Abstract
The mechanical properties and failure mechanisms of geomaterials are greatly affected by their heterogeneity. As a special complex rock medium, the mechanical response of red bed soft rock is of considerable importance in stability analyses and the protection of slopes. In this study, X-ray micro-computerized tomography (micro-CT) was used to obtain the spatial distribution of minerals in red bed soft rock. An image processing procedure was proposed to incorporate the extracted mesoscopic mineral and crack distribution into the model of the grain-based finite-discrete element method (GB-FDEM). Subsequently, a uniaxial compression test and Brazilian disc splitting test were performed to obtain the mechanical response and failure modes of mudstone. The microscopic fracture morphology and traces of intragranular and intergranular cracks under tensile and shear stress were analyzed in detail. The numerical results show that the GB-FDEM model successfully characterized the mechanical response, which was similar to that of the laboratory tests and the traditional homogeneous models. The presence of minerals and pre-existing cracks disturbed the stress distribution in the heterogeneous model, which resulted in a difference in local stress that reasonably explained the phenomenon of local fragmentation. The simulated macroscopic failure mode of the heterogeneous models was most consistent with the results of the laboratory tests. The systematic framework proposed in this study provides a powerful tool for further understanding the multiscale (micro, meso, and macro) failure mechanism of red bed soft rock and predicting a realistic fracture process while reducing the tedious and redundant laboratory tests.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ahrens J, Geveci B, Law C (2005) Paraview: An end-user tool for large data visualization. Visualization Handbook
Aurenhammer F (1991) Voronoi diagrams — A survey of fundamental geometric data structure. ACM Computing Surveys 23(3):345–405, DOI: https://doi.org/10.1145/116873.116880
Bahrani N, Kaiser PK, Valley B (2014) Distinct element method simulation of an analogue for a highly interlocked, non-persistently jointed rockmass. International Journal of Rock Mechanics and Mining Sciences 71:117–130, DOI: https://doi.org/10.1016/j.ijrmms.2014.07.005
Barenblatt GI (1962) The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics 7:55–129, DOI: https://doi.org/10.1016/S0065-2156(08)70121-2
Benedetti I, Aliabadi MH (2013) A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials. Computer Methods in Applied Mechanics and Engineering 265:36–62, DOI: https://doi.org/10.1016/j.cma.2013.05.023
Bewick RP, Kaiser PK, Bawden WF, Bahrani N (2014) DEM Simulation of direct shear: 1. Rupture under constant normal stress boundary conditions. Rock Mechanics and Rock Engineering 47:1647–1671, DOI: https://doi.org/10.1007/s00603-013-0490-8
Bobet A, Einstein HH (1998) Fracture coalescence in rock-type materials under uniaxial and biaxial compression. International Journal of Rock Mechanics and Mining Sciences 35(7):863–888, DOI: https://doi.org/10.1016/S0148-9062(98)00005-9
Buades A, Coll B, Morel JM (2005) A non-local algorithm for image denoising. 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition 3:60–65, DOI: https://doi.org/10.1109/CVPR.2005.38
Cardarelli F (2008) Materials handbook: A Concise Desktop Reference
Chen S, Yue ZQ, Tham LG (2004) Digital image-based numerical modeling method for prediction of inhomogeneous rock failure. International Journal of Rock Mechanics and Mining Sciences 41(6):939–957, DOI: https://doi.org/10.1016/j.ijrmms.2004.03.002
Dugdale DS (1960) Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids 8(2):100–104, DOI: https://doi.org/10.1016/0022-5096(60)90013-2
Eberhardt E, Stimpson B, Stead D (1999) Effects of grain size on the initiation and propagation thresholds of stress-induced brittle fractures. Rock Mechanics and Rock Engineering 32:81–99, DOI: https://doi.org/10.1007/s006030050026
