**5. Discussion**

**Figure 3.** Results of all tensile strength test. BDT: Brazilian Disc Test, MF: Minifrac, MTT: Modified Tension Test. Hollow

Acoustic emission data obtained during the tests give rough insights into the failure processes. It is obvious that all tests end with a spalling of the specimens in parts due to a complete tensile failure. Simple AE count analysis show that the BDT is accompanied with an immense hit-rate long before total failure in comparison to the relatively quiet pre-failure phases of the MF and MTT tests. In good agreement with theoretical considerations of the stress distribution in the Brazil disc [1] these events are most likely due to compressional failure at the top and bottom of the disc, accompanied with crack propagation and coalescence before peak load (Figure 4).

**Figure 4.** AE hits per 0.5 sec., BDT left, MF middle and MTT right showing the huge difference in AE hits before total

We investigate the effect of eccentricity of the overcoring for the MTT samples by a numerical simulation. A finite element study that has been performed by Plinninger et al. [10] that shows

circle in Bebertal sandstone MTT tests represents two results of the highly eccentrical MTT tests.

**3.3. Acoustic Emissions results**

988 Effective and Sustainable Hydraulic Fracturing

failure of the sample.

**4. Numerical model**

247 tensile strength test results of BDT, MF and MTT tests vary considerable within one lithology (Figure 6). Therefore it is not trivial to give a reliable prediction of the tensile strength parameter. Results of the BDT tests show no significant variation with respect to the specimen size, as long as the aspect ratio is held constant. Nevertheless the tensile strength data scattering is high, so that it may obscure existing trends. Acoustic Emission evaluation shows that during the BDT multiple fracturing mechanisms are present. Before total fracturing of the sample by a tensile rupture there is a high amount of AE activity that is most likely related to compres‐ sional failure at the top and bottom of the disc. Beside this, compressional stress concentrations and the inhomogeneous tensile stress distribution may lead to tensile cracks before peak load. MF results lead to the highest tensile strengths in this comparison where there seem to be no differences in tensile strength when using a 4 mm or a 6 m borehole for pressurization. Again one has to take into account that the high amount of tensile strength scattering for these tests inhibits a statement regarding a borehole size dependency.

with increasing area being set under tensile stress. That is reasonable in terms of the statistical theory of strength. Especially for the igneous rocks it seems evident, that the probability to set a healed joint under a critical tension rises with the size of the sample volume that is under tensional stress. For the selection of the tensile strength test one should keep in mind that depending on the lithology the apparent tensile strength appears to be a function of the area, or more exact of the volume under tensile stress. Thus, for a relative homogeneous rock a less severe reduction of the measured tensile strength with size will be visible as it will be at the

Comparison of Hydraulic and Conventional Tensile Strength Tests

http://dx.doi.org/10.5772/56300

991

It is arguable and may not be appropriate to study the effect of area/volume under tensile stress on the measured tensile strength using the combined results from different types of tests, especially if the different tests tend to give different average measured tensile strengths. Furthermore the negative trend of tensile strength with respect to the stressed area/volume is not that obvious for the single test methods. Especially the assumption of uniform tensile stress distribution close to peak load in the annulus [5] for the MTT samples seems not to be comprehensible. It may hold for ductile materials but not for brittle ones. Therefore the validity of equation (3) for the calculation of the tensile strength is questionable. Nevertheless the resulting tensile strengths are treated as the same rock property when used as input parameters for calculations. This is very problematic due to its huge variation as shown in the tests. The correlation of the calculated tensile strength with the stressed area/volume is one possible

This work is funded by the Federal Ministry of Environment, Nature Conservation and Nuclear Safety (funding mark 0325279B). Special thank goes to Kirsten Bartmann and Sabrina

, Ferdinand Stöckhert, Sebastian Brenne and Michael Alber

[1] Mellor, M, & Hawkes, I. Measurement of tensile strength by diametral compression

of discs and annuli. Engineering Geology. Elsevier; (1971). , 5(3), 173-225.

Hoenig for laboratory work and data evaluation done during their Master Theses.

\*Address all correspondence to: michael.molenda@rub.de

approach to account for the decreasing apparent tensile strength behavior.

highly fractured igneous rocks tested in this study.

**Acknowledgements**

**Author details**

Michael Molenda\*

**References**

Ruhr-University Bochum, Germany

The results of the MTT tests give the lowest tensile strengths and very low standard deviations. Latter may be related to the small amount of testes MTT per lithology. Furthermore all MTT are prepared using the same sample sizes. A major problem of the MTT experiments is the centralization of the boreholes. An eccentricity yields to a significant inhomogeneity of the tensile stress distribution in the sample (Figure 5). Numerical simulations of the MTT eccen‐ tricity effect together with the two eccentric MTT samples (Figure 3) show that the calculated tensile strength may be underestimated massively. One reason for the apparently lower tensile strength measured using the MMT might be the applicability of Equation (3). In deriving the equation, it was assumed that, when the peak load is approached, the tensile stress distribution is almost uniform in the area defined as *ATZ* [5]. This may only be true if the material is highly ductile. However, for brittle rocks, especially for highly fractured rocks, fracture propagation may occur and lead to ultimate failure at a much lower load as suggested by Equation (3) due to stress concentration (Figure 5).

**Figure 6.** Tensile strength results plotted against the assumed area under tension. BDT: diameter x thickness, MF: sur‐ face area of the borehole and MTT: twice the surface area between the outer and inner borehole, upper and lower.


**Table 4.** Estimated area subjected to tensile stress for the different tensile tests. *D*: BDT disc diameter, *t*: BDT disc thickness, *rbh* : MF borehole radius, *l*: MF sample height, *R*: MTT outer borehole radius, *r*: MTT inner borehole radius.

Main difference in all experiments and the reason for choosing these are the areas that are under tensile stress at the point of failure. The calculated tensile strengths compared to the area perpendicular to the maximum tensile stress show a negative trend for the tensile strength with increasing area being set under tensile stress. That is reasonable in terms of the statistical theory of strength. Especially for the igneous rocks it seems evident, that the probability to set a healed joint under a critical tension rises with the size of the sample volume that is under tensional stress. For the selection of the tensile strength test one should keep in mind that depending on the lithology the apparent tensile strength appears to be a function of the area, or more exact of the volume under tensile stress. Thus, for a relative homogeneous rock a less severe reduction of the measured tensile strength with size will be visible as it will be at the highly fractured igneous rocks tested in this study.

It is arguable and may not be appropriate to study the effect of area/volume under tensile stress on the measured tensile strength using the combined results from different types of tests, especially if the different tests tend to give different average measured tensile strengths. Furthermore the negative trend of tensile strength with respect to the stressed area/volume is not that obvious for the single test methods. Especially the assumption of uniform tensile stress distribution close to peak load in the annulus [5] for the MTT samples seems not to be comprehensible. It may hold for ductile materials but not for brittle ones. Therefore the validity of equation (3) for the calculation of the tensile strength is questionable. Nevertheless the resulting tensile strengths are treated as the same rock property when used as input parameters for calculations. This is very problematic due to its huge variation as shown in the tests. The correlation of the calculated tensile strength with the stressed area/volume is one possible approach to account for the decreasing apparent tensile strength behavior.
