research article elastoplastical analysis of the interface … · 2019. 7. 31. · dove and jarret...

Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2013, Article ID 673057, 12 pageshttp://dx.doi.org/10.1155/2013/673057

Research ArticleElastoplastical Analysis of the Interface between Clay andConcrete Incorporating the Effect of the Normal Stress History

Zhao Cheng, Zhao Chunfeng, and Gong Hui

Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Department of Geotechnical Engineering,Tongji University, Shanghai 200092, China

Correspondence should be addressed to Zhao Chunfeng; [email protected]

Received 8 June 2013; Revised 23 August 2013; Accepted 10 September 2013

Academic Editor: Ga Zhang

Copyright © 2013 Zhao Cheng et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The behaviour of the soil-structure interface is crucial to the design of a pile foundation. Radial unloading occurs during the processof hole boring and concrete curing, which will affect the load transfer rule of the pile-soil interface.Through large shear tests on theinterface between clay and concrete, it can be concluded that the normal stress history significantly influences the shear behaviourof the interface. The numerical simulation of the bored shaft-soil interaction problem requires proper modelling of the interface.By taking the energy accumulated on the interface as a hardening parameter and viewing the shearing process of the interface asthe process of the energy dissipated to do work, considering the influence of the normal stress history on the shearing rigidity, amechanical model of the interface between clay and concrete is proposed. The methods to define the model parameters are alsointroduced.The model is based on a legible mathematical theory, and all its parameters have definite physical meaning.The modelwas validated using data from a direct shear test; the validation results indicated that the model can reproduce and predict themechanical behaviour of the interface between clay and concrete under an arbitrary stress history.

1. Introduction

The bearing behaviour of geotechnical structures embeddedin soil, such as deep foundations, tunnels, and retainingstructures, is influenced by the contact behaviour at theinterface between the surface of the structure and the sur-rounding soil. A systematic understanding of the shearingbehaviour will enable a more accurate analysis and improvethe ability to design these structures more accurately. Themechanism that transfers the load through the interface tothe surrounding soil has received significant attention in theliterature. Over recent decades, many constitutive modelshave been developed for the soil-structure interface, such asthe hyperbolic model and the extended hyperbolic model[1, 2], the Ramberg-Osgood nonlinear elastic model [3], thedirectionally dependent constitutive model [4], the rate-typemodel [5], the elastoplastic model [6], and the damage model[7].

A series of shear tests on soil-concrete interfaces wereperformedusing the independent developed visual large scaledirect shear apparatus by G. A. Zhang and J. M. Zhang

[8, 9], by using that, the interface behaviour is visible withmatching imagemeasurement [10]. Evgin and Fakharian alsodeveloped the interface apparatus with the name of C3DSSIto carry out the two-way cyclic tangential-displacement-controlled tests and cyclic rotational tests [11]. In geotechni-cal engineering, the pre- and postconstruction stress pathsfollowed by the interface may be complex, as well as theunloading and reloading. Gómez et al. evaluated the effect ofthe unloading-reloading paths on the shear behaviour at thesand-concrete interface [12]. By analysing the test data of thegroups of staged shear, unload-reload and multidirectionalstress path tests, a four-parameter extended hyperbolicmodelwas developed to account for the complex stress paths.However, there are no tests or models for the clay-concreteinterface found in the literature that can consider the effectof the stress path; thus, there is a need for more investigation,although it may be more sensitive to stress history.Therefore,it is urgent to develop a model that can incorporate theinfluence of normal stress history.

In this study, a large direct test apparatus was used tostudy the clay-concrete interface. The model of the interface

2 Journal of Applied Mathematics

Table 1: Main properties of clay.

Water content Plastic limit Liquid limit Cohesion Internal friction angle𝜔 𝜔𝑝 𝜔𝑙 𝑐 (kPa) 𝜑 (

∘)30% 22.4% 45.6% 11.5 22.3

between clay and concrete is proposed, followed by thedefinition of the parameters in the model. Finally, the modelwas validated by a comparisonwith the results from the directtests.