Erarslan N (2016) Microstructural investigation of subcritical crack propagation and fracture process zone (FPZ) by the reduction of rock fracture toughness under cyclic loading. Engineering Geology 208:181–190, DOI: https://doi.org/10.1016/j.enggeo.2016.04.035
Fairhurst C, Hudson JA (1999) Draft ISRM suggested method for the complete stress-strain curve for intact rock in uniaxial compression. International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts 36(3):279–289, DOI: https://doi.org/10.1016/S0148-9062(99)00006-6
Fazio NL, Leo M, Perrotti M, Lollino P (2019) Analysis of the displacement field of soft rock samples during UCS tests by means of a computer vision technique. Rock Mechanics and Rock Engineering 52:3609–3626, DOI: https://doi.org/10.1007/s00603-019-01791-y
Gao FQ, Stead D, Elmo D (2016) Numerical simulation of microstructure of brittle rock using a grain-breakable distinct element grain-based model. Computers and Geotechnics 78:203–217, DOI: https://doi.org/10.1016/j.compgeo.2016.05.019
Griffith A (1920) The phenomena of rupture and flow in solid. Phil. Trans. Roy. Soc. London, A221
Guan YP, Liu XL, Wang EZ, Wang SJ (2017) The stability analysis method of the cohesive granular slope on the basis of graph theory. Materials 10(3):240, DOI: https://doi.org/10.3390/ma10030240
Hajiabdolmajid V, Kaiser PK, Martin CD (2002) Modelling brittle failure of rock. International Journal of Rock Mechanics and Mining Sciences 39(6):731–741, DOI: https://doi.org/10.1016/S1365-1609(02)00051-5
He GH, Wang EZ, Liu XL (2016) Modified governing equation and numerical simulation of seepage flow in a single fracture with three-dimensional roughness. Arabian Journal of Geosciences 9:81, DOI: https://doi.org/10.1007/s12517-015-2036-8
Hillerborg A, Modeer M, Petersson PE (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research 6(6):773–781, DOI: https://doi.org/10.1016/0008-8846(76)90007-7
Hoek E, Diederichs MS (2006) Empirical estimation of rock mass modulus. International Journal of Rock Mechanics and Mining Sciences 43(2):203–215, DOI: https://doi.org/10.1016/j.ijrmms.2005.06.005
Kazerani T, Zhao J (2010) Micromechanical parameters in bonded particle method for modelling of brittle material failure. International Journal for Numerical and Analytical Methods in Geomechanics 34(18):1877–1895, DOI: https://doi.org/10.1002/nag.884
Kim YY, Ribeiro L, Maillot F, Ward O, Eichhorn SJ, Meldrum FC (2010) Bio-inspired synthesis and mechanical properties of calcite—polymer particle composites. Advanced Materials 22(18):2082–2086, DOI: https://doi.org/10.1002/adma.200903743
Kranz RL (1983) Microcracks in rocks: A review. Tectonophysics 100(1–3):449–480, DOI: https://doi.org/10.1016/0040-1951(83)90198-1
Labuz JF, Shah SP, Dowding CH (1985) Experimental analysis of crack propagation in granite. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 22(2):85–98, DOI: https://doi.org/10.1016/0148-9062(85)92330-7
Li YP, Chen LZ, Wang YH (2005) Experimental research on pre-cracked marble under compression. International Journal of Solids and Structures 42(9–10):2505–2516, DOI: https://doi.org/10.1016/j.ijsolstr.2004.09.033
Lin P, Liu XL, Hu SY, Li PJ (2016) Large deformation analysis of a high steep slope relating to the laxiwa reservoir, China. Rock Mechanics and Rock Engineering 49:2253–2276, DOI: https://doi.org/10.1007/s00603-016-0925-0
Lin P, Liu XL, Zhou WY, Wang RK, Wang SY (2015) Cracking, stability and slope reinforcement analysis relating to the Jinping dam based on a geomechanical model test. Arabian Journal of Geosciences 8:4393–4410, DOI: https://doi.org/10.1007/s12517-014-1529-1
Lisjak A, Grasselli G, Vietor T (2014a) Continuum—discontinuum analysis of failure mechanisms around unsupported circular excavations in anisotropic clay shales. International Journal of Rock Mechanics and Mining Sciences 65:96–115, DOI: https://doi.org/10.1016/j.ijrmms.2013.10.006
