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Compressive Strength and Griffith Criterion Essays

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: here 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 perpendicular to the cylindrical axis 4. Sample sides smooth and straight Stress Distribution and Mode of Failure Figure 3: Propagation of loading — Shear and crushing failure Figure 2: Stress distribution along axes –Axial splitting along vertical diameter The compressive stress is non-uniformly distributed along the vertical diameter of the specimen with magnitude decreasing from a stress of x = 3y at the centre of the disc to progressively smaller values as the ends are approached.
According to the Griffith theory of failure, the critical point ought to be the centre where the ratio of compression to tension (in terms of magnitude) is 3. With a principal stress ratio of 3, failure ought to result from the application of the tensile stress alone, without any complication from the simultaneous compression parallel to the eventual rupture plane. There are 2 possible modes of failure of the splitting tension specimen: 1. Axial splitting along vertical diameter 2. Shear and crushing failure at loading (occurs when the width of the contact area between the jaws and the disc is large)
Theoretically, the rock specimen should fail at the centre of specimen (largest induced tensile stress), yet the experimental results shown that the failure occurs along the vertical diameter as the induced tensile stresses are more or less the same except for points next to the loading jaws. In other words, the rupture of the specimen in the Brazil test usually occurs along a single tensile-type fracture across the diameter aligned with the axis of loading. However, if the fracture plane deviates significantly from a straight line between jaw contacts, the test is considered invalid.
Noted that the tensile strength obtained from the Brazil test is found to be affected by a number of factors such as: the magnitude of the applied load, the loading rate, whether the loading jaws are clear, whether eccentricity of load has occurred as well as the width of the contact area between the specimens and the loading jaws, etc. The number of specimens per sample tested should be determined from practical considerations. Normally, 10 specimens are recommended. Yet, in our experiment, only 8 specimens will be tested to obtain the tensile strength of the rock sample. D.
Apparatus 1. Loading Machine It is a loading machine which applies compressive load to the rock specimens. It has a control panel showing the instantaneous applied load. At the moment when the rock specimen fails, one of the pointers will stop showing the failure compressive load 2. Steel Loading Jaws It fixed the rock specimen. Radius of jaws must be 1. 5 times of specimen radius; 25mm penetration of guide pin has a clearance of 0. 1mm; width of jaws must be 1. 1 times of specimen thickness. 3. Electronic Calipers Measures the dimension of rock specimen (thickness and diameter) . Masking Tape Wraps up the periphery of the rock specimens to reduce contact irregularities. It also prevents the specimens from breaking into pieces after failure, so that the failure plane can be observed. Figure 5: Schematic Diagram of the Setting Up of the Test Figure 4: Loading Machine E. Procedure 1. 8 test specimens were cut and prepared using clean water. The specimens should be prepared in such a way that: – (a) The cylindrical surfaces should be free from obvious tool marks; (b) Any irregularities across the thickness of the specimen should not exceed 0. 25mm (c) End faces shall be flat to within 0. 25mm and square and parallel to within 0. 25; (d) The specimen diameter should not be less than NX core size, approximately 54mm; (e) The thickness should be approximately equal to the specimen radius. 2. The test specimens were wrapped around its periphery with one layer of the masking tape. 3. The diameter and thickness of were measured 3 times, once at every 120 for each specimen. 4. The test specimens were numbered (1-8), and a line across the diameter was marked on each specimen. 5. The test specimen (no. ) was mounted into the loading jaws such that the curved platens load the specimen diametrically with the axes of rotation for specimen and apparatus coincident. The assembly was then mounted into the loading machine. 6. The test specimen was loaded continuously at a constant rate such that failure in the weakest rocks occurs within 15-30s. A loading rate of 200N/s was recommended. 7. The failure compressive load was recorded for each specimen, and the corresponding tensile strength was calculated. 8. Steps 5-7 were repeated for the remaining 7 specimens. F. Results and Calculation Lithologic Description of Rock
Figure 6: Features of Rock Specimen 8 rock specimens have been tested in this experiment. Specimens 17-20 were tested by the other group (Group 1), whereas specimens 21-24 were tested by our group (Group 2). In general, all the specimens are very similar in appearance. The lihologic of rock specimens are described as follows: 1. The rock specimens tested are Marble which is a metamorphic rock form composed of coarse crystals from parent limestone or dolostone rocks. 2. All specimens have marble non-foliated textures. 3. The marble specimens are composed of interlocking calcite grains. 4.
