基于分数阶热弹塑性理论的软岩力学特性描述

doi:10.13722/j.cnki.jrme. 2019.1243

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摘要软岩具有复杂的热力学行为，可能同时存在热增强和热减弱效应，即软岩的强度会随着温度升高增大或减小。为了描述软岩的力学特性，将其视作重超固结黏土，并假定其前期固结应力近似的等于单轴抗剪强度。基于分数阶热弹塑性理论，建立考虑温度影响的软岩分数阶下加载面模型，该模型能够在不引入塑性势函数的情况下统一描述相关联和非相关的流动法则。模型计算结果表明，软岩的热增强和热减弱效应与软岩的塑性流动方向和加载方向之间的夹角密切相关。在三轴压缩不排水试验过程中，采用非关联的流动法则会导致软岩的应力路径越过其临界状态线并最终达到临界状态，此时软岩的不排水剪切强度会随着温度的升高而逐渐上升；反之，则将观察到热减弱现象。此外，由于软岩的前期固结应力会随着温度的升高而减小，在p-q平面其初始下加载面可能会位于温度加载面外部，此时超固结比OCR将小于1。给出的模型能够合理地描述常温下太古石的三轴压缩排水试验结果，分析结果表明，软岩的应力–应变曲线具有应变硬化和软化特点，同时伴随着剪缩和剪胀现象的发生；针对不同温度下Ohya软岩的三轴压缩排水试验计算结果表明，随着温度的升高，软岩将逐渐由脆性破坏转变为延性破坏，其最终剪胀量也会随之减小。相比较修正剑桥模型，本文模型仅额外的引入了线膨胀系数和与软岩剪胀特性相关的模型参数m，两者具有明确的物理意义，可以通过常规的室内试验结果加以确定。

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	李海潮1
	马博1
	张升1
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	盛岱超3

关键词 ：岩石力学, 分数阶微分, 软岩, 连续方程

Abstract：Soft rocks have complex thermodynamic behaviors and their strength maybe increase or decrease with temperature. In this paper，the soft rocks were considered as heavily over-consolidated clays and their preconsolidation pressure was assumed to be the uniaxial compression strength. Based on the fractional thermal elastoplastic theory，a fractional sub-loading surface model for soft rocks considering the effects of temperature was proposed，which can decribe associated and non-associated flow rules without introducing the plastic potential. The analysis results show that the phenomena of heat-increase and heat-decrease are closely related to the angle of the plastic flow direction and the loading direction. Application of the non-associated flow rule in the undrained triaxial test results in that stress paths of soft rocks cross through the critical state line and finally reach the critical state，and the undrained shear strength of soft rocks will increase as temperature increases. On the other hand，the associated flow rule will do the opposite. In addition，the preconsolidation pressure of soft rocks will decrease as temperature increases，leading that the sub-loading surface is located outside the temperature loading surface in the p-q plane and that the overconsolidated ratio OCR is smaller than 1. Comparisons between the proposed model with test results indicate that soft rocks show the features of strain-softening and dilatancy，which can be captured by the proposed model，and that，increasing temperature will decrease the fragility of soft rocks as well as the dilatancy. Compared with the modified Cam-clay model，the proposed model introduces two extra parameters including the coefficient of linear expansion and dilative related parameter m，which have clear physical meanings and can be determined through conventional tests directly.

Key words： rock mechanics fractional derivative soft rock constitutive equations

引用本文:

李海潮1，马博1，张升1，2，盛岱超3. 基于分数阶热弹塑性理论的软岩力学特性描述[J]. 岩石力学与工程学报, 2020, 39(7): 1311-1320.
LI Haichao1，MA Bo1，ZHANG Sheng1，2，SHENG Daichao3. Mechanical behaviors of soft rocks based on the fractional thermal elastic-plastic theory#br#. , 2020, 39(7): 1311-1320.

链接本文:

http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme. 2019.1243 或 http://rockmech.whrsm.ac.cn/CN/Y2020/V39/I7/1311

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