Abstract
Elastic constants and crack propagation stress thresholds of brittle rocks are important mechanical properties for engineering applications. However, these properties are currently determined using methods with subjective interpreting procedures, which create cognitive biases leading to a higher degree of uncertainties. In this study, triaxial compression tests were conducted on Weber Sandstone collected from the Rock Springs Uplift, Wyoming. Nine rock specimens were treated in different geochemical conditions and tested for three different confining pressures at an in-situ pore pressure and temperature. A new method is proposed to systematically determine elastic constants and crack stress thresholds using linear and cubic regression functions to describe the linear and nonlinear stress–strain elastic behaviors, respectively. The statistical approach implemented in this new method eliminates bias due to the subjective interpretation of the nonlinear stress–strain data. The proposed method improves the consistency of elastic constant determinations by considering the linear elastic boundary of rocks and unambiguously determines the crack initiation threshold using the cubic regression function. Eliminating the subjectivity in data analysis, the new systematic method is beneficial for studying the nonlinear rock behavior and facilitating engineering applications.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andersson C, Martin CD, Stille H (2009) The Aspopillar stability experiment: part II—rock mass response to coupled excavation induced and thermal-induced stresses. Int J Rock Mech Min Sci 46(5):865–878
ASTM (2008) Standard practices for preparing rock core as cylindrical test specimens and verifying conformance to dimensional and shape tolerances. D4543, ASTM International, West Conshohocken
ASTM (2014) Standard test methods for compressive strength and elastic moduli of intact rock core specimens under varying states of stress and temperatures. D7012, ASTM International, West Conshohocken
Bieniawski ZT (1967a) Mechanism of brittle rock fracture. Part I. Theory of the fracture process. Int J Rock Mech Min Sci Geomech Abstr 4(4):395–406
Bieniawski ZT (1967b) Mechanism of brittle rock fracture. Part II. Experimental studies. Int J Rock Mech Min Sci Geomech Abstr 4(4):407–423
Brace WF (1964) Brittle fracture of rocks. In: Judd WR (ed) State of stress in the earth’s crust. Proceedings of the international conference, Santa Monica, Calif. Elsevier, New York, pp 110–178
Brace WF, Paulding BW, Scholz C (1966) Dilatancy in the fracture of crystalline rocks. J Geophys Res 71(16):3939–3953
David EC, Brantut N, Schubnel A, Zimmerman RW (2012) Sliding crack model for nonlinearity and hysteresis in the uniaxial stress–strain curve of rock. Int J Rock Mech Min Sci 52:9–17
Diederichs MS (2003) Manuel Rocha medal recipient: rock fracture and collapse under low confinement conditions. Rock Mech Rock Eng 36(5):339–381
Diederichs MS (2007) The 2003 Canadian Geotechnical Colloquium: mechanistic interpretation and practical application of damage and spalling prediction criteria for deep tunnelling. Can Geotech J 44(9):1082–1116
Diederichs MS, Martin CD (2010) Measurement of spalling parameters from laboratory testing. In: Rock mechanics and environmental engineering. Proceedings of the European rock mechanics symposium, pp 323–326
Eberhardt E, Stead D, Stimpson B, Read RS (1998) Identifying crack initiation and propagation thresholds in brittle rock. Can Geotech J 35(2):222–233
Fjær E, Holt RM, Raaen AM, Horsrud P (2008) Petroleum related rock mechanics, 2nd edn. Elsevier, New York
Jaeger JC, Cook NGW, Zimmerman RW (2007) Fundamentals of rock mechanics, 4th edn. Wiley-Blackwell, Oxford
Johnson PA, Rasolofosaon PNJ (1996) Manifestation of nonlinear elasticity in rock: convincing evidence over large frequency and strain intervals from laboratory studies. Nonlinear Process Geophys 3:77–88
Lajtai EZ (1974) Brittle fracture in compression. Int J Fract Mech 10:525–536
Lajtai EZ, Lajtai VN (1974) The evolution of brittle fracture in rocks. J Geol Soc Lond 130:1–18
Martin CD, Chandler NA (1994) The progressive fracture of Lac du Bonnet granite. Int J Rock Mech Min Sci Geomech Abstr 31(6):643–659
Nicksiar M, Martin CD (2012) Evaluation of methods for determining crack initiation in compression tests on low-porosity rocks. Rock Mech Rock Eng 45:607–617
Paterson MS, Wong TF (2005) Experimental rock deformation-the brittle field. Springer, Berlin
Shafer LR (2013) Assessing injection zone fracture permeability through the identification of critically stressed fractures at the Rock Springs Uplift CO2 sequestration site, SW Wyoming. Ms thesis, University of Wyoming
Stacey TR (1981) A simple extension strain criterion for fracture of brittle rock. Int J Rock Mech Min Sci Geomech Abstr 18(6):469–474
Walsh JB (1965) The effect of cracks on the uniaxial compression of rock. J Geophys Res 70:399–411
Walton G, Hedayat A, Kim E, Labrie D (2017) Post-yield strength and dilatancy evolution across the brittle-ductile transition in Indiana limestone. Rock Mech Rock Eng 50:1691–1710
Wawersik WR, Fairhurst C (1970) A study of brittle rock fracture in laboratory compression experiments. Int J Rock Mech Min Sci Geomech Abstr 7(5):561–575
Yu H, Ng K, Grana D, Kaszuba J, Alvarado V, Campbell E (2018) Experimental investigation of the effect of compliant pores on reservoir rocks under hydrostatic and triaxial compression stress states. Can Geotech J 56(7):983–991
Zoback MD (2007) Reservoir geomechanics. Cambridge University Press, New York
Acknowledgements
The authors wish to thank the funding support from United States Department of Energy (DOE) under the Award No. DE-FE0023328. This manuscript is the result of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. The authors also appreciate the research assistance from Dr. John Kaszuba, Dr. Dario Grana, Dr. Vladimir Alvarado, Dr. Erin Campbell, and Dr. Heng Wang.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Yu, H., Ng, K. New Systematic Method to Determine Elastic Constants and Crack Propagation Thresholds of Brittle Rocks Under Triaxial Compression. Geotech Geol Eng 39, 3931–3945 (2021). https://doi.org/10.1007/s10706-021-01737-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10706-021-01737-8