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A numerical method for analyzing fault slip tendency under fluid injection with XFEM

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Abstract

We propose a numerical method for analyzing fault slip tendency under fluid injection using the extended finite element method (XFEM) both for fluid flow and poroelasticity. The fault is modeled as a zero-thickness interface, and we use a reduced model for the fluid flow in the fault to account for its hydraulic behavior. We use the rate- and state-dependent friction model as the fault friction model, and Biot’s theory of poroelasticity to study the coupling between fluid flow and mechanical deformation in the surrounding porous media. Since a fully coupled method between fluid flow and poromechanics is computationally expensive, we have investigated the use of the so-called fixed-stress split in this context. In such a scheme, the fluid flow problem is solved firstly by freezing the total means stress field, and then the results are used to solve the mechanical problem. The fixed-stress split is unconditionally stable, consistent and more accurate for a given number of iterations compared with other type of splitting strategies. In order to verify our method, some test cases are presented. For the coupling between fluid flow and poromechanics, we consider the Terzaghi Problem and the Mandel Problem, comparing our results with those of previously published works. While, for the mechanic problem, we compare the results with those obtained using the software Pylith.

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Acknowledgements

LIU Daqing was supported by MOX in the Department of Mathematics of Politecnico di Milano and also supported by the China Scholarship Council (CSC) with a scholarship. This work was done mainly under Professor Luca Formaggia and Associate Professor Anna Scotti’s guidance and their help. Luigi Vadacca also plays an important role in supporting this work. This work was implemented on the basis of the Getfem++ library, http://download.gna.org/getfem/html/homepage/. Besides, thanks Franco Dassi, Bianca Giovanardi, Alessio Fumagalli, Davide Baroli, Alberto Ferroni, Abramo Agosti, Stefano Zonca, Claudia Colciago, Mattia Penati, Francesca Mesolella, Marianna Signorini, and Daniele Rossi’s help in the process of research.

Funding

LIU Daqing has received funding by the China Scholarship Council (CSC) through a scholarship.

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  1. Institute of Mechanics, Chinese Academy of Sciences, Beijing, China

    Daqing Liu

  2. Modelling and Scientific Computing Lab (MOX), Department of Mathematics, Politecnico di Milano, Milan, Italy

    Daqing Liu

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Liu, D. A numerical method for analyzing fault slip tendency under fluid injection with XFEM. Acta Geotech. 15, 325–345 (2020). https://doi.org/10.1007/s11440-019-00814-w

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