Rutting is one of the main failure modes of asphalt pavement. It is very important to study the rutting deformation evolution for the anti-rutting design of pavement. Burgers model is adopted to describe the viscoelasticity of asphalt matrix, and the model parameters are determined according to the laboratory data. The geometric models of test-pieces are built with the help of the digital image processing method. The discrete element method is used to investigate the rutting depth variation of asphalt mixture with aggregate distribution, load and temperature. It is found that temperature has an evident effect on rutting deformation near the softening point of asphalt but only a slight effect when far away from the softening point. At lower temperature, the mixture behaves good integrity, the aggregate distribution has a tiny effect on local rutting deformation, and the rutting increment caused by overloading is unobvious. However, when the softening point is reached or exceeded, the integrity of the mixture declines distinctly, the aggregate distribution has a significant effect on local rutting deformation, and the rutting increment caused by overloading is pretty remarkable. Therefore, rutting deformation will increase markedly when overloading and high temperature are combined, which can pose serious potential hazards to asphalt pavement.
Fatigue fracture is a common failure type of engineering structures under load cycles. The crack existed in the structure is often a mixed-mode crack because the direction of the resultant load is not perpendicular to the crack surface. The mixed-mode crack does not grow along the direction of the initial crack surface, and it is different from that of mode I crack. Accurately predicting the behavior of crack propagation is of significance for crack growth rate evaluation. A common method is to simplify the broken crack as a straight line crack, which, however, will bring an accumulated error into the prediction of crack propagation while using the existing crack propagation criterion. The path calculated using that method deflects downwards, deviating from the real situation. In the present study, the cleavage angle is revised on the basis of analyzing the error caused by the common method, and the actual crack is simplified as an equivalent linear crack. Then, an equivalent modified model is proposed for describing the fatigue growth path of mixed-mode crack. The crack propagation of the mixed-mode crack can be predicted by incorporating this model into ABAQUS XFEM module. The proposed model is validated by the fatigue crack propagation experiments of 2024 aluminum alloy plate with inclined crack. It is found that the results predicted by the model are in agreement with the experimental results. First, the number of fatigue loading cycles computed using the proposed model is lower than that tested by experiments if the specimens are of the same initial crack length. The prediction using the present method is conservative. Second, the accuracy of the prediction is good if the cracked structure is mainly subjected to mode I load, while the maximum computed error is less than 10% if mode Ⅱ load is more significant.
According to the mechanical characteristics of cable-stayed bridge and based on the classical dynamic theories of cable and shallow arch as well as the dynamic equilibrium conditions at the joint between them, the in-plane free vibration theory of a cable-stayed bridge was established. Simultaneously, the geometric nonlinearity of shallow arch and cables were considered in the model in order to account for the effects of both deck’s camber and cable’s sag in the practical long-span cable-stayed bridges. First, the shallow arch was divided into several parts according to the coupled joints of cables and deck. Based on this point and using the Hamilton principle, the in-plane free vibration equations and boundary conditions of multiple cable-stayed shallow-arch system were derived. Then, applying the method of separation of variables, the linearized equations and boundary conditions governing the in-plane free vibration of the system were established. Next, taking the double-cable-stayed shallow-arch as an example, the in-plane eigenvalue problem was solved using the proposed theory and method in this paper. At the same time, a finite element model of the double-cable-stayed shallow-arch was established to verify the analytical solutions, and consistent results were obtained. Finally, the analysis of some key parameters of the CFRP bridges was conducted. It can be found that modulating the rise of arch in a certain range can only affect a modal frequency of the system, while others are rarely influenced. The results show that CFRP cables can improve fundamental dynamic properties of the system, i.e., the bridge with CFRP cables can overcome the deterioration caused by stress relaxation of cables. The content of the paper focuses on the in-plane free vibration of multiple cable-stayed shallow-arch system and enriches the study of the mechanical properties of cable-stayed bridge, which can be used to guide the design of this kind of bridge in practice.
