A semi-analytical solution for the transient response of one-dimensional unsaturated single-layer poroviscoelastic media. (June 2016)

• Record Type: Journal Article
• Authors: Shan, Zhendong; Ling, Daosheng; Ding, Haojiang; Wang, Yungang
• Is Part Of: Computers and geotechnics. Volume 76(2016)
• Page Start: 75
• Page End: 82
• Publication Date: 2016-06
• Subjects: Semi-analytical solution -- Unsaturated porous media -- Poroviscoelastic -- Transient response -- Compressional wave -- Laplace transform; Engineering geology -- Data processing -- Periodicals; Soil mechanics -- Data processing -- Periodicals; Rock mechanics -- Data processing -- Periodicals; 624.1510285
• DOI: 10.1016/j.compgeo.2016.01.005
• Languages: English
• ISSNs: 0266-352X

Abstract

Abstract: 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.