Generalized Effective Stress Equation for Variably Saturated Frozen Soil

A unified effective stress equation for variably saturated frozen soil is proposed, theoretically verified, and experimentally evaluated. Cryostress, capillary suction stress, and adsorptive suction stress coexist when variably saturated soil is subject to freezing and thawing. Cryostress consists of three physically distinct forces at three interfaces: ice–ice bonding, ice–liquid capillary force, and ice–particle adsorptive force. Cryostress is a characteristic function of temperature and water content quantified by the cryostress characteristic curve. A generalized effective stress can be established by applying the principles of mechanical equilibrium and soil water potential equilibrium on the soil–water–ice–air representative element volume. A closed-form equation is developed where effective stress is equal to the total stress minus suction stress and cryostress. The generalized effective stress equation can be reduced to Bishop’s form of effective stress in saturated frozen soil when ice–particle adsorptive stress is neglected, to Lu and Likos’ suction stress-based effective stress in unfrozen unsaturated soil, and to Terzaghi’s effective stress in unfrozen saturated soil. The closed-form equation is experimentally evaluated using published shear strength test results for sandy soil, lean clay, and silty clay. The fitted parameters also show good consistency with independently measured soil water and soil freezing characteristic curves for lean clay. The proposed framework offers a practical and unified approach to describe the strength of variably saturated frozen soils.