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Discussion on Key Issues in the Application of Block Theory in Rock Engineering

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Abstract

Block theory, which successfully applies the geometric topology method to the field of rock mass stability analysis, is very suitable for analyzing the problem of local block stability caused by the cutting of structural planes (discontinuities) in engineering rock mass. It is a rare original theory in rock mechanics and engineering. However, compared with the completeness, progressiveness, and originality of the theory, the application of block theory in engineering is not widespread enough. Combining the authors’ long-term experience in fundamental research and engineering applications of block theory, this work first clarifies the differences in the connotation of block analysis before and after the excavation of rock masses. This difference reflects the main ideas of using block theory for engineering applications and also reflects the different focuses of block theory application at different construction stages. Furthermore, it is pointed out that before and after excavation, the core tasks are “block prediction-support drafting” and “block determination-support verification”, respectively. Before the excavation of the rock mass, the main tasks are to group and combine discontinuities, distinguish removable blocks and key blocks based on the whole-space stereographic projection (WSSP) for different discontinuity combinations, estimate the size and shape of unlocated blocks, analyze block stability, and draft support design parameters. After the excavation of the rock mass, the main tasks include analyzing the shape of the located block, analyzing the stability of the block, and verifying the support design parameters for rock blocks. Finally, combined with engineering cases, the key technical issues and work ideas in engineering applications were analyzed, such as how to estimate the size of the unlocated blocks, how to sort out the support-required blocks from key blocks, and how to draft or verify support parameters. The work is of great significance for the application and promotion of block theory in engineering.

Highlights

  • Different connotations of block analysis before and after rock excavation are clarified.

  • Before rock excavation, the core tasks are “block prediction-support drafting”.

  • After excavation, the core tasks are “block determination-support verification”.

  • Some key issues are discussed, such as distinguishing the support-required block.

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References

  • Carter-Greaves LE, Eyre M, Vogt D, Coggan J (2023) Algorithm development for automated key block analysis in tunnels from LiDAR point cloud data. Tunn Undergr Space Technol 132:104787

    Google Scholar 

  • Chen Z (2004) A generalized solution for tetrahedral rock wedge stability analysis. Int J Rock Mech Min Sci 41(4):613–628

    Google Scholar 

  • Chen N, Kemeny J, Jiang Q, Pan Z (2017) Automatic extraction of blocks from 3D point clouds of fractured rock. Comput Geosci 109:149–161

    ADS  Google Scholar 

  • Chen Q, Yin T, Niu W, Zheng W, Liu J (2018) Study of the geometrical size effect of a fractured rock mass based on the modified blockiness evaluation method. Arab J Geosci 11:286

    CAS  Google Scholar 

  • Cheng XL, Liu LP, Xiao J, Zhang QH, Xue J, Wang Y (2021) A general block stability analysis algorithm for arbitrary block shapes. Front Earth Sci 9:723320

    Google Scholar 

  • Deb D, Hariharan S, Rao UM, Ryu CH (2008) Automatic detection and analysis of discontinuity geometry of rock mass from digital images. Comput Geosci 34(2):115–126

    ADS  Google Scholar 

  • Elmouttie M, Poropat G, Krähenbühl G (2010) Polyhedral modelling of rock mass structure. Int J Rock Mech Min Sci 47(4):544–552

    Google Scholar 

  • Fu GY, Ma GW (2014) Extended key block analysis for support design of blocky rock mass. Tunn Undergr Space Technol 41:1–13

    CAS  Google Scholar 

  • Fu GY, Ma GW, Qu XL, Huang D (2016) Stochastic analysis of progressive failure of fractured rock masses containing non-persistent joint sets using key block analysis. Tunn Undergr Space Technol 51:258–269

    Google Scholar 

  • Goodman RE, Powell C (2003) Investigations of blocks in foundations and abutments of concrete dams. J Geotech Geoenvir Eng 129(2):105–116

    Google Scholar 

  • Goodman RE, Shi GH (1985) Block theory and its application to rock engineering. Prentice-Hall Inc, Englewood Cliffs, New Jersey

