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The current study aims to verify the existing equations for incipient motion for a rigid rectangular channel. Data from experimental work on incipient motion from a rectangular flume with two different widths, namely 0.3 and 0.6 m, were compared with the critical velocity value predicted by the equations of Novak & Nalluri and El-Zaemey. The equati...
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... slope for the best fit line for the points calculated using Equation (7) varied from 1.016 (for sediment deposition thickness of d 50 ) to 0.6612 (for sediment deposition thickness of 24 mm) which was an improvement compared with using the equation by El- Zaemey (). Table 1 shows the comparison of the discre- pancy ratio value obtained by using the equations by Novak & Nalluri () and El-Zaemey (), and Equation (7). Generally, Equation (7) performed better than the equations by Novak & Nalluri () and El-Zaemey () after taking into account the thickness of sediment deposit. ...
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... For the case of the velocity approach, relative particle size and particle Froude number were first used by Novak and Nalluri (1975). A similar approach was latter utilized in different studies for variety types of channels (Ab Ghani et al., 1999;Bong et al., 2013Bong et al., , 2016El-Zaemey, 1991;Novak & Nalluri, 1984;Safari et al., 2011Safari et al., , 2017. The aforementioned studies developed equations using conventional regression models applying shear stress or velocity approaches, separately. ...
The existing incipient sediment motion models typically apply conventional regression methods considering either velocity or shear stress. In the current study, incipient sediment motion is analyzed through a simultaneous and joint analysis of velocity and shear stress using the robust low-rank learning (RLRL) multi-output regression technique. Moreover, the experimental data compiled from five different channels are utilized to develop a generic incipient sediment motion model valid for a channel of any cross-sectional shape. The efficacy of the developed method is examined and compared against the available conventional regression models. The experimental results indicate that the RLRL model yields better results than its counterparts. In particular, while cross-section specific models fail to provide accurate estimates for shear stress or velocity for other cross sections, the proposed model provides satisfactory results for all channel shapes. The better performance of the recommended approach can be attributed to the joint modeling of the shear stress and the velocity which is realized by capturing the correlation between these parameters in terms of a low rank output mixing matrix which enhances the prediction performance of the approach.
... The first set of self-cleaning models may be further divided into two subgroups based on incipient motion and scouring processes. In contrast to scouring models, which are based on the flow velocity necessary for scouring the bed sediments (Mayerle et al. (1991) and Nalluri et al. (1994), incipient motion self-cleansing design uses the least velocity or shear stress required for the start of sediment motion as criteria (Ab Ghani et al. 1999;Safari et al. 2011;Bong et al. 2013). ...
The hydraulic capacity of the channel is significantly impacted by the deposition of sediment in sewers and urban drainage systems. Sediment deposition affects a channel's hydraulic capacity in urban drainage and sewage systems. To decrease the effects of this continuous deposition of silt particles, sewer systems frequently have a self-cleaning device to keep the channel bottom clear from sedimentation. Therefore, accurate particle Froude number (Fr) prediction is essential for sewage system design. This study looked at three datasets from the literature that covered a wide range of volumetric sediment concentration (Cv), dimensionless grain size of particles (Dgr), sediment median size (d), hydraulic radius (R), and pipe friction factor for the condition of non-deposition without deposited bed. We employed Kstar, M5P, and random forest (RF) models as standalone models as well as additive regression (AR) models as hybrid machine learning (ML) models for the prediction of Fr. In all, we looked at six ML methods: Kstar, AR-Kstar, M5P, AR-M5P, RF, and AR-RF. Several performance metrics, including mean absolute error (MAE), Nash–Sutcliffe efficiency (NSE), root-mean-square error (RMSE), Pearson correlation coefficient (R), etc., have been used to assess the performance of suggested models. In comparison to standalone ML models and empirical equations, hybrid ML models perform better. For the prediction of particle Froude number (Fr) in sewage system design under the condition of non-deposition without deposited bed, AR-Kstar (MAE = 0.435, NSE = 0.922, and RMSE = 0.623, and R2 = 0.923) performed the best, followed by AR-RF, Kstar, RF, AR-M5P, and M5P.
... At present, slope runoff is considered to be the main external factor that causes soil erosion in wide-grading soils, while particle characteristics (particle size, friction angle, and exposure degree) and slope characteristics (length and slope ratio) are thought to be the internal factors that cause wide-grading particle instability (Kirchner et al. 1990). In general, the critical shear stress (Dey 2003;Morris and Strevett 2015), critical water depth (Zuazo and Pleguezuelo 2008), and critical velocity (Bong et al. 2016(Bong et al. , 2013 of runoff are the basic criteria for judging particle erosion. Li et al. (2017) found that shear stress is the most suitable parameter for predicting soil erosion through laboratory tests, with the ratio of the Manning coefficient to the water depth as an alternative parameter. ...
