4.1 Test Program 1
4.1.1 Shear Strength Parameters
Fig. 5 plots the maximum shear stresses from the direct shear tests against the normal stresses. Linear regression equations with the data showed an intercept on the vertical axis, indicating a nonzero cohesion even for the dry sand. Cohesion is sometimes expected in dry sand due to interlocking between the particles (Lu and Likos 2013). However, the magnitudes of the cohesion (intercept on the vertical axis) ranges from a minimum value of 0.2 kPa for AH0 sample to a maximum value of 7.9 kPa for AH3 sample, which are practically negligible, considering the uncertainties involved in the measurements and data interpretations. Thus, the apparent cohesion for the moist soil at the water contents considered (1% to 3%) is considered negligible. The apparent cohesion in unsaturated granular material predominantly results from the capillary force due to negative pore-water pressure and surface tension (Lu et al. 2007). At very low moisture contents, air voids may be connected in the granular soil within the shear box, causing the air pressure to be the same as the atmospheric pressure. As a result, the negative pore-water pressures and the apparent cohesion can be negligible. Ravindran and Gratchev (2020) also reported a lower apparent cohesion at lower moisture content for a gravelly/sandy soil that increased initially and then decreases with the increase of water content. The slopes of the lines in Fig. 5 are different, indicating different friction angles, which is due to the combined effects of water contents and densities of the soil, as discussed later. As mentioned earlier, although the same compaction efforts were applied for the soil samples at different moisture contents, the dry densities of the soil were different.
4.1.2 Stress-Deformation Responses
Since the apparent cohesion of sand is negligible for the sand, the shear strength of the soil depends exclusively on the normal stress for each condition (i.e., stress level, density, and water content). The ratio of the shear strength to the normal stress (called herein as “stress ratio”) is therefore examined here against the shear displacements. The volumetric strain is examined in term of a dilation rate, defined as the ratio of the changes in vertical displacement change (dv) to the changes in the horizontal displacement (du) (i.e., Dilation rate ), after Simoni and Houlsby (2006).
Fig. 6 shows the variation of stress ratios with horizontal displacement for four conditions of the local sand subjected to high compaction. As seen in the figure, the peak stress ratios are almost the same for all normal stresses for the dry sample (Fig. 6 (a)). However, for the moist samples, the peak stress ratio decreases with the increase of normal stress. The peak stress ratio is around 1.2 for the dry sand, which corresponds to a peak friction angle of 50°. For the moist sand, the peak stress ratio varies from 0.8 to 1.25. These correspond to friction angle variations from 38° to 51°, with the lowest value for the normal stress of 50 kPa and the highest value for the normal stress of 12.5 kPa. It is also to be noted that post-peak degradation of the stress ratio is abrupt for the dry sand, whereas the post-peak degradation is gradual for the moist sands. This may be because of capillary forces in the moist sample. For the dry sand, the stress ratio is reduced from a peak value of 1.2 to a critical state value of around 0.7. Thus, the critical state friction angle for the soil is 35°. The critical state stress ratios for the moist samples range from 0.7 to 0.8, except for the normal stress of 12.5 kPa. For 12.5 kPa of normal stress, the stress ratios fluctuate beyond the peak values, potentially due to the low confining effects. The peak and post-peak behavior observed for the dry sand is commonly reported in the literature (Al Tarhouni et al., 2017). However, the behavior of moist sand has not been extensively investigated to examine the behaviors.
For the moist samples, the peak stress ratio is higher for soil AH1 having around 0.8% of moisture content than for AH2, having around 1.2% of moisture content at each of the stress levels considered. The shear strength is higher again for soil AH3 having a moisture content of around 2.6%. The shear strength changes are attributed to the changes in the densities of the soil prepared using the same method of compaction and the capillary actions.
Fig. 7 plots the calculated dilation rate against the horizontal displacement for the four conditions of the local sand subjected to high compaction. Each of the samples shows positive dilation rates, indicating an increase in the volume (dilation) during shearing. In general, the peak dilation rate occurs at the horizontal displacement of 1 to 2 mm. For the dry sample, the dilation rate drops rapidly after reaching the peak value. For the moist samples, the dilation rate decreases gradually with the increase in horizontal displacement, which is consistent with the changes in the stress ratios in Fig. 6. The dilation angle for each of the samples eventually reaches almost zero, which is essentially the critical state.
