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Impact of Confined Extension on the Failure Envelope of Intact Low-Porosity Rock

  • Author / Creator
    Shantanu Patel
  • A failure envelope that ignores the intermediate principal stress (s2) is typically adequate for the design of rock structures. To obtain the complete envelope, the rock cylinders should be tested using confined compression (CC) as well as confined extension (CE) tests. While CC tests are common, CE tests are rarely carried out. Current techniques available to test rocks under CE conditions require shaping the cylindrical specimens to a dog-bone geometry. The limited data available in the literature indicates that the results from these dog-boned shaped tests produces strengths that are considerably greater than the confined triaxial tests carried out on traditional cylindrical specimens. Whether this increased strength is real or simply an artifact of the stress path for triaxial CE tests (s2=s1) versus conventional CC tests (s2=s3) is unknown.This research describes a new experimental technique to test rocks under CE conditions with zero s2. The flattened Brazilian (FB) test was used and the s1 and s3 were calculated from the strain on the surface of the specimens. However, this required derivation of new equations for the s1 and s3 in a FB specimen considering the bi-modularity in the stress-strain equations and requires the Young’s modulus (E) and Poisson’s ratio (ν) in both tension and compression. The E and n in compression can be obtained from an UCS test while the tensile E and n values can be obtained from the direct tension test. A direct tension test is difficult to conduct, so, new experimental techniques were developed to obtain the tensile E and n from a Brazilian test. New equations for (a) the horizontal and vertical strain values at the center and (b) horizontal and vertical displacements on the surface in a Brazilian test were derived considering the bi-modularity in the stress-strain relations. The digital image correlation technique (DIC) and conventional strain gauges were used to extract the strain at the center of the Brazilian disks. DIC was used to monitor the displacements of different points along the horizontal and vertical diameter on the flat surface of the Brazilian disk. With the DIC technique, a spackle density of approximately 250 spackles/cm2 was needed to accurately capture the strain and displacement pattern. The strain measured using the DIC technique was consistent with the strain measured using conventional strain gauges. The major advantage of the DIC technique is the ability to map the complete strain pattern over the surface of the Brazilian disk and quantify the uniformity of loading. The E and n in tension obtained using the new equations were found to be in general agreement with the values obtained from the direct tension tests.After obtaining the E and n in compression and tension, FB samples of Lac du Bonnet granite were tested with increasing depth of flattening. With the change in flattening (1mm to 10 mm) the s1 was increased from 15% to 37% of its UCS. The corresponding s3 was found to remain in the range of Brazilian strength of the material.The flat jointed bonded particle model from ITASCA was then used to investigate the Lac du Bonnet granite in CE for a wide range of confinements and to investigate the impact of s2. A methodology was developed to capture the (a) initial non-linearity commonly observed in the stress-strain curve of a UCS test, (b) the bi-modularity, (c) crack initiation stress, (d) crack damage stress, and (e) peak strength in UCS, triaxial and direct tension tests. A set of micro parameters for the numerical sample could produce the behavior observed in the laboratory tests. The code was further modified to investigate the CE tests. The failure envelope from the numerical tests was found to align with the points from the Brazilian test and the FB tests implying a tension cut-off for the material investigated. The numerical results showed a clear influence of s2 on the strength in CE.The results from the laboratory testing and numerical samples suggest that the non-linear Hoek- Brown failure criterion based on only compressive triaxial results provides a reasonable estimate of the strength in CE for Lac du Bonnet granite. But this criterion could be improved for Lac du Bonnet granite by providing a tension cut-off.

  • Subjects / Keywords
  • Graduation date
    Fall 2018
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R3W95143K
  • License
    Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.