The engineering background of the current application is the stability control of thick frozen shaft with non-uniform temperature. The heterogeneities induced by thermal gradient present the non-linear behavior, and that can not be obtained by the current test method or theories. The key scientific issue of the current application is aiming at the action mechanism of thermal gradient to the deformation fracture of frozen soils. In this application, we will take the heterogeneities induced by thermal gradient on as the basic object, and the emphasis will be put on the existing form of the heterogeneities and the evolution laws. The comprehensive research approaches including frozen hollow cylinder test with single radial thermal gradient, numerical simulation tests on the frozen hollow cylinder with combinatorial radial thermal gradients based on the 3D deformable distinct element method, physical simulation test on the frozen shaft (frozen hollow cylinder with combinatorial radial thermal gradients) ,and theoretical analysis will be all under consideration. In addition, the K0DCGF (K0 consolidation, freezing with thermal gradient under loading) method, distribution strain measurement sensors composed by carbon black and silicon rubber, and digital photography technologies will be adopted according to the distinguishing features of the object investigated. On the basis of above mentioned, we will then carry out the investigation on the basic characteristics and basic laws for the formation and variation of the cracked frozen structures with non-uniform temperature. Furthermore, both the local and total deformation and strength for the frozen hollow cylinder will be further studied. In the end, the responses of non-uniform deformation-local fracture- the overall instability of the frozen hollow cylinder to the thermal gradient will be obtained. The anticipated achievement will provide a scientific and fundamental support for the stability dynamic control of the frozen shaft in thick alluvium.