基于Maxwell分布的砂岩本构模型研究

Study on constitutive model of sandstone based on Maxwell distribution

砂岩具有典型的颗粒结构,其力学参数与内部颗粒间的接触密切相关。由于砂岩内部颗粒接触数量巨大,具有统计分布特征,因此,通过引入颗粒接触强度的统计分布模型建立砂岩的本构理论,可以更好地从细观角度理解砂岩的变形发展。由于前期研究中的统计分布模型多是基于经验而提出的,没有统计学基础。严格的数理统计理论发现,砂岩内部颗粒接触强度符合Maxwell统计分布模型。结合岩石统计损伤理论,构建一种新的砂岩本构模型。该模型将微观颗粒之间胶结键的数量和强度视为影响砂岩宏观强度的主要因素,当断裂破坏的胶结键达到一定数量即可表现为宏观上的整体破坏。利用室内三轴压缩试验,对不同围压作用下砂岩的应力-应变特征进行试验研究,验证所推导的模型的适用性。研究结果表明:该本构模型能很好地反映应变发展的各个阶段,且本构模型参数具有实际的物理意义。从宏观层面,模型所引入的参数反映了岩石的宏观强度和延展性,其中,表示胶结键方向性的参数随围压的增大而线性减小,反映砂岩能量密度的参数随围压的增大呈现抛物线型增大。对岩石损伤与围压的关系的研究表明,围压的增大能有效抑制损伤的发展。

Sandstone has typical grain structure, and its mechanical parameters are closely related to the internal grain-contacts. Since the number of grain-contacts in sandstone is huge, which satisfies statistical distribution characteristics, the constitutive relation of sandstone can be established by introducing the statistical distribution model of grain-contact strength to better understand the deformation development of sandstone from a meso-level perspective. Since most of the statistical distribution models in the previous studies were obtained based on experiences, which have no statistical basis. It is found that the contact strength of particles in sandstone follows the Maxwell statistical distribution model based on strict mathematical statistical theory. Therefore, a new sandstone constitutive model was constructed in combination with the damage theory of rock. In this model, the number and strength of cemented bonds between micro particles are regarded as the main factors affecting the macro strength of sandstone. When the fracture damage of cementing bond reaches a certain number, it can be expressed as theoverallmacroscopic failure. By using triaxial compression tests, the stress-strain characteristics of sandstone under different confining pressures were tested and the applicability of the derived model was verified.It is found that the constitutive model can well reflect each stage of strain development, and the parameters of the constitutive model have actual physical meanings. From the macro level, the parameters introduced in the model reflect the macro-strength and ductility of the rock. The parameter indicating the directionality of the cement bond decreases linearly with the increase of confining pressure, and the parameter reflecting the energy density of sandstone increases with the increase of confining pressure, showing a parabolic increase. Finally, the relationship between rock damage and confining pressure shows that the increase of confining pressure can effectively inhibit the development of damage.