A New Constitutive Model for Shale under Hydro-Mechanical Coupling Based on the Disturbed State Concept Theory

Accurately describing the constitutive relation of hydrated shale is crucial, as it can provide theoretical support and a scientific basis for shale wellbore stability. The disturbed state concept theory has a unique advantage in describing the deformation and instability of materials. However, as the theory was proposed recently, it has not yet attracted much attention in the study of hydrated shales. There are few reports on this theory in relation to hydrated shale. Thus, the theory of the disturbed state concept method was employed to analyze the constitutive relation of hydrated shale. First, based on the uniaxial compression test, the initial state of dry shale and the uniaxial compression failure state of hydrated shale were separately employed to characterize the relative intact state and the fully adjusted state of hydrated shale, respectively. Then, two different approaches for the disturbance function were proposed, which were based on the stress deviation and the coupling of both hydration disturbance and stress disturbance, respectively. After that, two constitutive models corresponding to the two disturbance functions were constructed, and their relative errors were, respectively, 4.37% and 3.49%. The prediction of the stress-strain relationship showed that the relative errors between the predictions of the two constitutive models and the experimental results were 6.55% and 4.97%, respectively. They could predict the constitutive relation of the shale with any degree of hydration. In addition, the correlations between different parameters and water content were also clarified. This study provides not only a new idea for the constitutive relation of hydrated shale but also a reference and basis for the application of disturbed state concept theory in hydrocarbon development.