تحليل سه بعدي لرزه‌يي نامتقارن لوله‌هاي مدفون با در نظر گرفتن لغزش لوله نسبت به خاك

THREE DIMENSIONAL NON-AXISYMMETRIC VIBRATION ANALYSIS OF A BURIED PIPELINE WITH CONDITIONS OF SLIP

در اين نوشتار، رفتار لرزه‌يي لوله‌هاي مدفون در برابر ارتعاشات ناشي از امواج صفحه‌يي مورد بررسي قرار گرفته است. مدل به‌كار گرفته‌شده در اين تحقيق با فرض نداشتن اتصال كامل و صلب بين لوله و خاك، با منظور كردن ميرايي لزجي براي لغزش ايجاد شده است. لوله‌ي كشسان به‌طول بي‌نهايت در محيط هموژن و كشسان خاك در نظر گرفته شده است. براي تحليل سيستم تركيبي خاك و لوله‌ي مدفون، از روش كشساني سه بعدي استفاده شده و معادلات به‌صورت تحليلي حل و با روش اجزا محدود ارزيابي شده‌اند. در ادامه، مقادير دامنه‌ي بيشينه و بحراني موج ورودي جهت شروع لغزش و تسليم خاك ارايه و تاثير لغزش و نوع خاك بر تنش‌هاي ايجادشده ارزيابي شده‌اند.

The response of underground pipelines to wave propagation is influenced by many factors. Because of the large geometrical dimensions of pipelines, wave characteristics lie open to changes in ground motion phases and geotechnical conditions for different points alongside the pipeline axis, which provide technical hitches for an efficient solution. Based on the three-dimensional theory of elasticity, in this paper, an analytical formulation is presented for vibration analysis of a buried pipeline, to study the stresses and deformations. The succeeded governing equation is applicable for an infinite pipeline that is surrounded by an enormous soil medium lying open to an incident wave plane. The pipe-soil interaction is modeled concerning the occurrence of slip between the pipe and soil medium, and, in addition, the Coulomb frictional-force is supposed equal to the viscous damping on the interface. To investigate the unknown parameters, such as slippage and the variation of wave angle, as well as the damping coefficient of the bond, the succeeded algebraic equation is solved analytically. Regarding the elastic limitation, some numerical examples are provided to show the application of the presented model and demonstrate prediction of the critical value which may cause yielding in the pipe for incident-wave amplitude. The radial and shear stresses for the inside and outside diameter of the pipe are also evaluated in order to show the validity of the results. However, comparisons with some available FEM models display a respectable correlation for stress distribution on a cross section of buried pipeline. The effect of some parameters, such as soil porosity, thickness of pipe and, also, perfect and imperfect bonds between the soil and buried pipe, are discussed and demonstrated with relative graphs.