Influence of particle size on the drained shear behavior of a dense fluvial sand

Abstract

Particle morphology, including particle shape and particle size, has significant influence on the shear behavior of granular soils. The effect of particle shape has been investigated in several studies. However, the effect of particle size has not yet been paid much attention. In this study, the effect of particle size on the shear strength and the stress–dilatancy behavior of sands was assessed through a series of drained triaxial compression tests on dense uniform silica sands. The effect of particle size was analyzed on various aspects of mechanical behavior: the stress–strain response, the shear band formation, the peak-stress axial strain, the peak dilation angle, the peak friction angle, the critical-state friction angle, and the stress–dilatancy relations. Furthermore, we noticed that the particle shape of silica sands usually varies with particle size. The effect of this morphologic characteristic on mechanical behavior was also discussed by comparing the experimental results on silica sands with those reported on glass beads and Péribonka sand (Harehdasht et al. in Int J Geomech 17:04017077, 2017). The results show that particle size significantly influences the peak friction angle, the peak dilation angle and the stress–dilatancy behavior. The underlying mechanism for the effect of particle size was discussed from the perspective of kinematic movement at particle level.

Appendices

Appendix A: Sample variability

See Fig. 24.

The effect of sample variability on the stress–strain curves in Fig. 4 is carefully evaluated by repeating several tests under the same testing conditions. A set of typical repeated tests for the uniform sand #50-#80 with a confining pressure of 200 kPa are shown in this Appendix.

Figure 

Fig. 24

Experimental results of stress ratio and volumetric strain plotted against axial strain for two specimens of the uniform sand #50-#80 under the same condition

24 shows the stress–strain curves for two different specimens of the uniform sand #50-#80 under the same sample preparation method. The initial void ratios for the two specimens are 0.767 and 0.769. Both specimens were tested in the same triaxial cell under the same confining pressure (200 kPa).

The curves of these two tests are nearly identical before the peak stress. After the peak stress, there is small variation between the curves of the two tests. The variation is likely due to the difference in the locations of strain localization, which was initiated randomly in the two different specimens.

Although the variation is small for the stress–strain curve, we would like to evaluate the possible effect, which may be caused by this small variation, on various mechanical properties interpreted from the test results, such as peak friction angle, peak dilation angle, and critical-state friction angle.

For this purpose, in Fig. 

Fig. 25

The stress–dilatancy relations for two specimens of the uniform sand #50-#80 under the same condition

25, the stress–dilatancy curves is calculated and plotted. Using Fig. 25, the peak friction angle $\phi_{p}$, the friction angle at onset of dilation $\phi_{f}$, the equivalent peak friction angle $\overline{\phi }_{fp}$, and the peak dilation angle $\psi_{p}$ are computed for the two tests and listed in the figure. The critical state friction angle $\phi_{cv}$ is computed by Eq. (5) with $T_{n} = 1$ from each test result. The critical state angle is also listed in Fig. 25. For all computed angles from the stress–strain curves, the difference due to sample variation is less than 0.5 degree, which is acceptable.

Appendix B: Definition of Dilation angle

The expression of dilation angle (ψ) has been proposed by Vermeer and de Borst [35] for triaxial compression and plain strain conditions, which was derived from concepts of plasticity theory. The expression of dilation angle (ψ) is given by:

$${\text{sin}}\psi = \frac{{ - \left( {d\varepsilon_{v} /d\varepsilon_{1} } \right)}}{{2 - \left( {d\varepsilon_{v} /d\varepsilon_{1} } \right)}}$$

(11)

In plain strain conditions, Eq. (11) leads to the following expression:

$${\text{sin}}\psi = - \frac{{\left( {d\varepsilon_{1} + d\varepsilon_{3} } \right)}}{{\left( {d\varepsilon_{1} - d\varepsilon_{3} } \right)}}$$

(12)

where $d\varepsilon_{1}$ and $d\varepsilon_{3}$ are the principal stain increments and $d\varepsilon_{1}$ is the axial strain increment $d\varepsilon_{{\text{a}}}$ in triaxial compression conditions. Equation (11) has been extensively used for calculating the dilation angle of axisymmetric samples [12, 13, 21–23].

An alternative expression of the dilation angle for triaxial compression conditions has been proposed by Vaid and Sasitharan [52] and is given by:

$${\text{sin}}\psi = \frac{2}{{1 - 3/\left( {d\varepsilon_{v} /d\varepsilon_{a} } \right)}}$$

(13)

This expression has been used for calculating the dilation angle of axisymmetric samples [1, 53, 54]. This expression was derived from the definition of ψ for plain strain conditions originally introduced by Hansen (1958) given as:

$${\text{sin}}\psi = - \frac{{d\varepsilon_{v} }}{d\gamma } = - \frac{{d\varepsilon_{v} }}{{d\varepsilon_{1} - d\varepsilon_{3} }}$$

(14)

where $\gamma$ is shear strain.

For plain strain conditions, Eqs. (11) and (14) are identical. However, for triaxial compression conditions, the value of dilation angle (ψ) calculated from Eq. (11) is less than that calculated from Eq. (13) because the definition of $d\gamma$ is different (i.e., $d\gamma = d\varepsilon_{1} - 2d\varepsilon_{3}$ in Eq. (11) while $d\gamma = d\varepsilon_{1} - d\varepsilon_{3}$ in Eq. (13)).

Thus, it is noted that, for plain strain conditions, there is a universal and clear definition of dilation angle. But for triaxial compression conditions, there are two different definitions of dilation angle (Eqs.11 and 13). In this study, the definition of Eq. (11) was used.