Statistical Evaluation of Material Strength

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The statistical strength variation of sand and concrete is investigated through the assemblage of statistical data bank of their compressive strength and the application of the bifurcation theory to the data.For concrete, a series of compression tests are conducted on cylindrical specimens to obtain an ensemble of stress versus strain curves. First gless beads of the size of 0.5mm, 1.0mm, and 2.5mm were used for sggregates to observe the influence of the size. Through the application of the bifurcation theory, it has been noted that bifurcation is predominant when the size is small, whereas fracture is predominant when large. Next the influence of the water cement ratio was investigated by varying its values by 26%, 35%, and 62% to note that bifurcation is predominant when its value is large.For sand, a set of 50 triaxial compression tests were conducted on cylindrical Toyoura sand speciments to obtain an ensemble of stress versus strain curves. Since the present theory is applicable only for the case where the bifurcation mode is unique, the photos and sketches of the specimens were taken during the tests to identify the bifurcation modes, and those curves were categorized in view of these modes. The curves categorized in this manner accurately followed the bifurcation theory ; this assesses the validity of the theory.