunder the vacuum pressure is approximately 22ndash42m [15]Although the vacuum preloading method has been widelyused at present there has been no practical easy-to-usemethod for predicting the scope Based on the observed re-sults of case histories an empirical equation was proposed inthe present study for estimating the maximum value of thescope

e maximum value of the effected lateral displacement(ELD) which is a dimensionless parameter can be expressed as

ELD δhminuse

s (14)

where S is the ground surface settlement under the centre ofthe treated area e values of S and δhminuse at the end ofvacuum consolidation are desirable for substitution in thisequation

As the shallow soil is subjected to vacuum pressure toproduce tension cracks the soil can be considered to be closeto the isotropic consolidation However no tensile crackswere observed in the lower soil and the soil is considered tobe close to a one-dimensional consolidation According tothe settlement calculation formula proposed by Liu et al[16] S can be calculated as

S 1113944n

1αi middotΔσvac minus 20 times Δσvac middot hiZi( 1113857

Ei

middot hi for 0lt hi leZl

(15)

where Ei is the compression modulus of each soil layer andhi is the thickness of each soil layer e calculated settle-ment values in Sections 1 and 2 are 8214 and 11053mmrespectively It is obvious that the calculated value is less thanthat obtained in the in situ observations e defined errorsfor Sections 1 and 2 are 95 and 77 respectively andmeet the engineering requirements

According to the monitoring data analysis the re-lationship between ELD and Lx (the distance from thetreated area boundary) can be expressed as follows

ELD a ln Lx( 1113857 + b (16)

where Lx is the value of distance from the treated areaboundary (m) When the length of PVD is 6m a minus0185and b 0643 When the length of PVD is 15m a minus0185and b 06541 For a 6m PVD length when δhminuse 0 and30mm as the boundary Lx 3232 and 2653m re-spectively For a 15m PVD length when δhminuse 0 and 30mmas the boundary Lx 3432 and 2963m respectively erelationship between the values of Lx and ELD analysedfrom the measured results of the field cases and calculation isplotted in Figures 12(a) and 12(b)

6 Numerical Simulation

e present authors considered a PVD-induced horizontalradial consolidation and simulated through FEA (finite-elementanalysis) and analysed e FEA is performed by the use ofPlaxis 2D (version 201701) And the soft soil model (SSM) was

ndash11ndash10


0


Dep

th (m

)




adopted e model used in the FEA is shown in Figure 13Meshing is divided finely In Section 1 case there are 3882elements and 31789 nodes and there are 5326 elements and43241 nodes in Section 2 case Xmin0m Xmax345m andYminminus40m Ymax0m for case 1 and Xmin0mXmax276m and Yminminus40m Ymax0m for case 2

e values of the model parameters are listed in Table 2and Figure 3 Two ideal cases without the effect of smear andwell resistance were considered for the PVD-inducedconsolidation

It was assumed that the model ground was weightlesswith an initial vertical effective stress of K0 consolidationcondition and an incremental load of vacuum pressure wasthen applied at the top boundary e Taylor [17] equationwas used to consider the permeability variation with the voidratio reduction

k k0 times 10minus e0minuse( )ck( ) (17)

where e0 and e are the initial and current void ratios k0 and k

are the permeability corresponding to void ratios e0 and erespectively and ck is a constant e coefficient of con-solidation c can be calculated as

c (1 + e)k middot pprime

λ middot cw (18)

where pprime is the consolidation stress λ is the slope of the virgincompression curve in the eminus lnpprime plot and cw is the unitweight of water e duration of vacuum consolidationmaintained for 113 days in Section 1 and 103 days in Section 2After the vacuum was completed the horizontal displacementof the soil in each section case was shown in Figures 14 and 15

It can be seen from Figures 14 and 15 in the process of thevacuuming the soft soil in the affected area continuously movestowards the centre of the treated area under the influence of

vacuum and the maximum lateral displacement occurs at theboundary of the treated area e result of this deformation hasagreement with in situ data measured e surface lateral dis-placement development of the two affected areas is summarizedin Figure 16e surface lateral displacementwithin the range of0ndash15m outside the treated area greatly developed while thelateral displacement in the 15ndash25m range developed slowlyspecially the surface lateral displacement is smaller at the 25maway from the treated areaMeanwhile it can be considered thatLxmax is equal to 34m in Section 1 and Lxmax is equal to 37m inSection 2 is is basically close to the result of calculationAccording to the calculation results of (14)ndash(16) Lxmax ofSections 1 and 2 are equal to 3232 and 3432 respectively

