Effect of Spatial Variability in the Geometry of Fractures on Granite Slope Stability

A DFN-DEC (discrete fracture network-distinct element code) method based on the MATLAB platform is developed to generate heterogeneous DFN. Subsequently, the effects of the spatial variability (the mean $ \mu $ and the standard deviation $ \sigma $) of the geometric properties (i.e., the fracture dip D, the trace length T and the spacing S) of both the gently-dipping (denoted with 1) and the steeply-dipping (denoted with 2) fractures on the stability of granite slope are investigated. Results indicate that the proposed DFN-DEC method is robust, generating fracture networks that resemble reality. In addition, the spatial variability of fracture geometry, influencing the structure of granite slope, plays a significant role in slope stability. The mean stability of the slope decreases with the increase of $ {\mu }_{{\mathrm{D}}_{1}} $ (the mean of gently-dipping fracture dip), $ {\sigma }_{{\mathrm{D}}_{2}} $ (the mean of steeply-dipping fracture dip), $ {\mu }_{{\mathrm{T}}_{1}} $ (the mean of gently-dipping fracture trace length), $ {\mu }_{{\mathrm{T}}_{2}} $ (the mean of steeply-dipping fracture trace length), $ {\sigma }_{{\mathrm{T}}_{1}} $ (the standard deviation of gently-dipping fracture trace length), $ {\sigma }_{{\mathrm{T}}_{2}} $ (the standard deviation of steeply-dipping fracture trace length), and the decrease of $ {\sigma }_{{\mathrm{D}}_{1}} $ (the standard deviation of gently-dipping fracture dip), $ {\mu }_{{\mathrm{D}}_{2}} $ (the standard deviation of steeply-dipping fracture dip), $ {\mu }_{{\mathrm{S}}_{1}} $ (the mean of gently-dipping fracture spacing) and $ {\mu }_{{\mathrm{S}}_{2}} $ (the mean of steeply-dipping fracture spacing). Among them, $ {\mu }_{{\mathrm{T}}_{1}} $, $ {\mu }_{{\mathrm{D}}_{1}} $ and $ {\mu }_{{\mathrm{S}}_{1}} $ have the major impact. When the fracture spacing is large, the variability in the fracture geometry becomes less relevant to slope stability. When within some ranges of the fracture spacing, the spatial varying of dips can increase the slope stability by forming an interlaced structure. The results also show that the effects of the variability of trace length on slope stability depend on the variability of dip. These findings highlight the importance of spatial variability in the geometry of fractures to rock slope stability analysis.