Lisjak A, Tatone BSA, Grasselli G, Vietor T (2014b) Numerical modelling of the anisotropic mechanical behaviour of opalinus clay at the laboratory-scale using FEM/DEM. Rock Mechanics and Rock Engineering 47:187–206, DOI: https://doi.org/10.1007/s00603-012-0354-7
Liu QS, Deng PH (2019) A numerical investigation of element size and loading/unloading rate for intact rock in laboratory-scale and field-scale based on the combined finite-discrete element method. Engineering Fracture Mechanics 211:442–462, DOI: https://doi.org/10.1016/j.engfracmech.2019.02.007
Liu XL, Han GF, Wang EZ, Wang SJ, Nawnit K (2018) Multiscale hierarchical analysis of rock mass and prediction of its mechanical and hydraulic properties. Journal of Rock Mechanics and Geotechnical Engineering 10(4):694–702, DOI: https://doi.org/10.1016/j.jrmge.2018.04.003
Liu XL, Liang T, Wang SJ, Nawnit K (2019a) A fractal model for characterizing hydraulic properties of fractured rock mass under mining influence. Geofluids 8391803, DOI: https://doi.org/10.1155/2019/8391803
Liu C, Liu XL, Peng XC, Wang EZ, Wang SJ (2019b) Application of 3D-DDA integrated with unmanned aerial vehicle (UAV) photogrammetry for stability analysis of a blocky rock mass slope. Landslides 16: 1645–1661, DOI: https://doi.org/10.1007/s10346-019-01196-6
Liu XL, Wang F, Nawnit K, Lv XF, Wang SJ (2020) Experimental study on debris flow initiation. Bulletin of Engineering Geology and the Environment 79:1565–1580, DOI: https://doi.org/10.1007/s10064-019-01618-8
Liu XL, Wang SJ, Wang EZ (2011) A study on the uplift mechanism of Tongjiezi dam using a coupled hydro-mechanical model. Engineering Geology 117(1–2):134–150, DOI: https://doi.org/10.1016/j.enggeo.2010.10.013
Liu XL, Wang SJ, Wang SY, Wang EZ (2015) Fluid-driven fractures in granular materials. Bulletin of Engineering Geology and the Environment 74:621–636, DOI: https://doi.org/10.1007/s10064-014-0712-7
Lv QF, Liu XL, Wang EZ, Wang SJ (2013) Analytical solution to predicting gaseous mass flow rates of microchannels in a wide range of Knudsen numbers. Physical Review E 88(1):013007, DOI: https://doi.org/10.1103/PhysRevE.88.013007
Lv QF, Wang EZ, Liu XL, Wang SJ (2014) Determining the intrinsic permeability of tight porous media based on bivelocity hydrodynetics. Microfluidics and Nanofluidics 16:841–848, DOI: https://doi.org/10.1007/s10404-014-1332-z
Mahabadi OK (2012) Investigating the influence of micro-scale heterogeneity and microstructure on the failure and mechanical behaviour of geomaterials. PhD Thesis, University of Toronto, Toronto, Canada
Mahabadi OK, Grasselli G, Munjiza A (2010) Y-GUI: A graphical user interface and pre-processor for the combined finite-discrete element code, Y2D, incorporating material heterogeneity. Computers & Geosciences 36(2):241–252, DOI: https://doi.org/10.1016/j.cageo.2009.05.010
Mahabadi OK, Lisjak A, Munjiza A, Grasselli G (2012) Y-Geo: New combined finite-discrete element numerical code for geomechanical applications. International Journal of Geomechanics 12(6):676–688, DOI: https://doi.org/10.1061/(ASCE)GM.1943-5622.0000216
Mahabadi OK, Tatone BSA, Grasselli G (2014) Influence of microscale heterogeneity and microstructure on the tensile behavior of crystalline rocks. Journal of Geophysical Research: Solid Earth 119(7):5324–5341, DOI: https://doi.org/10.1002/2014JB011064
Mavko G, Mukerji T, Dvorkin J (2009) The rock physics handbook: tools for seismic analysis of porous media. 2nd ed. Cambridge, UK, New York: Cambridge University Press
Miller JT, Einstein HH (2008) Crack coalescence tests on granite. The 42nd U.S. Rock Mechanics Symposium (USRMS). American Rock Mechanics Association, San Francisco, California, 8
Moradian Z, Einstein HH, Ballivy G (2016) Detection of cracking levels in brittle rocks by parametric analysis of the acoustic emission signals. Rock Mechanics and Rock Engineering 49:785–800, DOI: https://doi.org/10.1007/s00603-015-0775-1