Fig. 8 shows the variation of stress ratio with horizontal displacement for the local sand samples prepared without compaction. For the loose condition of the soil, no post-peak degradation in the stress ratio is observed in any of the samples, as expected. As seen in Fig. 8 (b-d), the peak stress ratio is almost the same for all normal stresses for the moist samples. The peak ratios are 0.6, 0.55, and 0.5 for samples AN1, AN2, and AN3, respectively, which correspond to the friction angles of 31°, 29° and 26.5°, respectively. The moisture contents in these samples are 1.25%, 2.0%, and 2.7%, respectively. The friction angles for the loose soils are 30% to 40% less than the peak friction angles for the dense soils discussed above.
For the loose dry sand, the stress ratio appears to decrease with the increase of normal stress that varies from 0.69 to 0.88 (Fig. 8(a)). The stress ratios correspond to the friction angle of 34.5° to 41°. The higher value is for the normal stress of 12.5 kPa, and the lower value is for the normal stress of 50 kPa. Thus, the peak friction angle of the loose soil at 50 kPa is close to the critical state friction angle for the dense soil (discussed above). However, for the low normal stress of 12.5 kPa, the friction angle in the loose condition is higher than the critical state friction angle. Thus, the concept of critical state friction angle may not be applicable at the low confining pressure of the soil. Al Tarhouni et al. (2017) also questioned the critical state friction angle of sand at low confining pressure from direct simple shear and triaxial tests.
The dilation rate for the loose soil is generally negative, indicating a decrease of volume during the direct shear tests, as shown in Fig. 9. As the shearing of soil occurs at constant volume, the dilation rates become zero at the point of shear failure. However, the increase in the volume of the soil (positive dilation rate) is observed in the dry sample during shearing (Fig. 9(a)). It shows that although the dilation rate is negative at the beginning, it increases with the increase of horizontal displacement and reaches the maximum value at the horizontal displacement of around 2 mm. The stress ratio is also peak at the same horizontal displacement (i.e., 2 mm). Similar load-deformation behavior was observed for the silica sand but has not been included here for the sake of brevity.
4.1.3 Peak Stress Ratio
As discussed earlier, the peak stress ratios obtained from different tests are found to be different. The stress ratios generally depend on the stress levels, water contents, and the densities of the soil. To examine the effect of stress levels, the peak stress ratios for various soils are plotted against normal stress in Fig. 10. The figure reveals that the stress ratio is generally the highest at the normal stress of 12.5 kPa. The changes in the stress ratios are not significant beyond the normal stress of 25 kPa. In general, the stress ratio is the highest for the dry soils and decreases with the increase in water content, except for the silica sand. Tiwari and Al-Adhadh (2014) demonstrated for well-graded sand that the friction angle can decrease for changing from dry state to saturated state at the same relative density, which is likely due to the effect of lubrication around the soil particle by the water. However, the test results presented here can also depend on the density of the soil, as discussed below.
To examine the effect of water contents, the peak stress ratio at various normal stresses is plotted against the water contents in Fig. 11. Since the dry densities of the soil in the shear box are also expected to be different even under the same compaction effort, the calculated dry unit weights of the soil are also plotted against the moisture contents in this figure. It shows that the peak stress ratio and the dry unit weight of the soils decrease with the increase of moisture content. Thus, the reduction of the peak stress ratio with moisture content has a strong correlation with the reduction of the dry density. While both dry density and the water content are expected to contribute to the peak stress ratio of the soil, the contribution of each parameter could not be separated from this test program.
4.2 Test Program 2
4.2.1 Stress–Deformation Responses
Fig. 12 shows the changes in stress ratio with horizontal displacement for the compacted samples at various normal stresses. The responses are similar to those observed in Test Program 1. In Fig. 12, the changes in the peak stress ratio with the normal stress are insignificant for the dry sands (~1.2 for the normal stresses of 12.5 kPa to 100 kPa and 1.1 for the normal stresses of 200 kPa to 400 kPa). For the moist samples, the peak stress ratio is the highest for 12.5 kPa of normal stress that reduces with the increase of the normal stress. As observed in Test Program 1, the post-peak degradation of the stress ratio is rapid for the dry sand and is gradual (and less significant) for the moist sand. The dilation rates observed in this test program were also similar to those observed in Test Program 1 (not included in this paper).
4.2.2 Peak Stress Ratio
Fig. 13 shows the variation of peak stress ratio with normal stress for the compacted and loose samples. In general, the peak stress ratio is the highest at normal stress of 12.5 kPa that decreases with the increase of the normal stress. However, the effect is less significant for the dry sand. For the dense condition of the dry sand, the changes in the peak stress ratio with the normal stress are negligible. For loose conditions of the soil, the peak stress ratio was changed from 0.93 to 0.7 for increasing the normal stress from 12.5 kPa to 400 kPa.
