Support design in tunnels is challenging if the uncertainty in surrounding rock mass is high. Traditional reliability based design approach accounts for this uncertainty by selecting lowest cost design whose reliability index exceeds a threshold value. This traditional design is highly sensitive to the variation in statistics of input parameters (noise parameters) and leads to over/under designed system if an over/under estimation of noise parameters is made. Accurate estimation of noise parameters requires testing of large number of rock samples in the laboratory, which is often difficult in many geotechnical projects. In this article, a new design approach - robust geotechnical design (RGD) methodology is applied for selection of tunnel support system which is least sensitive to noise parameters, cost effective and satisfies the safety requirements. Rock mass is assumed to follow elastic - perfectly plastic Mohr Coulomb constitutive model, representing weak rock mass. Two performance functions are used to evaluate reliability index of the support system which are based on maximum support capacity and tunnel wall convergence. A design is assumed to satisfy all safety requirements if reliability index obtained from each of these performance function exceeds a threshold value. Probability of failure (Pf) of a support design is evaluated for different possible values of noise parameters. The value of standard deviation (SD) of Pf is adopted to quantify the robustness of a design and finally a minimum distance algorithm is applied to obtain a most cost-effective design.


Selection of appropriate support for rock tunnel is of great importance for fulfilling stability and serviceability requirements of the tunnel. Traditional design approach involves deterministic analysis of the tunnel problem with single values rock mass parameters along with candidate design sets. The design with satisfies design code specific requirements and is economically cheaper is selected. This is basically a trial and error process. Existence of uncertainty in determining rock mass parameters is well stablished among practising engineers. Deterministic designs are generally not favoured when the expected amount of uncertainty is high. In such cases reliability-based design methodology is found useful. Several researchers have applied reliability-based design and stability assessment of rock tunnels (Li and Low, 2010). Reliability based methods treat input parameters as random variables and involves estimation of probability of failure of system (Pf). Several techniques such as First order reliability method (FORM), Second order reliability method (SORM), Monte Carlo simulations (MCS) and Point estimate methods (PEM) are adopted to estimate the Pf. Another approach of selecting design for a target reliability index of the tunnel problem is called reliability-based design optimisation and is applied by Lü et al. (2017). These approaches will be referred as traditional reliability-based methods in this paper.

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