To fill the above research gaps, this thesis develops a suite of phase-field approaches to enable more reliable and systematic modeling of discontinuities and fractures in geologic materials. More importantly, all existing phase-field approaches dismissed the frictional contact, let alone the roughness effects. However, few phase-field studies considered the quasi-brittleness of geologic materials. To model the discontinuities and fracturing processes in geologic materials, the phase-field method has been increasingly applied, as it has an outstanding ability to handle complex crack geometries without using tracking algorithms. Also, the fractured surfaces exhibit a number of features including frictional contact and roughness effects. The fracturing process of geologic materials is characterized by its progressive softening, termed quasi-brittleness. Geologic materials contain a wide range of discontinuities and fractures, which are central to many engineering applications and geologic hazards.
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