... The particles are moved and transported due to conditions called incipient motion and incipient deposition, respectively (Safari et al. 2015). These conditions of defining sediment motion and transportation in rigid boundary channels were studied and investigated by Novak and Nalluri (1984), El-Zaemey (1991), Ab Ghani et al. (1999), Mohammadi (2005), Bong et al. (2013) and Safari et al. (2013a). Loveless (1992) performed experiments in University of London, UK, in circular-, rectangular-and U-shaped cross-sectional channels at incipient deposition condition. ...
The study was performed to estimate the weekly sediment load in Thal canal located in Mianwali district Punjab, Pakistan. Past records of sediments and discharge have been considered as the input parameters. The best input combinations have been identified with the help of advanced algorithms including full, sequential and increasing embedding, genetic algorithm and hill climbing in combination with the gamma test. Model training has been carried out using two artificial neural network-based algorithms, namely Broyden-Fletcher-Goldfarb-Shanno (BFGS), back-propagation and a local linear regression technique. A variety of statistical parameters including R square, root mean squared error, mean square error and mean bias error (MBE) has been calculated in order to evaluate the best models. The results strongly suggested that BFGS-based model performed better than all other models with remarkably low values of MBE. Significantly high values of correlation coefficient (R square) in both training and testing evidenced a close similarity between actual and predicted sediment load values for the same model.
... Furthermore, we investigate the variation of * on threshold criteria based on two definitions, i.e. bed slope product and the logarithmic law of the wall. Despite estimation of shear stress based criteria being hydraulically correct, presenting as simple mean velocity is more useful and straightforward, particularly concerning the self-cleansing design (Novak and Nalluri, 1975;Bong et al., 2013). Thus, analysis is extended to evaluate the incipient sediment motion on various bed thicknesses, based on the mean flow velocity. ...
This paper analyses experimental data on sediment incipient motion with varying sediment bed thickness (of d50, 5, 10 and 24 mm). Sediment particles (with sizes ranging from 0.5 mm to 4.78 mm) were used to evaluate the effect of deposited bed. Variation of shear velocity estimation was investigated where the critical Shields parameter was expressed using bed-slope product u∗cb, log-law u∗cl and was extended in terms of critical mean velocity. The critical Shields parameters obtained were significantly lower than the traditional Shields curve when u∗cl was used compared to u∗cb. Higher critical mean velocity is needed for shallower deposits.
... The obtained results of the statistical performance carried out for ACGY model is shown in Table 5. It reveals that the discrepancy ratio for ACGY model is 1.03 which is very close to ideal value as 1 (Bong et al., 2013). The results of model yield and actual yield are compared with consideration of the data during 1992 to 2016 (Fig. 2). ...
Prediction of the crop yield is need of time according to the change in climate conditions. In the present study, the Agro-Climatic Grape Yield (ACGY) model has been developed with monthly climatic parameters using multi-regression analysis approach. The developed model was statistically tested for its predictive ability. The discrepancy ratio, the standard deviation of discrepancy ratio, mean percentage error and standard deviation of mean percentage error for the model was obtained as 1.03, 0.19, 0.03% and 0.19, respectively. Sensitivity analysis was carried out for the developed ACGY model using the parametric sensitivity method. In order to know the future grape yield using ACGY model, climate scenarios were generated under Canadian Earth System Model (CanESM2) for three emissions representative concentration pathways as RCP2.6, RCP4.5, and RCP8.5. According to the analysis using ACGY model, increasing yield was observed in grape up to year 2050 as compared to current yield.
... If the R 2 pre value is significantly lower than R 2 p , it is almost certain the model is overfit with too many terms in the model. The mean square error, MSE, Table 1 Characteristic dimensionless parameters for incipient motion (Bong, 2013;Bong et al., 2013;El-Zaemey, 1991;Lamb et al., 2008;Novak & Nalluri, 1984;Salem, 1998;Shvidchenko et al., 2001 ...
