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A soft particle model for investigating on mode I fracture behaviors of layered slate following the Voronoi tessellation construction

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Abstract

It is well-known that the discrete element method (DEM) based on circular particle shape may not be fully suitable for modeling geotechnical materials due to the lack of frictional resistance after solid bond fracture. In this paper, a two-dimensional (2D) soft particle model based on Voronoi tessellation construction attempts to solve these problems. In terms of experiments, the Muzhailing tunnel layer was taken as the research object, the semi-circular bend (SCB) tests were carried out on the sample to systematically study the mode I fracture properties of layered carbonaceous slate, and a series of numerical simulations were carried out based on this test. Through comparative analysis, it can be seen that the numerical simulation results are in good agreement with the splitting modes and fracture toughness of the indoor layered slate samples. At the same time, the effects of different span lengths, bedding spacings, and the strength ratio between bedding and matrix on the fracture mode and fracture toughness of engineering structures in layered rock mass were explored. On the other hand, the anisotropy of the deformation modulus of the layered rock mass in the numerical simulation is also taken into account. In the selection of span, s/2R = 0.6\(-\)0.8 is more reasonable.

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References

  • Alshkane YM, Marshall AM, Stace LR (2017) Prediction of strength and deformability of an interlocked blocky rock mass using udec. J Rock Mech Geotech Eng 9(3):531–542

    Article  Google Scholar 

  • Bai QS, Tu SH, Zhang C (2016) Dem investigation of the fracture mechanism of rock disc containing hole(s) and its influence on tensile strength. Theoretical Appl Fracture Mech 86:197–216

    Article  Google Scholar 

  • Borino G, Failla B, Parrinello F (2003) A symmetric nonlocal damage theory. Int J Solids Struct 40:0020–7683

    Article  Google Scholar 

  • CHONG K P, KURUPPU M D (1984) New specimen for fracture toughness determination for rock and other materials. International Journal of Fracture, 26:R59–R62

  • Chaoyu C, Jingshan B, WenHao Q (2022) Study on instability and damage of a loess slope under strong ground motion by numerical simulation. Soil Dyn Earthq Eng 152:0267–7261

    Google Scholar 

  • Choi SO, Chung SK (2004) Stability analysis of jointed rock slopes with the barton-bandis constitutive model in udec. Int J Rock Mech Min Sci 41:581–586

    Article  Google Scholar 

  • Claesson J, Bohloli B (2002) Brazilian test: stress field and tensile strength of anisotropic rocks using an analytical solution. Int J Rock Mech Min Sci 39:991–1004

    Article  Google Scholar 

  • Cundall PA (1971) A computer model for simulating progressive large scale movements in blocky rock systems. Proceeding of the International Society on Rock Mechanics, Rock Fracture

    Google Scholar 

  • Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Geotechnique 29:47–65

    Article  Google Scholar 

  • D’Addetta GA, Ramm E (2006) A microstructure-based simulation environment on the basis of an interface enhanced particle model. Granular Matter 8(3–4):159–174

    Article  Google Scholar 

  • D’Addetta GA, Kun F, Ramm E (2002) On the application of a discrete model to the fracture process of cohesive granular materials. Granular Matter 4(2):77–90

    Article  Google Scholar 

  • Do Xuan Nam, Ibrahimbegovic A (2018) Crack propagation in dynamics by embedded strong discontinuity approach: Enhanced solid versus discrete lattice model. Comput Methods Appl Mech ana Eng 340:480–499

    Article  Google Scholar 

  • Dop A, Pac B (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364

    Article  Google Scholar 

  • Engelen R, Geers M, Baaijens F (2003) Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behaviour. Int J Plasticity 19(4):403–433

    Article  Google Scholar 

  • Grilli N (2020) Neper2cae. GitHub, doi: https://github.com/ngrilli/Neper2CAE

  • Han W, Jiang Y, Y Du (2020) Numerical investigation on the shear behavior of rock-like materials containing fissure-holes with fem-czm method. Computers and Geotechnics, 125

  • Han Wei, Jiang Yujing, Luan Hengjie, Liu Jiankang (2020) Numerical investigation on the shear behavior of rock-like materials containing fissure-holes with fem-czm method. Comput Geotech 125:103670

    Article  Google Scholar 

  • Hongxiang J, Huihe Z, Kuidong G (2020) Numerical investigation of hard rock breakage by high-pressure water jet assisted indenter impact using the coupled sph/fem method. Powder Technol 376:176–186

    Article  Google Scholar 

  • Kewei F, Duruo H, Gang W (2022) Physics-based large-deformation analysis of coseismic landslides: A multiscale 3d sem-mpm framework with application to the hongshiyan landslide. Engineering Geology, 297

  • Kuruppu MD, Chong KP (2012) Fracture toughness testing of brittle materials using semi-circular bed (scb) specimen. Eng Fracture Mech 91:133–150

    Article  Google Scholar 

  • Kuruppu MD, Obara Y, Ayatollahi MR (2014) Isrm-suggested method for determining the mode i static fracture toughness using semi-circular bend specimen. Rock Mech Rock Eng 47:267–74

