Critical state shear behavior of the soil-structure interface determined by discrete element modeling

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Critical state shear behavior of the soil-structure interface determined by discrete element modeling Xiaoqiang Gu a,b , Yuanwen Chen a,b , Maosong Huang a,b,∗ a b

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

a r t i c l e

i n f o

Article history: Received 9 October 2016 Received in revised form 21 December 2016 Accepted 1 February 2017 Available online xxx Keywords: Discrete element method Interface Direct shear test Shear band Dilatancy Critical state

a b s t r a c t The interface between soil and structure can be referred to as a soil-structure system, and its behavior plays an important role in many geotechnical engineering practices. In this study, results are presented from a series of monotonic direct shear tests performed on a sand-structure interface under constant normal stiffness using the discrete element method (DEM). Strain localization and dilatancy behavior of the interface is carefully examined at both macroscopic and microscopic scales. The effects of soil initial relative density and normal stress on the interface shear behavior are also investigated. The results show that a shear band progressively develops along the structural surface as shear displacement increases. At large shear displacement a unique relationship between stress ratio and void ratio is reached in the shear band for a certain normal stress, indicating that a critical state exists in the shear band. It is also found that the thickness and void ratio of the shear band at the critical state decreases with increasing normal stress. Comparison of the DEM simulation results with experimental results provides insight into the shear behavior of a sand-structure interface and offers a means for quantitative modeling of such interfaces based on the critical state soil mechanics. © 2017 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

Introduction The interface between soil and structure is very important in geotechnical engineering with respect to constructing pile foundations, retaining walls, and earth reinforcement. The soil-structure interface has therefore been widely studied because the mechanical behavior plays a crucial role in the overall behavior of the soil-structure system. Many experiments have been conducted to investigate the behavior of the interface between different soils (sand, clay, gravel) and construction materials (steel, concrete) under different load types (monotonic, cyclic) and boundary conditions (constant normal stress, constant normal stiffness, constant volume) (Brumund & Leonards, 1973; DeJong, Randolph, & White, 2003; Desai, Drumm, & Zaman, 1985; El Cheikh, Rémond, Pizette, Vanhove, & Djelal, 2016; Fioravante, Ghionna, Pedroni, & Porcino, 1999; Ghionna & Mortara, 2002; Kishida & Uesugi, 1987; Martinez & Frost, 2016; Peng, Ng, & Zheng, 2014; Potyondy, 1961; Shahrour & Rezaie, 1997; Tejchman & Wu, 1995; Uesugi & Kishida, 1986a,

∗ Corresponding author at: Department of Geotechnical Engineering, Tongji University, Shanghai, 200092, China. E-mail address: [email protected] (M. Huang).

1986b; Uesugi, Kishida, & Tsubakihara, 1989; Yoshimi & Kishida, 1981; Zeghal & Edil, 2002; Zhang & Zhang, 2006). Various experimental methods have been used in such interface shear tests, with direct shear tests and simple shear tests being the most commonly used. More modern and advanced techniques such as photography (Hu & Pu, 2004; Uesugi, Kishida, & Tsubakihara, 1988), radiography (Tejchman & Wu, 1995), and particle image velocimetry (PIV) (DeJong et al., 2003) have been incorporated to further explore the fundamental mechanisms related to soilstructure interface behavior. Previous investigations have revealed that the behavior of a sand-structure interface may be affected by factors such as surface roughness, soil relative density, particle shape, grain size, soil mineralogy, and normal stress level (DeJong & Westgate, 2009; Uesugi & Kishida, 1986b). Uesugi et al. (1988) and Hu and Pu (2004) showed that a smooth interface follows an elastic-perfectly plastic failure mode and the shear stress and volume change maxima are reached at a very limited interface displacement with very little dilatancy near the interface. Conversely, strain localization occurs in a thin layer of sand, a shear band, adjacent to the structural surface associated with large dilatancy for a rough interface. The interface consists of a strain-localized zone together with a contacting surface, and its

http://dx.doi.org/10.1016/j.partic.2017.02.002 1674-2001/© 2017 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.

