This paper presents a multiscale analysis of the classical borehole instability problem in high-porosity sandstones using a hierarchical multiscale approach. A rigorous, two-way message-passing coupling of finite element method and discrete element method is employed, where the finite element method is employed to solve a boundary value problem and the constitutive material responses required at each of its integration points are derived by the discrete element method solution to an embedded representative volume element instead of by using an assumed phenomenological model. We employ this multiscale approach to examine the successive failure of a borehole subjected to gradually decreased support stresses at the inner borehole wall or increased far-field stresses. To reproduce the material behavior of high-porosity sandstone, representative volume elements with a high-porosity structure and interparticle bonds are generated. It is found that stress concentration triggers the initial failure at the borehole wall, and the subsequent failure in form of deformation bands is driven by further stress concentration ahead of the band tips. The failure pattern around the borehole varies with initial stress state and global loading path. The comparison of the local stress paths of the initial failure points in various cases reveals that the change of failure pattern from shear failure to mixed-mode failure and to compaction failure is dominated by the increased mean stress. Cross-scale parametric studies show that the failure mode changes from clear compaction bands to multiple arrays of shear bands by changing the high-porosity specimen to a low-porosity one. The increase in cohesion strength expands the yield locus and enlarges the critical mean stress between different failure patterns. Hence, the failure mode may change from compaction failure to mixed-mode failure or from mixed-mode failure to shear failure due purely to the increased cohesion strength. The qualitative comparisons indicate greater length, larger area, and more severe damage of the diametrically opposite failure with the increase in minor principal stress σ0 and principal stress ratio. The diametrically opposite failure mode is found a good indicator for σ0 direction, but it may also occur under hydrostatic far-field stress due to material anisotropy.

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Journal of Geophysical Research: Solid Earth
Department of Civil and Environmental Engineering

Wu, H. (Huanran), Zhao, J. (Jidong), & Guo, N. (2018). Multiscale Insights Into Borehole Instabilities in High-Porosity Sandstones. Journal of Geophysical Research: Solid Earth, 123(5), 3450–3473. doi:10.1029/2017JB015366