در این مقاله روش اجـزای مرزی نیم‌صفحه در حوزه‌ی زمان برای تحلیل لرزه‌ای و تعیین پاسخ سطح زمین در حضور حفره پوشش‌دار زیرزمینی دایرهای در برابر امواج مهاجم برونصفحهی SH به‌کار گرفته شده است. با بهره‌گیری از روش مزبـور تنهـا لازم است مرزهــای پیــرامون پـوشش و حفــره المان‌بنـدی و گسسته‌سازی شوند. مبتنی بر روش زیرسازه‌سازی و تفکیک مدل به یک نیم‌صفحه حفـره‌دار و یک رینگ بسته توپـر، عناصر ماتریسهای مورد نظر برای هر دو محیط در هر گام زمانی تعیین می‌شود. در نهایت با در نظر گرفتن شرایط پیوستگی تنش و تغییر مکان در وجه میانی پوشش با فضای پیرامون، ماتریس کوپل نهایـی برای تعیین کلیه مقادیـر مجهـول مرزی اعم از تغییر مکان و تنش قابل حصول بوده و پس از آن به‌راحتی پاسخ‌های نقاط درونی به کمک مقادیر مزبور محاسبه می‌شود. به‌عنوان مطالعه عددی و با فرض یک تونل دایرهای پوشش‌دار بتنی مدفون در یک لایه خاک رس سیلت‌دار، به بررسی برخــی پارامتـرهـای حـاکـم از قبیـل ضخـامت پوشش، زاویــه مــوج مهاجـم و فرکانس پاسخ پرداختـه شده است. نتایج نشان می‌دهد الگوی بزرگنمایی سطح زمین در حضور حفره پوشش‌دار زیرزمینی متأثر از تمامی پارامترهای مزبور می‌باشد.
Ariman, T. and Muleski, G.E. (1981) A review of the response of buried pipelines under seismic excitations. Earth. Engin. and Struc. Dynam., 9, 133-151.
Panji, M. (2013) Seismic Analysis of Topographic Features due to Propagating Incident SH-Waves by Half-Plane Time-Domain BEM. Ph.D Dissertation, Islamic Azad University. Science and Research Branch. Tehran, Iran.
Lee, V.W. (1977) On the deformations near circular underground cavity subjected to incident plane SH-waves. Proc. of Symp. of Appl. of Comp. Meth. in Engin., University of Southern California. Los Angeles. 951-962.
Datta, S.K. and Shah, A.H. (1982) Scattering of SH waves by embedded cavities. Wave Moti., 4, 265-283.
Lee, V.W. and Trifunac, M.D. (1979) Response of tunnels to incident SH waves. Journal of Engineering Mechanics Division, 105(4), 643-659.
Balendra, T., Thambiratnam, D.P., Koh, C.G., and Lee, S.L. (1984) Dynamic response of twin circular tunnels due to incident SH-waves. Earthquake Engineering and Structural Dynamics, 12, 181-201.
Smerzini, C., Aviles, J., Paolucci, R., and Sanchez-Sesma, F.J. (2009) Effect of underground cavities on surface earthquake ground motion under SH wave propagation. Earthquake Engineering and Structural Dynamics, 38(12), 1441-1460.
Shi, S., Han, F., Wang, Z., and Liu, D. (1996) The interaction of plane SH-waves and non-circular cavity surfaced with lining in anisotropic media. Appl. Math. and Mech., 17(9), 855-867.
Hasheminejad, S.M. and Kazemirad, S. (2008) Dynamic response of an eccentrically lined circular tunnel in poroelastic soil under seismic excitation. Soil Dynamics and Earthquake Engineering, 28, 277-292.
Datta, S.K., Shah, A.H., and Wong, K.C. (1984) Dynamic stresses and displacements in buried pipe. Journal of Engineering Mechanics, 110, 1451-1466.
Moore, I.D. and Guan, F. (1996) Three-dimensional dynamic response of lined tunnels due to incident seismic waves. Earthquake Engineering and Structural Dynamics, 25, 357-369.
Manoogian, M.E. (2000) Scattering and diffraction of SH waves above an arbitrarily shaped tunnel. ISET Journ. of Earth. Tech., 37(1-3), 11-26.