2. Large Direct Test

2.1. Test Apparatus. Despite some inherent problems, thedirect shear apparatus is a commonly used device for interfacetesting because of its simplicity in sample preparation proce-dures and its suitability for interface testing.Therefore, a largedisplacement direct shear test machine in Tongji Universitywas used to conduct the shear strength test on the soil-concrete interface. Compared to conventional direct shearbox devices, the large displacement direct shear test resultsin more accurate interface shear measurements because theproportion of the overall interface affected by the boundariesis smaller for large devices than for smaller ones [13].

2.2. Soil Specimen. The soil specimen was remoulded clay.The main properties of the soil are listed in Table 1. The clayash was acquired thorough the procedure of airing, crushing,and screening through a sieve (pore size of 0.05mm). Toachieve the desired water content of 30%, appropriatelyselected amounts of clay ash were thoroughly mixed withcalculated amounts ofwater. Prior to being placed in the shearbox, the mixture was left to cure for a period of 12 hours toensure even water content in the specimen.

2.3. Concrete Plate Specimen. Ruled surface patterns wereused to model the concrete surface in this study.The asperityheight was changed to quantify the surface roughness, whilethe asperity angle was altered with the asperity height; thespan of the sawtooth was zero in the tests. The asperityheights of the concrete samples were 0, 10, and 20mm, withasperity angles of 0, 21.8 and 38.66 degrees, respectively. In theanalysis, samples number 0, #1, and #2 represent the concreteplateswith a sawtooth height of 0, 10, and 20mm, respectively.

The concrete specimen for testing was 600mm long by400mm wide by 50mm thick, as illustrated in Figure 1. Thespecimen was poured against plywood to produce the ruledsurface. A wooden frame was attached along the plywood.After the specimen was poured, it was left to cure for 28 daysto attain a standard strength. Subsequently, thewooden frameand plywood were removed.

2.4. Test Procedures. The prepared specimens were installedin the shear box in such a way that the bottom half containedthe concrete plate, while the top half contained the soil. Theinterface between the soil and concrete was located exactlybetween the two halves of the shear box, as shown in Figure 2,

Figure 1: The topography of the concrete plate in the test.

to investigate the effect of the normal stress history and thedegree of unloading on the shear behaviour and strength atthe soil-concrete interface. The specimens were consolidatedunder an initial normal stress 𝜎𝑛𝑖 of 400, 300, and 200 kPafor 1 hour, then unloaded to a specified normal stress (50 kPato 350 kPa). Both of the loading and unloading rates are1 KPa/min. After 1 hour of being under a constant appliednormal stress, the interface was sheared at a constant ratewhile the results were monitored. The normal load actingon the interface remained constant during the shear process.Each test was conducted with a rate of shear deformationof 0.3mm/min to a total of 30mm. This rate is sufficientlyslow to ensure that the excess pore water pressures of thespecimens are dissipated during the shearing.The 30mmdis-placement criterion was selected because it was observed thatunder operational conditions, the accumulation of 30mm oflateral displacement could result in excessive leakage of soil.All data regarding the test (horizontal shear force, shear, andnormal displacement) were collected by a computerised datalogging system. The results were monitored and saved usingthe computer software TEST.

2.5. Test Results

2.5.1. Effect of the Applied Normal Stress. Figure 3 showstypical test results for the interaction between clay andconcrete plate #0 with an identical initial normal stress of𝜎𝑛𝑖 = 400 kPa.The data from the direct shear tests performedon the interface between clay and concrete plates #1 and#2 are presented in Figures 4 and 5 for comparison. Atthe beginning of shearing, the shear stress increases sharplywith the horizontal displacement. For the applied normalstresses of 50 kPa and 100 kPa, as shear progresses, the stress-strain curves gradually trend to be flatter as the shear stressremains approximately constant for any further incrementin the horizontal displacement. However, for other highernormal stresses, the shear stress increases relatively slowlywith horizontal displacement in the later-shearing phase, andno strain-softening phenomenon is observed in the tests,which agrees with the results observed by Nasir and Fall[14]. From Figures 3, 4, and 5, it is also observed that thehigher applied normal stress during shearing offers a shear