    Article  Google Scholar 

  • LIM I L, JOHNSTON I W, CHOI S K (1994) Fracture testing of a soft rock with semi-circular specimens under three-point bending. part 2: mixed-mode. International Journal of Rock Mechanics and Mining Sciences & Geomechanics, 31:199–212

  • Monteiro Azevedo N, Candeias M, Gouveia F (2015) A rigid particle model for rock fracture following the voronoi tessellation of the grain structure: Formulation and validation. Rock Mech Rock Eng 48:535–557

  • Nikolić Mijo, Do Xuan Nam, Adnan Ibrahimbegovic Ž eljana Nikolić, (2018) Crack propagation in dynamics by embedded strong discontinuity approach: Enhanced solid versus discrete lattice model. Computer Methods in Applied Mechanics and Engineering 340:0045–7825

  • Nikolic M, Ibrahimbegovic A, Miscevic P (2016) Discrete element model for the analysis of fluidsaturated fractured poro-plastic medium based on sharp crack representation with embedded strong discontinuities. Computer methods in applied mechanics and engineering, 298(JAN.1):407–427

  • Pan C, Li X, He L (2021) Study on the effect of micro-geometric heterogeneity on mechanical properties of brittle rock using a grain-based discrete element method coupling with the cohesive zone model. Int J Rock Mech Min Sci 140(3–4):104680

    Article  Google Scholar 

  • Rozylo P, Wysmulski P (2021) Failure analysis of thin-walled composite profiles subjected to axial compression using progressive failure analysis (pfa) and cohesive zone model (czm). Composite Struct 262:0263–8223

    Article  Google Scholar 

  • Saadeh S, Al-Zubi Y, Mahmoud E (2020) Sensitivity analysis of semicircular bending test using plackett-burman matrix. Trans Res Record J Trans Res Board 2674(4):036119812090758

    Google Scholar 

  • Smith M (2009) Abaqus/standard user’s manual, version 6.9. United States: Dassault Systèmes Simulia Corp

  • Talischi C, Paulino GH, Pereira A (2012) Polymesher: a general-purpose mesh generator for polygonal elements written in matlab. Struct Multidisciplinary Opt 45:309–328

    Article  Google Scholar 

  • Vassaux M, Oliver-Leblond C (2016) Beam-particle approach to model cracking and energy dissipation in concrete: Identification strategy and validation. Cement Concrete Composites 70:1–14

    Article  Google Scholar 

  • Vermeer P A, Herrmann H J, Luding S (2001) From solids to granulates - discrete element simulations of fracture and fragmentation processes in geomaterials. Lecture Notes in Physics, 568(Chapter 17):231–258

  • Wang Y, Tonon F (2009) Modeling lac du bonnet granite using a discrete element model. Int J Rock Mech Min Sci 46(7):1124–1135

    Article  Google Scholar 

  • Wang P, Gao N, Ji K (2020) Dem analysis on the role of aggregates on concrete strength. Comput Geotech 119:0266-352X

    Article  Google Scholar 

  • Xiao Chuang X, Francesca Ceccato, Ming-Liang Zhou (2022) Hydromechanical behaviour of soils during water-soil gushing in shield tunnels using mpm. Computers and Geotechnics, 145:0266–352X

  • Yan JIN, Jianbo YUAN, Mian CHEN (2011) Determination of rock fracture toughness kic and its relationship with tensile strength. Rock Mechanics and Rock Engineering 44:621–627

    Article  Google Scholar 

  • Yu Z, Zhang J, Shen J (2021) Simulation of crack propagation behavior of nuclear graphite by using xfem, vcct and czm methods. Nucl Materials Energy 1:101063

    Article  Google Scholar 

  • Zhao NN, Feng JL (2021) Nonlocal plastic softening algorithm and numerical investigation based on the drucker-prager criterion. IOP Conf Ser 861(3):032007

    Article  Google Scholar 

  • Zhao NN, Feng JL (2021) Investigation on fracture mechanism of layered slate: experiment and beamparticle method. Environ Earth Sci 80:788

    Article  Google Scholar 

Download references

Acknowledgements

The present work is supported by the National Key Research and Development Program of China (No. 2016YFC0600901) and the National Science Foundation of China (Nos. 41172116 and U1261212).

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Authors and Affiliations

  1. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing, 100083, China

    Ningning Zhao & Jili Feng

  2. School of Civil Engineering, Luoyang Institute of Science and Technology, Luoyang, 471023, China

    Erqiang Li

  3. School of Mechanics and Civil Engineering, China University of Mining and Technology, Beijing, 100083, China

    Ningning Zhao & Jili Feng

Authors
  1. Ningning Zhao
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  2. Jili Feng
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  3. Erqiang Li
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Contributions

a. NZ—soft particle model construction, numerical simulation and article writing and modification. b. EL—contributes to the experiment c. Funded by Jili Feng.

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Correspondence to Erqiang Li.

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Zhao, N., Feng, J. & Li, E. A soft particle model for investigating on mode I fracture behaviors of layered slate following the Voronoi tessellation construction. Environ Earth Sci 82, 175 (2023). https://doi.org/10.1007/s12665-023-10857-8

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