    Google Scholar 

  • Hatzor YH (2003) Keyblock stability in seismically active rock slopes–Snake Path Cliff, Masada. J Geotech Geoenvir Eng 129(8):697–710

    Google Scholar 

  • Hatzor YH, Feintuch A (2005) The joint intersection probability. Int J Rock Mech Min Sci 42(4):531–541

    Google Scholar 

  • Hocking G (1976) A method for distinguishing between single and double plane sliding of tetrahedral wedges. Int J Rock Mech Min Sci Geomech Abstr 13:225–226

    Google Scholar 

  • Jiang Q, Zhou C (2017) A rigorous solution for the stability of polyhedral rock blocks. Comput Geotech 90:190–201

    Google Scholar 

  • Jimenez-Rodriguez R, Sitar N (2008) Influence of stochastic discontinuity network parameters on the formation of removable blocks in rock slopes. Rock Mech Rock Eng 41(4):563–585

    ADS  Google Scholar 

  • Jing L (2000) Block system construction for three-dimensional discrete element models of fractured rocks. Int J Rock Mech Min Sci 37(4):645–659

    Google Scholar 

  • Kottenstette JT (1997) Block theory techniques used in arch dam foundation stability analysis. Int J Rock Mech Min Sci 34:3–4

    Google Scholar 

  • Kulatilake PHSW, Wu TH (1984) Estimation of mean trace length of discontinuities. Rock Mech Rock Eng 17:215–232

    ADS  Google Scholar 

  • Kulatilake PHSW, Wang L, Tang H, Ye L (2011) Evaluation of rock slope stability for yujian river dam site by kinematic and block theory analyses. Comput Geotech 38(6):846–860

    Google Scholar 

  • Kuszmaul S (1999) Estimating keyblock sizes in underground excavations: accounting for joint set spacing. Int J Rock Mech Min Sci 36:217–232

    Google Scholar 

  • Lato MJ, Vöge M (2012) Automated mapping of rock discontinuities in 3D LiDAR and photogrammetry models. Int J Rock Mech Min Sci 54:150–158

    Google Scholar 

  • Lee IM, Park JK (2000) Stability analysis of tunnel keyblock: a case study. Tunn Undergr Space Technol 15(4):453–462

    Google Scholar 

  • Lemy F, Hadjigeorgiou J (2003) Discontinuity trace map construction using photographs of rock exposures. Int J Rock Mech Min Sci 40:903–917

    Google Scholar 

  • Li J, Jian X, Xiao J, Ying W (2012) Block theory on the complex combinations of free planes. Comput Geotech 40:127–134

    CAS  Google Scholar 

  • Lin D, Fairhurst C (1988) Static analysis of the stability of three-dimensional blocky systems around excavations in rock. Int J Rock Mech Min Sci 25(3):139–147

    Google Scholar 

  • Liu T, Deng J, Zheng J, Zheng L, Zhang Z, Zheng H (2017) A new semi-deterministic block theory method with digital photogrammetry for stability analysis of a high rock slope in China. Eng Geol 216:76–89

    Google Scholar 

  • Lucas JM (1980) A general stereographic method for determining possible mode of failure of any tetrahedral rock wedge. Int J Rock Mech Min Sci Geomech Abstr 17:57–61

    Google Scholar 

  • Mauldon M (1998) Estimating mean fracture trace length and density from observations in convex windows. Rock Mech Rock Eng 31(4):201–216

    ADS  Google Scholar 

  • Mauldon M, Ureta J (1996) Stability analysis of rock wedges with multiple sliding surfaces. Geotech Geol Eng 14:51–66

    Google Scholar 

  • Menendez-Diaz A, Gonzalez-Palacio C, Alvarez-Vigil AE, Gonzalez-Nicieza C, Ramirez-Oyanguren P (2009) Analysis of tetrahedral and pentahedral key blocks in underground excavations. Comput Geotech 36(6):1009–1023

    Google Scholar 

  • Öcal A, Ozgenoglu A (1997) Determination of sliding mode of tetrahedral wedges in jointed rock slopes. Rock Mech Rock Eng 30(3):161–165