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height is usually referred to as the thickness of the interface (Uesugi et al., 1988). It has also been revealed that the thickness of the interface shear band does not correlate with a certain range of values but can be normalized by the mean particle size (D50 ) of granular soil (DeJong & Westgate, 2009; DeJong et al., 2003; Uesugi et al., 1988; Yoshimi & Kishida, 1981). The ratio of shear band thickness to D50 varies approximately in the 5–10 range; the exact value depending on the particle angularity, crushability, and surface roughness. It is interesting to note that the thickness of the interface shear band is about half of that formed in soils in laboratory tests, e.g. 10–20 times that of mean particle diameter (Mühlhaus & Vardoulakis, 1987; Roscoe, 1970). It has been shown that the density-dependent and stressdependent characteristics of the interface between sand and a rough structure are very similar to those of granular soil. Boulon and Nova (1990) discussed the applicability of soil constitutive models to a rough interface and there is also experimental evidence that, at large shear deformation, the interface can reach a steady state at which the stress ratio is constant and no further volumetric changes occur (Fioravante et al., 1999; Hu & Pu, 2004). This phenomenon is reminiscent of the concept of critical state in soil behavior, although it is not yet well understood how a strainlocalized zone progressively forms at the soil-structure interface and develops to the critical state, especially at the soil particle scale. The evolution of soil behavior out of the strain-localized zone is also not known. The discrete element method (DEM) proposed by Cundall and Strack (1979) is a suitable and powerful tool for investigating the macroscopic behavior of granular material at the microscopic scale, especially for displacements and rotations of large particles. The DEM is advantageous for conveniently analyzing the evolution of soil microstructure and facilitates sample reproducibility. A number of DEM simulations have been performed to explore the soil-structure interface behavior at the microscopic scale. Jensen, Bosscher, Plesha, and Edil (1999), Jensen, Edil, Bosscher, Plesha, and Kahla (2001) and Jensen, Plesha, Edil, Bosscher, and Kahla (2001) studied the effects of surface roughness, particle shape and particle breakage using DEM in which periodic lateral boundaries were used and the particles were represented by three-spheres combined clusters. Their results showed that the displacement field of the particles was significantly affected by the interface roughness and the particle shape. As the particle angularity increased, particle rotation became more constrained, resulting in increased strength and the suppression of a well-defined shear zone. It was also found that grain crushing led to a more distinct shear zone without significant reduction in shear strength of the granular soil. Frost, DeJong, and Recalde (2002) conducted a series of DEM interface shear tests to investigate the effects of surface roughness and hardness on the shear behavior of a soil-structure interface. Wang, Dove, and Gutierrez (2007) conducted direct shear tests along an interface of densely packed spherical particles and a rough structural surface. The results showed that the mobilization of the interface strength was related to the development of fabric anisotropy and contact force anisotropy at the contacts between particles and the boundary. Using a strain calculation method considering the particle rotation, Wang, Gutierrez, and Dove (2007) also studied the initiation and development of a shear band. Peng et al. (2014) investigated the behavior of the interface between sand and piles using a series of DEM direct shear tests under various boundary conditions. The results showed that the initial normal stress and relative density of the surrounding soil affects the mobilized stress ratio and normal stress increment of the interface. Ngo, Indraratna, and Rujikiatkamjorn (2014) studied the interface behavior of a geogrid-reinforced ballast fouled with coal under direct shear using DEM and clumps of irregular shapes were employed as particles. Martinez and Frost (2016) made

