Isogeometric analysis through Bézier extraction for thermo-hydro-mechanical modeling of saturated porous media

Abstract We present a modeling framework developed based upon Isogeometric analysis (IGA) for fully coupled numerical simulation of thermo-hydro-mechanical (THM) problems in saturated porous media. The framework employs Bezier extraction to connect IGA with the conventional finite element method and to take advantage of the features offered by both methods. The mathematical model of non-isothermal multiphase geomaterials is based on the hybrid mixture theory. Using the standard Galerkin method, the weak formulations of linear momentum, mass, and energy balance equations of the overall continuum are developed. The Bezier extraction operator is used to derive Non-Uniform Rational B-Splines (NURBS) basis functions to discretize the governing equations in space. The generalized backward Euler scheme is implemented for time discretization. The final nonlinear system of equations is linearized using the Newton-Raphson scheme with a monolithic approach. The results from the proposed method are verified against an analytical solution. Several important considerations in modeling coupled THM processes in saturated porous media are presented and discussed. The application of the method is illustrated for two example problems. The results show that the proposed method offers a robust alternative for modeling THM problems especially where cubic approximation functions are used.

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