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On the effective viscoelastic properties of a fractured rock mass

Authors: 

Tuan Nguyen-Sy*, Minh-Ngoc Vu, Quy-Dong To, Minh-Quan Thai, Trung Nguyen-Thoi

Source title: 
Journal of Applied Geophysics, 169: 125-133, 2019 (ISI)
Academic year of acceptance: 
2019-2020
Abstract: 

The effective viscoelastic properties of a rock mass embedding many sets of planar fractures are estimated. The rock matrix is modeled by a standard Zener rheological model, while the linear elastic or a linear non ageing viscoelastic laws is considered to relate the opening displacement of a fracture and the stresses acting on its surfaces. The correspondence principle is considered to transform the problem in hand to an equivalent elastic problem in Laplace-Carson (LC) space. Then, closed form solutions to the creep parameters in time space are derived. For the case of elastic fractures, we show that the presence of the fractures modifies the instantaneous and long term compliances of viscoelastic fractured rocks by the same way as it does for the case of elastic fractured rocks. However, they do not affect the variations versus time of the creep parameters. Unlike the case of elastic fractures, viscoelastic fractures modify the variations versus time of the creep parameters. However for all the situations, we observe that the effective creep properties of a fractured medium made of a Zener solid matrix and Zener fractures can be explicitly expressed by an effective Generalized Maxwell rheology of which the rheological parameters are functions of the viscoelastic parameters of the matrix and the fractures.