a systematic comparison between interface behavior under axial loads and torsional loads using DEM simulation in which globaland particle-scale behaviors were revealed to have contributed to a comprehensive understanding of interface behavior. El Cheikh et al. (2016) simulated the shear behavior of spherical particles between two rough-surfaced walls and revealed how the shear velocity, wall roughness, and concentration of rough areas along the wall affected the effective friction coefficient and shear localization of the interface. However, there are few DEM simulations that investigate the effects of initial normal stress and soil density on interface behavior, although it is well agreed that they significantly affect the behavior of granular soil. Most importantly, how the soil-structure interface progressively develops into a shear band and finally reaches the critical state as observed in laboratory experiments has not been well known. It is also meaningful to investigate the characteristics of the interface shear band and the state of soil both within and outside of the shear band. In this paper, a series of DEM simulations of monotonic direct shear tests on the interface between sand and a rough surface are performed. The aim of these simulations is to investigate macroscopic shear behavior at the microscopic scale and to analyze the effects of soil relative density and normal stress on the macroscopic responses. The particle displacement field and distribution of the void ratio are also analyzed during shearing to explore the underlying mechanism of strain localization that leads to shear band formation. The distinct evolution of variables in the shear band and in the far-field is also explored to gain insight into the critical state behavior of the soil-structure interface. Discrete element modeling The DEM program PFC2D (Itasca, 2002) was used to perform the simulation. The program models the movement and interaction of discrete single circular particles or combined circular particles of arbitrary shape using an explicit time-step algorithm. The motions of particles are determined by Newton’s second law and the contact forces are derived from contact constitutive models which include a stiffness model, slip model, and bonding model. Moreover, damping is introduced to dissipate energy and allow mechanical equilibrium to be reached more quickly. More details about the DEM can be found in the PFC2D user manual (Itasca, 2002). The monotonic interface shear test conducted by DeJong et al. (2003) between medium dense sand and a rough aluminum plate to which sand grains adhered was simulated. Additional simulations with different initial densities of sand, and under different initial normal stresses, were performed. To decrease the stress fluctuations during the strain softening stage, the dimensions of the specimens in the simulations were enlarged to a rectangular space 200 mm wide and 60 mm high, compared to the original width (L) of 100 mm and height (H) of 30 mm. The D50 is 0.72 mm, which is the same as in the laboratory experiment. The values of L/D50 and H/D50 are sufficiently large to diminish the deleterious boundary effects and ensure the full development of a shear band (Jensen et al., 1999; Wang, Dove, Gutierrez, & Corton, 2005). Clumps of two circular particles with an aspect ratio of 1.5 were adopted to consider particle rolling resistance which is critical to the strength and dilatancy behavior inside the shear band of granular materials (Iwashita & Oda, 1998; Oda & Kazama, 1998). The clump cannot break apart throughout the simulation and behaves as a rigid body. In the laboratory test, particles near the interface may break during the shearing and reduce the dilatancy of the soil. Nevertheless, considering the initial normal stress levels (i.e. 100 kPa) in the experiment and the breakage strength of the sand particle, the amount of particle breakage should be very small and therefore the assumption of unbreakable clumps in the DEM simulation are appropriate.

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Fig. 2. Diagram of the rough bottom surface.

Table 1 Parameters used in the DEM simulation. Particle density (kg/m3 ) Inter-particle friction Wall stiffness (kN/m)a Local damping factor Fig 1. (a) Particle size distribution of sand in DEM simulations and (b) schematic illustration of the shape and dimensions of a clump consisting of two particles.

A linear force-displacement law at particle contacts was used and the stiffness correction scheme of Yan and Dong (2011) was adopted to obtain compatible macroscopic stiffness of the particle assemblage, regardless of particle size variation (Yang & Gu, 2013). The normal contact stiffness of a particle (kn ) varies according to the function: kn = k0 r,

(1) = 5 × 105

kN/m2

and r is the radius of the particle. The where k0 shear stiffness (kt ) was assumed to be equal to the normal stiffness. Gu, Huang, and Qian (2014a) deduced that the contact stiffness will not significantly affect the drained mechanical behavior of granular soil at large strains because the deformation mainly results from particle rearrangement rather than elastic deformation at particle contacts. The particle size distribution curve and schematic of a particle clump are shown in Fig. 1. The coefficient of uniformity of the soil was 1.2 and the sample was confined by two fixed lateral walls, a top wall that applies normal stress to the specimen via a servo mechanism and a bottom wall that represents a rough structural surface. Attempts were made to use a rough surface made of particles whose diameters varied according to the particle size distribution curve of the specimen. It was found that particles were able to leak through the gap between the lateral wall and bottom surface when small particles on the surface were just below the lateral wall during loading. Such particle leakage can lead to stress relaxation and fluctuation of the stress-displacement curve. Therefore, the rough surface was simulated with a compacted row of identical circular particles with diameters of 0.72 mm (Fig. 2). Such configuration resulted in sufficient roughness to engage the particles near the interface and avoid particle leakage from bottom corners during tests. The results were nearly identical when compared to the rough surface with varied particle sizes. The same friction coefficient and stiffness rules were applied to particles constituting the structural surface as for those in the samples. Table 1 lists the basic parameters used in the simulations. The simulated specimen was generated by the radius expansion method and a simple four-step procedure was used to ensure a uniform specimen. Firstly, a certain number of particles with one third of their original radii were generated randomly in the sample

