Skip to main content
Top
Published in: Geotechnical and Geological Engineering 5/2021

20-02-2021 | Original Paper

New Systematic Method to Determine Elastic Constants and Crack Propagation Thresholds of Brittle Rocks Under Triaxial Compression

Authors: Hua Yu, Kam Ng

Published in: Geotechnical and Geological Engineering | Issue 5/2021

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

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.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
go back to reference 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):865–878CrossRef 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):865–878CrossRef
go back to reference 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 (2008) Standard practices for preparing rock core as cylindrical test specimens and verifying conformance to dimensional and shape tolerances. D4543, ASTM International, West Conshohocken
go back to reference 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 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
go back to reference 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):395–406CrossRef 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):395–406CrossRef
go back to reference Bieniawski ZT (1967b) Mechanism of brittle rock fracture. Part II. Experimental studies. Int J Rock Mech Min Sci Geomech Abstr 4(4):407–423CrossRef Bieniawski ZT (1967b) Mechanism of brittle rock fracture. Part II. Experimental studies. Int J Rock Mech Min Sci Geomech Abstr 4(4):407–423CrossRef
go back to reference 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 (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
go back to reference Brace WF, Paulding BW, Scholz C (1966) Dilatancy in the fracture of crystalline rocks. J Geophys Res 71(16):3939–3953CrossRef Brace WF, Paulding BW, Scholz C (1966) Dilatancy in the fracture of crystalline rocks. J Geophys Res 71(16):3939–3953CrossRef
go back to reference 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 52:9–17CrossRef 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 52:9–17CrossRef
go back to reference Diederichs MS (2003) Manuel Rocha medal recipient: rock fracture and collapse under low confinement conditions. Rock Mech Rock Eng 36(5):339–381CrossRef Diederichs MS (2003) Manuel Rocha medal recipient: rock fracture and collapse under low confinement conditions. Rock Mech Rock Eng 36(5):339–381CrossRef
go back to reference 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):1082–1116CrossRef 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):1082–1116CrossRef
go back to reference 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 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
go back to reference Eberhardt E, Stead D, Stimpson B, Read RS (1998) Identifying crack initiation and propagation thresholds in brittle rock. Can Geotech J 35(2):222–233CrossRef Eberhardt E, Stead D, Stimpson B, Read RS (1998) Identifying crack initiation and propagation thresholds in brittle rock. Can Geotech J 35(2):222–233CrossRef
go back to reference Fjær E, Holt RM, Raaen AM, Horsrud P (2008) Petroleum related rock mechanics, 2nd edn. Elsevier, New York Fjær E, Holt RM, Raaen AM, Horsrud P (2008) Petroleum related rock mechanics, 2nd edn. Elsevier, New York
go back to reference Jaeger JC, Cook NGW, Zimmerman RW (2007) Fundamentals of rock mechanics, 4th edn. Wiley-Blackwell, Oxford Jaeger JC, Cook NGW, Zimmerman RW (2007) Fundamentals of rock mechanics, 4th edn. Wiley-Blackwell, Oxford
go back to reference 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 3:77–88CrossRef 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 3:77–88CrossRef
go back to reference Lajtai EZ (1974) Brittle fracture in compression. Int J Fract Mech 10:525–536CrossRef Lajtai EZ (1974) Brittle fracture in compression. Int J Fract Mech 10:525–536CrossRef
go back to reference Lajtai EZ, Lajtai VN (1974) The evolution of brittle fracture in rocks. J Geol Soc Lond 130:1–18CrossRef Lajtai EZ, Lajtai VN (1974) The evolution of brittle fracture in rocks. J Geol Soc Lond 130:1–18CrossRef
go back to reference Martin CD, Chandler NA (1994) The progressive fracture of Lac du Bonnet granite. Int J Rock Mech Min Sci Geomech Abstr 31(6):643–659CrossRef Martin CD, Chandler NA (1994) The progressive fracture of Lac du Bonnet granite. Int J Rock Mech Min Sci Geomech Abstr 31(6):643–659CrossRef
go back to reference Nicksiar M, Martin CD (2012) Evaluation of methods for determining crack initiation in compression tests on low-porosity rocks. Rock Mech Rock Eng 45:607–617CrossRef Nicksiar M, Martin CD (2012) Evaluation of methods for determining crack initiation in compression tests on low-porosity rocks. Rock Mech Rock Eng 45:607–617CrossRef
go back to reference Paterson MS, Wong TF (2005) Experimental rock deformation-the brittle field. Springer, Berlin Paterson MS, Wong TF (2005) Experimental rock deformation-the brittle field. Springer, Berlin
go back to reference 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 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
go back to reference Stacey TR (1981) A simple extension strain criterion for fracture of brittle rock. Int J Rock Mech Min Sci Geomech Abstr 18(6):469–474CrossRef Stacey TR (1981) A simple extension strain criterion for fracture of brittle rock. Int J Rock Mech Min Sci Geomech Abstr 18(6):469–474CrossRef
go back to reference Walsh JB (1965) The effect of cracks on the uniaxial compression of rock. J Geophys Res 70:399–411CrossRef Walsh JB (1965) The effect of cracks on the uniaxial compression of rock. J Geophys Res 70:399–411CrossRef
go back to reference 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 50:1691–1710CrossRef 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 50:1691–1710CrossRef
go back to reference 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):561–575CrossRef 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):561–575CrossRef
go back to reference 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):983–991CrossRef 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):983–991CrossRef
go back to reference Zoback MD (2007) Reservoir geomechanics. Cambridge University Press, New YorkCrossRef Zoback MD (2007) Reservoir geomechanics. Cambridge University Press, New YorkCrossRef
Metadata
Title
New Systematic Method to Determine Elastic Constants and Crack Propagation Thresholds of Brittle Rocks Under Triaxial Compression
Authors
Hua Yu
Kam Ng
Publication date
20-02-2021
Publisher
Springer International Publishing
Published in
Geotechnical and Geological Engineering / Issue 5/2021
Print ISSN: 0960-3182
Electronic ISSN: 1573-1529
DOI
https://doi.org/10.1007/s10706-021-01737-8

Other articles of this Issue 5/2021

Geotechnical and Geological Engineering 5/2021 Go to the issue