Thermoplastic constitutive modeling of shale based on temperature-dependent Drucker-Prager plasticity. (June 2020)

• Record Type: Journal Article
• Authors: Xing, Yuekun; Zhang, Guangqing; Li, Shiyuan
• Is Part Of: International journal of rock mechanics and mining sciences. Volume 130(2020)
• Publication Date: 2020-06
• Subjects: Thermoplastic -- Constitutive model -- Shale -- Temperature-dependent -- Drucker-prager plasticity; Rock mechanics -- Periodicals; Soil mechanics -- Periodicals; Mining engineering -- Periodicals; Roches, Mécanique des -- Périodiques; Sols, Mécanique des -- Périodiques; Technique minière -- Périodiques; 624.151305
• DOI: 10.1016/j.ijrmms.2020.104305
• Languages: English
• ISSNs: 1365-1609

Abstract

Abstract: High temperatures ( 120 ~ 238 °C ) from deep burial of shale affects strongly the eventual extractions of shale gas. Different from rocks at normal temperatures, the mechanical properties of shale change significantly at high-temperature of deep reservoirs, where its thermoplastic behavior needs further investigation. In this study, we propose a thermoplastic constitutive model for shale, incorporating temperature-dependent Drucker-Prager hardening rule, thermal loading/unloading criteria, and completely coupled stress-strain-temperature relation. The thermoplastic properties in the proposed model are obtained by further processing of published thermo-mechanical test data done on Tournemire shale by Masri et al. with the following key findings: (1) The hydrostatic-pressure-dependent (HPD) and stress-deviator-dependent (SDD) initial/critical yield parameters are found to be quadratically and linearly dependent on temperatures. (2) In the range of 20 ~ 250 °C, the HPD and SDD hardening parameters vary linearly and quadratically with internal variables κ 1 and κ 2, respectively. All three coefficients in the correlative equations between hardening parameters and internal variables depend linearly on temperatures. (3) The temperature sensitivity modulus, as a function of hydrostatic pressure, hardening parameters, and initial temperature, is used for characterizing the contraction or expansion of the yield surface with temperatures. This proposed model was validated with thermo-mechanical measurements of Tournemire shale, fitting well with experiment data (correlation coefficient: 93%). During the plastic loading, temperature-sensitive modulus was found to be positively corresponding to the expansion of the yield surface with temperatures, and the SDD loading/unloading discriminant coefficient is positive. The proposed model may be applicable to other rock materials. Highlights: We propose a completely coupled thermoplastic constitutive relation for rocks. The relation depends on hydrostatic pressure, stress deviator and temperature. Parameters characterizing effects of temperatures on thermo-plasticity are proposed.