2650 0.5 1 × 107 0.7

No. of clumps Wall–particle friction Particle normal stiffness kn Particle shear stiffness kt

16979 0.001 Variableb kt = kn

a

The stiffness value refers to both normal and shear stiffness. The particle normal stiffness kn = k0 r, where k0 = 5 × 105 kN/m2 and r is the radius of the particle. b

space and then expanded to their final sizes. Secondly, the generated specimen was cycled to an equilibrium state and then each particle was replaced by a clump with an identical area. The clump consists of two elementary particles whose relative positions and rotation angles remain fixed and behaves as an integrated whole particle. The clump cannot break apart and it contains no internal contact forces or contact number. The specimen is then cycled again to an equilibrium state. Note that the friction coefficient of the particle is temporarily set to zero during the aforementioned stages. Thirdly, the specimen was isotropically compressed to 1 kPa using the servo controlled walls. Generally, different inter-particle friction coefficients were used during the compression stage to generate specimens with different initial densities (Gu et al., 2014a; Muir Wood & Maeda, 2008; Yang & Dai, 2011). Three inter-particle friction coefficients (0.5, 0.1, 0.01) were used to generate loose, medium dense, and dense specimens, respectively. Finally, the bottom wall was replaced by the rough surface, the top of which touched the original bottom wall to avoid disturbing the generated specimen. The top wall applied a normal stress of 1 kPa while other boundaries remained fixed to keep particles in full contact with the bottom surface. Finally, the interparticle friction coefficient was set to 0.5 and the specimen was consolidated one-dimensionally to the designated normal stresses (from 50 to 800 kPa) by servo control of the top wall. During the interface direct shear test under each normal stress, the bottom rough surface was moved horizontally (to the right) at a speed of 5 mm/s until a total displacement of 24 mm was achieved. Each calculation step (time-step) was approximately 1.5 × 10−7 s during loading. Parameter studies verified that the mechanical behavior of the interface remained essentially unchanged at this rate of movement. Meanwhile, the ratio of average unbalanced force to average contact force was monitored during interface shearing to satisfy a quasi-static condition. If this ratio exceeded a threshold value of 0.001, the rough surface stopped moving temporarily and additional cycles were performed to meet this criterion. Furthermore, in accordance with the original laboratory experiment (DeJong et al., 2003), a constant normal stiffness of 250 kPa/mm was applied to the top wall by servo control during

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Fig. 4. Comparison of interface dilation from laboratory tests and DEM simulation.

Fig. 3. Comparison of interface shear behaviors obtained from laboratory tests and DEM simulations for (a)  vs. w and (b) / n vs. w.

shearing to replicate the field condition of vertically loaded pile foundations or other shaft friction applications. Results and discussions The results of the simulations are discussed in the following three subsections. The shear stress and normal stress of the interface () and ( n ) were obtained based on the horizontal and vertical components of contact forces at the soil-structure surface. The stress ratio is defined as the ratio of shear stress to normal stress of the interface and, since the lateral walls are fixed, the volumetric change is reflected in the vertical displacement (v) of the top wall. The interface displacement (w) is equal to the horizontal displacement of the bottom surface. In addition to these macroscopic responses, particulate and micromechanical information of the specimen, such as particle displacement field and void ratio distribution, were also monitored and analyzed. Macroscopic interface shear behavior A plot of  and / n vs. w in the DEM simulation of medium dense sand (e = 0.167) under an initial normal stress of 100 kPa is shown in Fig. 3. Note that the void ratio in a 2D situation is much lower than in 3D. The void ratio definition in 2D is based on the total void area, while in 3D it is based on the total void volume. However, specimens in both 2D and 3D simulations can be characterized as loose or dense according to their shear behavior. The relationship between the void ratio in 2D and 3D in the DEM simulation can be found in Wang et al. (2014). As seen in Fig. 3, the value of  increases rapidly before the w reaches 0.4 mm and then fluctuates with an increasing trend until the end of the test. The stress ratio increases sharply to a peak at a displacement of 0.4 mm and then gradually decreases to a constant value, and shows strain softening behavior. For comparison, the experimental results from a medium dense sand (DeJong et al., 2003) are also plotted in Fig. 3. It is inter-

