The Analytical, Numerical and Experimental Simulation of Drain Pipe Installation in Different Depths and Shapes of Trench

Document Type : Original Article

Authors

1 Associate Professor, Water Science and Engineering Department, Faculty of Agriculture, Bu-Ali Sina University, Hamadan, Iran

2 Former Graduate Student, Water Science and Engineering Department, Faculty of Agriculture, Bu-Ali Sina University, Hamadan, Iran

3 PhD Student, Water Science and Engineering Department, Faculty of Agriculture, Bu-Ali Sina University, Hamadan, Iran

Abstract

In this study the analytical and numerical solutions are used in the steady-state drainage problem in the three rectangular, semicircular, and triangular cross-section trenches. Equations that are derived by conformal mappings and complex potential theory were used for the analytical solution and SEEP/W software was used for the numerical simulation. Furthermore, physical sandbox models are designed for all the three sections in laboratory conditions and the outflows from the drainpipe are measured at 10, 20, 30, 40 and 50 cm depths. According to the three methods, in this study optimum installation depth of drainpipe that has maximum drainage outflow in the both rectangular and semicircular cross-sections is obtained at 40 cm and for the triangular cross-section is 32.5 cm using the analytical solution and 30 cm using the numerical solution and the experimental results. The results are assessed by the differences between the dimensionless discharges obtained from the analytical and numerical solutions and from the experimental conditions using relative root mean square error (RMSE) and coefficient of determination (R2). RMSE in the analytical solution for the triangular section 0.048, the semicircular section 0.061, and the rectangular section 0.071 and the R2 are 0.99, 0.98, and 0.98 and in the numerical solution 0.045, 0.056, and 0.041 for RMSE and 0.87, 0.97, and 0.97 for R2 are obtained, respectively. Comparison of the analytical and numerical solutions results with the experimental results showed that the both methods can simulate seepage flow in the trench with high accuracy. However, the accuracy of numerical solution was more than analytical solution, that it comes from some simplifications and assumptions considered in the analytical solution. In the analytical solution the ponded depth of water is considered small and negligible and the circular perimeter of the drainpipe is taken into account as a line that these are the reasons for the less accurate results of analytical solution. Additionally, the hydraulic of the flow in entrance to the drain pipe is not considered in the analytical solution.