Journal of Applied Mathematics 3

Figure 2: Setup of the specimen box.

stiffness increase for all the values of horizontal displacement.In the meantime, a dilative phenomenon was observedduring the tests. Figures 3, 4, and 5 also exhibit this dilativebehaviour for the interface between the clay and concreteplates. Before the dilation, the dilative force must offset theapplied normal stress acting on the soil specimen, so themore significant dilative displacement was observed in thetests in which a lower normal stress was applied. For thehighest applied normal stress of 350 kPa, the clay-concreteinterface first exhibits a short contracting behaviour followedby dilatation. The contracting behaviour can be attributed tothe lack of complete settlement due to the high normal stressand inadequate consolidation time for clay. For the appliednormal stress of 350 kPa and interface #0, no significantdilative behaviour was observed during the shearing process,whichmay be due to the higher applied normal stress and thelow roughness.

2.5.2. Effect of the Initial Normal Stress. Figure 6 showsthe test results for interface #0 with different initial nor-mal stresses of shearing under a normal stress of 100 kPa.The shear-stress—displacement and vertical-displacement—shear-displacement relationships for the interface betweenclay and concrete plates #1 and #2 are presented in Figures7 and 8, respectively. From these plots, it is observed thathigher initial normal stresses produce higher shear stressesduring shearing, apart form the curve of initial normal stress300 kPa on plate #1 and plate #2.This result may be attributedto shear test uncertainties and experimental variations fromsample to sample. The shear stiffness was not found to besignificantly influenced by the initial normal stress. Figures 6,7, and 8 exhibit the influence of the initial normal stresson the dilation phenomenon of the interface under thenormal stress of 100 kPa. For interfaces not experiencing theprogress of normal unloading, the soil near the interfaceis contracted before dilating. Note that the dilation fromthe start of shear for the interfaces of initial normal stressover 100 kPa experiences normal unloading. Moreover, agreater vertical displacement occurred for a higher initialnormal stress. Therefore, the results validate the effect of thenormal stress history on the deformational behaviour of theinterface.

2.5.3. Effect of Interface Roughness. For an interface not expe-riencing normal unloading, the conclusions that a rougherinterface exhibits higher shear strength and higher shearstiffness have been stated bymany researchers.The roughnessof the interface was found to have an effect on the shearzone thickness and shear failure model and to even controlthe movement style of the soil particles along the interface[7, 15]. However, the strength of the interface does notincrease indefinitely with the roughness, according to Zeghalet al. [15]. They identified a bilinear relationship betweenthe surface roughness and the interface friction. Below acertain “critical” roughness, the interface shear resistanceincreased with roughness, up to the point where the interfaceshear efficiency parameter reached 1.0. Dove and Jarret tookthe ruled topography interface to validate the existence ofa “critical” roughness; asperity angles greater than approx-imately 50 degrees caused shear within the soil above theinterface, resulting in the lack of the observation of increasingstrength [13]. In this experiment, the original planed heightsof asperity were 0, 1, 2, and 3 cm. The stress from #3interface was found to be below the corresponding value of#2 and, sometimes, even below that of the #1 interface. Thisphenomenon can be explained by the conclusion given byDove and Jarret [13]. Through a comparison of the shearstresses of #0, #1, and #2 interfaces in Figure 9, the sameconclusion can be made: higher asperity offers a highershear stress. The shear-contractive phase was found at thebeginning of the shear for the interfaces not experiencingnormal unloading, with a longer shear-contractive phasefor a smoother interface. Interface #0 traversed from theshear-contractive phase to the shear-dilative phase at a sheardisplacement of 11mm, while the traversal occurred at ashear displacement of 8mm for interface #1 and of 2mmfor interface #2. The higher contractive value was found tocorrespond to the smoother interface. The higher asperityresults in a higher asperity angle if the width of the asperityremains constant, and the soil near the interface was foundto receive more of the vertical component of the forcefor a higher asperity angle. Therefore, more shear-dilativedisplacement occurs for a rougher interface.

