Compressive Strength and Griffith Criterion

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  • Topic: Tensile strength, Compressive strength, Materials science
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The University of Hong Kong
Department of Civil Engineering

CIVL2002 M – Geology & Rock

Laboratory Report

Brazilian Test

A. Introduction
As shown by the Griffith criterion, tensile strength of brittle materials is theoretical 1/8 of the compressive strength. Typically, tensile strength of rock materials is about 1/10 to 1/8 of the compressive strength. Hence, rock fails easily under tension. In design, rock should be subjected to minimum tensile stress. Several methods are commonly used to test the tensile strength of rocks:

1. Direct tensile test:
Metal caps are cemented to the end-surfaces of the samples so that tensile load can be applied to the samples until failure. 2. Brazilian test:
Compressive stress is applied to the sample through the loading jaws enclosing the sample, so that tensile stress will be induced in the lateral direction of the applied load. 3. Flexural test (or Bending test):

International Society for Rock Mechanics (ISRM), Commission on Testing Methods (1978), has listed suggested methods for determining tensile strength of rock materials.

Brazilian test is more preferrable than the other two tests in the measurement of tensile strength of rock specimens.

One of the major reasons is that only small rock specimens are required for the Brazil test, thus ensuring the specimens to be intact and relatively free from cracks and joints or other discontinuities. In fact, the Brazil test has been found to give a tensile strength higher than that of the direct tensile test. This is most probably owing to the effect of fissures. Short fissures weaken a direct tension specimen more severely than they weaken a splitting tension specimen. The ratio of the ‘Brazilian tensile strength’ to direct tensile strength has been found to vary from unity to more than 10 as the length of preexisting fissures grows larger.

Another reason for the popularity of the Brazil test is that it usually gives unique failure plane. The results obtained are therefore more reliable and less affected by the actions of microfissures. (The dispersion of results from direct tensile tests is usually very large and a large number of results is required to obtain acceptable average values.) Besides, the Brazil is much easier to perform than the direct tensile test in which precise alignment of specimen and end preparations are required.

B. Objective
To evaluate the uniaxial tensile strength of rock specimens indirectly by Brazilian Test.

C. Theory
Concept of Brazilian Test
Brazilian test is an indirect test to measure the ultimate tensile strength of rock (impose axial stress in order to induce tensile stress on the specimen. Basically, the technique involves loading disc-shaped specimens in compression across their diameter at a constant stress rate of 200 N/s such that the failure occurs within 15 to 30 seconds of initial loading. Such loading generates a tensile stress at the center of the disc in a direction perpendicular to the direction of applied load (in the plane of the disc face). When the applied load reaches a critical level, the disc splits lengthwise in tension. By noting the peak compressive load P at failure, the ‘Brazilian tensile strength’ can be calculated from the following formula:

P = Load at primary failure (N)
D = Diameter of the test specimen (mm)
t = Sample thickness or length (mm)

The justification for the test is based on the experimental fact that most rocks in biaxial stress field fail in tension, at their uniaxial tensile strength when one principal stress is compressive with a magnitude not exceeding three times that of the tensile principal stress.

Figure 1: Schematic Diagram of the Operation of the Test

Requirements of the Test
1. Specimens must be prepared as right-angled circular cylinders 2. Length of sample approximately equal to the radius
3. Sample ends flat and...
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