Statical Calculation of Curved Wall for the Horseshoe Shaped Tunnel Lining

The behavior of a curved wall under earth pressures for a horseshoe shaped tunnel lining is considered to be closely related to the beha vior of a vertical beam with variable flexural sti-"ness on an elastic foundation. In stress analysis an approximate method which divides the axis of the tunnel lining into small finite lengths and replaces the integrals by summation is usually adopted. this method is extremely complicated and tedious. However the variations of the moment of inertia from point to point along the wall axis can be expressed by a power function inversely .eith the distance from the ll )ottom and the analytical method can still used. The equations for the calculation of deflection, rotation, bending moment, shearing urce, and soil reaction of the curved wall are derived in nondimensional forms in this paper.