考虑岩石微损伤的改进内时损伤本构模型研究

    Investigation on an improved endochronic damage constitutive model accounting for micro-damage in brittle rocks.

    • 摘要: 揭示岩石受荷载作用下不同变形阶段(压密,线弹性,弹塑性,残余变形)内部损伤机制对各阶段变形行为的影响,是开展岩石多阶段破坏分析的关键。然而现有岩石损伤模型很少考虑线弹性阶段岩石裂隙萌生所产生的损伤累积,并且屈服准则的准确定义也是一个挑战。因此,为更准确描述岩石在各变形阶段的损伤演化特征及其对变形的影响,解决传统弹塑性本构屈服面强化准则与岩石损伤之间在不同阶段定义较为复杂的问题。本文提出了考虑岩石微损伤的改进内时损伤本构模型,以便更好的反映岩石从从压密段,线弹性阶段微损伤萌生直至岩石破坏的过程损伤演化情况及其对各阶段变形的影响。首先,以可以不考虑屈服面计算的内蕴时间本构模型为基础,对传统内蕴时间本构岩石压密段反映不理想的问题进行改进,提出内时压密参数反映岩石孔隙闭合所引起的非线性特征。随后,考虑从岩石线弹性阶段起始的岩石微损伤累积,以内时量度作为Weibull分布的微元破坏变量建立损伤方程,用于反映各阶段岩石损伤累积情况,并对损伤演化方程中各Weibull分布参数所对应物理意义进行讨论。最后,与试验结果进行验证,将本文模型与传统内时本构及统计损伤本构方程进行对比。结果表明,所提出本构模型与试验结果吻合度高,与传统内时本构模型和统计损伤本构模型相比,改进的内时损伤本构模型在刻画岩石压密阶段的变形方面表现更优。而相较于统计损伤模型,本文模型更符合实际岩石因裂隙演化而导致的损伤变化趋势,更准确地反映各变形阶段损伤演化对整体变形的影响,从而有效验证了其合理性与优越性。

       

      Abstract: Revealing the internal damage caused by changes in internal pores and other factors, as well as the deformation characteristics at various stages, is key to the multi-stage failure analysis of rocks. To more accurately describe the influence of damage evolution on deformation in different rock deformation stages (compaction, linear elasticity, elastoplasticity, and residual deformation) and to address the complexity in defining the relationship between the traditional elastoplastic constitutive yield surface hardening criterion and rock damage at different stages, this study proposes an improved internal time damage constitutive model that considers rock micro-damage. This model aims to better capture the damage evolution process from the compaction stage to the initiation of micro-damage in the linear elastic stage and ultimately to rock failure, as well as its impact on deformation at each stage.First, based on the endochronic constitutive model, which does not require yield surface calculations, improvements were made to address the traditional model’s limitations in reflecting the rock compaction stage. A compaction parameter in the internal time framework was introduced to represent the nonlinear characteristics caused by pore closure. Subsequently, the accumulation of micro-damage from the onset of the linear elastic stage was considered, and a damage equation was established using the internal time measure as the infinitesimal failure variable in the Weibull distribution. This equation describes the accumulation of rock damage at each stage, and the physical significance of the Weibull distribution parameters in the damage evolution equation was analyzed. Finally, the model was validated against experimental results and compared with the traditional internal time constitutive model and the statistical damage constitutive model. The results show that the proposed constitutive model exhibits a high degree of agreement with experimental data. Compared to the traditional internal time constitutive model and the statistical damage constitutive model, the improved internal time damage constitutive model demonstrates superior performance in capturing rock deformation during the compaction stage. Furthermore, in contrast to the statistical damage model, the proposed model more accurately reflects the damage evolution trends caused by rock fracture propagation, providing a more precise representation of how damage evolution at different deformation stages influences overall deformation. This effectively validates the rationality and superiority of the proposed model.

       

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