Abstract
A three-dimensional representation of the random distribution of fractures in rock masses, known as the discrete fracture network (DFN), is widely used to analyze the stability of jointed rock slopes. In this paper, a new framework for constructing three-dimensional DFN models in rock masses has been proposed to overcome the limitations of conventional circular or polygon-based models. The framework utilizes the universal elliptical disc (UED) model and integrates it with the discrete element method in 3DEC for the stability evaluation of jointed rock slopes. This paper starts by introducing the basic principles of the UED model. The procedures for constructing a three-dimensional DFN using the UED model is then outlined. In the present study, a case study of a rock slope in Zhejiang Province, China is used to demonstrate the implementation of the proposed framework. A comprehensive comparative study is conducted to investigate the impacts of several UED model parameters, including the ratio of major axis to minor axis and rotation angle, and discontinuity density, on the stability of rock slopes and compared to the conventional Baecher disc model. The results show that the framework can effectively integrate the UED model into 3DEC and provide a realistic representation of the three-dimensional DFN, leading to improved accuracy and efficiency in the stability evaluation of jointed rock slopes. The framework also shed light on the interactive effects of the UED model parameters and discontinuity density on the rock slope stability, providing a strong reference for using the UED model in constructing DFN models for rock slopes.
Highlights
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Three-dimensional discrete fracture networks (DFNs) of rock masses are successfully constructed using the universal elliptical disc (UED) model.
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Python subroutines are developed in 3DEC to construct 3D DFNs using the UED model for improved discrete element analyses of jointed rock slopes.
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The effects of several characteristic parameters of the UED model on the stability of jointed rock slopes are investigated.
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Based on a key block model, the mechanisms underlying the relationship between jointed rock slope stability and fracture discontinuity are rigorously explained.
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The advantages of the UED model over the conventional Baecher disc model are comprehensively discussed based on a rock slope case study.
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Data Availability
All data that supports the findings of this study are available from the corresponding author upon reasonable request.
References
Baecher GB (1983) Statistical analysis of rock mass fracturing. J Int Assoc Math Geol 15:329–348. https://doi.org/10.1007/BF01036074
Bui TT, Limam A, Sarhosis V, Hjiaj M (2017) Discrete element modelling of the in-plane and out-of-plane behaviour of dry-joint masonry wall constructions. Eng Struct 136:277–294. https://doi.org/10.1016/j.engstruct.2017.01.020
Decker JB, Mauldon M, Wang X (2006) Real-time determination of fracture size and shape using trace data on tunnel walls. Tunn Undergr Space Technol 21(3):233–233. https://doi.org/10.1016/j.tust.2005.12.012
Dershowitz WS, Einstein HH (1988) Characterizing rock joint geometry with joint system models. Rock Mech Rock Eng 21(1):21–51. https://doi.org/10.1007/BF01019674
Espada M, Muralha J, Lemos JV, Jiang Q, Feng XT, Fan Y (2018) Safety analysis of the left bank excavation slopes of Baihetan arch dam foundation using a discrete element model. Rock Mech Rock Eng 51:2597–2615. https://doi.org/10.1007/s00603-018-1416-2
Firpo G, Salvini R, Francioni M, Ranjithet PG (2011) Use of digital terrestrial photogrammetry in rocky slope stability analysis by distinct elements numerical methods. Int J Rock Mech Min Sci 48(7):1045–1054. https://doi.org/10.1016/j.ijrmms.2011.07.007
Guo J, Zheng J, Lü Q, Cui Y, Deng J (2020) A procedure to estimate the accuracy of circular and elliptical discs for representing the natural discontinuity facet in the discrete fracture network models. Comput Geotech 121:103483. https://doi.org/10.1016/j.compgeo.2020.103483
Guo J, Zheng J, Lü Q, Deng J (2023) Estimation of fracture size and azimuth in the universal elliptical disc model based on trace information. J Rock Mech Geotech Eng 15(6):1391–1405. https://doi.org/10.1016/j.jrmge.2022.07.018
Itasca Consulting Group I (2016) 3DEC users' manual (version 5.2). Minneapolis, USA: Itasca Consulting Group, Inc
Ivanova VM, Sousa R, Murrihy B, Einstein HH (2014) Mathematical algorithm development and parametric studies with the GEOFRAC three-dimensional stochastic model of natural rock fracture systems. Comput Geosci 67:100–109. https://doi.org/10.1016/j.cageo.2013.12.004
