考虑黏土结构性影响的柱孔卸荷收缩问题解析及数值验证

Analytical Solution for Cylindrical Cavity Contraction with Unloading in Clay Considering Soil Structure Effects and Its Numerical Validation

圆孔收缩理论是岩土开挖问题的主要分析方法之一,然而已有研究中大多未考虑土体的结构性影响。为此,采用结构性参数和结构损伤速率分别表征土体结构性强弱和损伤快慢,基于S-CLAY1S模型求解了不排水条件下各向异性天然结构性黏土中的圆柱孔卸荷收缩问题。首先推导了反映应力-应变关系的弹塑性刚度矩阵,进而联立硬化法则和塑性区大变形理论,得到了关于有效应力分量、各向异性分量和结构性参数的微分方程组,并结合边界条件进行了求解;同时编写了S-CLAY1S模型的显式积分算法,通过相应的有限元数值解验证了理论解的正确性。结果表明:土体结构性对圆孔卸荷收缩过程影响显著,结构损伤使得孔周有效应力减小和超孔隙水压力增大,该现象随着土体结构性增强变得更为明显;土体抗剪强度随其结构破坏而降低,土体表现出应变软化特征,分析认为是缩孔过程中土体结构破坏引起的应力释放所致。参数分析表明结构损伤速率越大,缩孔过程中土体结构损伤效应的影响越显著。研究结果可为隧道围岩压力计算、竖井收缩变形预估以及钻孔泥浆护壁压力预测等提供理论依据。

The cavity contraction theory is one of the most popular analytical methods for modeling excavations in rocks and soils.However,most cavity contraction solutions do not consider the structure of natural clay.By using the structural parameters and destructuring rate to represent the structural strength and removal rate of the soil structure,the undrained solution for cylindrical cavity contraction in anisotropic natural clay was derived based on the S-CLAY1S model.First,the elastoplastic stiffness matrix of the S-CLAY1S model was deduced.Then,combining the hardening laws and large strain theory in the plastic region,the differential equations of the effective stress components,anisotropic components,and structural parameters were formulated,and the initial value problem was solved according to the boundary conditions.The explicit integration of the S-CLAY1S model was developed,and the validity of the analytical solution was demonstrated through the corresponding numerical solution using the finite element method.The results showed that soil structure has a significant effect on the cavity contraction process.Because of the damaged soil structure,the effective stresses and excess pore pressure decreased and increased,respectively.This phenomenon is more pronounced for the soil with a stronger structure.When the shear strength of the soil decreased,the soil exhibited strain softening characteristics,which can be attributed to the stress release due to the soil structure damage.The parametric study showed that with the increase in the destructuring rate,the effects of structural damage also became more significant.The results provide a theoretical basis for calculating the ground pressure of tunnels,estimating the contraction deformation of shaft walls,and predicting the mud pressure of boreholes.