For the interfaces experiencing normal unloading, theeffect from the roughness can be analysed through themaximum shear stress during shear. Similar to the interface


0

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𝜎n = 50kPa𝜎n = 100 kPa𝜎n = 150kPa𝜎n = 200 kPa

𝜎n = 250kPa𝜎n = 300kPa𝜎n = 350kPa

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Interface shear displacement (mm)

Figure 3: Test results for the interface between clay and #0 plate (initial normal stress of 400 kPa).



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not experiencing normal unloading, the rougher interfaceexhibits a higher maximum shear stress, as depicted inFigure 10; #2 interface exhibited the highest maximum shearstress under the same stress history, the second highestwas for #1 interface, and #0 interface had the lowest value.As the initial normal stress increased, the effect from theroughness on the maximum shear stress became increas-ingly obvious. To analyse the effect of roughness on thedilative phenomenon, we take the data from the interfacesexperiencing normal stress unloading in the range from200 kPa to 100 kPa as an example (the other interfaces had thesame shear-dilative trend). Figure 11 shows the higher dilativedisplacement observed for a rougher interface; themaximum

vertical displacement was 2.87mm for #2 interface, 2.49mmfor #1 interface, and only 1.81mm for #0 interface.

3. Model Description

Due to the analogy between the behaviours of soil and theinterface between soils and structures, the proposed modelframe is based on the model of internal shear in soils [16].According to Liu et al. [16], the incremental stress tensor canbe expressed as

{𝑑𝜎} = {

𝑑𝜎𝑛

𝑑𝜏} = [𝐾] {

𝑑𝑢𝑛

𝑑𝑢𝑠

} , (1)


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orm

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r stre

ss (k

Pa)

0

5

10

15

20

25

30

35

𝜎ni = 400kPa𝜎ni = 300kPa

𝜎ni = 200 kPa𝜎ni = 100 kPa

−0.5



Figure 6: Test results for the interface between plate #0 and clay (applied normal stress of 100 kPa).

in which 𝑑𝜎𝑛 and 𝑑𝜏 are the incremental normal and shearstresses, respectively, and 𝑑𝑢𝑛 and 𝑑𝑢𝑠 are the incrementalnormal and tangential displacements, respectively. All theparameters can be obtained directly from the test. While theinterface is not purely smooth, the researchers [7, 12, 17, 18]found that a shear band exists near the interface duringshear. The thickness 𝑡 was observed to equal five times thediameters of the sand at the interface between the sand andthe structure. For the interface with clay, determining thevalue of 𝑡 has not been studied. In the direct shear test, thethickness of the shear band cannot be determined becausethe shear is limited along the plane. As a result, the value of

𝑡 is set to a constant value in the sections below. An internalstrain was assumed, even in the shear band. Consider

𝑑𝜀𝑛 =𝑑𝑢𝑛

𝑡

,

𝑑𝜀𝑠 =𝑑𝑢𝑠

𝑡

,

(2)

where 𝑑𝜀𝑛 and 𝑑𝜀𝑠 are the incremental normal and shearstrain, respectively. Thus, the matrix can be expressed as

[𝐾] = 𝑡 [𝐷𝑒𝑝] . (3)



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4


Here, [𝐷𝑒𝑝] is the elastoplastic constitutive matrix;Morched Zeghal et al. and Zhou Guo-qing et al. proposedthe expression of [𝐷𝑒𝑝]. To simplify the model, the associatedflow rule is applied in the proposed model as follows:

[𝐷𝑒𝑝] = [𝐷

𝑒] −

[𝐷𝑒] {𝑛}𝑇{𝑛} [𝐷

𝑒]

𝐻 + 𝑀 + {𝑛} [𝐷𝑒] {𝑛}𝑇, (4)

where 𝐻 is the hardening parameter, while 𝑀 describes theinfluence of the change in the interfacial frictional coefficientwith the stress state. In this proposed model, the interfacialfrictional coefficient is assumed to be constant during shear(𝑀 = 0) to perform the research on the effect of normal stress

history.The energy accumulated at the interface,𝑊𝑝, is takenas the hardening parameter:

𝐻 = 𝑊𝑝 = ∫

loading𝑑𝜎 𝑑𝜇𝑛 + ∫

loading𝜎𝑛𝑖 𝑑𝜇𝑛 − ∫

unloading𝑑𝜎 𝑑𝜇𝑛

− ∫

sheering𝑑𝜎 𝑑𝜇𝑛 − ∫

sheering𝑑𝜏 𝑑𝜇𝑠.

(5)

During the loading, the initial energies accumulatedat the interface are ∫loading 𝑑𝜎𝑑𝜇𝑛 and ∫loading 𝜎𝑛𝑖 𝑑𝜇𝑛,and the energy released during the normal unloading is∫unloading 𝑑𝜎𝑑𝜇𝑛. During shearing, the energy consumed to



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Number 0Number 1Number 2


Figure 9: Test results for an interface not experiencing normal unloading (normal stress of 100 kPa).

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Max

imum

inte

rfaci

al st

reng

th (k

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Normal stress (kPa)100


Figure 10: The maximum shear stress versus the normal stress forinterfaces of different roughness.

do work is ∫sheering 𝑑𝜏 𝑑𝜇𝑠. Meanwhile, energy continues to beaccumulated in the amount of ∫sheering 𝑑𝜎 𝑑𝜇𝑛 for the shear-contractive interface but is consumed for the shear-dilatantinterface.

[𝐷𝑒] is the elastic constitutive matrix, in which nonlinear

elasticity is used. For simplicity, the elastic moduli in the nor-mal and tangential directions are assumed to be uncoupled:

[𝐷𝑒] = [

𝐷𝑛 0

0 𝐷𝑠

] , (6)

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Figure 11: The vertical dilative displacement for interfaces ofdifferent roughness.

where 𝐷𝑛 and 𝐷𝑠 are the normal and tangential moduli,respectively, which are both influenced by the stress historyand stress state, according to Desai C. S.

Liu et al. [16] identified the loading direction vector {𝑛} as

{𝑛} = (

𝑑𝑓

√1 + 𝑑2

𝑓

1

√1 + 𝑑2

𝑓

) . (7)

The parameter 𝑑𝑓 is related to the stress state and theinitial state of the interface; however, it cannot capture theloading direction of the sawtooth interface in our large test.Morched Zeghal and coworkers modelled the interface as


B

A

Unloading line𝜅

𝜆

un/t

Loading line

lnp

ln𝜎n ln𝜎ni

Figure 12: 𝑢𝑛-ln𝑝 plots of the loading and unloading process in thetests.

a ruled sawtooth. According to their approach, the loadingdirection of the sawtooth should be

{𝑛} = {

𝜕𝐹

𝜕𝜎𝑛

𝜕𝐹

𝜕𝜏

}

= {sin𝛼𝑘 + 𝑢 cos𝛼𝑘 cos𝛼𝑘 − 𝑢 sin𝛼𝑘} .(8)

Here, 𝑢 is the frictional coefficient of the interface whenthe sawtooth height is equal to zero. 𝛼𝑘 is the topographyparameter.