Keywords


اصلانی،ف.، ناظمی،ا.ح.، صدرالدینی،ع.ا.، فاخری­فرد،ا و قربانی،م.ع. 1389. برآورد عمق و فاصله مناسب زهکش‌های زیر‌زمینی بر اساس کیفیت زه‌آب. مجله تحقیقات آب و خاک ایران.2 . 41: 139 - 146.
رضی،ف. 1390. بررسی اثر عمق‌های مختلف نصب زهکش‌ها بر کیفیت آب خروجی. پایان‌نامه کارشناسی ارشد رشته آبیاری و زهکشی، دانشکده فنی و مهندسی، دانشگاه بین‌المللی امام خمینی (ره) قزوین.
رضی،ف.، ستوده‏نیا،ا.، دانش‏کارآراسته،پ.، اکرم،م. 1391. بررسی آزمایشگاهی اثر عمق نصب زهکش‏ها بر شوری زه­‏آب. مجله تحقیقات آب و خاک. 43.3: 288-281.
ستوده‌نیا،ع و جعفری،م. 1395. بررسی اثر زهکش حائل شوره‌زار قزوین برسطح ایستابی منطقه با استفاده از مدلSeep/w. تحقیقات آب و خاک ایران. 47 .2: 245-237.
ستوده‏نیا،ع. نوروزپور اصل،ا و دانش‏کار آراسته،پ. 1393. بررسی آزمایشگاهی اثر عمق نصب زهکش‌های زیرزمینی در شست‌و‌شوی نیترات از خاک شن‌لومی. نشریه پژوهش آب در کشاورزی 28 .3 ب: 634-625.
سلیمانی ننادگانی،م.، پارسی‌نژاد،م و نوری،ح. 1392. برآورد هزینه‌های نصب زهکش‌های زیر‌زمینی لوله‌ای. پژوهش‌های آبخیزداری. 98:34 تا 41.
شاه­نظری،ع.، ضیا تباراحمدی،ع،. ضیاءتباراحمدی،م.خ و آقاجانی مازندرانی،ق. 1392. بررسی کارایی زهکش­های زیرزمینی در شرایط جلوگیری از ورود آب از سطح فوقانی. نشریه آب و خاک. علوم و صنایع کشاورزی. 27 .2: 440-432.
شیری،ج.، ناظمی،ا.ح.، صدرالدینی،ع.ا و فاخری­فرد،ا. 1389. تأثیر مقاومت ورودی بر مشخصه­های هیدرولیکی جریان در زهکشی زیرزمینی. دانش آب و خاک. 4.20: 67-47.
ضیاتبار احمدی،ع. 1390. بررسی کارایی زهکش­های زیرزمینی در شرایط جلوگیری از ورود جریان عمودی. پایان­نامه دوره کارشناسی ارشد رشته آبیاری و زهکشی. دانشگاه علوم کشاورزی و منابع طبیعی ساری. دانشکده مهندسی زراعی. گروه مهندسی آب.
مازندرانی‌زاده،ح. 1395 طراحی سیستم زهکشی با استفاده از الگوریتم بهینه‌سازی چند هدفه NSGA-II با رویکرد اقتصادی- زیست محیطی. تحقیقات منابع آب ایران. 12 .3: 152-142.
مجتهدی،س.ح و فغفور مغربی،م. 1389. روش تحلیلی محاسبه نشت از کانال نیمه بیضی به روش نگاشت کانفرمال. آبیاری و زهکشی ایران. 4.1: 30-22.
نظری،ب.، لیاقت،ع.، پارسی‌نژاد،م و ناصری،ع. 1387. بهینه‌سازی عمق نصب زهکش‌های زیر‌زمینی با ملاحظات اقتصادی و زیست‌ محیطی. پنجمین کارگاه فنی زهکشی و محیط زیست، 16 آبان ماه ، تهران، صفحه‌های 108 تا 122.
نوذری،ح.، زالی،ع و آزادی،س. 1395. بررسی آزمایشگاهی تغییرات شوری زه‌آب در فواصل و اعماق مختلف زهکش در حضور آب زیرزمینی شور. دانش آب و خاک. 29 .2/2: 150-139.
Afruzi,A., Nazemi,A.H and Sadraddini,A.A. 2014. Steady-state subsurface drainage of ponded fields by rectangular ditch drains. Irrigation and Drainage. 63.5: 668-681.
Arnold,L.A. 2004. Effects of drain depth on nitrogen losses in drainage in shallow water table soils. MSc. Thesis. North Carolina State University. North Carolina.
Christen,E and Skehan,D. 2001. Design and management of subsurface horizontal drainage to reduce salt loads. Journal of Irrigation and Drainage Engineering. 127.3: 148-155.
Corey,AT. 1986. Mechanics of immiscible fluids in porous media. Water Resources Publications. Littleton, Colorado. Pp. 255.
Dennis,C.W and Trafford,B.D., 1975. The effect of permeable surrounds on the performance of clay field drainage pipes. Journal of Hydrology. 24.3:239-249.
Deverel,S.J., Fio,J.L. 1991. Groundwater flow and solute movement to drain laterals, western San Joaquin Valley, California: 1. Geochemical assessment. Water resources research. 27.9: 2233-2246.
Dierickx,W. 1993. Research and developments in selecting subsurface drainage materials. Irrigation and Drainage Systems. 6:291-310.
Geo-Slope, 2009. Seepage modeling with SEEP/W 2007. 4th edi, Geo-Slope International ltd, Calgary, Canada, 319 pp.
Harr,ME. 1962. Groundwater and Seepage. McGraw-Hill: New York.
Iqbal,M and Ahmad,M. 2007. Optimal design of a subsurface pipe drainage system. Pakistan Journal of Agricultural Sciences (Pakistan) 44.1:159-163.
Jacobsen,O.H and Kjaer,J. 2007. Is tile drainage water representative for root zone leaching of pesticides–a review. Pest Management Science. 63:417-428.
Klute,A and Dirksen,Ch. 1986. Hydraulic conductivity and diffusivity: Laboratory methods. Methods of Soil Analysis: Part 1—Physical and Mineralogical Methods-Agronomy Monograph no.9, pp 687-734.
Nangia,V., Gowda,P.H., Mulla,D.J and Sands GR. 2010. Modeling impacts of tile drain spacing and depth on nitrate-nitrogen losses. Vadose Zone. 9.1: 61-72.
 
Peukert,S., Griffith,B.A., Murray,P.J., Macleod,C.J.A., Brazier,R.E. 2016. Spatial variation in soil properties and diffuse losses between and within grassland fields with similar shortterm management. European Journal of Soil Science. 67.4: 386-396.
Rimidis,A., Dierickx,W. 2004. Field research on the performance of various drainage materials in Lithuania. Agricultural water management. 68.2: 151-175.
Schwab,G.O., Kirkham,D. 1951. The effect of circular perforations on flow into subsurface drain tubes. Part II. Experiments and results, Agricaltural Engineering. 32.5:270-4.
Smith,D.R., Livingston,S.J., Zuercher,B.W., Larose,M., Heathman,G.C., Huang,C. 2008. Nutrient losses from row crop agriculture in Indiana. Journal of Soil and Water Conservation. 63.6: 396-409.
Stuyt,L.C., Dierickx,W. 2006. Design and performance of materials for subsurface drainage systems in agriculture. Agricultural Water Management. 86.1:50-9.
Tao,Y., Wang,S., Xu,D., Qu,X. 2016. Experiment and analysis on flow rate of improved subsurface drainage with ponded water. Agricultural Water Management. 177:1-9.
Tod,I.C., Grismer,M.E. 1991. Drainage of Clay Overlying Artesian Aquifer. II: Technical Analysis. Irrigation and Drainage Engineering. 117.2:271-84.
Youngs,E.G. 1982. Calculations of ponded water drainage for flow regions of various geometries to demonstrate effect of disturbed soil-zone shape on drain performance. Agricultural Engineering Research. 27.541-54.