Extension fracture formation in mechanical layers :

Analytical calculation by assuming linear-elastic media

Abstract

This paper introduces analytical solutions of stress fields in mechanical layers which consist of stiff and soft layers. The paper examines possible geological conditions of mode I (extension) fracture development with various Young's modulus, Poisson's ratio, layer thickness, external stress fields and pore-fluid pressure. Linear elastic model with two different mechanical layers is assumed for the calculations. Layer-parallel stresses caused by the given external stresses and pore-fluid pressure are mathematically calculated in both stiff and soft layers. Relative Young's modulus and relative thickness between the two types of layers are applied to simplify the associated equations. Poisson's ratio ν is assumed to be same between the two. This is because the possible range of Poisson's ratio between rocks is much smaller than that of Young's modulus. The calculated ratio of minimum to maximum principal stresses within each layer is used to estimate fracture type which can develop under the geological conditions. The results indicate extension fracture preferably develop in stiff layers in mechanical layers when vertical compression stress increases (during basin burial). The ratio of minimum to maximum principal stresses is primarily controlled by relationship among external horizontal stress σ_XX, vertical stress σ_ZZ and pore-fluid pressure P_f : no tensile fracture forms when σ_XX>P_f+ν(σ_ZZ-P_f)/(1-ν); tensile fractures can form only in stiff layers in soft-layer-dominant formation when P_f+ν(σ_ZZ-P_f)/(1-ν)>σ_XX>P_f ; tensile fractures form in stiff layers in both stiff-layer-dominant and soft-layer-dominant formations when P_f>σ_XX>4P_f/3-σ_ZZ/3 ; tensile fracture can form in both stiff and soft layers in soft-layer-dominant formation with small relative Young's modulus when 4P_f/3-σ_ZZ/3>σ_XX. Only shear fractures can form in soft layers, except the rare geological condition of 4P_f/3-σ_ZZ/3>σ_XX with very small relative Young's modulus. The results provide potential criterion to estimate when and where layer-scale extension fracture network develops in relation with geological history. An implication of the results is that extension fracture formation is not necessarily related with regional horizontal tensile stress field but ratio among horizontal stress, vertical stress and pore-fluid pressure. This implies that extension fracture network can form in mechanical layers not only during crustal uplift/exhumation but also during basin-burial in which horizontal stresses, vertical stress and pore-fluid pressure are increasing.