Evaluation of tunnel support structure reliability

Abstract

Variability has been treated most frequently within civil engineering by imposing factors of safety in classical deterministic analyses. These factors are intended to account for uncertainty in material properties and construction quality (geometry and materials) among other items. More recently, probabilistic methods have been adopted to separate the effects of the different sources of variability. Among such methods, the Load and Resistance Factor Design (LFRD) appears to be powerful and efficient. The paper presents an application of LFRD to evaluate the reliability of an urban, shallow, shotcrete supported tunnel. The construction has not been completed yet, and part of the tunnel has only the top heading excavated. The tunnel is 14 m wide and has 8 m overburden. The soil around the shotcrete support has been treated with jet grouting In order to consider the live loads of a railway at the surface, a 3-D elastoplastic finite element analysis was carried out. The classical factor of safety was obtained by the stress reduction technique. The probability of failure was evaluated for two different failure modes: one involving the strip footing for foundation of the shotcrete arch, and the other involving the structural capacity of shotcrete under axial force and bending moments. The strip footing was obtained by jet grouting ahead of the excavation face. Monte Carlo simulations were run to obtain the margin of safety and to evaluate the probability of failure according to LFRD principles for both failure modes. For the failure mode involving the shotcrete arch foundation, the simulations considered the variability of both strength parameters of the soil beneath the strip footing. By varying those parameters, the distribution of bearing capacity was obtained, and compared to the load on the footing obtained from the finite element analysis. In order to save computational efforts, a simplifying assumption was made, according to which the load was not affected by the soil strength variation. For the failure mode involving the shotcrete structural capacity, the analysis took into account the variability of shotcrete thickness and uniaxial compressive strength. Cores were taken from the shotcrete arch and the two parameters were obtained by direct measurement of length and by laboratory testing. Mean values and standard deviations for both parameters were also obtained. Moment-thrust interaction diagrams were generated in Monte Carlo simulations, taking into account the distributions of shotcrete thickness and strength. The same simplifying assumption was also made in this analysis, considering that the variations of shotcrete strength and thickness did not affect the internal forces. Pairs of values of bending moments and axial force obtained from the finite element analysis for all the support elements from the most critical cross-section were plotted in the same space of the moment-thrust interaction diagram. Points inside the diagram indicated elastic equilibrium. Points outside the interaction diagram would indicate that a plastic hinge could be formed, but were taken as indications of failure so as to be on the safe side. An upper limit for the probability of failure was calculated as the ratio of the number of the latter cases to the total number of cases analyzed. (A) This paper was presented at Safety in the underground space - Proceedings of the ITA-AITES 2006 World Tunnel Congress and the 32nd ITA General Assembly, Seoul, Korea, 22-27 April 2006. For the covering abstract see ITRD E129148. Reprinted with permission from Elsevier.