4. Identification of the Model Parameters

4.1. Elastic Moduli: 𝐷𝑛 and 𝐷𝑠. The normal elastic moduli𝐷𝑛 can be determined from the loading-unloading curve of𝑢𝑛-ln𝑝, as shown in Figure 12; the displacement of the ABsection is deduced from the primary consolidation of the clayunder the initial normal stress, and the resilience occurring asthe initial normal stress 𝜎𝑛𝑖 is unloaded to the normal stress𝜎𝑛. The slope coefficient of the resilience line was signified by𝜅. Thus, the normal moduli can be determined as.

𝐷𝑛 =𝜎𝑛

𝜅

. (9)

The hyperbolic model was validated by many test results,which measured the shear moduli changes with shear dis-placement. Consider

𝐷𝑠 =𝑎

(𝑎 + 𝑏𝜀𝑠)2, (10)

where 𝑎 = 1/𝐷𝑠𝑖, 𝑏 = 𝜎𝑛/𝜏ult, and 𝜏ult is the ultimate shearstrength of the critical state in the test; thus, 𝑏 = 1/𝜂𝑐.From Figures 3–8, the peak shear strength is not yet reached,even when the shear displacement is accumulated to 30mm,which is the limit displacement of this test because, underoperational conditions, the accumulation of 30mm of lateral

displacement was observed to possibly result in excessiveleakage of soil.Thus, the destructional ratio 𝑅𝑓 is introduced:

𝑅𝑓 =

𝜏𝑓

𝜏ult, (11)

𝐷𝑠 = 𝐷𝑠𝑖(1 − 𝑅𝑓

𝜏

𝜏𝑓

)

2

, (12)

where 𝜏𝑓 is the shear stress as the shear displacement reaches30mm and 𝜏ult is determined through curve fitting. 𝐷𝑠𝑖 arethe initial tangent shear moduli, which are described byAnubhavP.K. and coworkers; where an increase in the normalstress will result in steeper shear-relative displacement curvesand a higher strength, and the values of𝐷𝑠𝑖 and 𝜏ult thereforewill increase with the increase in normal stress. This stressdependence is taken into account by using empirical equa-tions to represent the variation of 𝐷𝑠𝑖 with normal stress:

𝐷𝑠𝑖 = 𝐾𝑃𝑎(𝜎𝑛

𝑃𝑎

)

𝑛

, (13)

where 𝐾 is the modulus number and 𝑛 is the modulusexponent (both are dimensionless numbers), and 𝑃𝑎 is theatmospheric pressure. However, the modulus number andthe modulus exponent must be determined through curvefitting, which limits the application of the proposed model.At the beginning of shear, the deformation can be assumedto be elastic, so the initial shear modulus can be expressedas follows. According to the relationship between the normalelastic modulus and the shear elastic modulus and by analogybetween the behaviours of soil and the interface between soiland structures,

𝐷𝑠𝑖 =𝐷𝑛

2 (1 + ])=

𝜎𝑛

2𝜅 (1 + ]), (14)

where ] is Poisson’s ratio of the soil. However, the aboveequation cannot incorporate the influence of normal stresshistory on the initial shear modulus. G.T. Houlsby and C.P.Wroth performed a research on the stress history of soil; theinitial shear modulus that can account for the effect of stresshistory was expressed as

𝐺𝑜𝑐 = 𝐺𝑛𝑐(𝜎𝑛𝑖

𝜎𝑛

)

0.7

, (15)

where 𝐺𝑜𝑐 is the initial shear modulus during overconsolida-tion of soil and𝐺𝑛𝑐 is the initial shearmodulus during normalconsolidation of soil. Note that the exponent has the value of0.7 only for the situation of an overconsolidation ratio below10.Therefore, the initial shearmodulus of the proposedmodelcan be given by

𝐷𝑠𝑖 =𝜎𝑛

2𝜅 (1 + ])(

𝜎𝑛𝑖

𝜎𝑛

)

0.7

. (16)

Finally, the shear modulus that accounts for the effect ofnormal stress history is

𝐷𝑠 =𝜎𝑛

2𝜅 (1 + ])(

𝜎𝑛𝑖

𝜎𝑛

)

0.7

(1 − 𝑅𝑓

𝜏

𝜏𝑓

)

2

. (17)


Figure 13: The topography parameters of the concrete plate used inthe test.

