A semi-analytical solution for the transient response of one-dimensional unsaturated single-layer poroviscoelastic media
A semi-analytical solution for the transient response of one-dimensional unsaturated single-layer poroviscoelastic media
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DOI：
10.1016/j.compgeo.2016.01.005
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发表时间：
2016-06
影响因子：
5.3
通讯作者：
Zhendong Shan;D. Ling;H. Ding;Yungang Wang
中科院分区：
文献类型：
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作者：
Zhendong Shan;D. Ling;H. Ding;Yungang Wang
本文利用拉普拉斯变换和状态空间法，给出了含两种不混溶流体的非饱和单层多孔粘弹性介质瞬态响应的半解析解。利用弹性-粘弹性对应原理，将Kelvin-Voigt模型引入Zienkiewicz的非饱和多孔弹性模型。将这两种模型结合起来，假设润湿和非润湿流体是可压缩的，固体骨架和固体颗粒是粘弹性的，并考虑了惯性和机械耦合，得到了非饱和多孔材料的振动响应。采用拉普拉斯变换和状态空间法求解基本方程组及相应的初边值条件，得到了在拉普拉斯域内的解析解。为了计算时域响应，采用Durbin的数值逆拉普拉斯变换方法得到半解析解。在含有两种不混溶流体的多孔介质中，存在三种纵波。此外，为了清楚地观察三个压缩波，我们假设两种不混溶流体是水和油。最后，通过算例验证了半解析解的有效性，并分析了粘性系数和动渗透系数对三种纵波的影响。
This paper develops a semi-analytical solution for the transient response of an unsaturated single-layer poroviscoelastic medium with two immiscible fluids by using the Laplace transformation and the state-space method. Using the elastic–viscoelastic correspondence principle, we first introduce the Kelvin–Voigt model into Zienkiewicz’s unsaturated poroelastic model. The vibrational response for unsaturated porous material can be obtained by combining these two models and assuming that the wetting and non-wetting fluids are compressible, the solid skeleton and solid particles are viscoelastic, and the inertial and mechanical couplings are taken into account. The Laplace transformation and state-space method are used to solve the basic equations with the associated initial and boundary conditions, and the analytical solution in the Laplace domain is developed. To evaluate the responses in the time domain, Durbin’s numerical inverse Laplace transform method is used to obtain the semi-analytical solution. There are three compressional waves in porous media with two immiscible fluids. Moreover, to observe the three compressional waves clearly, we assume the two immiscible fluids are water and oil. Finally, several examples are provided to show the validity of the semi-analytical solution and to assess the influences of the viscosity coefficients and dynamic permeability coefficients on the behavior of the three compressional waves.