Changes in permeability of sand during triaxial loading: effect of fine particles production

Abstract

Various mechanisms can affect the permeability of dense unconsolidated sands: Volumetric dilation can lead to permeability increase, whereas strain localization in shear bands may increase or decrease the permeability depending on the state of compaction and on the level of grains breakage inside the band. To investigate these various mechanisms, an experimental study has been performed to explore the effect of different factors such as grain size and grain shape, confining pressure, level of shear, stress path, and formation of one or several shear bands on the permeability of dense sands under triaxial loading. The experimental results show a reduction of permeability during the consolidation phase and during the volumetric contraction phase of shear loading, which can be related to the decrease of porosity. The experimental results also show that, depending on the confining pressure, the permeability remains stable or decreases during the volumetric dilation phase despite the increase of total porosity. This permeability reduction is attributed to the presence of fine particles, which result from grains attrition during pre-localization and grains breakage inside the shear band during the post-localization phase.

Appendices

Appendix 1: Correction of the measured permeability taking into account the deformed specimen shape

In the performed constant head permeability tests, the hydraulic conductivity of the specimen is evaluated using Darcy’s law for a one-dimensional flow, k = QL/SΔH, where Q is the water discharge, S is the section of the specimen, ΔH is the hydraulic load, and L is the length of the specimen. During shearing phase, due to deformation and barreling of the specimen, the flow lines are modified and it is necessary to correct the evaluated permeability. This is done by introducing a correction factor obtained from a numerical modeling of the fluid flow in the deformed specimen. Figure 23 shows the geometry of the finite element axisymmetric model of the specimen with length L and a barrel shape defined by the radius R + e of the middle cross section (Fig. 23). The upper and lower sections of the specimen are assumed to keep the initial radius R. The material is assumed to be homogeneous and isotropic, i.e., k _x  = k _y  = k, k _xy  = 0.

Fig. 23

Geometry, finite element mesh, and flow lines in the deformed specimen

Several constant head permeability experiments have been simulated for different values of e, and the permeability k′ is calculated and compared with the real material permeability k. Figure 24 shows that the ratio k′/k can be fitted with a linear trend:

Fig. 24

Variation of the ratio of the measured permeability k′ on the actual permeability (corrected) k with e/R

$$ \frac{{k^{\prime } }}{k} = 1 + 1.25\frac{e}{R} $$

(2)

The above correction factor is applied to the measured permeabilities during the triaxial tests. From the measurement of the volume V of the deformed specimen given by the volumeter, the barreling parameter e is calculated from the following relation:

$$ V = \pi R^{2} L + \uppi{e}\left( {\frac{{e^{2} }}{3} + \frac{{L^{2} }}{4}} \right) $$

(3)

The correction of the measured permeability is of the order of 5 % with a maximum of 10 % at large strains.

Appendix 2: Strain–stress curves of the triaxial tests under constant confining pressure

Figure 25 presents the strain–stress curves of the triaxial tests under constant confining pressure.

Fig. 25

Mechanical response for all specimens subjected to a classical triaxial path with constant confining pressure. a Deviatoric stress–axial strain curves. b Volumetric strain–axial strain