Rill flow resistance law under equilibrium bed‐load transport conditions

In this paper, a recently deduced flow resistance equation for open channel flow was tested under equilibrium bed‐load transport conditions in a rill. First, the flow resistance equation was deduced applying dimensional analysis and the incomplete self‐similarity condition for the flow velocity distribution. Then, the following steps were carried out for developing the analysis: (a) a relationship (Equation  13 ) between the Γ function of the velocity profile, the rill slope, and the Froude number was calibrated by the available measurements by Jiang et al.; (b) a relationship (Equation  17 ) between the Γ function, the rill slope, the Shields number, and the Froude number was calibrated by the same measurements; and (c) the Darcy–Weisbach friction factor values measured by Jiang et al. were compared with those calculated by the rill flow resistance equation with Γ estimated by Equations  13 and 17 . This last comparison demonstrated that the rill flow resistance equation, in which slope and Shields number, representative of sediment transport effects, are introduced, is characterized by the lowest values of the estimate errors.     

Testing slope effect on flow resistance equation for mobile bed rills

In this paper, a recently theoretically deduced rill flow resistance equation, based on a power‐velocity profile, is tested experimentally on plots of varying slopes in which mobile bed rills are incised. Initially, measurements of flow velocity, water depth, cross‐sectional area, wetted perimeter and bed slope conducted in 106 reaches of rills incised on an experimental plot having a slope of 14% were used to calibrate the flow resistance equation. Then, the relationship between the velocity profile parameter Γ, the channel slope, and the flow Froude number, which was calibrated using the 106 rill reach data, was tested using measurements carried out in plots having slopes of 22% and 9%. The measurements carried out in the latter slope conditions confirmed that (a) the Darcy–Weisbach friction factor can be accurately estimated using the proposed theoretical approach, and (b) the data were supportive of the slope independence hypothesis of rill velocity stated by Govers.     

Testing a theoretical resistance law for overland flow on a stony hillslope

Overland flow, sediments, and nutrients transported in runoff are important processes involved in soil erosion and water pollution. Modelling transport of sediments and chemicals requires accurate estimates of hydraulic resistance, which is one of the key variables characterizing runoff water depth and velocity. In this paper, a new theoretical power–velocity profile, originally deduced neglecting the impact effect of rainfall, was initially modified for taking into account the effect of rainfall intensity. Then a theoretical flow resistance law was obtained by integration of the new flow velocity distribution. This flow resistance law was tested using field measurements by Nearing for the condition of overland flow under simulated rainfall. Measurements of the Darcy–Weisbach friction factor, corresponding to flow Reynolds number ranging from 48 to 194, were obtained for simulated rainfall with two different rainfall intensity values (59 and 178 mm hr⁻¹). The database, including measurements of flow velocity, water depth, cross-sectional area, wetted perimeter, and bed slope, allowed for calibration of the relationship between the velocity profile parameter Γ, the slope steepness s, and the flow Froude number F, taking also into account the influence of rainfall intensity i. Results yielded the following conclusions: (a) The proposed theoretical flow resistance equation accurately estimated the Darcy–Weisbach friction factor for overland flow under simulated rainfall, (b) the flow resistance increased with rainfall intensity for laminar overland flow, and (c) the mean flow velocity was quasi-independent of the slope gradient.     

Testing a new rill flow resistance approach using the Water Erosion Prediction Project experimental database

In this paper, a recently theoretically deduced rill flow resistance equation, based on a power‐velocity profile, was tested using the Water Erosion Prediction Project database. This database includes measurements of flow velocity, water depth, cross section area, wetted perimeter, and bed slope that were made in rills shaped on experimental sites distributed across the continental United States. In particular, three different experimental conditions (only rainfall, only flow, and rain with flow) were examined, and for each condition, the theoretically based relationship for estimating the Γ function of the power velocity profile was calibrated. The results established that (a) the Darcy‐Weisbach friction factor can be accurately estimated using the proposed theoretical approach, and (b) the flow resistance increases with the effect of rainfall impact.     

