calculationapproachforlateralbearingcapacityofsingle ...downloads.hindawi.com › journals › ace...

Research ArticleCalculation Approach for Lateral Bearing Capacity of SinglePrecast Concrete Piles with Improved Soil Surrounds

Guangyin Du1 Anhui Wang1 Liye Li2 and Dingwen Zhang 1

1School of Transportation Southeast University Nanjing Jiangsu 210096 China2Tianjin Municipal Engineering Design amp Research Institute Tianjin 300392 China

Correspondence should be addressed to Dingwen Zhang zhangdwseueducn

Received 11 January 2018 Revised 21 May 2018 Accepted 13 June 2018 Published 12 July 2018

Academic Editor Li Li

Copyright copy 2018 Guangyin Du 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

Precast concrete (PC) piles with cement-improved soil surrounds have been widely used for soft ground improvement Howeververy few calculation approaches have been proposed to predict the lateral bearing capacity is study aims at investigating thelateral capacity of a single PC pile reinforced with cement-improved soil through a series of 3D finite element analyses andtheoretical studies It is revealed that application of cement-improved soil around the PC pile can obviously reduce the inducedlateral deflections and bending moments in the pile and can significantly increase its capacity to resist lateral loading To accountfor the reinforcement effect of cement-treated soil a modified m approach is proposed by introducing a modified coefficient toenable the predictions of the lateral bearing capacity for such reinforced PC piles It is revealed that the modified coefficient isapproximately linearly related to the compressive bearing capacity of improved soil surrounds

1 Introduction

Deep cement-mixing (DCM) column has many advantagessuch as a large volume limited environmental disturbancerapid construction and low cost so it is extensively usedin soft ground improvement However the DCM columnstrength is significantly affected by soil conditions whichresults in a low column uniformity and poor reinforcementeffect [1] Although a precast concrete (PC) pile has manyadvantages with various applications the strength of theconcrete pile cannot be sufficiently utilized under eithervertical or lateral loading and failure caused by soil failurecan always occur which makes it uneconomical for use insoft ground improvement [2] To solve the abovementionedproblems the PC pile with improved soil surrounds pro-duced by inserting a PC pile into a DCM column before theinitial setting of cement-improved soil (Figure 1) has re-cently been proposed [1 2] In this way the high-strengthPC pile is designed to bear a load and the improved soilsurrounds act to transfer axial force into the surroundingsoils by skin frictions [2] To date this new type of compositepile has attracted considerable attention owing to its low cost

and high effectiveness and has been successfully applied tosoft ground improvement [3ndash5]

To investigate the vertical bearing characteristics of PCpiles with improved soil surrounds a series of pile load testsnumerical simulations and theoretical models have beencarried out [5ndash9] ese studies verified that the applicationof cement-improved soil surrounds could greatly improvethe vertical bearing capacity of the PC pile and reduce itssettlement However further studies are also needed toevaluate the contribution of improved soil surrounds to thelateral performance of PC piles Liu [10] performed full-scalelateral load tests on several PC piles with improved soilsurrounds e test results showed that owing to the pres-ence of outer improved soil surrounds the lateral bearingcapacity and the lateral stiffness of the PC piles are significantlyincreased Rollins et al [11] performed lateral loading tests onan existing pile group modified with jet-grouting and cement-mixing column reinforcement around the pile caps It wasobserved that the lateral resistance of the existing pilegroup foundations could be significantly increased with jet-grouting and cement-mixing reinforcement Based on thefield tests of Rollins et al [11] Lin et al [12] used the finite

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 5127927 12 pageshttpsdoiorg10115520185127927

dierence simulation method to model the laterally loadedpile groups in soft clay with or without the jet-groutingcolumns In addition Wang et al [13] and He et al [14]carried out monotonic and cyclic lateral loading tests toinvestigate the contributions of the jet-grouting columnreinforcement to improve the lateral performance of thesingle cast-in-place pile

Although eld observations and numerical modeling oflaterally loaded piles with jet-grouting or cement-mixingcolumn reinforcement have been reported systematic studiespertaining to the contributions of cement-treated soil sur-rounds to the lateral capacity of PC piles are still somewhatlacking Indeed there is still much that is not well understoodabout the lateral capacity of PC piles with such improved soilsurrounds In addition there has generally been a limitedamount of theoretical studies pertaining to the lateral bearingcapacity of single PC piles with improved soil surrounds sothis requires further investigation

is paper aims at conducting a comprehensive study onthe lateral response of PC piles with improved soil surroundsas well as them approach for predicting the bearing capacityunder lateral loading To achieve the research objectivesthree-dimensional (3D) numerical analyses that were rstvalidated against eld test results were performed usingMidasGTS nite element software e eect of outerimproved soil surrounds on the lateral response of PC pileswas further assessed Moreover a modied m approach ac-counting for the cement-improved soil reinforcement wasproposed for the reinforced piles within the cohesive soil andthe suitability of the proposed m approach for predicting thelateral bearing capacity of such reinforced piles was alsoassessed

2 Numerical Simulations

In order to evaluate the eect of cement-improved soilsurrounds on the lateral bearing performance of a PC pilethe MidasGTS software was used to establish three-dimensional models of PC piles with and without im-proved soil surrounds under lateral loading according to

the full-scale pile load tests e test project was performedin Nantong which is located along the southeast coast ofChina Extensive eld tests and laboratory tests wereperformed to characterize the subsoil conditions Specif-ically conventional laboratory soil tests were carried out todetermine the unit weight compression modulus andrelevant shear parameters of the soil mass Moreovera cone penetration test (CPT) which is one of the mostcommonly used eld test approaches in geotechnicalinvestigations was performed to determine the ultimateunit skin friction and tip resistance e soil prole andengineering properties of the test site are presented inFigure 2 It can be seen that the soil prole near theground surface consists of a marine silty clay layer un-derlain by a silty sand deposit e deection and bendingmoment distribution of the two types of piles are theninvestigated in detail e detailed information of the testpiles is shown in Table 1

