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Analysis of the Historic Bondi Pumping Chamber Case Study Using the Adjusted Voussoir Beam Analog

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Abstract

Analytical methods in engineering design use simplifying assumptions to reduce the number of variables considered for a given problem. In rock engineering design, this reduction in complexity increases practical applicability but often must be applied with a degree of conservatism, as relevant mechanisms may remain unaccounted for in a given analytical solution. To date, the voussoir beam analog has seen relatively limited application to complex roof stability problems. Previous research by the authors has used numerical modeling to expand the voussoir beam analog by developing analytical solution adjustments to account for important factors such as horizontal bedding and passive bolts. This paper presents the application of the adjusted voussoir beam analytical solution in a case study of the historic Bondi Pumping Chamber. Discrete element method numerical models are also presented to elucidate the mechanisms governing stability and deflection of the supported roof beam. The results of this study provide a novel real-world validation of the adjusted voussoir beam analog and insight into its practical applicability and limitations.

Highlights

  • Successful field application of a voussoir beam analytical solution that accounts for supported flat-roof excavations in discontinuous rockmasses

  • Effects of roof support installation timing and variations in discontinuity strength and stiffness identified through numerical models

  • Self-supporting capacity of flat-roof excavations explored through comparison of numerical and analytical results

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Availability of Data and Materials

Data taken from published literature (see references).

Code availability

Available upon request.

Abbreviations

E:

Young’s modulus

sj :

Joint spacing

jkn :

Joint normal stiffness

Erm :

Rockmass modulus

Ermn :

Adjusted rockmass modulus

C:

Scaling coefficient

n:

Number of passively bolted layers

Ti :

Individual layer thickness

Te :

Effective beam thickness

References

  • Abousleiman R, Sinha S, Walton G (2021) Expanding application of the voussoir beam analog to horizontally bedded and passively bolted flat-roof excavations using the discrete element method. Int J Rock Mech Min Sci 148:104919

    Article  Google Scholar 

  • Alejano LR, Taboada J, García-Bastante F, Rodriguez P (2008) Multi-approach back-analysis of a roof bed collapse in a mining room excavated in stratified rock. Int J Rock Mech Min Sci 45:899–913. https://doi.org/10.1016/J.IJRMMS.2007.10.001

    Article  Google Scholar 

  • Bahrani N, Hadjigeorgiou J (2017) Explicit reinforcement models for fully-grouted rebar rock bolts. J Rock Mech Geotech Eng 9:267–280. https://doi.org/10.1016/j.jrmge.2016.07.006

    Article  Google Scholar 

  • Bandis S (1980) Experimental studies of scale effects on shear strength, and deformation of rock joints. PhD dissertation, University of Leeds

  • Beer G, Meek J (1982) Design curves for roofs and hanging-walls in bedded rock based on “voussoir” beam and plate solutions. Inst Min Metall Trans

  • Bertuzzi R, Pells P (2002) Geotechnical parameters of Sydney sandstone and shale. Aust Geomech J News Aust Geomech Soc 37:41–54

    Google Scholar 

  • Boon CW, Houlsby GT, Utili S (2015) Designing tunnel support in jointed rock masses via the DEM. Rock Mech Rock Eng 48:603–632. https://doi.org/10.1007/s00603-014-0579-8

    Article  Google Scholar 

  • Brady BHG, Brown ET (2013) Rock mechanics: for underground mining. Springer Science & Business Media, Berlin

    Google Scholar 

  • Carvalho JL, Carter TG (2020) Revision of the voussoir beam analogue for crown pillars. In: 54th U.S. rock mechanics/geomechanics symposium, American Rock Mechanics Association

  • Chryssanthakis P, Barton N, Lorig L, Christianson M (1997) Numerical simulation of fiber reinforced shotcrete in a tunnel using the discrete element method. Int J Rock Mech Min Sci Geomech Abstr 34:590. https://doi.org/10.1016/S1365-1609(97)00094-4