4.2. The Topography Parameter 𝛼𝑘. The ruled topographyconcrete plates were used in the large shear test. For such asawtooth interface, Morched Zeghal defined 𝛼𝑘 as

𝛼𝑘 =𝜋ℎ

2𝐿𝑘

sin 𝜋2

(1 +

𝑢𝑠

𝐿𝑘

) (18)

in which ℎ and 𝐿𝑘 are the height and width, respectively, ofthe sawtooth, as illustrated in Figure 13.

4.3. Hardening Parameter 𝐻. ∫loading 𝑑𝜎𝑑𝜇𝑛 and ∫unloading 𝑑𝜎𝑑𝜇𝑛 could by computed from the normal loading-unloadingcurve, as shown in Figure 12. Consider

∫

loading𝑑𝜎 𝑑𝜇𝑛 = ∫

𝜎𝑛𝑖

1

(𝑢𝑛0 + 𝜆 ln𝑝) 𝑑𝑝, (19)

∫

unloading𝑑𝜎 𝑑𝜇𝑛 = ∫

𝜎𝑛

𝜎ni

(𝑢𝑛𝑖 − 𝜅 ln𝑝) 𝑑𝑝, (20)

where 𝑢𝑛0 is the normal displacement at the normal stress of1 kPa and 𝑢𝑛𝑖 is the normal displacement at the beginningof unloading (the B point in Figure 12), while 𝜆 and 𝜅 arethe slope coefficients of the loading and unloading lines,respectively.

∫loading 𝜎𝑛𝑖 𝑑𝜇𝑛 is the power accumulated during theprogress of consolidation under the initial normal stress, andthe stress remains constant in this period. Thus, the power is

∫

loading𝜎𝑛𝑖 𝑑𝜇𝑛 = 𝜎𝑛𝑖 (𝑢𝑛𝐵 − 𝑢𝑛𝐴) . (21)

As illustrated in Figure 11, 𝑢𝑛𝐴 and 𝑢𝑛𝐵 are the displace-ment at the end of the loading period and the beginning ofthe unloading, respectively.

Both ∫sheering 𝑑𝜏 𝑑𝜇𝑠 and ∫sheering 𝑑𝜎𝑑𝜇𝑛 should be deter-mined through iteration. First, assuming the relationship 𝜏-𝜇𝑠follows a hyperbolic model, the initial value of 𝜏 can becomputed by substituting the shear displacement (0–30mm)into the hyperbolic model. Next, the initial value of 𝜏 canbe substituted into (1) to determine the new displacementvalue, which enables the initial hardening parameter to becomputed. The new value of 𝜏 is then recomputed basedon the initial hardening parameter, and then, the new sheardisplacement and new shear stress are calculated. The finalshear stress and displacement are computed when the errortolerance is satisfied.

5. Model Validation

The predicted results of the model are shown in Figures14(a), 14(b), and 14(c) together with the experimental resultsfor the #0, #1, and #2 interfaces first under the initialnormal stress of 400 kPa then being unloaded to the normalstress of 50–350 kPa. The model is able to reproduce thebehaviour of the clay-concrete interfacewith different normalstresses, different initial normal stresses, and roughness.Note that the model simulated the shear-stress-displacementrelationship to a satisfactory degree, which is very importantfor pile-soil interface and retaining wall problems. FromFigure 14, the shear stress is found to increase quickly withdisplacement, and as shear progressed, the dissipative power∫sheering 𝑑𝜏 𝑑𝜇𝑠 increased; meanwhile, the power accumulatedat the interface H was consumed slowly. During the lasthalf of the shear progress, the shear stress increases grad-ually with displacement and finally approaches a constantvalue.