Morgan SP, Johnson CA, Einstein HH (2013) Cracking processes in Barre granite: Fracture process zones and crack coalescence. International Journal of Fracture 180:177–204, DOI: https://doi.org/10.1007/s10704-013-9810-y
Munjiza A (2004) The combined finite-discrete element method, John Wiley & Sons, Chichester, West Sussex, England
Munjiza A, Andrews KRF (1998) NBS contact detection algorithm for bodies of similar size. International Journal for Numerical Methods in Engineering 43(1):131–149, DOI: https://doi.org/10.1002/(SICI)1097-0207(19980915)43:1<131::AID-NME447>3.0.CO;2-S
Munjiza A, Owen DRJ, Bicanic N (1995) A combined finite-discrete element method in transient dynamics of fracturing solids. Engineering Computations 12(2):145–174, DOI: https://doi.org/10.1108/02644409510799532
Nguyen NHT, Bui HH, Nguyen GD, Kodikara J (2017a) A cohesive damage-plasticity model for DEM and its application for numerical investigation of soft rock fracture properties. International Journal of Plasticity 98:175–196, DOI: https://doi.org/10.1016/j.ijplas.2017.07.008
Nguyen NHT, Bui HH, Nguyen GD, Kodikara J, Arooran S, Jitsangiam P (2017b) A thermodynamics-based cohesive model for discrete element modelling of fracture in cemented materials. International Journal of Solids and Structures 117:159–176, DOI: https://doi.org/10.1016/j.ijsolstr.2017.03.027
Potyondy DO (2010) A grain-based model for rock: Approaching the true microstructure. Rock Mechanics in the Nordic Countries 225–234
Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. International Journal of Rock Mechanics and Mining Sciences 41(8):1329–1364, DOI: https://doi.org/10.1016/j.ijrmms.2004.09.011
Rabczuk T, Belytschko T (2004) Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering 61(13):2316–2343, DOI: https://doi.org/10.1002/nme.1151
Rabczuk T, Belytschko T (2007) A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering 196(29–30):2777–2799, DOI: https://doi.org/10.1016/j.cma.2006.06.020
Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H (2010) A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering 199(37): 2437–2455, DOI: https://doi.org/10.1016/j.cma.2010.03.031
Saadat M, Taheri A (2019) Modelling micro-cracking behaviour of precracked granite using grain-based distinct element model. Rock Mechanics and Rock Engineering 52:4669–4692, DOI: https://doi.org/10.1007/s00603-019-01862-0
Sun H, Liu XL, Zhu JB (2019) Correlational fractal characterisation of stress and acoustic emission during coal and rock failure under multilevel dynamic loading. International Journal of Rock Mechanics and Mining Sciences 117:1–10, DOI: https://doi.org/10.1016/j.ijrmms.2019.03.002
Tatone BSA, Grasselli G (2015) A calibration procedure for two-dimensional laboratory-scale hybrid finite-discrete element simulations. International Journal of Rock Mechanics and Mining Sciences 75: 56–72, DOI: https://doi.org/10.1016/j.ijrmms.2015.01.011
Wong Tf, Wong RHC, Chau KT, Tang CA (2006) Microcrack statistics, Weibull distribution and micromechanical modeling of compressive failure in rock. Mechanics of Materials 38(7):664–681, DOI: https://doi.org/10.1016/j.mechmat.2005.12.002
Wu XY, Baud P, Wong TF (2000) Micromechanics of compressive failure and spatial evolution of anisotropic damage in Darley Dale sandstone. International Journal of Rock Mechanics and Mining Sciences 37(1–2):143–160, DOI: https://doi.org/10.1016/S1365-1609(99)00093-3
Yu QL, Tang CA, Liang Z, Tang S (2007) Digital image based modeling of rock failure at meso-scale. Progresses in Fracture and Strength of Materials and Structures pt.2
Yu Y, Wang EZ, Zhong JW, Liu XL, Li PH, Shi M, Zhang ZG (2014) Stability analysis of abutment slopes based on long-term monitoring and numerical simulation. Engineering Geology 183(9):159–169, DOI: https://doi.org/10.1016/j.enggeo.2014.10.010
Zhang ZX (2002) An empirical relation between mode I fracture toughness and the tensile strength of rock. International Journal of Rock Mechanics and Mining Sciences 39(3):401–406, DOI: https://doi.org/10.1016/S1365-1609(02)00032-1
