تعیین تنش مماسی اطراف تونلهای مربع شکل با استفاده از توابع پتانسیل مختلط

نوع مقاله: مقاله پژوهشی

نویسندگان

1 استاد دروس تخصصی

2 دانشجوی کارشناسی ارشد همندسی خاک و پی

چکیده

از منظر ریاضی در طبیعت بر هر پدیده ای یک معادله دیفرانسیل حاکم است. بر رفتار مکانیکی محیط اطراف فضاهای زیرزمینی نیز یک معادله ی دیفرانسیل حاکم است .با حل این معادله، میدان جابجائی ها و تنش ها در هر یک از نقاط توده سنگ اطراف فضای زیرزمینی محاسبه شده و برای تحلیل پایداری سازه مورد استفاده قرار می گیرد. در این مقاله نحوه فرمو ل بندی و راه حل تحلیلی برای تعیین تنش اطراف تونل مربعی تحت تنش های برجا با استفاده از روش پتانسیل مختلط ارائه شده است. همچنین با استفاده از نگاشت همدیس مقطع تونل مربعی به شکل دایره ای تبدیل شد. توده سنگ بصورت الاستیک و ایزوتروپ در نظر گرفته شده است. سپس با افزایش جملات سری نگاشت، به بررسی تغییرات تنش های مماسی اطراف تونل پرداخته و نتایج در قالب نمودار نشان داده شده است. نتایج نشان می دهد با افزایش جملات سری نگاشت، شکل مربع در گوشه ها صاف تر شده و تنش های مماسی در آن ها افزایش می یابند.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Analytical solution of stress around square tunnels by complex potential function method

نویسندگان [English]

  • mahdi zamani lenjani 1
  • sanaz amjadian 2
  • reza khordad 1
چکیده [English]

Any physical problem can be explained by the mathematical model. Most of those models are partial differential equations. The mechanic behaviors of rock mass around any underground structure can be defined by partial differential equations. By solving this equation, the stresses and deformations around the tunnel can be calculated .The stability of tunnel can be defined by using the calculated stress concentration around tunnel. In this paper the stress concentration around the square tunnel is obtained by the analytical solution and using complex potential equations. The square cross-section of tunnel transfer to circular one by the method of conformal mapping. Here the rock mass considered elastic and isotropic. The results show, with increasing the components of mapping series, the tunnel surface becomes smoother. Also for the above cases, the tangential stress around tunnel increases.

کلیدواژه‌ها [English]

  • complex potential function
  • conformal mapping
  • the tangential stress
  • square tunnel
  • theory of elasticity
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