Analytical solution based on state-space method for cracked concrete pavement subjected to arbitrary concentrated loading

Abstract

• A new analytical solution is developed for pavement structures. • Cracks in the pavement structure and the horizontal friction are considered. • Solutions for the internal forces and deformations can be obtained efficiently. • The proposed solution allows for any crack positions and load distributions. Numerous studies have been conducted to determine the responses of pavement structures. However, general insufficiency and complex solution processes remain critical problems. Based on the state-space method and Euler–Bernoulli beam theory, this paper proposes a new analytical solution for the response of a pavement structure subjected to arbitrary loads. A joint model including tension–compression, shear, and bending springs that can reflect the stiffness degradation is introduced to simulate cracks in the pavement structure. In addition, an improved Winkler foundation model (considering both the horizontal friction between the beam and foundation soil as well as the vertical soil resistance) is used to simulate the subgrade properties. Analytical solutions for the deformations and internal forces of the pavement structure with cracks under arbitrary horizontal and vertical loads are obtained, and a corresponding MATLAB program is developed for the calculations. The performance of the proposed analytical solutions is verified using the finite element method. Furthermore, the effects of the bending stiffness, horizontal load, horizontal friction, ratio of the resistance coefficients of the horizontal and vertical springs, and crack position are discussed in detail. The results show that the horizontal braking force will cause rotations of the entire pavement structure, and the horizontal friction effect can effectively reduce the influence of the horizontal load on the deformation of the pavement structure. Cracks has a great effect on the deformation response of the pavement structure, which could not be ignored. Moreover, the proposed method exhibits high efficiency and generality for the analysis of pavement structures and can fully consider the effects of the aforementioned factors.