劈裂注浆可以有效改善土体的变形参数，大大降低土体在受力状态改变时的变形量，对劈裂注浆后复合土体的等效变形参数进行研究十分重要。在综合分析劈裂注浆扩散机制和工程应用实际的基础上，基于均质化理论提出了劈裂注浆后复合土体的三维单元体几何模型，按等效原则给出了浆-土体积及受力分配关系模型图；接着基于横向各向同性本构关系推导了模型的等效弹性模量和等效泊松比的解析解。然后采用有限元方法取得了模型特定条件下的等效弹性模量和等效泊松比，并与解析结果进行对比分析。最后把模型和相应的解析结果引入Flac3D岩土工程专业分析软件，结合一个热力隧道工程实例对隧道劈裂注浆后关键位置的沉降进行预测分析，并与实测值进行了对比。研究表明：对所提出的计算模型，解析计算与有限元方法计算结果吻合度较高，说明了解析结果的正确性；基于该模型及其解析结果得到的隧道开挖后的沉降预测值与实测值具有良好的一致性，说明所提出的模型和相应的解析计算方法具有一定的可靠性和实用性。

Fracturing grouting could effectively improve elastic deformation properties of soils, and thus the soil deformation induced by excavation will be greatly reduced, so it is important to study the equivalent elastic properties of the composite soils. By investigating the fracturing-grouting mechanism and some case histories comprehensively, a three-dimensional geometric model is firstly proposed for composite soils with fracturing grouting based on homogenization theory. A volume ratio and stress distribution diagram of grout-soil is developed following equivalent principle. Then the analytical solutions of the equivalent elastic modulus and equivalent Poisson’s ratio of the proposed model are derived based on transversely isotropic constitutive law. The same elastic parameters of this model for specific conditions are calculated by finite element method (FEM). At the same time, the FEM results are compared with the analytical solutions. The Flac3D is employed to predict the ground settlements of a heat-supplying tunnel using the proposed model and its analytical solutions. The predicted results are then compared with monitoring data. The study shows that: the analytical solutions of the proposed model highly agree with FEM results; the proposed model and its analytical solutions are reliable and valid for engineering practice.