Origin of Regular Networks of Joints: Experimental Constraints, Theoretical Background, and Numerical Modeling

Abstract

Experimental data show that inelastic straining occurs even at very low pressure before and during brittle fracturing. This process is therefore investigated within the framework of elastoplasticity using 2‐D, three‐layer finite difference modeling. The constitutive model includes both tensile and shear failure mechanisms coupled at the level of the strain softening law. The modeling results show that sets of parallel joints initiate as pure dilation bands, the narrow σ3‐normal bands of localized dilatant damage (inelastic deformation). The band thickness, length, and the initial strain softening degree within it are proportional to the ductility of the material, which increases with the effective stress level (σ1) or pressure. The strength reduction within the bands is accelerated at a certain stage, and the strength locally reaches zero resulting in fracture initiation. The initial fracture then propagates in Mode I following the propagating band. The fracture (joint) appears thus as a band of damaged material with the increased porosity, which is maximum along the axial zone of the band where the material is completely broken. The damage is due to both tensile and shear mechanisms. The role of shear failure increases with the ductility (pressure) increase, which also leads to the band thickness increase. These processes can result in small (band thickness)‐scale oblique shear fractures within the band, causing the increase in the roughness of fracture walls organized in plumose patterns typical of both natural and experimentally generated joints.

Origin of Strong Nonlinear Dependence of Fracture (Joint) Spacing on Bed Thickness in Layered Rocks: Mechanical Analysis and Modeling

“…Therefore, the conclusion is that the modeling results are not very sensitive to the model resolution (if it is not very small, smaller than the ones used in this work) or the setups in Figures 4a and 4f. Despite very different d 0 values, the average apparent fracture aperture Δl calculated as defined in (Chemenda, 2019) is close in the models in Figures 4b, 4c, and 4h with different Δz and the same fracture number: it is around 2 mm. This suggests that the mesh size has been appropriately integrated into the constitutive formulation in Equation 9.…”

“…To deal with the mesh dependence of the modeling results, the mesh (numerical zone) size Δz is included in the constitutive formulation by relating ε 0 and Δz (Chemenda, 2019)  …”

“….67 GPa, and (Chemenda, 2019). It is assumed here that the numerical resolution of small and large models in terms of geometrical sizes is the same or that T/T GR =Δz/Δz GR .…”

“…In should be noted, that what matters is not merely the C value but the value of the product  0 C , Equation 9. Therefore, one can vary  0 instead of C, which has been done in (Chemenda, 2019) where  0 was varied in wide limits, …”

“…Here we reproduce dependencies T ( S ) and D ( T ) like those in Figures 1d and 1e in three‐layer numerical models and show that they are entirely (or at least mostly) due to the mechanical interaction between the layers. This study is based on theoretical and numerical models developed by Chemenda (2019). They are summarized in the next two sections where the modifications made for this study are shown.…”