Analytical calculation of steady seepage in unsaturated layered soils

The analytical calculations of unsaturated steady-state seepage in the widespread layered soils wewre relatively rare. Based on the Darcy seepage theorem and the continuity condition of soil layer interface, a mathematical model describing the steady seepage process of unsaturated layered soil was constructed. The analytical expressions of matric suction, effective saturation, and suction stress along the elevation for the same profile of layered soil were obtained by using the separation variable technique and mathematical induction. The analytical algorithm was validated based on the COMSOL numerical analysis platform, which enabled the analytical solution of the steady-state seepage process in unsaturated layered soils. Then, the influence of soil layer interface on seepage process was discussed and the sensitivity analysis of parameters was carried out. The analysis shows that: (1) Under the same infiltration conditions, the matric suction of sand at the same elevation is the highest, while that of clay is the lowest. The difference in surface seepage rate has the greatest impact on the distribution of effective saturation in the silt layer, while it has the smallest impact in the sand layer. (2) The suction stress in the clay layer increases almost linearly, while the suction stress in sand increases first and then decreases along the elevation. The presence of soil interface can affect the growth rate of matric suction along the elevation, leading to a sudden change in the distribution of effective saturation and suction stress along the elevation. (3) The smaller Gardner model parameter α, the greater the matric suction value at the same elevation, while the smaller the ks value of saturated soil, the slower the growth rate of matric suction. The smaller the values of ks and α, the slower the rate of effective saturation reduction. The smaller the value of α or the larger the value of ks, the greater the suction stress value at the surface. The research results can provide theoretical support for engineering geological problems such as slope stability.