To confirm the safe distance between the boundary oftreated area and structure a series of factors must be con-sidered carefully which consist of the ability to resist structuraldeformation type of structural infrastructure and soil prop-erties inside and outside the treated area According to thecalculation results from (14) to (16) and simulation it is feasiblefor engineering practice that the safe distances away from thetreated area can be determined to 3232 and 3432m

0 5 10 15 20 25 30 35 4000

02

04

06

08

10EL

D

Lx (m)

MeasuredCalculated SCalculated δ

Calculated δ SFormula

(a)

00

02

04

06

08

10

0 5 10 15 20 25 30 35 40


Calculated δ S

ELD

Lx (m)

Formula

(b)

Figure 12 Relationship between the values of Lx and ELD (a) Section 1 and (b) Section 2

Y

X

PVD

Drained

Drained

SymmetryFixed impervious

The midpoint of the long sideReinforcement area boundary

Figure 13 Model for FEA


7 Conclusions

e performance of vacuum preloading with PVDs was usedto reinforce soft soils at the Oujiang Wenzhou reclamationproject Based on the in situ measurements and subsequent

analyses an empirical formula is proposed to calculate theinfluence scope of the vacuum preloading method At thesame time the field case was simulated by the finite-elementmethod e safe distance away from the treated area is inagreement with simulated results According to the workdone in this paper we can get the following conclusions

(1) When the soft soil foundation is consolidated using thevacuum preloadingmethod a generalisation formula oflateral deformation is proposed to calculate the lateraldeformation of the soil at the affected area provided thesoil properties of the affected area are known

(2) Based on the observed results of the case history anempirical equation is proposed for calculating theinfluence scope of the vacuum preloading method

(3) According to the deformation analysis of the soil atthe affected area the safety distance between thereinforcement area boundary and the surroundingbuilding should be determined to 3432m or morewhen the soft soil foundation is strengthened throughvacuum preloading

Data Availability

e authors worked with a reputable foundation treatmentcompany and thuswere accessible to the data In the agreement

A ndash4000B 000C 4000D 8000E 12000F 16000

H 24000I 28000J 32000K 36000L 40000M 44000N 48000O 52000P 56000Q 60000R 64000S 68000T 72000U 76000

[lowast10ndash3m]Max

G 20000

Figure 14 Lateral displacement of the soil outside Section 1

A ndash010B 000C 010D 020E 030F 040

H 060G 050

I 070J 080K 090L 100M 110

(m)Max


0100200300400500600700800900

100011001200

0 5 10 15 20 25 30 35 40

Section 1

Calculated-section 2

Calculated-section 1La

tera

l disp

lace

men

t (m

m)

Lx (m)

Section 2

Figure 16 Variation of surface lateral displacement in the affectedarea


of their collaboration any kinds of data including testing andrecords were owned by the company and thus are confidentialto anybody else

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e presented work was supported by the National Key Re-search and Development Program of China (Grant no2016YFC0800203) Program of the International Science andTechnology Cooperation (Grant no 2015DFA71550) Programsof National Natural Science Foundation of China (Grant nos51778500 51778501 51622810 51620105008 and 51478364)Key Research and Development Programs of Zhejiang Prov-ince (Grant no 2018C03038) Natural Science FoundationPrograms of Zhejiang Province (Grant nos LR18E080001 andLY17E080010) and Programs of Science and Technology ofWenzhou (Grant nos S20150015 and S20150030) ese fi-nancial supports were gratefully acknowledged

References

[1] J C Chai J P Carter and S Hayashi ldquoGround deformationinduced by vacuum consolidationrdquo Journal of Geotechnicaland Geoenvironmental Engineering vol 131 no 12pp 1552ndash1561 2005

