Skip to main content
SpringerLink
Log in

Dynamic stress concentration in pre-stressed poroelastic media due to moving punch influenced by shear wave

  • ORIGINAL ARTICLE
  • Published:
Journal of Seismology Aims and scope Submit manuscript

Abstract

During the occurrence of earthquake, the shear wave propagates in the rocks present inside/at the Earth’s crust. The propagation of shear wave may lead to the progression of punch present inside the rock medium. As a result of this, substantial stress accumulated at the vicinity of propagating punch inside rock medium which significantly affects the stability of various geological and human-made structure and, hence, may cause failure of structure. Therefore, the analysis of stress concentration at the vicinity of punch moving due to shear wave propagation has become prominent in the area of seismology. In the present paper, an analytical perspective has been employed to discuss the influence of velocity of moving punch associated with the propagation of shear wave on developed dynamic stress concentration (DSC) in three types of pre-stressed vertical transversely isotropic (VTI) poroelastic media viz. granite (an igneous rock); sandstone (a sedimentary rock); and marble (a metamorphic rock). The closed form expression of DSC for the force of constant intensity has been derived with the aid of Weiner-Hopf technique along with Galilean and two-sided Fourier integral transformations. The noticeable influence of different affecting parameters (viz. velocity of moving punch associated with the shear wave propagation, horizontal compressive/tensile initial stresses, vertical compressive/tensile initial stress, porosity, and anisotropy parameter) on dynamic stress concentration has also been reported. Numerical computation and graphical illustrations have been carried out for the aforementioned three different types of porous rocks to investigate the profound impact of affecting parameters on DSC. Moreover, some noteworthy peculiarities have also been derived from the obtained expression of dynamic stress concentration.

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

Similar content being viewed by others

References

  • Aben FM, Doan ML, Mitchell TM, Toussaint R, Reuschlé T, Fondriest M, Gratier JP, Renard F (2016) Dynamic fracturing by successive coseismic loadings leads to pulverization in active fault zones. J Geophys Res: Solid Earth 121(4):2338–2360. https://doi.org/10.1002/2015JB012542

    Article  Google Scholar 

  • Batugin SA, Nirenburg RK (1972) Approximate relation between the elastic constants of anisotropic rocks and anisotropy parameters. Soviet Mining  8(1):5–9

  • Berryman JG (2012) Poroelastic response of orthotropic fractured porous media. Transport Porous Med 93(2):293–307

    Article  Google Scholar 

  • Biot MA (1940) The influence of initial stress on elastic waves. J Appl Phys 11(8):522–530

    Article  Google Scholar 

  • Biot MA (1956a) Theory of elastic waves in a fluid-saturated porous solid, I. Low frequency range. J Acoust Soc Am 28(2):168–178

    Article  Google Scholar 

  • Biot MA (1956b) Theory of elastic waves in a fluid-saturated porous solid, II. High frequency range. J Acoust Soc Am 28(2):179–191

    Article  Google Scholar 

  • Biot MA (1962a) Mechanics of deformations and acoustic propagation in porous media. J Appl Phys 33(4):1482–1498

  • Biot MA (1962b) Generalized theory of acoustic propagation in porous media. J Acoust Soc Am 34(9A):1254–1264

    Article  Google Scholar 

  • Biot MA (1963) Internal buckling under initial stress in finite elasticity. In proceedings of the Royal Society of London a: mathematical. Phys Eng Sci 273(1354):306–328 The Royal Society

    Article  Google Scholar 

  • Chattopadhyay A (1995) Effect of punch on the propagation of shear waves in a self-reinforced medium. Proc Indian Natl Sci Acad Part A 61:37–46

    Google Scholar 

  • Chattopadhyay A, De RK (1983) Love waves in a porous layer with irregular interface. Int J Eng Sci 21(11):1295–1303

    Article  Google Scholar 

  • Deresiewicz H (1965) The effect of boundaries on wave propagation in a liquid-filled porous solid: IX. The Love waves in a porous internal stratum. Bull Seismol Soc Am 55(5):919–923

    Google Scholar 

  • Deresiewicz H, Skalak R (1963) On uniqueness in dynamic poroelasticity. Bull Seismol Soc Am 53(4):783–788

  • Dey S, Sarkar MG (2002) Torsional surface waves in an initially stressed anisotropic porous medium. J Eng Mech 128(2):184–189

    Article  Google Scholar 

  • Dhaliwal RS, Singh BM (1984) Closed form solutions to dynamic punch problems by integral transform methods. ZAMM-J Appl Math Mech 64(1):31–34

  • Diederichs MS (2007) The 2003 Canadian geotechnical colloquium: mechanistic interpretation and practical application of damage and spalling prediction criteria for deep tunnelling. Can Geotech J 44(9):1082–1116. https://doi.org/10.1139/T07-033

  • Dineva P, Wuttke F, Manolis G (2012) Elastic wavefield evaluation in discontinuous poroelastic media by BEM: SH waves. J Theoretical Appl Mech 42(3):75–100

    Article  Google Scholar 

  • Gladwell GML (1980) Contact problems in the classical theory of elasticity. Springer, Netherlands

