Structural analysis and optimum design for elastic foundation beam of tunnel in water-eroded groove

Structural scheme of elastic foundation beam for tunnel was introduced to span water-eroded groove,and the theory of Timoshenko beam on Winkler foundation was used to calculate the extreme internal forces,positions and deflections.The influences of different bearing lengths on moments and shear forces for elastic foundation beam were compared.Based on the optimum object of positive moment and negative moment being equal,the optimum bearing length was derived.The influences of foundation modulus of filling material and settlement on internal forces were studied.The results show that Euler beam theory under-estimates the reaction of foundation.The interface of the two different foundation mediums is the most dangerous position of shear for elastic foundation beam.The extreme negative moment occurs near the interface on bearing side.The extreme positive moment occurs in water-eroded groove.Settlements of filling materials change the internal forces of elastic foundation beam.For full hanging state,extreme positive moment and negative moment change 41.56 times and 37.52 times,respectively;extreme positive shear force and negative shear force change 32.67 times and 12.55 times,respectively.So this problem should be noticed during design and construction periods.