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Cyclic and Fatigue Behaviour of Rock Materials: Review, Interpretation and Research Perspectives

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Abstract

The purpose of this paper is to provide a comprehensive state of the art of fatigue and cyclic loading of natural rock materials. Papers published in the literature are classified and listed in order to ease bibliographical review, to gather data (sometimes contradictory) on classical experimental results and to analyse the main interpretation concepts. Their advantages and limitations are discussed, and perspectives for further work are highlighted. The first section summarises and defines the different experimental set-ups (type of loading, type of experiment) already applied to cyclic/fatigue investigation of rock materials. The papers are then listed based on these different definitions. Typical results are highlighted in next section. Fatigue/cyclic loading mainly results in accumulation of plastic deformation and/or damage cycle after cycle. A sample cyclically loaded at constant amplitude finally leads to failure even if the peak load is lower than its monotonic strength. This subcritical crack is due to a diffuse microfracturing and decohesion of the rock structure. The third section reviews and comments the concepts used to interpret the results. The fatigue limit and S–N curves are the most common concepts used to describe fatigue experiments. Results published from all papers are gathered into a single figure to highlight the tendency. Predicting the monotonic peak strength of a sample is found to be critical in order to compute accurate S–N curves. Finally, open questions are listed to provide a state of the art of grey areas in the understanding of fatigue mechanisms and challenges for the future.

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Acknowledgements

This work is supported by the Walloon Region (Belgium) through SMARTWATER project. The authors would like to gratefully acknowledge Pr. Imai for providing useful papers and references as well as Pr. Michael Heap for providing original figures and data.

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  1. Allee de la Decouverte, 9, 4000, Liège, Belgium

    B. Cerfontaine & F. Collin

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  1. B. Cerfontaine
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Correspondence to B. Cerfontaine.

Appendix: List of Papers

Appendix: List of Papers

References

Material

Frequency, rate

Type

N max

Fatigue limit

Load signal

Grover et al. (1950)

Limestone

–

Uniaxial

–

0.65

Constant

Shreiner and Pavlova (1958)

–

–

–

–

–

–

Burdine (1963)

Sandstone

15–50 Hz

Uniaxial, triaxial

1 × 106

0.74

Constant

Haimson and Kim (1971)

Marbre

2–4 Hz

Uniaxial

1 × 106

0.75

Constant

Attewell and Farmer (1973)

Limestone

0.3–20 Hz

Uniaxial

4.1 × 104

–

Constant

Brown and Hudson (1974)

Gypsum plaster

0.5–2 Hz

Uniaxial

1.4 × 104

–

Constant

Scholz and Kranz (1974)

Granite

1 × 10−5 /s

Uniaxial

2 × 101

–

Constant

Rajaram (1981)

Westerly granite

1 Hz

Uniaxial

1 × 106

0.73

Constant

Singh (1989)

Sandstone

1 Hz

Uniaxial

1 × 104

0.87

Constant

Tien et al. (1990)

Sandstone

0.1–1 Hz

Triaxial

1 × 103

–

Constant

Zhenyu and Haihong (1990)

Sandstone, marble

0.0019–0.005 Hz

Uniaxial

–

–

Constant, ramp

Li et al. (1992)

Sandstone

0.5 Hz

Brazilian

3 × 104

–

Constant

Martin and Chandler (1994)

Granite

0.75 Mpa/s

Uniaxial, triaxial

–

–

Damage

Celestino et al. (1995)

Granite

7 kN/min

Brazilian

2.3 × 101

–

Constant

Eberhardt et al. (1999)

Granite

0.25 MPa/s

Uniaxial

–

–

Damage

Yamashita et al. (1999)

Tuff, sandstone, marble, granite

1 Hz

Uniaxial

1 × 106

0.55–0.80

Constant

Royer-Carfagni and Salvatore (2000)

Marble

1–2 Mpa/s

Uniaxial

1.8 × 102

–

Constant

Cattaneo and Labuz (2001)

Marble

–

Flexion

–

–

Damage

Lavrov (2001

Limestone

–

Uniaxial, Brazilian

–

–

Damage

Gatelier et al. (2002)

Sandstone

0.025–0.2 Hz

Uniaxial, triaxial

–

–

Damage

Li et al. (2003)

Sandstone

2–20 Hz

Uniaxial

–

–

Damage

Åkesson et al. (2004)

Granite

4 Hz

Uniaxial

3.5 × 104

0.6

Constant

Ko (2005)

Gypsum

0.5 Hz

Uniaxial

4 × 103

–

Constant

Bagde and Petroš (2005a)

Sandstone

0.1–1–10 Hz

Uniaxial

–

–

Ramp

Zhang et al. (2008)

Reconstituted

0.02, 2, 1 Hz

Uniaxial

–

–

Constant

Heap and Faulkner (2008)

Granite

2.5 MPa/min

Uniaxial

–

–

Damage

Mitchell and Faulkner (2008)

Granite, granodiorite

3.3 × 10−4 Hz

Triaxial

1 × 101

–

Constant

Xiao et al. (2009)

Granite

0.2 Hz

Uniaxial

–

–

Constant

Heap et al. (2009)

Basalt

–

Uniaxial

–

–

Damage

Heap et al. (2010)

Basalt, sandstone, granite

7 × 10−6 s−1

Triaxial

–

–

Damage

Xiao et al. (2010)

Granite

0.2 Hz

Uniaxial

3 × 103

–

Constant

Xiao et al. (2010)

