Three-Dimensional Ground Loss Models And Complex Variable Calculation Method For Shallow Tunnel Excavations

ABSTRACT:Ground loss induced by tunnel excavation is the cause for ground deformation. Tunnel excavation in vicinity of existing structure foundations may result in ground loss patterns different from those due to tunnel excavation in green field. Exiting models of the ground loss are in general two-dimensional and for green field with no consideration of the effects of existing foundation loads. Besides, the complex variable solutions for the ground deformation induced by the ground loss need improvement. Concentrating on the problems above, the content and results of the research are as follows:(1) Three-dimensional ground loss models induced by circular cross-section tunnel excavations are proposed, using combinations of different two-dimensional transverse and longitudinal ground loss models synthesized from the literature.Two-dimensional transverse ground loss models are composed of uniform radial displacement-uε, ovalization displacement-uδ and vertical displacement-uv, which could be obtained from measured values or empirical values. Longitudinal ground loss models are determined by tunnel boundary displacement on the excavation face, the forward and rearward influenced distance from the excavation face.(2) A simplified model for foundation load is proposed. A theoretical approach is developed, using Mindlin’s displacement solution and its integration, for prediction of the three-dimensional ground loss induced by circular cross-section tunnel excavations in vicinity of existing foundation loads.Example of pile conducted indicates that the ground loss patterns are different from those under green field conditions, with the ground loss on the pile side increased, that the influence is relatively small when the pile tip is located laterally above or below the tunnel, but becomes most significant when the pile tip is located laterally near the tunnel center, and that the degree of influence increases with the increase of the pile load magnitude and with the decreases of the relative transverse and longitudinal distances of the pile shaft with respect to the tunnel face.(3) The boundary function of vertical displacement for the complex variable solution is given. And the complex variable solution is used for calculation of ground deformation induced by tunnel excavation in vicinity of foundation loads. Besides, the corresponding viscoelastic solutions are given by using the correspondence principle of the linear viscoelasticity theory.Example of tunnel excavation in green field conducted indicates that the values of complex variable solution are larger than the values of FEM solution in the case that the tunnel is relatively shallow. However, with the increasement of the depth, the trend reverses gradually.The boundary displacement of the tunnel excavated in vicinity of foundation loads can be fitted by using OLS.The fitted function are composed of symmetrical (uε,uδ,uv) and unsymmetrical(ur=u3cos θ, ur=u4sin2θ) displacements.The viscoelastic complex variable solutions are used to calculate the ground deformation induced by time. The resultant trend confirmed to reality.