Development of theory and analysis method for localization and progressive failure

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A theory and an analysis method for cracking localization are presented. The method to judge the initiation of localization and to find the localized is solution is presented through consideration of spring-crack element models. It is shown that the problem is reduced to a minimization problem under constraint conditions. The theory is generalized and applied to problems of cracking localization in concrete. The proposed method can reproduce the localization of initially distributed cracks into a single crack in a four-point bending test. It is shown that to capture the ultimate strength of structures treatment of the localization of cracks or shear failure planes is necessary in many cases, and minimization problems under constraint conditions are the problems to be solved.A finite element with displacement discontinuities is developed and finite element analysis for cracking localization is carried out using the proposed theory of cracking localization. It is demonstrated that crack growth and localization in concrete dam under large earthquake excitation is captured by the present method.The progressive failure in soft rock is also considered, and an analysis method for progressive failure in soft rock is presented. Plane strain biaxial compression tests on artificial soft rock are carried out and the pre-peak constitutive relationship, the failure condition and the behavior of failure plane are modeled. Analysis of progressive failure in soft rock are carried out and results are compared with that of model tests with soft rock.