پراکنش امواج برون‌صفحه‌ی SH ناشی از حفره پوشش‌دار دایره‌ای

نوع مقاله : Articles

نویسندگان

1 گروه عمران، دانشگاه آزاد اسلامی، واحد زنجان

2 دانشگاه آزاد اسلامی ، واحد زنجان

چکیده

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.

کلیدواژه‌ها


عنوان مقاله [English]

Antiplane SH-Waves Scattering by a Circular Lined Cavity

نویسندگان [English]

  • Mehdi Panji 1
  • Bahman Ansari 2
1 Department of Civil Engineering, Zanjan Branch, Islamic Azad University, Zanjan, Iran
2 Department of Civil Engineering, Zanjan Branch, Islamic Azad University, Zanjan, Iran
چکیده [English]

According to the extensive development of urban texture and the vital necessity of lifelines, infrastructure and underground openings have found an important role in human societies. A full understanding of the behaviors of underground tunnels including tunnels for transportation, water, and facilities, can assist in presenting an optimum layout. The importance of this issue has increased because of the complex performance of the tunnels against seismic loads. The seismic analysis of underground tunnels has been used by the researchers for almost halfa century. Technically speaking, there are some analytical as well as semi-analytical methods for analyzing the ground response subjected to subsurface structures such as lined/unlined tunnels. Although these methods have high accuracy and used in the benchmark purposes, arbitrary shaped models with different boundary conditions cannot be easily applied in establishing the real problems. On the other hand, by developing the computers and software knowledge, the numerical approaches are frequently used for analyzing the continuum media in recent two decades, especially in soil mechanics. Based on the formulation, numerical approaches used in dynamic problems analysis can be usually divided into domain and boundary methods. In domain methods, such as finite element method (FEM) and finite difference method (FDM), it is required to discretize the whole body including internal parts and its boundaries. Although the simplicity of domain methods makes them favorite for analyzing seismic finite mediums, the models are complicated by discretizing the whole body and closing the boundaries in a distance far away from the interested zone for dynamic analysis of soil medium. In the response to the mentioned issues, the boundary element method (BEM) can be practically used for analyzing infinite/semi-infinite soil mediums in a better manner, due to discretizing only the boundaries of the problem. The BEM approaches can be formulated in the classes of full-plane (FBEM) and half-plane (HBEM) boundary element method.In this study, a direct half-plane time-domain boundary element method (HBEM) was developed and successfully applied to analyze the transient response of ground surface in the presence of circular lined tunnels, embedded in a linear elastic half-plane, subjected to propagating incident plane SH-waves. The Fundamental solutions for the case of propagating SH-waves in single-medium environments in the presence of unlined tunnels and ground surface topographies have been developed by Panji et al. [30]. For Multi-medium problems such as lined tunnels embedded in deep/shallow soil, the use of single-medium fundamental solutions was expanded by considering substructure procedure such that the problem was decomposed into a pitted half-plane and a closed ring-shaped domain.To solve the model, only the interface and inner boundary of the lining need to be discretized. After computing the matrices and satisfying the compatibility as well as boundary conditions, the coupled equations were solved to obtain the boundary values. There are two types of boundary conditions on interface boundaries, the first of which is the equality of displacement between mediums, and the second one is the equality of normal and shear stresses along the interface. These two conditions must be considered when the boundary equation is formed. In addition, to boundary conditions it is required to apply free-field displacement effects on the displacement of boundary and internal points. Free-field displacement provides the effects of wave incident and reflectance when the wave arrives to boundary or internal nodes. For Multi-medium problems such as lined tunnels embedded in deep/shallow soil, the free-field displacement accomplishes in the same way that it was done for single-medium problems.
 The mentioned method was successfully implemented in a developed computer code called DASBEM [30]. To validate the responses, a practical example was analyzed and compared with those of the published works. Manoogian [13] has obtained ground surface frequency domain responses for the case of embedded lined circular tunnel in shallow soil medium. By implementing the problem into the DASBEM, the results were obtained and compared with those of Manoogian [13]. The results showed that the analytical and numerical responses are in good agreement. Finally, in a parametric study, a circular lined tunnel was evaluated and the effect of depth and incident wave angle on ground surface response was analyzed. The results mainly showed that the ground surface frequency response due to tunnels without lining is more than that of lined tunnels. The method used in this paper is recommended to obtain the transient response of underground structures in combination with other numerical methods.

کلیدواژه‌ها [English]

  • Half-Plane BEM
  • Time Domain
  • SH Waves
  • Circular Lined Cavity
  • Seismic Analysis
  • Surface Response
  1. 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.
  2. 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.
  3. 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.
  4. Datta, S.K. and Shah, A.H. (1982) Scattering of SH waves by embedded cavities. Wave Moti., 4, 265-283.
  5. Lee, V.W. Chen, S., Hsu, I.R. (1999) Antiplane diffraction from canyon above subsurface unlined tunnel. Journal of Engineering Mechanics, 125(6), 668-675.
  6. Lee, V.W. and Trifunac, M.D. (1979) Response of tunnels to incident SH waves. Journal of Engineering Mechanics Division, 105(4), 643-659.
  7. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. Beskos, D.E. (1987) Boundary element methods in dynamic analysis. Appl. Mech. Revi., 40(1), 1-23.
  18. 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.
  19. 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.
  20. Crouch, S.L. and Starfield, A.M. (1983) Boundary Elements Methods in Solid Mechanics. Department of Civil and Mineral Engineering. University of Minnesota.
  21. Yang, L. and Sterling, R.L. (1989) Back analysis of rock tunnel using boundary element method. Journ. of Geot. Engin., 115(8), 1163-1169.
  22. Xiao, B. and Carter, J.P. (1993) Boundary element analysis of anisotropic rock masses. Engi. Anal. with Boun. Elem., 11, 293-303.
  23. 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.
  24. 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.
  25. 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.
  26. 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.
  27. 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.
  28. 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.
  29. 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.
  30. 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.
  31. 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.
  32. 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.
  33. 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.
  34. 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.
  35. 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.
  36. 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.
  37. 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.
  38. 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.
  39. 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.
  40. 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), 871–887.
  41. 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.
  42. 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.
  43. Belytschko, T. and Chang, H.S. (1988) Simplified direct time integration boundary element method. Jour. of Engi. Mech., 114(1), 117-134.
  44. 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.
  45. 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.
  46. 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.
  47. 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.
  48. Panji, M. and Ansari, B. (2017) Transient SH‐wave scattering by a lined tunnel embedded in an elastic half‐plane. Engi. Anal. with Boun. Elem. 84, 220-230.
  49. Eringen, A.C. and Suhubi, E.S. (1975) Elastodynamics Linear Theory. Academic Press, New York.
  50. Brebbia, C.A. and Dominguez, J. (1989) Boundary Elements an Introductory Course. Computational Mechanics Publications. Southampton, Boston.
  51. Dominguez, J. (1993) Boundary Elements in Dynamics. Computational Mechanics Publications. Southampton, Boston.
  52. 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.
  53. 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.
  54. Ricker, N. (1953) The form and laws of propagation of seismic wavelets. Geoph., 18(1), 10-40.