The Riemann problems for two-dimensional zero-pressure gas dynamics are solved completely when the initial data take three constant states having discontinuities on x, y-positive and x-negative axes. With the help of characteristic analysis, by studying interactions among delta-shocks, vacuums and contact discontinuities, the Riemann solutions constructed exhibit nine different explicit configurations. The Mach-reflection-like configurations appear in some solutions.

Continuous welded rail (CWR) has been widely applied to the Chinese high-speed railways. It is interesting to reduce the effect of rail longitudinal force on the long-span cable-stayed bridges. Taking the pile-soil interaction into account, the finite element model of CWR on the long-span cable-stayed bridge is established based on the bridge-track interaction theory. The rail longitudinal force can be reduced and the track stability can be improved significantly by installing Rail Expansion Joint (REJ). The layout scheme of REJ plays a controlling role on designing CWR on bridges. Results show that the unidirectional REJ should be laid on both ends of the long-span cable-stayed bridge. Switch rails of REJ are set up on the main beam, stock rails are laid on the simply supported beams and crossing over beam joints, and several-meter long small resistance fasteners need to be laid on the sides of stock rails to reduce the fixed pier longitudinal force near the main beam. The range of REJ laid on cable-stayed bridge is mainly determined by temperature, rail breaking, and seismic condition; the bending and braking loads have little influence on it. Multiple field tests are carried out to prove the validity of the numerical model and the design methodology.

In order to ensure driving safety and comfort, it is necessary to figure out the complex interaction between continuous welded rail (CWR) and suspension bridges for high-speed railway. A spatial finite element model for a 1092 m main span suspension bridge was established based on the bridge-track interaction theory. A specific correction method was put forward to keep the rail in a zero-stress state when just laid. Three rail expansion joint (REJ) layout schemes were proposed according to practical engineering experience. Both static and dynamic analysis methods were used to evaluate the feasibility of these schemes. The results show that the REJ should be laid at the position with a distance away from the primary beam end, and the beam with more substantial integral stiffness should be preferentially selected. For the recommended scheme, the REJ expansion reaches more than 380 mm under expansion load. The factors affecting the REJ expansion from major to minor are temperature, earthquake, rail fracture, braking, and bending load. The superposition effect of the above factors is suggested to be considered in the selection of REJ range.