[2] J Wang J F Ni and Y Q Cai ldquoCombination of vacuumpreloading and lime treatment for improvement of dredgedfillrdquo Engineering Geology vol 227 pp 149ndash158 2017

[3] C Y Ong and J C Chai ldquoLateral displacement of soft groundunder vacuum pressure and surcharge loadrdquo Frontiers ofArchitecture and Civil Engineering in China vol 5 no 2pp 239ndash248 2011

[4] G Mesri and A Q Khan ldquoGround improvement usingvacuum loading together with vertical drainsrdquo Journal ofGeotechnical and Geoenvironmental Engineering vol 138no 6 pp 680ndash689 2012

[5] Z G Jiang and Z A Yao ldquoDeformation and consolidationeffect of soft soils treated by vacuum preloading methodrdquoGeotechnical Engineering Technique vol 1 pp 36ndash38 2005

[6] B Indraratna C Rujikiatkamjorn J Ameratunga et alldquoPerformance and prediction of vacuum combined surchargeconsolidation at port of brisbanerdquo Journal of Geotechnical andGeoenvironmental Engineering vol 137 no 11 pp 1009ndash1018 2011

[7] J Wang Y Q Cai J J Ma and J Chu ldquoImproved vacuumpreloading method for consolidation of dredged clay-slurryfillrdquo Journal of Geotechnical and Geoenvironmental Engi-neering vol 142 no 11 article 06016012 2016

[8] G Robinsonretnamony I Buddhima and R CholachatldquoFinal state of soils under vacuum preloadingrdquo CanadianGeotechnical Journal vol 49 no 6 pp 729ndash739 2012

[9] R L Kondner ldquoHyperbolic stress-strain response cohesivesoilsrdquo Journal of the Soil Mechanics amp Foundations Divisionvol 89 no 1 pp 115ndash143 1963

[10] S X Chen P P Ling and S Xiu ldquoExperimental study ondeformation behavior of silty clay under unloadingrdquo Rock ampSoil Mechanics vol 213 no 4 pp 548ndash566 2007

[11] H G Poulos and E H Davis Elastic Solutions for Soil andRock Mechanics John Wiley amp Sons New York NY USA1974

[12] J C Chai N Miura and D T Bergado ldquoPreloading clayeydeposit by vacuum pressure with cap-drain analyses versusperformancerdquo Geotextiles and Geomembranes vol 26 no 3pp 220ndash230 2008

[13] Q F Zhu C S Gao and S H Yang ldquoTransfer properties ofvacuum degree in treatment of super-soft muck foundationrdquoChinese Journal of Geotechnical Engineering vol 9pp 1429ndash1433 2010

[14] Y D Wu H S Wu R P Luo and C C Zeng ldquoAnalyticalsolutions for vacuum preloading consolidation consideringvacuum degree attenuation and change of permeability co-efficient in smear zonesrdquo Journal of Hehai University (NaturalSoiences) vol 2 pp 122ndash128 2016

[15] H L Li and W Li ldquoResearch on influence range of vacuumpreloading for horizontal displacement of dredger-filled siltfoundationrdquo Port Engineering Technology vol 6 pp 85ndash912016

[16] Z Z Liu J W Ding and G Wang ldquoCalculation method forvacuum preloading induced settlement considering vacuumdegree attenuationrdquo Journal of Southeast University (NaturalScience Edition) vol 46 pp 191ndash195 2016

[17] D W Taylor Fundamentals of Soil Mechanics John Wiley ampSons Inc New York NY USA 1948


International Journal of

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Hindawiwwwhindawicom Volume 2018


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Shock and Vibration


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Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

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wwwhindawicom Volume 2018

Advances in

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Submit your manuscripts atwwwhindawicom

noteworthy that the above methods are not used to solve thedeformation of the soil influenced by the different lengths ofa prefabricated vertical drain (PVD) Generally the afore-mentioned methods can be used to calculate or analyse thelateral deformation of soil at the boundary of the treated areaAs shown in Figure 1 in spite of the lateral displacement soilcrevices at the affected area are often induced by vacuumpressure Till now there is no practical easy-to-use method toevaluate the effect of the scope induced by vacuum pressure toadjacent engineering structures

