Abstract

The interaction between a foundation and its supporting soil involves several different energy dissipation mechanisms. For example, sliding of a foundation element is a soil-structure interaction component that can alter the seismic demand on a foundation as well as its superstructure. Experimental data from tests with realistic boundary and stress conditions is required to characterize the frictional properties at the soil-foundation interfaces in order to model sliding of shallow foundations. To this end, a series of large-scale monotonic laboratory shear tests were performed to study the interface between a shallow concrete foundation element and Ottawa F-55 sand under varying normal pressures, shearing rates, and foundation surface roughnesses and textures. The soil-foundation interface behavior was evaluated through a combination of global measurements of force and displacement, as well as by capturing the localized effects around the interface. This article describes the dependency of the interface behavior on each of the aforementioned variables. The results indicate that when subrounded fine sand comes into contact with surfaces of varying roughness, it exhibits different shear resistance behaviors. The findings further reveal insights into the dependency of the interface frictional characteristics and shear failure zone on the real area of contact, which includes irregularities on the surface. The data further utilized to study the impact of adopting different interface friction assumptions on the finite element model’s interface shear response being subjected to monotonic loading. Using the internal friction angle, or a factored down value, as an estimation for interface friction may lead to an erroneous or unconservative prediction of the superstructure response.

Introduction

Soil-structure interaction (SSI) is an important consideration in the analysis and design of civil infrastructure, including nuclear power plants, processing centers, hospitals, semiconductor manufacturing facilities, and hydroelectric dams. Based on past earthquake observations, the seismic load transmitted to a shallow foundation may result in nonlinear behavior at the soil-foundation interface, which includes sliding, gapping, uplift, and bearing capacity failure (Gazetas and Apostolou n.d.). It is well recognized that these nonlinear sources affect the seismic design demand for a given structure (Raychowdhury 2011). Previous exploratory studies (e.g., Crouse and McGuire 2001; Ugalde et al. n.d.; Kausel 2010; Pitilakis, Karapetrou, and Fotopoulou 2014; Bolisetti, Whittaker, and Coleman 2018; Tahghighi and Mohammadi 2020) have shown that the nonlinearities associated with SSI modify the spectral acceleration demands in the structure that are caused by energy dissipation and stiffness changes. One of these nonlinear sources is attributable to the sliding and rocking of the foundation, i.e., geometric nonlinearities at the soil-structure interface (American Society of Civil Engineers 2016). These behaviors are not limited to the analysis of buildings. For example, the foundation of a bridge could be designed to allow sliding when subjected to high levels of seismic excitation (Pecker and Teyssandier 1998). Current practice in seismic foundation design aims to ensure that the seismic demands on the foundation system remain well below a series of thresholds that would conventionally imply failure. Although such a restriction may seem reasonable, it can lead to nonconservative oversimplifications, especially when strong geometric nonlinearities are present (Anastasopoulos et al. 2010). The academic community has extensively explored the rocking behavior of foundations and demonstrated that it has beneficial energy dissipation characteristics, which enhances the seismic performance of a soil-foundation-structure system (Gajan and Kutter 2009; Anastasopoulos et al. 2010; Deng, Kutter, and Kunnath 2012; Drosos et al. 2012; Liu et al. 2013; Kutter et al. 2016). However, the sliding response of shallow footings has not been studied comprehensively, as in most of the published research on geometric nonlinearities, rocking dominates sliding by virtue of having moment-to-shear ratios greater than one (Hakhamaneshi et al. 2020). This lack of data necessitates a detailed investigation on the sliding behavior at the soil-structure interface to better model this phenomenon.

In order to characterize sliding of a shallow footing, with interface shearing being the primary component of interest, understanding the shearing mechanism and quantifying the frictional properties of soil-foundation interfaces is needed. According to previous studies, parameters such as surface roughness and texture, confining pressure, and shearing rate could affect the interface shear response. Frost and Han (1999) investigated the interaction between sand and fiber-reinforced polymers as a potential solution to the offshore foundation durability problem. According to their tests, the relative roughness, normal stress level, soil mass initial density, and the particles’ angularity all influenced the interface shear behavior between fiber-reinforced polymers composites and granular materials. Dove and Frost (1999) used contact mechanics and fundamental friction theory to examine shear mechanisms at particle-smooth geomembrane interfaces, demonstrating a relationship between normal stress and the hardness of the interface materials. In experiments from Hu and Pu (2004), two different failure modes were observed during the interface tests of different relative roughness of steel in contact with sand. They indicated that interfaces could be classified as smooth and rough based on a critical relative roughness. DeJong and Westgate (2009) examined localized SSI through a series of monotonic direct interface shear tests. Relative density, particle angularity, hardness, surface roughness, normal stress, and normal stiffness are among the parameters studied. The relationship between particle properties and surface roughness, followed by confining stress and stiffness conditions, was demonstrated to have the largest effect on local interface behavior.