Zhang YM, Gao ZR, Li YY, Zhuang XY (2020) On the crack opening and energy dissipation in a continuum based disconnected crack model. Finite Elements in Analysis and Design 170:103333, DOI: https://doi.org/10.1016/j.finel.2019.103333
Zhang YM, Gao ZR, Wang XY, Liu Q (2023) Image representations of numerical simulations for training neural Networks. Computer Modeling in Engineering & Sciences 134(2):821–833, DOI: https://doi.org/10.32604/cmes.2022.022088
Zhang YM, Huang JG, Yuan Y, Mang HA (2021) Cracking elements method with a dissipation-based arc-length approach. Finite Elements in Analysis and Design 195:103573, DOI: https://doi.org/10.1016/j.finel.2021.103573
Zhang YM, Lackner R, Zeiml M, Mang HA (2015) Strong discontinuity embedded approach with standard SOS formulation: Element formulation, energy-based crack-tracking strategy, and validations. Computer Methods in Applied Mechanics and Engineering 287: 335–366, DOI: https://doi.org/10.1016/j.cma.2015.02.001
Zhang YM, Mang HA (2020) Global cracking elements: A novel tool for Galerkin-based approaches simulating quasi-brittle fracture. International Journal for Numerical Methods in Engineering 121(11): 2462–2480, DOI: https://doi.org/10.1002/nme.6315
Zhang YM, Yang XQ, Wang XY, Zhuang XY (2021) A micropolar peridynamic model with non-uniform horizon for static damage of solids considering different nonlocal enhancements. Theoretical and Applied Fracture Mechanics 113:102930, DOI: https://doi.org/10.1016/j.tafmec.2021.102930
Zhang YM, Zhuang XY (2018) Cracking elements: A self-propagating Strong Discontinuity embedded Approach for quasi-brittle fracture. Finite Elements in Analysis and Design 144:84–100, DOI: https://doi.org/10.1016/j.finel.2017.10.007
Zhang YM, Zhuang XY (2019) Cracking elements method for dynamic brittle fracture. Theoretical and Applied Fracture Mechanics 102:1–9, DOI: https://doi.org/10.1016/j.tafmec.2018.09.015
Zhou XP, Cheng H, Feng YF (2014) An experimental study of crack coalescence behaviour in rock-like materials containing multiple flaws under uniaxial compression. Rock Mechanics and Rock Engineering 47:1961–1986, DOI: https://doi.org/10.1007/s00603-013-0511-7
Zhou SW, Zhuang XY, Rabczuk T (2019) Phase-field modeling of fluid-driven dynamic cracking in porous media. Computer Methods in Applied Mechanics and Engineering 350:169–198, DOI: https://doi.org/10.1016/j.cma.2019.03.001
Zhu JB, Liao ZY, Tang CA (2016) Numerical SHPB tests of rocks under combined static and dynamic loading conditions with application to dynamic behavior of rocks under in situ stresses. Rock Mechanics and Rock Engineering 49(10):3935–3946, DOI: https://doi.org/10.1007/s00603-016-0993-1
Zhu JB, Zhou T, Liao ZY, Sun L, Li XB, Chen R (2018) Replication of internal defects and investigation of mechanical and fracture behaviours of rocks using 3D printing and 3D numerical methods with combination of X-ray computerized tomography. International Journal of Rock Mechanics and Mining Sciences 106:198–212, DOI: https://doi.org/10.1016/j.ijrmms.2018.04.022
Zhuang XY, Zhou SW, Sheng M, Li GS (2020) On the hydraulic fracturing in naturally-layered porous media using the phase field method. Engineering Geology 266:105306, DOI: https://doi.org/10.1016/j.enggeo.2019.105306
Acknowledgments
This work was supported by the National Key R&D Program of China (Grant No. 2018YFC1504902), and the National Natural Science Foundation of China (Grant No. 51522903, 41772246), and the State Key Laboratory of Hydroscience and Hydraulic Engineering (Grant No. 2019-KY-03).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, C., Liu, X., Wu, C. et al. Investigation of Multiscale Failure Mechanism of Red Bed Soft Rock using Grain-Based Finite-Discrete Element Method Combined with X-Ray Micro-computerized Tomography. KSCE J Civ Eng 27, 1350–1367 (2023). https://doi.org/10.1007/s12205-023-1445-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12205-023-1445-6