Besharat, V., Davoodi, M., and Jafari, M.K. (2012) Effect of underground structures on free-field ground motion during earthquakes. 15th World Conference on Earthquake Engineering, Lisbon, Portugal.
Esmaeili, M., Vahdani, S., and Noorzad, A. (2006) Dynamic response of lined tunnel to plane harmonic waves. Tunn. and Unde. Spac. Tech., 21, 511-519.
Faccioli, E., Maggio, F., Paolucci, R., and Quarteroni, A. (1997) 2D and 3D elastic wave propagation by a pseudo-spectral domain decomposition method. Journal of Seismology, 1, 237-251.
Beskos, D.E. (1987) Boundary element methods in dynamic analysis. Appl. Mech. Revi., 40(1), 1-23.
Stamos, A.A. and Beskos, D.E. (1995) Dynamic analysis of large 3-D underground structures by the BEM. Earthquake Engineering and Structural Dynamics, 24, 917-934.
Dominguez, J. and Meise, T. (1991) On the use of the BEM for wave propagation in infinite domains. Engi. Anal. With Boun. Elem., 8(3), 132-138.
Crouch, S.L. and Starfield, A.M. (1983) Boundary Elements Methods in Solid Mechanics. Department of Civil and Mineral Engineering. University of Minnesota.
Yang, L. and Sterling, R.L. (1989) Back analysis of rock tunnel using boundary element method. Journ. of Geot. Engin., 115(8), 1163-1169.
Xiao, B. and Carter, J.P. (1993) Boundary element analysis of anisotropic rock masses. Engi. Anal. with Boun. Elem., 11, 293-303.
Panji, M., Asgari Marnani, J., and Tavousi Tafreshi, Sh. (2011) Evaluation of effective parameters on the underground tunnel stability using BEM. Journ. of Struc. Engin. and Geot., 1(2), 29-37.
Panji, M., Koohsari, H., Adampira, M., Alielahi, H., and Asgari Marnani, J. (2016) Stability analysis of shallow tunnels subjected to eccentric loads by a boundary element method. Journ. of Rock Mech. and Geot. Engin., 8, 480-488.
Kattis, S.E., Beskos, D.E., and Cheng, H.D. (2003) 2D dynamic response of unlined and lined tunnels in poroelastic soil to harmonic body waves. Earth. Engin. and Struc. Dynam., 32, 97-110.
Liu, Z. and Liu, L. (2015) An IBEM solution to the scattering of plane SH-waves by a lined tunnel in elastic wedge space. Earth. Sci., 28(1), 71-86.
Luco, J.E. and de Barros, F.C.P. (1994) Dynamic displacements and stresses in the vicinity of a cylindrical cavity embedded in a half-space. Earth. Engin. and Struc. Dynam., 23(3), 321-340.
Manolis, G.D. and Beskos, D.E. (1983) Dynamic response of lined tunnels by an isoparametric boundary element method. Comp. Meth. in Appl. Mech. and Engin., 36, 291-307.
Parvanova, S.L., Dineva, P.S., Manolis, G.D., and Wuttke, F. (2014) Seismic response of lined tunnels in the half-plane with surface topography. Bull. of Earth. Engin., 12(2), 981-1005.
Panji, M., Kamalian, M., Asgari Marnani, J., and Jafari, M.K. (2013) Transient analysis of wave propagation problems by half-plane BEM. Geop. Journ. Inter., 194(3), 1849-1865.
Dong, C.Y., Lo, S.H., and Cheung, Y.K. (2004) Numerical solution for elastic half-plane inclusion problems by different integral equation approaches. Engin. Anal. with Boun. Elem., 28, 123-130.
Dong, C.Y. and Lo, S.H. (2013) Boundary element analysis of an elastic half-plane containing nanoinhomogeneities. Journ. of Comp. Mate. Sci. 73, 33-40.
Panji, M. and Ansari, B. (2017) Modeling pressure pipe embedded in two-layer soil by a half-plane BEM. Comp. and Geot. 81, 360-367.
Telles, J.C.F. and Brebbia, C.A. (1980) Boundary element solution for half-plane problems. Inter. Jour. of Soli. and Stru., 12, 1149-1158.
