A constitutive model for caprock siltstone subject to three-dimensional compression with emphasis on plastic potential and hardening law

Abstract

Investigation of the strength, deformation and constitutive model of rocks under true three-dimensional stress is of much significance to scientifically and accurately predict the integrity of underground gas storage caprock. In general the intermediate principal stress and the minimum principal stress to which the caprock is subjected are not equal, and there is uncertainty in the in-situ stress test. In this study, the siltstone is taken from the caprock of the Hutubi gas storage in Xinjiang, with a buried depth of 3600 m. A series of true triaxial compression tests on siltstones were carried out using a true triaxial testing system for rocks, and the strength and deformation characteristics of siltstones under different intermediate principal stress conditions were studied. The elastoplastic constitutive model of rocks has been established: in the plastic part, the Mogi-Coulomb yield criterion has been modified so as to obtain the triple-mean-normal-stress yield function and triple-mean-normal-stress potential function suitable for rocks under the true three-dimensional stress state. The hardening law has been determined by fitting the relationship between the plastic deviatoric shear strain and the deviatoric stress in the true triaxial compression test. The constitutive model and the test data of siltstones have been verified by fitting. Finally, the influence of true triaxial stress on the permeability and breakthrough pressure of caprock siltstones has been discussed. The result indicates that with the increase of intermediate principal stress within a certain range, the peak strength of siltstones will also increase, and deformation in the direction of the intermediate principal stress will be restrained. Compared with the potential functions in other constitutive models, the triple-mean-normal-stress potential function proposed in this paper can accurately describe the plastic flow direction of siltstones under the true three-dimensional stress state. And the hardening law truly reflects the plastic deformation of siltstone specimens under different stress states during the loading process. The calculation result of the constitutive model is in good agreement with the test result. Under the true three-dimensional stress, the permeability of siltstones shows anisotropy. With the increase of the intermediate principal stress, the minimum value of siltstone permeability decreased by 8%, and the maximum value of breakthrough pressure increased by 4.3%.