In this study according to a practical application of thevacuum preloading method to engineering practice thestrain method was generalised to calculate the lateral dis-placement of soil at the affected area Furthermore based onthe observed results of the case history and the strainmethod an empirical equation is proposed for calculatingthe influence scope of vacuum preloading method con-sidering the different lengths of PVD Finally the FEA wasapplied to compare the simulated range of influence with thecalculated value Lx to evaluate the feasibility of the empiricalequation

2 Site and Soil Conditions

Wenzhou Vocational Secondary School is located in the newdistrict of Oujiang estuary China e site of this project isshown in Figure 2 e treated area covers approximately157820m2

e field is located in a reclamation area with differentthicknesses of dredger fill at the ground surface For theconvenience of construction the test site should be reinforcedusing the vacuum preloading method for preliminary shallowlayer treatment During this process the strengthened depth is

approximately 3ndash5m Figure 3 shows the physical propertiesof the soil after shallow treatment where the moisture contentis still greater than 62 and the compression index is ap-proximately 11ese characteristics cause the soil to producea large postconstruction settlement [5 6] which can onlysatisfy the bearing capacity for the smooth functioning of thelight-weight machine but cannot meet the requirements of thefoundation treatment us the test site should be furtherreinforced using a vacuum preloading method again becauseof the poor engineering properties of soft soil

3 In Situ Instrumentation

According to different reinforcement requirements twoPVD lengths (01m wide and 40mm thick) were applied tothis project To prevent the pile of buildings from slopinginto the construction a 6m PVD was adopted at Section 1Similarly a 15m PVD was adopted at Section 2 to preventthe cracking of the pavement and playground in use Boththe PVDs were arranged in a winter sweet shape witha spacing of 08m

Vacuum pressure was applied using the air-sealing sheetmethod [7] and the sheet used for this project was a 05mmthick polyvinyl chloride (PVC) membrane Before placingthe sealing membrane three layers of geotextiles were laiddown and a sealing membrane was placed around in thesealing groove In addition the groundwater level at the sitewas approximately 048m from the ground surface To avoidair leakage through the top unsaturated zone the edges ofthe sealing sheet were embedded in a 15m deep trench

After installing the PVDs 13 surface settlement plates53 multilevel settlement gauges and 11 inclinometers wereinstalled to monitor the performance of the treated groundFigures 4(a) and 4(b) present the general plan views of thetest sites and Table 1 tabulates the installed depths of thelayered settlement gauges

e measured vacuum pressure applied under the air-sealing sheet was over 80 kPa At the time of stopping thevacuumpump themeasured ground surface average settlementfrom Sections 1 and 2 was approximately 908 and 1197mmrespectively e curve of the settlement over time in eachtreated area is shown in Figures 5(a) and 5(b)

4 Lateral Displacement

41 At the Boundary of Treated Area For the soft soilfoundation the soil can be considered in the K0 consoli-dation state If only the vacuum pressure is larger than thelateral stress required for a no horizontal strain condition aninward lateral displacement is observed Based on a series oftest results Chai et al [1] reported an approximate methodfor calculating the ground lateral displacement induced byvacuum pressure eir method was used in the currentstudy to calculate the lateral displacement of soil at boundaryof the treated area e dimensions of Sections 1 and 2 were230mtimes 101m and 185mtimes 140m (lengthtimeswidth) re-spectively Table 2 lists the information needed to calculatethe lateral displacement induced by vacuum consolidationby using the approximate method

Figure 1 Deformation of the soil under vacuum consolidation

Figure 2 Location of the test


ndash27

ndash24

ndash21

ndash18

ndash15

ndash12

ndash9

ndash6

ndash3

0

3

20 40 60 1 2 3 0 2 4

Muddysilt

Mud-1

Dredgerfill


(10ndash6cms)

Elevation(m)


(10ndash6cms)


()

ndash30

ndash27

ndash24

ndash21

ndash18

ndash15

ndash12

ndash9

ndash6

ndash3

0

GL(m)

Mud-2

nWWlWp


LD5

LD4LD1

LD2

LD3

S5 S1

S6 S4 S2

230m

101m


S3

(a)