esting to note that the DEM simulation of the present study shows very similar trends to the experiment, although the shear stress and stress ratio are much lower in the DEM simulation. Additional simulations with a higher value of inter-particle friction coefficient (0.7) were carried out and the results show that the stress ratio at the steady state does not show an apparent increase, which is consistent with the observations from other DEM simulations (Thornton, 2000). The possible reason for this is that the rolling resistance of clumps used in the simulation may still be significantly underestimated compared to the rolling resistance of real particles, taking into consideration the differences in particle shape that result in a lower relative strength. Particle shape is an important factor that affects the mechanical behavior of granular material. Yang, Wang, and Cheng (2016) showed that soil shear strength and dilatancy in the critical state increase with increasing aspect ratio, especially at values >1.1. Detailed examination of the effects of particle shape is beyond the scope of this study, but will be of value in future investigations. The value of w that corresponds to the peak stress ratio in the simulation is lower than that in the experiment, which is probably caused by the absence of particle asperity fatigue or particle breakage in the numerical simulation. Vertical displacement (dilatancy) of the specimen plays a significant role in interface shear behavior under conditions of a constant normal stiffness boundary, as it affects the normal stress applied to the interface. Fig. 4 shows a comparison of the vertical displacement plotted against the horizontal displacement between the DEM simulation and experiment. It is interesting to note that the vertical displacements increase rapidly in both the DEM simulation and experiment, and there is general agreement within the first 1.6 mm of horizontal displacement. After 1.6 mm the vertical displacement in the simulation increases gradually and is less than that in the experiment. At the maximum horizontal displacement in the experiment (12 mm), the vertical displacement reaches a constant, but not yet in the simulation. The horizontal displacement in the simulation increases to 30 mm and the vertical displacement finally reaches a steady value close to that obtained in the experiment. Particle movements can be accurately and easily tracked in the DEM simulation. Fig. 5 shows the total displacement vectors of particles in the specimen at different values of w. It is interesting to observe that a strain-localized zone progressively forms during interface shearing, as indicated by the high gradient of displacement (i.e. strain) at the bottom interface. The DEM simulation indicates that the central 1/3 of the specimen deforms uniformly along the interface with only a minor lateral boundary effect. This is consistent with the laboratory observation of particle movement using particle image velocimetry (PIV) (DeJong et al., 2003). Fig. 6 shows details of the particle displacement vectors around the interface at the center of the specimen at a w value of 12 mm. The upper

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Fig. 5. Particle displacement vectors at horizontal displacements of (a) 0.4 mm, (b) 1.0 mm, (c) 2.0 mm, (d) 6.0 mm, and (e) 12.0 mm.

boundary of the strain-localized zone fluctuates remarkably, as opposed to the commonly assumed smooth horizontal plane (Oda & Kazama, 1998). Therefore, to quantify the particle displacement distribution, the central third of the sample is divided equally in the vertical direction at intervals of mean particle diameter. Then, the average displacement of the particles, whose centroids locate within the same band, is taken as the representative value. The distribution of horizontal particle displacement vs. their vertical positions at different values of w in both the DEM simulation and laboratory tests (DeJong et al., 2003) are shown in Fig. 7. The results of the DEM simulation agree very well with the laboratory test results and, as expected, the horizontal particle displacement is highest at the base of the model and decreases with

increasing distance from the interface. Particle slippage in the bottom layer occurs throughout the simulation and the percentage of slippage (% displacement difference between the lowermost particles and the base of the structure) increases sharply when the horizontal displacement is <2 mm and then remains relatively stable (e.g. 7.0% at 0.4 mm, 17.7% at 1 mm, 20.0% at 2 mm, 23.5% at 4 mm, 24.3% at 6 mm, and 23.2% at 12 mm). Moreover, there is a notable change in the gradient of horizontal displacement that defines the shear band and the far-field of the specimen. Large shear strain occurs in the shear band while the particles in the far-field undergo limited horizontal displacement and negligible shearing. The thickness of the shear band increases slightly during shearing, and reaches a value of around 9.0D50 (about 6.5 mm) at an interface