Ye, G.W. and Sawada, T. (1989) Some numerical properties of boundary element analysis using half-plane fundamental solutions in 2-d elastostatics. Journ. of Comp. Mech., 4, 161-164.
Ba, Z. and Yin, X. (2016) Wave scattering of complex local site in a layered half-space by using a multidomain IBEM: incident plane SH waves. Geoph. Journ. Inter., 205, 1382-1405.
Benites, R., Aki, K., and Yomogida, K. (1992) Multiple scattering of SH waves in 2-D media with many cavities. Pure and Appl. Geoph., 138(3), 353-390.
Alielahi, H., Kamalian, M., Asgari Marnani, J., Jafari, M.K., and Panji, M. (2013) Applying a time-domain boundary element method for study of seismic ground response in the vicinity of embedded cylindrical cavity. Inter. Jour. of Civil Engi., 15, 45-54.
Kamalian, M., Jafari, M.K., Sohrabi-Bidar, A., Razmkhah, A., and Gatmiri, B. (2006) Time-domain two-dimensional site response analysis of non-homogeneous topographic structures by a hybrid FE/BE method. Soil. Dynam. and Earth. Engin., 26(8), 753-765.
Kamalian, M., Gatmiri, B., Sohrabi-Bidar, A., and Khalaj, A. (2007) Amplification pattern of 2D semi-sine shaped valleys subjected to vertically propagating incident waves. Inter. Journ. of Num. Meth. Biom. Engin., 23(10), 871â887.
Kamalian, M., Jafari, MK., Sohrabi-Bidar, A., and Razmkhah, A. (2008) Seismic response of 2D semi-sines shaped hills to vertically propagating incident waves: amplification patterns and engineering applications. Earth. Spec., 24(2), 405-430.
Takemiya, H. and Fujiwara, A. (1994) SH-wave scattering and propagation analyses at irregular sites by time domain BEM. Bull. of the Seis. Soci. of Ame., 84(5), 1443-1455.
Belytschko, T. and Chang, H.S. (1988) Simplified direct time integration boundary element method. Jour. of Engi. Mech., 114(1), 117-134.
Hirai, H. (1988) Analysis of transient response of SH wave scattering in a half-space by the boundary element method. Engineering Analysis, 5(4), 189-194.
Panji, M., Kamalian, M., Asgari Marnani, J., and Jafari, M.K. (2013) Amplification pattern of semi-sine shaped valleys subjected to vertically propagating incident SH waves. Jour. of Comp. Meth. in Engin., 32(2), 87-111.
Panji, M., Kamalian, M., Asgari Marnani, J., and Jafari, M.K. (2014) Analyzing seismic convex topographies by a half-plane time-domain BEM. Geoph. Journ. Inter., 197(1), 591-607.
Panji, M., Kamalian, M., Asgari Marnani, J., and Jafari, M.K. (2014) Antiplane seismic response from semi-sine shaped valley above embedded truncated circular cavity: a time-domain half-plane BEM. Inter. Journ. of Civil Engin., 12(2), 193-206.
Panji, M. and Ansari, B. (2017) Transient SHâwave scattering by a lined tunnel embedded in an elastic halfâplane. Engi. Anal. with Boun. Elem. 84, 220-230.
Eringen, A.C. and Suhubi, E.S. (1975) Elastodynamics Linear Theory. Academic Press, New York.
Brebbia, C.A. and Dominguez, J. (1989) Boundary Elements an Introductory Course. Computational Mechanics Publications. Southampton, Boston.
Dominguez, J. (1993) Boundary Elements in Dynamics. Computational Mechanics Publications. Southampton, Boston.
Ohtsu, M. and Uesugi, S. (1985) Analysis of SH wave scattering in a half space and its applications to seismic responses of geological structures. Engi. Anal., 2(4), 198-204.
Reinoso, E., Wrobel, L.C., and Power, H. (1993) Preliminary results of the modeling of the Mexico City valley with a two-dimensional boundary element method for the scattering of SH waves. Soil. Dyna. and Earth. Engin., 12(8), 457-468.
Ricker, N. (1953) The form and laws of propagation of seismic wavelets. Geoph., 18(1), 10-40.
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