Prior research has thoroughly investigated a wide variety of structures and foundations in contact with different soil conditions. However, the majority of these data points are from interface shear tests that were performed using element-scale laboratory equipment, mostly comprised of direct shear tests, which have idealistic boundary conditions around the tested interface with respect to shallow foundation behavior (Potyondy 1961; Desai and Rigby 1995; Frost and Han 1999; Hu and Pu 2004; Westgate and DeJong 2006; Mortara, Mangiola, and Ghionna 2007; Farhadi and Lashkari 2017; Su et al. 2018). For example, one such limitation of the conventional direct shear test concerns edge effects that are attributable to passive thrusting against the wall of the shear box (Gómez et al. 2008). Although utilizing a large displacement shear box (Zhang and Zhang 2006; Gómez et al. 2008; Feng, Zhang, and Deng 2018) can reduce the aforementioned effect by using a soil specimen that is relatively longer when compared to its thickness, it is still limited in its representation of sliding of shallow foundations. However, these shear test boxes can reasonably predict the frictional behavior for geo-structures, such as pile foundations, soil anchors, retaining walls, and geotextile reinforcements in embankments and retaining structures, where the whole area of soil is in contact and confined by the structural surface, as the test setup requires structural material larger than the soil sample to maintain a constant contact area. In the case of a sliding shallow foundation, the interface surface is in contact with a large body of soil and the failure zone is considered to be a critical parameter for characterizing the dissipated energy. In order to reduce the uncertainties in the load transfer mechanism in model development, experimental data with realistic boundary conditions for shallow foundations, which are not confined in the same way as in a direct shear box, is required.

The results of such tests have high importance for the assessment of sliding behavior with respect to the seismic demand of a structure, as the soil stiffness and energy dissipation changes could differ based on the boundary limitations. The objectives of this article are as follows: (1) to generate interface data on the sliding of a shallow foundation with conditions close to realistic scenarios, (2) to characterize the corresponding interface friction, and (3) to verify and benchmark initial finite element models (FEMs) using the obtained experimental data. Although the tests presented herein focus on shallow foundation sliding, the findings and conclusion may be expanded into various interfaces with similar boundary conditions.

Material and Methods

TEST SETUP

A series of large-scale laboratory shear tests were performed in Structural Engineering and Earthquake Simulation Laboratory (SEESL) to investigate sliding behavior at the soil-foundation interface. The studied interface had dimensions of 50.8 by 50.8 cm and was subjected to a displacement-controlled actuation with a maximum stroke of 15 cm. The soil depth was taken to be twice the foundation width (z/B = 2), where the stress distribution would be 0.1 of applied stress on the foundation, assuming uniform loading (Lambe and Whitman 1969). Given this, the models were constructed in a container with interior plan dimensions of 305 by 305 cm and an interior height of 100 cm in order to reduce the effect of boundary conditions, both in the lateral and vertical directions. An annotated photograph of the test setup and instrumentation layout of the experiments are presented in figure 1 . The instrumentation includes a load cell, a displacement transducer, an accelerometer, and a camera system adjacent to the interface. This article aims to present the global measurement of force-displacement at the soil-structure interface.

FIG. 1
Experimental trial prior to testing annotated with a close-up schematic sectional view of test setup.
FIG. 1
Experimental trial prior to testing annotated with a close-up schematic sectional view of test setup.
Close modal

More than 72 monotonic tests were conducted on dense Ottawa F-55 sand with varying normal pressures, shearing rates, surface roughnesses, and textures. Different normal pressures were obtained utilizing 0, 2, 5, 8, 11, and 15 steel plates as surcharge, which provided nominal contact pressures of 6.1, 15.0, 28.1, 41.2, 54.2, and 71.7 kPa, respectively. In each test, lateral force was applied to the foundation block by a hydraulic actuator until relative displacement occurred, which is a similar procedure to a direct shear test, with the aim of capturing the pure frictional sliding behavior of the soil-structure interface. The hydraulic actuator provides the ability to control velocity of the tests through an adjustable pressure valve. The majority of the tests were performed at a lowest attainable shearing rate of 2.5 mm/s, and a few tests were performed at a maximum achievable shearing rate of 31.5 mm/s to study its effect. The latter are identified as “fast” hereafter. Each test was performed at least two times in identical testing conditions, and additional substantiating tests were performed for samples that provided inconsistent results. The actuator displaced the foundation block by 5 cm during tests on dry sand to capture the residual shear performance of the soil.

SOIL PROPERTIES

Ottawa F-55 sand, a well-characterized fine-grained soil commonly used in geotechnical physical modeling research, was used in the experiments. This standard testing soil was utilized to ensure consistency and repeatability of the test results by reducing the sources of uncertainty, as well as to provide a link to element tests in literature. The physical properties of the sand are presented in Table 1  and additional data on the characteristics of this soil are given in Thevanayagam, Shenthan, and Kanagalingam (2003).