LD1

LD2

LD4

LD3

LD5

LD6S5 S3 S1

S6 S4 S2

S7

140m

1845m


(b)





0 30 60 90 120 150ndash1000

ndash800

ndash600

ndash400

ndash200

0

Pumpstopped


S2 (GL-45m)S3 (GL-75m)

Elasped time (day)

Settl

emen

t (m

m)

(a)


S2 (GL-45m)S3 (GL-75m)

0 30 60 90 120 150ndash1400

ndash1200

ndash1000

ndash800

ndash600

ndash400

ndash200

0

Pumpstopped

Settl

emen

t (m

m)

Elapsed time (day)

(b)








Zc 2cprime

ctKa


Zc 1

ct minus cw

2cprimeKa





1minusK0 (4)






(5)


εvol λ


1113888 1113889 (6a)

εh 12(1minus α)

λ1 + e


1113888 1113889 (6b)




δh εhB (7)


















χ(1minus ])minus ]

(1 + χ)(1minus 2]) (10)


] K0

1 + K0 (11)





(13)


ndash15

ndash12

ndash9

ndash6

ndash3

0

0 150 300 450 600 750

Dep

th (m

)


Measured


(a)

Dep

th (m

)


Measured

ndash20

ndash15

ndash10

ndash5

0


(b)






ndash10

ndash8

ndash6

ndash4

ndash2

0

0 20 40 60 80 100 120 140 160 180 200

Measured


Dep

th (m

)



00 01 02 03 04 05 06 07 08 09 10ndash8

ndash7

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1


Late

ral s

trai

n fa

ctor



ndash7

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0


Dep

th (m

)








0


Dep

th (m

)













ELD δhminuse

s (14)



S 1113944n


Ei


(15)



ELD a ln Lx( 1113857 + b (16)




ndash11ndash10


0


Dep

th (m

)











λ middot cw (18)





0 5 10 15 20 25 30 35 4000

02

04

06

08

10EL

D

Lx (m)



(a)

00

02

04

06

08

10

0 5 10 15 20 25 30 35 40


Calculated δ S

ELD

Lx (m)

Formula

(b)


Y

X

PVD

Drained

Drained





7 Conclusions






Data Availability


A ndash4000B 000C 4000D 8000E 12000F 16000

H 24000I 28000J 32000K 36000L 40000M 44000N 48000O 52000P 56000Q 60000R 64000S 68000T 72000U 76000


G 20000


A ndash010B 000C 010D 020E 030F 040

H 060G 050

I 070J 080K 090L 100M 110

(m)Max


0100200300400500600700800900

100011001200

0 5 10 15 20 25 30 35 40

Section 1



tera

l disp

lace

men

t (m

m)

Lx (m)

Section 2






Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


ndash27

ndash24

ndash21

ndash18

ndash15

ndash12

ndash9

ndash6

ndash3

0

3

20 40 60 1 2 3 0 2 4

Muddysilt

Mud-1

Dredgerfill


(10ndash6cms)

Elevation(m)


(10ndash6cms)


()

ndash30

ndash27

ndash24

ndash21

ndash18

ndash15

ndash12

ndash9

ndash6

ndash3

0

GL(m)

Mud-2

nWWlWp


LD5

LD4LD1

LD2

LD3

S5 S1

S6 S4 S2

230m

101m


S3

(a)

LD1

LD2

LD4

LD3

LD5

LD6S5 S3 S1

S6 S4 S2

S7

140m

1845m


(b)





0 30 60 90 120 150ndash1000

ndash800

ndash600

ndash400

ndash200

0

Pumpstopped


S2 (GL-45m)S3 (GL-75m)

Elasped time (day)

Settl

emen

t (m

m)

(a)


S2 (GL-45m)S3 (GL-75m)

0 30 60 90 120 150ndash1400

ndash1200

ndash1000

ndash800

ndash600

ndash400

ndash200

0

Pumpstopped

Settl

emen

t (m

m)

Elapsed time (day)

(b)








Zc 2cprime

ctKa


Zc 1

ct minus cw

2cprimeKa





1minusK0 (4)






(5)


εvol λ


1113888 1113889 (6a)

