Research on unsteady creep empirical model of rocks based on statistical laws

In view of the shortcomings of most rock unsteady creep models under conventional triaxial compression conditions, such as complex functions, numerous parameters and difficulty in determining, based on 31 sets of unsteady creep test data of different types of rocks, the strain functions and time functions were constructed, and the linear relationship between the two was statistically analyzed. Based on this, a new empirical model for unsteady creep of rocks was established, using creep test data of shale, marble, mudstone and sandy shale at different stress levels to verify the accuracy and rationality of the model. The results show that the empirical model function of rock unsteady creep based on statistical laws is a unified expression containing only four model parameters. Its creep curve is approximately an inverse S-shape, and the creep velocity curve is approximately a positive U-shape, both of which are consistent with the actual rock creep laws. The creep test results of shale, marble, mudstone, and sandy shale at different stress levels are highly consistent with the theoretical curve of the empirical model. Its rationality and accuracy have been verified. The model can not only describe instantaneous elastic strain, attenuation creep, and constant velocity creep, but also describe accelerated creep with particularly obvious nonlinear characteristics.