Visible cracks can be observed in some of the specimens, e. g. specimen 20. 5. It is grey, white and black in color. The main component of the rock samples should be mainly calcite, dolomite. It also contains calcium carbonate and ophiolite in small amount. 6. The grains of the marble specimens are fine-grained. 7. It is vulnerable to weathering since calcium carbonate content is readily attacked by acid rain. Orientation of Loading Axis The orientation of loading axis is marked at the centre line of rock specimen which cut across the discontinuities on the rock (joints, fissures, crack).
To illustrate, rocks tend to fail along or parallel to the discontinuities. Hence, in order to increase the accuracy of the experiment, the orientation o loading axis is chosen to cut across the discontinuity of rocks. Dimension of Specimen and Tensile Strength Recall that Brazilian tensile strength’ can be calculated from the following formula: Group 1 Specimen No| Diameter (mm)| Thickness (mm)| Failure Load (kN)| Tensile Strength (MPa)| | Upper| Middle| Lower| Average| Upper| Middle| Lower| Average| | | 17| 63. 15| 63. 11| 63. 09| 63. 12| 35. 09| 34. 89| 34. 82| 34. 93| 19. 61| 5. 66| 18| 63. 2| 63. 34| 63. 51| 63. 39| 33. 18| 33. 24| 33. 22| 33. 21| 24. 56| 7. 43| 19| 63. 11| 63. 09| 63. 03| 63. 08| 35. 00| 34. 88| 34. 91| 34. 93| 24. 54| 7. 09| 20| 62. 98| 63. 09| 63. 11| 63. 06| 34. 75| 34. 88| 34. 73| 34. 79| 20. 70| 6. 01| Average Tensile Strength (Group 1) = 5. 66 + 7. 43 + 7. 09 + 6. 014 =6. 55 MPa Group 2 Specimen No| Diameter (mm)| Thickness (mm)| Failure Load (kN)| Tensile Strength (MPa)| | Upper| Middle| Lower| Average| Upper| Middle| Lower| Average| | | 21| 63. 37| 63. 29| 63. 26| 63. 31| 32. 99| 33. 11| 33. 12| 33. 07| 24. 62| 7. 49| 22| 63. 6| 63. 36| 63. 47| 63. 40| 33. 09| 33. 06| 33. 16| 33. 10| 20. 80| 6. 31| 23| 63. 39| 63. 47| 63. 42| 63. 43| 33. 31| 33. 34| 33. 12| 33. 26| 23. 20| 7. 00| 24| 62. 99| 63. 02| 62. 97| 62. 99| 33. 11| 33. 61| 33. 24| 33. 32| 15. 33| 4. 65| ** Noted that specimen 24 is rejected due to the experimental results deviates a lot from the other (further explanation will be given in discussion session) Average Tensile Strength (Group 2) = 7. 49 + 6. 31 + 7. 00 3 =6. 93 MPa Average Tensile Strength (All Specimens) = 6. 55 + 6. 932 =6. 74 MPa Test Duration and Stress Rate
All specimens were loaded at a constant stress rate of 200N/s. Test duration: Specimen| 17| 18| 19| 20| 21| 22| 23| 24| Time (s)| 98. 05| 122. 8| 122. 7| 103. 5| 123. 1| 104| 116| 76. 65| Mode of Failure Group 1 Figure 7: Rock Specimens Before Test (Group 1) Figure 8: Rock Specimens After Test (Group 1) Specimen No| Mode of Failure| 17| Axial splitting parallel to vertical diameter | 18| Axial splitting parallel to vertical diameter| 19| Axial splitting parallel to vertical diameter and crushing failure| 20| Axial splitting parallel to vertical diameter and crushing failure| Group 2 Figure 9: Rock Specimens Before Test (Group 2)
Figure 10: Rock Specimens After Test (Group 2) Specimen No| Mode of Failure| 21| Axial splitting parallel to vertical diameter and crushing failure| 22| Axial splitting parallel to vertical diameter| 23| Axial splitting parallel to vertical diameter| 24| Axial splitting parallel to vertical diameter and shear failure| G. Discussion Interpretation of Experimental Results A. Tensile Strength It is found that specimen 24 has a loading at primary failure (15. 33kN) which is substantially lower than the other specimens. This can be explained as eccentricity of loads on the specimen occurs during the test.
