应变软化及剪胀性土体中考虑大应变的孔扩张问题解析

采用应力跌落模型模拟土体的应变软化,以Mohr-couloub屈服准则和不相关联的流动法则考虑土体屈服塑性流动和剪胀特性,引进对数应变考虑土体的大变形,给出了应变软化及剪胀性土体中考虑大应变的孔扩张问题的弹塑性解析解,为了对比,还给出了小应变情况下位移的解析表达式.分析了大、小应变理论、不同剪胀特性、不同软化程度和考虑塑性区弹性变形与否对结果的影响.结果表明:在孔扩张压力较大时,用小应变理论会引起很大误差,必须考虑大应变;在相同扩张力作用下,土体的软化程度越高,扩张率越大,土体的剪胀角越大则扩张率越小.土体的软化和剪胀特性还影响极限扩张压力,软化越严重,极限扩张压力越小;剪胀角越大,极限扩张压力越大.

Analysis of cavity expansion in soil with shear dilation and strain softening considering large deformation

Stress dropping model was introduced to simulate the strain softening behavior of soils; Mohr-couloub yield criterion and non-associated flow principle were used to consider the plastic flow and the shear dilation; and for large deformation, the logarithmic strain was introduced. The elastic-plastic analytic solution to the cavity expansion was obtained in consideration of the shear dilation, strain softening, and large deformation of soils. For comparison, the displacement formula from small strain theory was also given. The influences of using large or small strain theory, different dilation angles, different softening extent, and considering the elastic deformation of the plastic zone or not were discussed. The analysis results show that using large strain theory is necessary in case of relatively great expansion pressure, because using small strain theory results in great error; that higher extent of soil softening leads to greater expansion ratio, greater dilation angle leads to smaller expansion ratio under the same expansion pressure; that higher extent of soil softening leads to smaller limit expansion pressure, and greater shear-dilation angle leads to greater limit expansion pressure.