Based on the vertical straight artificial freezing engineering in Northern Shaanxi, a three-dimensional (3D) physical simulation test system was developed, consisting of six parts, which are simulation box, shaft model, loading system, freezing system, external environment simulation system, and data acquisition system. The physical model and actual test results show that the 3D physical simulation test system is reasonable and reliable. The test model results show that the distance from the freezing pipe significantly affects the freezing wall temperature. For the case of four adjacent, two adjacent tangential freezing, and two adjacent axial freezing pipes, the cooling rates were 1.37, 2.79, and 1.96°C/h, respectively. The field measurement showed that the proximity to the freezing pipe increases the cooling rates. The cooling rates of points 1k#, 2k#, and 3k# were 25.61, 25.32, and 25.35 mm/d, respectively. The increment rates of vertical and horizontal freezing pressures with temperature were 8.78 and 2.97 kPa/°C, respectively. Furthermore, the freezing pressure time fitting formula was given. The calculated results of temperature and freezing pressure are consistent with the measured results, indicating the reasonability and reliability of the 3D physical simulation test scheme of the artificial freezing-inclined shaft in this work.

The bearing capacity of unsaturated soft soil foundations is affected by natural or artificial hard crust, due to the stress diffusion and closure effect. Based on the triple-shear unified solution of shear strength for unsaturated soil, the analytical solutions of critical edge load and critical load of unsaturated soft soil with hard crust are derived with the consideration of the lateral pressure coefficient K 0 ≠ 1 . The formulas are degraded and compared. Meanwhile, the influences of stress diffusion, increased load, matric suction, intermediate principal, and lateral pressure coefficient are conducted on the bearing capacity of unsaturated soft soil foundations with hard crust. The results show that the critical edge load and critical load increased, and the stress diffusion coefficient decreased with the increase of the ratio of elastic modulus between hard crust and soft soil. The bearing capacity of soft soil foundation increased with the consideration of the stress diffusion and closure effect of hard crust. The effect of matric suction is remarkable, and the critical edge load and critical load linearly increase with the increase of low matric suction and variate with the dual influence of high matric suction. The bearing capacity of unsaturated soft soil foundation is obviously higher than that of saturated soil. The critical edge load and critical load increased with the increase of intermediate principal stress and lateral pressure coefficient. The triple-shear unified solution for bearing capacity of unsaturated soft soil foundation with hard crust contains different solutions under various working conditions, which has important theoretical significance and widely engineering application.