The soil beneath buildings constructed in cold regions is affected by frost heave, causing the walls to crack and even the buildings to incline and collapse. Therefore, predicting the frost heave when subjected to overburden pressure is crucial for engineering buildings in cold areas. Utilizing the conservation equation of mass, Darcy's equation, and the assumption that the pore water pressure at the top of a frozen fringe, denoted as uw, during the quasi-steady state can be approximately estimated using the Clapeyron equation, a quasi-steady frost heave rate model considering the overburden pressure was proposed. This study considered the difference in pore water pressure within the frozen fringe, which causes water to move from the unfrozen zone to the ice lens, where it subsequently accumulates and freezes into ice. The pore water pressure at the bottom of the frozen fringe, denoted as uu, can be estimated using the soil water characteristic curve (SWCC). The thickness of the frozen fringe was determined using the freezing temperature, segregation temperature, and temperature gradient. The segregation temperature was determined using the two-point method. Additionally, the model suggested that, when uw = uu, the movement of water stopped, leading to the end of frost heave. To validate the proposed model, three existing frost-heaving experiments were analyzed. The findings demonstrated that the estimated rates of frost heave of the samples closely matched the experimental data. Additionally, external pressure delayed water migration. This study can offer theoretical support for building engineering in cold regions.

The principle of effective stress is widely recognized as the cornerstone of soil mechanics, with its application extending beyond soils to other porous materials such as rocks and concrete. In recent decades, there has been a significant surge in scientific research and engineering practice in cold regions, where the classical framework of effective stress in soil mechanics is frequently invoked. However, there is no consensus either on mathematical expressions or especially on the physical nature of effective stress in a soil when ice is involved. This paper starts from Terzaghi's principle of effective stress for saturated soils, and subsequently Bishop's work for unsaturated soils and the Clapeyron equation for phase change are introduced as the basis for further discussions. Focus is laid on a comprehensive analysis on formulas for effective stress with respect to cold regions geotechnical engineering. Two categories are classified, in which the effective stress is considered to be undertaken by soil skeleton only and by soil skeleton-ice system together, respectively. They may generate calculated results that can efficiently interpret experiments or observations, while both are rather speculative and faced with major challenges. Controversies on effective stress for unfrozen soils are analyzed with respect to cold regions geotechnical engineering. It is recognized hardly possible to develop a mechanism-based principle of effective stress based on the current understandings, while it is questionable to develop it based on that for unfrozen soils. Two potential approaches are suggested that might be applicable for cold regions geotechnical engineering.

Recently, there has been a revival in the development of models simulating coupled heat and water transport in cold regions. These models represent significant advances in our ability to simulate the sensitivity of permafrost environments to future climate change. However, there are considerable differences in model formulations arising from the diverse backgrounds of researchers and practitioners in this field. The variability in existing model formulations warrants a review and synthesis of the underlying theory to demonstrate the implicit assumptions and limitations of a particular approach. This contribution examines various forms of the Clapeyron equation, the relationship between the soil moisture curve and soil freezing curve, and processes for developing soil freezing curves and hydraulic conductivity models for partially frozen soils. Where applicable, results from recent laboratory tests are presented to demonstrate the validity of existing theoretical formulations. Identified variations in model formulations form the basis for briefly comparing and contrasting existing models. Several unresolved questions are addressed to highlight the need for further research in this rapidly expanding field. (C) 2013 Elsevier Ltd. All rights reserved.