21 Numerical Modeling In general there are dierentnumerical approaches for analysis of the lateral bearingcapacity of a single pile [15] One approach is to establishthe pile-soil model based on the lateral pile-soil interactione other is to establish the pile-spring model by replacingthe pile-surrounding soil with equivalent spring anddamping based on the Winkler elastic foundation beamtheory Although the pile-spring model can simulate thecompressive and nontensile behavior of pile-surroundingsoil it cannot reect the plasticity of pile-surrounding soil Itis well known that with a gradual increase in the lateral loadapplied at the pile head the pile-surrounding soil changesfrom behaving elastically to plastically and the plastic zonearound the pile is gradually extended In addition in thepile-spring model the size of the pile-soil contact surface isassumed to be constant under dierent loading conditionsIn the pile-soil model however the contact surface maychange with varying loading conditions which is moreconsistent with the actual pile-soil interactionerefore thepile-soil model was adopted in this study

Surroundingsoil

PC pile

Improved soil surround

(a)

PC pile


(b)

Figure 1 (a) Schematic diagram of PC pile with improved soil surround (b) photo of eld excavation

2 Advances in Civil Engineering

e typical 3D finite element models used for the an-alyses are shown in Figures 3(a) and 3(b) In the horizontaldirection the surrounding soil was extended by 10 timesgreater than the pile diameter Meanwhile in the verticaldirection the surrounding soil was the same length as thepile e soil and pile were modeled using 3D eight-nodelinear brick elements with a refined mesh of 33600 ele-ments Particularly the mesh used for the soil was suffi-ciently fine in the region close to the pile Regarding themeshing convergence issue a numerical test shows thatfurther halving the current mesh size can only result ina change of numerical results of no more than 06 issuggests that sufficiently accurate simulation results can beachieved with the mesh size adopted in this study

A total stress analysis under undrained conditions wasadopted in this study to simulate the field lateral load tests onthe PC pile with improved soil surround which did notaccount for the pore water pressure response Such a mod-eling technique has been used by many scholars [16ndash20] ininvestigations of the behavior of a single pile subjected tolateral loading Accordingly the total stress parameters forboth the undrained modulus and shear strength of thecement-treated and untreated soil were assigned in thisnumerical study e MohrndashCoulomb failure criterion wasadopted to compute the failure loads of pile-surroundingsoils deforming under undrained conditions e undrainedshear strength Cu 20 kPa and undrained Youngrsquos modulusEu 750Cu for the silty clay were then determined throughthe undrained shear tests and the work of He et al [20]respectively e cement-treated soil was also assumed to

obey the MohrndashCoulomb failure criterion Specifically theundrained shear strength and Youngrsquos modulus of thecement-treated soil were obtained from the work ofJamsawang et al [21] and Tyagi et al [22] According toJamsawang et al [23] the tensile strength (σt) of cement-treated soil can be defined as 015 times the compressivestrength e constitutive models and parameters used inthis study are listed in Table 2 It is worth noting that thecement-improved soil is considered as homogeneouswithout varying with depth

e interaction between the PC pile and the improvedsoil surrounds was modeled by defining zero-thicknessinterface bond-slip elements at their contact surfaces soas to allow for the relative shear displacement between andthe separation of the two objects e interface cohesionand friction coefficient between the pile and cement-treated soil were derived as 200 kPa and 065 re-spectively Considering that slippage and gapping occursduring lateral loading the interaction between thecement-improved soil and the surrounding soil wasmodeled using the Coulomb friction model An interfacefriction coefficient of 035 was applied in this study efinite element analyses were comprised of two primarysteps First the initial stress field of the pile-soil systemwas balanced In the next step lateral loads were applied atthe pile head by multiple-step loading

22ValidationandResults Figure 4 compares the measuredand computed lateral load (P) versus the deflection (Y0)curve at the head of the piles with and without improved soil

Table 1 Detailed information about test piles (PCI-1 and PC-1)

Pile identifier Concrete gradePC piles Improved soil surrounds

Outer diameter (mm) Wall thickness (mm) Length (m) Outer diameter (mm) Length (m)PCI-1 C80 400 95 12 800 12PC-1 C80 400 95 12 mdash mdashNote PCI PC pile with improved soil surround PCPC pile without improved soil surround

2 4 6

Unit skin frictionfs (kPa)

Tip resistanceqc (MPa)

Compression modulusEs (MPa)

Unit weightγ (kgm3)

Undrained shear strengthCu (kPa)

14 16 18 20 0 5 10 15 20 0 40 80 120 0 15 30 4500

4

8

12

16

20

24

Dep

th (m

)

Silty clay

Silty sand

Figure 2 Soil profile and engineering properties of the test site

Advances in Civil Engineering 3

surrounds respectively It can be seen that the computedpile-head deections agreed well with the numerical resultsin the case of a lateral load less than 100 kN However whenthe lateral load exceeded 100 kN the computed results weresignicantly dierent from the corresponding measuredvalues For laterally loaded exible piles failure of the pile-soil system can always be a result of the plastic damage of thepile following yielding of the pile-surrounding soil [20 24]Additionally the lateral bearing capacities of these two typesof piles were determined to be 125 kN and 95 kN re-spectively according to Technical Code for Building PileFoundations [25] erefore in this study once the lateralload was applied up to 100 kN the severe tension-induceddamage in the pile occurred and its exural rigidity obviouslydecreased resulting in a steep increase in the pile deectionHowever the numerical modeling does not take the piledamage into account which leads to the foregoing dierence Itis worth mentioning that the lateral bearing capacity of the PC

pile with cement-treated soil reinforcement was approximately30 larger than that of the unreinforced PC pile which in-dicates an essential strengthening eect with the application ofcement-improved soil around a PC pile

