Lining support optimization design of a deep-buried tunnel in consideration of the broken rock zone support

Considering the broken rock zone support,tangential and radial stress component analytical solutions of each layer in full contact conditions are deduced in a deep circular tunnel based on the elastoplastic theory. Then an optimization objective function of circular concrete lining layers with different elastic moduli is constructed by choosing different failure criteria and different stress states of concrete and rock materials and by introducing the idea of functionally graded materials,that is,when the objective function is minimum,the most reasonable design is that the Ⅰ,Ⅱ and Ⅲ layer structures destroy at the same time. Finally,the elastic modulus and thickness of the lining is designed separately. The analysis of examples shows the following.(1) With the increase of surrounding rock stress,E₂/E₁ and E₂/E₃ both decrease. Under the same stress,there is always E₂/E₁ E₂/E₃,therefore it is suggested that the elastic modulus of the Ⅰ layer should be greater than the broken rock zone supporting's.(2) With the increase of surrounding rock stress,the thickness of the Ⅰ layer increases. Under the same stress,when E₂/E₁ E₂/E₃,the thickness of the Ⅰ layer is always less than that obtained when E₂/E₁ E₂/E₃,therefore the thicknesses of the Ⅰ and Ⅱ layers can be adjusted by changing the elastic moduli of the Ⅰ layer and the broken rock zone support.