• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.1A
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• pp.39-48
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• 2012

This study deals with numerical determination of stress intensity factors of adhesively patch-repaired plates with cracks at V-shaped or semicircular notches. The p-convergent anisoparametric model are considered and then three-dimensional virtual crack closure technique is presented using formulations of anisoparametric elements. In assumed displacement fields of an element, strain-displacement relations and three-dimensional constitutive equations are derived with three-dimensional hierarchical shape functions expanded from one-dimensional Lobatto functions. Transfinite mapping technique is used to represent a circular boundary. The present model provides accuracy and simplicity in terms of stress concentration factor, stress distribution, the number of degrees of freedom, and non-dimensional stress intensity factor as compared with previous works in literatures. Stress intensity factors obtained by the three-dimensional virtual crack closure technique are estimated with respect to the variation of width of finite plate, radius of notch root, angular inclination of V-shaped notch, and crack length.

• Tunnel and Underground Space
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• v.30 no.4
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• pp.404-416
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• 2020

An analytical procedure for calculating the failure load of a V-shaped rock notch under two-dimensional stress conditions was developed based on the slip-line plastic analysis method. The key idea utilized in the development is the fact that the α-line, one of the slip-lines, extends from the rock notch surface to the horizontal surface outside the notch when the rock around the notch is in the plastic state, and that there exists an invariant which is constant along the α-line. Since the stress boundary condition of the horizontal surface outside the rock notch is known, it is possible to calculate the normal and shear stresses acting on the rock notch surface by solving the invariant equation. The notch failure load exerted by the wedge was calculated using the calculated stress components for the notch surface. Rock notch failure analysis was performed by applying the developed analytical procedure. The analysis results show that the failure load of the rock notch increases with exponential nonlinearity as the angle of the notch and the friction of the notch surface increase. The analytical procedure developed in this study is expected to have applications to the study of fracture initiation in rocks through wedge-shaped notch formation, calculation of bearing capacity of the rock foundation, and stability analysis of rock slopes and circular tunnels.