SUMMARY AND CONCLUSIONS

The preceding discussion shows how overall shear modulus dependence on pore-fluid mechanics arises in simple anisotropic (the specific example used was transversely isotropic) media. The results demonstrate in an entirely elementary fashion how compression-to-shear coupling enters the analysis for anisotropic materials, and furthermore how this coupling leads to overall shear dependence on mechanics of fluids in the pore system.

These effects need not always be large. However, the effect can be very substantial (on the order of a 10% to 20% increase in the overall shear modulus) in cracked or fractured materials, when these pores are liquid-filled. The anisotropy and liquid stiffening effects then both come strongly into play in the results we see, such as those illustrated in Figures 1-8. In particular, if $\beta_1 \simeq \beta_3$, then soft anisotropy does not make a significant contribution. But, if either $\beta_1 << \beta_3$ or $\beta_1 \gt\gt \beta_3$, then the contribution can be significant. For example, we might expect these cases to be relevant for systems with either vertical or horizontal fractures.