طراحی بهینه مقطع کانال بتنی برای حداقل کردن هزینه تلفات آب، پوشش و عملیات خاکی

نویسندگان

چکیده

طراحی مقطع کانال با کمترین هزینه شامل کمینه کردن مجموع هزینه‌های هر متر از طول کانال تحت شرایط جریان یکنواخت است. این هزینه‌ها شامل هزینه‌های مربوط به پوشش هر متر از طول کانال،‏ هزینه هر مترمکعب عملیات خاکی و هزینه مرتبط با تلفات آب (شامل تلفات نشت و تبخیر) هستند که به‌عنوان تابع هدف در این بررسی درنظر گرفته شده است. تلفات نشت به هندسه کانال و تلفات تبخیر از سطح آزاد آب بستگی دارد. در این بررسی از معادله مانینگ به‌عنوان قید اصلی مسئله استفاده شده است. علاوه بر این قید،‏ در طراحی مقطع بهینه کانال‌ها از دو قید فرعی شامل حداقل سرعت مجاز و عدد فرود،‏ استفاده شده است. برای بهینه‌سازی ابعاد کانال،‏ از الگوریتم بهینه‌سازی مبتنی بر جستجوی مستقیم استفاده شد. با استخراج نتایج مدل بهینه‌سازی در قالب نمودارهای بی‌بعد،‏ امکان طراحی ساده ابعاد بهینه کانال در جهت حداقل کردن هزینه‌های هر متر از طول کانال فراهم می‌شود. با بررسی نتایج این پژوهش می‌توان دریافت که کانال ذوزنقه‌ای با دبی مشخص در شیب جانبی 75‎/0 دارای بیشترین و در شیب جانبی 5‎/1 دارای کمترین عمق نرمال است. همچنین در طراحی بهینه کانال مثلثی،‏ عمق نرمال کانال در شیب‌های جانبی بیشتر دارای مقدار کمتری است در حالیکه عرض سطح آب در این حالت افزایش می‌یابد.

کلیدواژه‌ها


عنوان مقاله [English]

Optimal design of concrete canal section for minimizing cost of water loss, lining and earthwork

نویسندگان [English]

  • Dr Mahmoud M.R. Tabari
  • shiva tavakoli
  • mohsen mazak mari
چکیده [English]

Design of a minimum cost canal section involves minimization of the sum of costs per unit length of the canal, subject to uniform flow condition. These costs are included with the costs related to covering every meter of channel length, the cost per cubic meter earthworks and costs associated with water loss (including seepage and evaporation losses) which is considered as the objective function in this study. Seepage and evaporation are forms of water loss in an irrigation canal, while the seepage loss depends on the canal geometry and the evaporation loss is proportional to the area of water free surface. In this study, the Manning’s Formula is considered as the main constraint equation. In addition, the minimum permissible velocity and Froud number are used for optimizing design canal as subsidiary constraints. The optimization algorithm based on directly search is used for optimizing the canal section. Presenting the results of optimization model in the form of the dimensionless curves, provides the possibility of easy design of optimized canal section in order to minimize costs per unit of length of canal. By analyzing the results of this study, it can be found that the trapezoidal canal with a given discharge have the maximum and minimum normal depth in side slopes of 0.75 and 1.5, respectively. Also, by increasing side slope in optimal design of triangular canals, the normal depth decreases and the width of water surface increases.
Design of a minimum cost canal section involves minimization of the sum of costs per unit length of the canal, subject to uniform flow condition. These costs are included with the costs related to covering every meter of channel length, the cost per cubic meter earthworks and costs associated with water loss (including seepage and evaporation losses) which is considered as the objective function in this study. Seepage and evaporation are forms of water loss in an irrigation canal, while the seepage loss depends on the canal geometry and the evaporation loss is proportional to the area of water free surface. In this study, the Manning’s Formula is considered as the main constraint equation. In addition, the minimum permissible velocity and Froud number are used for optimizing design canal as subsidiary constraints. The optimization algorithm based on directly search is used for optimizing the canal section. Presenting the results of optimization model in the form of the dimensionless curves, provides the possibility of easy design of optimized canal section in order to minimize costs per unit of length of canal. By analyzing the results of this study, it can be found that the trapezoidal canal with a given discharge have the maximum and minimum normal depth in side slopes of 0.75 and 1.5, respectively. Also, by increasing side slope in optimal design of triangular canals, the normal depth decreases and the width of water surface increases.
Design of a minimum cost canal section involves minimization of the sum of costs per unit length of the canal, subject to uniform flow condition. These costs are included with the costs related to covering every meter of channel length, the cost per cubic meter earthworks and costs associated with water loss (including seepage and evaporation losses) which is considered as the objective function in this study. Seepage and evaporation are forms of water loss in an irrigation canal, while the seepage loss depends on the canal geometry and the evaporation loss is proportional to the area of water free surface. In this study, the Manning’s Formula is considered as the main constraint equation. In addition, the minimum permissible velocity and Froud number are used for optimizing design canal as subsidiary constraints. The optimization algorithm based on directly search is used for optimizing the canal section. Presenting the results of optimization model in the form of the dimensionless curves, provides the possibility of easy design of optimized canal section in order to minimize costs per unit of length of canal. By analyzing the results of this study, it can be found that the trapezoidal canal with a given discharge have the maximum and minimum normal depth in side slopes of 0.75 and 1.5, respectively. Also, by increasing side slope in optimal design of triangular canals, the normal depth decreases and the width of water surface increases.

کلیدواژه‌ها [English]

  • Optimization-Water losses.-Manning’s equation-Concrete canal-Cost function-