层理灰岩三维损伤本构模型及试验验证

THREE-DIMENSIONAL DAMAGE CONSTITUTIVE MODEL AND TEST VERIFICATION FOR BEDDING LIMESTONE

  • 摘要: 为揭示层理灰岩加载过程的三维损伤演化机理,将Lemaitre等效应变假设与Weibull统计损伤理论相结合,推导损伤有效矩阵,建立三维主损伤分量与主应变分量之间的演化方程,构建三维损伤横观各向同性本构模型;通过不同层理倾角灰岩岩样的三轴压缩试验,计算三维主损伤分量并修正理论计算曲线,验证模型的合理性和准确性,并分析损伤分量各向异性演化规律。研究表明:经损伤有效矩阵修正的横观各向同性弹性矩阵,用于计算不同层理角度灰岩岩样加载过程的理论应力-应变曲线,与试验曲线吻合程度高,理论曲线预测结果较好。岩样峰值强度、弹性模量随层理倾角的增大呈现“V”型分布,试样破坏模式由岩块张拉破坏转变为沿层理压剪破坏,再到层理劈裂张拉破坏。不同层理倾角岩样的损伤演化曲线总体相似,随着应变增大呈现出缓慢增加-急剧增长-趋于平稳的趋势。随着层理倾角的增大,三维主损伤分量由第三主损伤分量大于第二主损伤分量转变为第二主损伤分量大于第三主损伤分量,最后基本一致;不同层理倾角岩样损伤演化曲线增长速率不同,其中60°试样的增长速率最快。研究结果揭示了层理灰岩在三轴加载条件下的力学参数各向异性以及非均质损伤演化的过程与机理,可为工程设计与稳定性计算提供理论支持。

     

    Abstract: To reveal the three-dimensional damage evolution mechanism of bedding limestone during the loading process, the Lemaitre equivalent strain hypothesis was integrated with the Weibull statistical damage theory, so as to facilitate the derivation of the effective damage matrix, the establishment of the evolution equation connecting the three-dimensional primary damage component to the principal strain component, and the construction of a three-dimensional damage transverse isotropic constitutive model. Through triaxial compression tests on limestone samples with varying bedding angles, the three-dimensional primary damage component was calculated and theoretical calculation curves were then adjusted to verify the rationality and accuracy of the model, and the anisotropic evolution laws of the damage components were analyzed. Research indicated that the transversely isotropic elastic matrix, modified by the damage effective matrix, was utilized to calculate the theoretical stress-strain curves during the loading process of limestone samples with varying bedding angles. The results showed a high consistency with the experimental curve, and the predictions of the theoretical curve were favorable. The peak strength and elastic modulus of the rock sample showed a 'V' type distribution with the increase of the inclination angle. The failure mode of the specimen transitioned from tensile failure of the rock blocks to compression-shear failure along the bedding, and subsequently to tensile failure characterized by bedding splitting. The damage evolution curves of rock samples with different bedding dip angles were generally similar, showing a trend of slow increase-rapid increase-tend to be stable with the increase of strain. As the bedding inclination angle increased, the three-dimensional damage components transitioned from the third main damage component being greater than the second main damage component, to the second main damage component exceeding the third main damage component, and the latter two are basically identical. The growth rate of the damage evolution curve of rock samples with different bedding dip angles was different, and the growth rate of 60° samples was the fastest. The research results revealed the anisotropy of mechanical parameters and the evolution process and mechanism of heterogeneous damage of bedding limestone under triaxial loading conditions, which can provide a theoretical support for engineering design and stability calculation pertinent to bedding limestone.

     

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