TABLE 1

Properties of the soil used for interface testing

Grain Size DistributionDensity and Void RatioInternal FrictionElastic Properties
D10, mmD30, mmD50, mmCuCcGsρmax(kgm3)ρmin(kgm3)eminemaxØ, °G, MPaυ
0.190.250.31.11.62.671,688.61,509.10.610.8032300.25
Grain Size DistributionDensity and Void RatioInternal FrictionElastic Properties
D10, mmD30, mmD50, mmCuCcGsρmax(kgm3)ρmin(kgm3)eminemaxØ, °G, MPaυ
0.190.250.31.11.62.671,688.61,509.10.610.8032300.25

Note: Cc = coefficient of curvature; Cu = uniformity coefficient; D10 = effective particle size; D30 = diameter of the soil particles for which 30 % of the particles are finer; D50 = average particle size; emin = minimum void ratio of soil corresponding to the densest state; emax = maximum void ratio of soil corresponding to the loosest state; G = shear modulus; Gs = specific gravity of soil; ρmax=dry unit weight at the densest state; ρmin=dry unit weight at the loosest state; υ = Poisson ratio.

The soil was initially installed and compacted in four layers to ensure a consistent density through the depth. The average dry density was measured to be 1,690 kg/m3 using a sand cone as per ASTM D1556, Standard Test Method for Density and Unit Weight of Soil in Place by the Sand-Cone Method. The sand cone was calibrated and then used three times on each layer to obtain the density of the soil, and it had little variability from trial to trial. According to the findings of O’Rourke, Druschel, and Netravali (1990), the interface friction angle increases linearly to a dry unit density of 1,680 kg/m3 and it remains relatively constant after, even for soils that are prepared with densities as high as 1,800 kg/m3. After tamping, each layer had a final depth of 25 cm, and the overall height of the soil was 100 cm. A small amount of water (approximately 3 % water content) was utilized during the initial soil installation in order to improve the compaction process and reduce air-borne silica particulates. The specimen was then dried out over the span of a few weeks prior to testing to produce dry soil conditions. After each test, the top layer of soil was retreated, compacted, and leveled to produce the same initial condition for subsequent tests. The affected depth of the soil attributable to foundation sliding was comprehensively captured using the camera mounted adjacent to the foundation.

FOUNDATION PROPERTIES

A 50.8 by 50.8 by 25 cm (L by W by H) concrete block was cast using Quikrete 5000, which is a commercial-grade mix of gravel, sand, and cement designed for high early strength. Compression tests on cylinders, taken during concrete preparation, showed that the concrete achieved an average compressive strength of 21.8 MPa after 28 days. The block was designed to have different textures on two opposing faces (smooth and rough). A smooth concrete surface (S) was prepared by pouring concrete over a polished surface, and a rough concrete surface (R) was prepared by brushing the top surface of the concrete early in the curing process. It has been observed that the asperities of the surface affect the interface behavior, and the maximum peak-to-valley height (Rmax) was the effective parameter resulting in varied behaviors. Therefore, using a surface roughness meter and the method described by Fakharian (1996), Rmax is determined by averaging the five peak-to-valley sample lengths, as illustrated in figure 2 . Using the mean diameter of the soil particle (D50), the normalized roughness of each surface was also evaluated (Rn = Rmax/D50).

FIG. 2
A sketch of the tested surfaces showing the measured roughness.
FIG. 2
A sketch of the tested surfaces showing the measured roughness.
Close modal

The rough and smooth surfaces had a maximum roughness (Rmax) of about 1,050 μm and 350 μm, respectively. A third interface condition utilized a plastic waterproofing membrane (M) with Rmax of approximately 0.8 μm. This surface was created by attaching a 6-mm-thick plastic sheet to the concrete block using adhesive spray, which has a high shear strength to prevent the concrete block itself from sliding on the membrane sheet. The plastic sheeting is representative of the membranes commonly used as part of the in situ foundation casting process, where they are installed on top of the soil, and are frequently composed of recycled polyethylene. Figure 3  shows three types of concrete surface textures: a smooth surface, a rough surface, and a membrane surface, with normalized roughness values of 1.17, 3.5, and 0.003, respectively. A threaded rod was embedded in the concrete to serve as a connector between the foundation and loading system.

FIG. 3
Three foundation surfaces used in this study.
FIG. 3
Three foundation surfaces used in this study.
Close modal

The mass of the concrete block was measured as 161.5 kg and steel plates with dimensions of 76 by 76 by 2.54 cm were used to achieve higher contact pressure at the interface. Each steel plate has a mass of 114.8 kg. The fasteners and threaded rods used to attach the plates to the foundation have a total mass of 4.5 kg.

Results and Discussion

Figure 4  presents shear stress and normalized shear stress (shear stress/normal stress) versus horizontal displacement graphs for dry Ottawa sand in contact with the smooth, rough, and waterproofing membrane foundation interfaces under multiple normal pressures. The results were recorded under a slow shearing rate (approximately 2.5 mm/s) and are plotted up to 25-mm displacement to better observe trends in the data. All samples exhibit nonlinear behavior, and the results follow expected trends of increasing peak shear stress with increasing normal pressure. At lower normal pressures, the shear stress increases gradually, reaches a peak, and then remains constant. A distinct peak can be observed in higher normal pressures, which is followed by strain softening. This behavior is expected as the soil is densely compacted.

