An Innovative Combination of Scratch Test and Weibull's Statistical Fracture Theory

The scratch test is fast and reproducible, as confirmed by recent research. To evaluate the high consistency of these two methods, which is scratch and uniaxial compression, respectively, the comparison of strengths have been conducted. Scratch tests are performed on Gulong shale and sandstone, and the statistical analysis of the experimental results is carried out detailly, which further reveals the longitudinal heterogeneity of Uniaxial Compressive Strength (UCS) of the rock samples. Besides, the original tensile stress state of Weibull distribution is extended to a compressive stress state, and a UCS-based model of Weibull distribution is developed and validated. The results provide evidence that the UCS profiles of sandstone and shale, can be considered to follow the two-parameter Weibull distribution with a significance level of 0.05. In conclusion, the scratch test provides an effective approach to obtain the continuous high-resolution UCS profile of the rocks. Meanwhile, the combination of the scratch test and the Weibull's theory, can further contribute innovative ideas and methods to clarify the geomechanical characteristics of the reservoirs. 1. INTRODUCTION As a natural heterogeneous mixed material, rock is of great interest to us, and the effective determination of its properties is indispensable in many fields. In particular, the accurate test of strength[1-3] is very important. Traditionally, Uniaxial Compressive Strength (UCS), is usually performed on a rigid servo testing machine[4]. However, this test is destructive, relatively time and cost consuming. Recently, the development of Continuous Scratch Testing (CST) techniques[5-7] has provided us with a powerful and fast strength testing method. Based on the strong correlation between specific energy and UCS[8], CST can offer us a continuous high-resolution UCS profile, which can be understood as the point strength located in each microcell of the rock sample. In this way, a large number of specimen data can be obtained at low cost, which can support other studies easily. This principle coincides with the content of the Weibull's statistical fracture theory. Weibull distribution data set only needs the critical stress of each microcell for rocks, even if it is based on the assumption of tensile stress initially. For the Weibull distribution, which is mainly used for reliability analysis and life estimation, it has been studied by large numbers of scholars, who developed the theory[9] and tried to combine it with rock mechanics tests[10,11]. And, many achievements have been made.