In other word, the specimen is not located properly on the steel loading jaw. Hence, despite of axial stress, it is also subjected to shear stress and hence it fail at a relatively lower load. Thus, its test result should be rejected. As mentioned earlier, the average tensile strengths of specimens in Group 1 and 2 are 6. 55MPa and 6. 93MPa respectively. It is found that Group 1 has lower average tensile strength than Group 2. Such deviations can be explained by the presence of some microfissures and joints which were oriented parallel to the failure planes, thereby lowering the tensile strengths in these samples.
Although weathering of the rock specimens might also give rise to deviations in results, this was not be true in our experiment as no evidence of weathering could be observed on the circumferential surfaces or the failure planes of specimens in Group 1 The overall average tensile strength of the 8 specimens was calculated to be 6. 74MPa. If we compare the tensile strength with the compressive strength which is about 200-300MPa, we can observe that the tensile strength is much lower than the compressive strength. As mention in the theory part, rock is weak in tension while strong in compression.
This is because rocks fail to offer cohesive force or other kind of bonding to resist tension. Notice that the tensile strengths obtained by this test are in general larger than those obtained by direct tensile test, as the presence of microfissures in the specimen will reduce the measured tensile strength to a larger extent in the direct tensile test. While for the Brazil test, only fissures oriented parallel to the applied load will affect the measured results. B. Mode of Failure As mentioned earlier, there are 2 possible modes of failure of the splitting tension specimen: 1.
Axial splitting along vertical diameter 2. Shear and crushing failure at loading (occurs when the width of contact area between the jaws and the disc is large) In this experiment, all specimens are failed by axial splitting along the diameter aligned with the axis of loading. This reveals that the induced tensile force which was acting perpendicular to the applied compressive force. Consequently, the plane on which the maximum tensile force was acting would be parallel to the compressive load. (Figure 11) Figure 11: Compressive Force Induced Tensile Force in Perpendicular Plane
For specimen 19, 20 and 21, they were also failed along the discontinuity on the rock. As observed from this experiment, tension failure of rock would result in cracking along the discontinuities (such as joints and fissures, or faults in large rock masses) that were most severely stressed. Also, the contact area provides friction and the frictional force provides confinement to result in crack development. C. Comparison between Direct Tensile Strength Test and Indirect Tensile Strength Test The direct tensile test is done by sticking the caps to the ends of a cylindrical rock sample and applying uniaxial tensile force to it.
However, due to the poor installation of the caps and bending during loading, the results do not have high accuracy. In Brazil test, disc specimens have much smaller sizes. The chance of having weak planes or large crack is largely reduced. Also, the simple preparation process of disc specimens makes the test more convenient. Besides, the loading is applied along the diameter of the specimen and there is no eccentricity of loading. As a result, Brazil test is an easy way to test the tensile strength of rock. Due to the effect of fissures, Brazilian test has been found to give a tensile strength higher that of the direct tensile strength test.