FIG. 4
Shear stress and normalized shear stress-displacement behavior on the (A) rough, (B) smooth, and (C) waterproofing membrane interface under the slow shearing rate.
FIG. 4
Shear stress and normalized shear stress-displacement behavior on the (A) rough, (B) smooth, and (C) waterproofing membrane interface under the slow shearing rate.
Close modal
The foundation experienced nonzero accelerations and body tilting while being pulled. The shear stresses in the graphs are post-processed with a bandpass filter (between 0.001 and 5 Hz) to remove noise and are modified to capture the effects of tilting and inertial forces by using the equilibrium equation of motion as follows:
(1)
(2)
where F is the force recorded by the load cell, N is the normal load, θ is the angle of inclination, and a is the acceleration read by the accelerometer. Trials with the concrete block directly in contact with the surface of the soil (i.e., the smooth and rough surfaces) resulted in plowing of the dry sand, which was the main reason for tilting of concrete foundation. As the block moved, the sand grains were pushed upward in front of the foundation. A failure zone formed in front of the concrete block, which was almost equal to the block’s width in the cases with high normal pressure (shown as a red dotted line in fig. 5A ). The failure zone did not appear in front of the concrete block in the trials with waterproofing membranes, as indicated in figure 5B . In this case, less pronounced plowing indicates that the failure and sliding occurred at the interface without engaging the sand particles to an appreciable depth. Furthermore, the shearing caused the front of the block to move downward during the tests. The amount of tilting observed on the membrane was less than that measured on the rough and smooth concrete surfaces under the same normal load (e.g., fig. 5C  versus fig. 5D ). These findings and observations on plowing and tilting are most likely caused by interlocking between surface asperities and the soil particles, which allows the particles to translate and roll over one another. Therefore, the membrane can be said to have a smooth surface with a roughness close to zero (0.8 μm), resulting in failure at the interface. With increasing surface roughness, the failure occurs within the sand mass rather than at the interface.
FIG. 5
Comparison of plowing and tilting behavior in two interface conditions under 54.2-kPa nominal normal pressure: (A) Plowing of rough surface; (B) plowing of waterproofing membrane; (C) tilting of rough surface; and (D) tilting of waterproofing membrane.
FIG. 5
Comparison of plowing and tilting behavior in two interface conditions under 54.2-kPa nominal normal pressure: (A) Plowing of rough surface; (B) plowing of waterproofing membrane; (C) tilting of rough surface; and (D) tilting of waterproofing membrane.
Close modal

For each test, the soil was methodically prepared to produce the same initial conditions. The preparation process entailed removing the foundation, compacting and leveling the top layer of soil, and installing a new waterproofing membrane on the concrete interface. The results of trials using a waterproofing membrane varied if the same (i.e., previously tested) membrane was used for a subsequent test. The relative displacement between sand particles and the base produced scratches on or infiltration of the membrane, which resulted in a higher resistance, demonstrating the impact of roughness and irregularities on sliding behavior.

Table 2  presents the average measured tilting and the extent of the influenced area in front of the block for trials on the smooth, rough, and waterproofing membrane interfaces after 5 cm of sliding.

TABLE 2

Captured failure zone and tilting of the block

Surface TypeNormal Pressure, kPaCaptured Failure Zone in Front of Block, mmTilting, °
Smooth6.1250
15.0250
28.11522
41.22032
54.22032.3
71.73043
Rough6.1760
15.0760
28.13553
41.24313.2
54.24312.8
71.74572.8
Membrane6.100
15.000
28.100
41.2120.2
54.2120.6
71.7120.6
Surface TypeNormal Pressure, kPaCaptured Failure Zone in Front of Block, mmTilting, °
Smooth6.1250
15.0250
28.11522
41.22032
54.22032.3
71.73043
Rough6.1760
15.0760
28.13553
41.24313.2
54.24312.8
71.74572.8
Membrane6.100
15.000
28.100
41.2120.2
54.2120.6
71.7120.6

EFFECT OF NORMAL PRESSURE AND SURFACE TEXTURE

The influence of normal pressure was investigated by repeating the experiments with six different normal pressures for each interface type. Figure 6  presents the results for the highest and lowest pressures tested with respect to the surfaces.

FIG. 6
Surface roughness effect for the lowest and the highest tested normal pressures showing (A) shear stress and (B) normalized shear stress displacement behavior.
FIG. 6
Surface roughness effect for the lowest and the highest tested normal pressures showing (A) shear stress and (B) normalized shear stress displacement behavior.
Close modal

As seen in the figure, the normalized shear stress ranges between 0.3 to 0.6 for smooth and rough surfaces, whereas it is almost constant for the waterproofing membrane under the same range of normal pressure. The hypothesis is that friction has a stress-dependency as a result of changes in the real contact area. Essentially, as normal pressure is increased, sand particles filled the asperities on the concrete surface, resulting in a new contact area that differs from the apparent one (fig. 7 ). The real contact area is the aggregate of contact areas between two surfaces, including asperities (Bowden and Tabor 1939). The concept of real area was likewise reported at the sliding interface of a seismic isolator (Constantinou et al. 2007). This real (or true) area of contact could be smaller, equal, or even larger than the apparent area based on the grain size and the existing asperities on the structural surface.

