Rock Mechanics and Rock Engineering: From the Past to the Future – Ulusay et al. (Eds)© 2016 Taylor & Francis Group, London, ISBN 978-1-138-03265-1

Kimachi sandstone does not have to fail under larger stress
Y. Wang, Y. Fujii, D. Fukuda & J. Kodama
Rock Mechanics Laboratory, Hokkaido University, Sapporo, Japan

ABSTRACT: Series of uniaxial compression tests combining constant strain rate and four patterns of cyclicloading were carried out on Kimachi sandstone to clarify the timing of rock failure. It was found that rock failure
timing was random in triangular, reverse triangular and small amplitude triangular loading tests and all rocks
failed during larger strain in large amplitude triangular loading tests. The results suggest that rock specimens did
not have to fail under larger strain when the stress amplitude was smaller than a certain value and gave us clues
to explain why rocks do not always fail under larger stress. The mechanism behind the experimental results wasexplained based on strain rate-dependent rock strength and fatigue damage.

1INTRODUCTION

It is instinctively expected that giant earthquakes occur
around spring tide because the tidal stress variation
around spring tide is the largest. Fujii et al. (2013)
however found that there were dangerous lunar phases
in which giant earthquakes concentrated for each subduction zone and the lunar phases did not have to
be around spring tides. Another example is that rockcliffs do not always collapse during earthquakes whilebuildings always collapse. These phenomena demonstrate that rock masses do not have to fail under larger
triggering forces.
To clarify the mechanism behind these phenomena,series of uniaxial compression tests were carried out on
Kimachi sandstone. In the experiments, constant loading of 10−5 s−1 for 50 s and five triangular waves withdifferent amplitudes for 50 s were alternatively applied
to the specimens. This paper describes the results ofthe experiments and discusses the mechanism behind
the results based on strain rate-dependent rock strengthand fatigue damage.

2Figure 1. Thin sectional image of Kimachi sandstone (Dassanayake, 2015).

EXPERIMENT

Kimachi sandstone was sampled at Shimane prefecture, Japan, and is a relatively well-sorted clastic rockwith a typical grain size range of 0.4–1.0 mm (Fig. 1).
It mostly consists of rock fragments of andesite; crystal fragments of plagioclase, pyroxene, hornblende,biotite, and quartz; calcium carbonate and iron oxides;
and matrix zeolites (Dhakal et al., 2002). The 30 mm
φ × 60 mm cylindrical specimens were made with aparallelism of 20 ìm at both ends through drilling, cutting and grinding. Then specimens were dried in an80◦ C oven for 48 hours and kept at room temperature

at least 5 days before the test. Specimens were alternatively subjected to constant loading rate of 10−5 s−1 for
50 s and five waves of triangular loading, reverse triangular loading, small amplitude triangular loading orlarge amplitude triangular loading (Fig. 2) for 50 s until
failure. Experimental results (Figs. 4–7) were summarized based on rock failure timing. A sudden stressdrop was considered to be rock failure. The explanation for failure timing including “constant loading”
and “cyclic loading” is shown in Figure. 3.
The probability p of the random null hypothesis
which assumes that rock failure timing is random for159

Figure 3. Explanation of “constant loading” and “cyclicloading”.

Table 1. Summary of the results (p: the probability of therandom null hypothesis to have m or more specimens failing
during cyclic loading).
Loading pattern

Constant

Cyclicp (%)

Triangular
Reverse
Large
Small

10100
28165376
16350

the case where m or more rock specimens fail during cyclic loading was calculated using the following
equation.

Figure 2. Four loading patterns. (a) Triangular loading, (b)Reverse triangular loading, (c) Small amplitude triangularloading and (d) Large amplitude triangular loading.

where n = the total number of specimens; h = theprobability that a rock specimen fails during cyclicloading (0.5); n Cj = the number of combination forthe case where j specimens are selected from n specimens. Usually the random null hypothesis is rejected
when p is smaller than 5%.
Results of rock failure timing and the probability p
are shown in Table 1. For the triangular loading test,
reverse triangular loading test and small amplitude
triangular loading test, many rock specimens failed
during constant rate loading. The probability is muchlarger than 5% and the rock failure timing is statistically considered to be random. These results correspond with the phenomena that rock cliffs do not haveto fail during giant earthquakes and some giant earthquakes occur during neap tide other than spring tide.
While in the large amplitude triangular loading test(n = 5 and m = 5), all rocks failed during larger strain

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Figure 4. Examples of triangular loading test.

Figure 5. Examples of reverse triangular loading test.