εh 12(1minus α)

λ1 + e


1113888 1113889 (6b)




δh εhB (7)


















χ(1minus ])minus ]

(1 + χ)(1minus 2]) (10)


] K0

1 + K0 (11)





(13)


ndash15

ndash12

ndash9

ndash6

ndash3

0

0 150 300 450 600 750

Dep

th (m

)


Measured


(a)

Dep

th (m

)


Measured

ndash20

ndash15

ndash10

ndash5

0


(b)






ndash10

ndash8

ndash6

ndash4

ndash2

0

0 20 40 60 80 100 120 140 160 180 200

Measured


Dep

th (m

)



00 01 02 03 04 05 06 07 08 09 10ndash8

ndash7

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1


Late

ral s

trai

n fa

ctor



ndash7

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0


Dep

th (m

)








0


Dep

th (m

)













ELD δhminuse

s (14)



S 1113944n


Ei


(15)



ELD a ln Lx( 1113857 + b (16)




ndash11ndash10


0


Dep

th (m

)











λ middot cw (18)





0 5 10 15 20 25 30 35 4000

02

04

06

08

10EL

D

Lx (m)



(a)

00

02

04

06

08

10

0 5 10 15 20 25 30 35 40


Calculated δ S

ELD

Lx (m)

Formula

(b)


Y

X

PVD

Drained

Drained





7 Conclusions






Data Availability


A ndash4000B 000C 4000D 8000E 12000F 16000

H 24000I 28000J 32000K 36000L 40000M 44000N 48000O 52000P 56000Q 60000R 64000S 68000T 72000U 76000


G 20000


A ndash010B 000C 010D 020E 030F 040

H 060G 050

I 070J 080K 090L 100M 110

(m)Max


0100200300400500600700800900

100011001200

0 5 10 15 20 25 30 35 40

Section 1



tera

l disp

lace

men

t (m

m)

Lx (m)

Section 2






Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




0 30 60 90 120 150ndash1000

ndash800

ndash600

ndash400

ndash200

0

Pumpstopped


S2 (GL-45m)S3 (GL-75m)

Elasped time (day)

Settl

emen

t (m

m)

(a)


S2 (GL-45m)S3 (GL-75m)

0 30 60 90 120 150ndash1400

ndash1200

ndash1000

ndash800

ndash600

ndash400

ndash200

0

Pumpstopped

Settl

emen

t (m

m)

Elapsed time (day)

(b)








Zc 2cprime

ctKa


Zc 1

ct minus cw

2cprimeKa





1minusK0 (4)






(5)


εvol λ


1113888 1113889 (6a)

εh 12(1minus α)

λ1 + e


1113888 1113889 (6b)




δh εhB (7)


















χ(1minus ])minus ]

(1 + χ)(1minus 2]) (10)


] K0

1 + K0 (11)





(13)


ndash15

ndash12

ndash9

ndash6

ndash3

0

0 150 300 450 600 750

Dep

th (m

)


Measured


(a)

Dep

th (m

)


Measured

ndash20

ndash15

ndash10

ndash5

0


(b)






ndash10

ndash8

ndash6

ndash4

ndash2

0

0 20 40 60 80 100 120 140 160 180 200

Measured


Dep

th (m

)



00 01 02 03 04 05 06 07 08 09 10ndash8

ndash7

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1


Late

ral s

trai

n fa

ctor



ndash7

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0


Dep

th (m

)








0


Dep

th (m

)













ELD δhminuse

s (14)



S 1113944n


Ei


(15)



ELD a ln Lx( 1113857 + b (16)




ndash11ndash10


0


Dep

th (m

)











λ middot cw (18)





0 5 10 15 20 25 30 35 4000

02

04

06

08

10EL

D

Lx (m)



(a)

00

02

04

06

08

10

0 5 10 15 20 25 30 35 40


Calculated δ S

ELD

Lx (m)

Formula

(b)