    Article  Google Scholar 

  • Clancy KG (1984) Design and Construction Planning for Sydney’s Sewerage Outfalls General Report June 1984. In: Fifth Australian tunnelling conference: state of the art in underground development and construction; preprints of papers. Institution of Engineers, Australia, p 98

  • Diederichs MS, Kaiser PK (1999) Stability of large excavations in laminated hard rock masses: the voussoir analogue revisited. Int J Rock Mech Min Sci 36:97–117. https://doi.org/10.1016/S0148-9062(98)00180-6

    Article  Google Scholar 

  • Evans WH (1941) The strength of undermined strata. Am Inst Min Metall Eng 50:475–500

    Google Scholar 

  • Fayol H (1885) Note sur les mouvements de terrain provoquée par l’exploitation des mines

  • He L, Zhang QB (2015) Numerical investigation of arching mechanism to underground excavation in jointed rock mass. Tunn Undergr Space Technol 50:54–67

    Article  Google Scholar 

  • Henderson ADD, Windsor CRR (1988) Investigations, planning and construction control I for the Sydney ocean outfalls tunnels. In: Cost effective tunnelling in the Sydney Basin: AUCTA seminar, Sydney, July 1988. Australian Underground Construction and Tunnelling Association, p 44

  • Hillis RR, Enever JR, Reynolds SD (1999) In situ stress field of eastern Australia. Aust J Earth Sci 46:813–825. https://doi.org/10.1046/j.1440-0952.1999.00746.x

    Article  Google Scholar 

  • Itasca Consulting Group Inc. (2014) UDEC‐universal distinct element code, version 6.0

  • McQueen LB (2004) In situ rock stress and its effect in tunnels and deep excavations in Sydney. Aust Geomech 39:43–57

    Google Scholar 

  • Nye E, Rowe A, McQueen LB (2005) Bondi STP RIAMP underground facility. In: Proceedings of the 12th Australian tunnelling conference. Australian Underground COnstruction and Tunnelling Association, Brisbane, Qld., pp 212–221

  • Oliveira D, Paramaguru L (2016) Laminated rock beam design for tunnel support. Aust Geomech J 51:1–17

    Google Scholar 

  • Oliveira D, Pells P (2014) Revisiting the applicability of voussoir beam theory for tunnel design in Sydney. Artic Aust Geomech J 49:29–44

    Google Scholar 

  • Pells P (1993) Rock mechanics and engineering geology in the design of underground works. EH Davis Meml Lect 1993:3–21

    Google Scholar 

  • Pells P (2004) Substance and mass properties for the design of engineering structures in the Hawkesbury sandstone. Aust Geomech 39:1–21

    Google Scholar 

  • Pells P, Best RJ (1991) Aspects of primary support design for tunnels in the Sydney Basin. Trans Inst Eng Aust Civ Eng CE33:57–66. Int J Rock Mech Min Sci Geomech Abstr 29:261–262. https://doi.org/10.1016/0148-9062(92)90957-2

    Article  Google Scholar 

  • Pells P, Pells SE, Pan L (2018) On the resistance provided by grouted rock reinforcement to shear along bedding planes and joints. Aust Geomech 53:55–74

    Google Scholar 

  • Ran JQ, Passaris EKS, Mottahed P (1994) Shear sliding failure of the jointed roof in laminated rock mass. Rock Mech Rock Eng 27:235–251. https://doi.org/10.1007/BF01020201

    Article  Google Scholar 

  • Shabanimashcool M, Li CC (2015) Analytical approaches for studying the stability of laminated roof strata. Int J Rock Mech Min Sci 79:99–108. https://doi.org/10.1016/j.ijrmms.2015.06.007

    Article  Google Scholar 

  • Sofianos AI (1996) Analysis and design of an underground hard rock voussoir beam roof. Int J Rock Mech Min Sci Geomech Abstr 33:153–166. https://doi.org/10.1016/0148-9062(95)00052-6

