Presenting and evaluating a new empirical relationship for estimating the rate of infiltration in trenches
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Abstract:
Empirical formulas are indispensable tools in water engineering and hydraulic structure design. Derived from meticulous field observations, experiments, and diverse datasets, these formulas help to estimate water leakage in structures such as dams, tunnels, canals, and pipelines. By utilizing a few easily measurable parameters, engineers can employ these formulas to generate preliminary leakage rate estimates before proceeding with more detailed analyses. In this study, a physical model was developed, and a series of experiments were conducted, considering variables such as inflow rate, materials constituting the unsaturated medium, and variations in infiltration trench depth and width. As a result, a novel artificial recharge method was introduced, and an empirical equation, $ {\text{Q}}_{\text{out}} $=
0.0066 ×$ {{\mathrm{D}}_{50}}^{0.64} $× L ×$ {\mathrm{P}}^{\;0.36} $, was proposed to estimate the infiltration capacity of the trench. This equation incorporates factors such as the wetted perimeter, mean soil particle diameter, trench length, and a coefficient. A comparative analysis between the observed data from nine Iranian earthen canals and the values calculated using the proposed equation revealed an average relative error of 15% between the two datasets. In addition, the Pearson correlation coefficient was determined to be 0.981 and the Root Mean Square Error (RMSE) was 0.381, demonstrating the strong predictive performance of the equation. The parameters considered in the proposed equation allow for its application across diverse regions. Given its accurate performance, this equation provides a reliable initial estimate of the leakage rate, thereby helping to reduce costs and save time.-
Key words:
- Groundwater /
- Artificial recharge /
- Desert area /
- Infiltration rate /
- Physical model
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Table 1. Data obtained from the experiments conducted on the physical model with medium sand and fine sand materials
Row Trench width
/cmTrench depth
/cmTrench volume
/cm3The ratio of
the depth to
the
width of
the trenchQoutmax
(Lit/Min) (Medium sand)Qoutmax
(Lit/Min) (Fine sand)Performance
(Medium sand)
(Qout to Qin)Performance
(Fine sand)
(Qout to Qin)1 8 10 6,400 1.25 1.990 0.740 0.905 0.902 2 8 5 3,200 0.63 1.820 0.640 0.827 0.780 3 8 7.5 4,800 0.94 1.930 0.688 0.877 0.839 4 8 12.5 8,000 1.56 2.050 0.775 0.932 0.945 5 8 15 9,600 1.88 2.140 0.810 0.973 0.988 6 4 10 3,200 2.5 1.960 0.690 0.891 0.841 7 6 10 4,800 1.67 1.980 0.720 0.900 0.878 8 10 10 8,000 1 2.010 0.752 0.914 0.917 9 12 10 9,600 0.83 2.030 0.770 0.923 0.939 
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Table 2. Comparison of observed values of
$ {{Q}}_{{out}} $ and calculated values of$ {{Q}}_{{out}} $ using the provided equation for different dimensions of the trench in the physical model with medium sand materialsRow Trench width
/cmTrench depth
/cmTrench
length
/cm$ \boldsymbol{Q_{out}} $
(Observational)
/L/Min$ \boldsymbol{Q_{out}} $
(Computational) /L/MinPearson
correlation
(r)RMSE 1 8 10 80 1.990 1.969 0.983 0.073 2 4 10 80 1.960 1.863 3 6 10 80 1.980 1.917 4 10 10 80 2.010 2.019 5 12 10 80 2.030 2.066 6 8 5 80 1.820 1.680 7 8 7.5 80 1.930 1.835 8 8 12.5 80 2.050 2.089 9 8 15 80 2.140 2.198
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Table 3. Comparison of observed values of
$ {{Q}}_{{out}} $ and calculated values of$ {{Q}}_{{out}} $ using the provided equation for different dimensions of the trench in the physical model with fine sand materialsRow Trench width