Comparing flow resistance law for fixed and mobile bed rills

Rills caused by run‐off concentration on erodible hillslopes have very irregular profiles and cross‐section shapes. Rill erosion directly depends on the hydraulics of flow in the rills, which may differ greatly from hydraulics of flow in larger and regular channels. In this paper, a recently theoretically deduced rill flow resistance equation, based on a power–velocity profile, was tested experimentally on plots of varying slopes (ranging from 9% to 26%) in which mobile and fixed bed rills were incised. Initially, measurements of flow velocity, water depth, cross‐section area, wetted perimeter, and bed slope, carried out in 320 reaches of mobile bed rills and in 165 reaches of fixed rills, were used for calibrating the theoretical flow resistance equation. Then the relationship between the velocity profile parameter Γ, the channel slope, and the flow Froude number was separately calibrated for the mobile bed rills and for the fixed ones. The measurements carried out in both conditions (fixed and mobile bed rills) confirmed that the Darcy–Weisbach friction factor can be accurately estimated using the proposed theoretical approach. For mobile bed rills, the data were supportive of the slope independence hypothesis of velocity, due to the feedback mechanism, stated by Govers. The feedback mechanism was able to produce quasicritical flow conditions. For fixed bed rills, obtained by fixing the rill channel, by a glue, at the end of the experimental run with a mobile bed rill, the slope independence of the flow velocity measurements was also detected. Therefore, an experimental run carried out by a rill bed fixed after modelling flow action is useful to detect the feedback mechanism. Finally, the analysis showed that, for the investigated conditions, the effect of sediment transport on the flow resistance law can be considered negligible respect to the grain roughness effect.     

Roughness coefficients and velocity estimation in well-inundated sheet and rilled overland flow without strongly eroding bed forms

Even with the flow of water over a soil surface in which roughness elements are well inundated, and in less erosive situations where erosional bed forms are not pronounced, the magnitude of resistance coefficients in equations such as those of Darcy–Weisbach, Chezy or Manning vary with flow velocity (at least). Using both original laboratory and field data, and data from the literature, the paper examines this question of the apparent variation of resistance coefficients in relation to flow velocity, even in the absence of interaction between hydraulics and resulting erosional bed forms. Resistance equations are first assessed as to their ability to describe overland flow velocity when tested against these data sources. The result is that Manning's equation received stronger support than the Darcy–Weisbach or Chezy equations, though all equations were useful. The second question addressed is how best to estimate velocity of overland flow from measurements of slope and unit discharge, recognizing that the apparent flow velocity variation in resistance coefficients is probably a result of shortcomings in all of the listed resistance equations. A new methodology is illustrated which gives good agreement between estimated and measured flow velocity for both well-inundated sheet and rill flow. Comments are given on the predictive use of this methodology. Copyright © 1999 John Wiley & Sons, Ltd.     

Flow resistance in gravel‐bed channels with large‐scale roughness

A previously published mixing length (ML) model for evaluating the Darcy–Weisbach friction factor for a large‐scale roughness condition (depth to sediment height ratio ranging from 1 to 4) is brie?y reviewed and modi?ed (MML). Then the MML model and a modi?ed drag (MD) model are experimentally tested using laboratory measurements carried out for gravel‐bed channels and large‐scale roughness condition. This analysis showed that the MML gives accurate estimates of the Darcy–Weisbach coef?cient and for Froude number values greater than 0·5 the MML model coincides with the ML one. Testing of the MD model shows limited accuracy in estimating ?ow resistance. Finally, the MML and MD models are compared with the performance of a quasi‐theoretical (QT) model deduced applying the P‐theorem of the dimensional analysis and the incomplete self‐similarity condition for the depth/sediment ratio and the Froude number. Using the experimental gravel‐bed data to calibrate the QT model, a constant value of the exponent of the Froude number is determined while two relationships are proposed for estimating the scale factor and the exponent of the depth/sediment ratio. This indirect estimate procedure of the coef?cients (b₀, b₁ and b₂) of the QT model can produce a negligible overestimation or underestimation of the friction factor. Copyright © 2003 John Wiley & Sons, Ltd.     

