The concept of porothermoelasticity has been developed to investigate the thermal and mechanical behavior of elastic materials with porosity. This approach combines the theory of heat conduction with poroelastic constitutive equations and by incorporating the coupling of temperature field with the stresses and pore pressure. The mathematical modeling of the porothermoelastic material to various practical problems has attracted researchers in recent years due to its wide applications to geomechanics, where the coupled thermal and poro-mechanical processes play an essential role. The porothermoelasticity theory with relaxation parameter and predicting the finite speed for the isotropic medium has been established by Youssef (Int J Rock Mech Min 44(2):222–227, 2007) and by Sherief and Hussein (Transp Porous Med 91(1):199–223, 2012). However, the governing equations of the porothermoelasticity theory including the effects of temperature as well as temperature-rate terms for an anisotropic medium are yet to be derived. Hence, in view of the useful applications of the subject, the present work is motivated to derive the set of governing equations for the theory of temperature-rate-dependent fluid-saturated anisotropic poroelastic medium from the fundamental laws of thermodynamics. Further, we establish a uniqueness theorem for the general porothermoelastic problem of an anisotropic medium based on the present theory. Lastly, we solve a half-space problem of porothermoelasticity for isotropic medium to show the implementation of the present theory and investigate the effects of the relaxation times and porosity parameter over the distributions of various field variables by considering kerosene-saturated sandstone medium.

已经开发了多孔热弹性的概念来研究具有多孔性的弹性材料的热和机械行为。这种方法将热传导理论与多孔弹性本构方程相结合，并结合了温度场与应力和孔隙压力的耦合。由于多孔热弹性材料在地质力学中的广泛应用，多孔热弹性材料对各种实际问题的数学建模近年来吸引了研究人员，其中耦合热和多孔机械过程起着至关重要的作用。Youssef (Int J Rock Mech Min 44(2):222–227, 2007) 和 Sherief 和 Hussein (Transp Porous Med 91(1) 建立了具有松弛参数并预测各向同性介质的有限速度的多孔热弹性理论:199–223, 2012)。然而，多孔热弹性理论的控制方程包括温度的影响以及各向异性介质的温度-速率项还有待推导出。因此，鉴于该主题的有用应用，本工作旨在从热力学基本定律推导出温度速率相关的流体饱和各向异性多孔弹性介质理论的控制方程组。此外，我们基于现有理论建立了各向异性介质的一般多孔热弹性问题的唯一性定理。最后，