Analytical Solution for Circular Tunnel under Obliquely Incident P Waves considering Different Contact Conditions

An analytical solution for the seismic-induced thrust and moment of the circular tunnel in half-space under obliquely incident P waves is developed in this study, which is the superposition of the solution for deep tunnels under incident and reflected P waves and the reflected SV waves. To consider tangential contact stiffness at the ground-tunnel interface, a spring-type stiffness coefficient is introduced into the force-displacement relationship. Moreover, the tunnel lining is treated as the thick-wall cylinder, providing more precise forecasts than beam or shell models used in previous analytical solution, especially for tunnels with thick lining. The reliability of the proposed analytical solution is assessed by comparing with the dynamic numerical results. Based on the proposed analytical solution, parametrical studies are conducted to investigate the effect of some critical factors on the tunnel’s seismic response, including the incident angles, the tangential contact stiffness at the ground-tunnel interface, and the relative stiffness between the ground and the tunnel. The results demonstrate that the proposed analytical solution performs well and can be adopted to predict the internal forces of circular tunnels under obliquely incident P waves in seismic design.

Fatigue life analysis of wheel-rail contacts at railway turnouts using finite element modelling approach.

The article deals with wheel-rail contact analysis at railway turnout using a finite element modelling approach. The focus is understanding the wheel-rail contact problems and finding the means of reducing these problems at railway turnouts. The main aim of the work reported in this article is to analyse fatigue life and simulate the wheel-rail contact problems for a repeated wheel loading cycle by considering the effect of normal and tangential contact force impact under different vehicle loading conditions. The study investigates the impact of tangential contact force generated due to different-angled shapes of the turnout and aims to reveal how it affects the life of contacting surfaces. The obtained results show that the maximum von-Mises equivalent alternating stress, maximal fatigue sensitivity, and maximum hysteresis loop stresses were observed under tangential contact force. These maximum stresses and hysteresis loops are responsible for rolling contact fatigue damage, and excessive deformation of the wheel-rail contact surface. At a constant rotational velocity, the tangential contact force has a significant impact on the fatigue life cycle and wheel-rail material subjected to fatigue damage at lower cycles compared to the normal contact force. The finite element modelling analysis result indicated that the contact damages and structural integrity of the wheel-rail contact surface are highly dependent on contact force type and can be affected by the track geometry parameters.

Analysis of Rail Corrugation Characteristics on High-Speed Rail Based on Transient Finite Element Method

By using the transient finite element method, a three-dimensional wheelset-track coupled rolling contact model for high-speed rail is established, and the rationality and effectiveness of the model are verified by field measurements. Next, the wheel-rail contact stress states and relative slip characteristics are calculated and analyzed to reveal the cause of inner rail corrugation. Then, the vertical vibration acceleration of the rail/wheel is taken as the output variable to study the dynamic responses of the wheelset-track system. Finally, the parameter sensitivity analysis is carried out. The results show that the maximum normal/tangential contact stress between the inner wheel and inner rail is greater than that between outer wheel and outer rail due to the unbalanced load of inner rail caused by the excess superelevation of track structure, which indicates that the unbalanced load of the inner rail may aggravate the development of rail wear, and the rationality of the model established in this paper is verified. The wheel-rail relative slip region on the inner rail side appears periodically, and the distance between the two adjacent slip regions is close to the characteristic wavelength of the measured inner rail corrugation, which illustrates that the periodic variation of slip regions on the inner rail surface plays an important role in the formation of rail corrugation, and the validity of the model is verified. The periodic distribution of wheel-rail relative slip regions on the outer rail surface is not obvious, demonstrating that the outer rail tends to form uniform wear, which is consistent with the fact that the outer rail corrugation is slight in the measured section. The wheelset-track system has been in the process of unstable continuous oscillation in the analysis interval, combined with the analysis results of the wheel-rail relative slip characteristics, it can be concluded that the unstable self-excited vibration of wheelset-track system under the condition of tangential contact force reaching saturation is the main cause of rail corrugation. The dominant characteristic frequencies of vertical vibration accelerations of rail and wheel are all 561 Hz, the corresponding characteristic wavelength (148 mm) is close to the distance (150 mm) between the calculated adjacent slip regions, and is also close to the characteristic wavelengths (125 mm and 160 mm) of inner rail corrugation, which shows that the resonance phenomenon occurs in the wheelset-track system at the above frequency, thus leading to the increase of dynamic responses of wheelset-track system. The fastener vertical stiffness and wheel-rail coefficient of friction have significant effect on the development of rail corrugation, and the running speed determines the occurrence probability of inner/outer rail corrugation by affecting the track superelevation state.

Micromechanism of the Breakage of Two Spherical Gypsum Particles under Normal–Tangential Contact Conditions

Contact breakage of particles makes a large difference in the strength of coarse-grained soils, and exploring the characteristics within the process of the breakage is of great significance. Ignoring the influence of particle shape, the micromechanism of two spherical particles breaking under normal–tangential contact conditions was investigated theoretically and experimentally. Through theoretical analysis, the breakage form, the shape and size of the conical core, and the relationship between the normal and tangential forces at crushing were predicted. Particle contact tests of two gypsum spheres were carried out, in which the breakage forms, features of the conical cores and the normal and tangential forces at crushing were recorded for comparison with the predicted values. The test results and the theoretical predictions showed good agreement. Both the analysis and test demonstrate that the presence of tangential forces causes the conical core to assume the shape of an oblique cone, and the breakage form to change. Moreover, with increasing normal contact force, the tangential force needed for crushing increases gradually first and then decreases suddenly.