Asymmetric friction refers to different friction forces that resist sliding in opposing directions. Asymmetric friction can for instance be induced by an anisotropic block with an anisotropy axis inclined to the direction of sliding progressing in a constraint environment, (Bafekrpour et al., 2015). This study examines a Burridge-Knopoff-type model of multiple blocks connected through springs. Each block is connected to an external oscillating surface through a leaf spring; some blocks slide with asymmetric friction, while others experience conventional symmetric friction. Asymmetric friction favours slip in the direction of low friction. This increases spring forces to counteract the slip within the assembly, creating regions of tension and compression. When this model represents geological faults, regions of tension and compression can produce fractures oriented normal (in the tensile phase) or parallel (in the compressive phase) to the sliding surface.
Velocity spectra produced by the model excited by an external oscillating surface reveal that the presence of asymmetric friction creates spectra with a frequency falloff of 1/f2, where f is the frequency. This is in contrast with the case of only symmetric friction blocks where oscillations result in velocity spectra with a frequency falloff of 1/f.
Recent triaxial compression of rock samples have shown slip events over shear fracture produce velocity spectra with frequency falloff that approximates 1/f2(Beeler et al., 2020). Using the results found from the model, a hypothesis on the mechanism that produces the 1/f2falloff is proposed: the shear fracture in the compression test is produced by formation of vertical micro-cracks within the rock samples. This effectively creates an anisotropic material with axes of symmetry inclined to the shear fracture, which explains the 1/f2spectra.
Acknowledgement. EP and AVD acknowledge support from the Australian Research Council through project DP210102224.
BAFEKRPOUR, E., DYSKIN, A., PASTERNAK, E., MOLOTNIKOV, A. & ESTRIN, Y. 2015. Internally architectured materials with directionally asymmetric friction. Scientific reports, 5, 10732-10732.
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