Numerical Investigation of Closed-Form Solutions for Seismic Design of a Circular Tunnel Lining (by Quasi-Static Method)

In this paper, four known analytical methods including Wang (1993), Penzien (2000), Park et al. (2009), and Bobet (2010) were Evaluated based on seismic design of circular tunnel in Tehran Metro Line 6. For this purpose, a quasi-static numerical method was applied in the framework of finite difference method (FDM) under the same assumptions. In both numerical and analytical methods, to consider the nonlinear behavior of soil, linear equivalent properties of soil derived from ground analysis were incorporated in EERA software. obtained results shown that the Park’s analytical solution under various conditions of interaction between the tunnel lining and soil provides very close results to the of numerical modeling. Afterward, a comprehensive validation was performed to assess the impact of the rigidity of the surrounding ground and the maximum shear strain value. In this regard, several earthquake scenarios with different shear wave rates were used to achieve a wide range of flexibility ratio (F) and maximum shear strain. The results showed a significant difference between the results of Penzine’s and Bobet’s methods under the no-slip conditions and those of numerical analyses for a certain range of flexibility and shear strain ratios. In the final part of the paper, a quasi-static seismic numerical study was performed under realistic soil-structure interaction conditions to illustrate the importance of the actual interaction between the tunnel lining and surrounding soil. The results showed that the actual interaction conditions governing estimation of the axial force play a very important role. Also, it was found that Park’s solution, because of the ability to consider the slip at the interface provides results very close to those of the numerical modeling. In contrast, one of the serious limitations of the other analytical methods is their inability to simulate the slip interface between the tunnel lining and soil

New Development to Measure Mode I. Fracture Toughness in Rock

Tensile fracture toughness is one of the dominant characteristics of rocks that play an important role in fracture mechanics of rock structures. In spite of the substantial amount of work that has been conducted as suggested methods to determine the fracture toughness of rock in Mode I., research on new methods are still demanded. The compact tension (CT) specimen is widely used to determine the fracture toughness of metals and is a standard method in accordance with ASTM standard. To conduct similar direct tests in rock, preparation of rock specimen a difficult task and needs some special tools to create notched sample. To address these issues, experimental techniques based direct tensile apparatus have been developed. Developed experimental procedure involves the use of the specimens having a central hole and two notches or cracks at both inner side of proposed specimen. The stress intensity factor formula at the crack tip of a CT specimen can be availed through the literature. However a new expression of stress intensity factor is needed for the developed test in order to account geometry and loading configuration. To develop a new stress intensity factor expression, the numerical models of suggested method were worked out. The focus of the current work is on development of the experimental technique, which involves determining the optimum sample size and shape, loading procedure, fracture toughness for different rock types, and verification of suggested method based on CT test which has been carefully considered in this investigations