It is a fundamental and important topic to study the probability distribution of M-C strength parameters in reliability analysis of geotechnical engineering. The Legendre polynomial is introduced to infer the probability distribution functions of geotechnical shear strength parameters. With the conventional triaxial test data as the original information, an information basis of internal friction angle, friction coefficient f and cohesion c is constructed based on combination theory and linear regression analysis method. Subsequently, hypothesis testing of the probability distribution functions of sample data is conducted. The optional classical probability distribution types of M-C strength parameters are normal distribution, as verified by limited comparison method. The probability distribution functions of internal friction angle, friction coefficient and cohesion are deduced by Legendre orthogonal polynomial numerical approximation method. The K-S test method is used to compare the results of the presented method and normal distribution. It is shown that the K-S test results of probability distribution functions of M-C shear strength parameters deduced by Legendre polynomial are smaller than those of the normal distribution and can be more close to the actual probability distribution.

probability distribution function  /  M-C strength parameters  /  the Legendre polynomial  /  K-S test method  /  combination theory