SpringerLink
Log in

Seismic interaction between a semi-cylindrical hill and a nearby underground cavity under plane SH waves

  • Original Article
  • Published:
Geomechanics and Geophysics for Geo-Energy and Geo-Resources Aims and scope Submit manuscript

Abstract

Seismic waves might be unavoidably triggered during underground energy and resource exploitation. Surface irregularities and subsurface cavities have significant effects on seismic wave propagation and cause amplification or reduction of ground motion. Hence, it is significant to address the scattering problem of SH waves induced by topography features and subsurface cavities in earthquake engineering. In this paper, based on the wave function expansion method coupling with the conjunction concept and the Graf’s addition formula, a series solution to this scattering problem of SH waves induced by a semi-cylindrical hill and a nearby cylindrical cavity in a homogeneous, isotropic, linear elastic half-space is derived. The displacement amplitudes on the hill surface and its environs are calculated, and compared with the results in the existing works to verify the validity of the deriving process. Then, parametric studies are performed to analyze the effects of the cavity (its location and size), and the characteristics of incident waves (the frequency and incident angle) on the seismic response of the semi-cylindrical hill. Finally, the seismic behavior of the cylindrical cavity near or away from the hill for different frequencies and incident angles is examined.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

Abbreviations

\(a_{1}\) :

Semi-cylindrical hill radius

\(d\) :

Burial depth of the cavity

\(\theta\), \(\theta_{ 1}\), \(\theta_{ 2}\) :

Polar angles measured from the vertical y-, y1-, y2-axes, respectively

\(\alpha\) :

Incident angle

u f :

Steady-state out-of-plane motion corresponding to free field

i :

\(\sqrt { - 1}\)

c :

Shear wave velocity

k :

Shear wavenumber

\(J_{n} \left( \cdot \right)\) :

nth order Bessel function of the first kind

\(\varepsilon_{n}\) :

Neumann factor

\(\left| u \right|\) :

Displacement amplitude

\(\lambda\) :

Wavelength of incident SH wave

Im():

Imaginary part of a complex expression

\(a_{2}\) :

Subterranean cylindrical cavity radius

\(l\) :

Horizontal distance between the centers of the hill and the cavity

\(\omega\) :

Circular frequency of incident SH wave

\(u^{\left( j \right)}\) :

Steady-state out-of-plane motion in the region j

u s :

Steady-state out-of-plane motion corresponding to scattered field

t :

Time

\(\mu\) :

Shear modulus

\(\tau\) :

Shear stress

\(H_{n}^{\left( 1 \right)} \left( \cdot \right)\) :

nth order Hankel function of the first kind

\(x\) :

Abscissa corresponding to the rectangular coordinate system x–o–y

\(\eta\) :

Dimensionless frequency

Re():

Real part of a complex expression

n, q, s, m :

Summation indexes

N, QQ, SS, M :

Values corresponding to n, q, s, m, respectively, when the infinite series is truncated to a finite number

References

  • Abramowitz M, Stegun IA (1972) Handbook of mathematical functions, with formulas, graphs, and mathematical tables. Dover, New York

    MATH  Google Scholar 

  • Alielahi H, Adampira M (2016) Effect of twin-parallel tunnels on seismic ground response due to vertically in-plane waves. Int J Rock Mech Min Sci 85:67–83

    Article  Google Scholar 

  • Alielahi H, Kamalian M, Adampira M (2015) Seismic ground amplification by unlined tunnels subjected to vertically propagating SV and P waves using BEM. Soil Dyn Earthq Eng 71:63–79

    Article  Google Scholar 

  • Alielahi H, Kamalian M, Adampira M (2016) A BEM investigation on the influence of underground cavities on the seismic response of canyons. Acta Geotech 11(2):391–413

    Article  Google Scholar 

  • Assimaki D, Kausel E, Gazetas G (2005) Wave propagation and soil–structure interaction on a cliff crest during the 1999 Athens Earthquake. Soil Dyn Earthq Eng 25(7–10):513–527

    Article  Google Scholar 

  • Buech F, Davies TR, Pettinga JR (2010) The little red hill seismic experimental study: topographic effects on ground motion at a bedrock-dominated mountain edifice. Bull Seismol Soc Am 100(5A):2219–2229

    Article  Google Scholar 

  • Cen WJ, Du XH, Li DJ, Yuan LN (2018) Oblique incidence of seismic wave reflecting two components of design ground motion. Shock Vib 4127031-16

