Numericalandexperimentaldirectsheartestsforcoarse-grainedsoils.doc

Numerical and experimental direct shear tests for coarse-grained soils
Ahad Bagherzadeh-Khalkhali,,
Ali Asghar Mirghasemi
School of Civil Engineering, College of Engineering, University of Tehran, Tehran, Iran
Received 15 February 2008. Accepted 18 November 2008. Available online 15 January 2009
http://dx.doi.org/10.1016/j.partic.2008.11.006, How to Cite or Link Using DOI
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Abstract
The presence of particles larger than the permissible dimensions of conventional laboratory specimens causes difficulty in the determination of shear strength of coarse-grained soils. In this research, the influence of particle size on shear strength of coarse-grained soils was investigated by resorting to experimental tests in different scale and numerical simulations based on discrete element method (DEM). Experimental tests on such soil specimens were based on using the techniques designated as “parallel” and “scalping” to prepare gradation of samples in view of the limitation of laboratory specimen size. As a second approach, the direct shear test was numerically simulated on assemblies of elliptical particles. The behaviors of samples under experimental and numerical tests are presented and compared, indicating that the modification of sample gradation has a significant influence on the mechanical properties of coarse-grained soils. It is noted that the shear strengths of samples produced by the scalping method are higher than samples by the parallel method. The scalping method for preparing specimens for direct shear test is therefore recommended. The micromechanical behavior of assemblies under direct shear test is also discussed and the effects of stress level on sample behavior are investigated.
Keywords
Discrete element method;
Direct shear test;
Micromechanics;
Coarse-grained soil;
Shear strength

1. Introduction
Experimental tests on coarse-grained soils always involve difficulties, and it is often necessary to remove large particles due to dimensional limitation of laboratory specimens. [Marsal, 1967] and [Marsal, 1973], Marachi, Chan, and Bolton (1972) and Varadarajan, Sharma, Venkatachalam, and Gupta (2003) attempted to investigate coarse-grained soil properties by experimental tests on reduced-particle-size samples, and presented a positive relationship between maximum particle size and the mobilized internal friction angle. Marachi et al. (1972) and Charles and Watts (1980), indicated that the influence of maximum particle size is not clearly understood, while Varadarajan et al. (2003), using large-scale triaxial test on rockfill, found that the friction angle increases when the particle size of sample increases.
This article investigated the effects of particle size on macro and micro mechanical behavior of coarse-grained soils, using both experimental tests and numerical simulations, on a series of both small- (6 cm × 6 cm × 2 cm) and large- (30 cm × 30 cm × 15 cm) scale direct shear tests on selected coarse-grained soils to determine the effect of stress level on the relationship between particle size and friction angle and behavior of samples. Parallel numerical models of the samples as assemblages of distinct particles under direct shear test were formulated using the discrete element method (DEM), to acquire qualitative information on the micro and macroscopic features of the particle assemblies. In an assembly of particles, each particle interacts with its neighbors through particle-to-particle contacts, as was noted by Cundall, Marti, Beresford, Last, and Asgain (1978) in their geotechnical study on the dynamic behavior of rock masses and numerical simulation of granular materials (Cundall & Strack, 1979). These results presented the influence of particle gradation and stress level on shear strength of coarse-grained soils under direct shear test using the program ELLIPSE originally developed by Rothenburg and Bathurst (1992) for assemblies of two-dimensional elliptical-shaped particles (Bagherzadeh-khalkhali & Mirghasemi, 2004).
There are four different methods for preparing laboratory specimens; namely, parallel gradation technique (Lowe, 1964), scalping method (Zeller & Wullimann, 1957), quadratic gradation curve method (Fumagalli, 1969) and replacement technique (Frost, 1973). The first two methods, commonly used by engineers, were adopted to investigate the effect of particle size on direct shear test. In the parallel gradation technique, the reduced-particle-size laboratory specimens were formed with size distributions parallel to that of the original sampled material. In the scalping method, all particles considered oversize were removed (scalped) from the original material. These techniques were used to determine the gradation of specimens in the tests and the numerical simulations related to the scale of shear boxes. In this way the effect of sample preparation methods in direct shear tests could be investigated.
2. Test programs
Five samples with different grain size distributions were used in this research. The original sample was taken from coarse-grained soil of Tehran, the capital of Iran. The first sample (Sample 0) was modeled on the original size distribution of the soil. The remaining four reduced-particle-size specimens were prepared by using both modification techniques, parallel and scalping, on the basis of the dimensions of the shear boxes used. Fig. 1 and Fig. 2 show the particle size distributions used for both experimental and numerical tests. To investigate the effect of stress level on shear behavior of the samples, tests were carried out under the normal stress of 1, 2 and 3 kg/cm2 (98.1, 196.2 and 294.3 kPa; designated as T1, T2 and T3, respectively). Table 1 shows the tests with different normal stresses.

