Mechanics of stratified anisotropic poroelastic media

Coefficient $\gamma$

The relationship of coefficient $\gamma$ to the other coefficients is easily established because I have already discussed the main issue, which involves determining the role of the various other constants contained in Skempton's second coefficient $B$ (Skempton, 1954). This result is

$$B = \left(\frac{1}{K_R^d} - \frac{1}{K_R^g}\right)\left[\left(\fr... ...{K_R^g}\right) + \phi \left(\frac{1}{K_f}-\frac{1}{K_R^\phi}\right)\right]^{-1}$$ (19)

From (1), I find that

$$-\zeta = 0 = -\left(\beta_1 + \beta_2 + \beta_3\right)\sigma_c -\gamma p_f,$$ (20)

for undrained boundary conditions. Thus, I find again that

$$\frac{p_f}{p_c} \equiv B = \frac{\beta_1+\beta_2+\beta_3}{\gamma},$$ (21)

where $p_c = - \sigma_c$ is the confining pressure. Thus, the scalar coefficient $\gamma$ is determined immediately and given by

$$\gamma = \frac{\beta_1+\beta_2+\beta_3}{B} = \frac{\alpha_R/K_R^d}{B} = \alpha_R/K_R^d + \phi\left(\frac{1}{K_f}-\frac{1}{K_R^\phi}\right).$$ (22)

Alternatively, I could say that

$$B \equiv \frac{\alpha_R}{\gamma K_R^d}.$$ (23)

I have now determined the physical/mechanical significance of all the coefficients in the poroelastic matrix (1). These results are as general as possible without considering poroelastic symmetries that have less than orthotropic symmetry, while also taking advantage of my assumption that I do typically know the three directions of the principal axes of symmetry.

Mechanics of stratified anisotropic poroelastic media