For the moist sand, the peak stress ratio consistently reduced with the increase of normal stress for the dense condition of the soil. However, for the loose conditions, the peak stress ratio remains almost constant (~0.67) for normal stresses between 100 and 400 kPa, indicating a less effect of normal stress on the peak stress ratio at high stress levels.
4.2.3 Effect of Shearing Rate
The effect of the rate of shearing on the stress ratio is studied under four normal stresses 50,100, 200, and 400 kPa for dry sand samples only. However, no significant variation of the stress ratios with the shearing rate was observed both for dense and loose conditions of the soil. Fig. 14 shows the typical variation of stress ratio with the shearing rate observed during the tests. Lade and Nam (2009) also reported no effect of shearing on the shear strength for dry sand.
4.2.4 The Angle of Internal Friction
The above study revealed that the angle of internal friction depends on the density, stress level, and moisture content of the sand. To examine these further, the peak shear stresses from the tests are plotted against the normal stresses in Fig. 15. Test results showed that the peak shear stress versus normal stress response is almost linear at low densities of the soil (Fig. 15(a)). Beyond the density of 17 kN/m3, the responses are nonlinear (Fig. 15(b)). Thus, at lower densities (or unit weights) of the soil, the effect of the normal stress on the friction angle (the slope) is insignificant. However, at the higher unit weights of the soil, the friction angle is higher at lower stress levels and relatively lower at higher stress levels. In both cases, the intercepts of the shear strength versus normal stress plot are negligible even for the moist soil. Thus, the effect of suction on the shear strength (i.e., apparent cohesion) of the soil is considered negligible during the direct shear tests.
Fig. 15 reveals that the shear strength of the soil is higher for a higher density of the soils. The rate of increase of shear strength with density is relatively less for the sand with a density of less than 17 kN/m3. For an increase of the density from 11.5 kN/m3 to 16.1 kN/m3, the shear strength increases from 256.6 kPa to 273.8 kPa at the normal stress of 400 kPa. However, for the increase of density from 17 kN/m3 to 19 kN/m3, the shear stress increases from 290.1 kPa to 578.8 kPa at the same normal stress (i.e., 400 kPa). Thus, the effect of density on the shear strength (hence, the angle of internal friction) is very significant at the dense condition of the soil (>17 kN/m3).
Note that even at different moisture contents, the shear strengths are the same for the same levels of densities. In Fig. 15(b), the responses for the moisture contents of 1.5% (with gd = 17.4 kN/m3) and 6% (with gd = 17.2 kN/m3) match with each other. Similarly, the test results with dry unit weights of 18~19 kN/m3 match reasonably (less than 10% difference) with each other. Thus, the contribution of the moisture contents is apparently insignificant to the shear strength for the levels of moisture contents considered.
The angles of internal friction of the sand are calculated from the slope of linear trendlines of the peak shear stress versus normal stresses data from the tests. The calculated angles of internal friction and the dry densities are plotted against the water contents in Fig. 16. The maximum angle of internal friction of 49° is found for the compacted dry samples, which is reduced with the increase of moisture content. For the uncompacted sample, the maximum angle of internal friction is ~34.5° for the dry sand that is reduced with the moisture contents. Dry unit weights of the sand are also reduced with the increase of moisture content for both compacted and uncompacted soil. This observation confirms that the reduction of the angle of internal friction with moisture content in the tests is due to the reduction of the density (dry unit weight). Thus, the degree of compaction is the most significant controlling parameter for the shearing resistance of the soil. Note that the peak shear stress of the dry sand is close to that of the moist sand with 5.6% moisture in Fig. 15(b), as the dry unit weights of the soils are similar.
Fig. 17 plots the friction angles against the relative compaction calculated using the maximum dry density obtained from the Standard Proctor Compaction tests. As expected, the friction angle increases with the increase of the relative compaction. The rate of increase is less at lower relative compactions (loose condition), which is significantly high at high relative compactions. As seen in Fig. 17, the friction angle increases at a lower rate up to the relative compaction of 90%, a moderately high rate from 90% to 100% of relative compaction, and a very high rate beyond 100% of relative compaction. The poorly graded silica sand samples showed lower friction angles than those for the local sand at the same level of relative compactions.