不同拉压模量及软化特性材料的球形孔扩张问题的统一解

UNIFIED SOLUTION FOR THE EXPANSION OF SPHERICAL CAVITY IN STRAIN-SOFTENING MATERIALS WITH DIFFERENT ELASTIC MODULI IN TENSILE AND COMPRESSION

对于具有不同的拉压模量及软化特性的岩土类材料,提出了不同拉压模量及软化特性的控制参数,采用双剪统一强度理论推导了球形孔扩张问题的应力及位移的统一解。分析了模量、模型和软化等控制参数对球形孔扩张时的扩张压力、塑性区开展规律及应力场的影响。结果表明:圆孔极限扩张压力,塑性区的发展规律,应力场,位移场等均随着模量控制参数、模型参数及软化参数的变化而变化,因此若采用经典的弹性理论、单一的模型参数及传统的不考虑应变软化来对岩土类的工程材料进行设计计算,必会带来较大的误差。

For strain-softening materials with different elastic moduli of tensile compression, two controlling parameters were introduced to take into account the different moduli and strain-softening properties. By means of twin shear unified strength theory, unified solutions for calculating stress and displacement fields of expansion of spherical cavity were derived. The effects caused by different elastic moduli in tensile and compression, by different models and strain-softening rates on stress and displacement fields, and by the development of plastic zone were analyzed. The results show that the ultimate expansion pressure, stress and displacement fields, and development of plastic zone vary with the changes of＇elastic moduli, models, and strain-softening properties. If classical elastic theory and single model are adopted and strain-softening properties are neglected, large errors may be induced.