Analytical Force and Deformation Analysis Model of an Asphalt Concrete Core Based on the Winkler Elastic Foundation Plate Theory

With regard to the antiseepage structure of rockfill dams, the force and deformation safety of an asphalt concrete core are of great concern. At present, the main methods for studying the force and deformation of the asphalt concrete core are numerical simulation methods, model test methods, and on-site monitoring methods. However, the simulation process of numerical simulation methods is relatively complex. It is difficult to select the appropriate material scale for model test methods, while on-site monitoring methods are found wanting on the issue of design and construction. Therefore, an analytical prediction model (APM) that offers important theoretical values and engineering application prospects to quickly and easily investigate the force and deformation of the asphalt concrete core is explored in this study. The deformation functions of the rectangular thin plate with three edges clamped and one edge free (CCCF rectangular thin plate) on the Winkler elastic foundation under the coaction of horizontal loads (hydrostatic pressure and active earth pressure) and vertical load (gravity) are solved via the small deflection bending theory of thin plates, the plane stress theory of thin plates, and the Rayleigh–Ritz method. Then, the stress functions of the CCCF rectangular thin plate are derived via the geometric and physical equations of the thin plate. The one-to-one mapping relationship between the CCCF rectangular thin plate and the asphalt concrete core is established. Furthermore, the deformation and stress of the CCCF rectangular thin plate are transformed into the trapezoid asphalt concrete core, the polyline asphalt concrete core, and the arbitrary asphalt concrete core via the one-to-one mapping relationship. The analytical force and deformation analysis model of the asphalt concrete core is established. Finally, the reliability of the APM is verified by the FEM. The APM is applied to analyze the force and deformation characteristics of the asphalt concrete core with 150 m height. The results show that the deformation laws of the two methods are basically consistent. The maximum difference values of settlement, axial deformation, and flexural deformation for the two methods are 3.1%, 0.8%, and 18.8%, respectively. The APM is found to be reliable. For asphalt concrete core rockfill dams with heights of 150 m or higher, the asphalt concrete core experiences large tensile stress and the risk of tensile failure. Therefore, improvement measures should be taken to reduce the tensile stress of the asphalt concrete core. The APM can be more convenient and easier to estimate the force and deformation of the asphalt concrete core than the FEM. The APM has expanded the calculation methods for the force and deformation of the asphalt concrete core.