Frost-heaving mechanical model of concrete lining trapezoidal canal based on two-parameter elastic foundation beam theory

Abstract: An elastic foundation beam theory can be used to properly and effectively deal with the interaction between soil and structure. The theory application has also been gradually promoted in the frost-heaving mechanical analysis of frozen soil engineering structures in recent years. However, the existing Winkler model cannot consider the continuity of frozen soil. It is very necessary to presuppose the distribution of tangential freezing force. In this study, the governing differential equations were presented for the normal and tangential directions. The Pasternak shear layer was also introduced to connect the adjacent soil springs and contact interface layer between the frozen soil and concrete lining plate. Then, the frost-heaving mechanical model of the trapezoidal concrete lining canal was established using the two-parameter Pasternak elastic frozen soil foundation. The model was effectively connected with the SL23-2006"Specification for Design of Anti-freeze of Canal Engineering". The frost-heaving mechanical analysis was applied to the concrete lining canals with the deep groundwater table. The computational accuracy of the frost-heaving mechanical model was improved significantly, where the shear layer was introduced to describe the interaction between the Winkler soil springs. The distribution of tangential freezing force was incorporated into the elastic foundation beam theory through the introduction of the contact interface layer. As such, there was no need for an improved model for the distribution of tangential freezing force. Taking the trapezoidal main canal of the Jinghui irrigation area in Gansu Province of China as the prototype, the improved model was applied to calculate the normal frost-heaving displacement of each point on the concrete lining plate. A comparison was then made on the Winkler model, the Finite Element Model (FEM) and test values. The comparative analysis indicated that there was consistent overall variation and tendency in the presented model, Winkler model, and FEM simulation. The critical test points were set on the concrete lining plates. The two-parameter elastic foundation beam model was much more consistent with the test values than those in the Winkler model and FEM. Furthermore, the two-parameter elastic foundation beam model was reduced to the Winkler model, when the shearing factor of frozen soil g was equal to 0. These results demonstrated the rationality and reliability of the presented model. The presented model was also applied to calculate the tangential displace and tangential freezing force of each section of the concrete lining plate. A parameter analysis was then carried out for the tangential contact stiffness. Among them, different tangential contact stiffness was set as the contact surface layer between concrete lining plates and frozen soil. Consequently, there was a nonlinear distribution in the section tangential displace and tangential freezing force along the concrete lining plates. A general decreasing trend was found in the tangential displace of each section with the increment of tangential contact stiffness. The distribution of tangential freezing force showed that "when one side is relatively large, then the other side is small". In addition, there was a linear and uniform distribution of tangential freezing force, when the tangential contact stiffness was smaller. By contrast, the more nonlinear and non-uniform distribution was observed with the increase of tangential contact stiffness. The finding can provide a strong reference to designing the frost heave damage resistance of canals.