Sample statistics (mean, standard deviation, coefficient of variation, regression line slope and intercept, correlation coefficient) obtained from statistical analyses of a total of 371 tests for unconfined compressive strength and Young''s modulus performed on test cylinders having nominal diameters of 1, 2, 4, 6, 8 and 12 inches (2.5, 5, 10, 15, 20 and 30 cm) and height to diameter ratios of 1/2, 1, 1-1/2, and 2 are presented. Regression line equations for each diameter in the form of the long standing size effects equation C = C1(aD/L+b) are discussed. The quantity in parenthesis is viewed as an "end effects"; a decrease in C1 with diameter is viewed as a "size effect". The latter is attributed to heterogeneity. A consequence of heterogeneity is scatter in test data; variability in test results is therefore more than that associated with the usual differences in experimental procedure between samples. Repeated tests provide the statistical data necessary to quantify variability as well as to determine average values of strength and modulus. The consequences of variability will be a weakening of the pillar with respect to a homogeneous pillar of the same average strength.
The purpose of this paper is twofold: (1) to present the results of a statistical analysis of compressive strength and modulus data obtained from a series of laboratory tests performed on coal cylinders of different diameters and height to diameter ratios, and (2) to discuss some of the possible implications of such data for "size effects" and the design of production pillars in coal mines. As part of a recently completed experimental, analytical and field investigation of coal pillar strength 3, Hustrulid and Swanson have obtained paired observations of the unconfined compressive strength and Young''s modulus of 371 test cylinders of a Utah coal.