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.

中文翻译：

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基于温度相关的 Drucker-Prager 塑性的页岩热塑性本构模型

摘要 页岩深埋高温（120 ~ 238 °C）对页岩气的最终开采有很大影响。与常温岩石不同，深部储层高温下页岩力学性质发生显着变化，其热塑性行为有待进一步研究。在这项研究中，我们提出了页岩的热塑性本构模型，结合了温度相关的 Drucker-Prager 硬化规则、热加载/卸载标准和完全耦合的应力-应变-温度关系。所提出模型中的热塑性特性是通过进一步处理 Masri 等人在 Tournemire 页岩上完成的已发表的热机械测试数据获得的。有以下主要发现：(1) 发现静水压力相关 (HPD) 和应力偏差相关 (SDD) 初始/临界屈服参数与温度呈二次线性相关。(2)在20～250℃范围内，HPD和SDD硬化参数分别随内变量κ 1 和κ 2 呈线性和二次变化。硬化参数和内部变量之间的相关方程中的所有三个系数都与温度呈线性关系。(3) 作为静水压力、硬化参数和初始温度的函数的温度敏感性模量用于表征屈服面随温度的收缩或膨胀。该模型通过 Tournemire 页岩的热机械测量进行了验证，与实验数据非常吻合（相关系数：93%）。在塑性加载过程中，发现温度敏感模量正对应于屈服面随温度的膨胀，并且 SDD 加载/卸载判别系数为正。提出的模型可能适用于其他岩石材料。