论文标题
Mohr-Coulomb地板中圆柱腔扩展的图形理论框架
A Graphical Theoretical Framework for Cylindrical Cavity Expansion in Mohr-Coulomb Geomaterials
论文作者
论文摘要
本文通过使用图形方法和Lagrangian对空腔边界值问题的表述（通过追踪腔壁上单个土壤粒子的响应），为非相关的Mohr-Coulomb土壤中排水（干）的圆柱腔扩张提供了完整的分析解决方案。新解决方案的新颖性不仅在于先前分析中通常采用的垂直应力的严格中间人假设的放松，而且还全面考虑了K_0任意值（也是静止的地球压力系数）。所谓的图形方法的本质，即，通过利用变形需求，在排干膨胀过程中，径向和切向菌株的逐步发展必须分别保持为压缩和拉伸性，可以实现偏斜应力轨迹的独特几何分析和跟踪。随着径向平衡条件的结合，对于涵盖了k_0的所有不同场景，就可以针对内部空腔辅助变量解决内部空腔压力的单个一阶微分方程。通过示例分析，为计算出的空腔膨胀曲线提供了一些选定的结果，并限制了腔压力。
This paper develops a complete analytical solution for the drained (or dry) cylindrical cavity expansion in non-associated Mohr-Coulomb soil, by using the graphical approach and Lagrangian formulation of the cavity boundary value problem (through tracing the responses of a single soil particle at the cavity wall). The novelty of the new solution lies not only in the relaxation of the strict intermediacy assumption for the vertical stress as usually adopted in the previous analyses, but in the comprehensive consideration of arbitrary values of K_0, the coefficient of earth pressure at rest, as well. The essence of the so-called graphical method, i.e., the unique geometrical analysis and tracking of the deviatoric stress trajectory, is fulfilled by leveraging the deformation requirement that during drained expansion the progressive development of the radial and tangential strains must maintain to be compressive and tensile, respectively. With the incorporation of the radial equilibrium condition, the problem is formulated to solve a single first-order differential equation for the internal cavity pressure with respect to a pivotal auxiliary variable, for all the distinct scenarios of K_0 being covered. Some selected results are presented for the calculated cavity expansion curve and limit cavity pressure through an example analysis.