The current study aims at the development of an incipient motion equation and a self-cleansing design chart based on the critical shear stress approach for a rectangular channel. Data from previous experimental work on incipient motion for rectangular flumes were subjected to multiple linear regression analysis. Selected regression models were further assessed through cross validation using the remaining data from the previous experimental work and a performance test using another three sets of existing data from the literature. The best regression model from the current study was
found to perform much better than two of the existing equations in the literature by Novak and Nalluri and El-Zaemey with respect to having 95% of the predicted value fall within the acceptable discrepancy ratio range of 0.5 to 2.0. The equations by Novak and Nalluri and El-Zaemey only managed to have 10 and 16%, respectively, of the predicted
values fall within the acceptable discrepancy ratio. The developed best regression model has a coefficient of determination (Rp
216 ) value of 0.9960, adjusted coefficient of determination (Radj
2 ) value of 0.9960, predicted coefficient of determination (Rpre
2 17 ) value of 0.9958, mean square error (MSE) value of 0.0004, and Mallow’s Cp value of 3.0. The best regression model was further chosen to develop a self-cleansing design chart for rectangular channels. The design chart which relates the minimum sewer slope Smin with the minimum critical shear stress, τc, for the respective standard rectangular channel size of an open channel system could be used to check and determine the suitable minimum
slope for self-cleansing design purposes.
... With the same laboratory conditions, experimental results for two types of soil are evaluated for incipient motion using the velocity approach technique. Using the velocity approach, new equations Is predict for sewer and irrigation channel shown in Table IV equations (14,15). ...
... This indicates that higher velocity is needed for irrigation sediment particular more than sewer sediment . It is seen that all these three curve in Fig (9) has incipient motion models based on the velocity approach with same structure, the coefficient for equations (14,15) ranging from 0.29 to 0.5 and the power ranging from − 0.4 to − 0.52. Table IV shows two equations (12,13) for shear stress obtained by the graphs in Fig (7,8) for d50 for irrigation and sewer channel, respectively, as well as two equations (14,15) for velocity approach obtained by the graph in Fig (9) for irrigation and sewer channel, respectively. ...
... It is seen that all these three curve in Fig (9) has incipient motion models based on the velocity approach with same structure, the coefficient for equations (14,15) ranging from 0.29 to 0.5 and the power ranging from − 0.4 to − 0.52. Table IV shows two equations (12,13) for shear stress obtained by the graphs in Fig (7,8) for d50 for irrigation and sewer channel, respectively, as well as two equations (14,15) for velocity approach obtained by the graph in Fig (9) for irrigation and sewer channel, respectively. ...
The initiation of sediment motion is one of the most critical parameters in the sedimentation process. In this paper, sediment incipient motion was investigated in a laboratory of rectangular flume cross-section smooth channels using two different types of sands, irrigation and sewer types. The experiment was conducted at five different slopes (0.001, 0.0015, 0.002, 0.0025, and 0.003) for irrigation channels and (0.005, 0.01, 0.015, 0.02, and 0.025) for sewer channel. The methods of shear stress and velocity are used to evaluate experimental results The results are compared with the corresponding models available for Shields, Novak and Nalluri. The resulting data from velocity approaches in this study are found in an acceptable agreement with existing models, while the resulting data from the shear stress method provided an overestimation value for each type. Channel bed slope has a negative relationship to the incipient motion of the sediment, while positive to the specific gravity of the sediment.
... With the same laboratory conditions, experimental results for two types of soil are evaluated for incipient motion using the velocity approach technique. Using the velocity approach, new equations Is predict for sewer and irrigation channel shown in Table IV equations (14,15). Novak and nalluri compared the experimental results to the corresponding models in the literature, and the experimental data were found to display acceptable agreement with the current models [10]. ...
... This indicates that higher velocity is needed for irrigation sediment particular more than sewer sediment . It is seen that all these three curve in Fig (9) has incipient motion models based on the velocity approach with same structure, the coefficient for equations (14,15) ranging from 0.29 to 0.5 and the power ranging from − 0.4 to − 0.52. Table IV shows two equations (12,13) for shear stress obtained by the graphs in Fig (7,8) for d 50 for irrigation and sewer channel, respectively, as well as two equations (14,15) for velocity approach obtained by the graph in Fig (9) for irrigation and sewer channel, respectively. ...
... It is seen that all these three curve in Fig (9) has incipient motion models based on the velocity approach with same structure, the coefficient for equations (14,15) ranging from 0.29 to 0.5 and the power ranging from − 0.4 to − 0.52. Table IV shows two equations (12,13) for shear stress obtained by the graphs in Fig (7,8) for d 50 for irrigation and sewer channel, respectively, as well as two equations (14,15) for velocity approach obtained by the graph in Fig (9) for irrigation and sewer channel, respectively. ...
