Analytical solutions are often not available due to the complexity of engineering conditions. Circular tunnels are special cases which have analytical solutions and can be used for preliminary analysis of underground excavations and to guide the design. It is more logical to regard the properties or input data of geomaterials as random variables rather than constant values because of their uncertainties. In this paper reliability analysis of a circular tunnel in elastic-strain-softening rock mass subjected to a hydrostatic in situ stress field is conducted. Computational procedures for the response surface method and first-order reliability methods (RSM/FORM) are used in the reliability analyses of the elastic-strain-softening model. System reliability-based design of support pressure to achieve an overall target reliability index is carried out. The positive correlation between the compressive strength and the elastic modulus, are also investigated.
Convergence confinement method is widely used for underground excavations in rock masses which consists of three basic graphs: longitudinal deformation profile, support characteristic curve and ground reaction curve. This research focuses on the last one. Circular tunnels are special cases which have analytical solutions (Ogawa & Lo 1987; Duncan-Fama 1993; Wang 1996; Carranza-Torres & Fairhurst 1999; Sharan 2003, 2008; Park et al. 2008) and can be used for preliminary analysis of underground excavations and to guide the design although analytical solution is usually not available due to the complexity of engineering conditions. Hoek & Brown (1997) suggested different constitutive models for varied rock masses: elastic-brittle-plastic one for very good rock masses, elastic-strain-softening one for average rock masses and elastic-perfectly-plastic one for very poor quality soft rock masses. According to the survey, a great deal of rock masses belongs to the average classification. The extent of the plastic zone and free face displacement are important indexes for the design of the tunnel. Those investigations are commonly carried out by deterministic approaches which consider only the mean or average properties of the strength and deformation characteristics of the rock masses, which cannot explicitly reflect the uncertainty of the individual underlying parameters and their correlation structure. However, parametric uncertainty is inherent in geotechnical engineering, it is more logical to regard the properties or input data of geomaterials as random variables in reliability analysis rather than constant values in deterministic analysis, because of their uncertainties. Work done in this realm includes Mollon et al. 2009, Li & Low 2010, among others, using elastic-perfectly-plastic model. This paper deals with more complex constitutive model, namely elastic-strain-softening model. Further investigations are conducted in the present study.