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ارزیابی برآورد هدایت هیدرولیکی اشباع با مدل‏های فرکتال جرمی و منفذی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری آبیاری و زهکشی، گروه مهندسی آب، دانشگاه ارومیه، ارومیه، ایران

2 گروه مهندسی آب، پژوهشکده مطالعات دریاچه ارومیه، دانشگاه ارومیه، ارومیه، ایران

چکیده

در طول چند دهه گذشته، هندسه فرکتالی به‌ طور گسترده‌ای به عنوان یک ابزار توانمند در بیان خصوصیات محیط متخلخل و مدل‌سازی هیدرولیکی خاک استفاده شده است. در این تحقیق، قابلیت کاربرد مقادیر بعد فرکتال حاصل از منحنی دانه‌بندی (DPSD) و منحنی رطوبتی (DSMC) در برآورد هدایت هیدرولیکی اشباع با مدل جدید فرکتالی قنبریان و همکاران (2018) مقایسه و ارزیابی گردید. به این منظور، هشت نمونه خاک شنی با دانه‌بندی مختلف در استوانه‌هایی با قطر داخلی 4/4 و ارتفاع 5 سانتی‌متر تهیه شدند. دانه‌بندی نمونه‌ها با روش ترکیبی الک خشک و خیس تعیین گردید. میزان رطوبت در هشت مکش‌ مختلف از صفر (وضعیت اشباع) تا 10 کیلوپاسکال در جعبه شنی و در 19 فشار مختلف از 18 تا 1500 کیلوپاسکال با صفحات فشاری اندازه‌گیری شدند. برای تمام نمونه‌ها، جرم مخصوص ظاهری و حقیقی، میزان تخلخل کل نمونه‌ها و هدایت هیدرولیکی اشباع (به روش بار ثابت) نیز اندازه‌گیری گردید. DPSD و DSMC نمونه‌ها به ترتیب با استفاده از داده‌های منحنی دانه‌بندی و منحنی رطوبتی تعیین شدند. میزان شاخص خطای جذر میانگین مربعات حاصل از برآورد منحنی رطوبتی (RMSE) با بکارگیری DSMC و DPSD به ترتیب در بازه 004/0 تا 022/0 و 009/0 تا 069/0 به‌دست آمدند. نتایج نشان داد که با کاربرد DSMC، منحنی رطوبتی خاک با دقت بالاتری نسبت به DPSD پیش‌بینی شد. همچنین، بررسی‌ها نشان داد مقادیر بعد فرکتال جرمی نمونه‌ها، همبستگی معنی‌داری با بعد فرکتال منفذی نداشت. خطای جذر میانگین لگاریتمی مربعات (RMSLE) در مورد مقادیر برآوردی هدایت هیدرولیکی اشباع با استفاده از DSMC و DPSD به ترتیب برابر با 286/0 و 306/0 حاصل شد. با وجود عدم اختلاف معنی‌دار بین دو بعد فرکتال مورد مطالعه، به کارگیری مقادیر DSMC به عنوان تصویری از خصوصیات میکروسکوپیک محیط و ترکیب آن با تئوری پرکولاسیون، دقت برآورد منحنی رطوبتی و هدایت هیدرولیکی اشباع را ارتقاء داده است.

کلیدواژه‌ها

عنوان مقاله [English]

Evaluation of Saturated Hydraulic Conductivity Estimation by Mass and Pore Space Fractal Models

نویسندگان [English]

  • Elnaz Rezaei 1
  • Kamran Zeinalzadeh 2

1 Ph.D. Candidate in Irrigation and Drainage, Department of Water Engineering, Urmia University, Urmia, Iran.

2 Department of Water Engineering,Urmia Lake Research Institute, Urmia University, Urmia, Iran

چکیده [English]

Over the past few decades, fractal geometry has been extensively used as a powerful tool in characterizing porous media properties and hydraulic soil modeling. In this study, the applicability of fractal dimension values derived from particle size distribution (DPSD) and soil moisture curve (DSMC) in estimating saturated hydraulic conductivity (SHC) were compared and evaluated using the new fractal Ghanbarian et al. (2018) model. For this purpose, eight sandy samples were prepared in cylinders with an internal diameter of 4.4 cm and a height of 5 cm. The particle size distribution was determined by the combination of dry and wet sieve methods. Water content was measured in eight tension heads from zero (saturation) to 10 kPa in the sandbox and at 19 higher tension heads, from 18 to 1500 kPa with the pressure plate. For all samples, the bulk and particle density, total porosity, and SHC were also measured. The mass fractal (DPSD) and pore space fractal (DSMC) dimensions were determined using the particle size distribution and soil moisture curve (SMC) data, respectively. The root mean square error (RMSE) of fitting SMC by applying the DSMC and DPSD were found in the range of 0.004 to 0.022 and 0.009 to 0.069, respectively. The results showed that the DSMC fits the SMC with higher accuracy than the DPSD and the DPSD had no specific correlation with the DSMC of the samples. The root mean square logarithmic error (RMSLE) for the estimated values ​​of SHC using DSMC and DPSD was found to be 0.286 and 0.306, respectively. Although there is no significant difference between the two fractal dimensions, the application of DSMC values ​​as an image of the microscopic properties of the porous medium and its combination with the percolation theory has improved the accuracy of estimating the SMC and SHC.

کلیدواژه‌ها [English]

  • Particle size distribution curve
  • Percolation theory
  • PSF models
  • Soil moisture curve
  • Theoretic models
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تحقیقات کاربردی خاک
دوره 9، شماره 1
خرداد 1400
صفحه 117-129
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سابقه مقاله
  • تاریخ دریافت: 30 آذر 1398
  • تاریخ بازنگری: 22 دی 1399
  • تاریخ پذیرش: 25 خرداد 1400
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