    ADS  Google Scholar 

  • Priest SD, Hudson JA (1981) Estimation of discontinuity spacing and trace length using scanline surveys. Int J Rock Mech Min Sci 18:183–197

    Google Scholar 

  • Shapiro A, Delport JL (1991) Statistical analysis of jointed rock data. Int J Rock Mech Min Sci 28(5):375–382

    Google Scholar 

  • Shi GH (1977) The stereographic projection method for rock mass stability analysis. Sci Sinica 3:260–271 (in Chinese)

    Google Scholar 

  • Shi GH (1982) A geometric method for stability analysis of discontinuous rocks. Sci Sinica 25(3):318–336

    MathSciNet  Google Scholar 

  • Shi GH (2006) Producing joint polygons, cutting joint blocks and finding key blocks from general free surfaces. Chin J Rock Mech Eng 25(11):2161–2170

    Google Scholar 

  • Starzec P, Andersson J (2002) Application of two-level factorial design to sensitivity analysis of keyblock statistics from fracture geometry. Int J Rock Mech Min Sci 39(2):243–255

    Google Scholar 

  • Sun G, Zheng H, Huang Y (2015) Stability analysis of statically indeterminate blocks in key block theory and application to rock slope in Jinping-I hydropower station. Eng Geol 186:57–67

    Google Scholar 

  • The Chinese Society of Rock Mechanics and Engineering ( 2021) Specification for rock slope engineering design of open-pit mine (T/CSRME 009–2021). (in Chinese)

  • Wang S, Zhang Z, Huang X, Huang Y, Lei Q (2021) A generalized joint pyramid method for removability analysis of rock blocks: theoretical formulation and numerical implementation. Comput Geotech 132:103972

    Google Scholar 

  • Wang H, Song F, Chen Y, Li T, Ma G (2023) Stability analysis of fractured rock masses based on an extended key block theory considering the forces between blocks and block rotation. Tunn Undergr Space Technol 132:104895

    Google Scholar 

  • Wu A (2019) Series methods of analyzing rock mass stability based on key block theory and their applications to Three Gorges Project. J Yangtze River Sci Res Inst 36(2):1–7

    Google Scholar 

  • Wu W, Zhuang X, Zhu H, Liu X, Ma G (2017) Centroid sliding pyramid method for removability and stability analysis of fractured hard rock. Acta Geotech 12(3):1–18

    ADS  Google Scholar 

  • Young DS, Hoerger SF (1989) Probabilistic and deterministic key block analyses. In: Khair (ed) Rock mechanics as a guide for efficient utilization of natural resources. Balkema, Cape Town, pp 227–234

    Google Scholar 

  • Zhang QH (2010) Fundamental research on application of rock mass block theory. Hubei Science and Technology Press, Wuhan (in Chinese)

    Google Scholar 

  • Zhang QH (2015) Advances in three-dimensional block cutting analysis and its applications. Comput Geotech 63:26–32

    Google Scholar 

  • Zhang ZX, Lei QH (2013) Object-oriented modeling for three-dimensional multi-block systems. Comput Geotech 48:208–227

    Google Scholar 

  • Zhang QH, Liu QB, Wang SH, Liu HL, Shi GH (2022) Progressive failure of blocky rock system: geometrical-mechanical identification and rock-bolt support. Rock Mech Rock Eng 55:1649–1662

    ADS  Google Scholar 

  • Zheng J, Kulatilake PHSW, Deng J (2015a) Development of a probabilistic block theory analysis procedure and its application to a rock slope at a hydropower station in china. Eng Geol 188:110–125

    Google Scholar 

  • Zheng Y, Xia L, Yu Q (2015b) A method for identifying three-dimensional rock blocks formed by curved fractures. Comput Geotech 65:1–11

    Google Scholar 

Download references

Acknowledgements

This research was sponsored by the General Program of the National Natural Science Foundation of China (Grant No. 52079129).

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This article is funded by National Natural Science Foundation of China, 52079129, Qihua Zhang.

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Zhang, QH., Shi, GH. Discussion on Key Issues in the Application of Block Theory in Rock Engineering. Rock Mech Rock Eng 57, 2017–2033 (2024). https://doi.org/10.1007/s00603-023-03667-8

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