Fig. 1. Particle size distribution of experimental test samples.
View thumbnail images
Fig. 2. Size distribution of numerically simulated samples.
View thumbnail imagesTable 1. Normal stresses employed in numerical and experimental direct shear tests.
Test number
Applied vertical stress kg/cm2 (kPa)
Test 1 (T1)
σv = 1 (98.1)
Test 2 (T2)
σv = 2 (196.2)
Test 3 (T3)
σv = 3 (294.3)
Full-size table
2.1. Experimental tests
According to two available small- and large-scale shear boxes, scalping and parallel methods were used to modify the gradation of the sample for each box. A shear box with 6 cm × 6 cm area was used for Samples 2 and 4, and a large shear box (30 cm × 30 cm) was selected for Samples 1 and 3. The maximum particle sizes of samples were selected based on the dimension of the boxes according to ASTM-D3080: 4.76 mm (sieve No. 4) for Samples 2 and 4 and 25.4 mm (1 in. sieve) for other two samples. Table 2 presents the properties of the samples to be tested in laboratory and simulated by DEM.
Table 2. Properties of samples.
Samples
Modification technique
Numerical simulations
Experimental tests

Maximum particle size (mm)
Maximum particle size (mm)
Sample 0
–
38
–
Sample 1
Parallel
25
25.4
Sample 2
Parallel
9.5
4.76
Sample 3
Scalping
25
25.4
Sample 4
Scalping
9.5
4.76
Full-size table
Tests were carried out under consolidated drained condition, and the remolded method of Lambe and William (1951) was used for preparing samples, which was claimed to have negligible influence on changing the real shear resistance of coarse-grained soil samples. Relative densities of the remolded samples were over 95% (Table 3); that is, the tested samples were all dense soil. All direct shear tests were carried out in accordance with ASTM-D3080 (1998).
Table 3. Densities of numerical and experimental samples after compaction.
Samples
Numerical simulations

Experimental tests

γa(average coordination number)
Densitya
Relative density (%)
Sample 0
4.75
0.73
–
Sample 1
4.74
0.75
94.8
Sample 2
4.92
0.66
96.4
Sample 3
4.78
0.74
95.7
Sample 4
4.95
0.65
97.5
a
These parameters are dimensionless.
Full-size table
2.2. Numerical simulations
In numerical simulation, all samples were prepared to simulate experimental samples. However due to limitation of the discrete element method, fine particles <5 mm were removed from the simulated assemblies, thus causing difference between experimental and numerical procedures. Five assemblies were simulated according to the above mentioned requirements. The dimensions of simulated shear boxes, determined according to ASTM-D3080, were similar to experimental tests. Table 2 shows the properties of the simulated samples and Fig. 2 shows the particle size distribution of the samples.
Sample 0 is simulated according to the original gradation of sampled soil to compare the behavior of original soil to reduced-particle-size specimens. Because of removal of fine particles from the simulated samples, to avoid a uniform gradation, the maximum particle size of Samples 2 and 4 was increased to 9.5 mm. The same samples used in the experimental tests remained unchanged (4.76 mm). The size of the simulated shear box was also increased accordingly.
For the numerical simulations, the program ELLIPSE was adopted and modified in order to simulate the direct shear test (Bagherzadeh-khalkhali & Mirghasemi, 2004). For this purpose, the shape of assembly boundary was changed from circular to rectangular using six elliptical particles with high eccentricity (Fig. 3). Also, the assembly boundary control modes were modified to simulate the conditions of direct shear test. Each assembly consists of 650 two-dimensional elliptical-shaped particles with each of them randomly placed within the area surrounded by predefined six boundary particles (Fig. 3a). The diameters of particles in an assembly are determined based on the modified particle size distribution of the sample. The eccentricity of simulated particles was chosen 0.1. Normal and shear stiffness of each particle was selected 2500 MPa. Fig. 3 shows Sample 0 at different stages of numerical simulations.