Figure 5 shows the computed lateral deection along thePC pile with and without improved soil surrounds in thecase of a lateral load of 100 kN It can be observed that bothtypes of piles behaved as exible piles and the pile deectiondecreased nonlinearly from the pile head with the deectionprimarily distributed at the upper part of the pile body issuggests that the shallow soil layer which ranged from 0m toapproximately 5m below the ground surface played a keyrole in the bearing performance of the PC pile subjected tolateral loading A comparison indicates that the lateral de-ection along the PC pile with improved soil surrounds wasobviously smaller than that of the PC pile alone in the soilis is because the pile deection at a certain depth wasclosely related to the pile-soil modulus ratio When a PC pile

80 m

80

m4

0 m

(a)

08 m

120

m

(b)

Figure 3 3D nite element models of (a) entire pile-soil system and (b) pile with improved soil surround

Table 2 Material models and parameters used in this study

Material type Model c (kgm3) Eu (MPa) v Cu (kPa) Φ (deg) σt (kPa)Shallow silty clay MohrndashCoulomb 1780 15 049 20 mdash mdashDeep silty sand MohrndashCoulomb 1920 35 049 mdash 30 mdashCement-improved soil MohrndashCoulomb 2100 300 049 450 mdash 300PC pile Linear elastic 2400 38000 020 mdash mdash mdash


was concentrically inserted into the cement-improved soilsurrounds the greater constraint eect provided by the outercement-improved soil undoubtedly caused a noticeabledecrease in pile deection

Figure 6 shows the computed bendingmoment along thePC piles with and without improved soil surrounds in thecase of a lateral load of 100 kN It is evident that the vari-ations in the bending moment along the PC pile with im-proved soil surrounds were consistent with that along the PCpile alone in soil To be specic the bending momentincreased monotonically to a peak and then graduallydecreased which had also been reported by Liu [10] It isclearly observed that the maximum bending moment ofthe PC pile with improved soil surrounds was signicantlysmaller than that of the PC pile alone in soil is can beattributed to the fact that the presence of the improved soilsurrounds resulted in a large equivalent diameter of thepile which could generate greater soil resistance to thepile deection thus signicantly reducing the bendingmoment in the PC pile e reduction is also in agreementwith Voottipruex et al [6] and Liu [10] who found thatthe outer improved soil surrounds may play a critical rolein load transfer and can eectively transfer the lateral loadfrom the PC pile to the surrounding soil

Although the application of cement-improved soilaround a PC pile could greatly reduce the accumulationof pile deection and bending moment both types ofpiles experienced similar trends when subjected to lateral

0

10

20

30

40

50

60

Y 0 (m

m)

PCI-1 (measured)PC-1 (measured)

PCI-1 (computed)PC-1 (computed)

0 50 100 150 200

Lateral bearing capacity

P (kN)

Figure 4 Comparisons between the measured and computed P-Y0curves for pile PCI-1 and pile PC-1

0

2

4

6

8

10

12

Dep

th (m

)

Lateral deflection (mm)

PCI-1PC-1

ndash1 1 3 5 7 9 11

Figure 5 Computed lateral deection along pile PCI-1 and pilePC-1 at a lateral load of 100 kN

PCI-1PC-1

0

2

4

6

8

10

12

Dep

th (m

)

Bending moment (kNmiddotm)ndash5 15 35 55 75 95

Figure 6 Computed bending moment along pile PCI-1 and pilePC-1 at a lateral load of 100 kN


loading is suggests that the lateral bearing behavior ofthe PC pile with improved soil surrounds was similarto that of the PC pile alone in soil erefore the mapproach applicable to a single PC pile without improvedsoil surrounds can still be used to calculate the lateralbearing capacity of a single PC pile with improved soilsurrounds But related parameters in the existing m ap-proach need to be modified so as to reflect the re-inforcement effect of improved soil surrounds on thelateral bearing performance of PC piles

3 Modified m Approach for PC Piles withImproved Soil Surrounds

31mApproach em approach was proposed based on theWinkler elastic foundation model and EulerndashBernoulli beamtheory and it is assumed that the lateral soil resistance ata certain depth equals the product of the corresponding lateralresistance coefficient and pile deflection Moreover the lateralresistance coefficient linearly increases with the depth and isequal to zero at the ground surface

According to the Technical Code for Building Pile Foun-dations [25] the calculation formula for the lateral bearingcapacity of a single PC pile is expressed as

Rha βα3EI

vxχ0a (1)

where Rha design value of the lateral bearing capacity ofsingle PC piles (kN) β reduction coefficient generallytaken as 10 χ0a allowable lateral deflection at pile head(m) vx pile-head deflection coefficient EI flexural stiff-ness of pile (kNmiddotm2) and α lateral deformation coefficientof pile which is given as

α

mb1

EI5

1113970

(2)

where b1 calculation width of pile (m) and m proportionalcoefficient of lateral resistance coefficient (kNm4) which canbe determined by the Technical Code for Building Pile Foun-dations [25] as summarized in Table 3

It should be noted that for the PC piles with improvedsoil surrounds the flexural stiffness and tensile strength of

the outer cement-improved soil are significantly lower thanthat of the inner PC pile and severe cracking in cement-improved soil can be easily induced under lateral loading Inother words slippage and separation is likely to occur at theinterface of the PC pile and the cement-improved soil duringloading us the two parts of the reinforced piles cannotwork together to support and transfer the lateral load ef-fectively especially in cases of cement-improved soil withlow strength Based on the above analysis it is reasonable totreat the outer improved soil surrounds as the pile-surrounding soil with greater soil resistance rather thanas the extended diameter of a PC pile As a result the pa-rameters EI and b1 of the PC pile were used to predict thelateral bearing capacity of a PC pile with improved soilsurrounds

It is well known that the proportional coefficient m isa key parameter for analysis of laterally loaded piles whenusing the m approach However the m value is closelydependent on soil properties pile material loading condi-tions and so on [26] Hence in order to determine the mvalue applicable to PC piles with improved soil surrounds itis required to consider the reinforcement effect of improvedsoil surrounds on the lateral PC pile