FIG. 7
Illustration of real contact area between fine subrounded sand and a concrete block.
FIG. 7
Illustration of real contact area between fine subrounded sand and a concrete block.
Close modal

Increasing the normal pressure at the membrane interface did not produce any significant changes in the real contact area because the membrane surface was glossy, i.e., continuous and without asperities at the scale of interest, and as a result the normalized shear stress remained constant. It can also be seen in figure 6  that the waterproofing membrane shear stress results are significantly lower than the results of two direct concrete interfaces for both high and low normal pressure.

The results of the smooth and rough concrete interface tests are close for low normal pressures. In higher normal pressures, larger resistance was observed on the tests using the smooth interface surface, which initially appears counter intuitive. However, during testing, the larger grooves on the rough interface surface are initially empty. As the block displaced, the asperities on the rough side made it easier for the soil particles to dilate and fill the vacant areas, resulting in less resistance.

EFFECT OF SHEARING RATE

The previous results were tested under a low shearing rate (approximately 2.5 mm/s). Additional tests were conducted at a relatively higher rate to study the influence of the shearing rate. Figure 8  shows the shearing rate effect for three different normal pressures on smooth and rough surfaces in contact with dry Ottawa sand. Increasing the shearing rate in these trials has a negligible effect on shear behavior of the interface. The average shearing rate for the experiments corresponding to the faster rate is 31.5 mm/s.

FIG. 8
Shear stress and normalized shear stress versus displacement for (A) rough and (B) smooth surfaces in contact with dry sand under slow (2.5 mm/s) and fast (31.5 mm/s) shearing rate.
FIG. 8
Shear stress and normalized shear stress versus displacement for (A) rough and (B) smooth surfaces in contact with dry sand under slow (2.5 mm/s) and fast (31.5 mm/s) shearing rate.
Close modal

Friction Characterization

A summary of global interface measurements of shear stress and displacement for the performed experiments is presented in Table 3 . Different trials for each specific test condition showed consistent results. The listed shear stress and horizontal displacement to the peak for each case is the average of the two closest results obtained from identical conditions. As the sliding behavior at the interface of the soil and structure is mainly governed by friction, the interface friction angle (δ) and the corresponding coefficient of friction (μ) are also characterized for all tests (μ=tanδ). The soil interface friction angle results from the contribution of the sliding of grains in contact with the interface, resistance to volume change (dilatancy), grain rearrangement, and grain crushing (Mitchell and Soga 2005). Additionally, various mechanisms such as adhesion, plowing, and viscoelasticity contribute to the generation of friction between different structural materials, depending on the situation. The coefficient of friction is calculated as the ratio of the measured interface strength to the applied normal force based on early work by Coulomb and Amontons (Popova and Popov 2015). The findings show that surface roughness affects the shear strength sliding displacement response. The horizontal displacement at peak stress increased with increasing roughness, but the average was almost equal for a normal pressure of 71.7 kPa. Little to no difference was observed for the peak and residual strengths for the membrane results.

TABLE 3

Summary of interface shear tests results on dry Ottawa F-55 sand

Interface TypeNormal
Pressure, kPa, σ
Horizontal Displacement
to Peak, mm, u
Shear Stress, kPaInterface Friction Angle, °Coefficient of Friction
τpτrδpδrμpμr
Rough6.13–53.533.4730300.580.57
15.03–68.428.1929290.560.55
28.14–713.6411.2526220.490.40
41.23–816.4814.0222190.400.34
54.23–721.1718.1821190.390.34
71.73–826.922.5921180.380.32
Smooth6.11–43.373.3729290.550.55
15.01–47.827.8227270.520.52
28.11–414.6214.0727270.520.50
41.21–420.1918.7626250.490.46
54.21–424.4323.3324230.450.43
71.74–731.223.324180.440.33
Membrane6.10–21.661.6615150.270.27
15.00–44.214.3616160.280.29
28.10–17.737.8716160.280.28
41.20–210.7111.1215150.260.27
54.20–213.313.1614130.250.24
71.70–320.4417.2216130.290.24
Interface TypeNormal
Pressure, kPa, σ
Horizontal Displacement
to Peak, mm, u
Shear Stress, kPaInterface Friction Angle, °Coefficient of Friction
τpτrδpδrμpμr
Rough6.13–53.533.4730300.580.57
15.03–68.428.1929290.560.55
28.14–713.6411.2526220.490.40
41.23–816.4814.0222190.400.34
54.23–721.1718.1821190.390.34
71.73–826.922.5921180.380.32
Smooth6.11–43.373.3729290.550.55
15.01–47.827.8227270.520.52
28.11–414.6214.0727270.520.50
41.21–420.1918.7626250.490.46
54.21–424.4323.3324230.450.43
71.74–731.223.324180.440.33
Membrane6.10–21.661.6615150.270.27
15.00–44.214.3616160.280.29
28.10–17.737.8716160.280.28
41.20–210.7111.1215150.260.27
54.20–213.313.1614130.250.24
71.70–320.4417.2216130.290.24

Note: Interface type = relative description of interface texture; u = the displacement that maximum shear stress achieved; δp = friction angle at the interface corresponding to maximum shear stress; δr = friction angle at the interface corresponding to residual shear stress; μp = coefficient of friction corresponding to peak friction angle; μr = coefficient of friction corresponding to residual friction angle; τp = maximum shear stress throughout full interface displacement (i.e., either strain-hardened value at full displacement or peak value for strain softening); τr = minimum or constant shear stress attained at large displacements; σ = nominal normal pressure at the interface.