/cmTrench depth
/cmTrench length
/cm$ \boldsymbol{Q_{out}} $ (Observational) /L/Min$ \boldsymbol{Q_{out}} $ (Computational) /L/MinPearson correlation (r) RMSE 1 8 10 80 0.740 0.745 0.992 0.012 2 4 10 80 0.690 0.705 3 6 10 80 0.720 0.726 4 10 10 80 0.752 0.764 5 12 10 80 0.770 0.782 6 8 5 80 0.640 0.636 7 8 7.5 80 0.688 0.694 8 8 12.5 80 0.775 0.791 9 8 15 80 0.810 0.832
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Table 4. Compares the observed values of leakage from the channel with its calculated values from the given equation
Row Channel name L/m P/m $ {{D}}{_{50}} $ /mQ/m3/d/m2 Observational Q/m3/d/m2 Computational Relative error of the main equation/% Pearson correlation
(r)RMSE 1 Sharifabad 0.35 2.85 0.0003 1.89 1.62 16 0.981 0.381 2 Sirian 0.32 3.14 0.0002 1.78 1.36 30 3 Cichi 0.96 1.04 0.00015 1.96 1.99 −1.5 4 Nahr Lulham 0.38 2.6 0.0016 5.58 5.02 11 5 Nahr Sarmast 0.26 3.88 0.0012 3.87 3.24 19 6 Garkan 1 0.39 2.59 0.00005 0.55 0.55 0 7 Garkan 2 0.38 2.61 0.00005 0.59 0.55 7 8 Najafabad 1 0.76 1.32 0.00015 1.12 1.70 −34 9 Najafabad 2 0.43 2.34 0.00015 0.95 1.18 −19
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Afzali SH, Abedini MJ, Monajemi P. 2009. Simulation of flow in porous media using coupled pressurized-free surface interconnected conduit network 1- network analysis. Iran-Water Resources Research, 5(2): 62–70. (in Persian
Ali H. 2011. Practices of irrigation & on-farm water management. Springer Science & Business Media, New York, USA, 546. DOI:10.1007/978-1-4419-7637-6.
Bagarello V, Sferlazza S, Sgroi A. 2009. Testing laboratory methods to determine the anisotropy of saturated hydraulic conductivity in a sandy–loam soil. Geoderma, 154(1): 52–58. DOI:10.1016/j.geoderma.2009.09.012.
Beckwith C, Baird A, Heathwaite AL. 2003. Anisotropy and depth-related heterogeneity of hydraulic conductivity in a bog peat. I: Laboratory measurements. Hydrological Processes, 17(1): 89–101. DOI:10.1002/hyp.1116.
Cui YL, Li YH, Mao Z, et al. 2004. Strategies for improving the water supply system in HCID, upper reaches of the Yellow River Basin, China. Agricultural Engineering International: The CIGR Journal of Scientific Research and Development. Manuscript LW 02 005.
Detay M, L Bersillon J. 1996. La réalimentation artificielle des nappes profondes: Faisabilité et conséquences. La Houille Blanche, Revue Internationale De l'eau, 4: 57–61. (in French) DOI:10.1051/lhb/1996040.
El Mansouri B, El Mezouary L. 2015. Enhan-cement of groundwater potential by aquifer artificial recharge techniques: An adaptation to climate change. Proceedings of the Inter- national Association of Hydrological Sci- ences, 366: 155−156. DOI:10.5194/piahs-366-155-2015.
Foreman TL. 2014. Managed Aquifer Recharge (MAR) and design and construction of hydraulic barriers against seawater intrusion: The California case. Boletín Geológico y Minero, 125 (2): 133–142.
Heidarizadeh M, Salemi HR. 2014. Comparison of Wedernikow theoretical method with Ingham empirical method in estimation of seepage from earth channels in Roodasht Region of Isfahan. Agricultural Water Research Journal, 28(4): 703−712. DOI:10.22092/jwra.2015.100825.
Hiscock KM, Balashova N, Cooper RJ, et al. 2024. Developing Managed Aquifer Recharge (MAR) to augment irrigation water resources in the sand and gravel (Crag) aquifer of coastal Suffolk, UK. Journal of Environmental Management, 35: 119639. DOI:10.1016/j.jenvman.2023.119639.
Iraq Alavi S. 1993. Management of Zayandeh Rud water distribution based on the estimation of water conveyance efficiency in downstream canals. Isfahan University of Technology, Master's Thesis in Irrigation and Drainage, Department of Irrigation and Drainage, 150.
