Rock Mechanics and Rock Engineering

, Volume 52, Issue 12, pp 5013–5023 | Cite as

Relaxation Response of Critically Stressed Macroscale Surficial Rock Sheets

  • B. D. CollinsEmail author
  • G. M. Stock
  • M. C. Eppes
Original Paper


Rock environments both underground and on Earth’s surface show indications of energetic macroscale fracture. In tunnels and excavations, these manifest as rockbursts—energetic explosions of rock that can damage engineering projects, and may pose ongoing financial and safety risk as rock stresses adjust during post-failure relaxation. In natural settings at the surface, evidence for rockbursts exist in the form of tent-like structures of ruptured exfoliation sheets, but few direct observations of such events exist, precluding the analysis of how natural rock formations may evolve after rupture. Here we investigate the post-failure evolution of a granitic rock dome following rapid fracture events (i.e., surficial rockbursts) that occurred in California, USA during 2014–2016. Building upon previous work that showed a thermal stress origin for the observed fracturing, we investigate the return to background stress conditions (i.e., stress relaxation) observed in both short- (week, month) and long-term (multi-year) rock deformation trends. Acoustic emissions, deformation, and environmental monitoring data indicate that partially detached rock sheets forming the surface of the dome undergo fracture aperture closing during cooling periods, concurrent with reduction of rock stress by the source of forcing (i.e., thermal stress). However, with sufficient critical and/or subcritical fracture, our observations also show that rock sheets can become decoupled from the source of stress, resulting in a long-term return to background stress conditions. Our results provide insight into the cyclic and likely ephemeral nature of rock fracture in surficial rock domes, as well as in underground rockburst environments.


Exfoliation Fracture Rockburst Subcritical Thermal Stress Twain Harte California Granite 



We thank Dennis Wykoff and Lauren Gerber, Twain Harte Lake Directors for their assistance with our research efforts. We also acknowledge the contributions of our colleagues S. Lewis of Condor Earth Technologies, and S. Corbett and J. Smith (both U.S. Geological Survey; USGS) who worked with us on other parts of this project, and to R. Putnam (Moorpark College) and H. Wood (Condor Earth) who assisted with installation of instrumentation. Primary funding for this project was provided by the USGS Landslide Hazards Program. Acoustic emissions instrumentation was acquired by M. Eppes for a prior project through funding by the National Science Foundation EAR-0844335. We thank J. Perkins (USGS), R. Schulz (ARMA), and an anonymous reviewer for providing helpful feedback on earlier versions of this work. The data analyzed during the current study are available in the supplemental material accompanying this paper and/or from the corresponding author on reasonable request. Some of the work shown herein was originally presented as part of the 2018 Annual Meeting of the American Rock Mechanics Association held in Seattle, Washington in June 2018. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the US Government.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest with the research presented herein.

Supplementary material

603_2019_1832_MOESM1_ESM.xlsx (17.3 mb)
Supplementary material (XLSX 17752 kb)


