Dynamic response of a lined tunnel to plane SH waves in a bi-material space. (English) Zbl 1521.74119
Summary: In this paper, an analytical solution for the scattering of plane SH waves by a lined tunnel buried in an inhomogeneous medium is presented via the complex variable method. The problem model is a bi-material with a homogeneous medium containing a circular cavity and an inhomogeneous one embedding a lined tunnel. For the convenience of calculation, the physical domain including straight and circular interfaces is transformed into the image plane with four concentric circles by introducing the conformal mapping functions. The boundary conditions are applied to find the unknown coefficients of the wave functions. Then, the factors affecting the dynamic response to SH wave are investigated through the calculation results for the dynamic stress concentration factor (DSCF) at several boundary surfaces.
MSC:
| 74J20 | Wave scattering in solid mechanics |
| 74L10 | Soil and rock mechanics |
| 74S70 | Complex-variable methods applied to problems in solid mechanics |
| 74H35 | Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics |
| 74E05 | Inhomogeneity in solid mechanics |
Keywords:
wave scattering; inhomogeneous rock; circular cavity; complex variable method; conformal mapping; dynamic stress concentration factorReferences:
| [1] | Gregory, RD, An expansion theorem applicable to problems of wave propagation in an elastic half-space containing a cavity, Math Proc Cambridge, 63, 4, 1341-1367 (1967) · Zbl 0155.53104 · doi:10.1017/S0305004100042377 |
| [2] | Gregory, RD, The propagation of waves in an elastic half-space containing a cylindrical cavity, Math Proc Cambridge, 67, 689-710 (1970) · Zbl 0218.73030 · doi:10.1017/S0305004100046016 |
| [3] | Lee, VW; Trifunac, MD, Response of tunnels to incident SH-waves, J Eng Mech Div (ASCE), 105, 4, 643-659 (1979) · doi:10.1061/JMCEA3.0002511 |
| [4] | Lee, VW, Three-dimensional diffraction of elastic waves by a spherical cavity in an elastic half space, I: closed-form solutions, Soil Dyn Earthq Eng, 7, 3, 149-161 (1988) · doi:10.1016/S0267-7261(88)80019-8 |
| [5] | Lee, VW; Karl, J., Diffraction of SV waves by underground, circular, cylindrical cavities, Soil Dyn Earthq Eng, 11, 8, 445-456 (1992) · doi:10.1016/0267-7261(92)90008-2 |
| [6] | Lee, VW; Karl, J., Diffraction of elastic plane P waves by circular, underground unlined tunnels, Eur Earthq Eng, 6, 1, 29-36 (1993) |
| [7] | Smerzini, C.; Avilés, J.; Paolucci, R.; Sánchez-Sesma, FJ, Effect of underground cavities on surface earthquake ground motion under SH wave propagation, Earthquake Eng Struct Dynam, 38, 12, 1441-1460 (2009) · doi:10.1002/eqe.912 |
| [8] | Liu, D.; Gai, B.; Tao, G., Applications of the method of complex functions to dynamic stress concentrations, Wave Motion, 4, 1982, 293-304 (1982) · Zbl 0484.73007 · doi:10.1016/0165-2125(82)90025-7 |
| [9] | Liu, D.; Han, F., The scattering of plane SH-waves by noncircular cavity in Anisotropic media, J Appl Mech September, 60, 1993, 769-772 (1993) · Zbl 0808.73019 |
| [10] | Verruijt, A., A complex variable solution for a deforming circular tunnel in an elastic half-plane, Int J Numer Anal Met, 21, 77-89 (1997) · Zbl 0894.73127 · doi:10.1002/(SICI)1096-9853(199702)21:2<77::AID-NAG857>3.0.CO;2-M |
| [11] | Verruijt, A., Deformations of an elastic half plane with a circular cavity, Int J Solids Struct, 35, 21, 2795-2804 (1998) · Zbl 0918.73014 · doi:10.1016/S0020-7683(97)00194-7 |
| [12] | Fang, XQ; Hu, C.; Du, SY, Strain energy density of a circular cavity buried in semi-infinite functionally graded materials subjected to shear waves, Theor Appl Fract Mec, 46, 2, 166-174 (2006) · doi:10.1016/j.tafmec.2006.07.008 |
