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

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.

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