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Fig. 6. Details of the particle displacement vectors near the soil-structure interface at a horizontal displacement of 12 mm.

Fig. 7. Distribution of horizontal particle displacement at different horizontal displacements of the soil-structure interface from (a) DEM simulation and (b) laboratory tests (modified from DeJong et al., 2003).

displacement of 12 mm in the DEM simulation, which is slightly higher than 7.5D50 (about 5.4 mm) in the laboratory. It is noteworthy that the particles in the far-field in the DEM simulation move in the same direction as the interface for the first 1.6 mm and then are drawn back in the opposite direction, compared to the laboratory test data in which they always move in the

same direction as the interface. By carefully examining the particle displacement vectors in Fig. 6, it is found that a counterclockwise particle flow occurs inside the specimen at large values of interface displacement. Such a phenomenon results from the lateral boundary effect in which soil close to the right boundary experiences stress concentration and becomes dense, while soil near the left boundary becomes loose and is accompanied by stress relaxation, especially at the basal interface. In the laboratory tests of DeJong et al. (2003), there is a gap of ½ D50 wide between the shear box and the bottom surface through which a few sand grains will leak, possibly resulting in a smaller increase in soil density and related stress concentration. Meanwhile, the natural sand particles will also be worn and may even be crushed during shearing, thus reducing the stress concentration. On the contrary, particles can neither leak nor be crushed in the DEM simulation. DeJong et al. (2003) stated that particle crushing also hindered the transmission of displacement further within the specimen and gave rise to a lower thickness of the shear band. Such discrepancies between the DEM simulation and laboratory test results may cause the differences of horizontal displacement patterns of particles in the far-field of the specimen. Distributions of particle vertical displacement (i.e. volume change) vs. vertical position at different values of w in the DEM simulation are shown in Fig. 8. Similarly, the sharp change of gradient in the particle vertical displacement distinguishes the dilation zone or shear band from the far-field. The overall dilation of the sample is caused by dilation of the shear zone, while the far-field of the sample is pushed upward as a nearly rigid block by the shear zone with negligible volume strain. The volume change within the shear zone increases with increasing w and reaches a relative constant value at larger interface displacement, which indicates the establishment of a steady state condition. The thickness of the shear band has a value of 9.5D50 (about 7.0 mm) at an interface displacement of 12 mm in the DEM simulation, nearly the same as that based on the distribution of particle horizontal displacement. The distribution of particle rotation, an important factor in the shear band (Gu, Huang, & Qian, 2014b), is plotted in Fig. 9 based on the DEM simulation. A maximum rotation angle of 94◦ is evident in the bottom layer of particles at an interface displacement

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Fig. 8. Distribution of vertical particle displacement at different horizontal displacements of the soil-structure interface from DEM simulation.

Fig. 9. Distribution of particle rotation at different horizontal displacements of the soil-structure interface from DEM simulation.

of 12 mm and the rotational angle decreases rapidly away from the interface. Particles in the far-field of the specimen rotate in a scattered way between ±10◦ at the beginning of shearing but do not rotate any more in subsequent loading, which indicates negligible shear strain in the far-field. The distribution of particle rotation is consistent with that of horizontal and vertical particle displacements and it illustrates that the occurrence of rotation within the shear band is coupled with the onset of shear strain and volumetric strain therein. Based on Fig. 9, the thickness of the shear band is determined to have a value of 9.5D50 (about 7.0 mm) at an interface displacement of 12 mm, nearly identical to that based on the distribution of horizontal or vertical particle displacement. One important characteristic of the shear zone in the specimen is the large void ratio (Gu et al., 2014b). Fig. 10 shows the void ratio contour of the specimen during loading, which is generally uniform before shearing. As shear displacement increases a thin band with increasing void ratio appears adjacent to the rough surface while the void ratio of the rest of the specimen remains essentially unchanged, indicating the formation of the shear band. The void ratio and the shear band thickness increase as interface displacement increases, ultimately reaching a steady state. At the peak stress ratio (displacement of 0.4 mm), the void ratio distribution is nearly the same as the initial void ratio distribution and no shear band is observed. Fig. 10 also clearly shows that soil near the right boundary becomes denser and soil near the left boundary becomes looser. Effects of initial density and normal stress on interface behavior For granular material it is well recognized that its mechanical behavior depends on the initial soil state, including soil density

