Cryostress in Frozen Soil. II: Closed-Form Equation for Effective Stress in Saturated Frozen Soil

Abstract

Recently, cryostress has been conceptualized as part of effective stress to describe the shear strength of soil under frozen conditions. Cryostress is defined as the interparticle stress due to the formation of ice grain and is a characteristic function of temperature. Three physicochemical soil–ice–liquid interaction mechanisms are responsible for the cryostress characteristic curve (CCC): capillarity, adsorption, and ice bonding. These three mechanisms are explicitly considered to develop a closed-form equation for the CCC and effective stress following the principles of energy equilibrium and mechanical equilibrium at the representative elementary volume of soil–water–ice system. A soil water characteristic curve–based soil-freezing characteristic curve is developed and used to describe unfrozen soil water content as a characteristic function of temperature. The CCC data from the literature for variety of soil ranging from clean sand to silty and clayey soils are used to validate the equation, indicating that the equation can well represent the shear strength behavior of frozen soil. The generality of the cryostress equation is demonstrated through its reduction to the Bishop’s form of effective stress for frozen soil when capillarity dominates soil–ice–liquid interaction and its further reduction to the Terzaghi’s classical effective stress equation when soil is completely unfrozen.