原煤弹塑性局部化损伤的本构模型

Study on the elastoplastic localized damage constitutive model of raw coal

  • 摘要: 随着人类能源和资源刚性需求的增加,必将促使矿产资源开采进一步朝地球深部发展. 深部工程高地应力赋存条件导致岩体表现出明显的非线性力学响应. 由于煤岩的非均质性,外部荷载作用下其内部微裂纹会逐渐萌生、扩展,并聚合成局部宏观裂纹,形成局部剪切带,表现出应变局部化现象,最终导致试样失稳破坏. 且原煤的三轴压缩试验结果表明:低围压条件下峰后出现明显的应力跌落,表现出脆性破坏特征;随着围岩的增加,应力跌落现象逐渐放缓,表现出延性变形行为. 基于煤岩的损伤破裂内在物理机制,如何在本构尺度准确描述岩石的脆延转变现象仍需进一步研究. 传统模型忽略了局部剪切区域内与区域外之间的关系以及局部区域的力学特征,导致模拟结果不能有效地反映岩石材料应变局部化破坏特征. 正确描述深部岩体灾变过程中局部化破坏问题是工程结构设计的关键. 为此,基于原煤三轴压缩力学响应特征,考虑局部化损伤效应,提出适应于原煤的Mohr–Coulomb型屈服准则和损伤准则,建立了原煤弹塑性局部化损伤本构模型. 通过能量等效原理,建立局部带内外力学变量与宏观力学响应之间联系. 采用损伤变量作为内在驱动变量控制屈服面的膨胀和收缩,描述煤岩的峰前应变硬化和峰后应变软化行为. 并采用指数函数形式损伤准则描述岩石断裂破坏过程中损伤演化行为,建立了局部带尺寸与损伤变量之间函数关系. 通过数值模拟结果与原煤三轴压缩试验数据对比论证提出模型的有效性. 结果表明:该模型能够较好地捕捉原煤不同围压加载过程中主要的非线性变形特征,且峰后应变软化现象是局部化损伤快速增加所致. 通过控制损伤演化速率和局部化损伤程度,本构模拟结果可以较好地再现原煤的脆延转变行为,且最大损伤水平随着围压的增加呈现指数衰减. 因此,本文提出的本构模型能够反映原煤的局部化变形破坏力学特征,进一步丰富了岩石损伤力学理论,相关研究工作可为深部岩石工程理论模型研究提供新的研究思路.

     

    Abstract: The growing need for energy and resources is driving the search and extraction of mineral resources from deeper earth layers, resulting in significant nonlinear mechanical responses in rock masses under high ground stress. The heterogeneous nature of raw coal leads to the development of internal microcracks, which evolve into larger, visible cracks when external forces are applied. This process involves the initiation, propagation, and coalescence of internal microcracks, causing strain localization phenomena and creating localized shear zones. Such developments can lead to instability and failure of the coal samples. Triaxial compression tests on raw coal indicate a substantial drop in stress after reaching peak strength, demonstrating brittle failure characteristics under low confining pressure. As the confining pressure increases, this drop in stress gradually slows, exhibiting a shift to ductile deformation. Further research is needed at the constitutive scale to accurately describe the brittle–ductile transition in raw coal, focusing on the intrinsic physical mechanisms of coal rock damage and failure. Conventional models often overlook the relationship between the local shear zone and their surroundings, as well as the mechanical properties of these zones. As a result, simulation results may not accurately reflect the localized failure characteristics of rock materials. Recognizing localized failure in deep rock masses is crucial for engineering structural designs. This paper introduces a new elastoplastic localized damage constitutive model for raw coal based on the Mohr–Coulomb (MC) yield criterion and the mechanical behavior observed in triaxial compression mechanical responses of the rock. By applying energy equivalence principles, we can establish a relationship between internal and external mechanical variables and overall macroscopic mechanical responses. Damage variables, as an intrinsic driving variable, are used to control the expansion and contraction of the yield surface, describing both prepeak strain hardening and postpeak strain softening behaviors in raw coal. An exponential damage criterion is used to represent damage progression during rock fracturing, linking the size of localized bands to damage variables. The effectiveness of the proposed model is demonstrated by comparing numerical simulations with triaxial compression test data of raw coal. The results demonstrate that the model can capture the primary nonlinear characteristics of raw coal during triaxial compression tests. The postpeak strain softening is attributed to the rapid increase in localized damage. By controlling the evolution rate and extent of damage, the constitutive simulation results can effectively replicate the brittle–ductile transition behavior of raw coal, with the maximum level of damage decreasing exponentially as the confining pressure increases. The proposed constitutive model effectively captures the main mechanical features of localized deformation and failure of the raw coal. This enriches understanding of rock damage mechanics and introduces a fresh perspective for theoretical models in deep rock engineering.

     

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