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Abstract:The multi-piped freezing method is usually applied in artificial ground freezing (AGF) projects to fulfill special construction requirements, such as two-, three-, or four-piped freezing. Based on potential superposition theory, this paper gives analytical solutions to steady-state frozen temperature for two, three, and four freezing pipes with different temperatures and arranged at random. Specific solutions are derived for some particular arrangements, such as three freezing pipes in a linear arrangement with equal or unequal spacing, right and isosceles triangle arrangements, four freezing pipes in a linear arrangement with equal spacing, and rhombus and rectangle arrangements. A comparison between the analytical solutions and numerical thermal analysis shows that the analytical solutions are sufficiently precise. As a part of the theory of AGF, the analytical solutions of temperature fields for multi-piped freezing with arbitrary layouts and different temperatures of freezing pipes are approached for the first time.

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The reasonable determination of ultimate bearing capacity is crucial to an optimal design of shallow foundations. Soils surrounding shallow foundations are commonly located above the water table and are thus in an unsaturated state. The intermediate principal stress has an improving effect on the unsaturated soil strength. In this study, the ultimate bearing capacity formulation of strip foundations in unsaturated soils is presented by using Terzaghi’s theory. The unified shear strength equation of unsaturated soils under a plane strain condition is utilized to capture the intermediate principal stress effect. Furthermore, two profiles of matric suction are considered and a hyperbolic function of the friction angle related to matric suction (φb) is adopted to describe strength nonlinearity. The validity of this study is demonstrated by comparing it with model tests and a theoretical solution reported in the literature. Finally, parameter studies are conducted to investigate the effects of intermediate principal stress, matric suction, and base roughness on the ultimate bearing capacity of strip foundations. Besides, the effect of strength nonlinearity is discussed with two methods representing the angle φb.