| [13] | Fang, X.; Hu, C.; Huang, W., Dynamic stress of a circular cavity buried in a semi-infinite functionally graded piezoelectric material subjected to shear waves, European J Mech A, Solids, 26, 6, 1016-1028 (2007) · Zbl 1123.74026 · doi:10.1016/j.euromechsol.2007.05.003 |
| [14] | Fang, X.; Hu, C.; Huang, W., Strain energy density of a circular cavity buried in a semi-infinite slab of functionally graded materials subjected to anti-plane shear waves, Int J Solids Struct, 44, 21, 6987-6998 (2007) · Zbl 1166.74378 · doi:10.1016/j.ijsolstr.2007.03.024 |
| [15] | Fang, X.; Liu, J.; Wang, D.; Zhang, L., Dynamic stress from a subsurface cavity in a semi-infinite functionally graded piezoelectric/piezomagnetic material, Appl Math Model, 34, 10, 2789-2805 (2010) · Zbl 1201.74157 · doi:10.1016/j.apm.2009.12.013 |
| [16] | Fang, X.; Liu, J.; Zhang, L.; Kong, Y., Dynamic stress from a subsurface cylindrical inclusion in a functionally graded material layer under anti-plane shear waves, Mater Struct, 44, 1, 67-75 (2011) · doi:10.1617/s11527-010-9609-5 |
| [17] | Martin, PA, Scattering by a cavity in an exponentially graded half-space, J Appl Mech, 76, 31001-31009 (2009) · doi:10.1115/1.3086585 |
| [18] | Martin, PA, Scattering by defects in an exponentially graded layer and misuse of the method of images, Int J Solids Struct, 48, 14-15, 2164-2166 (2011) · doi:10.1016/j.ijsolstr.2011.03.020 |
| [19] | Liu, Q.; Zhao, M.; Zhang, C., Antiplane scattering of SH waves by a circular cavity in an exponentially graded half space, Int J Eng Sci, 78, 61-72 (2014) · Zbl 1423.74436 · doi:10.1016/j.ijengsci.2014.02.006 |
| [20] | Liu, Q.; Zhang, C.; Todorovska, MI, Scattering of SH waves by a shallow rectangular cavity in an elastic half space, Soil Dyn Earthq Eng, 90, 147-157 (2016) · doi:10.1016/j.soildyn.2016.08.027 |
| [21] | Liu, Q.; Zhao, M.; Liu, Z., Wave function expansion method for the scattering of SH waves by two symmetrical circular cavities in two bonded exponentially graded half spaces, Eng Anal Bound Elem, 106, 389-396 (2019) · Zbl 1464.74086 · doi:10.1016/j.enganabound.2019.05.015 |
| [22] | Yang, Z.; Hei, B.; Wang, Y., Scattering by circular cavity in radially inhomogeneous medium with wave velocity variation, Appl Math Mech, 36, 5, 599-608 (2015) · doi:10.1007/s10483-015-1937-7 |
| [23] | Yang, Z.; Zhang, C.; Jiang, G.; Yan, P.; Yang, Y., A complex function method of SH wave scattering in inhomogeneous medium, Acta Mech, 228, 10, 3469-3481 (2017) · Zbl 1384.74021 · doi:10.1007/s00707-017-1876-6 |
| [24] | Yang, Z.; Jiang, G.; Sun, B.; Yang, Y., Scattering of shear waves by a cylindrical inclusion in an anisotropic half space, Acta Mech, 228, 11, 4039-4053 (2017) · Zbl 1380.74061 · doi:10.1007/s00707-017-1941-1 |
| [25] | Yang, Z.; Jiang, G.; Tang, H.; Sun, B.; Yang, Y., Dynamic analysis of a cylindrical cavity in inhomogeneous elastic half-space subjected to SH waves, Math Mech Solids, 24, 1, 299-311 (2019) · Zbl 1425.74245 · doi:10.1177/1081286517739520 |
| [26] | Yang, Z.; Bian, J.; Song, Y.; Yang, Y.; Sun, M., Scattering of cylindrical inclusions in half space with inhomogeneous shear modulus due to SH wave, Arch Appl Mech, 91, 7, 3449-3461 (2021) · doi:10.1007/s00419-021-01975-5 |
| [27] | Yang, Z.; Bian, J.; Jiang, G.; Yang, Y.; Sun, M., Dynamic response of a cylindrical cavity to SH wave in inhomogeneous continuum with modulus varying two-dimensionally, Wave Random Comp, 32, 3, 1289-1306 (2022) · Zbl 1490.74037 · doi:10.1080/17455030.2020.1818873 |
| [28] | Liu, D.; Lin, H., Scattering of SH-waves by an interacting interface linear crack and a circular cavity near bimaterial interface, Acta Mech Sin, 20, 3, 317-326 (2004) · doi:10.1007/BF02486724 |
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