Skip to main content
SpringerLink
Log in

Investigation on fracture mechanism of layered slate: experiment and beam-particle method

  • Original Article
  • Published:
Environmental Earth Sciences Aims and scope Submit manuscript

Abstract

The layered rock masses with structural planes are widely distributed, among which the transverse isotropy caused by the bedding structural plane has a great influence on the stability of the slope and surrounding rock. Construct a beam-particle model (BPM) to reveal the layered slate fracture characteristics is of great significance. This paper takes the layered carbonaceous slate of the Muzhailing tunnel in Shanxi as the research specimens, carries out the Brazilian split test and uniaxial compression test of the layered slate with different bedding inclination angles, and conducts out a systematic numerical analysis based on the BPM solver. The test and numerical results show that: (1) In the Brazilian split test, the load–displacement curve of the layered slate has the development trend of the initial stage, the rock specimens compaction, nearly linear elasticity, and finally complete collapse. As the bedding inclination angle changes from \(0^{\circ }\) to \(90^{\circ }\), the tensile strength of slate decreases successively. (2) In the uniaxial compression test, when the bedding inclination angle is \(0^{\circ }\) and \(90^{\circ }\), the compressive strength is greater, and the bedding inclination angle is \(30^{\circ }\), \(45^{\circ }\) and \(60^{\circ }\), the compressive strength is small and the value is close, showing a “U”-shaped change as a whole. (3) With the change of bedding inclination angle and the comprehensive influence of matrix and bedding, the split failure mode of layered slate is complex and changeable, and roughly presents split tensile failure, shear slip failure and comprehensive tensile shear failure. (4) Through the comparative analysis of test load–displacement response and failure mode, the BPM solver can better reproduce the split evolution process of layered slate under different bedding inclination angles, and prove the robustness and stability of the program. The BPM solver can provide a new numerical research method for the widespread engineering practice of layered rock masses.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32

Similar content being viewed by others

References

  • Andre D, Girardot J, Hubert C (2019) A novel DEM approach for modeling brittle elastic media based on distinct lattice spring model. Comput Methods Appl Mech Eng 350:100–122

    Article  Google Scholar 

  • Al-Bayati H, Oyeyi AG, Tighe SL (2020) Experimental assessment of mineral filler on the volumetric properties and mechanical performance of HMA mixtures. Civ Eng J 6(12):2312–2331

    Article  Google Scholar 

  • Barr AH (1981) Superquadrics and angle-preserving transformations. IEEE Comput Graph Appl 1:11–23

    Article  Google Scholar 

  • Bazant Z, Planas J (1998) Fracture and size effect in concrete and other quasibrittle materials. CRC Press, Boca Raton

    Google Scholar 

  • Bobet A, Fakhimi A, Johnson S, Morris J, Tonon F, Yeung MR (2009) Numerical models in discontinuous media: review of advances for rock mechanics applications. J Geotech Geoenviron Eng 135:1547–1561

    Article  Google Scholar 

  • Balamuralikrishnan R, Saravanan J (2021) Effect of addition of alccofine on the compressive strength of cement mortar cubes. Emerg Sci J 5(2):155–170

    Article  Google Scholar 

  • Cho JW, Kim H, Jeon S et al (2012) Deformation and strength anisotropy of Asan gneiss, Boryeong shale, and Yeoncheon schist. Int J Rock Mech Min Sci 50(2):158–169

    Article  Google Scholar 

  • Claessona 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(9):991–1004

    Article  Google Scholar 

  • Cundall PA (1971) A computer model for simulating progressive large scale movements in blocky rock systems. In: Symposium on International Society of Rock Mechanics. International Society for Rock Mechanics, Nancy

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

    Article  Google Scholar 

  • Cundall PA (1988) Formulation of a three-dimensional distinct element model - Part I: a scheme to detect and represent contacts in a system composed of many polyhedral blocks. Int J Rock Mech Min Sci Geomech Abstr 25:107–116

    Article  Google Scholar 

  • Celigueta MA, Latorre S, Arrufat F, Oñate E (2017) Accurate modelling of the elastic behavior of a continuum with the discrete element method. Comput Mech 60:997–1010

