分数导数黏弹性深厚冲积层竖井井壁冻结压力分析

Freezing pressure analysis of shaft wall in deep alluvium with fractional derivative viscoelasticity

考虑到竖井冻结壁的蠕变特点,结合黏弹性理论、分数阶导数理论,将冻结壁位移考虑为黏弹性变形,并结合目前黏弹性理论研究中应用较多的分数阶导数理论,推导并分析竖井冻结壁-井壁共同作用下冻结压力的分布及变化特点,最后将理论计算结果和实测现场数据对比,并分析影响冻结压力大小的部分因素。结果表明:采用分数阶导数模型的理论计算结果和实测数据基本吻合,能较好地模拟黏弹性冻结壁的“长期蠕变”,分数阶数大小和冻结壁剪切模量等因素会显著影响冻结压力的大小,研究结果丰富了冻结压力分析理论,可为井壁的施工设计提供理论参考。

Considering the creep characteristics of shaft freezing wall,combining viscoelasticity theory and fractional derivative theory,the displacement of freezing wall is considered as viscoelasticity deformation,and combining fractional derivative theory,the distribution and variation characteristics of freezing pressure under shaft freezing wall-shaft wall interaction are deduced and analyzed.Finally,the theoretical calculation results are compared with measured field data,and some factors affecting freezing pressure are analyzed.The results show that the theoretical calculation results using fractional derivative model are basically consistent with the measured data,which can better simulate the“long-term creep”of viscoelastic frozen wall.Factors such as fractional order and shear modulus of frozen wall can significantly affect the freezing pressure.The research results enrich the freezing pressure analysis theory and can provide theoretical reference for the construction design of borehole wall.