Granite

0.2 Hz

Uniaxial

1 × 103

–

Constant

Fuenkajorn and Phueakphum (2010)

Salt

0.001–0.03 Hz

Triaxial

1 × 103

–

Constant

Erarslan and Williams (2012b)

Tuff

1 Hz

Brazilian

1 × 105

0.7

Constant, ramp

Erarslan and Williams (2012a)

Brisbane

1 Hz

Brazilian

2.9 × 103

–

Ramp

Liu and He (2012)

Sandstone

1 Hz

Triaxial

6.2 × 102

–

Constant

Guo et al. (2012)

Salt

1 Hz

Uniaxial

1.5 × 104

0.75

Constant

David et al. (2012)

Sandstone, granite

2 × 10−6 s−1

Uniaxial

–

–

Damage

Wang et al. (2013)

Granite

50 N/s

Triaxial

–

–

Damage

Ma et al. (2013)

Salt

0.025 –0.1 Hz

Triaxial

8.5 × 102

–

Constant

Song et al. (2013)

Salt

0.36–10 kN/s

Uniaxial

6 × 102

–

Constant

Trippetta et al. (2013)

Evaporites

7 × 10−6 s−1

Uniaxial

–

–

Damage

Faoro et al. (2013)

Granite, basalt

5 × 10−6 m/s

Triaxial

–

–

Damage

Kendrick et al. (2013)

Volcanic

1 × 10−5 s−1

Uniaxial

–

–

Damage

Bastian et al. (2014)

Sandstone

1–6 mm/min

Uniaxial, triaxial

1 × 102

–

Constant

Erarslan et al. (2014)

Tuff

–

Brazilian

\(8\times 10^5\)

0.68

Constant, ramp

Nejati and Ghazvinian (2014)

Marble, sandstone, limestone

1 Hz

Brazilian

\(3\times 10^3\)

0.6/0.7/0.8

Constant

Le et al. (2014)

Sandstone

1 Hz

Flexion

\(5.5 \times 10^3\)

–

Constant

Liu et al. (2014)

Salt

1 Hz

Uniaxial

–

–

Damage

Pola et al. (2014)

Lava, pyroclastic, tuff, ignimbrite

4 mm/h

Uniaxial

–

–

Damage

Ni (2014)

Granite

0.01–1 Hz

Uniaxial

–

–

Constant

Momeni et al. (2015)

Granite

0.1–5 Hz

Uniaxial

\(2.4\times 10^3\)

–

Constant

Voznesenskii et al. (2015)

Limestone, gabbro, marble

–

Uniaxial

200

–

Constant

Yang et al. (2015)

Sandstone

0.08 mm/min

Triaxial

–

–

Damage

Schaefer et al. (2015)

Basalt

\(10^{-5}\) s\(^{-1}\)

Uniaxial

–

–

Damage

Voznesenskii et al. (2016)

Gypsum

–

Uniaxial

\(1\times 10^2\)

–

Constant

Taheri et al. (2016)

Sandstone

0.5 mm/min

Triaxial

\(2.2\times 10^3\)

–

Constant, damage

Ghamgosar and Erarslan (2016)

Tuff

1–5 Hz

Brazilian

–

–

Ramp, damage

Erarslan (2016)

Tuff

–

Brazilian

–

–

Constant, ramp

Wang et al. (2016)

Salt

0.05 kN/s

Brazilian

\(5.2 \times 10^3\)

–

Damage

Fan et al. (2016)

Salt

2 kN/s

Uniaxial

\(9 \times 10^1\)

–

Interval

Jiang et al. (2016)

Salt

2 kN/s

Uniaxial

\(6 \times 10^1\)

–

Interval

Song et al. (2016)

Sandstone

0.12 mm/min

Uniaxial

–

–

Damage

Meng et al. (2016)

Sandstone

0.5–4 kN/s

Uniaxial

–

–

Damage

Karakus et al. (2016)

Sandstone

–

Uniaxial

\(1\times 10^4\)

–

Constant

Fan et al. (2017)

Salt

2 kN/s

Uniaxial

\(9 \times 10^1\)

–

Interval

Jobli et al. (2017)

Granite

1 Hz

Uniaxial

\(1\times 10^2\)

–

Constant

Yang et al. (2017)

Marble

0.02 mm/s

Triaxial

–

–

Damage

Wang et al. (2017)

Sandstone

–

Triaxial

–

–

Damage

Ghamgosar et al. (2017)

Tuff/monzonite

1, 5 Hz

Brazilian

–

–

Ramp

Voznesenskii et al. (2017)

Salt

0.0001–2 mm/min

Uniaxial

\(\times 10^2\)

–

Constant

Liu et al. (2017)

Sandstone

1 Hz

Brazilian

\(8.5 \times 10^2\)

–

Constant

Liu et al. (2017)

Artificial

0.01–20 Hz

Uniaxial

\(1.2\times 10^3\)

–

Constant

Jamali Zavareh et al. (2017)

Gabbro, onyx, limestone

5 Hz

Bending

\(>1\times 10^6\)

0.4–0.6

Constant

Munoz and Taheri (2017)

Sandstone

\(0.18 \times 10^{-4}\) s\(^{-1}\)

Uniaxial

–

–

Damage

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Cerfontaine, B., Collin, F. Cyclic and Fatigue Behaviour of Rock Materials: Review, Interpretation and Research Perspectives. Rock Mech Rock Eng 51, 391–414 (2018). https://doi.org/10.1007/s00603-017-1337-5

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