Poroelastic measurements resulting in complete data sets for granular and other anisotropic porous media

Deducing anisotropic drained constants from undrained: Heterogeneous grains and pores

One difficulty for heterogeneous grains comes from the additional constant $K_R^\phi$ that I do not know how to determine independently from the other poroelastic measurements. But this fundamental problem is actually no different for the anisotropic case than it was for the isotropic one, and the solution is also the same. In both cases, I need more information, and in both cases the necessary information will most likely come from our knowledge of the Skempton (1954) coefficient $B$. If I assume that $B$ can be directly measured (which is plausible, since $B = p_f/p_c$ in the undrained case when a uniform confining pressure is applied to the system), then the problem is completely solved, because $B$ is the key to solving for the coefficients $\beta_i$ in (48). The only new difficulty is that the terms of the form $1/3K_R^g$ must also be replaced by the partial grain compliance sums $\frac{1}{3\overline{K}_i^g}$, as shown in (30). So I now have

$$\beta_i = s_{i1}^d + s_{i2}^d + s_{i3}^d - \frac{1}{3\overline{K}_i^g} = s_{i1}^u + s_{i2}^u + s_{i3}^u - \frac{1}{3\overline{K}_i^g} + B\beta_i.$$ (49)

Rearranging, I find that, for heterogeneous grains, the result is:

$$\beta_i (1-B) = s_{i1}^u + s_{i2}^u + s_{i3}^u - \frac{1}{3\overline{K}_i^g}.$$ (50)

So, I am almost done now, but I still need either to determine the values of the anisotropic grain correction terms $\frac{1}{3\overline{K}_i^g}$, or to find some way of avoiding the necessity of doing so.

In principle, this can be done experimentally by actually performing a test on the porous sample that applies the same pressure inside and outside. Then, measurements of the change in strain in the three orthogonal directions $i = 1,2,3$ would provide direct measures of the quantities $\overline{K}_i^g$ needed. So this approach is one that is experimentally feasible.

An alternative that I have not considered so far would be to perform shear tests by applying nonzero deviatoric stress changes (Lockner and Stanchits, 2002; Skempton, 1954). The undrained fluid pressure is given by $p_f = Bp_c = B(-\sigma_m)$, where the mean stress is $\sigma_m = (\sigma_{11} + \sigma_{22} + \sigma_{33})/3$. But, if the $\sigma_{ii}$'s are not uniform, then there are also deviatoric stresses present, due to the nonuniformity of the principal stresses.

Poroelastic measurements resulting in complete data sets for granular and other anisotropic porous media