拉压模量不同的剪胀土体中的球孔扩张问题

Spherical cavity expansion in dilatant soils with different tension and compression moduli

土体具有不同的拉压模量和剪胀特性。为使球形孔扩张问题的解答更符合实际情况,根据不同模量弹性理论和非关联Mohr-Coulomb流动法则研究了球形孔扩张时弹性区和塑性区的应力和位移,得到了弹性区和塑性区的径向应力和环向应力的解析解以及最大塑性区半径与扩张压力的计算表达式。探讨了不同拉压模量之比、拉压泊松比和剪胀角对球形孔扩张的扩张压力及塑性区半径的影响。结果表明:拉压模量比、拉压泊松比和剪胀角对球孔扩张时塑性区的开展和扩张后土体的应力有重要影响,计算中忽略这些参数将带来较大的误差。

Soil has different moduli in tension and compression. In order to obtain a more precise solution of spherical cavity expansion, an analysis of spherical cavity expansion in elasto-plastic soil is presented based on the elastic theory considering different moduli in tension and compression. The characteristics of dilation are taken into account by using the non-associated Mohr-Coulomb yield criterion. The analytical solutions for the stresses in elastic and plastic zones, maximum radius of the plastic zone and expansion pressure are obtained. The influences of different tension and compression modulus ratios, Poisson＇s ratios and dilation angles on the expansion pressure and radius of plastic zones are discussed. The results show that different tension and compression modulus ratios, Poisson＇s ratios and dilation angles have significant influences on the development of plastic zones and the stresses in the soil. Large errors will occur if these parameters are ignored.