Origin Of Strong Nonlinear Dependence Of Fracture (Joint) Spacing On Bed Thickness In Layered Rocks: Mechanical Analysis And Modeling

Fracturing (jointing) affects large volumes of rocks and strongly impacts their mechanical stability and permeability. In layered sedimentary basins, the fractures typically form subparallel sets with different fracture spacing S. This parameter has been extensively studied both in the field and in mechanical models in relation to the thickness T of the fractured layers. A linear relation was suggested by most studies. A few geological investigations involving wide ranges of T values have shown that the T(S) relation is generally strongly nonlinear and that in thick beds (T >similar to 1.5 m), S practically does not depend on T. The origin of this relation remained hitherto unexplained. Here we obtained such a relation in 2-D finite-difference models of 3-layer sedimentary sequences where layers interact through the interfaces of strength R. The middle layer has elastoplastic properties with coupled tensile and shear failure mechanisms. The number of fractures forming in this layer increases under horizontal extension to a saturation value S depending on R. At T < similar to 0.5 m, the increase of S with T is near-linear. At similar to 1 m < T < 2 m, it is strongly nonlinear; and S changes little at larger T where S is more than certain value S-cr. The increase of ratio D = T/S with T is, on the contrary, close to linear. This behavior is explained by the fact that for D >similar to 2, the stress state in the upper and lower horizons of the middle layer between fractures spaced 2S(cr) apart is practically independent of T.