3(Fig. 8). The probability p was smaller than 5% andthe random null hypothesis was rejected. It can be statistically concluded that the specimens failed during
larger strain under larger triangular loading.

MECHANISM OF THE DIFFERENCE
IN FAILURE TIMING

According to Sano (1981), logarithm of rock strength
σmax increases linearly with logarithm of strain rate161

Figure 7. Examples of large amplitude triangular loadingtest.

ε̇ (Fig. 9) and their relationship can be expressed asEquation 2.

Figure 6. Examples of small amplitude triangular loading
test.

where A = constant; n = the stress corrosion index.
The stress corrosion index n and constant A wasevaluated as 63 and 44.8 MPa for Kimachi sandstone through the one specimen method proposed by
Hashiba et al (2006). Substituting n, ε̇ and A into Equation 2, theoretical strength increase due to the cyclicloading can be calculated.
For triangular and small amplitude triangular loading tests, actual stress increase (Fig. 11) is similar
to theoretical strength increase (Fig. 10). Rock failures were therefore random. A significant differencein neither stress increase nor stress amplitude was162

Table 2. Average stress increase and average stress amplitude in the last cyclic loading before failure as value ±standard deviation (number of specimens).

Loading pattern

Stress increase(MPa)

Stress amplitude(MPa)

Triangular
ReverseLarge
Small

1.39 ± 0.09 (18)
1.74 ± 0.16 (26)
14.09 ± 1.28 (5)0.26 ± 0.04 (5)1.75 ± 0.37 (18)
2.43 ± 0.47 (26)28.37 ± 3.23 (5)0.36 ± 0.07 (5)Figure 10. Theoretical strength increase and actual stressincrease due to larger strain rate at the loading part of thecyclic loading. a: small amplitude triangular loading test, b:
triangular loading test, c: reverse triangular loading test andd:large amplitude triangular loading test.

Figure 8. Explanation of “larger strain” and “smallerstrain”.

Figure 11. Stress increase σI and stress amplitude σA .
Figure 9. Relationship between rock strength σmax andstrain rate ε̇found among specimens failing during constant rateand cyclic loading (Fig. 12).
Stress increase and stress amplitude in the reverse
triangular loading tests were larger than those under
triangular loading (Table 2 and Fig. 12). This would be
one of the reasons why more rocks failed during cyclicloading in reverse triangular loading tests than triangular loading tests. Not only the larger stress but also

severer fatigue damage due to the larger stress amplitude in reverse triangular loading may facilitate rock
failure during the cyclic loading. A significant difference in neither stress increase nor stress amplitude
was found among specimens failing during constantrate and cyclic loading again (Fig. 12).
For the large amplitude triangular loading tests,
actual stress increase is much larger than the theoretical strength increase (Fig. 9). It is natural that all
specimens failed during larger strain (Fig. 8).

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small amplitude triangular loading tests and all rocks
failed during larger strain in large amplitude triangularloading tests. The results suggest that rock specimens
did not have to fail under larger strain when the stressamplitude was smaller than a certain value and gave
us clues to explain why rocks do not always fail underlarger stress. The mechanism behind the experimental
results was explained based on strain rate-dependentrock strength and fatigue damage. Examination should
be carried out either on other rock types or under
triaxial compression for the next step.
REFERENCES

Figure 12. Stress increase and stress amplitude (Fig. 10) for
the triangular and the reverse triangular loading tests.

4

CONCLUSIONS

Series of uniaxial compression tests combining constant strain rate and four patterns of cyclic loadingwere carried out on Kimachi sandstone to clarify thetiming of rock failure. It was found that rock failure
timing was random in triangular, reverse triangular andDassanayake. A.B.N. 2015. Effective Stress Coefficient forRocks of Peak and Residual Strengths, Ph.D thesis,
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Dhakal G., Yoneda T., Kato M., & Kaneko K. 2002. Slake
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Fujii, Y., Ozaki, Y., Fukuda, D. & Kodama, J. 2013. Why Do
Giant Earthquakes Occur at Lunar Phases Specific to Each
Subduction Zone? Proceedings of the 6th International
Symposium on In-situ Rock Stress, RS2013-1021.
Hashiba, K., Okubo, S., & Fukui, K. 2006. A New Testing Method for Investigating the Loading Rate Dependency of Peak and Residual Rock Strength. Int. J. RockMechanics & Mining Sciences.
Sano, O. 1981. Influence of Strain Rate on Dilatancy andStrength of Oshima Granite under Uniaxial Compression.
Journal of Geophysical Research.

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