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and stress level. To investigate these factors, DEM simulations of interface shear tests are performed on soil specimens in different initial states. The initial relative densities tested include 18% (loose), 59% (medium dense), and 97% (dense), at initial normal stresses of 50, 100, 200, 400, and 800 kPa. Fig. 11 shows a comparison of shear stress, stress ratio, and vertical displacement of the interface at different initial states in the DEM simulation. As expected, Fig. 11(a) shows that the peak shear stress increases significantly as the initial normal stress increases. Meanwhile, at the same value of normal stress, the shear stress of the dense specimen increases rapidly to a peak value, and then decreases gradually to a constant and shows strain softening behavior. It is also evident that the strain corresponding to the peak stress at higher normal stress is larger while, for the loose specimen, there is evidence of strain softening behavior. In a constant normal stiffness test, the normal stress changes because of volume change in the specimen. Hence, the stress ratio of the specimen is plotted as a function of w in Fig. 11(b). It is observed that the peak stress ratio decreases as the confining pressure increases and density decreases, which is consistent with the evolution of dilatancy of the specimen (Fig. 11(c)). It is clear that the dilatancy of the specimen also decreases with increasing normal stress and decreasing soil density. Moreover, at large values of w, the stress ratio reaches a unique constant in spite of the initial density and normal stress of the specimen. Meanwhile, the vertical displacement of the specimen also remains nearly constant, indicating a lack of volume change of the specimen. These observations are consistent with critical state characteristics in soil mechanics. The effects of initial density and normal stress on the distributions of particle movements in the specimen are illustrated in Fig. 12. By analyzing particle movements, the effects of initial density and normal stress on the shear band thickness can be estimated. For example, Fig. 12(a) shows that slippage occurs at the soil-structure interface and the horizontal particle displacement decreases sharply in the shear band with increasing distance from the interface. For the same value of normal stress, the shear band thickness increases as density decreases while, for the same density, the shear band thickness increases as normal stress decreases. These results agree well with the experimental observations of Mühlhaus and Vardoulakis (1987). It also appears that the transition zone generally becomes larger and the boundary between the shear band and the far-field becomes ambiguous when both the density and normal stress decrease. With regards to the vertical displacement (dilatancy), it is interesting to note that the shear band dilates significantly in spite of the initial density and normal stress (Fig. 12(b)). However, in the farfield it is evident that the loose soil undergoes contraction, while the dense soil maintains a constant volume. This observation is quite different from the results of conventional triaxial tests in which loose soil demonstrates contractive behavior. Therefore, there is convincing evidence that shear band behavior determines the overall behavior of the soil-structure interface, and that the thickness of the shear band generally increases as the density and normal stress decrease. It is found that the shear band thickness varies within the range of 8–10D50 for the normal stress range of 100–800 kPa. It can be noted that the interface shear band thickness is about half of that formed in soils (10–20D50 ) in laboratory tests within the same stress range (Mühlhaus & Vardoulakis, 1987; Roscoe, 1970). Critical state of the soil-structure interface The above results indicate that a critical state of the soilstructure interface exists. To further explore critical state behavior of the interface, the stress paths in different interface shear tests are plotted together in Fig. 13. From such plots it is observed that the

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Fig. 10. Contours of void ratio distribution in specimens at horizontal displacements of (a) 0 mm, (b) 0.4 mm, (c) 2.0 mm, (d) 6.0 mm, and (e) 12.0 mm.

