Displacement-Based Estimation of the Best Time for Secondary Lining Construction Using Grey Model GM (1,1)

Abstract

Large deformation or collapse often occurs in tunnels due to the high ground stress and rock rheology. When it cannot be effectively curbed by primary support, the secondary lining construction at a reasonable time comes to be particularly important in maintaining the stability of surrounding rock. In this paper, an efficient approach to estimating the best time for secondary lining construction in circular tunnels is presented based on Grey Prediction Model GM (1,1). Taking the tunnel in Hunan Province as an example, according to the classic rock-support interaction model, the limit displacement of tunnel roof is determined by investigating the stress–strain relationship of the surrounding rock in the framework of elastic–plastic theory. Subsequently, the GM (1,1) is employed and modified by optimizing the weight coefficient of background value μ and boundary condition D to predict the time sequence of the displacement of tunnel roof. Accordingly the best time for secondary lining construction is reasonably predicted. The results show that the greater μ is, the higher the model precision will be. The dispersion of the predicted results can be significantly reduced with the optimized D. The predicted displacement of tunnel roof reaches 55.840 mm in the 23rd observation period while the theoretical limit displacement of surrounding rock is 55.33 mm. Hereby, it is suggested that the secondary lining construction should be completed just before the 23rd observation period. The biggest advantage of the proposed approach is that it can be efficiently performed with resort to less parameters, and proves to be practical and feasible in tunnel design and construction.