Karim I, Abd Ali AM. 2018. Artificial recharge of groundwater by injection wells: A case study. International Journal of Science Engineering and Technology, 6(1): 6193–6196.
Lhassan MS, Bouabid EL M, Badr B, et al. 2019. Improvement of groundwater resources potential by artificial recharge technique: A case study of Charf El Akab aquifer in the Tangier region, Morocco. Journal of Groundwater Science and Engineering, 7(3): 224−236. DOI:10.19637/j.cnki.2305-7068.2019.03.003shu.
Li HX, Han SB, Wu X, et al. 2021. Distribution, characteristics and influencing factors of fresh groundwater resources in the Loess Plateau, China. China Geology, 4(3): 509−526. DOI:10.31035/cg2021057.
Moghazi HEM, Ismail ES. 1997. A study of losses from field channels under arid region conditions. Irrigation Science, 17(3): 105−110. DOI:10.1007/s002710050028.
Murillo Díaz JM. 2004. Recarga de acuíferos. Evaluación y análisis de condicionantes técnicos y económicos. Acuífero aluvial del Bajo Guadalquivir. Minas. (in Spanish
Nan T, Shao JL, Cui YL. 2016. Column test-based features analysis of clogging in artificial recharge of groundwater in Beijing. Journal of Groundwater Science and Engineering, 4(2): 88−95. DOI:10.26599/JGSE.2016.9280011.
Nouri Mohammadieh M, Sohrabi T, Rahimi H. 2010. Evaluation of empirical equations of seepage estimation from earthen canals (Case study: Ghazvin Plain). Iranian Water Research Journal, 4(2): 125–128.
Pishro F, Morteza Bakhtiari M, Shahni Karamzadeh N. 2017. Laboratory investigation of soil mechanical indices on anisotropic permeability of non-uniform coarse-grained materials: With emphasis on grain size, shape factor and density. Journal of Advanced Applied Geology, Shahid Chamran University of Ahvaz, 7(2): 57–64. (In Persian) DOI:10.22055/aag.2017.21062.1665.
Pyne RDG. 2005. Aquifer storage and recovery: A guide to groundwater recharge through wells Edition. ISBN 0-9774337-090000.
Qabadian R, Khalaj M. 2012. Numerical estimating of earth channel seepage in Nzloo Area of Uromye Province and correction of empirical relation constant coefficient. Journal of Water and Soil (Agricultural Sciences and Industries), 26(1): 193−202. DOI:10.22067/jsw.v0i0.13648.
Rognon P. 2000. Comment développer la recharge artificielle des nappes en régions sèches. Sécheresse, 11(4): 289−296. (in French
Rostamian R, Abedi Koupai J. 2012. Assessment of SEEP/W Model to estimate seepage from earth canals (Case study: Irrigation Network of Downstream Zayandehrud). JWSS-Isfahan University of Technology, 15 (58) : 13–22.
Salemi HR, Sepaskhah AR. 2006. Estimation of canal seepage loss in Rudasht Region of Isfahan. Journal of Agricultural and Natural Resources Sciences, 10(2): 42–29.
Scanlon B, Keese K, Flint A, et al. 2006. Global synthesis of groundwater recharge in semiarid and arid regions. Hydrological Processes, 20(15): 3335–3370. DOI:10.1002/hyp.6335.
Sebbar A. 2013. Etude de la variabilité et de l'évolution de la pluviométrie au Maroc (1935-2005): Réactualisation de la carte des précipitations. Thèse national, Université Hassan II Mohammedia-Casablanca, Maroc. (in French) DOI:10.13140/2.1.1206.6084.
Senent-Alonso M. 1984. Problems of the artificial recharge of aquifers. Spanish achievements and their possibilities in the southeast of Spain. Doctoral Thesis, University Polytechnic of Madrid.
Tavakoli E, Ghorbani B, Samadi Borujeni H, et al. 2017. Modifying empirical equations of seepage estimation using dimensional analysis (Boldaji earth canal, Chaharmahal and Bakhtiari province). Water and Soil Conservation Journal, 6(2): 105–119.
Zhang G, Lu N, Liu J, et al. 2015. River leakage ratio and leakage amount in the Qaidam Basin. Geological Bulletin of China, 34(11): 2083−2086. (in Chinese)
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