Thermoplastic constitutive modeling of shale based on temperature-dependent Drucker-Prager plasticity

• Published in: International journal of rock mechanics and mining sciences (Oxford, England : 1997) England : 1997), 2020-06, Vol.130, p.104305, Article 104305
• Main Authors: Xing, Yuekun, Zhang, Guangqing, Li, Shiyuan
• Format: Article
• Language: English
• Subjects: Constitutive model; Constitutive models; Contraction; Correlation coefficient; Correlation coefficients; Drucker-prager plasticity; Hardening; High temperature; Hydrostatic pressure; Mathematical models; Mechanical measurement; Mechanical properties; Mechanical tests; Parameter sensitivity; Plasticity; Pressure dependence; Rocks; Shale; Shale gas; Shales; Temperature; Temperature dependence; Temperature-dependent; Thermomechanical treatment; Thermoplastic; Unloading
• ISSN: 1365-1609; 1873-4545
• DOI: 10.1016/j.ijrmms.2020.104305

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 κ1 and κ2, 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. •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.