Model Fracture Formation in Mechanical Layers During Basin Burial Effects of Mechanical Properties Stress Fields Pore-Pressure and Layer Thickness

Abstract

Abstract The aim of this paper is to provide analytical solutions of stress fields in mechanical layers which consist of stiff and soft or compliant layers. The paper examines possible geological conditions of mode I (extension) fracture development on the basis of the analytical calculations with various layer thicknesses, Young's moduli, Poisson's ratios, external stress fields and pore-fluid pressure. Linear elastic model with two different mechanical layers is assumed for the calculations. Fluid-driven fractures, hydrofractures, are discussed in detail elsewhere and are not considered here. Layer-parallel stresses in the model caused by external stresses and pore-fluid pressure are mathematically calculated for 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 v is assumed to be same between the two. This is because the possible variation of Poisson's ratio between rocks is much smaller than those of the other parameters. The calculated ratio of minimum to maximum principal stresses within each layer is used to estimate fracture type which can develop under various geological conditions. The results indicate extension fracture preferably develop in stiff layer. Stress conditions in the model are primarily controlled by relationship among external horizontal stress σXX, vertical stress σZZ and pore-fluid pressure Pf: no tensile fracture forms when σXX > Pf + v(σZZ - Pf)/(1 - v); tensile fractures can form only in stiff layers in soft-layer-dominant system when Pf + v(σZZ - Pf)/(1 - v) > σXX > Pf; tensile fractures form in stiff layers in both stiff-layer-dominant and soft-layer-dominant systems when Pf > σXX > 4Pf/3 - σZZ/3; tensile fracture can form in both stiff and soft layers in soft-layer-dominant formation with small relative Young's modulus when 4Pf/3 - σZZ/3 > σXX. Only shear fractures can form in soft layers, except the rare geological condition of 4Pf/3 - σZZ/3 > σXX with very small relative Young's modulus. The results of analytical calculations provide potential criterion to estimate when and where layer-scale extension fracture network develops in relation with geological history. One implication of the results is that extension fracture formation is not necessarily related to regional 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 stress, vertical stress and pore-fluid pressure are increasing.