劈裂注浆复合土体平面等效弹性模型理论研究

Theoretical study of plane equivalent elastic model of composite soils with fracturing grouting

控制隧道开挖引起的土体沉降变形是劈裂注浆的主要目的之一,隧道在劈裂注浆后复合土体的等效弹性参数取值直接关系着隧道在劈裂注浆后沉降变形的预测精度。首先在对已有劈裂扩散模型研究的基础上,按面积等效原则提出了隧道劈裂注浆后复合土体的二维简化等效单元体模型,并基于均质化理论按变形协调原则推导了二维简化单元体模型的等效弹性参数解析解。然后采用有限元方法分别计算并分析了模型在简化前后的等效弹性参数;同时把二维简化等效单元体模型的有限元计算结果和解析计算结果也做了对比分析。最后基于解析结果分析了土体和浆液结石体各自的弹性参数以及浆液注入率对等效弹性参数的影响。结果表明:(1)按面积等效原则对模型进行简化处理的方法是可行的,可以按照简化模型进行弹性阶段的理论分析;(2)解析结果与有限元结果具有良好的一致性,说明了解析结果的合理性;(3)复合土体的等效弹性模量和等效泊松比主要受浆液注入率和浆液固结体本身模量的影响;浆液固结体的泊松比对等效弹性模量的影响几乎可以忽略。

Control of soil deformation induced by tunnelling is one of the major objectives of fracturing grouting. Prediction accuracy of tunnel deformation depends mainly on the equivalent elastic parameters of composite soils with fracture grouting. Firstly, according to equivalent grouting area and the existing model of fracturing grouting, a simplified 2D model for equivalent unit cell is developed for composite soils with fracturing grouting, and the analytical solutions of the equivalent elastic parameters of this model are derived based on deformation compatibility principle and homogenization theory. Secondly, finite element method is employed to calculate and analyze the equivalent elastic parameters of the simplified model and existing model, respectively; meanwhile, the comparisons are made between the finite element and analytical results of the simplified model. Lastly, the influence of grouting volume ratio, soil elastic parameters, and grouting concretion elastic parameters on equivalent elastic parameters are analyzed by means of the analytical solution. The results indicate： （1） the equivalent grouting area method is feasible, and the simplified model can be applied to theoretical analysis in the elastic deformation stage; （2） the analytical results are in good agreement with the finite element results, and hence the analytical results are reasonable; （3） the equivalent elastic modulus and equivalent Poisson＇s ratio of composite soils are mainly influenced by the grout volume ratio and modulus of grouting concretion body; the Poisson＇s ratio of grouting concretion has slight influence on the equivalent elastic modulus of composite soils.