Interval parameters and credibility of representative values of tensile and compression strength tests on rock

The interval parameters of rock tensile and compression strength to meet the strength of the limited laboratory tests and the characteristics of randomness and to reflect the range of features and the possibility of distribution are studied. Firstly, the concepts of the interval compression strength and the tensile strength are proposed. Secondly, based on the interval analysis, the blind data theory and laboratory practice, the solution method for the interval strength is proposed. Representative values of rock tensile and compression strength tests and their corresponding faith degrees are obtained using the theory of unascertained mathematics in favor of the project selection. Finally，the availability of the proposed methods is demonstrated by analying small and big samples. The small-sample results show that representative values of the rock strength and tensile strength by the proposed methods are smaller than those of the recommended methods by the conventional average values when the faith degree is 95%, and the faith degree of the conventional average values of rock strength is about 65%. It can be seen the representative conventional average values are dangerous. 320 rock specimens (big-sample) in a mine are divided into 64 groups, and each group has 5 rock specimens. The results show that 320 rock specimens follow the normal distributions. The average value of 238.17 MPa is regarded as the true value, and half of 64 conventional average values of strength are larger than the true value. It means that the warrant rate is 50%. 55 of 64 interval values of strength contain the true value, and the accuracy rate is 86%. The upper values from another 6 interval strengths are larger than the true value, which means that the warrant rate is 95% when the interval values of strength are representative values. It shows that the method is reasonable. The interval parameters of rock tensile and compression strength improve the rock strength parameters. It provides a new method to select rock strength parameters for conducting the reliability analysis, design and safety verification in actual engineering.