Abstract
A numerical finite element (FE) analysis technology is presented for efficient and reliable solutions of rock with hydraulic-mechanical (HM) coupling, researching the seepage characteristics and simulating the damage evolution of rock. To be in accord with the actual situation, the rock is naturally viewed as heterogeneous material, in which Young’s modulus, permeability, and strength property obey the typical Weibull distribution function. The classic Biot constitutive relation for rock as porous medium is introduced to establish a set of equations coupling with elastic solid deformation and seepage flow. The rock is subsequently developed into a novel conceptual and practical model considering the damage evolution of Young’s modulus and permeability, in which comprehensive utilization of several other auxiliary technologies, for example, the Drucker-Prager strength criterion, the statistical strength theory, and the continuum damage evolution, yields the damage variable calculating technology. To this end, an effective and reliable numerical FE analysis strategy is established. Numerical examples are given to show that the proposed method can establish heterogeneous rock model and be suitable for different load conditions and furthermore to demonstrate the effectiveness and reliability in the seepage and damage characteristics analysis for rock.
Highlights
The finite element (FE) analysis technology presented in this paper takes rock as the research object, a typical porous medium with heterogeneous material property, dispersedly distributed damage region under applied load and in situ stress, and inorganic and organic pores to form the complex structure [1]
The effective stress of porous medium will change with the fluid flow, pressure diffusion in pores, and solid deformation correspondingly; in other words, hydraulic-mechanical (HM) coupling makes the response of the rock reflect complex timedependent effect obviously
The numerical examples presented later have shown that utilizing petrophysical heterogeneity simulation is well effective and feasible; in addition to the reliability, the results show that the method is almost consistent with damage evolution under different load conditions, considering HM coupling is necessary for effective stress analysis
Summary
The finite element (FE) analysis technology presented in this paper takes rock as the research object, a typical porous medium with heterogeneous material property, dispersedly distributed damage region under applied load and in situ stress, and inorganic and organic pores to form the complex structure [1]. Heterogeneous distribution and degeneration of material property (i.e., Young’s modulus and permeability) or strength property (i.e., compressive and tensile strength) make the assumption of homogeneousness and continuity is not consistent with the actual situation; for some extreme cases, the state-of-the-art strength theory of rock based on continuum mechanics confronts severe problems challenging the researchers’ best knowledge [2] Some technology, such as heterogeneous Young’s modulus simulation to describe the heterogeneity of rock, is developed [3], and the authors of this paper have adopted this technology to form the heterogeneous rock with heterogeneous Young’s modulus and strength [4]. Young’s modulus and permeability with damage under the current load would be used to form a new heterogeneous physical model; the procedure returns to the second step until the load steps are progressively completed This yields a simple, efficient, reliable, and practical FE analysis technology that is able to make rock modeling and damage analysis in mining and petroleum engineering applications. The numerical examples presented later have shown that utilizing petrophysical heterogeneity simulation is well effective and feasible; in addition to the reliability, the results show that the method is almost consistent with damage evolution under different load conditions, considering HM coupling is necessary for effective stress analysis
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