  • Chang KH, Tsaur DH, Wang JH (2016) Ground motions around a semicircular canyon with a dip** edge under SH plane wave incidence. J Seismol 20:117–136

    Article  Google Scholar 

  • Clarke H, Eisner L, Styles P, Turner P (2014) Felt seismicity associated with shale gas hydraulic fracturing: the first documented example in Europe. Geophys Res Lett 41:8308–8314

    Article  Google Scholar 

  • Ducellier A, Aochi H (2012) Interactions between topographic irregularities and seismic ground motion investigated using a hybrid FD–FE method. Bull Earthq Eng 10:773–792

    Article  Google Scholar 

  • Gao YF, Dai DH, Zhang N, Wu YX, Mahfouz AH (2017) Scattering of plane and cylindrical SH waves by a horseshoe shaped cavity. J Earthq Tsunami 11(2):1650011–1650023

    Article  Google Scholar 

  • Gao YF, Chen X, Zhang N, Dai DH, Yu X (2018) Scattering of plane SH waves induced by a semicylindrical canyon with a subsurface circular lined tunnel. Int J Geomech 06018012-10

    Article  Google Scholar 

  • Gizzi FT, Masini N (2006) Historical damage pattern and differential seismic effects in a town with ground cavities: a case study from Southern Italy. Eng Geol 88:41–58

    Article  Google Scholar 

  • Glinsky N, Bertrand E, Régnier J (2019) Numerical simulation of topographical and geological site effects. Applications to canonical topographies and Rognes hill, South East France. Soil Dyn Earthq Eng 116:620–636

    Article  Google Scholar 

  • Graizer V (2009) Low-velocity zone and topography as a source of site amplification effect on Tarzana hill, California. Soil Dyn Earthq Eng 29(2):324–332

    Article  Google Scholar 

  • Hough SE, Altidor JR, Anglade D, Given D, Janvier MG, Maharrey JZ, Meremonte M, Mildor BSL, Prepetit C, Yong A (2010) Localized damage caused by topographic amplification during the 2010M 7.0 Haiti earthquake. Nat Geosci 3(11):778–782

    Article  Google Scholar 

  • Jafarzadeh F, Shahrabi MM, Jahromi HF (2015) On the role of topographic amplification in seismic slope instabilities. J Rock Mech Geotech Eng 7(2):163–170

    Article  Google Scholar 

  • Jayalakshmi S, Raghukanth STG (2016) Regional ground motion simulation around Delhi due to future large earthquake. Nat Hazards 82:1479–1513

    Article  Google Scholar 

  • Kamalian M, Jafari MK, Sohrabi-bidar A, Razmkhah A, Gatmiri B (2006) Time-domain two-dimensional site response analysis of non-homogeneous topographic structures by a hybrid BE/FE method. Soil Dyn Earthq Eng 26:753–765

    Article  Google Scholar 

  • Kang JQ, Zhu JB, Zhao J (2019) A review of mechanisms of induced earthquakes: from a view of rock mechanics. Geomech Geophys Geo-Energy Geo-Resour 5:171–196

    Article  Google Scholar 

  • Karkooti E, Shomali ZH, Pakzad M (2016) Investigating the role of source mechanism, surface topography, and attenuation on the observed PGA pattern in May 28, 2004, Mw 6.2 Baladeh earthquake (Iran). J Seismol 20:495–510

    Article  Google Scholar 

  • Lee VW, Trifunac MD (1979) Response of tunnels to incident SH-waves. J Eng Mech 105:643–659

    Google Scholar 

  • Lee VW, Chen S, Hsu IR (1999) Antiplane diffraction from canyon above subsurface unlined tunnel. J Eng Mech 125(6):668–675

    Article  Google Scholar 

  • Lee VW, Luo H, Liang JW (2006) Antiplane (SH) waves diffraction by a semicircular cylindrical hill revisited: an improved analytic wave series solution. J Eng Mech 132(10):1106–1114

    Article  Google Scholar 

  • Lenti L, Martino S (2012) The interaction of seismic waves with step-like slopes and its influence on landslide movements. Eng Geol 2012:19–36

    Article  Google Scholar 

  • Lenti L, Martino S (2013) A parametric numerical study of the interaction between seismic waves and landslides for the evaluation of the susceptibility to seismically induced displacements. Bull Seismol Soc Am 103(1):33–56

    Article  Google Scholar 

  • Li JC, Li HB, Ma GW, Zhou YX (2013) Assessment of underground tunnel stability to adjacent tunnel explosion. Tunn Undergr Space Technol 35:227–234

