This work reviews the transient two-phase flow in porous media with engineering applications in Geotechnics. It initially overviews constitutive relationships, conventional theories, and experiments. Then, corresponding limitations are discussed according to conflicting observations and multiphase interfacial dynamics. Based on those findings, the dynamic nonequilibrium effects were so defined, which could also be abbreviated as dynamic/transient effects. Four advanced theories have already been developed to resolve these effects. This review collects them and discusses their pros and cons. In addition, this work further reviews the state-of-art in terms of experimental methods, influential factors in dynamic/transient effects, and modelling performance, as well as micromodel and numerical methods at pore-scale. Last, the corresponding geotechnical applications are reviewed, discussing their applicability in effective stress, shear strength, and deformation. Finally, the entire review is briefed to identify research gaps in Geotechnics.

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SUMMARYIn this paper, a radial basis collocation method (RBCM) based on the global space-time multiquadric (MQ) is proposed to solve the inverse heat conduction problem (IHCP). The global MQ is simply constructed by incorporating time dimension into the MQ function as a new variable in radial coordinate. The method approximates the IHCP as an over-determined linear system with the use of two sets of collocation points: one is satisfied with the governing equation and another is for the given conditions. The least-square technique is introduced to find the solution of the over-determined linear system. The present work investigates two types of the ill-posed heat conduction problems: the IHCP to recover the surface temperature and heat flux history on a source point from the measurement data at interior locations, and the backward heat conduction problem (BHCP) to retrieve the initial temperature distribution from the known temperature distribution at a given time. Numerical results of four benchmark examples show that the proposed method can provide accurate and stable numerical solutions for one-dimensional and two-dimensional IHCP problems. The sensitivity of the method with respect to the measured data, location of measurement, time step, shape parameter and scaling factor is also investigated.