Short fissures weaken a direct tension specimen more severely than they weaken a splitting tension specimen. And the other reason is the disc specimens have less chance of have weak planes or large cracks as mentioned above. Hence, the ratio of direct tensile strength to the Brazilian tensile strength is used as an indicator of the degree of fissuring, as presented by geologists, Tourenq and Denis. They recommend that the rock should be classified as: essentially non-fissured if the ratio > 0. 8; very fissured if the ratio < 0. 2. Sources of Errors
We can observe from the results of the Brazil test that the tensile strengths of the specimens range from 5. 66 MPa to 7. 49 MPa. There is small deviation of the tensile strength from the average tensile strength (6. 74 MPa). The deviation can be explained by the following sources of error: 1. Rock is an aggregate rather than a single material. So rock samples vary in physical properties even the samples are taken from the same source and rock is heterogeneous in nature. 2. We have assumed the rock to be intact but it is not true. There are different kinds of discontinuities exist in the rock specimens. 3.
The contact between specimen and platen (jaw) is not perfectly point contact which is assumed in the derivation of the formula. 4. The compressive load may be subjected to eccentricity due to technical problems of the loading machine or imperfect steel jaws manufacturing. 5. The crack initiation load is usually smaller that the peak load because the test does not ensure crack initiation occurs at maximum tensile stress. A 4-point-beam test or 3-point-beam test should be used instead to ensure crack initiation is accompanied by peak load. It is often, however, difficult to obtain an intact rock beam sample from nature. . The specimens are not having perfect vertical and horizontal surfaces. 7. The indicated load is higher than the actual load because there is friction within the hydraulic ram. 8. Induction of the tensile stress is hindered as the masking tape is confining the specimen. In other words, compressive stress is induced by the masking tape and true induced tensile stress can not be revealed. 9. Although we cannot see any weathering on the rock specimens’ surface, there may be weathering in between the specimen which we may not be notified. Precaution 1.
As discussed in the theory section, the measured tensile strength is dependent on the width of the contact area between the specimen and the loading jaws. If the width of the contact area is larger than 10 o at failure, its effect should be taken into account when calculating the tensile strength. 2. As mentioned in the theory section, the tensile strength obtained from the Brazil test might be affected by the loading rate, the average tensile strength we obtained in this experiment could only represent the tensile strength of the rock sample with an applied loading rate of 200 N/s.
More tests with different loading rates should be carried out. 3. The applied compressive load should not be larger than the induced tensile stress by three times, or the specimen may not fail by tension in the lateral direction. 4. As results obtained from the Brazil test might show large deviations, more specimens (normally 10-15 specimens are recommended) should be used in order to achieve a more reliable average tensile strength. H. Conclusion The Brazilian or split-tensile strength is significantly more convenient and practicable for routine measurements than the direct tensile strength test.
The test gives very similar results to those from direct tension (Jaeger & Cook, 1976). It is a more fundamental strength measurement of the rock material, as this corresponds to a more likely failure mode in many situations than compression. To sum up, the average tensile strength of the rock samples was found to be 6. 74MPa. In the experiment, sample 24 was rejected due to undesirable failure plan. For the other 7 specimen, there is a small deviation and error associated with the mean result.
The tensile strength of the rock samples is studied and the lithologic description, mode of failure, location and orientation of the failure planed are discussed. We can conclude that the experiment is successful and the objective of the experiment is achieved. I. References 1. Obert, L. , Windes, S. L. and Duvall, W. I. , 1946, “Standardized Tests for Determining the Physical Properties of Mine Rock,” U. S. Bureau of Mines, Rept. Inv. 3891, Augs. , 67 p. 2. Obert, L. and Duvall, W. I. , 1967, “Rock Mechanics and the Design of Structures in Rock,” John Wiley and Sons, Inc. New York, pp. 318-339. 4 3. American Society for Testing Materials (ASTM), Standard Test Method for Unconfined Compressive Strength of Intact Rock Core Specimens. ASTM D2938-71a. ASTM Book of Standards Part 19, 1979, pp. 440-442. 4. International Society for Rock Mechanics, Suggested Methods for Deter mining the Uniaxial Compressive Strength and Deformability of Rock Materials. Int. J. Rock Mech. Mi Sci. vol. 16, 1979, pp. 135-140. (ISRM Committee on Laboratory Tests, Sept. 1978, enclosed)

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