    Article  Google Scholar 

  • Dan DQ, Konietzky H, Herbst M (2013) Brazilian tensile strength tests on some anisotropic rocks. Int J Rock Mech Min Sci 58(2):1–7

    Article  Google Scholar 

  • D’Addetta G, Kun F, Ramm E (2002) On the application of a discrete model to the fracture process of cohesive granular materials. GM 4:77–90. https://doi.org/10.1007/s10035-002-0103-9

  • De Borst R, Muhlhaus HB (1992) Gradient-dependent plasticity: formulation and algorithmic aspects. Int J Numer Methods Eng 35:521–539

    Article  Google Scholar 

  • Davie CT, Bicanic N (2003) Failure criteria for quasi-brittle materials in lattice-type models. Commun Numer Methods Eng 19:703–713

    Article  Google Scholar 

  • Changdong D, Dawei H et al (2019) Brazil test of slate considering three-dimensional schistosity effect. Chin J Rock Mech Eng 38(02):90–101 (In Chinese)

    Google Scholar 

  • Azéma E, Radjai F, Peyroux R, Richefeu V, Saussine G (2008) Short-time dynamics of a packing of polyhedral grains under horizontal vibrations. Eur Phys J E Soft Matter Biol Phys 26:327–335

    Article  Google Scholar 

  • Garcia-Fernandez CC, Gonzalez-Nicieza C, Alvarez-Fernandez MI et al (2019) New methodology for estimating the shear strength of layering in slate by using the Brazilian test. Bull Eng Geol Environ 78(4):2283–2297

    Article  Google Scholar 

  • Gholami R, Rasouli V (2014) Mechanical and elastic properties of transversely isotropic slate. Rock Mech Rock Eng 47(5):1763–1773

    Article  Google Scholar 

  • Gear CW (1971) Numerical initial value problems in ordinary differential equations. Prentice-Hall Series in Automatic Computation. Prentice-Hall, Hoboken

    Google Scholar 

  • Gregoire D, Rojas-Solano L, Lefort V, Grassl P, Pijaudier-Cabot G (2014) Size and boundary effects during failure in quasi-brittle materials: experimental and numerical investigations. Procedia Mater Sci 3:1269–1278

    Article  Google Scholar 

  • Hatzor YH, Ma GW, Shi G-H (2018) Discontinuous deformation analysis in rock mechanics practice. CRC Press, Taylor & Francis Group, London

    Google Scholar 

  • Herrmann HJ, Hansen A, Roux S (1989) Fracture of disordered, elastic lattices in two dimensions. Phys Rev B 39:1637–1648

    Article  Google Scholar 

  • Herrmann HJ, Roux S (1990) Statistical models for the fracture of disordered media. North-Holland, Amsterdam

    Google Scholar 

  • Herrmann HJ, Tillemans HJ (1995) Simulating deformations of granular solids under shear. Phys A 217:261–288

    Article  Google Scholar 

  • Johnson KL (1985) Contact mechanics. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Khanlari G, Rafiei B, Abdilor Y (2015) An experimental investigation of the brazilian tensile strength and failure patterns of laminated sandstones. Rock Mech Rock Eng 48(2):843–852

    Article  Google Scholar 

  • Kun LV, Xu GAO, Zheng WU et al (2018) Weakly bonding composite layered roof risk classification method and its application. J Min Sci Technol 3(3):253–259 (In Chinese)

    Google Scholar 

  • De-jian LI, Hao QI, Chun-xiao LI et al (2020) Brazilian disc splitting tests and numerical simulations on coal samples containing bedding planes. J Min Sci Technol 5(2):150–159 (In Chinese)

    Google Scholar 

  • Liu SL, Chen SX, Yu F et al (2012) Anisotropic properties study of chlorite schist. Rock Soil Mech 33(12):3616–3623 (in Chinese)

  • Li Z et al (2017) Experimental study on anisotropic properties of silurian silty slates. Geotech Geol Eng 35(2):1–12

    Google Scholar 

  • Yunsi L, Helin F, Rao J et al (2012) Research on Brazilian disc splitting tests for anisotropy of slate under influence of different bedding orientations. Chin J Rock Mech Eng 31(4):785–791 (In Chinese)

    Google Scholar 

  • Zhigang L et al (2018) Mechanical and anisotropic properties of silty slate. Rock Soil Mech 288(05):200–209 (In Chinese)