Figures 15(a), 15(b), and 15(c) show the shear stressversus horizontal displacement along the interface betweenconcrete plates #0, #1, and #2, respectively, and clay withdifferent initial normal stresses and shearing under a normalstress of 100 kPa. The higher initial normal stress results inhigher power ∫loading 𝑑𝜎𝑑𝜇𝑛 and ∫loading 𝜎𝑛𝑖 𝑑𝜇𝑛 accumulatedat the interface and results in higher shear stiffness. Fromthe microcosmic viewpoint, the higher initial normal stresscauses the soil near the interface to reach a higher compres-sive strength. Another reasonable explanation is that the clayis more closely embedded into the sawtooth topography forthe higher initial normal stress. The cohesive section of theshear strength of the interface is formed by the absorptionof water molecules in the clay and the surface of the concreteplate; under the pressure of the initial normal stress, the watermolecules in the claywill penetrate into the concrete plate andkeep inside.

6. Conclusions

First, using sawtooth-surfaced concrete plates to quantifythe roughness of the interface, a series of shear tests wereconducted to analyse the effects of roughness and unloadingon the shear behaviour of the interface between clay andconcrete. Based on the results of direct shear tests on theclay-concrete interface, the following conclusions can beproposed.

Through the process of loading to an initial normal stress,unloading to normal stress and shearing under this normalstress, the shear behaviour of the interface between clay andconcrete was found to be influenced by the initial normalstress and the roughness of the interface. A higher initialnormal stress results in a higher shear stress during theshearing. Under the same initial normal stress, a lower valueof shear stiffness was observed for a higher unloading ratio (alower normal stress during shearing).The effect of roughnesson the shear behaviour is revealed through the shear stress-displacement relation and the normal dilative phenomenon.Regardless of whether normal unlading occurred or not the


0

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0 30252015105Shear displacement (mm)



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Figure 14: Shear-stress-displacement curves of the interface between clay and concrete (𝜎𝑛𝑖 = 400 kPa).

rougher interface offers a higher shear stress and verticaldisplacement.

The shear-dilative behaviour is significantly influenced bythe stress history. The shear-contractive phase occurs at thebeginning of shear for the interfaces that do not experiencenormal unloading, while no such contractive displacementwas found for interfaces experiencing unloading of the initialnormal stress 𝜎𝑛𝑖 to the applied normal stress 𝜎𝑛 beforeshear.

Finally, a model that can account for the effect of normalstress history was proposed. The parameters of the model allhave definite physical meanings. The calibration and valida-tion of the model were performed by simulating laboratorytest results conducted in a newly developed large direct shearapparatus.The results demonstrated that themodel is capableof predicting the behaviour of clay-concrete interfaces andof capturing the effects of different normal stress history androughness.



Shea

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Figure 15: Shear-stress-displacement curves of the interface between clay and concrete (𝜎𝑛 = 100 kPa).

Acknowledgments

The present study was supported by the National NaturalScience Foundation Project (41202193), the Shanghai PujiangProgram (11PJ1410100), and the Kwang-Hua Fund for theCollege of Civil Engineering, Tongji University.

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[13] J. E. Dove and J. B. Jarrett, “Behavior of dilative sand interfacesin a geotribology framework,” Journal of Geotechnical andGeoenvironmental Engineering, vol. 128, no. 1, pp. 25–37, 2002.

[14] O. Nasir and M. Fall, “Shear behaviour of cemented pastefill-rock interfaces,” Engineering Geology, vol. 101, no. 3-4, pp. 146–153, 2008.

[15] M. Zeghal, T. B. Edil, and M. E. Plesha, “Discrete elementmethod for sand-structure interaction,” in Proceedings of the 3rdInternational Conference on Discrete Element Methods, pp. 317–322, Santa Fe, NM, USA, September 2002.

[16] H. Liu, E. Song, and H. I. Ling, “Constitutive modeling of soil-structure interface through the concept of critical state soilmechanics,”Mechanics Research Communications, vol. 33, no. 4,pp. 515–531, 2006.

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