Estimating flow resistance in steep slope rills

Recent research recognized that the slope of 18% can be used to distinguish between the ‘gentle slope’ case and that of ‘steep slope’ for the detected differences in hydraulic variables (flow depth, velocity, Reynolds number, Froude number) and those representatives of sediment transport (flow transport capacity, actual sediment load). In this paper, using previous measurements carried out in mobile bed rills and flume experiments characterized by steep slopes (i.e., slope greater than or equal to 18%), a theoretical rill flow resistance equation to estimate the Darcy-Weisbach friction factor is tested. The main aim is to deduce a relationship between the velocity profile parameter Γ, the channel slope, the Reynolds number, the Froude number and the textural classes using a data base characterized by a wide range of hydraulic conditions, plot or flume slope (18%–84%) and textural classes (clay ranging from 3% to 71%). The obtained relationship is also tested using 47 experimental runs carried out in the present investigation with mobile bed rills incised in a 18%—sloping plot with a clay loam soil and literature data. The analysis demonstrated that: (1) the soil texture affects the estimate of the Γ parameter and the theoretical flow resistance law (Equation 25), (2) the proposed Equation (25) fits well the independent measurements of the testing data base, (3) the estimate of the Darcy-Weisbach friction factor is affected by the soil particle detachability and transportability and (4) the Darcy-Weisbach friction factor is linearly related to the rill slope.     

Overland runoff erosion dynamics on steep slopes with forages under field simulated rainfall and inflow

Although numerous studies have acknowledged that vegetation can reduce erosion, few process-based studies have examined how vegetation cover affect runoff hydraulics and erosion processes. We present field observations of overland flow hydraulics using rainfall simulations in a typical semiarid area in China. Field plots (5 × 2 m²) were constructed on a loess hillslope (25°), including bare soil plot as control and three plots with planted forage species as treatments—Astragalus adsurgens, Medicago sativa and Cosmos bipinnatus. Both simulated rainfall and simulated rainfall + inflow were applied. Forages reduced soil loss by 55–85% and decreased overland flow rate by 12–37%. Forages significantly increased flow hydraulic resistance expressed by Darcy–Weisbach friction factor by 188–202% and expressed by Manning's friction factor by 66–75%; and decreased overland flow velocity by 28–30%. The upslope inflow significantly increased overland flow velocity by 67% and stream power by 449%, resulting in increased sediment yield rate by 108%. Erosion rate exhibited a significant linear relationship with stream power. M. sativa exhibited the best in reducing soil loss which probably resulted from its role in reducing stream power. Forages on the downslope performed better at reducing sediment yield than upslope due to decreased rill formation and stream power. The findings contribute to an improved understanding of using vegetation to control water and soil loss and land degradation in semiarid environments.     

Hydrodynamic characteristics of rill flow on steep slopes

Rill erosion is a dominant sediment source on sloping lands. However, the amount of soil loss from rills on steep slopes is vastly more than that on gentle slopes because of differences in rill shape and hydraulic patterns. The aims of this paper are to determine the hydrodynamic characteristics of rills and the friction coefficients in steep slope conditions and to propose modifications of some hydraulic parameters used in soil loss prediction models. A series of inflow experiments was conducted on loess slopes. The results show that the geometric and hydraulic properties of rill on the steep loess slopes, which are characterized by the mean width of cross sections, mean velocity and mean depth of flow, are related to discharge and slope gradient in power functions. However, the related exponents to discharge are 0.26, 0.48 and 0.26, respectively, which are different from the exponents derived in previous studies, which were conducted on gentle slopes. The Manning roughness coefficient ranged from 0.035 to 0.071, with an average of 0.0536, and the Darcy–Weisbach friction coefficients varied from 0.4 to 1.9. The roughness coefficients are closely related to the Reynolds numbers and flow volumes; however, the correlations vary with slope gradient. The roughness coefficients are directly proportional to the Reynolds number and the flow volume on steep slopes, in contrast with the roughness coefficients found on gentle slopes, which decrease as the Reynolds number and flow volume increase. This difference is caused by the interactions among the hydraulics of the flow, the shape of the rills and the sediment concentrations on steep slopes. The results indicate that parameters used in models to predict rill erosion have to be modified according to slope gradient. Copyright © 2015 John Wiley & Sons, Ltd.     