32 Back-Calculation of m Value In cases of the lateral loadon the free-head pile is applied at the ground surface thecoefficient m is determined from (1) and (2) as follows

m vxP( 1113857

53

b1Y530 (EI)23 (3)

where P and Y0 lateral load (kN) and pile-head deflection(m) corresponding to Rha and χ0a respectively

From (3) it can be seen that the variation of m with Y0can be deduced according to the P-Y0 curve derived frompile load tests In general at a pile-head deflection of 10mmthe applied load P is defined as the design value of lateralbearing capacity of single piles As a result the m value usedto determine the lateral bearing capacity of single piles canbe obtained from the m-Y0 curve

Figure 7 shows the deduced m-Y0 curves for single PCpiles with and without improved soil surrounds based on

Table 3 Value of proportional coefficient m of soil lateral resistance coefficient (JGJ 94-2008)

Type of foundation soilPC piles

m (kNm4) Corresponding lateral deflection of asingle pile at ground surface (mm)

Muck and muddy soil saturated collapsible loess 2000sim4500 10Liquefied plastic (ILgt 1) soft plastic (075lt ILle 1)clayey soil egt 09 silty soil loose silty fine sand looseand slightly dense fill

4500sim6000 10

Plastic (025lt ILle 075) clayey soil e 075sim09 siltysoil collapsible loess medium dense fill slightlydense fine sand

6000sim10000 10

Hard plastic (0lt ILle 025) and hard (ILle 0) clayeysoil collapsible loess elt 075 dense silty soil mediumdense medium sand dense old fill

10000sim22000 10


the results of pile load tests which were conducted inNantong China and reported by Jamsawang et al [4] edetailed information of such test piles is summarized inTables 1 and 4 Generally under large deection levels them value gradually decreased with the increasing de-ection At a pile-head deection of 10mm the back-calculated and recommendedm values (shown in Figure 7and Table 3 resp) are compared in Table 5 From theseresults it is clearly demonstrated that the back-calculatedm value for the PC pile without improved soil surroundswas very close to the recommendedm value However theback-calculated m values for PC piles with improved soilsurrounds were 16 to 50 times larger than the recom-mended values for PC piles alone in soil is denotes that

the improved soil surrounds led to an obvious increase inthe m values of the PC piles

33 Modied Coecient In order to clearly distinguish thesignicant dierence between the back-calculated and rec-ommendedm values a modied coesectcient ξm is dened asfollows

ξm the back minus calculated m value

the recommended m value (maximum) (4)

Table 6 shows the modied coesectcients for dierent testpiles and several parameters of outer improved soil sur-rounds It can be seen from Table 6 that the strength of

Table 4 Detailed information of test piles (PCI-2simPCI-4 PCI-L1simPCI-L8)

Pileidentier

Concretegrade

PC piles Improved soil surroundsOuter diameteredge length (mm) Wall thickness (mm) Length (m) Outer diameter (mm) Length (m)

PCI-2 C80 400 95 12 800 15PCI-3 C80 600 110 9 800 9PCI-4 C80 600 110 9 800 9PCI-L1 L2lowast C35 220 mdash 6 600 7PCI-L3 L4lowast C35 220 mdash 4 600 7PCI-L5 L6lowast C35 180 mdash 6 600 7PCI-L7 L8lowast C35 180 mdash 4 600 7lowastNote PCI-L1simPCI-L8 are solid square PC piles with improved soil surrounds reported by Jamsawang et al [4]

0

11000

22000

33000

44000

55000

66000

Y0 (mm)

PCI-1PC-1PCI-2PCI-3PCI-4PCI-L1PCI-L2

PCI-L3PCI-L4PCI-L5PCI-L6PCI-L7PCI-L8

m (k

Nm

4 )

0 8 16 24 32 40

Figure 7 Deduced m-Y0 curves for lateral test piles


cement-treated soil with the wet spraying method wasgenerally lower than that with the dry spraying method It isknown that the improvement of the soil with cementtreatment is referred to as the chemical reactions betweencement and the soil particles and the water-cement ratiohas an important influence on the mechanical properties

of cement-treated soil Once the water-cement ratio ex-ceeds the optimum level the strength of cement-treatedsoil obviously decreases with the increasing water-cementratio [27 28] It is worth noting that in practical engi-neering the initial water content of the natural clayundoubtedly increases the water-cement ratio of thecement-treated soil us it can be concluded that thelower strength of a DCM column can always occur whenconstructed using the wet spraying method especially incoastal areas with a high groundwater level and watercontent

It can be observed that the m value for PC piles withimproved soil surrounds was not only dependent on soilproperties but also closely related to the compressivestrength and cross-sectional area of outer improved soilsurrounds e larger the cross-sectional area and the higherthe compressive strength of the improved soil surrounds thelarger the modified coefficient is can be attributed to thedifferent reinforcement effects of outer improved soil sur-rounds Fortunately the reinforcement effect of outerimproved soil surrounds was found to be positivelyrelated to its compressive bearing capacity (denoted asQu (kN)) us a correlation relationship between ξm andQu can be established As shown in Figure 8 for PC pileswith improved soil surrounds ξm exhibited an

Table 6 Modified coefficients for different test piles and several parameters of outer improved soil surrounds

Pile identifierImproved soil surrounds

Modified coefficient ξmCross-sectional area (m2) Compressive strength (MPa) Compressive bearing capacity (kN)PCI-1 03768 200 7536 (dry spraying) 50PCI-2 03768 077 2901 (wet spraying) 25PCI-3 02198 060 1319 (wet spraying) 16PCI-4 04067 120 4880 (dry-wet spraying) 35PCI-L1 02342 094 2195 (wet spraying) 25PCI-L2 02342 091 2127 (wet spraying) 24PCI-L3 02342 088 2058 (wet spraying) 24PCI-L4 02342 088 2058 (wet spraying) 24PCI-L5 02502 093 2336 (wet spraying) 30PCI-L6 02502 090 2253 (wet spraying) 29PCI-L7 02502 090 2253 (wet spraying) 29PCI-L8 02502 087 2170 (wet spraying) 28