    Article  Google Scholar 

  • Lin ML, Wang KL (2006) Seismic slope behavior in a large-scale shaking table model test. Eng Geol 86:118–133

    Article  Google Scholar 

  • Lin CH, Lee VM, Todorovska MI, Trifunac MD (2010) Zero-stress, cylindrical wave functions around a circular underground tunnel in a flat, elastic half-space: incident P-waves. Soil Dyn Earthq Eng 30:879–894

    Article  Google Scholar 

  • Liu HX, Xu Q, Li YR, Fan XM (2013a) Response of high-strength rock slope to seismic waves in a shaking table test. Bull Seismol Soc Am 103(6):3012–3025

    Article  Google Scholar 

  • Liu QJ, Zhao MJ, Wang LH (2013b) Scattering of plane P, SV or Rayleigh waves by a shallow lined tunnel in an elastic half space. Soil Dyn Earthq Eng 49:52–63

    Article  Google Scholar 

  • Liu QJ, Zhang C, Todorovska MI (2016) Scattering of SH waves by a shallow rectangular cavity in an elastic half space. Soil Dyn Earthq Eng 90:147–157

    Article  Google Scholar 

  • Liu XB, Chen JY, Zhao ZC, Lan HQ, Liu FP (2018) Simulating seismic wave propagation in viscoelastic media with an irregular free surface. Pure Appl Geophys 175:3419–3439

    Article  Google Scholar 

  • Lovati S, Bakavoli MKH, Massa M, Ferretti G, Pacor F, Paolucci R, Haghshenas E, Kamalian M (2011) Estimation of topographical effects at Narni ridge (Central Italy): comparisons between experimental results and numerical modelling. Bull Earthq Eng 9:1987–2005

    Article  Google Scholar 

  • Luo YH, Gaudio VD, Huanga R, WangY S, Wasowski J (2014) Evidence of hillslope directional amplification from accelerometer recordings at Qiaozhuang (Sichuan, China). Eng Geol 183:193–207

    Article  Google Scholar 

  • Massa M, Lovati S, Alema ED, Ferretti G, Bakavoli M (2010) An experimental approach for estimating seismic amplification effects at the top of a ridge, and the implication for ground-motion predictions: the case of Narni, Central Italy. Bull Seismol Soc Am 100(6):3020–3034

    Article  Google Scholar 

  • Moghadam MR, Baziar MH (2016) Seismic ground motion amplification pattern induced by a subway tunnel: shaking table testing and numerical simulation. Soil Dyn Earthq Eng 83:81–97

    Article  Google Scholar 

  • Nagashima F, Matsushima S, Kawase H, Sánchez-Sesma FJ, Hayakawa T, Satoh T, Oshima M (2014) Application of horizontal-to-vertical spectral ratios of earthquake ground motions to identify subsurface structures at and around the K-NET site in Tohoku, Japan. Bull Seismol Soc Am 104(5):2288–2302

    Article  Google Scholar 

  • Nguyen KV, Behrouz G (2007) Evaluation of seismic ground motion induced by topographic irregularity. Soil Dyn Earthq Eng 27:183–188

    Article  Google Scholar 

  • Panji M, Kamalian M, Asgari Marnani J, Jafari MK (2014) Analysing seismic convex topographies by a half-plane time-domain BEM. Geophys J Int 197:591–607

    Article  Google Scholar 

  • Parvanova SL, Dineva PS, Manolis GD, Wuttke F (2014) Seismic response of lined tunnels in the half-plane with surface topography. Bull Earthq Eng 12(2):981–1005

    Article  Google Scholar 

  • Patil M, Choudhury D, Ranjith PG, Zhao J (2018) Behavior of shallow tunnel in soft soil under seismic conditions. Tunn Undergr Space Technol 82:30–38

    Article  Google Scholar 

  • Poursartip B, Fathi A, Kallivokas LF (2017) Seismic wave amplification by topographic features: a parametric study. Soil Dyn Earthq Eng 92:503–527

    Article  Google Scholar 

  • Schultz R, Stern V, Novakovic M, Atkinson G, Gu YJ (2015) Hydraulic fracturing and the Crooked Lake Sequences: insights gleaned from regional seismic networks. Geophys Res Lett 42:2750–2758

    Article  Google Scholar 

  • Sills LB (1978) Scattering of horizontally-polarized shear waves by surface irregularities. Geophys J R Astron Soc 54:319–348

