The objective of this study is to propose an alternative way for the probabilistic structural design of tunnel supports in combination with a deterministic numerical analysis code, FLAC2D. We proposed an approach for linking a point estimate method to the FLAC2D solver and developed a software program, called TunnelRA, which facilitates the probabilistic reliability assessment of tunnel supports. The validity of the present approach was investigated based on a lined-circular tunnel problem with an analytical solution and was demonstrated in the accurate estimation of the statistical moments of the performance functions related to the lined-tunnel. Additionally, we applied the present approach to the structural design of a steel liner which is installed in a pressurized tunnel for storing compressed natural gas at a pressure of 15 MPa. In this application, we investigated the probability of failure for the steel liner by varying the liner’s strength and thickness, and provided information for decision making in structural design. The results of the present work demonstrated that the present numerical approach could be used for designing tunnel supports and for making relevant decisions in a quantitative manner.


Most of geotechnical parameters, such as the mechanical properties of soils and rocks, are uncertain. The uncertainties should be properly taken into account in geotechnical and structural designs. Probabilistic approaches are more useful in dealing with the uncertainties than conventional deterministic approaches in which the geotechnical parameters are conservatively assigned as single-fixed values determined by a designer’s engineering judgment. Probabilistic approaches quantify the geotechnical uncertainties by statistical probability distributions. As a result, the reliability of structures can be quantitatively assessed in terms of the probability of failure in a limit-state. Regarding the probabilistic analysis of tunnel supports, there have been several researches such as Laso et al. [1], Li & Low [2], and Oreste [3]. For the probabilistic stability evaluation of tunnel supports, Laso et al. [1] and Li & Low [2] used a ground-support interaction diagram for a circular excavated tunnel for which analytical solutions are available, but it is not possible to apply their approaches to non-circular tunnels. Oreste [3] suggested a probabilistic approach for the reliability assessment of tunnel supports by using a hyperstatic reaction method. However, as indicated in his study, the hyperstatic reaction method has such limitations that the active loads which are applied to tunnel supports should be exactly evaluated and the normal and shear stiffness values between the surrounding ground and tunnel supports should be defined in advance. The previous studies have focused on the probability-based reliability assessment of tunnel supports using analytical solutions that can be applicable only to limited conditions, rather than combined with numerical methods that are more useful for solving a variety of underground problems with various shapes and analysis conditions.

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