Unified Effective Stress Equation for Soil

Since the early 2000s, suction stress has been conceptualized as a unitary way to quantify effective stress in soil, i.e., effective stress equal to total stress minus suction stress. Suction stress is the part of effective stress purely due to soil-water interaction. When soil is saturated, suction stress is the pore water pressure, whereas when soil is unsaturated, suction stress is a characteristic function of soil called the suction stress characteristic curve (SSCC). Two physicochemical soil-water retention mechanisms are responsible for the SSCC: capillarity and adsorption. These two mechanisms are explicitly considered to develop a closed-form equation for the SSCC and effective stress. The SSCC data from the literature for a variety of soils ranging from clean sand to silty and clayey soils are used to validate the equation, indicating that the equation can well represent the data. Additional validation is achieved using experimental data of the apparent elastic modulus and the SSCC to predict the soil shrinkage curves. The equation can be reduced to Lu et al.'s previous closed-form equation for the SSCC when capillarity dominates soil-water retention, can be reduced to the Bishop's effective stress equation when capillarity is the sole soil-water retention mechanism, and can be reduced to the Terzaghi's classical effective stress equation when soil is saturated.