Closed-form expressions for poroelastic coefficients are derived for anisotropic materials exhibiting single and double porosity. A novel feature of the formulation is the use of the principle of superposition to derive the governing mass conservation equations from which analytical expressions for the Biot tensor and Biot moduli, among others, are derived. For single-porosity media, the mass conservation equation derived from the principle of superposition is shown to be identical to the one derived from continuum principle of thermodynamics, thus confirming the veracity of both formulations and suggesting that this conservation equation can be derived in more than one way. To provide further insight into the theory, numerical values of the poroelastic coefficients are calculated for granite and sandstone that are consistent with the material parameters reported by prominent authors. In this way, modelers are guided on how to determine these coefficients in the event that they use the theory for full-scale modeling and simulations.

对于具有单孔和双孔孔隙率的各向异性材料，可以推导出孔隙弹性系数的封闭形式。该制剂的一个新颖特征是利用叠加原理来推导主要的质量守恒方程，由此推导了Biot张量和Biot模量等的解析表达式。对于单孔介质，从叠加原理推导的质量守恒方程与从热力学连续原理推导的质量守恒方程相同，从而证实了这两种公式的准确性，并表明该守恒方程可以用以下公式推导。单程。为了进一步了解该理论，计算出花岗岩和砂岩孔隙弹性系数的数值，这些数值与著名作者报道的材料参数一致。这样，在建模人员使用理论进行全面建模和仿真时，将指导他们如何确定这些系数。