    Article  Google Scholar 

  • Srilatha N, Madhavi Latha G, Puttappa CG (2013) Effect of frequency on seismic response of reinforced soil slopes in shaking table tests. Geotext Geomembr 36:27–32

    Article  Google Scholar 

  • Trifunac MD (1973) Scattering of plane SH waves by a semi-cylindrical canyon. Earthq Eng Struct Dyn 1:267–281

    Article  Google Scholar 

  • Tripe R, Kontoe S, Wongc TKC (2013) Slope topography effects on ground motion in the presence of deep soil layers. Soil Dyn Earthq Eng 50:72–84

    Article  Google Scholar 

  • Tsaur DH (2011) Scattering and focusing of SH waves by a lower semielliptic convex topography. Bull Seismol Soc Am 101(5):2212–2219

    Article  Google Scholar 

  • Tsaur DH, Chang KH (2009) Scattering and focusing of SH waves by a convex circular-arc topography. Geophys J Int 177:222–234

    Article  Google Scholar 

  • Wang G, Du CY, Huang D, ** F, Kooc RCH, Kwanc JSH (2018) Parametric models for 3D topographic amplification of ground motions considering subsurface soils. Soil Dyn Earthq Eng 115:41–54

    Article  Google Scholar 

  • Watson GN (1958) A treatise on the theory of Bessel functions, 2nd edn. Cambridge University Press, Cambridge

    Google Scholar 

  • Wu W, Zhao ZH, Duan K (2017) Unloading-induced instability of a simulated granular fault and implications for excavation-induced seismicity. Tunn Undergr Space Technol 63:154–161

    Article  Google Scholar 

  • Yang GX, Qi SW, Wu FQ, Zhan ZF (2018) Seismic amplification of the anti-dip rock slope and deformation characteristics: a large-scale shaking table test. Soil Dyn Earthq Eng 115:907–916

    Article  Google Scholar 

  • Yu YZ, Deng LJ, Sun X, Lu H (2008) Centrifuge modeling of a dry sandy slope response to earthquake loading. Bull Earthq Eng 6(3):447–461

    Article  Google Scholar 

  • Yuan XM, Liao ZP (1996) Surface motion of a cylindrical hill of circular-arc cross-section for incident plane SH waves. Soil Dyn Earthq Eng 15:189–199

    Article  Google Scholar 

  • Yuan XM, Men FL (1992) Scattering of plane SH waves by a semi-cylindrical hill. Earthq Eng Struct Dyn 21:1091–1098

    Article  Google Scholar 

  • Zhang N, Gao YF, Cai YQ, Li DY, Wu YX (2012) Scattering of SH waves induced by a non-symmetrical V-shaped canyon. Geophys J Int 191:243–256

    Article  Google Scholar 

  • Zhang ZL, Wang T, Wu SR, Tang HM, Liang CY (2017) Seismic performance of loess-mudstone slope in Tianshui–Centrifuge model tests and numerical analysis. Eng Geol 222:225–235

    Article  Google Scholar 

  • Zhang ZZ, Fleurisson JA, Pellet FL (2018a) A case study of topographic site effects on seismic ground motions at **shan Park ridge in Zigong, Sichuan, China. Eng Geol 243:308–319

    Article  Google Scholar 

  • Zhang ZZ, Fleurisson JA, Pellet FL (2018b) The effects of slope topography on acceleration amplification and interaction between slope topography and seismic input motion. Soil Dyn Earthq Eng 113:420–431

    Article  Google Scholar 

  • Zhao J, Zhou YX, Hefny AM, Cai JG, Chen SG, Li HB, Liu JF, Jain M, Foo ST, Seah CC (1999) Rock dynamics research related to cavern development for ammunition storage. Tunn Undergr Space Technol 14(4):513–526

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by National Natural Sciences Foundation of China (41525009, 41831281).

Author information

Authors and Affiliations

  1. Institute of Underground Space Technology, School of Civil Engineering, Southeast University, Nan**g, 211189, China

    Z. L. Li, J. C. Li & X. Li

Authors
  1. Z. L. Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. C. Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. X. Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. C. Li.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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

Li, Z.L., Li, J.C. & Li, X. Seismic interaction between a semi-cylindrical hill and a nearby underground cavity under plane SH waves. Geomech. Geophys. Geo-energ. Geo-resour. 5, 405–423 (2019). https://doi.org/10.1007/s40948-019-00120-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40948-019-00120-5

Keywords

Search

Navigation