  1. Al Heib M (2018) Description of rockbursts in mines. In: Feng X-T (ed) Rockburst—mechanisms, monitoring, warning, and mitigation. Butterworth-Heinemann, OxfordGoogle Scholar
  2. Atkinson BK (1984) Subcritical crack growth in geological materials. J Geophys Res 89(B6):4077–4114. CrossRefGoogle Scholar
  3. Bahat D, Grossenbacher K, Karasaki K (1999) Mechanism of exfoliation joint formation in granitic rocks, Yosemite National Park. J Struct Geol 21:85–96. CrossRefGoogle Scholar
  4. Bain GW (1931) Spontaneous rock expansion. J Geol 29:715–735CrossRefGoogle Scholar
  5. Blake W, Hedley DGF (2003) Rockbursts—case studies from North American hard-rock mines. Society for Mining, Metallurgy, and Exploration, LittletonGoogle Scholar
  6. Cai M, Kaiser PK (2018) Rockburst support reference book (volume 1): rockburst phenomenon and support characteristics. Mirarco, Laurentian University, SudburyGoogle Scholar
  7. Carlsson A, Olsson T (1982) Rock bursting phenomena in a superficial rock mass in southern central Sweden. Rock Mech 15(2):99–110. CrossRefGoogle Scholar
  8. Chen BR, Feng XT, Li QP, Luo R-Z, Li S (2015) Rock burst intensity classification based on the radiated energy with damage intensity at Jinping II Hydropower Station, China. Rock Mech Rock Eng 48(1):289–303. CrossRefGoogle Scholar
  9. Collins BD, Stock GM (2016) Rockfall triggering by cyclic thermal stressing of exfoliation fractures. Nat Geosci 9:395–401. CrossRefGoogle Scholar
  10. Collins BD, Stock GM, Eppes MC, Lewis S, Corbett S, Smith J (2018) Thermal influences on spontaneous rock dome exfoliation. Nat Commun 9(762):1–12. CrossRefGoogle Scholar
  11. Cook NGW (1963) The basic mechanics of rockbursts. J South Afr Inst Min Metall 66:56–70Google Scholar
  12. Eppes MC, Keanini R (2017) Mechanical weathering and rock erosion by climate-dependent subcritical cracking. Rev Geophys 55(2):470–508. CrossRefGoogle Scholar
  13. Eppes MC, McFadden LD, Wegmann KW, Scuderi LA (2010) Cracks in desert pavement rocks: further insights into mechanical weathering by directional insolation. Geomorphology 123(1–2):97–108. CrossRefGoogle Scholar
  14. Eppes MC, Magi B, Hallet B, Delmelle E, Mackenzie-Helnwein P, Warren K, Swami S (2016) Deciphering the role of solar-induced thermal stresses in rock weathering. Geol Soc Am Bull 128:1315–1338. CrossRefGoogle Scholar
  15. Eppes MC, Hancock GS, Chen X, Arey J, Dewers T, Huettenmoser J, Kiessling S, Moser F, Tannu N, Weiserbs B, Whitten J (2018) Rates of subcritical cracking and long-term rock erosion. Geology. CrossRefGoogle Scholar
  16. Ericson K, Olvmo M (2004) A-Tents in the central Sierra Nevada, California: a geomorphological indicator of tectonic stress. Phys Geogr 25:291–312. CrossRefGoogle Scholar
  17. Feng X-T (2018) Rockburst—mechanisms, monitoring, warning, and mitigation. Butterworth-Heinemann, OxfordGoogle Scholar
  18. Feng G-L, Feng X-T, Chen B, Xiao Y-X, Yu Y (2015) A microseismic method for dynamic warning of rockburst development processes in tunnels. Rock Mech Rock Eng 48(5):2061–2076. CrossRefGoogle Scholar
  19. Gilbert GK (1904) Domes and dome structures of the High Sierra. Geol Soc Am Bull 15:29–36CrossRefGoogle Scholar
  20. Goodman RE, Kieffer DS (2000) Behavior of rock in slopes. J Geot Geoenviron Eng 126:8. CrossRefGoogle Scholar
  21. Grosse CU, Ohtsu M (2008) Acoustic emission testing. Springer, BerlinCrossRefGoogle Scholar
  22. Holzhausen GR (1989) Origin of sheet structure. 1. Morphology and boundary conditions. Eng Geol 27:225–278. CrossRefGoogle Scholar
  23. Jahns RH (1943) Sheet structure in granites: its origin and use as a measure of glacial erosion in New England. J Geol 51:71–98CrossRefGoogle Scholar
  24. Jones C, Keaney G, Meredith PG, Murrell SAF (1997) Acoustic emission and fluid permeability measurements on thermally cracked rocks. Phys Chem Earth 22(1–2):13–17. CrossRefGoogle Scholar
  25. Kaiser PK, Tannant DD, McCreath DR (1996) Canadian rockburst support handbook. Geomechanics Research Centre, Laurentian University, SudburyGoogle Scholar
  26. Kontogianni VA, Stiros SC (2005) Induced deformation during tunnel excavation: evidence from geodetic monitoring. Eng Geol 79(1–2):115–126. CrossRefGoogle Scholar
  27. Lawn B (1993) Fracture of brittle solids, 2nd edn. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  28. Leger J-P (1991) Trends and causes of fatalities in South African mines. Saf Sci 14(3–4):169–185. CrossRefGoogle Scholar