The variation of the peak coefficient of friction for the block in contact with dry Ottawa F-55 sand sheared at different specific normal pressures for the three surface roughnesses, as well as at different normalized roughness for six tested normal pressure, is shown in figure 9A  and 9B .

FIG. 9
Variation of the peak coefficient of friction with (A) increasing normal pressure for three surfaces roughness in contact with dry sand and (B) increasing normalized roughness for tested normal pressures.
FIG. 9
Variation of the peak coefficient of friction with (A) increasing normal pressure for three surfaces roughness in contact with dry sand and (B) increasing normalized roughness for tested normal pressures.
Close modal

As shown in the figure, the coefficient of friction is almost constant with changing normal stress when the waterproofing membrane is used. The average coefficient of friction between the membrane and dry sand is about 0.27 for stress levels between 6 to 70 kPa. Therefore, the coefficient of friction of the soil-membrane interface is concluded to be independent of normal load when subjected to monotonic loading. In contrast, there is a nonlinear relationship between increasing normal pressure and the calculated coefficient of friction on the Ottawa sand in contact with smooth and rough surfaces. A consistent drop was observed in the coefficient of friction with increasing normal pressure for both smooth and rough surfaces. On the other hand, the tests on crushed gravel are unaffected by the amount of normal pressure and are influenced by surface roughness and gravel particle engagement at the interface according to Shahraki et al. (2022a).

Although increasing the normal pressure had a significant effect on the coefficient of friction (e.g., dropping the amount from 0.58 to 0.38 for the rough concrete interface), the two tested roughnesses caused on average a ±0.05 change on the coefficient of friction under each specific normal pressure. The rough surface results in a lower coefficient of friction with increasing the normal pressure and this is attributable to a modification of the real area of contact. As the asperities (Rmax = 1,050 μm) were much larger than the average soil diameter, the initially empty brushed tracts were eventually filled with dilated soil as the block was displaced during testing.

Figure 10A C  shows interface shear envelopes for the rough, smooth, and membrane interfaces in contact with dry Ottawa sand. These envelopes were drawn using six different normal stresses and the corresponding peak and residual shear stress for each specific interface.

FIG. 10
Peak and residual shear envelopes for (A) rough, (B) smooth, and (C) membrane surfaces in contact with dry sand.
FIG. 10
Peak and residual shear envelopes for (A) rough, (B) smooth, and (C) membrane surfaces in contact with dry sand.
Close modal

The monotonic shear strength exhibited a reasonably linear relationship with the corresponding normal stress, suggesting that the interface behaved in accordance with the Mohr-Coulomb failure criterion (Feng, Zhang, and Deng 2018). Table 4  presents the interface friction angle of three different interfaces obtained from figure 10A C  based on Mohr-Coulomb failure criterion.

TABLE 4

The Mohr-Coulomb failure criterion parameter for the fitted line into experimental data

Soil TypeSurface TypePeak Interface Friction Angle, °Residual Interface Friction Angle, °
Dry Ottawa sandSmooth22.817.8
Rough18.815.6
Membrane15.013.0
Soil TypeSurface TypePeak Interface Friction Angle, °Residual Interface Friction Angle, °
Dry Ottawa sandSmooth22.817.8
Rough18.815.6
Membrane15.013.0

Note: Peak interface friction angle δpm = the angle of the fitted line to the peak shear stress data; Residual interface friction angle δrm = the angle of the fitted line to the residual shear stress data.

The interface friction angles for the smooth and rough concrete surfaces, obtained from the shear envelopes presented in Table 4 , are smaller than the friction angle that is calculated at each different normal pressure (Table 3 ) for the corresponding interface. This is most likely because of the nonlinear relationship between increasing normal pressure and the calculated coefficient of friction on Ottawa sand. As the full contact area is yet to develop, the linear interpolation for normal stress-shear stress may result in a misleading interpretation under conditions of relatively low normal pressure. At the point in which the deformation becomes essentially plastic, the contact area stabilizes, and the linear interpolation captures the interface friction angle, resulting in a constant friction coefficient. The calculated shear force is independent of the area of contact and is proportional to the normal load. This deviation in shear stress demand specially for the rough surface is caused by asperities have a significant influence on the results. The values of the peak friction angle (δpm) and the residual friction angle (δrm) obtained from the lines of best fit have a difference of less than 5°. As expected, the data also show that the interface friction angle is smaller than the internal friction angle of the soil (presented in Table 1 ). Additionally, the results on dry sand exhibit lower interface friction angles than those determined by conventional direct shear testing in the literature. The influence of the shear box itself on the tested interface as well as the contact surface changes during the test procedure may be responsible for the higher result achieved utilizing the direct shear test apparatus. Shahraki et al. (2022b) provides a comparison of the findings of a conventional direct shear test versus those obtained from a membrane-soil interface with unconstrained boundaries.