ξm = 00056Qu + 10R2 = 08841

00

10

20

30

40

50

60

ξm

Qu (kN)0 150 300 450 600 750 900

Figure 8 Correlation between the modified coefficient andcompressive bearing capacity of improved soil surrounds

Table 5 Back-calculated and recommended m values at a pile-head deflection of 10mm

Pile identifier Type of foundation soil Back-calculated m value (kNm4) Recommended m value (kNm4)PCI-1 Silty clay silty sand 50000 6000sim10000PC-1 11000 6000sim10000PCI-2

Silty soil silty sand25000 6000sim10000

PCI-3 16000 6000sim10000PCI-4 35000 6000sim10000PCI-L1

Weathered soil soft soil

15000 4500sim6000PCI-L2 14400 4500sim6000PCI-L3 14400 4500sim6000PCI-L4 14400 4500sim6000PCI-L5 18000 4500sim6000PCI-L6 17400 4500sim6000PCI-L7 17400 4500sim6000PCI-L8 16800 4500sim6000


approximately linear increase with Qu Moreover whenQu 0 (corresponding to the PC pile without improvedsoil surrounds) the modified coefficient ξm should bedetermined as 10 us the linear correlation function isfitted as follows

ξm 00056Qu + 1 (5)

In summary for laterally loaded single PC piles withimproved soil surrounds the m value can be obtained byintroducing the modified coefficient us a modified mapproach is proposed by modifying them value based on theexisting m approach that is by substituting the modified mvalue into the existing equation e proposed m approachcan account for the cement-treated soil reinforcement

4 Evaluation of the Modified and Existing mApproach for Piles with ImprovedSoil Surrounds

According to the pile load test data presented in this studythe lateral bearing capacities of these test piles were calcu-lated using the modified and existing m approach as shownin Figure 9 It is clearly seen that the lateral bearing capacitiesobtained by the modified m approach were all in goodagreement with the measured results with a relative errorrange of 15ese results also indicate that the modifiedmapproach was able to effectively account for the re-inforcement effect of outer improved soil surroundserefore it is feasible and appropriate to predict the lateralbearing capacity of PC piles with improved soil surrounds byusing the modified m approach However the calculatedbearing capacities from the existing m approach were ob-viously smaller than that measured indicating that the

existing m approach would significantly underestimate thelateral capacity of such reinforced piles is implies thatdesigns of laterally loaded single PC piles with improved soilsurrounds using the existing m approach would tend to beconservative

To further assess the suitability of the modified m ap-proach for the analysis of laterally loaded piles with im-proved soil surrounds the deflection and moment responsesderived using the modified and existing m approach werecompared with the numerical results (from Figures 5 and 6)as demonstrated in Figures 10 and 11 respectively It isevident that both the pile deflection and moment from theexisting m approach were significantly larger than thosefrom the numerical results However compared with thenumerical results the modified m approach can accuratelypredict the lateral response of a reinforced PC pile is alsofurther indicates that the proposedm approach is applicablefor laterally loaded single PC piles with improved soilsurrounds and would be especially useful in practice

5 Conclusions

In this paper the numerical and theoretical investigation onthe lateral bearing capacity of a single PC pile with improvedsoil surrounds was presented e existing m approach(recommended by Technical Code for Building Pile Foun-dations (JGJ 94-2008)) was modified by taking into accountthe reinforcement effect of outer improved soil surroundse primary conclusions that can be obtained from thisstudy are summarized below

(1) By applying cement-improved soil around a PC pilethe lateral deflection and the maximum bendingmoment of the PC pile are significantly reduced

Measured resultsModified m approachExisting m approach

PCI-1 PCI-2 PCI-3 PCI-4 PCI-L1 PCI-L2 PCI-L3 PCI-L4 PCI-L5 PCI-L6 PCI-L7 PCI-L80

20

40

60

80

100

120

140

Late

ral b

earin

g ca

paci

ty (k

N)

Figure 9 Comparison of lateral bearing capacity using the modified and existing m approach and measured results


0

2

4

6

8

10

12

Dep

th (m

)


Numerical resultsModified m approachExisting m approach

ndash1 1 3 5 7 9 11

Figure 10 Comparison of predicted pile deections from the modied and existing m approach and numerical results at a lateral load of100 kN


0

2

4

6

8

10

12

Dep

th (m

)


Figure 11 Comparison of predicted pile moments from the modied and existing m approach and numerical results at a lateral load of100 kN


Nevertheless the lateral performance of the PC pilewith improved soil surrounds is similar to that of thePC pile alone in soil us the lateral bearing ca-pacity of a single PC pile with improved soil sur-rounds can still be calculated using the m approach

(2) To account for the reinforcement effect of improvedsoil surrounds on the laterally loaded single PC pilesa modifiedm approach was proposed by introducinga modified coefficient based on the existing m valuee modified coefficient ξm is approximately line-arly related to the compressive bearing capacity ofcement-improved soil surrounds

(3) Compared with numerical results the proposed mapproach can accurately predict the lateral bearingcapacity of single PC piles with improved soil sur-rounds In addition the existing m approach obvi-ously underestimates the lateral bearing capacity ofsuch reinforced PC piles thus leading to a conser-vative prediction of their lateral performance

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

is study was supported by the National Key RampD Programof China (Grant no 2016YFC0800200) and the NationalNatural Science Foundation of China (Grant no 41372308)

References

[1] P Dong R Qin and Z Chen ldquoBearing capacity and set-tlement of concrete-cored DCM pile in soft groundrdquo Geo-technical and Geological Engineering vol 22 no 1pp 105ndash119 2004

[2] X N Gao S Liu and P Dong ldquoApplication of concrete-coredDCM pile in soft ground treatment of highway bridgeheadrdquoin Proceedings of the Fourth International Conference onGrouting and Deep Mixing New Orleans LA USA February2012