  29. Leith K, Perras M, Siren T, Rantanen T, Wolter A, Heinonen S, Loew S (2017) Development of a new thermally-induced fracture in a 12,000 year old bedrock surface. In: Leith K, Ziegler M, Perras M, Loew S (eds) Proc progressive rock failure conf. ETH Zurich, Zurich, pp 17–19Google Scholar
  30. Leveille P, Sepehri M, Apel DB (2017) Rockbursting potential of kimberlite: a case study of Diavik Diamond Mine. Rock Mech Rock Eng 50(12):3223–3231. CrossRefGoogle Scholar
  31. Liu GF, Feng X-T, Feng G-L, Chen B-R, Chen D-F, Duan S-Q (2016) A method for dynamic risk assessment and management of rockbursts in drill and blast tunnels. Rock Mech Rock Eng 49:3257–3279. CrossRefGoogle Scholar
  32. Martel SJ (2006) Effect of topographic curvature on near-surface stresses and application to sheeting joints. Geophys Res Lett 33:L01308. CrossRefGoogle Scholar
  33. Martel SJ (2017) Progress in understanding sheeting joints over the past two centuries. J Struct Geol 94:68–86. CrossRefGoogle Scholar
  34. Matthes FE (1930) Geologic history of the Yosemite Valley. US Geol Surv Prof Paper 160Google Scholar
  35. McFadden LD, Eppes MC, Gillespie AR, Hallet B (2005) Physical weathering in arid landscapes due to diurnal variation in the direction of solar heating. Geol Soc Am Bull 117(1–2):161–173. CrossRefGoogle Scholar
  36. Meredith PG, Atkinson BK (1985) Fracture toughness and subcritical crack growth during high-temperature tensile deformation of Westerly granite and Black gabbro. Phys Earth Planet Interiors 39:33–51. CrossRefGoogle Scholar
  37. Potvin Y (2009) Surface support in extreme ground conditions—HEA Mesh. In: Dight PM (ed) Proceedings of the first international seminar on safe and rapid development mining. Australian Centre for Geomechanics, Perth, pp 111–119Google Scholar
  38. Rosser N, Lim M, Petley D, Dunning S, Allison R (2007) Patterns of precursory rockfall prior to slope failure. J Geophys Res 112:4014. CrossRefGoogle Scholar
  39. Senfaute G, Duperret A, Lawrence JA (2009) Micro-seismic precursory cracks prior to rock-fall on coastal chalk cliffs: a case study at Mesnil-Val, Normandie, NW France. Nat Haz Earth Sci 9:1625–1641. CrossRefGoogle Scholar
  40. Stock GM, Martel SJ, Collins BD, Harp E (2012) Progressive failure of sheeted rock slopes: the 2009–2010 Rhombus Wall rock falls in Yosemite Valley, California, USA. Earth Surf Process Landf 37:546–561. CrossRefGoogle Scholar
  41. Twidale CR (1973) On the origin of sheet jointing. Rock Mech 5:163–187CrossRefGoogle Scholar
  42. Twidale CR, Bourne JA (2009) On the origin of A-tents (pop-ups), sheet structures, and associated forms. Prog Phys Geogr 33:147–162CrossRefGoogle Scholar
  43. Warren K, Eppes M-C, Swami S, Garbini J, Putkonen J (2013) Automated field detection of rock fracturing, microclimate, and diurnal rock temperature and strain fields. Geosci Instrum Methods Data Syst Discuss 3:371–406. CrossRefGoogle Scholar
  44. White WS (1946) Rock-bursts in the granite quarries at Barre, Vermont. US Geological Survey Circular, New York, p 13Google Scholar
  45. Xiao Y-X, Feng X-T, Chen B-R, Feng G (2018) Microseismic monitoring method of the rockburst evolution process. In: Feng X-T (ed) Rockburst—mechanisms, monitoring, warning, and mitigation. Butterworth-Heinemann, Oxford, pp 301–315Google Scholar
  46. Yong C, Wang C-y (1980) Thermally induced acoustic emission in Westerly granite. Geophys Res Lett 7(12):1089–1092. CrossRefGoogle Scholar
  47. Zhang C, Feng X-T, Zhou H, Qiu S, Wu W (2012) Case histories of four extremely intense rockbursts in deep tunnels. Rock Mech Rock Eng 45(3):275–288. CrossRefGoogle Scholar
  48. Zhao T, Guo W, Tan Y, Yin Y, Cai L, Pan J (2018) Case studies of rock bursts under complicated geological conditions during multi-seam mining at a depth of 800 m. Rock Mech Rock Eng 51(5):1539–1564. CrossRefGoogle Scholar
  49. Ziegler M, Loew S, Bahat D (2014) Growth of exfoliation joints and near-surface stress orientations inferred from fractographic markings observed in the upper Aar valley (Swiss Alps). Tectonophysics 626:1–20. CrossRefGoogle Scholar
  50. Zimmer V, Collins BD, Stock GM, Sitar N (2012) Rock fall dynamics and deposition: an integrated analysis of the 2009 Ahwiyah Point rockfall, Yosemite National Park, USA. Earth Surf Process Landf 37(6):680–691. CrossRefGoogle Scholar

Copyright information

© This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2019

Authors and Affiliations

  1. 1.U.S. Geological SurveyMenlo ParkUSA
  2. 2.National Park Service, Yosemite National ParkEl PortalUSA
  3. 3.University of North Carolina at CharlotteCharlotteUSA

Personalised recommendations