    Google Scholar 

  • Li D, Wong LNY (2013) The Brazilian disc test for rock mechanics applications: review and new insights. Rock Mech Rock Eng 46(2):269287

    Article  Google Scholar 

  • Matuttis H-G, Chen J (2014) Understanding the discrete element method: simulation of non-spherical particles for granular and multi-body systems. Wiley, New York

    Book  Google Scholar 

  • Munjiza AA, Knight EE, Rougier E (2012) Computational mechanics of discontinua. Wiley, New York

    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(1):267–274

    Article  Google Scholar 

  • Nezhad MM, Fisher QJ, Gironacci E et al (2018) Experimental study and numerical modeling of fracture propagation in shale rocks during Brazilian disk test. Rock Mech Rock Eng 51(6):1755–1775

    Article  Google Scholar 

  • Schauffert EA, Cusatis G (2012) Lattice discrete particle model for fiber-reinforced concrete. I: theory. J Eng Mech 138(7):826–833

  • Schauffert EA, Cusatis G, Pelessone D, O’Daniel JL, Baylot JT (2012) Lattice discrete particle model for fiber-reinforced concrete. II: tensile fracture and multiaxial loading behavior. J Eng Mech 138(7):834–841

  • Tavallali A, Vervoort A (2010) Failure of layered sandstone under Brazilian test conditions: effect of micro-scale parameters on macro-scale behavior. Rock Mech Rock Eng 43(5):641–653

    Article  Google Scholar 

  • Xin T, Konietzky H (2014) Brazil test and numerical simulation of heterogeneous gneiss with bedding structure [J]. Chin J Rock Mechan Eng 33(5):938–946 (In Chinese)

    Google Scholar 

  • Tang CA, Tham LG, Lee PKK, Tsui Y, Liu H (2000) Numerical studies of the influence of microstructure on rock failure in uniaxial compression Đ part II: constraint, slenderness and size effect. Int J Rock Mech Min Sci 37:571–583

  • Tarokh A, Makhnenko RY, Fakhimi A et al (2017) Scaling of the fracture process zone in rock. Int J Fract 204:191–204

    Article  Google Scholar 

  • Talischi C, Paulino GH, Pereira AA, Menezes IFM (2012) PolyTop: A Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes. J Struct Multidiscip Optim 45(3):309–328

    Article  Google Scholar 

  • Vassaux M, Richard B, Ragueneau F, Millard A, Delaplace A (2015) Lattice models applied to cyclic behavior description of quasi-brittle materials: advantages of implicit integration. Int J Numer Anal Meth Geomech 39:775–798

    Article  Google Scholar 

  • Wu Z, Yu F, Zhang P, Liu X (2019) Micro-mechanism study on rock breaking behavior under water jet impact using coupled SPH-FEM/DEM method with Voronoi grains. Eng Anal Bound Elem 108:472–483

    Article  Google Scholar 

  • Wang YP, Xiong LX (2020) Numerical analysis of the influence of bolt set on the shear resistance of jointed rock masses. Civ Eng J 6(6):1039–1055

    Article  Google Scholar 

  • Zhipeng Y et al (2015) Shale strength and failure model by Brazil test. Chin J Geotech Eng 36(12):3447–3456 (In Chinese)

    Google Scholar 

  • Zhao G-F, Fang J, Zhao J (2011) A 3D distinct lattice spring model for elasticity and dynamic failure. Int J Numer Anal Methods Geomech 35(8):859–885

    Article  Google Scholar 

  • Zhu WC, Tang CA (2006) Numerical simulation of Brazilian disk rock failure under static and dynamic loading. Int J Rock Mech Min Sci 43:236–252

    Article  Google Scholar 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

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

    N. N. Zhao & J. L. Feng

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

    N. N. Zhao & J. L. Feng

Authors
  1. N. N. Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. L. Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. N. Zhao.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Informed consent

Informed consent was obtained from all individual participants included in the study.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, N.N., Feng, J.L. Investigation on fracture mechanism of layered slate: experiment and beam-particle method. Environ Earth Sci 80, 788 (2021). https://doi.org/10.1007/s12665-021-10106-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12665-021-10106-w

Keywords

Search

Navigation