A constitutive model based on modified mixture theory for unsaturated rocks

Non-equilibrium thermodynamics and Biot poro-elasticity have been combined to give a coupled hydro-mechanical formulation for unsaturated rock. Darcy’s law for unsaturated flow has been derived from the dissipation process by using standard arguments of non-equilibrium thermodynamics, whereas Helmholtz free energy has been used to derive the relationship between stress and pore pressure changes. The resulting general framework accommodates both large and small deformation theories. When small deformations are assumed, the formulation is comparable with coupled equations derived using an alternative approach. For illustrative purposes, the formulation has been used to analyse a seasonally affected tunnel model. Numerical results for the desaturation in winter and resaturation in summer, of the zone near the tunnel wall, have been evaluated and compared with the findings of other researchers.     

An elasto‐plastic three phase model for partially saturated soil for the finite element simulation of compressed air support in tunnelling

This paper presents a fully coupled finite element formulation for partially saturated soil as a triphasic porous material, which has been developed for the simulation of shield tunnelling with heading face support using compressed air. While for many numerical simulations in geotechnics use of a two‐phase soil model is sufficient, the simulation of compressed air support demands the use of a three‐phase model with the consideration of air as a separate phase. A multiphase model for soft soils is developed, in which the individual constituents of the soil—the soil skeleton, the fluid and the gaseous phase—and their interactions are considered. The triphasic model is formulated within the framework of the theory of porous media, based upon balance equations and constitutive relations for the soil constituents and their mixture. An elasto‐plastic, cam–clay type model is extended to partially saturated soil conditions by incorporating capillary pressure according to the Barcelona basic model. The hydraulic properties of the soil are described via DARCY 's law and the soil–water characteristic curve after VAN GENUCHTEN . Water is modelled as an incompressible and air as a compressible phase. The model is validated by means of selected benchmark problems. The applicability of the model to geotechnical problems is demonstrated by results from the simulation of a compressed air intervention in shield tunnelling. Copyright © 2009 John Wiley & Sons, Ltd.     

Reflection–transmission matrix method for the consolidation of a multilayered saturated soil

The consolidation of the layered saturated soil is an important issue in civil engineering and has been investigated extensively during the past decades. In this study, based on the Biot's theory, the reflection–transmission matrix (RTM) method for treating the layered saturated soil under axisymmetric consolidation is developed. To decouple the governing equations of the Biot's theory, the McNamee displacement functions are introduced, and the general solution for the saturated soil is obtained using the Laplace and Hankel transforms. In order to develop the RTM method for the layered saturated soil, based on the obtained general solution, the static wave vector corresponding to the state vector of the saturated soil and the transform matrix relating the aforementioned two vectors are defined. Also, the transfer matrices corresponding to the two vectors are introduced, and the representations of the RTMs for the static wave vector of the saturated soil are presented. As the state vector, static wave vector, and the transform matrix relating the two vectors are all defined in the global coordinate system, the RTMs obtained in this study thus have a reasonable physical meaning. By using the RTMs for the layered saturated soil, the solutions for the layered saturated soil subjected to external sources are derived. Comparison of results due to the proposed RTM method with some existing results and results due to the transfer matrix method validates the developed RTM method. Some numerical results are obtained based on the proposed RTM method for the layered saturated soil. Copyright © 2016 John Wiley & Sons, Ltd.     

Poroelastic model for pile–soil interaction in a half‐space porous medium due to seismic waves

In this paper, frequency domain dynamic response of a pile embedded in a half‐space porous medium and subjected to P, SV seismic waves is investigated. According to the fictitious pile methodology, the problem is decomposed into an extended poroelastic half‐space and a fictitious pile. The extended porous half‐space is described by Biot's theory, while the fictitious pile is treated as a bar and a beam and described by the conventional 1‐D structure vibration theory. Using the Hankel transformation method, the fundamental solutions for a half‐space porous medium subjected to a vertical or a horizontal circular patch load are established. Based on the obtained fundamental solutions and free wave fields, the second kind of Fredholm integral equations describing the vertical and the horizontal interaction between the pile and the poroelastic half‐space are established. Solution of the integral equations yields the dynamic response of the pile to plane P, SV waves. Numerical results show the parameters of the porous medium, the pile and incident waves have direct influences on the dynamic response of the pile–half‐space system. Significant differences between conventional single‐phase elastic model and the poroelastic model for the surrounding medium of the pile are found. Copyright © 2007 John Wiley & Sons, Ltd.     

An approach for providing quasi‐convexity to yield functions and a generalized implicit integration scheme for isotropic constitutive models based on 2 unknowns

Yield and plastic potential surfaces are often affected by problems related to convexity. One such problem is encountered when the yield surface that bounds the elastic domain is itself convex; however, convexity is lost when the surface expands to pass through stress points outside the current elastic domain. In this paper, a technique is proposed, which effectively corrects this problem by providing linear homothetic expansion with respect to the centre of the yield surface. A very compact implicit integration scheme is also presented, which is of general applicability for isotropic constitutive models, provided that their yield and plastic potential functions are based on a separate mathematical definition of the meridional and deviatoric sections and that stress invariants are adopted as mechanical quantities. The elastic predictor‐plastic corrector algorithm is based on the solution of a system of 2 equations in 2 unknowns only. This further reduces to a single equation and unknown in the case of yield and plastic potential surfaces with a linear meridional section. The effectiveness of the proposed convexification technique and the efficiency and stability of the integration scheme are investigated by running numerical analyses of a notoriously demanding boundary value problem.