Dimensional analysis of numerical solution of the rigid ice model frost heave with hints on how to implement the solution in Matlab

Each year, frost action in the ground causes very costly problems in various constructions like highways, airport pavements, railways, pipelines and building foundations in the urban cold regions of the world. This thesis contains a survey of the rigid ice model, which is the most complete model of frost heave from a microscopic and physical point of view. The physical foundations of the model are explained and used in a derivation of the mathematical model. In contrast to earlier texts on this subject, we have translated the mathematical model to dimensionless variables and documented in much more detail how to solve it using a finite element method. (The reason for this is that the model is more accessible if not everyone has to ``reinvent the wheel''.) The resulting equations are presented in full detail and some of the computations are done in Maple, to simplify future changes. We also outline how to write a Matlab program for implementation of the rigid ice model. [1] and [2] give some further advice on computational details needed in a complete program. [1] Kevin O'Neill and Robert D. Miller Exploration of a rigid ice model of frost heave. Water Resourses Research, 21(3):281-296, March 1985. [2] Daichao Sheng. THERMODYNAMICS OF FREEZING SOILS - Theory and application. Doctoral thesis 1994:141d, Luleå University of Technology - SE 971 87 Luleå, Sweden, February 1994.Validerat; 20101217 (root