Study On System Reliability Of Subway Tunnel Composite Lining

The design of tunnel support structure has great blindness due to many uncertain factors in the supporting structure design. In recent years, the application of reliability theory, the implementation of probability limit state design and the development of appropriate standards have become an inevitable trend. For the subway construction of composite lining system, the system reliability was analyzed based on the stochastic finite element method. Meanwhile, the influence law of composite lining structure system reliability was revealed and the corresponding reliability analysis theory was proposed. The theoretical foundation for the realization of composite lining structure reliability design was established.For tunnels buried in very shallow depth, the calculation method based on basic idea of pillar theory is used. For the method, the pressure acting on the tunnel support is equal to the full weight of overlying rock, and surrounding rock pressure is assumed to be only dependent on the tunnel buried depth, and independent of the tunnel span. When the buried depth is slightly larger, partial friction resistance is deducted considering the stress transfer of rock pillar. Ultimately, an expression for the overburden vertical load of subway tunnels constructed with mining method is proposed.Based on the stratum-structure model, the calculation method for composite lining structures was established. By comparing the main stress vector diagrams before and after the excavating of tunnel, pressure arch was confirmed to be existed in surrounding tunnel after excavating. The loads acting on the rear and upside of pressure arch were smoothly transferred to the stable rock at arch foot and surrounding pressure arch by the surrounding rock in pressure arch, and the support structure only with stood the load of surrounding rock in the range of pressure arch. Results of numerical simulation revealed that when tunnel was buried in shallow depth, the principal stress at the dome of pressure arch deflected after the excavating of tunnel, and there was no intersection between the horizontal stress and vertical stress quadratic curves, that is, no pressure arch was formed until the horizontal stress on the surface level had been the maximum principal stress. With the depth increasing, the intersection appeared between the horizontal stress and vertical stress quadratic curves, that is, a stable pressure arch was formed due to the deflection of quadratic curves. The buried depth of tunnel, corresponding to the first appearance of intersection, is the critical buried depth, and the depth at the intersection point is established as the calculation boundary of pressure arch. Meanwhile, influences of the span and buried depth of tunnel, as well as the physical and mechanical parameters of surrounding rock, on the critical buried depth and calculation boundary of pressure arch were investigated. Results indicated that the critical buried depth and calculation boundary of pressure arch were increased with the increase of tunnel span; and with the level of surrounding rock increasing, which represents the stability of surrounding rock is gradually weaken, the critical buried depth and calculation boundary were also increased. Based on the theory of nonlinear multivariate regression analysis, both critical buried depth and calculation boundary of pressure arch were fitted as a function of the level of the surrounding rock and the span of tunnel.A calculation model for composite lining with load acting on the stratum was proposed by comparing the two calculation methods:load-structure model and stratum-structure model. Comparison of results predicted with the proposed model and load-structure model revealed that the internal force predicted with the proposed model was smaller than that with load-structure model. The reason for this result is the interaction between the surrounding rock and supporting structure is simulated with spring supports in load-structure model, while this interaction is considered more accurately in the proposed model. For the proposed model, initial supports are treated as the main load-bearing structure, in which the development of force is similar to the actual situation. Therefore, the calculation model proposed in this paper conforms to the basic idea of composite lining well.The subway tunnel composite lining section was analyzed with Monte carlo stochastic finite method. Analytical results indicated that sampling about 50,000 times could get more reliable result in the statistic characteristics analysis of action effects. So, sampling with 50,000 times was used to model random variables. From the gram of action effects, it can be seen that the action effects of initial support and secondary lining approximately follow a normal distribution, so in the reliability analysis, action effects were assumed to submit normal distribution. By investigating the influences of basic random variables on action effects, it was concluded that for load-structure model, stratum load parameters, such as friction angle and cohesion, were the most important factor, followed by the elastic modulus of material and the thickness of structure, while for the model proposed in this paper, the elastic modulus of lining material and the thickness of structure were the most important factor.According to the features of subway tunnel, limit state equation for reinforced concrete support structures was derived, and the performance functions corresponding to various circumstances were divided. The reliability analyses of initial support and secondary lining in composite lining tunnels with load-structure model and the proposed model, was conducted for two conditions:secondary lining bearing load only; initial support and secondary lining bearing load together. Analysis results indicated that the reliabilities of initial support and secondary lining with the proposed model were higher than these with load-structure model.The reliability of subway tunnel structure is an important measure of the overall security of composite lining section. Traditional reliability analysis method of structural system relies on the branch path of structural failure and the bounding technique, while subway tunnel composite lining structure is a statically indeterminate structure with high statically indeterminate number. For the reliability analysis of composite lining structure, lining is usually divided into several sections, and there liability of entire lining is influenced by each section. Due to the different positions and force conditions of different sections, the reliability situation of each section is different. So, it is hard to recognize the main failure mode and difficult to calculate the failure probability of structure system. Stochastic elastic modulus reduction method, which are developed by combining elastic modulus reduction method and stochastic finite element method, were used for the reliability of subway tunnel structure. According to the bending moment diagram and the bending failure form of support, the tunnel lining was divided into several sub-systems. Every sub-system was composed of several sections. The reliable indicator of critical section in every sub-system was regarded as the representative value of the sub-system, which was used to judge the convergence in iterative process. The stochastic elastic modulus reduction method proposed in this paper, was used for the reliability analyses of initial support and secondary lining in composite lining tunnels with load-structure model and the proposed model. And also two conditions were considered:secondary lining bearing load only; initial support and secondary lining bearing load together. Results revealed that the reliabilities of initial support and secondary lining were higher than that with 'critical section'.