    Article  Google Scholar 

  • Sofianos AI, Kapenis AP (1998) Numerical evaluation of the response in bending of an underground hard rock voussoir beam roof. Int J Rock Mech Min Sci 35:1071–1086. https://doi.org/10.1016/S0148-9062(98)00166-1

    Article  Google Scholar 

  • Talesnick ML, Ya’Acov NB, Cruitoro A (2007) Modeling of a multiply jointed voussoir beam in the centrifuge. Rock Mech Rock Eng 40:383–404. https://doi.org/10.1007/s00603-006-0104-9

    Article  Google Scholar 

  • Tsesarsky M (2012) Deformation mechanisms and stability analysis of undermined sedimentary rocks in the shallow subsurface. Eng Geol 133–134:16–29. https://doi.org/10.1016/j.enggeo.2012.02.007

    Article  Google Scholar 

  • Vlachopoulos N, Diederichs MS (2009) Improved longitudinal displacement profiles for convergence confinement analysis of deep tunnels. Rock Mech Rock Eng Rock Engng 42:131–146. https://doi.org/10.1007/s00603-009-0176-4

    Article  Google Scholar 

  • Walton G, Diederichs MS, Punkkinen A (2015) The influence of constitutive model selection on predicted stresses and yield in deep mine pillars—a case study at the Creighton mine, Sudbury, Canada. Geomech Tunn 8:441–449. https://doi.org/10.1002/geot.201500023

    Article  Google Scholar 

  • Wright F (1972) Arching action in cracked roof beams. In: Fifth international strata control conference. Morgantown, West Virginia

  • Wright F, Mirza M (1963) Stress distribution around a vertical crack in a mine roof beam. Trans Inst Min Eng 226:174–179

    Google Scholar 

  • Yiouta-Mitra P, Sofianos AI (2018) Μulti-jointed stratified hard rock roof analysis and design. Int J Rock Mech Min Sci 106:96–108

    Article  Google Scholar 

  • Zhang ZX, Xu Y, Kulatilake PHSW, Huang X (2012) Physical model test and numerical analysis on the behavior of stratified rock masses during underground excavation. Int J Rock Mech Min Sci 49:134–147

    Article  Google Scholar 

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Acknowledgements

The views, opinions, and recommendations expressed herein are solely those of the authors and do not imply any endorsement by the ALPHA FOUNDATION, its directors and staff. Part of the modeling effort for this study was conducted as part of the first author’s course of study using educational licenses of UDEC provided by Itasca Consulting, Ltd. The authors appreciate Itasca’s support in this capacity. The authors also thank David Oliveira and Phillip Pells for their correspondence, guidance, and insight into the Bondi Pumping Chamber case study.

Funding

This study was primarily sponsored by the Alpha Foundation for the Improvement of Mine Safety and Health, Inc. (ALPHA FOUNDATION). The research conducted for this study was also partially funded by the National Institute of Occupational Health and Science (NIOSH) under Grant Number 200–2016-90154.

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Authors and Affiliations

  1. Knight Piésold and Co., Denver, CO, USA

    Rami Abousleiman

  2. WSP, Phoenix, AZ, USA

    Sankhaneel Sinha

  3. Colorado School of Mines, Golden, CO, USA

    Sankhaneel Sinha & Gabriel Walton

Authors
  1. Rami Abousleiman
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  2. Sankhaneel Sinha
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  3. Gabriel Walton
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Contributions

Rami Abousleiman: conceptualization, methodology, validation, formal analysis, investigation, data curation, writing—original draft, writing—review & editing, visualization. Sankhaneel Sinha: conceptualization, methodology, writing—review & editing. Gabriel Walton: conceptualization, methodology, resources, writing—review & editing, supervision, project administration, funding acquisition.

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Correspondence to Rami Abousleiman.

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Abousleiman, R., Sinha, S. & Walton, G. Analysis of the Historic Bondi Pumping Chamber Case Study Using the Adjusted Voussoir Beam Analog. Rock Mech Rock Eng 56, 6357–6374 (2023). https://doi.org/10.1007/s00603-023-03396-y

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