Reliability analysis of deep pressurized tunnels excavated in the rock mass with rheological behavior

Design of pressurized tunnels in rock masses which have a time -dependent behavior is a challenging task. On the one hand, time -dependent behavior not only imposes extra pressure to the tunnel lining but also leads the rock mass hydraulic conductivity to vary continuously; this aspect can exert another adding pressure to the lining. On the other hand, the uncertainty of the rock mass properties, which can differ from one point to another one, is another source of instability. Furthermore, the excavation method, i.e., poor blasting, which creates a weaker damaged zone around the tunnel, intensifies the complexity of the problem. This paper presents a probabilistic approach to investigate the influencing factors on the behavior of underwater tunnels. The behavior of the original and damaged rock masses is considered as visco-elastoplastic (using the CVISC model) in order to be able to consider its rheological character. Four parameters including Geological Strength Index (GSI), rock mass permeability, thickness of the damaged zone, and Kelvin shear modulus, which showed the most influencing effects in a developed sensitive analysis, were chosen as random variables. The Monte Carlo Method (MCM) was used to generate random values for these variables, adopting the normal distribution. Then, the response surface methodology (RSM) was used to intelligently lessen the number of generated values, and then to prepare datasets with the inclusion of all variables. The calculations were carried out for each provided dataset by a tridimensional numerical model (FLAC3D code) to obtain the tunnel wall displacement and the lining pressure, over time, as the results of the calculation. The RSM is again employed to obtain the relationships between inputs and output values and finally to have the probability function of the outputs. The results show that a right-skewed Gamma distribution governs the outputs: i.e. the distribution mass is concentrated on the left side of the probability distribution. Furthermore, when the water pressure is enhanced, the skewness of the probability distribution for the tunnel wall convergence and the lining pressure increases and decreases, respectively. Finally, it was possible to detect how the designing of pressurized tunnels using a deterministic approach, which adopts a unique value for the input parameters, may be misleading when the internal water pressures are high.