1、Numerical and experimental direct shear tests for coarse-grained soilsAhad Bagherzadeh-Khalkhali , ,Ali Asghar MirghasemiSchool of Civil Engineering, College of Engineering, University of Tehran, Tehran, IranReceived 15 February 2008. Accepted 18 November 2008. Available online 15 January 2009.http:
2、/dx.doi.org/10.1016/j.partic.2008.11.006, How to Cite or Link Using DOICited by in Scopus (7)Permissions Direct shear test;Micromechanics;Coarse-grained soil;Shear strength1. IntroductionExperimental tests on coarse-grained soils always involve difficulties, and it is often necessary to remove large
3、 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, a
4、nd 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 triaxi
5、al 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
6、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 di
7、stinct 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
8、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 namely, parallel gradation technique (Lowe, 1964), scalping method (Zeller designated as T1, T2 and
9、T3, respectively). Table 1 shows the tests with different normal stresses.Fig. 1. Particle size distribution of experimental test samples.Fig. 2. Size distribution of numerically simulated samples.Table 1. Normal stresses employed in numerical and experimental direct shear tests.Test number Applied
10、vertical stress kg/cm2 (kPa)Test 1 (T1) v = 1 (98.1)Test 2 (T2) v = 2 (196.2)Test 3 (T3) v = 3 (294.3)Full-size table2.1. Experimental testsAccording 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 she
11、ar 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.
12、 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 techniqueNumerical simulations Experimental testsMaximum particle size (mm)Maximum particle size (mm)Sample 0 38 Sample 1P
13、arallel 25 25.4Sample 2Parallel 9.5 4.76Sample 3Scalping 25 25.4Sample 4Scalping 9.5 4.76Full-size tableTests 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 c
14、hanging 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 expe
15、rimental samples after compaction.Samples Numerical simulations Experimental testsa(average coordination number)Densitya Relative density (%)Sample 04.75 0.73 Sample 14.74 0.75 94.8Sample 24.92 0.66 96.4Sample 4.78 0.74 95.73Sample 44.95 0.65 97.5aThese parameters are dimensionless.Full-size table2.
16、2. Numerical simulationsIn 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
17、. 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 th
18、e 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
19、 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 (Bagherzad
20、eh-khalkhali (b) compacted assembly; (c) after loading; (d) sheared assembly.The 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 diff
21、erent 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 a
22、pplied 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 () mobilized in the assembly as a function of volumetric strain. As expected, bulk module of sample at the first stages of compaction is low
23、 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.Densities in Table 3 are defined as the ratio of sum of area occupied by all particles to
24、 total area of the assembly, while average coordination number () 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 numbe
25、r 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
26、. 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 ass
27、emblies 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 asse
28、mbly. The normal stress (v) 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 p
29、eak strength, the failure is assumed to occur at the shear stress corresponding to 1520% shear strain.3. Sample behavior in experimental testsFig. 5 shows the behavior of Samples 2 and 4 under shear test with small-scale box. The stressstrain behavior of Sample 2 is plotted in Fig. 5 Sample 2(a) and
30、 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 MohrCoulomb criteria, which was fitted to the results to determine the apparent cohesion c and mobilized friction angle , is shown in Fig. 5 Sample 2(c).Fig. 5. Con
31、stitutive behavior of Samples 2, 4 in small-scale and Sample 3 in large-scale experimental direct shear tests, with (a) for stressstrain curve, (b) for vertical-shear strain curve, and (c) for best failure envelope based on MohrCoulomb criteria.Generally, the behavior of Sample 2 was contractivedila
32、tive 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 i
33、n 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