Fig. 3. Assembly of Sample 0 at different stages of numerical simulation. (a) Generated assembly; (b) compacted assembly; (c) after loading; (d) sheared assembly.
View thumbnail imagesThe numerical simulations were carried out in three stages. The required boundary forces or displacements or servo controlled boundary conditions are applied on the boundary particles to simulate the test conditions in different stages. In the first stage, the generated loose assembly was compacted hydrostatically. Vertical stress was applied on the assembly in the next stage. Finally the assembly was sheared in the direct shear box under constant vertical stress.
At the first stage, a constant compression strain was applied on an assembly until a mean confining pressure of 0.5 kg/cm2 (49.05 kPa) was induced within the assembly. Fig. 4 shows the variation of average pressure (σω) mobilized in the assembly as a function of volumetric strain. As expected, bulk module of sample at the first stages of compaction is low but increases with increasing the compaction of Sample 3 as an example. In Table 3 the density and coordination number of assemblies at the end of first stage are shown.

Fig. 4. Compaction on simulated Sample 3.
View thumbnail imagesDensities in Table 3 are defined as the ratio of sum of area occupied by all particles to total area of the assembly, while average coordination number (γ) represents the ratio of the sum of contacts number for all particles in an assembly to the total number of particles. Accordingly, assemblies with the same range of particle sizes (Table 2) have the same density and coordination number at the end of compaction (Table 3). On the other hand, the initial densities of the samples, which will be compared to determine the effects of modification techniques on the shear strength are the same (Samples 1 and 3 or Samples 2 and 4), therefore, its effect on the discussions can be neglected. Also, the densities and coordination numbers of the assemblies show that the assemblies were dense in the numerical simulations similar to the produced experimental samples.
In the second stage, the vertical load is applied on the compacted assemblies. Applied vertical stresses on the simulated assemblies were similar to the experimental tests (Table 2). Shear load is applied with a constant rate of strain by moving laterally the upper half of the boundary particles. As a result, the shear stress across the horizontal plane between both upper and lower boundary particles is applied in an assembly. The normal stress (σv) is kept constant during the tests. The shearing force starts at zero and increases until the simulated sample fails. The failure is determined when the computed shear force begins to decrease after having reached the maximum. For the samples which have not presented the peak strength, the failure is assumed to occur at the shear stress corresponding to 15–20% shear strain.
3. Sample behavior in experimental tests
Fig. 5 shows the behavior of Samples 2 and 4 under shear test with small-scale box. The stress–strain behavior of Sample 2 is plotted in Fig. 5 – Sample 2(a) and the strain behavior (vertical-shear strain curve) of Sample 2 is shown in Fig. 5 – Sample 2(b). Also, the best failure envelope based on Mohr–Coulomb criteria, which was fitted to the results to determine the apparent cohesion c and mobilized friction angle φ, is shown in Fig. 5 – Sample 2(c).

Fig. 5. Constitutive behavior of Samples 2, 4 in small-scale and Sample 3 in large-scale experimental direct shear tests, with (a) for stress–strain curve, (b) for vertical-shear strain curve, and (c) for best failure envelope based on Mohr–Coulomb criteria.
View thumbnail imagesGenerally, the behavior of Sample 2 was contractive–dilative during the tests. Furthermore, with increasing vertical stress in the tests, the behavior of sample changes to be more contractive initially. In T3, for the vertical stress equal to 3 kg/cm2, the lowest sample dilation was observed.
According to Fig. 5 – Sample 2(b), the maximum dilation happens in a shear strain corresponding to the maximum shear stress. The vertical strain of the sample has an initial value due to the applied vertical stress before shearing the sample. It is clear that increasing vertical stress causes increase of the initial contractive vertical strain of the sample. The induced shear strain at the maximum shear stress, increases as vertical stress increases. Sample 4, produced by scalping method, shows the results similar to Sample 2, but the strain behavior of Sample 4 is more dilative than Sample 2. Also, the mobilized shear strength in Sample 4 is greater than Sample 2 at the same stress level.
Fig. 5 also shows the results of Sample 3, which was prepared by the scalping technique for the direct shear test with large-scale box. Since most of the parameters such as moisture content, relative density and vertical stress were kept constant i