The Elastic Multi-Layered System Calculation Method For Foundations Under Track

The traditional semi-empirical method based on the test data is used for the structural calculation and design of the foundation under track in China, due to the lack of systematic theoretical calculation method. That design method is lack of flexibility and pertinence. However, for the highway pavement and subgrade structures, there are many mature theories and design theory systems, especially for the asphalt pavement, the theory of Multi-layered System is used for mechanic calculation and the structure design. In addition, there are many similarities for highway pavement and railway foundation. Based on the considerations, in this paper the theory of Multi-layered System is applied to develop a new calculation method for railway foundation by using the stiffness matrix method, and also the Laplace transform and Fourier transform method are used to get the numerical calculation results. Furtermore, the Finite Element Method is applied to set up the calculation model for track structures, and the new calculation method developed in this paper for railway foundation is applied here to establish the whole model for railway system.Based on the above theoretical model, the computer program is compiled by using the mathematical software platform MATLAB. The case study is made for the dynamic and static mechanic analysis for ballasted track and ballastless track railways by using the program and the software ABAQUS. For the ballasted track, the compared results show that the maximum vertical displacement on the top of foundation is1.50mm and1.95mm, the maximum vertical stress on the top of foundation is0.34MPa and0.21MPa, the difference is very small. And for the ballastless track, the compared results show that the maximum vertical displacement on the top of foundation is0.40mm and1.20mm, the maximum vertical stress on the top of foundation is0.11MPa and0.26MPa, the difference is relatively larger, but the calculation results by using the program in this paper is more close to the real response.The dynamic analysis results show that the maximum vertical stress is about83.0kPa and the maximum vertical displacement is about0.58mm on the top of foundation in Qinshen railway, which are similar to the test results and calculation results showed in the references. The analysis results verify the reliability of the theoretical model developed in this paper.Finally, based on the theoretical models developed by using the Multi-Layer System method in this paper, the highway pavement structure design method and the research results of others are used for reference to set up the structure design method and its control index system for the railway foundation. Furtermore, the case study results show that the layer thickness of track bed should be more than20cm to meet the design indexes and the service life requirement of the whole railway, the design method and its index system is relatively reasonable and feasible for the railway foundation structure design.