An effective stress law is derived analytically to describe the effect of pore (fracture pore and matrix-block pore) fluid pressure on the linearly elastic response of ani- sotropic saturated dual-porous rocks, which exhibit anisot- ropy. For general anisotropy the difference between the ef- fective stress and the applied stress is not hydrostatic simply multiplied by Biot coefficient. The effective stress law in- volves four constants for transversely isotropic response; these constants can be expressed in terms of the moduli of the single porous material, double porous material and of the solid material. These expressions are simplified considerably when the anisotropy is structural rather than intrinsic, i.e. in the case of an isotropic solid material with an anisotropic pore structure. In this case the effective stress law involves grain bulk modulus, four moduli and two compliances of the porous material for transverse isotropy. The law reduces, in the case of isotropic response, to that suggested by Li Shuiquan (2001). And reduction to the single-porosity (de- rived analytically by Carroll (1979)) is presented to demon- strate the conceptual consistency of the proposed law.
