Abstract:

A simplified analytical formula for vertical displacement calculation of crossed tunnels is proposed to analyze the deformation characteristics of crossed tunnels under surcharge loading and make a quick estimation based on Boussinesq Equations and Mindlin Equations considering interaction between soil and tunnel and that between tunnels. The programming solution is carried out by analyzing displacement coordination of soiltunnel and bending deformation of tunnels. The calculation results of the model are compared with those of 3D finite element under condition of surface surcharge loading, of which the results show 10% of calculation error, which indicates the rationality of the analytical solution method mentioned above. The results of parametric study of the influence of span and angle between crossed tunnels on vertical displacement show that: (1) The vertical displacement of the upper tunnel decreases; while the vertical displacement of the lower tunnel increases under the interaction between crossed tunnels. (2) The vertical displacement of the upper tunnel decreases; while the vertical displacement of the lower tunnel increases with the span or angle between crossed tunnels decrease; the maximum displacement of the upper tunnel reduces by 30% when the angle between crossed tunnels reduces from 90° to 0°; hence the interaction between crossed tunnels should be carefully considered when the angle between crossed tunnels is small.

Key words: crossed tunnels, vertical displacement, simplified calculation method, surface surcharge loading, analytical solution