A modified Hoek-Brown failure criterion for unsaturated intact shale considering the effects of anisotropy and hydration

Abstract

The mechanical strength of shale is highly influenced by anisotropy and hydration, which cannot be ignored for the stability evaluation of the geotechnical structures related to shale after water invasion. In the present work, a modified Hoek-Brown failure criterion for unsaturated intact shale considering the effects of anisotropy and hydration has been developed in order to obtain an accurate strength evaluation for unsaturated intact shale. In this proposed failure criterion (abbreviated as the proposed criterion), the effect of anisotropy on shale strength is determined by a piecewise functions for uniaxial compression and the parameter kβ added in Hoek-Brown (HB) failure criterion for triaxial compression condition, and the effect of incomplete hydration on shale strength is regarded as an effective stress decrease by incorporating a discount function related to moisture content. The proposed criterion is defined by 8 parameters, including a material parameter of HB failure criterion (m), 4 material parameters (ξ, η, R and r) describing the hydration effect and 3 model parameters (g, h and kβ) describing the anisotropy effect. The physical meanings and determination procedures of these parameters are described. The predicted values of the proposed criterion agree well with the experimental data, showing that R2 = 0.966 and AAREP (average absolute relative error percentage) = 4.393% for all the predicted results. The proposed criterion is then compared with other two failure criteria which consider the effects of water invasion and anisotropy on rock strength, showing that the proposed criterion has higher accuracy and better stability. The error of the predicted values for the proposed criterion compared with the tested results increases for the shale specimen for which β (bedding plane orientation relative to the axial loading in degrees, °) is closer to 30°, is bigger for the shale specimen with a higher moisture content, and is bigger for the shale specimen under a higher confining pressure. The sensitivity analysis of the 4 hydration parameters on the predicted results shows that the predicted values are more sensitive to R and r than ξ and η. This proposed criterion can improve the reliability for the stability evaluation of the geotechnical structures related to shale after water invasion.