[3] V P Faro N C Consoli F Schnaid A ome and L daSilva Lopes ldquoField tests on laterally loaded rigid piles incement treated soilsrdquo Journal of Geotechnical and Geo-environmental Engineering vol 141 no 6 article 060150032015

[4] P Jamsawang D T Bergado and P Voottipruex ldquoFieldbehaviour of stiffened deep cement mixing pilesrdquo Proceedingsof the Institution of Civil Engineers-Ground Improvementvol 164 no 1 pp 33ndash49 2011

[5] AWonglert and P Jongpradist ldquoImpact of reinforced core onperformance and failure behavior of stiffened deep cementmixing pilesrdquo Computers and Geotechnics vol 69 pp 93ndash1042015

[6] P Voottipruex T Suksawat D T Bergado andP Jamsawang ldquoNumerical simulations and parametric study

of SDCM and DCM piles under full scale axial and lateralloadsrdquoComputers and Geotechnics vol 38 no 3 pp 318ndash3292011

[7] J J Zhou X N Gong K H Wang R H Zhang andT L Yan ldquoA model test on the behavior of a static drill rootednodular pile under compressionrdquo Marine Georesources andGeotechnology vol 34 no 3 pp 293ndash301 2016

[8] J J Zhou X N Gong K H Wang R H Zhang and J J YanldquoTesting and modeling the behavior of pre-bored groutingplanted piles under compression and tensionrdquo Acta Geo-technica vol 12 no 5 pp 1061ndash1075 2017

[9] S iyyakkandi M Mcvay M P Lai and M R HerreraldquoSuitability of jetted and grouted precast pile for supportingmast arm structuresrdquo Canadian Geotechnical Journal vol 54no 9 pp 1231ndash1244 2017

[10] B P Liu ldquoExperimental study on the reinforced mixing pilerespectively subjected to a vertical load or a lateral loadrdquo MSthesis School of Civil Engineering Tianjin UniversityTianjin China 2006 in Chinese

[11] K M Rollins M E Adsero and A B Dan ldquoJet grouting toincrease lateral resistance of pile group in soft clayrdquo inProceedings of the International Foundation Congress andEquipment Expo pp 265ndash272 Orlando FL USA March2009

[12] C Lin J Han S L Shen and Z S Hong ldquoNumericalmodeling of laterally loaded pile groups in soft clay improvedby jet-groutingrdquo in Proceedings of the Fourth InternationalConference on Grouting and Deep Mixing pp 15ndash18 NewOrleans LA USA February 2012

[13] L Wang B He Y Hong Z Guo and L Li ldquoField tests of thelateral monotonic and cyclic performance of jet-grouting-reinforced cast-in-place pilesrdquo Journal of Geotechnical andGeoenvironmental Engineering vol 141 no 5 article06015001 2015

[14] B He L Z Wang and Y Hong ldquoField testing of one-way andtwo-way cyclic lateral responses of single and jet-groutingreinforced piles in soft clayrdquo Acta Geotechnica vol 12 no 5pp 1021ndash1034 2017

[15] Z Yang and B Jeremic ldquoNumerical analysis of pile behaviourunder lateral loads in layered elasticndashplastic soilsrdquo In-ternational Journal for Numerical and Analytical Methods inGeomechanics vol 26 no 14 pp 1385ndash1406 2002

[16] Y Kim and S Jeong ldquoAnalysis of soil resistance on laterallyloaded piles based on 3D soilndashpile interactionrdquo Computersand Geotechnics vol 38 no 2 pp 248ndash257 2011

[17] L F Miao A T C Goh K S Wong and C I Teh ldquoree-dimensional finite element analyses of passive pile behaviourrdquoInternational Journal for Numerical amp Analytical Methods inGeomechanics vol 30 no 7 pp 599ndash613 2010

[18] K Georgiadis S W Sloan and A V Lyamin ldquoUndrainedlimiting lateral soil pressure on a row of pilesrdquo Computers andGeotechnics vol 54 no 10 pp 175ndash184 2013

[19] Z H Zhao D Y Li F Zhang and Y Qiu ldquoUltimate lateralbearing capacity of tetrapod jacket foundation in clayrdquoComputers and Geotechnics vol 84 pp 164ndash173 2017

[20] B He LZ Wang and Y Hong ldquoCapacity and failuremechanism of laterally loaded jet-grouting reinforced pilesfield and numerical investigationrdquo Science China Techno-logical Sciences vol 59 no 5 pp 763ndash776 2016

[21] P Jamsawang N Yoobanpot Nanasisathit P Voottipruexand P Jongpradist ldquoree-dimensional numerical analysis ofa DCM column-supported highway embankmentrdquo Computersand Geotechnics vol 72 pp 42ndash56 2016


[22] A Tyagi M F B Zulkefli Y Pan S H Goh and F H LeeldquoFailure modes of tunnels with improved soil surroundsrdquoJournal of Geotechnical and Geoenvironmental Engineeringvol 143 no 11 article 04017088 2017

[23] P Jamsawang P Voottipruex P Boathong W Mairaing andS Horpibulsuk ldquoree-dimensional numerical investigationon lateral movement and factor of safety of slopes stabilizedwith deep cement mixing column rowsrdquo Engineering Geologyvol 188 pp 159ndash167 2015

[24] L J Zhu Y M Cheng and D B Yang ldquoe analysisof instrumented piles under lateral loadrdquo Geomechanicsamp Geoengineering vol 7 no 1 pp 27ndash37 2012

[25] JGJ 94-2008 Technical Code for Building Pile FoundationsChina Architecture and Building Press Beijing China 2008in Chinese

[26] X M Lou H Wu and J F Huang ldquoDetermination of slopecoefficient of subgrade reaction of saturated clay based on p-ycurverdquo Chinese Journal of Geotechnical Engineering vol 34no 12 pp 2206ndash2212 2012 in Chinese

[27] F H Lee Y Lee S H Chew and K Y Yong ldquoStrength andmodulus of marine clay-cement mixesrdquo Journal of Geo-technical and Geoenvironmental Engineering vol 131 no 2pp 178ndash186 2005

