Usage of Assembled Functions Theory for Compute Dynamic Response of a Tunnel

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی عمران سازه، دانشکده فنی و مهندسی، دانشگاه رازی کرمانشاه، ایران

2 گروه آموزشی عمران سازه، دانشکده فنی و مهندسی، دانشگاه لرستان، ایران

3 گروه مهندسی عمران ژئوتکنیک، دانشکده فنی و مهندسی، دانشگاه آزاد، واحد تبریز، ایران

چکیده

در این پژوهش یک پاسخ تحلیلی برای ارزیابی پاسخ دینامیکی تونل در محیط های متخلخل ایزوتروپ با استفاده از تئوری تجمع توابع ارائه شده است. برای حل معادلات، دو گروه از توابع پیچیده برای ساختمان جامد و مایع نفوذی در یک سیستم پیچیده دو بعدی معرفی شده اند. تنش، جابجایی و فشارهای منفی ناشی از حوادث حاد در محیط و به ویژه در مجاورت حفره در این طرح پیچیده ارزیابی می شود. اعتبار راه حل پیشنهادی با نمونه های مختلف عددی نشان داده شده است. یک مطالعه پارامتری شامل اثرات تغییر فشردگی مایع، مدول برشی و تغییرات نفوذپذیری، تعداد مختلف موج و انواع موج (امواج سریع، آهسته و برشی) انجام می شود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Usage of Assembled Functions Theory for Compute Dynamic Response of a Tunnel

نویسندگان [English]

  • Peyman Beiranvand 1
  • Arash Bayat 1
  • Hamid reza Ashrafi 1
  • F. Omidinasab 2
  • Masoud Gohari 3
1 Department of Civil Engineering, Razi University, Kermanshah, Iran
2 Assistant Professor, Department of Civil Engineering, Lorestan University, Khorramabad, Iran
3 Department of Civil Engineering, Islamic Azad University, Tabriz Branch, Iran
چکیده [English]

An analytical solution for the evaluation of dynamic response of a tunnel in infinite isotropic elastic porous media is presented. Tunnel is considered as a circular cavity. Two groups of complex functions for solid skeleton and pore fluid in a two-dimensional (2D) complex plane are introduced in order to solve the Biot equations. Stress, displacement and pore pressure fields induced by incident and scattered waves in the medium and especially in the vicinity of the cavity are evaluated in this complex plane. The validation of the proposed solution is shown by various numerical examples. A parametric study including the effects of fluid compressibility changes, shear modulus and permeability variations, several wave numbers and wave types (fast, slow and shear waves) is performed.

کلیدواژه‌ها [English]

  • Analytical solution
  • Complex functions
  • Porous media
  • Wave scattering
Alielahi, H., Kamalian, M., and Adampira, M. (2016). A BEM investigation on the influence of underground cavities on the seismic response of canyons. Acta Geotechnica, 11(2), 391-413.
Biot, M.A. (1956). Theory of propagation of elastic waves in fluid-saturated porous solid. J. Acoust. Soc. Am, (Vol. 28, pp. 168-191).
Degrande, G., Clouteau, D., Othman, R., Arnst, M., Chebli, H., Klein, R., Chatterjee, P., Janssens, B. (2017). A numerical model for ground-borne vibrations from underground railway traffic based on a periodic finite element–boundary element formulation. Journal of Sound and Vibration, 293 (3-5), 645-666.
Degrande, G., and De Roeck, G. (1993). An absorbing boundary condition for wave propagation in saturated poroelastic media- part I: Formulation and efficiency evaluation. Soil Dynamics and Earthquake Engineering, (Vol. 12, pp. 411-421).
Degrande, G. and De Roeck, G. (1993). An absorbing boundary condition for wave propagation in saturated poroelastic media- part II: Finite element formulation. Soil Dynamics and Earthquake Engineering, (Vol. 12, pp. 423-432).
Dominguez, J. (1992). Boundary element approach for dynamic poroelastic problems. International Journal for Numerical Methods in Engineering, (Vol. 35, pp. 307-324).
Eringen, A.C., and Suhubi, E.S. (1964). Elastodynamics, New York: Academic press.
Gatmiri, B. (1992). Response of a cross-anisotropic seabed to ocean waves. Journal of Geotechnical Engineering, 118(9), 1295-1314.
Gatmiri, B. (1990). A Simplified finite element analysis of wave-induced effective stresses and pore pressure in permeable sea beds. Géotechnique, 40(1), 15-30.
Jeng, D.S. (1997). Soil response in cross-anisotropic seabed due to standing waves. Journal of Geotechnical & Geoenvironmental Engineering, 123(1), 9-19.
Kaynia, A.M. (1992). Transient green’s functions of fluid-saturated porous media. Computers and Structures, 44(1), 19-27.
Liu, D., Gai, B., and Tao, G. (1982). Applications of the method of complex functions to dynamic stress concentrations.Wave Motion, (Vol. 4, pp. 293-304).
Mei, C.C., Si, B.I. and Cai, D. (1984). Scattering of simple harmonic waves by a circular cavity in a fluid-infiltrated poro-elastic medium. Wave Motion, (Vol. 6, pp. 265-278).
Muskhelishvili, N.I. (1963). Some Basic Problems of the Mathematical Theory of Elasticity. trans. from 4th Edn. (In Russian) by J.R.M. Radok, New York: University of Groningen, Netherlands, Noordhoff.
Nowinski, J.L. (1982). Stress concentration around holes in a class of rheological materials displaying a poroealstic structure. Developments in Mechanics, (Vol. 6, pp. 445-458).
Pao, Y.H., and Mow, C.C. (1973). Diffraction of Elastic Waves and Dynamic Stress Concentrations. New York: Crane and Russak.
Zimmerman, C.H. and Stern, M. (1993). Scattering of plane compressional wave by spherical inclusions in a poroelastic medium. J. Acoust. Soc. Am., 94(1), 527-536.