shear stress of all interfaces increases to a peak value and then gradually decreases, showing strain softening behavior regardless of the values of initial relative density and normal stress. More importantly, the final stress states concentrate along a straight line that passes through the origin with a slope of 0.45, which is indicative of a unique critical state stress ratio. The inter-particle friction coefficient and particle shape may have an effect on this critical state stress ratio (Thornton, 2000; Yang et al., 2016), but the detailed examination of such effect is beyond the scope of the current work. Other than the stress ratio, the unique stress-dependent void ratio is also a characteristic of the critical state. Fig. 14 compares the evolution of the void ratios in the shear band and far-field of the specimens with different initial void ratios at a normal stress of 100 kPa. It is evident that the void ratio in the shear band increases significantly at first with increasing w and finally reaches a steady state, despite their different initial values. On the contrary, the void ratio in the far-field remains nearly constant throughout the interface shearing. The unique void ratio of the shear band in the steady state provides clues to the critical state of the interfacial shear band. To better understand this phenomenon, the relationships between the final void ratio and the final normal stress of specimens with different initial conditions are plotted in Fig. 15. The void ratio in the shear band is evidently much higher than that in the far-field of the specimen, and the generation of large voids in the shear band accords well with the X-ray observations in plane strain tests conducted by

Oda and Kazama (1998). It should be noted that the void ratio in the shear band can be even greater than the maximum void ratio of the soil under compaction. Meanwhile, the void ratio in the shear band decreases markedly with increasing normal stress, while the void ratio in the far-field of the specimen decreases only slightly with increasing normal stress. The final void ratio in the shear band merges along a straight line in Fig. 15 known as the critical state line (CSL) in the e −  n plane. Therefore, the critical void ratio here refers to the value in the shear band, rather than the void ratio in the far-field or the overall void ratio of the specimen. The CSL found in the e −  n −  space confirms the existence of a critical state in the interfacial shear band and may provide evidence for the constitutive theory of soil-structure interface based on the framework of critical state soil mechanics.

Summary and conclusions Shear behavior of the soil-structure interface has been investigated using a series of DEM simulations under conditions of constant normal stiffness. The effects of soil initial relative density and initial normal stress on strain localization have been systematically studied. The critical state of the soil-structure interface has also been carefully examined. The main conclusions are summarized as follows:

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Fig. 12. Effects of initial density and normal stress on (a) particle displacement and (b) particle rotation at the soil-structure interface at a displacement of 12 mm in the DEM simulation.

Fig. 11. Effects of initial density and normal stress on the shear behavior of the soil-structure interface: (a)  vs. w, (b) / n vs. w, and (c) v vs. w.

1. DEM simulation using clump particles successfully captures the shear behavior of a sand-structure interface observed in laboratory testing. The stress ratio initially increases to a peak and then decreases gradually to a steady value. 2. The distribution of particle displacement indicates that soil deformation is localized within a thin shear band adjacent to the rough structural surface. The shear band is characterized by a large void ratio and significant particle rotations, despite the initial relative density. The void ratio in the far-field (i.e. soil out of the shear band) remains nearly constant with negligible particle rotation, suggesting that the overall deformation of the soil-structure interface is mainly determined by the shear band. The ratio of shear band thickness to mean particle diameter is found to be about 8–10. 3. At large shear deformations, the stress ratio of interfaces with various initial conditions finally reaches a unique value, indicating the existence of the critical stress ratio. The void ratio in the shear band increases significantly as shearing proceeds and finally approaches a constant value much larger than that in the initial state, even for very loose soils, and the critical void ratio in the shear band is found to decrease linearly with increasing nor-

Fig. 13. Graphical illustration of the relationship between shear stress and normal stress in the critical state (CSL = critical state line).

Fig. 14. Evolution of the void ratios in the shear band and far-field of specimens at an initial normal stress of 100 kPa.

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Fig. 15. Relationships between void ratio and normal stress in the shear band and far-field in the specimen at the critical state.

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Please cite this article in press as: Gu, X., et al. Critical state shear behavior of the soil-structure interface determined by discrete element modeling. Particuology (2017), http://dx.doi.org/10.1016/j.partic.2017.02.002