Evaluation method of rock brittleness based on statistical constitutive relations for rock damage

Brittleness is an important feature of rock and is related to many mechanical behavior of rock. An accurate evaluation of rock brittleness lays an analytical foundation of drilling and hydraulic fracturing. At present, there are several evaluation methods of rock brittleness, but none of them has taken the evolution of internal damage into consideration during the loading process, and thus will not effectively indicate the influence of damage on brittleness during loading. We have conducted a series of uni-axial compressive tests on coal rock, shale and tight sand, and have obtained the stress-strain curves of different types of rock. Then we have established the damage constitutive model of micro damage for each type of rock based on power function distribution, Weibull distribution and Gaussian distribution. We have proposed an evaluation method of brittleness index based on energy method, established the evaluation model of brittleness based on three types of damage constitutive relations, and have finally analyzed the effects of the damage variable of peak strain of different rocks on brittleness. The results of this paper have proved that the damage constitutive model of micro damage can effectively describe the stress strain curves of different rocks before the peak strength. On the other hand, it indicates that the increase of damage variable of peak strain will undermine rock brittleness, and the relation between brittleness and damage variable of peak strain obeys different rules of the three types of damage constitutive models damage constitutive model based on Gaussian distribution benefits evaluation of brittleness of different types of rock, and based on power function distribution makes for the same types of rock. This paper has proposed a fresh perspective of studying brittleness, the results of which will improve the present evaluation methods and enrich our understanding of rock brittleness.