The impact of flow discharge on the hydraulic characteristics of headcut erosion processes in the gully region of the Loess Plateau

Headcut erosion is associated with major hydraulic changes induced by the gully head of concentrated flow. However, the variation in the hydraulic characteristics of the headcut erosion process is still not clear in the gully region of the Loess Plateau. A series of rainfall combined scouring experiments (flow discharges ranging from 3.6 to 7.2 m³ hr⁻¹, with 0.8 mm min⁻¹ rainfall intensity) were conducted on experimental plots to clarify the variation in the hydraulic parameters induced by gully head and erosion processes under different flow discharges. The results showed that concentrated flows in the catchment area and gully bed were turbulent (Reynolds number ranging from 1,876 to 6,693) and transformed between supercritical and subcritical (Froude number ranging from 0.96 to 3.73). The hydraulic parameters, such as the flow velocity, Reynolds number, shear stress, stream power, Darcy–Weisbach friction factor, and unit stream power in the catchment area were 0.45–0.59 m s⁻¹, 2086–6693, 1.96–5.33 Pa, 0.89–2.86 W m⁻², 0.08–0.16, and 0.023–0.031 m s⁻¹, respectively. When the concentrated flows dropped from the gully head, the hydraulic parameters in the gully bed decreased by 3.39–26.07%, 1.49–29.99%, 65.19–67.14%, 67.25–74.96%, 28.53–61.31%, and 67.82–77.14%, respectively, which contributed to the flow energy consumption at the gully head. As flow discharge increased, Reynolds number, shear stress, and stream power increased, while flow velocity, Froude number, unit stream power, and Darcy–Weisbach friction factor did not. The flow energy consumption at the gully head was 9.66–10.13, 13.25–13.74, 15.68–16.41, and 19.28–20.25 J s⁻¹, respectively, under different flow discharges and accounted for 60.58–68.50% of the flow energy consumption of the experimental plots. Generally, the sediment discharges increased rapidly at the initial stage, then increased slowly, and finally reached a steady state condition, which showed a significant declining logarithmic trend with experimental duration (P<.01) and increased with increasing flow discharge. Accordingly, the flow energy consumption was significantly correlated with the sediment yield. These findings could improve our understanding of the hydraulic properties and flow energy characteristics of headcut erosion.     

Interpolation between Darcy–Weisbach and Darcy for laminar and turbulent flows

An equation describing flow in an open channel with obstacles is derived, following the conservation of momentum approach used by Bélanger and St. Venant. When the obstacles are all submerged the result yields the Darcy–Weisbach equation for turbulent flow in pipes and open channels. When the obstacles are only partially submerged the result leads to the governing equation in a porous medium. If the flow is turbulent the square of the velocity is proportional to the hydraulic gradient and if the flow is laminar, which is the usual case, the velocity is proportional to the hydraulic gradient. This last result is in agreement with Darcy’s law in porous media. Thus our equation interpolates between and reduces to, the two fundamental results of Darcy. In general our equation should prove useful in practice for open flow in a channel with both submerged and emerging obstacles.     

Effects of sediment load on hydraulics of overland flow on steep slopes

Eroded sediment may have significant effects on the hydraulics of overland flow, but few studies have been performed to quantify these effects on steep slopes. This study investigated the potential effects of sediment load on Reynolds number, Froude number, flow depth, mean velocity, Darcy–Weisbach friction coefficient, shear stress, stream power, and unit stream power of overland flow in a sand‐glued hydraulic flume under a wide range of hydraulic conditions and sediment loads. Slope gradients were varied from 8·7 to 34·2%, unit flow rates from 0·66 to 5·26×10^?3 m² s^?1, and sediment loads from 0 to 6·95 kg m^?1 s^?1. Both Reynolds number (Re) and Froude number (Fr) decreased as sediment load increased, implying a decrease in flow turbulence. This inverse relationship should be considered in modeling soil erosion processes. Flow depth increased as sediment load increased with a mean value of 1·227 mm, caused by an increase in volume of sediment‐laden flow (contribution 62·4%) and a decrease in mean flow velocity (contribution 37·6%). The mean flow velocity decreased by up to 0·071 m s^?1 as sediment load increased. The Darcy–Weisbach friction coefficient (f) increased with sediment load, showing that the total energy consumption increased with sediment load. The effects of sediment load on f depended on flow discharge: as flow discharge increased, the influence of sediment load on f decreased due to increased flow depth and reduced relative roughness. Flow shear stress and stream power increased with sediment load, on average, by 80·5% and 60·2%, respectively; however, unit stream power decreased by an average of 11·1% as sediment load increased. Further studies are needed to extend and apply the insights obtained under these controlled conditions to real‐world overland flow conditions. Copyright © 2010 John Wiley & Sons, Ltd.     

