The Analytical Solution Of The Winkele Beam Under The Uniform Distributed Load And Its Application In The Longitudinal Calculation Of The Sheild Tunnel

With subway being constructed in our country, more and more problems in the construction of subway are emerged continuously. Among the problems, longitudinal differential settlement of tunnel, and leading to water leakage of tunnel, crack of track-bed, crack between tunnel lings, etc. are endangering the normal operations of subway .Taking these problems above as a background and in the view of overcoming and reducing the longitudinal different settlement in the theory of the longitudinal calculation of shield tunnels, this article has launched the research work and obtained the following achievements:Through analyzing the present situation of the design in the soft soil shield tunnels, combining with the characteristics of the Winkler elastic foundation beam and according to the two conditions of the Winkler elastic foundation beam under a force that the values of shear is equal to the half value of the force and the displacement is equal to zero in the infinite place, this article firstly proposed a concept ofαthat was a ratio of bearing capacity of foundation soil on the area of uniform distributed load. Then according to the concept ofα, the analytical solution of the infinite beams bearing uniform distributed load on the Winkler foundation was deprived through the basic differential equation in the article directly. In order to prove existence ofα, relying on the mathematics significance of the analytical solution and the measured datum of the big chassis thick raft foundation, the existence of a had been elaborated in the article.In order to explain the correction of the analytical solution, a calculating example of applying to the numerical program BEAMK is proved. Then the results of applying to the analytical solution and BEAMK were contrasted and analyzed. The results of the analytical solution were different when a had been equal to different values. The results of the two methods were closer when the value ofαhad been equal to 0.8- 0.9. Because the results of the numerical solution BEAMK synthesizes the concept ofα, it is a unique solution. Then by back analysis of the results of BEAMK, Both were closest whenαwas equal to 0.888. Therefore, it was explained that above 80 percent of the load had been resisted by the ground under the area of the load and proved the rationality of the analytical solution which had been deprived in the article.Taking a subway as an example, this article applied the ANSYS procedure to simulate it. Then comparing the result with the analytical solution s and the BEAMK s, when the uniform distributed load of trains was acting on the shield tunnels, it was showed that the rule of the three results had been consistent and the results of ANSYS and the analytical solution were closer. the results of ANSYS and the analytical solution were closest whenαwas equal to 0.9. So it was concluded that the ground under the area of the loads acting had resisted 90 percent of the load. It was proved reasonably that the concept ofαthat was proposed and the analytical solution that was deprived in the article. The results of the article have the theoretical and applied value on the design and calculation of longitudinal shield tunnels.