Parametric analysis of horse-shoe hydraulic tunnels with respect to influential elements in concrete lining designing employing complex potential functions

Summary
In this study, horse-shoe tunnels have been analyzed with respect to the ratio of stiffness, relative thickness, and the ratio of in situ stress under the presence of earth pressure, and water pressure inside tunnels. Surrounding rock mass and concrete have been assumed as elastic materials, and complex potential functions along with conformal mapping have been used in the investigation. it was observed that an enhance in concrete stiffness resulted in increasing circumferential stress at key points. A critical value for lining thickness was obtained that for values smaller than which the circumferential stress exceedingly increased.
Tunnels are the main infrastructures widely used for transportation, water passage, and other purposes such as underground mining. Among various tunnels configurations, horse-shoe tunnels are more popular for their merit of suitable stress distribution in surrounding rock, which makes them capable of maintenance in a wide variety of rocks, from soft to hard ones.
Here a sensitivity analysis was conducted on the most important parameters for lining design of hydraulic horse-shoe tunnels. These parameters consist lining thickness, rock and concrete stiffness, initial in situ stress ratio and inside water pressure. To this aim, Muskhilishvili complex potential functions combined with conformal mapping were used. Concrete lining and the surrounding rock mass were assumed as linearly elastic materials, and the problem was tackled based on a plane strain scheme.
Methodology and Approaches
The impact of variation of input parameters were investigated on circumferential stress produced through lining and rock mass regions. Muskhilishvili complex potential functions along with conformal mapping were used in order to implement this investigation.
Results and It is demonstrated that increasing the ratio of stiffness will enhance circumferential stress at key points in the concrete, while reduce that at the roof in the rock mass. It is observed that for high ratio of stiffness when relative thickness is less than 0.04, the circumferential stress boosts, which should be evaded in design. An enhancement in the ratio of in situ stresses also raised circumferential stress at the roof, and reduced that at the wall. The investigations implied that the amount of the variations of circumferential stress corresponding to a ratio of in situ stress, where the ratio of stiffness is less than 1, were exceedingly lower than that when the ratio of stiffness is more than 1.