34、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 S
35、ample 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 in all the tests, th
36、e differences in the results are mostly attributed to particle size and the modification technique employed. With higher vertical stress, the measured maximum shear stress has an increasing trend. The sample dilation decreases with the increase of the stress level (Fig. 5 Sample 3(b). Generally, bot
37、h small and large-scale tests show the same behavior from the point of view of stress level influences. However, samples in large-scale tests show more dilation than those of small-scale tests. Also, the softening behavior of the samples increases with increasing the particle size.To compare the two
38、 mechanical parameters c and obtained with small and large-scale tests, it is necessary to evaluate the soil behavior in these tests. Table 4 summarizes the results of the direct shear tests including the maximum mobilized friction angles at single tests, max, while Table 5 presents mechanical param
39、eters c and of the samples based on MohrCoulomb criteria as the failure envelope with denoting friction angles of the samples based on the selected failure envelope of tests at three different vertical stresses.Table 4. Comparison of experimental direct shear tests.Testmax() Strain behaviordmax(mm)
40、() cv()Sample 1T1 51.0 Dilative 25.4 13.546T2 51.0 Dilative 25.4 11.346T3 50.0 Contractivedilative25.4 8.5 47.5Sample 2T1 55.0 Dilative 4.76 17.551T2 51.5 Contractivedilative4.76 11.147T3 49.0 Contractivedilative4.76 6.0 46.5Sample 3T1 53.0 Dilative 25.4 19.347T2 54.0 Dilative 25.4 13.547T3 51.5 Con
41、tractivedilative25.4 13.045Sample 4T1 59.5 Dilative 4.76 20.852T2 55.0 Dilative 4.76 14.050.0T3 52.0 Contractivedilative4.76 7.4851.5max: Maximum mobilized friction angle; : maximum dilation angle; cv: mobilized friction angle at constant volume.Full-size tableTable 5. Values of resulted mechanical
42、parameters in the experimental tests.Sample dmax(mm) () c(kg/cm2) (kPa)max(kg/cm2)Sample 125.4 49.5 0.07 (6.9) 1.24, 2.41, 3.58Sample 24.76 44.1 0.48 (47.1) 1.44, 2.41, 3.38Sample 325.4 49.9 0.23 (22.6) 1.41, 2.61, 3.79Sample 44.76 46.9 0.64 (62.8) 1.71, 2.77, 3.84: Friction angle; c: apparent cohes
43、ion; max: maximum shear stress.Full-size tableAs shown in Table 4, increase of the vertical stress causes the decrease of the maximum mobilized friction angle. The maximum mobilized internal friction angle for the samples prepared using scalping method is larger than that for samples modified by par
44、allel method. As shown in this table the maximum dilation angle for samples prepared by scalping technique causes more dilation in comparison with those by parallel method. This relation is not affected by the particle size (test scale).Table 5 shows that with the increase of the test scale and part
45、icle size, the calculated apparent cohesion according to MohrCoulomb criteria decreases. It was found that samples with scalping modification have higher shear strength than other samples. The comparison between Samples 1 and 2 shows that the initial density of the sample with smaller particle size
46、is higher than another sample. The difference in initial density is the cause for the increase of the maximum mobilized shear strength of Sample 2 in comparison with Sample 1. Similar behavior can be observed for Samples 3 and 4 (Table 5 and Fig. 6). Sample 4 with higher initial density and lower ma
47、ximum particle size provided higher shear strength in comparison with Sample 3.Fig. 6. Maximum mobilized shear stress for experimental tests.Results of samples with the same maximum particle size from Table 4 and Table 5 reveal that use of the scalping technique for preparing the specimens is more a
48、ppropriate than the parallel method to determine the mechanical parameters based on the predicted behavior of coarse-grained soils.4. Results of numerical simulations4.1. Case study of Sample 3Results of numerical simulation by DEM for Sample 3 are selected to evaluate the goal of this research, sin
49、ce the behavior of this sample is found to be similar to the original soil.Micromechanical approach for modeling soil behavior offers physical understanding and assumes the granular material as an assembly of distinct particles interacting by means of forces at contacts. For any angle , the portion of the total number of contacts in the system, which are oriented at angle is E. Rothenburg (1980) showed that the distribution of such contacts takes the form:(1)where, a is referred to as parameter of anisotropy and 0 i
