International Journal of Rock Mechanics and Mining Sciences
Technical noteRock variability and establishing confining pressure levels for triaxial tests on rocks
Introduction
In teaching rock mechanics, often the theoretical part of the lectures are demonstrated by laboratory sessions, which are helpful in supplementing the teaching of rock mechanics principles to the students. In these laboratory sessions, an unconfined compressive strength (UCS) test can be followed by a conventional triaxial compressive strength (TCS) test on similar rock specimens. The former test is the one used most in the characterization of rock strength and in many rock classification systems; while the latter test has been widely used for the determination of design parameters such as C and φ because of the equipment simplicity and convenient specimen preparation and testing procedures. However, the experience of the authors in conducting such sessions has shown that problems are encountered while performing the conventional triaxial compressive strength tests and these can be misleading to the students.
The conventional TCS test consists of applying a hydraulic pressure to the external surface of a cylindrical rock specimen and at the same time axially loading the specimen in compression with increasing increments until failure of the rock. The procedure for measuring the rock strengths has been standardized by the American Society for Testing and Materials (ASTM) [1], [2] and the International Society for Rock Mechanics (ISRM) [3], [4]. Neither in the ASTM nor in the ISRM suggested methods for the triaxial test, is it mentioned clearly what procedure should be followed to establish the pre-test confining pressure levels. Terms such as “the desired lateral pressure”, “the desired value”, “the pre-determined test level” and “the prescribed value” are used. So, the test instructor has to arbitrarily settle these pressure values by himself/herself based on his/her past experience.
Ideally, at each increment of the confining pressure the same rock specimen should be used for the test, but since rock specimens are broken after each test, obviously the failed specimen has to be replaced by a new sample. Thus, some conflicting results may be obtained due to inherent variability in the failure characteristics of a substituted rock specimen, e.g. sometimes the new rock specimen is broken at a lower axial load for a higher confining pressure applied than for the previous one. Although Kovari et al. [5], [6] have suggested that in a “continuous failure state” triaxial test it is possible to determine the failure envelope of a rock with the aid of a single cylindrical test specimen, it is still necessary to define a pre-test confining pressure level for this test and also for the conventional TCS test, since it is more universal and fundamental for the students.
In this Technical note, a practical approach will be introduced for establishment of pre-determined confining pressure levels for the triaxial test on rocks by directly using the UCS and TCS test values collected from past laboratory sessions of a rock mechanics course. Also, for the purpose of this study, the possible probability distribution models, which take into account the uncertainty and variability dictated by the nature of the strength of rocks under compression, have been evaluated and the acceptability of the assumption about the proposed distribution model can be further investigated.
Section snippets
Uncertainty and variability in rock mechanics
Most engineering problems involve some degree of uncertainty and variability. The causes of such uncertainty in an engineering content have been detailed by Bury [7] and in particular for rock engineering by Duzgun et al. [8]. Bury [7] classifies sources of uncertainty as (1) data uncertainty; (2) statistical uncertainty; (3) event uncertainty; and (4) model uncertainty.
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Data uncertainty is caused mostly by the inherent variability of a measured quantity. No matter how carefully one measures
Ankara andesite
The rock type used in the experiments for the rock mechanics course taught by the authors is broadly described as Ankara andesite [23], [24], [25], [26]. Andesite is a fine-grained igneous, volcanic (extrusive) rock, of intermediate composition, with aphanitic to porphyritic texture. It is intermediate because it contains some minerals that are common to rhyolite and some common to basalt. It can appear very much like basalt, but it is usually less dark or greenish in color. The variability in
Approach to setting the minimum confining pressure
Since the distribution of UCS (Fig. 1) is fairly symmetrical in shape and it has been previously approved by the χ2 test that the UCS of samples follows probability rules for a normal distribution, it is applicable in the establishment of confining pressures. This rule formally states that ±3 times the standard deviation from the mean should contain almost all of the sample values [28], [29]. Therefore, a practical and simple way can be the addition of 3 times the standard deviation to the
Conclusions and recommendations
A probabilistic approach has been explicitly detailed in this study towards the solution of a testing problem that can be encountered frequently in rock mechanics. Because of vague terminology usage in the Suggested Methods, researchers and students were facing difficulties concerning the pre-setting of confining pressure levels for a conventional TCS test on rock. This work reported here aims to solve this problem and some of the conclusions drawn from this work are as follows:
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UCS frequency
Acknowledgments
The authors gratefully acknowledge the following for their help during the course of this study: Technicians Nizamettin Aydemir and Hakan Uysal for their kind help in the preparation of the rock specimens and conducting the tests; Research Assistants, Sinem Sener for providing the UCS test results and Arman Kocal for providing some components of the TCS test values.
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