Abstract
Based on the plastic upper bound theorem, a three-dimensional kinematically admissible velocity field is constructed for the collapse of the soil masses above a shallow tunnel. In this field, this paper considers the influences of the roof stratification, pore water pressure, ground overload, and support pressure. This study deduced the upper bound solutions of the weight of the collapsed soil masses and the corresponding collapse surfaces by utilizing the nonlinear failure criterion, associated flow rule, and variation principle. Furthermore, we verified the validity of the proposed method in this paper by comparing this research with the existing work and numerical simulation results. This study obtains the influence laws of varying parameters on the area and weight of the collapsed soil masses. The results reveal that the area and weight of the collapsed soil masses increase with increasing support pressure and soil cohesion, but decrease with increasing thickness of the upper soil layer, nonlinear coefficient, pore water pressure, and ground overload. Among them, the roof stratification, pore water pressure, soil cohesion, and nonlinear coefficient have a significant influence on tunnel collapse, which should be given special consideration in engineering design.
Highlights
With the rapid development of the world economy and the wide application of advanced technology, the transportation industry has developed rapidly in recent years. e tunnel, due to its superiority, is widely used in underground engineering such as subways, highways, railways, and municipal engineering
Most tunnels are classified as rock tunnels and soil tunnels according to the strata they pass through or deep tunnels and shallow tunnels according to the burial depth
When the tunnel burial depth H < Hc, the failure of the soil masses at the roof will penetrate the ground surface, which is the collapse mechanism proposed in this paper
Summary
With the rapid development of the world economy and the wide application of advanced technology, the transportation industry has developed rapidly in recent years. e tunnel, due to its superiority, is widely used in underground engineering such as subways, highways, railways, and municipal engineering. Fraldi et al [10] proposed a general characterization of tunnels depth based on the profundity of the excavation and on the variability of the rock mass parameters, and compared the stability of shallow tunnels, intermediate tunnels, and deep tunnels On this basis, Yang et al [11, 12] and Huang et al [13] focused on the circular and rectangular shallow tunnels and constructed the two-dimensional roof failure mechanisms. Yang et al [23,24,25] as well as Qin et al [26,27,28,29] once incorporated the nonhomogeneous and stratified characteristics of the strata into their analysis of the roof collapse, which may provide a good theoretical basis for this paper; their research is only applicable to deep tunnels. According to the nonlinear Mohr–Coulomb failure criterion, associated flow rule, and upper bound theorem, we deduce the analytical solutions of the weight of the collapsed soil masses and the corresponding collapse surfaces in the three-dimensional model. e research in this paper may provide theoretical guidance for tunnel support design and collapse warning in similar conditions
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