A Solution of Subgrade Modulus for Response Displacement Method of Circular Underground Structures

In the seismic analysis and design of the underground structure, the response displacement method, as a pseudostatic method, has been widely adopted for its solid theoretical background, clear physical concept, and ease of implementation. The subgrade modulus is an essential parameter to the response displacement method, and a few approaches are available to determine its value. However, the existing methods neglect the interaction between the radial and tangential subgrade modulus and the influence of actual ground deformation, resulting in an inaccurate estimation. This study presents a solution to overcome these defects for the response displacement method adopted in the transverse seismic analysis of the shield tunnel with a circular cross section. First, the analytical solutions of subgrade modulus for ground deformation modes described by the Fourier series are derived based on the theory of elasticity. The ratio of the radial displacement to tangential displacement is introduced to create a link between the radial and tangential subgrade modulus. Based on the solutions of subgrade modulus for different ground deformation modes, the displacement fitting method is proposed to derive the subgrade modulus corresponding to the actual ground deformation. With this method, the subgrade modulus would adjust according to the ground displacement. Finally, a case study is conducted to illustrate the validity of the displacement fitting method.

Pasternak Model-Based Tunnel Segment Uplift Model of Subway Shield Tunnel during Construction

Segment uplift is a frequent problem during the construction of shield tunnels. The phenomenon of segment uplift in Xuzhou Metro Line 1 is investigated. The segment uplift magnitude in the shale layer is quite smaller than that in the clay layer. A tunnel segment uplift calculation model based on the Pasternak foundation beam model is proposed, which considers the hardening process of the grouted body with time. The finite difference method is adopted to calculate the magnitude of segment uplift during different tunnel construction stages, and a numerical solution of segment uplift on the longitudinal direction is obtained. The applicability of the numerical solution is studied by comparing with the field test results and parametric analyses are also performed to investigate the effects of different factors on segment uplifting. The results show that the coefficient of subgrade modulus, shear stiffness of the shear layer, and grout pressure all influence the segment uplifting of the tunnel. The influence of the coefficient of subgrade modulus and grout pressure on segment uplift is more significant.

Structural response and sensitivity analysis of granular and asphaltic overlayment track considering linear viscoelastic behavior of asphalt

This study investigated the structural response of granular and asphaltic overlayment of rail track considering the linear viscoelastic behavior of asphalt. The calculation of the tensile strains at the bottom of the asphalt layer, the compressive stresses at the top of the subgrade layer, and the service life of the granular and the asphaltic overlayment rail track were conducted using the KENTRACK software. Furthermore, the sensitivity analysis by changing different factors was studied in this paper. The results of this study indicate that the asphaltic overlayment rail track structure has a much longer predicted service life than the granular rail track. It was also shown that the sub-grade compressive stress is more sensitive to the change in subgrade modulus than the change in ballast-sub-ballast-asphalt layer thickness and the change in binder type, respectively. In addition, the asphalt tensile strain is more sensitive to the change in asphalt layer thickness than the change in subgrade modulus and the change in binder type, respectively. These findings also enhance our understanding that subgrade compressive stress and asphalt tensile strain in the asphaltic overlayment track are more sensitive to the change in asphalt layer thickness than the change in binder type.