مدل ریاضی سه‌بعدی در حل تحلیلی معادله تحکیم در خاک اشباع همگن

نوع مقاله: مقاله پژوهشی

نویسندگان

1 گروه سازه های آبی، دانشگاه شهید چمران اهواز

2 گروه ریاضی، دانشگاه شهید چمران اهواز

چکیده

در مواردی که نیاز به تسریع در نشست تحکیمی باشد، طول مسیر زهکشی می­تواند به­وسیله­ی زهکش­های عمودی کاهش یابد و جریان به­صورت شعاعی و قائم زهکشی شود. ازآنجاکه معادله تحکیم در سه بعد، یک معادله­ی پیچیده ریاضی است، در این تحقیق معادله­ی سه­بعدی سرعت زمانی تحکیم در مختصات استوانه­ای با شرایط مرزی مرتبط با تحقیق حاضر، مورداستفاده واقع شد، سپس اقدام به حل تحلیلی معادله یادشده گردید. پس از حل معادله، تحلیل نتایج با استفاده از نرم‌افزار MATLAB انجام شد و تغییرات درصد نشست متوسط نسبت به زمان بررسی شد و با نتایج حاصل از روش یک­بعدی و روش‌های استفاده‌شده توسط محققین در تحقیقات قبلی مقایسه شد. نتایج نشان داد که روش تحلیلی مورداستفاده در این تحقیق، در تطابق با روش‌های عددی به کار گرفته‌شده در تحقیقات گذشته است.

کلیدواژه‌ها


عنوان مقاله [English]

A 3-D Mathematical Modeling in Solving Analytical Consolidation Equation in a Homogeneous Saturated Soil

نویسندگان [English]

  • Reza Poursaki 1
  • Java Ahadian 1
  • Mansour Seraj 2
1 Department of Water Sciences Engineering, Shahid Chamran University
2 Department of Mathematics, Shahid Chamran University
چکیده [English]

The drainage length can be artificially decreased using vertical drains where need to accelerate in the consolidation settlement, so that the flow can be drained radially and vertically. In this research, the three dimensional consolidation equation with appropriate boundary conditions was used in cylindrical coordinates, and then was solved analytically. After the analytical solution, analysis of the results was done on using MATLAB software. Moreover, the average degree of consolidation versus time was obtained and compared with the results of one-dimensional method. Findings showed that, the analytical method in this research is in accordance with another numerical method in the previous researches.

کلیدواژه‌ها [English]

  • Three-dimensional consolidation
  • Cylindrical coordinates
  • Boundary condition
  • Radial-vertical drainage
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