Finite Element Analysis of the Interface

Numerical simulations were also conducted to evaluate the accuracy of a series of FEMs considering different interface parameter assumptions. In the context of sliding behavior analyses, understanding the sensitivity of the response prediction to the interface friction characterization is an important aspect of successful performance-based design. For this purpose, a three-dimensional model based on the experimental shear tests was developed using LS-DYNA, one of the most common finite element codes for SSI analysis of infrastructure. The software is equipped with a variety of material and contact models suitable for SSI modeling (Hallquist 2007). The block was modeled as elastic, having a Young’s modulus of 20 GPa, Poisson’s ratio of 0.2, density of 2,400 kg/m3, and the soil material is modeled using *MAT_FHWA_SOIL. This soil model is based on modified Drucker-Prager plasticity theory and is capable of modeling pre-peak hardening, post-peak strain softening (damage), strain-rate effects (strength enhancement), and pore-water effects (moisture effects). The required parameters for this material model were calculated based on the manual by Lewis (2004) using the properties presented in Table 1 . Solid brick elements were used to model the soil and concrete block. The displacement-controlled loading system was simulated utilizing a PRESCRIBED_MOTION_SET, which allows a gradual displacement to increase from 0 to 2.5 cm over 10 s (i.e., a rate of 0.25 cm/s).

An appropriate contact model is also required to obtain realistic and accurate results. A simplified model like TIED contact, which does not allow separation, is likely unsuitable as it does not present a realistic contact scenario between soil and structural materials. A more realistic contact model that is frequently used for modeling the interface is the “SURFACE-TO-SURFACE” contact model in LS-DYNA. This model allows for loss of contact between the soil and foundation and simulates Coulomb friction in sliding. Sensitivity analyses indicate that among the soil-structure input parameters, the coefficient of friction is a major governing parameter (Raychowdhury and Hutchinson 2010).

To this end, several different approaches were considered to estimate the coefficient of friction for the interface modeling, one based on the internal friction angle and the other using the characterized interface friction angle. An upper bound solution to the interface problem would assume that the interface coefficient of friction is equal to tanϕ, where ϕ is the internal friction angle of the in-contact soil. Another potential estimation of the coefficient of friction used in practice is to assume a fraction of the soil’s internal friction angle, commonly (0.66–0.75)ϕ (Das 2015). The other two assumed friction parameters are based on the previously described test data, namely the specific interface friction angle (δr) and the Mohr-Coulomb interface friction angle (δrm), which are listed in Table 3  and Table 4 , respectively. As an example, the shear stress-horizontal displacement results for the smooth and membrane surfaces, under the nominal contact pressures equal to 6.1 and 54.2 kPa, obtained from finite element modeling utilizing these four interface frictions are presented in figure 11 . The rest of the numerical results are not included in this article, but they were verified using the experimental results. As can be seen in figure 11 , the results of the LS-DYNA simulation using tan(δr) as the interface friction angle is a near perfect match with the experimental data for both the smooth concrete (S) and membrane (M) surfaces.

FIG. 11
Comparison of experimental and numerical data using different friction angles for the interfaces under two different normal pressures: (A) smooth surface under 6.14-kPa normal pressure; (B) smooth surface under 54.26-kPa normal pressure; (C) membrane surface under 6.14-kPa normal pressure; and (D) membrane surface under 54.26-kPa normal pressure.
FIG. 11
Comparison of experimental and numerical data using different friction angles for the interfaces under two different normal pressures: (A) smooth surface under 6.14-kPa normal pressure; (B) smooth surface under 54.26-kPa normal pressure; (C) membrane surface under 6.14-kPa normal pressure; and (D) membrane surface under 54.26-kPa normal pressure.
Close modal

Although the surface-to-surface contact element provides a good match by using the specific friction angle, the shear softening response at the interface is not properly captured using this method. The soil material itself exhibited contractive and dilative strain behavior under different loading conditions. This will be a topic of future research wherein the interface will be captured via digital imaging and processed to advance knowledge in this area. The tendency of soil to move underside and in front of the block was also similar to what occurred in the experiments for the rough and smooth surfaces. Figure 12  presents a sample of displacement and velocity vectors output from the FE model demonstrating the heaving behavior in front of the block.

FIG. 12
A close-up section of FE model for conducted shear test showing the (A) displacement vectors (mm) in the xz-direction and (B) velocity vectors (mm/s) in the z-direction for the test on smooth surface under normal pressure of 54.26 kPa.
FIG. 12
A close-up section of FE model for conducted shear test showing the (A) displacement vectors (mm) in the xz-direction and (B) velocity vectors (mm/s) in the z-direction for the test on smooth surface under normal pressure of 54.26 kPa.
Close modal

It is shown in figure 11  that tan(δrm) is also a good representative parameter of the interface behavior for the membrane; however, it is less appropriate in simulating the smooth concrete surface. The variation in the coefficients of friction for both the smooth and rough concrete surfaces under different normal pressures (fig. 9 ) means that the Mohr-Coulomb fit is not a suitable predictor for a low range of normal pressures.

