引用本文: 刘冬桥, 郭允朋, 李杰宇, 凌凯. 基于耗散能演化的层状黄砂岩损伤本构模型及其验证[J]. 工程科学学报, 2024, 46(5): 784-799.
LIU Dongqiao, GUO Yunpeng, LI Jieyu, LING Kai. Damage constitutive model for layered yellow sandstone based on dissipative energy evolution and its verification[J]. Chinese Journal of Engineering, 2024, 46(5): 784-799.
 Citation: LIU Dongqiao, GUO Yunpeng, LI Jieyu, LING Kai. Damage constitutive model for layered yellow sandstone based on dissipative energy evolution and its verification[J]. Chinese Journal of Engineering, 2024, 46(5): 784-799.

## Damage constitutive model for layered yellow sandstone based on dissipative energy evolution and its verification

• 摘要: 层理构造影响工程岩体力学性质及稳定性. 为探究层理倾角对岩石变形损伤过程的影响，开展了0°，15°，30°，45°，60°，75°，90°共7种不同层理角度的黄砂岩纵波波速测试和单轴压缩试验，分析了层理角度对黄砂岩峰值强度、弹性模量及破裂模式的影响，基于弹性模量劣化程度和耗散能演化特征分别表征黄砂岩初始层理损伤变量和荷载损伤变量，并借助Logistic函数模拟了层理与荷载耦合损伤变量演化全过程，探讨了层理角度对黄砂岩损伤演化规律的影响，进一步结合损伤力学理论与有效介质理论，建立了能够模拟单轴压缩下层状黄砂岩变形全过程的分段本构模型. 结果表明：随层理倾角增大，黄砂岩纵波波速逐渐增大，峰值抗压强度和弹性模量呈现先减小后增大再减小的倒N型变化趋势，各向异性特性明显；黄砂岩破裂模式与层理倾角密切相关，倾角在0°～60°范围内时，主要发生穿切层理弱面的劈裂型张拉破坏，倾角为75°和90°时，岩样发生沿层理弱面的剪切滑移和劈裂张拉破坏；基于耗散能表征的损伤演化曲线可分为初始无损伤、损伤开始、损伤加速及损伤减速终止4个过程，借助Logistic函数构建的理论损伤模型可以很好的模拟和预测层状黄砂岩损伤演化全过程；初始层理损伤最大值与最小值之比约为1.41，表明层理倾角对黄砂岩初始损伤影响较大；建立的分段本构模型可以较好的描述层状黄砂岩单轴压缩应力–应变全过程，且理论模型曲线与试验数据吻合度高.

Abstract: Bedding structure affects the mechanical properties and stability of engineering rock masses. To elucidate the influence of bedding angle on rock deformation and damage process, longitudinal wave velocity tests and uniaxial compression tests were performed on yellow sandstone at bedding angles of 0°, 15°, 30°, 45°, 60°, 75°, and 90°. Furthermore, the influence of the bedding angle on the peak strength, elastic modulus, and failure mode was analyzed. Initial bedding damage and load damage were characterized based on the degradation degree of elastic modulus and evolution characteristics of dissipative energy; moreover, the entire evolution process of coupled layer–load damage was simulated using the logistic function. The influence of the bedding angle on the damage evolution law of yellow sandstone was discussed, and a piecewise constitutive model for simulating the entire deformation process of uniaxial compression was established, combined with the damage mechanics and effective medium theories. The results reveal that with increasing bedding angle, longitudinal wave velocity increases gradually, peak strength and elastic modulus decrease first, then increase, and then decrease, and anisotropy is obvious. The failure mode is closely related to the bedding dip angle. When the dip angle ranges from 0° to 60°, splinter-type tensile failure occurs mainly through the weak side of shear bedding. Moreover, when the dip angle is 75° and 90°, shear slip and splinter tensile failure occur along the weak side of the bedding. The damage evolution curve based on dissipative energy can be divided into four processes: initially undamaged, damage initiation, damage acceleration, and damage deceleration termination. A theoretical damage model constructed using the logistic function can effectively simulate and predict the entire damage evolution process. The ratio of maximum value to minimum value of initial bedding damage is approximately 1.41, indicating that bedding angle substantially affects the initial damage. The piecewise constitutive model can describe the entire stress–strain process of layered yellow sandstone under uniaxial compression, and the theoretical model curves agree well with experimental data. Parameters a and r represent the initial damage degree and damage evolution rate, respectively. Larger a values typically correspond to a lower initial damage degree and higher peak strength. The larger r is, the faster the damage variable develops and the greater the maximum damage evolution rate is. Thus, the theoretical curve shape of the constructed constitutive model is determined by parameters a and r.

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