Jiang SH, Ouyang S, Feng YW (2021) Reliability analysis of jointed rock slopes using updated probability distributions of structural plane parameters. Rock Soil Mech 42(9):2589–2599. https://doi.org/10.16285/j.rsm.2020.1792
Jiang SH, Liu X, Wang ZZ, Li DQ, Huang J (2023a) Efficient sampling of the irregular probability distributions of geotechnical parameters for reliability analysis. Struct Saf 101:102309. https://doi.org/10.1016/j.strusafe.2022.102309
Jiang SH, Zhu GY, Wang ZZ, Huang ZT, Huang J (2023b) Data augmentation for CNN-based probabilistic slope stability analysis in spatially variable soils. Comput Geotech 160:105501. https://doi.org/10.1016/j.compgeo.2023.105501
Jin W, Gao M, Zhang R, Zhang G (2014) Analytical expressions for the size distribution function of elliptical joints. Int J Rock Mech Min Sci 70:201–211. https://doi.org/10.1016/j.ijrmms.2014.04.017
Kemeny J, Post R (2003) Estimating three-dimensional rock discontinuity orientation from digital images of fracture traces. Comput Geosci 29(1):65–77. https://doi.org/10.1016/S0098-3004(02)00106-1
Lei Y, Wang S (2006) Stability analysis of jointed rock slope by strength reduction method based on UDEC. Rock Soil Mech 27(10):1693–1698. https://doi.org/10.16285/j.rsm.2006.10.010
Liu R, Jiang Y, Li B, Wang X (2015) A fractal model for characterizing fluid flow in fractured rock masses based on randomly distributed rock fracture networks. Comput Geotech 65:45–55. https://doi.org/10.1016/j.compgeo.2014.11.004
Liu B, He K, Han M, Hu X, Wu T, Wu M, Ma G (2021) Dynamic process simulation of the Xiaogangjian rockslide occurred in shattered mountain based on 3DEC and DFN. Comput Geotech 134:104122. https://doi.org/10.1016/j.compgeo.2021.104122
Marschner S, Shirley P (2015) Fundamentals of computer graphics, 5th edn. A. K. Peters, CRC Press, Boston, USA
Priest SD, Hudson JA (1976) Discontinuity spacings in rock. Int J Rock Mech Min Sci Geomec Abstr 13(5):135–148. https://doi.org/10.1016/0148-9062(76)90818-4
Stewart J (2015) Calculus: early transcendentals, 8th edn. Cengage Learning, Stamford, USA
Strang G (2016) Introduction to linear algebra, 5th edn. Wellesley-Cambridge Press, Boston, USA
Vyazmensky A, Stead D, Elmo D, Moss A (2010) Numerical analysis of block caving-induced instability in large open pit slopes: a finite element/discrete element approach. Rock Mech Rock Eng 43(1):21–39. https://doi.org/10.1007/s00603-009-0035-3
Wang H, Zhang B, Mei G, Xu N (2020) A statistics-based discrete element modeling method coupled with the strength reduction method for the stability analysis of jointed rock slopes. Eng Geol 264:105247. https://doi.org/10.1016/j.enggeo.2019.105247
Warburton PM (1980) Stereological interpretation of joint trace data: influence of joint shape and implications for geological surveys. Int J Rock Mech Min Sci Geomec Abstr 17(6):305–316. https://doi.org/10.1016/0148-9062(80)90513-6
Wu Q, Kulatilake PHSW (2012) REV and its properties on fracture system and mechanical properties, and an orthotropic constitutive model for a jointed rock mass in a dam site in China. Comput Geotech 43:124–142. https://doi.org/10.1016/j.compgeo.2012.02.010
Xu C, Dowd P (2010) A new computer code for discrete fracture network modelling. Comput Geosci 36(3):292–301. https://doi.org/10.1016/j.cageo.2009.05.012
Zhan J, Chen J, Xu P, Han X, Chen Y, Ruan Y, Zhou X (2017) Computational framework for obtaining volumetric fracture intensity from 3D fracture network models using Delaunay triangulations. Comput Geotech 89:179–194. https://doi.org/10.1016/j.compgeo.2017.05.005
Zhang QH (2004) Basic study on application of block theory and development of analytical software. [Doctoral dissertation, Wuhan University]
Zhang L, Einstein HH, Dershowitz WS (2002) Stereological relationship between trace length and size distribution of elliptical discontinuities. Geotechnique 52(6):419–433. https://doi.org/10.1680/geot.52.6.419.38737
Zheng J, Guo J, Wang J, Sun H, Deng J, Lv Q (2022) A universal elliptical disc (UED) model to represent natural rock fractures. Int J Min Sci Technol 32(2):261–270. https://doi.org/10.1016/j.ijmst.2021.12.001
Zhou CB, Chen YF, Hu R, Yang ZB (2023) Groundwater flow through fractured rocks and seepage control in geotechnical engineering: theories and practices. J Rock Mech Geotech Eng 15(1):1–36. https://doi.org/10.1016/j.jrmge.2022.10.001
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 52222905, 52179103, 42272326 and 41972280), and Jiangxi Provincial Natural Science Foundation (Grant Nos. 20224ACB204019 and 20232ACB204031) and Open Research Fund of Jiangxi Academy of Water Science and Engineering (Grant No. 2021SKSG02). The financial supports are gratefully acknowledged.
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Jiang, SH., Chen, JD., Wang, Z.Z. et al. Three-Dimensional Discrete Element Analysis of Jointed Rock Slope Stability Based on the Universal Elliptical Disc Model. Rock Mech Rock Eng 57, 505–525 (2024). https://doi.org/10.1007/s00603-023-03575-x
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DOI: https://doi.org/10.1007/s00603-023-03575-x