[28] T Tsuchida and Y X Tang ldquoEstimation of compressivestrength of cement-treated marine clays with different initialwater contentsrdquo Soils and Foundations vol 55 no 2pp 359ndash374 2015


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

dierence simulation method to model the laterally loadedpile groups in soft clay with or without the jet-groutingcolumns In addition Wang et al [13] and He et al [14]carried out monotonic and cyclic lateral loading tests toinvestigate the contributions of the jet-grouting columnreinforcement to improve the lateral performance of thesingle cast-in-place pile

Although eld observations and numerical modeling oflaterally loaded piles with jet-grouting or cement-mixingcolumn reinforcement have been reported systematic studiespertaining to the contributions of cement-treated soil sur-rounds to the lateral capacity of PC piles are still somewhatlacking Indeed there is still much that is not well understoodabout the lateral capacity of PC piles with such improved soilsurrounds In addition there has generally been a limitedamount of theoretical studies pertaining to the lateral bearingcapacity of single PC piles with improved soil surrounds sothis requires further investigation

is paper aims at conducting a comprehensive study onthe lateral response of PC piles with improved soil surroundsas well as them approach for predicting the bearing capacityunder lateral loading To achieve the research objectivesthree-dimensional (3D) numerical analyses that were rstvalidated against eld test results were performed usingMidasGTS nite element software e eect of outerimproved soil surrounds on the lateral response of PC pileswas further assessed Moreover a modied m approach ac-counting for the cement-improved soil reinforcement wasproposed for the reinforced piles within the cohesive soil andthe suitability of the proposed m approach for predicting thelateral bearing capacity of such reinforced piles was alsoassessed

2 Numerical Simulations

In order to evaluate the eect of cement-improved soilsurrounds on the lateral bearing performance of a PC pilethe MidasGTS software was used to establish three-dimensional models of PC piles with and without im-proved soil surrounds under lateral loading according to

the full-scale pile load tests e test project was performedin Nantong which is located along the southeast coast ofChina Extensive eld tests and laboratory tests wereperformed to characterize the subsoil conditions Specif-ically conventional laboratory soil tests were carried out todetermine the unit weight compression modulus andrelevant shear parameters of the soil mass Moreovera cone penetration test (CPT) which is one of the mostcommonly used eld test approaches in geotechnicalinvestigations was performed to determine the ultimateunit skin friction and tip resistance e soil prole andengineering properties of the test site are presented inFigure 2 It can be seen that the soil prole near theground surface consists of a marine silty clay layer un-derlain by a silty sand deposit e deection and bendingmoment distribution of the two types of piles are theninvestigated in detail e detailed information of the testpiles is shown in Table 1

21 Numerical Modeling In general there are dierentnumerical approaches for analysis of the lateral bearingcapacity of a single pile [15] One approach is to establishthe pile-soil model based on the lateral pile-soil interactione other is to establish the pile-spring model by replacingthe pile-surrounding soil with equivalent spring anddamping based on the Winkler elastic foundation beamtheory Although the pile-spring model can simulate thecompressive and nontensile behavior of pile-surroundingsoil it cannot reect the plasticity of pile-surrounding soil Itis well known that with a gradual increase in the lateral loadapplied at the pile head the pile-surrounding soil changesfrom behaving elastically to plastically and the plastic zonearound the pile is gradually extended In addition in thepile-spring model the size of the pile-soil contact surface isassumed to be constant under dierent loading conditionsIn the pile-soil model however the contact surface maychange with varying loading conditions which is moreconsistent with the actual pile-soil interactionerefore thepile-soil model was adopted in this study

Surroundingsoil

PC pile


(a)

PC pile


(b)

Figure 1 (a) Schematic diagram of PC pile with improved soil surround (b) photo of eld excavation










2 4 6






14 16 18 20 0 5 10 15 20 0 40 80 120 0 15 30 4500

4

8

12

16

20

24

Dep

th (m

)

Silty clay

Silty sand






80 m

80

m4

0 m

(a)

08 m

120

m

(b)








0

10

20

30

40

50

60

Y 0 (m

m)



0 50 100 150 200


P (kN)


0

2

4

6

8

10

12

Dep

th (m

)


PCI-1PC-1

ndash1 1 3 5 7 9 11


PCI-1PC-1

0

2

4

6

8

10

12

Dep

th (m

)








Rha βα3EI

vxχ0a (1)


α

mb1

EI5

1113970

(2)






m vxP( 1113857

53

b1Y530 (EI)23 (3)








4500sim6000 10


6000sim10000 10


10000sim22000 10









Pileidentier

Concretegrade



0

11000

22000

33000

44000

55000

66000

Y0 (mm)



m (k

Nm

4 )

0 8 16 24 32 40









ξm = 00056Qu + 10R2 = 08841

00

10

20

30

40

50

60

ξm

Qu (kN)0 150 300 450 600 750 900










ξm 00056Qu + 1 (5)






5 Conclusions





20

40

60

80

100

120

140

Late

ral b

earin

g ca

paci

ty (k

N)



0

2

4

6

8

10

12

Dep

th (m

)



ndash1 1 3 5 7 9 11



0

2

4

6

8

10

12

Dep

th (m

)







Data Availability




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










2 4 6






14 16 18 20 0 5 10 15 20 0 40 80 120 0 15 30 4500

4

8

12

16

20

24

Dep

th (m

)

Silty clay

Silty sand






80 m

80

m4

0 m

(a)

08 m

120

m

(b)








0

10

20

30

40

50

60

Y 0 (m

m)



0 50 100 150 200


P (kN)


0

2

4

6

8

10

12

Dep

th (m

)


PCI-1PC-1

ndash1 1 3 5 7 9 11


PCI-1PC-1

0

2

4

6

8

10

12

Dep

th (m

)








Rha βα3EI

vxχ0a (1)


