关键词: homotopy analysis, Melnikov function, chaos, sub-harmonic resonance

Abstract: In this paper, the author describes, and comments on the traditional thermal theory on artificial ground freezing, and points out its important significance and shortcomings. The frozen-wall is analysed by system analysis methods. According to matter levels, the frozen-wall is divided into three sub-systems: frozen colloid system, frozen soil system and frozen-wall system. They correspond to different characteristics. The frozen-wall system is a large open system with multi-levels and multi-aspects. The problems of stability of the system and its control are the key problems in the techniques of artificial ground freezing. Based on non-equilibrium thermodynamics and dissipative structure theory methods, the author discusses and reveals the problems of the formation and stability of the frozen-wall system and its thermodynamic nature, and proposes the thermodynamic entropy models of the system. The result is a great satisfaction.

Key words: homotopy analysis, Melnikov function, chaos, sub-harmonic resonance