Barre Granite Research Articles

Residual elastic strain in rocks

Residual elastic strains (stresses) consist of locked-in strains, reflecting crystal distortions related to past external loads, and those that constrain them, the locking strains. The forces or stresses giving rise to locked-in and locking strains exist in rocks with no external loads across their boundaries and satisfy internal equilibrium conditions i.e., their sum is zero. The strains are stored by cementation and physical and chemical interactions between anisotropic grains while under load. The measure of residual strain provided by strain relief or X-ray methods consists of some unknown combination of locking and locked-in strains that depends on the distribution, relative magnitudes, and degrees of relaxation (strain relief method) of these components and the special bias of the measuring technique. With the X-ray technique, the bias is toward detection of strains in the most voluminous rock elements satisfying the Bragg condition for diffraction. In sandstone, therefore, the residual strains in the grains are sampled preferentially to those in the cement. The special view of residual stresses obtained from X-ray diffraction studies and supported by data from strain relief techniques has yielded significant information as follows: 1. (1) Magnitudes can be large; differential stresses between 300 and 400 bar have been measured in quartzites, sandstones, and granites. 2. (2) Residual stresses relating to Mesozoic and possibly even to Precambrian geologic events have been mapped. 3. (3) Principal axes correlate with the geometry of large-scale folds and to stresses inferred from nearby fractures and calcite twin lamellae. 4. (4) Residual stresses have been found to vary systematically along fault surfaces in such a manner as to be related to the process of sliding. Items 1–4 suggest that rocks have long-term fundamental strength; volumetric stored strain energy is commonly of the order of 10 4 erg/cm 3. 5. (5) Stored stresses relax when grains are freed from constraints of nearest neighbors. 6. (6) They relax within 5 mm of an induced tensile fracture in sandstone probably because movements along grain boundaries occur that far from the fracture surface. 7. (7) Residual stresses influence the orientations of tensile and shear fractures induced experimentally under certain conditions of loading. 8. (8) Observed residual stresses can contribute to strength anisotropy. Items 7 and 8 are explicable from superposition of applied loads on the observed residual stresses. 9. (9) In the Barre Granite the principal axes of residual strain are subparallel to the principal directions of ultrasonic attenuation and velocity fields.

Hoop-Stress Loading - A New Method of Determining the Tensile Strength of Rock

Abstract Although it is well known that rock commonly fails in tension under numerous field conditions, a satisfactory standard procedure for determination of the tensile strength of such materials has not as yet been established. With suitable precautions, direct-pull tests may be used; however, precise specimen preparation and extremely uniform and concentric loading must be utilized if meaningful results are to be obtained using this method. Recently, the authors completed a 3-year study in which a variety of methods for determining tensile strength were evaluated. One method, involving the hoop-stress loading of thick-walled hollow cylinders, was found to be particularly attractive. This paper describes the theory, apparatus, and test technique associated with this method. In evaluating this new technique a number of specimens of Barre granite, Lauders and Indiana limestone, and Berea and Tennessee sandstone were tested. Reproducibility for each rock type was fund to be excellent, with the percentage standard deviation ranging from a maximum of 10.9 percent for Lauders limestone down to 0.9 percent for Berea sandstone. Values of tensile strength determined from hoop-stress tests were found to correspond closely to those determined by direct pull, provided the former were analyzed in terms of pull, provided the former were analyzed in terms of an equation based on a suitable elastic-plastic analysis. Under these conditions the ratio of hoop-stress to direct-pull tensile strength values ranged from 0.86 to 1.10 for the five rocks tested. Although studies on additional rock types are required, it appears that the hoop-stress loading method would be a strong candidate as a standard test for determination of the tensile strength of rock. Introduction Although it is well known that tensile stresses play an important role in the behavior of underground play an important role in the behavior of underground openings associated with petroleum, natural gas and mining operations, suitable techniques for the determination of the tensile strength of rock are limited.

Effects of stress on velocity anisotropy in rocks with cracks

The effective elastic compliance of rock that contains cracks is evaluated from energy considerations, as first proposed by Eshelby [1957]. The compliance of rock depends on the compliance of the solid matrix, the directional distribution of the cracks, an ‘inhomogeneity’ interaction tensor, and the shape distribution of cracks, which are assumed to be shaped like pennies. The effective compliance is linearly elastic for small-amplitude elastic waves. Anisotropic crack distribution causes elastic anisotropy, with associated acoustic birefringence. Nonhydrostatic stress causes stress-induced anisotropy, owing to anisotropic closure of cracks. Although velocities are uniquely determined from the distribution of cracks, the distribution cannot be determined uniquely from the velocities. The theoretical results compare favorably with measured compressional velocities and crack distribution in Salisbury granite and with measured stress-induced compressional and shear velocity anisotropy in Barre granite.

Microstructural techniques in the study of physical properties of rock

Techniques have been developed to further understanding of rock behavior in terms of its microstructure. The techniques measure certain fabric parameters on rock discs and in thin sections with the petrographic microscope, for correlation with physical property laboratory tests. They include (a) diametric mineralogical analysis, (b) defect analysis, (c) grain elongation analysis, (d) macro-grid analysis, and (e) transgranular-intergranular analysis. Pulse velocities and breaking strengths in samples of granite and limestone are compared with their fabric properties obtained through these techniques. Examples of such comparisons include the influence of feldspar and quartz abundance in Salisbury Granite on longitudinal pulse velocity, the tendency for the frequency of microscopic defects to be inversely proportional to breaking strength in Barre Granite, the proportionality of average grain size parallel with foliation to breaking strength in Yule Marble, and the inverse proportionality of the ration of transgranular to intergranular failure to breaking strength in Tennessee marble.

On the penetration of rock by three-dimensional indentors

An experimental and theoretical investigation was undertaken of the rock-penetrating characteristics of five statistically loaded, three-dimensional indentors; two cones, two spheres and a pyramid. Two rock types were used in the study, Barre granite and Indiana limestone. The indentors are compared on the basis of the forces necessary to penetrate to a given distance by crushing, the stress required to cause chipping, and the amount of energy required to fracture a unit volume of rock. In addition the indentor results are compared to some wedge results obtained under identical conditions. In order to gain some insight into the penetration of rock by three-dimensional indentors, the two-dimensional static penetration theory of Paul and Sikarskie has been extended in this report to three-dimensional indentors.