α

mb1

EI5

1113970

(2)






m vxP( 1113857

53

b1Y530 (EI)23 (3)








4500sim6000 10


6000sim10000 10


10000sim22000 10









Pileidentier

Concretegrade



0

11000

22000

33000

44000

55000

66000

Y0 (mm)



m (k

Nm

4 )

0 8 16 24 32 40









ξm = 00056Qu + 10R2 = 08841

00

10

20

30

40

50

60

ξm

Qu (kN)0 150 300 450 600 750 900










ξm 00056Qu + 1 (5)






5 Conclusions





20

40

60

80

100

120

140

Late

ral b

earin

g ca

paci

ty (k

N)



0

2

4

6

8

10

12

Dep

th (m

)



ndash1 1 3 5 7 9 11



0

2

4

6

8

10

12

Dep

th (m

)







Data Availability




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





80 m

80

m4

0 m

(a)

08 m

120

m

(b)








0

10

20

30

40

50

60

Y 0 (m

m)



0 50 100 150 200


P (kN)


0

2

4

6

8

10

12

Dep

th (m

)


PCI-1PC-1

ndash1 1 3 5 7 9 11


PCI-1PC-1

0

2

4

6

8

10

12

Dep

th (m

)








Rha βα3EI

vxχ0a (1)


α

mb1

EI5

1113970

(2)






m vxP( 1113857

53

b1Y530 (EI)23 (3)








4500sim6000 10


6000sim10000 10


10000sim22000 10









Pileidentier

Concretegrade



0

11000

22000

33000

44000

55000

66000

Y0 (mm)



m (k

Nm

4 )

0 8 16 24 32 40









ξm = 00056Qu + 10R2 = 08841

00

10

20

30

40

50

60

ξm

Qu (kN)0 150 300 450 600 750 900










ξm 00056Qu + 1 (5)






5 Conclusions





20

40

60

80

100

120

140

Late

ral b

earin

g ca

paci

ty (k

N)



0

2

4

6

8

10

12

Dep

th (m

)



ndash1 1 3 5 7 9 11



0

2

4

6

8

10

12

Dep

th (m

)







Data Availability




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

10

20

30

40

50

60

Y 0 (m

m)



0 50 100 150 200


P (kN)


0

2

4

6

8

10

12

Dep

th (m

)


PCI-1PC-1

ndash1 1 3 5 7 9 11


PCI-1PC-1

0

2

4

6

8

10

12

Dep

th (m

)








Rha βα3EI

vxχ0a (1)


α

mb1

EI5

1113970

(2)






m vxP( 1113857

53

b1Y530 (EI)23 (3)








4500sim6000 10


6000sim10000 10


10000sim22000 10









Pileidentier

Concretegrade



0

11000

22000

33000

44000

55000

66000

Y0 (mm)



m (k

Nm

4 )

0 8 16 24 32 40









ξm = 00056Qu + 10R2 = 08841

00

10

20

30

40

50

60

ξm

Qu (kN)0 150 300 450 600 750 900










ξm 00056Qu + 1 (5)






5 Conclusions





20

40

60

80

100

120

140

Late

ral b

earin

g ca

paci

ty (k

N)



0

2

4

6

8

10

12

Dep

th (m

)



ndash1 1 3 5 7 9 11



0

2

4

6

8

10

12

Dep

th (m

)







Data Availability




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






Rha βα3EI

vxχ0a (1)


α

mb1

EI5

1113970

(2)






m vxP( 1113857

53

b1Y530 (EI)23 (3)








4500sim6000 10


6000sim10000 10


10000sim22000 10









Pileidentier

Concretegrade



0

11000

22000

33000

44000

55000

66000

Y0 (mm)



m (k

Nm

4 )

0 8 16 24 32 40









ξm = 00056Qu + 10R2 = 08841

00

10

20

30

40

50

60

ξm

Qu (kN)0 150 300 450 600 750 900










ξm 00056Qu + 1 (5)






5 Conclusions





20

40

60

80

100

120

140

Late

ral b

earin

g ca

paci

ty (k

N)



0

2

4

6

8

10

12

Dep

th (m

)



ndash1 1 3 5 7 9 11



0

2

4

6

8

10

12

Dep

th (m

)







Data Availability




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









Pileidentier

Concretegrade



0

11000

22000

33000

44000

55000

66000

Y0 (mm)



m (k

Nm

4 )

0 8 16 24 32 40









ξm = 00056Qu + 10R2 = 08841

00

10

20

30

40

50

60

ξm

Qu (kN)0 150 300 450 600 750 900










ξm 00056Qu + 1 (5)






5 Conclusions





20

40

60

80

100

120

140

Late

ral b

earin

g ca

paci

ty (k

N)



0

2

4

6

8

10

12

Dep

th (m

)



ndash1 1 3 5 7 9 11



0

2

4

6

8

10

12

Dep

th (m

)







Data Availability




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








ξm = 00056Qu + 10R2 = 08841

00

10

20

30

40

50

60

ξm

Qu (kN)0 150 300 450 600 750 900










ξm 00056Qu + 1 (5)






5 Conclusions





20

40

60

80

100

120

140

Late

ral b

earin

g ca

paci

ty (k

N)



0

2

4

6

8

10

12

Dep

th (m

)



ndash1 1 3 5 7 9 11



0

2

4

6

8

10

12

Dep

th (m

)







Data Availability




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



ξm 00056Qu + 1 (5)






5 Conclusions





20

40

60

80

100

120

140

Late

ral b

earin

g ca

paci

ty (k

N)



0

2

4

6

8

10

12

Dep

th (m

)



ndash1 1 3 5 7 9 11



0

2

4

6

8

10

12

Dep

th (m

)







Data Availability




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

2

4

6

8

10

12

Dep

th (m

)



ndash1 1 3 5 7 9 11



0

2

4

6

8

10

12

Dep

th (m

)







Data Availability




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





Data Availability




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


calculationapproachforlateralbearingcapacityofsingle ...downloads.hindawi.com › journals › ace...

Documents