Abstract: The Load/Unload Response Ratio (LURR) method is proposed as a new approach to predict the failure of heterogeneous brittle materials, namely using the ratio between response rates occurred during the time periods of loading and unloading to describe the process of damage evolution quantitatively. In laboratory studies and inspection of real earthquake cases we have found that the LURR time series climb to an anomalously high peak and then decrease rapidly prior to the rupture of the rock specimens or the occurrence of earthquakes, which demonstrates that peak values of the LURR time series possess good significance of a catastrophic failure prediction. We also find the characteristic time of LURR peak abnormity appears regional features. Thusly, firstly, we simulate the process of damage evolution to failure of rock specimens under compression on the basis of a Chain-Network Model and also find the appearance of a peak value and fall of the LURR value successively before the macro-failure of specimens, which validates that LURR’s peak value is a good precursor for catastrophic failure from the viewpoint of numerical simulation again. Furthermore, LURR evolutions of heterogeneous brittle specimens with different heterogeneity are investigated emphatically, and the heterogeneity of specimens is achieved by introducing Weibull distribution as a probability distribution function. It finds that the time gaps T2 between the peak values and the ruptures are influenced by Weibull modulus m used to describe the heterogeneous extent of the specimens. T2 will be smaller if m value is larger, which means the time gap T2 is smaller if the homogeneity of specimens is higher and the rupture will be also more abruptly. The research in this paper will provide some clues to improve the time accuracy in the earthquake prediction by using the LURR method.