Y

X

PVD

Drained

Drained





7 Conclusions






Data Availability


A ndash4000B 000C 4000D 8000E 12000F 16000

H 24000I 28000J 32000K 36000L 40000M 44000N 48000O 52000P 56000Q 60000R 64000S 68000T 72000U 76000


G 20000


A ndash010B 000C 010D 020E 030F 040

H 060G 050

I 070J 080K 090L 100M 110

(m)Max


0100200300400500600700800900

100011001200

0 5 10 15 20 25 30 35 40

Section 1



tera

l disp

lace

men

t (m

m)

Lx (m)

Section 2






Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







Zc 2cprime

ctKa


Zc 1

ct minus cw

2cprimeKa





1minusK0 (4)






(5)


εvol λ


1113888 1113889 (6a)

εh 12(1minus α)

λ1 + e


1113888 1113889 (6b)




δh εhB (7)


















χ(1minus ])minus ]

(1 + χ)(1minus 2]) (10)


] K0

1 + K0 (11)





(13)


ndash15

ndash12

ndash9

ndash6

ndash3

0

0 150 300 450 600 750

Dep

th (m

)


Measured


(a)

Dep

th (m

)


Measured

ndash20

ndash15

ndash10

ndash5

0


(b)






ndash10

ndash8

ndash6

ndash4

ndash2

0

0 20 40 60 80 100 120 140 160 180 200

Measured


Dep

th (m

)



00 01 02 03 04 05 06 07 08 09 10ndash8

ndash7

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1


Late

ral s

trai

n fa

ctor



ndash7

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0


Dep

th (m

)








0


Dep

th (m

)













ELD δhminuse

s (14)



S 1113944n


Ei


(15)



ELD a ln Lx( 1113857 + b (16)




ndash11ndash10


0


Dep

th (m

)











λ middot cw (18)





0 5 10 15 20 25 30 35 4000

02

04

06

08

10EL

D

Lx (m)



(a)

00

02

04

06

08

10

0 5 10 15 20 25 30 35 40


Calculated δ S

ELD

Lx (m)

Formula

(b)


Y

X

PVD

Drained

Drained





7 Conclusions






Data Availability


A ndash4000B 000C 4000D 8000E 12000F 16000

H 24000I 28000J 32000K 36000L 40000M 44000N 48000O 52000P 56000Q 60000R 64000S 68000T 72000U 76000


G 20000


A ndash010B 000C 010D 020E 030F 040

H 060G 050

I 070J 080K 090L 100M 110

(m)Max


0100200300400500600700800900

100011001200

0 5 10 15 20 25 30 35 40

Section 1



tera

l disp

lace

men

t (m

m)

Lx (m)

Section 2






Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












χ(1minus ])minus ]

(1 + χ)(1minus 2]) (10)


] K0

1 + K0 (11)





(13)


ndash15

ndash12

ndash9

ndash6

ndash3

0

0 150 300 450 600 750

Dep

th (m

)


Measured


(a)

Dep

th (m

)


Measured

ndash20

ndash15

ndash10

ndash5

0


(b)






ndash10

ndash8

ndash6

ndash4

ndash2

0

0 20 40 60 80 100 120 140 160 180 200

Measured


Dep

th (m

)



00 01 02 03 04 05 06 07 08 09 10ndash8

ndash7

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1


Late

ral s

trai

n fa

ctor



ndash7

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0


Dep

th (m

)








0


Dep

th (m

)













ELD δhminuse

s (14)



S 1113944n


Ei


(15)



ELD a ln Lx( 1113857 + b (16)




ndash11ndash10


0


Dep

th (m

)











λ middot cw (18)





0 5 10 15 20 25 30 35 4000

02

04

06

08

10EL

D

Lx (m)



(a)

00

02

04

06

08

10

0 5 10 15 20 25 30 35 40


Calculated δ S

ELD

Lx (m)

Formula

(b)


Y

X

PVD

Drained

Drained





7 Conclusions






Data Availability


A ndash4000B 000C 4000D 8000E 12000F 16000

H 24000I 28000J 32000K 36000L 40000M 44000N 48000O 52000P 56000Q 60000R 64000S 68000T 72000U 76000


G 20000


A ndash010B 000C 010D 020E 030F 040

H 060G 050

I 070J 080K 090L 100M 110

(m)Max


0100200300400500600700800900

100011001200

0 5 10 15 20 25 30 35 40

Section 1



tera

l disp

lace

men

t (m

m)

