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

Abstract

Fractures are ubiquitous in the Earth's crust. They strongly impact the mechanical stability, strength, and permeability of geological structures or rock masses and thereby play an essential role in many societally important processes in the upper crust as well as in the management of subsurface engineering operations. The most common are the so-called opening mode (extension or tensile/tension) fractures or joints. They often form regular sets of parallel, orthogonal, or more complex fracture networks. Because of their practical importance, notably for the oil and gas industry, joints have been extensively studied for more than a century (e.g., Pollard & Aydin, 1988), mostly in sedimentary basins composed of alternating layers with contrasted lithology (Figures 1a-1c) and hence mechanical properties. Particular attention has been paid to the joint spacing S or the ratio D of the fractured layer thickness T to S (D=T/S). The main practical aim has been to predict the fracture spacing at depth from bed thickness. The spacing of natural fractures cannot be observed directly in the subsurface, whereas the bed thickness can be defined from petrophysical well data or core analysis. These works stimulated research in rock/fracture mechanics and modeling

Gravity‐Driven Jointing in Layered Rocks: Mechanical Analysis and Numerical Modeling

“…However, it is important to note that for the old setup, the modeling results are largely insensitive to ν (1) and E (1) (Chemenda et al., 2021), whereas in the new setup, these parameters directly define the maximum achievable extension strain $${\varepsilon }_{xx}^{\mathit{max}}$$ and, consequently, the fracture density. For instance, with the new setup and reference parameters including ν (1) = 0.4 and $${\varepsilon }_{xx}^{\mathit{max}}=-2\times {10}^{-3}$$, 7 fractures were formed (Figure 7 stage 8).…”

“…A theoretical analysis of strain localization at the origin of fracturing has resulted in the following condition (Chemenda et al, 2021)…”

“…A theoretical analysis of strain localization at the origin of fracturing has resulted in the following condition (Chemenda et al., 2021) $$$\frac{{\eta }_{s}{\eta }_{{\sigma }_{t}}}{{\eta }_{G}{\eta }_{\varepsilon }{\eta }_{C}}=1$$$ where η S = T / T ′, $${\eta }_{G}={G}^{(2)}/{{G}^{(2)}}^{\prime }$$, η C = C / C ′, $${\eta }_{\varepsilon }={\widetilde{\varepsilon }}^{0}/{{\widetilde{\varepsilon }}^{0\prime}}$$, with T representing the model size, and G (2) being the shear modulus of the competent layer. Since $${\nu }^{(2)}={{\nu }^{(2)}}^{\prime }$$, $${\eta }_{{G}^{(2)}}={\eta }_{{E}^{(2)}}$$.…”

Episodic Reactivation of Carbonate Fault Zones with Implications for Permeability – an Example from Provence, Southeast France

“…6d) was likely controlled by bed interfaces (e.g. Rives et al, 1992;Bao et al, 2019;Chemenda et al, 2021), further indicating that this is a pre-Castellas fault, regional fracture set. By contrast, Set 2 calcite-filled opening-mode fractures follow the same orientation as the main fault, have larger kinematic apertures (Fig.…”

Constitutive Model of Rock, Nonlinearity and Localization

“…At high confining pressure, the orientation of the compaction bands is close to orthogonal with respect to the axis of greatest compression. Analysis of postcritical deformation at the softening stage and numerical modeling of the unstable process involve significant difficulties [1][2][3][4][37][38][39][40][41][42][43][44]. The stress drop rate is determined by the rock properties and the width of localization bands, which in turn depends on the loading conditions and confining pressure.…”