The initiation of sediment motion is one of the most critical parameters in the sedimentation process. In this paper, sediment incipient motion was investigated in a laboratory of rectangular flume cross-section smooth channels using two different types of sands, irrigation and sewer types. The experiment was conducted at five different slopes (0.001, 0.0015, 0.002, 0.0025, and 0.003) for irrigation channels and (0.005, 0.01, 0.015, 0.02, and 0.025) for sewer channel. The methods of shear stress and velocity are used to evaluate experimental results The results are compared with the corresponding models available for Shields, Novak and Nalluri. The resulting data from velocity approaches in this study are found in an acceptable agreement with existing models, while the resulting data from the shear stress method provided an overestimation value for each type. Channel bed slope has a negative relationship to the incipient motion of the sediment, while positive to the specific gravity of the sediment. I. INTRODUCTION The movement of sediment in open channels is a complicated mechanism, and the mechanics of this phenomenon has not yet been fully understood. Irrigation and sewer systems channels, and rivers in general, are treated by the deposition of sediment that comes from water collection processes, such as soft soil carried by air, roads, suspended soil in water intake. In rigid boundary channels like irrigation and sewers channels sedimentation is a common economic and technological problem. Continued deposition in the channels decreases its section's efficiency. It decreases the channel's hydraulic capacity by reducing the flow cross-sectional area or blocking it. The deposition has an impact on drainage system performance and efficiency. To maintain the channel bed clear, self-cleaning models tend to move all sediment particles without deposition. In order to solve the sedimentation problem, the irrigation channel must also be built with self-cleaning requirements.
... It can be seen in Fig. 3 that in a rectangular channel, Sand A-type particles start to move as blocks slowly forming small ripples, and as the Re * increases, the ripples turn into seemingly small dunes toward the downstream of the rough bed. The formation of ripples and dunes is due to the bed roughness resistance against the flow (Simons and Sentürk 1992;Bong et al. 2013). The relatively bigger particle diameter induces relatively stronger bed roughness effect that can be confirmed by just observing the imagery results depicted in Fig. 3 and comparing the bed formations generated by the flow for Sand A and Sand B. On the contrary, for Sand A the started Incipient Motion (IM) formed almost small dunes at the upstream of the rough bed and towards downstream the small dunes slowly dissipated and moved together in a relatively quick fashion. ...
... Furthermore, the experimental data collected from the rectangular and circular cross-sectional channels under bed roughness influence are quantitatively compared to examine the effect of the bed roughness for different channel cross-sectional shapes towards the threshold conditions of sediment transport. The experimental data generated in the presented study is a practical effort made to fill the gap that still exists in the literature about the bed roughness effects in rigid boundary channels (Buffington and Montgomery 1997;Bong et al. 2013). Numerous works have been presented and the bed roughness has been an important discussion topic for decades in loose boundary channels (Shields 1936;Paintal 1971;Salem 2013) yet the lack of extended research on the effect of bed roughness influence on the critical condition of sediment motion in rigid boundary channels is remarkable. ...
... It is important to highlight the fact that these conclusions are for uniform non-cohesive sand particles. Furthermore, Fig. 6, also illustrates the experimental data of Paintal (1971), Helland-Hansen (1971), and Safari et al. (2017) obtained in smooth rigid boundary channels and Bogardi (1965) and Bong et al. (2013) in rough rigid boundary channels for quantitative comparison. Consequently, the results of the present study exhibited strong agreement with those of Bogardi (1965) and Bong et al. (2013) regarding the effect of deposition thickness on the critical condition of sediment motion in stable circular and rectangular open channels, respectively. ...
In the present study, with the comprehension of different types of bedforms are generated by different bed roughness, in rectangular and circular cross-sectional rigid boundary channels, the resistance generated by the bed roughness against the flow and consequently the critical condition of sediment motion under bed roughness influence is investigated. This study presents novel contributions in solving engineering problems that suffer from the lack of knowledge on the incipient motion of sediment particles in rigid boundary channels under bed roughness effects. Furthermore, soft computing and evolutionary computation methods have been combined to develop a new novel predictive model. The Evolutionary GENOFIS also aims at improving the ANFIS tool depends on Sugeno Fuzzy Inference System. The advantages of the proposed hybrid GENOFIS approach over the ANFIS tool is its novel ability to tackle the incipient prediction problem by using less fuzzy based rules and to represent the consequent part of the model as a constant, linear or non-linear function as well as with possible simultaneous combinations of them. For validation and comparison purposes, model performances of hybrid GENOFIS and ANFIS approaches are evaluated via experimental data partitioned for testing purposes. The model results are compared through corresponding RMSE and CE values. It is found that the hybrid GENOFIS model results outperformed the ANFIS model values. Consequently, novel experimental data-driven incipient motion formula and the hybrid GENOFIS approach are proposed to modeling complex incipient motion problems that are full of uncertainty and complication.
