Frost heave mechanical model of concrete lining trapezoidal canal based on elastic foundation beam theory

Frost heaving damage is the main way for channel lining damage in cold regions. It is a basic work to build a rational mechanical model of frost heaving for the anti-freeze design of channel lining. Based on Winkler's assumption, this paper considers that the frost heave effect of the foundation soil of channel is equivalent to a set of springs which are independent of each other and are vertical or parallel to the lining board. The amount of frost heaving is reflected by the elongation of the springs. The frost heave force is reflected by the reaction force generated by the compression of the springs. The frost heave mechanics model of concrete lining plate of trapezoidal channel is established based on the elastic foundation beam theory. It abandons the boundary condition of simplifying the lining board to the simple support at both ends, and directly establishes the boundary condition according to the coordination of the force and deformation of the channel lining plate in the frost heaving process, and applies the calculation result of frost heaving amount of the SL23-2006 "Specification for Design of Anti-freeze of Canal Engineering". By analyzing the force characteristics during the frost heaving process of the channel lining plate, it is considered that the top of the slope lining plate will produce a certain frost heave displacement when the channel foundation soil is frost heaving. The frost heave at the end of the slope lining plate is restrained due to the bottom lining plate. Therefore, when the slope lining board is separately analyzed, it can be considered that the end of the slope lining plate is subjected to a pair of restraining reaction forces from the bottom plate. When the bottom lining plate is frost heave, the frost heaving at both ends of the bottom lining plate is restrained due to the two slope lining plate. Therefore, the two ends of the bottom lining are respectively subjected to a pair of restraining reaction forces from the slope lining plate. Applying the "short beam" theory of elastic foundation beams, the analytical expressions of frost heave amount, frost heave reaction force, bending moment and shearing force of the channel lining board after frost heaving are derived, and the calculation methods of tangential freezing force and axial force is given by the frost heave mechanical balance of trapezoidal channel lining board. Taking the trapezoidal channel of the main canal of Jinghui in Gansu Province as an example, the frost heave and frost heave reaction calculated by the model of this paper are compared with the previous experiment and numerical simulation, which the regularities of distribution is basically the same. Meanwhile, the overall average relative error of the frost heave amount obtained by this paper model is 4.72% compared with the results of the previous experiment, in which the rationality of the model is verified. The model of this paper applies the frost heave amount obtained from the SL23-2006 "Specification for Design of Anti-freeze of Canal Engineering", which is organically linked with the design specification, and provides a reference for the anti-freeze design of canal in cold regions.