基于统一强度准则的柱孔扩张问题及扩孔孔径分析

Theoretical Analysis of Expansion and Expanded Radius of Cylindrical Cavity Based on Unified Strength Criterion

摘要:

通过轴对称问题的应变协调方程，利用统一强度准则和相关联流动法则分析了柱孔扩张问题.利用柱孔扩张问题的基本位移公式和塑性区孔口位移条件，推导了柱孔初始半径a0、扩孔半径a和对应的孔压p三者的理论关系式.通过此关系式和塑性区半径相关公式求得柱孔扩张问题的塑性区半径rp，进而求出相关扩孔问题的应力场、应变场和位移场.探讨了统一强度理论和土体的参数问题，并且通过算例分析，对柱孔扩张问题中的应力场和位移场的分布规律、塑性区半径和扩孔压力的变化规律进行了分析.

Abstract:

The problem of cylindrical cavity expansion in soil was analyzed with the unified strength yield criterion, strain compatibility equations in cylindrical coordinates and the associative flow rule. The theoretical relationship among the initial radius a0，expansion radius a and expansion pressure p of the cylindrical bore was derived by employing the basic displacement formula of plastic zone and the displacement changes of soil around the cylindrical bore. Then, the radius of plastic zone rpwas obtained by this theoretical relationship and the relative formulas about the radius of plastic zone rp. In addition, the closed form solutions of stresses, strains, displacements in the elastic and plastic regions were obtained in concrete problems of cavity expansion. Furthermore, the parameters of the unified strength theory and the soil were analyzed. Finally, an illustrative example was taken to analyze the change rules of stress and displacement fields, the radius of plastic zone a0 and expansion pressure p.