As expected, the shear stresses obtained for all tests utilizing the soil’s internal friction angle as the interface coefficient of friction was greater than experimental results. The difference is significant for the soil-membrane interface case. For the concrete block-sand interface under high normal pressure, assuming an interface friction of 3/4Ø can produce a shear stress-displacement response that is close to the experimental results. In some cases, using 0.9 as another fraction of the internal friction angle to predict interface behavior might be effective, but not in all cases. Table 5  shows the computed error based on the friction angle parameter assumption.

TABLE 5

Error with respect to experimental data for using different interface friction angle parameters

Surface TypeNormal Pressure, kPaInternal Friction AngleInterface Friction Angle
Ø0.9Ø0.75Øδrδrm
Smooth6.1+15 %+3 %−16 %+2 %−40 %
54.2+45 %+29 %+6 %+1 %−25 %
Membrane6.1+141 %+115 %+76 %−9 %+5 %
54.2+161 %+132 %+90 %+1 %+3 %
Surface TypeNormal Pressure, kPaInternal Friction AngleInterface Friction Angle
Ø0.9Ø0.75Øδrδrm
Smooth6.1+15 %+3 %−16 %+2 %−40 %
54.2+45 %+29 %+6 %+1 %−25 %
Membrane6.1+141 %+115 %+76 %−9 %+5 %
54.2+161 %+132 %+90 %+1 %+3 %

In geotechnical design, using a larger than realistic friction angle is dangerous and can potentially lead to failure while utilizing a smaller friction angle is generally considered conservative. Although a range of reduction values are typically presented to capture the soil-interface friction in many aspects of geotechnical design, in this instance, accuracy in this parameter is critical in capturing a realistic response. As shown in Table 5 , using the Mohr-Coulomb fit to describe the interface friction angle (δrm) might also result in deviation in the shear stress demand.

The classical laws of friction, named after Coulomb and Amontons, stated that the friction force is independent of the area of contact and is proportional to the normal load. Although these laws are applicable in many cases, the experiments at the soil-structure interface have shown that the foundation’s asperities have a significant influence on the results. The asperities modify the real area of contact and as a result, the shear force does not increase proportionally. The asperities also influenced the deformation (plowing) that occurred along the underside of the foundation and as a result, the formation of a shear zone in front of the concrete block. For the cases with a membrane, there were almost no irregularities observed, and the real area of contact did not change with increasing normal pressure. Therefore, for this interface case, the shear force is proportional to the normal load, and the friction at the interface is independent of the area. As a result, the Coulomb failure line presents the interface response closest to the experimental data. Thus, to reduce uncertainty in response estimation, proper characterization of friction at the soil-structure interface is of primary importance. In fact, a reduction of uncertainty in the friction behavior alone will result in a significant reduction of the design demand uncertainty.

Conclusions

This article provides large-scale experimental data with appropriate boundary conditions that capture the shallow foundation sliding failure mechanism for use in realistic interface modeling, with the eventual aim of assisting in the development of models that can capture energy dissipation during seismic shaking. A summary of the key points of the experimental study are as follows:

  • Three different interfaces (smooth concrete, rough concrete, and a membrane) were tested against dry Ottawa F-55 sand at varying levels of vertical stress, and the shear behavior results were presented.

  • The experimental data showed that the membrane produced failure directly at the interface and did not mobilize soil strength to any appreciable depth, which is in contrast with the smooth and rough concrete surfaces.

  • Increasing the normal pressure produced different shear stress responses for the membrane and concrete surfaces in contact with the Ottawa F-55 sand.

  • Because the depth of the asperities on both the smooth and rough concrete surfaces was greater than the grain size, the interface shear resistance did not increase proportionally with the increase in normal pressure for these surfaces because of the change in the real interface area.

  • The roughness of the foundation surface is linked to two effects on sliding behavior as it influences: (1) the true soil-foundation contact area and thus affects actual normal pressure, and (2) the mobilization of the shear strength of the soil as well as shear zone formation, which can potentially affect energy dissipation.

  • The magnitude of shear resistance was almost independent of the shearing rate in the range of tested normal pressures.

  • The shear envelope failure line (Mohr-Coulomb criterion) is a reasonable interface friction parameter, if the real area of contact does not affect the actual normal pressure nonlinearly (i.e., membrane surface).

  • The presented results can be used as a baseline to model sliding behavior at a soil-structure interface. Additional tests on larger size foundations with higher normal pressures are needed to better match pressures expected in typical construction applications. This will require a novel loading system that produces normal stress without inducing undesired moments. Cyclic loading tests, on the other hand, are required to address changes in soil-structure characteristics and to appropriately capture and simulate SSI under dynamic loading (e.g., capture the degradation of the membrane).

  • To further understand the interface shear response behavior under all of the varied parameters, a detailed local/microscopic analysis of soil particle displacement and shear zone formation at the soil-structure interface is required. This might be demonstrated using discrete element modeling to investigate volume changes at the interface for rough and smooth concrete surfaces.

ACKNOWLEDGMENTS

The research presented in this article was funded by the US Department of Energy. Any opinions, findings, and conclusions of the authors expressed herein do not necessarily state or reflect those of the US Government or any agency thereof. The authors thank the Structural Engineering and Earthquake Simulation Laboratory (SEESL) at University at Buffalo for helping in setting up the experiment for this study.

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