岩石の曲げ強さに関する統計学的研究

概要

論文の詳細を見る
One of the chief reasons why the bending strength is greater than the tensile strength in rocks, is that fractures can be caused on the parts of the rocks also where the tensile stresses are not maximum, by the effect of Griffith cracks distributed at random in a specimen. For the distribution of the strength of Griffith cracks, the present writer has adopted Weibull's distribution introduced by the other investigators, and because the two distributions are closely approximate unless the variation is too great, and the coefficient of uniformity m in Weibull's distribution can be related, by the use of Γ functions, to the coefficient of variation c. By applying the theory of the probability of minimum value to the strength of Griffith cracks in a specimen, the distribution of the bending and tensile strengths can be calculated. The both strengths accord with Weibull's distribution, and the ratio of the two strengths are given as the function of m. The experiments the writer carried on with Akiyoshi marble show that the bending and tensile strengths accord with the distribution by Weibull, and the ratio of the two strengths coincides with its theoretical value on a coefficient of confidence of 90%. Theoretically the coefficients of variation of the two strengths are equal, and it has been tested in the experiment also that those of the experimental values are equal.
社団法人日本材料学会の論文
1960-06-15