Lx (m)

Section 2






Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





ndash10

ndash8

ndash6

ndash4

ndash2

0

0 20 40 60 80 100 120 140 160 180 200

Measured


Dep

th (m

)



00 01 02 03 04 05 06 07 08 09 10ndash8

ndash7

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0

1


Late

ral s

trai

n fa

ctor



ndash7

ndash6

ndash5

ndash4

ndash3

ndash2

ndash1

0


Dep

th (m

)








0


Dep

th (m

)













ELD δhminuse

s (14)



S 1113944n


Ei


(15)



ELD a ln Lx( 1113857 + b (16)




ndash11ndash10


0


Dep

th (m

)











λ middot cw (18)





0 5 10 15 20 25 30 35 4000

02

04

06

08

10EL

D

Lx (m)



(a)

00

02

04

06

08

10

0 5 10 15 20 25 30 35 40


Calculated δ S

ELD

Lx (m)

Formula

(b)


Y

X

PVD

Drained

Drained





7 Conclusions






Data Availability


A ndash4000B 000C 4000D 8000E 12000F 16000

H 24000I 28000J 32000K 36000L 40000M 44000N 48000O 52000P 56000Q 60000R 64000S 68000T 72000U 76000


G 20000


A ndash010B 000C 010D 020E 030F 040

H 060G 050

I 070J 080K 090L 100M 110

(m)Max


0100200300400500600700800900

100011001200

0 5 10 15 20 25 30 35 40

Section 1



tera

l disp

lace

men

t (m

m)

Lx (m)

Section 2






Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











ELD δhminuse

s (14)



S 1113944n


Ei


(15)



ELD a ln Lx( 1113857 + b (16)




ndash11ndash10


0


Dep

th (m

)











λ middot cw (18)





0 5 10 15 20 25 30 35 4000

02

04

06

08

10EL

D

Lx (m)



(a)

00

02

04

06

08

10

0 5 10 15 20 25 30 35 40


Calculated δ S

ELD

Lx (m)

Formula

(b)


Y

X

PVD

Drained

Drained





7 Conclusions






Data Availability


A ndash4000B 000C 4000D 8000E 12000F 16000

H 24000I 28000J 32000K 36000L 40000M 44000N 48000O 52000P 56000Q 60000R 64000S 68000T 72000U 76000


G 20000


A ndash010B 000C 010D 020E 030F 040

H 060G 050

I 070J 080K 090L 100M 110

(m)Max


0100200300400500600700800900

100011001200

0 5 10 15 20 25 30 35 40

Section 1



tera

l disp

lace

men

t (m

m)

Lx (m)

Section 2






Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









λ middot cw (18)





0 5 10 15 20 25 30 35 4000

02

04

06

08

10EL

D

Lx (m)



(a)

00

02

04

06

08

10

0 5 10 15 20 25 30 35 40


Calculated δ S

ELD

Lx (m)

Formula

(b)


Y

X

PVD

Drained

Drained





7 Conclusions






Data Availability


A ndash4000B 000C 4000D 8000E 12000F 16000

H 24000I 28000J 32000K 36000L 40000M 44000N 48000O 52000P 56000Q 60000R 64000S 68000T 72000U 76000


G 20000


A ndash010B 000C 010D 020E 030F 040

H 060G 050

I 070J 080K 090L 100M 110

(m)Max


0100200300400500600700800900

100011001200

0 5 10 15 20 25 30 35 40

Section 1



tera

l disp

lace

men

t (m

m)

Lx (m)

Section 2






Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


7 Conclusions






Data Availability


A ndash4000B 000C 4000D 8000E 12000F 16000

H 24000I 28000J 32000K 36000L 40000M 44000N 48000O 52000P 56000Q 60000R 64000S 68000T 72000U 76000


G 20000


A ndash010B 000C 010D 020E 030F 040

H 060G 050

I 070J 080K 090L 100M 110

(m)Max


0100200300400500600700800900

100011001200

0 5 10 15 20 25 30 35 40

Section 1



tera

l disp

lace

men

t (m

m)

Lx (m)

Section 2






Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Acknowledgments


References





















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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