Analytical Solutions for Long Tunnels Under Arbitrary Dynamic Loadings

Abstract:

Assuming the long lined tunnel as an infinite homogeneous beam resting on a Pasternak foundation, the governing equation of the dynamic problem can be established based on EulerBernoulli beam theory. Integration transform and Residue theorem are applied to solve the differential equation, thus the analytical solutions of displacement, velocity, acceleration, bending moment, shear force for long lined tunnels subjected to arbitrary dynamic loads are obtained. The specified solutions for harmonic line loads, moving line loads and travelling loads are discussed and compared with the exiting solutions, and therefore, the validation of the presented generic form of solutions is verified. Taking travelling loads as an example, parametric analyses are performed to investigate the influence of the velocity and frequency of travelling loads and the shear modulus of foundation on the tunnel dynamic responses. The proposed solution is of value for seismic design of long line tunnel.

Key words:long lined tunnel; dynamic loads; longitudinal response; integration transform; analytical solution