**Acknowledgements**

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

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

**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.

**Testmethod BDT MF MTT** Area under 1,51,5 450-3400 mm2 1005-3393 mm2 4624 mm2 Calculation *D*⋅ *t* 2⋅π ⋅ *rbh* ⋅ *l* 2⋅ (π ⋅ (R2 - r

**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

2))

inhibits a statement regarding a borehole size dependency.

to stress concentration (Figure 5).

990 Effective and Sustainable Hydraulic Fracturing

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