INTEGRAL SOLUTIONS FOR THE ONE-DIMENSIONAL TRANSIENT RESPONSE OF UNSATURATED SEMI-INFINITE POROUS MEDIA
SHAN Zhendong1，LING Daosheng2，3，DING Haojiang2，3
(1. Key Laboratory of Earthquake Engineering and Engineering Vibration，Institute of Engineering Mechanics，China Earthquake Administration，Harbin，Heilongjiang 150080，China；2. MOE Key Laboratory of Soft Soils and Geoenvironmental
Engineering，Zhejiang University，Hangzhou，Zhejiang 310058，China；3. Institute of Geotechnical Engineering，
Zhejiang University，Hangzhou，Zhejiang 310058，China)
Abstract：Based on the basic equations for unsaturated porous media，the transient response of an unsaturated semi-infinite porous medium saturated with water and oil was studied. The integral solutions for the one-dimensional transient response of an unsaturated semi-infinite porous medium with two types of nonhomogeneous boundary conditions were developed. Using the sine and cosine transforms，the basic equations were first transformed into a set of ordinary differential equations. Then，the state-space method was employed to solve these equations and the analytical solution in the transform domain was obtained. Finally，the integral solutions were obtained by using the inverse sine and cosine transforms. The integrands of the integral solutions were real functions，which had great advantages on the numerical calculations. Numerical examples were provided to verify the validity of the proposed solutions and investigated the dynamic behavior of unsaturated porous media，and it was verified that three types of compressional waves exists in unsaturated porous media that contained two immiscible fluids.