Analytical solution to mapping rail deformation under bridge transverse deformation using energy variational principle

The track geometry is a critical factor that affects the running safety and riding comfort of trains moving on a high-speed railway bridge.This study addresses the mapping relationship between the track deformation and lateral deformations of bridges.Equilibrium equations and natural boundary conditions of the track-bridge system are established based on the energy variational principle,and an analytical solution is derived for the track deformation accounting for lateral bridge deformations.A five-span simply-supported bridge with continuous welded rail has been selected as the case study.The mapping rail deformations are compared to the finite element results,and both results agree well with each other,validating the analytical method proposed in this paper.The influence factors on the mapping rail deformation are further evaluated.Results show that the mapping rail deformation is consistent with the girder displacement at the area that is away from the girder ends when the flexural stiffness ratio between the track and the bridge girder is low.The interlayer stiffness has a significant effect on the mapping rail deformation when the track flexural stiffness is of a high value.

Joint Bearing Mechanism of Coal Pillar and Backfilling Body in Roadway Backfilling Mining Technology

In the traditional mining technology,the coal resources trapped beneath surface buildings,railways,and water bodies cannot be mined massively,thereby causing the lower coal recovery and dynamic disasters.In order to solve the aforementioned problems,the roadway backfilling mining technology is developed and the joint bearing mechanism of coal pillar and backfilling body is presented in this paper.The mechanical model of bearing system of coal pillar and backfilling body is established,by analyzing the basic characteristics of overlying strata deformation in roadway backfilling mining technology.According to the Ritz method in energy variation principle,the elastic solution expression of coal pillar deformation is deduced in roadway backfilling mining technology.Based on elastic-viscoelastic correspondence principle,combining with the burgers rheological constitutive model and Laplace transform theory,the viscoelastic solution expression of coal pillar deformation is obtained in roadway backfilling mining technology.By analyzing the compressive mechanical property of backfilling body,the time formula required for coal pillar and backfilling body to play the joint bearing function in roadway backfilling mining technology is obtained.The example analysis indicates that the time is 140 days.The results can be treated as an important basis for theoretical research and process design in roadway backfilling mining technology.

SOME PROBLEMS IN ELECTROSTRICTIVE AND MAGNETOSTRICTIVE MATERIALS

Some of the previous theories in the electrostrictive and magnetostrictive materials and their differences are discussed in this paper. A variational principle in the general thermodynamic sense is given and the governing equations can be derived from this principle. Illustrational examples are given.

A nonlinear rheological model of backfill material for retaining roadways and the analysis of its stability

The long-term stability of backfill material is the key to retaining roadways successfully. In order to study the rheological deformation of backfill material and its long-term stability, given the visco-elastoplastic properties of this material, we introduced a softening and a hardening function for a new nonlinear the- ological model with time-varying parameters. Based on this, we presented the instability condition of this model by using the principle of minimum potential energy. Combined with engineering practice, we cal- culated the urlstable time period of backfill material. The results show that the time of instability of the backfill material relate to the initial parameters of the material, ＂the coefficients decided by temperature and the ratio of the plastic zone of the backfill material. Based on the results of our analysis from the point of view of energy, we can quickly obtain the time of instability of this model from our graphical analysis. The time of instability of the backfill material obtained from our investigation coincides with an actual project.