  • Gurevich B (2003) Elastic properties of saturated porous rocks with aligned fractures. J Appl Geophys 54(3-4):203–218

  • Gurevich B, Schoenberg M (1999) Interface conditions for biots equations of poroelasticity. J Acoust Soc Am 105(5):2585–2589

  • Iwona SK, Idziak AF (2008) Anisotropy of elastic properties of rock mass induced by cracks. Acta Geodyn Geomater 5(2):153–159

  • King RB (1987) Elastic analysis of some punch problems for a layered medium. Int J Solids Struct 23(12):1657–1664

    Article  Google Scholar 

  • Leith K, Moore JR, Amann F, Loew S (2014) In situ stress control on microcrack generation and macroscopic extensional fracture in exhuming bedrock. Journal of Geophysical Research: Solid Earth 119(1):594–615

    Google Scholar 

  • Liu D, Gai B, Tao G (1982) Application of the method of complex functions to dynamic stress concentration. Wave Motion 4(3):293–304

  • Manolis GD, Beskos DE (1981) Dynamic stress concentration studies by boundary integrals and Laplace transform. Int J Numer Method Eng 17(4):573–599

  • Matczynski M (1963) Elastic wedge with discontinuous boundary conditions. Arch Mechaniki Stosowa 15(6):833–855

    Google Scholar 

  • Nandal JS, Saini TN (2013) Reflection and refraction at an imperfectly bonded interface between poroelastic solid and cracked elastic solid. J Seismol 17(2):239–253

    Article  Google Scholar 

  • Noble B (1958) Method based on Wiener-Hopf technique for the solution of partial differential equations. Pergamon Press, London

    Google Scholar 

  • Pal J, Ghorai AP (2015) Propagation of Love wave in sandy layer under initial stress above anisotropic porous half-space under gravity. Transport Porous Med 109(2):297–316

  • Sanyal DC (1980) Deformation of a semi-infinite poroelastic medium under the compressive action of a rigid body. Indian J Pure Appl Math 11(10):1388–1396

    Google Scholar 

  • Sanyal DC, Singh JN (1987) On the deformation of a poroelastic medium containing a very thin internal crack. Indian J Pure Appl Math 18(1):91–99

    Google Scholar 

  • Sayers CM, Kachanov M (1995) Microcrack-induced elastic wave anisotropy of brittle rocks. J Geophys Res: Solid Earth 100(B3):4149–4156

    Article  Google Scholar 

  • Sharma MD, Gogna ML (1991) Propagation of Love waves in an initially stressed medium consist of a slow elastic layer lying over a liquid-saturated porous solid half-space. J Acoust Soc Am 89(6):2584–2588

  • Singh AK, Kumar S, Chattopadhyay A (2014) Effect of irregularity and heterogeneity on the stresses produced due to a normal moving load on a rough monoclinic half-space. Meccanica 49(12):2861–2878

    Article  Google Scholar 

  • Singh AK, Parween Z, Chatterjee M, Chattopadhyay A (2015) Love-type wave propagation in a pre-stressed viscoelastic medium influenced by smooth moving punch. Waves Random Complex Media 25(2):268–285

    Article  Google Scholar 

  • Son MS, Kang YJ (2012) Propagation of shear waves in a poroelastic layer constrained between two elastic layers. Appl Math Model 36:3685–3695

    Article  Google Scholar 

  • Tait RJ, Moodie TB (1981) Complex variable methods and closed form solutions to dynamic crack and punch problems in the classical theory of elasticity. Int J Eng Sci 19(2):221–229

    Article  Google Scholar 

  • Titchmarsh EC (1939) Theory of Fourier integrals. Oxford University Press, London

    Google Scholar 

  • Toussaint R, Pride SR (2002) Fracture of disordered solids in compression as a critical phenomenon. II. Model Hamiltonian for a population of interacting cracks. Phys Rev E 66(3), art. no. 036136). https://doi.org/10.1103/PhysRevE.66.036136

  • Wang YS, Zhang ZM (1998) Propagation of Love waves in a transversely isotropic fluid-saturated porous layered half-space. J Acoust Soc Am 103(2):695–701

  • Zhu L, Rivera LA (2002) A note on the dynamic and static displacements from a point source in multilayered media. Geophys J Int 148(3):619–627

    Article  Google Scholar 

Download references

Acknowledgements

The authors express their sincere thanks to the National Board of Higher Mathematics (NBHM) for their financial support to carry out this research work through Project no. NBHM/R.P. 78/2015/Fresh/2017/24.1.2017 entitled “Mathematical modeling of elastic wave propagation in highly anisotropic and heterogeneous media.”

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, India

    Abhishek Kumar Singh, Anil Negi & Ram Prasad Yadav

  2. Department of Mining Engineering, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, India

    Amit Kumar Verma

Authors
  1. Abhishek Kumar Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anil Negi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ram Prasad Yadav
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Amit Kumar Verma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anil Negi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singh, A.K., Negi, A., Yadav, R.P. et al. Dynamic stress concentration in pre-stressed poroelastic media due to moving punch influenced by shear wave. J Seismol 22, 1263–1274 (2018). https://doi.org/10.1007/s10950-018-9766-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10950-018-9766-5

Keywords

Search

Navigation