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A new method for analyzing the fracture of concrete structures is proposed in which concrete is considered a granular assembly. Because concrete is a complex, extremely heterogeneous material, it is difficult to analyze it's failure properties by the Finite Element Method (FEM) in which concrete is considered a homogeneous, continuous medium. We have developed a Modified Distinct Element Method (MDEM) that can be applied to the problems of fracture of concrete structures. In the MDEM the respective major constituents of concrete, gravel and mortar, are represented as circular particle elements and nonlinear springs, called pore-springs. We have used the MDEM to simulate the dynamic fracture behavior of concrete structures. The numerical results obtained are in good agreement with the seismic damage recorded during past earthquakes.

Various liquefaction analyses have been made. No numerical liquefaction analysis in which sand is considered a non-continuous material, however, has yet been reported. In 1971, the Distinct Element Method (DEM) was introduced by Cundall. This method is a numerical simulation by which rock behavior is analyzed based on the assumption that individual rock elements satisfy the equation of motion. We developed a modified DEM that takes into account pore water pressure based on Darcy's law. We analyzed the liquefaction of saturated sand under seismic excitation. Excessive pore water pressure in the numerical results rose gradually due to the effect of shaking. This result agrees with results of past laboratory tests.

Usual Distinct Element Method (DEM), in which soil is represented as a system of numerous discrete particles, does not account for two factors; the continuity of the medium and wave propagation. The modified method, which is proposed in this paper, has another physical structure which presents the effect of the internal material between particles as pore water or clay. We simulated the two dimensional dynamic fracture of a cliff using this method. The fracture process is as follows; many small cracks occur widely then they form fracture lines. Results confirmed that this method can simulate the continuous and discontinuous medium.

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