Concentrated flow erosion rates reduced through biological geotextiles

Soil erosion by concentrated flow can cause serious environmental damage. Erosion‐control geotextiles have considerable potential for reducing concentrated flow erosion. However, limited data are available on the erosion‐reducing potential of geotextiles. In this study, the effectiveness of three biological geotextiles in reducing soil losses during concentrated flow is investigated. Hereto, runoff was simulated in a concentrated flow flume, filled with an erodible sandy loam on three slope gradients (13·5, 27·0 and 41·5%). Treatments included three biological geotextiles (borassus, buriti and bamboo) and one bare soil surface. Darcy–Weisbach friction coefficients ranged from 0·01 to 2·84. The highest values are observed for borassus covered soil surfaces, followed by buriti, bamboo and bare soil, respectively. The friction coefficients are linearly correlated with geotextile thickness. For the specific experimental conditions of this study, borassus geotextiles reduced soil detachment rate on average to 56%, buriti geotextiles to 59% and bamboo geotextiles to 66% of the soil detachment rate for bare soil surfaces. Total flow shear stress was the hydraulic parameter best predicting soil detachment rate for bare and geotextile covered surfaces (R² = 0·75–0·84, p <0·001, n = 12–15). The highest resistance against soil detachment was observed for the borassus covered soil surfaces, followed by buriti, bamboo and bare soil surfaces, respectively. Overall, biological geotextiles are less effective in controlling concentrated flow erosion compared with interrill erosion. Copyright © 2009 John Wiley & Sons, Ltd.     

Volumetric displacement of flow depth by obstacles,and the determination of friction factors in shallow overland flows

Large roughness elements such as stones or plant stems (obstacles) influence the depth of overland flows in two ways. The first effect is a dynamic one, involving frictional retardation of the flow and associated reduction in flow speeds. The second influence is static, and arises from the upward volumetric displacement of flow depth because of the submerged volume of the obstacles. Depending upon the distribution of submerged obstacle volume with height above the soil surface, the proportion of the flow volume occupied (and so, the perturbation of flow depth arising from volumetric displacement) can vary irregularly or systematically with flow stage. Furthermore, the amount of volumetric displacement of flow depth would vary among surfaces carrying different cover fractions of identical obstacles. Consequently, estimates of the change in friction factors arising from the drag on flow traversing varying obstacle cover fractions are confounded with the parallel shift volumetric displacement. To understand the true frictional drag arising from obstacles, a correction must be made for the volumetric displacement. A method for making this correction is outlined. New laboratory experiments provide precise observations of depths and friction coefficients in laminar flows passing fields of regular obstacles. After making the proposed correction for volumetric displacement, increases of 40 to 75 per cent in the derived value of the Darcy–Weisbach friction factor, f, are found for an obstacle cover of 20 per cent. Many published studies of friction coefficients in shallow overland flows, such as those on stone‐covered dryland soils, involve larger obstacle cover fractions, and evidently involve the significant confounding effect of volumetric displacement. Copyright © 2002 John Wiley & Sons, Ltd.     

Flow resistance in steep mountain streams

Resistance to flow at low to moderate stream discharge was examined in five small (12–77 km² drainage area) tributaries of Chilliwack River, British Columbia, more than half of which exhibit planar bed morphology. The resulting data set is composed of eight to 12 individual estimates of the total resistance to flow at 61 cross sections located in 13 separate reaches of five tributaries to the main river. This new data set includes 625 individual estimates of resistance to flow at low to moderate river stage. Resistance to flow in these conditions is high, highly variable and strongly dependent on stage. The Darcy–Weisbach resistance factor (ff) varies over six orders of magnitude (0·29–12 700) and Manning's n varies over three orders of magnitude (0·047–7·95). Despite this extreme range, both power equations at the individual cross sections and Keulegan equations for reach‐averaged values describe the hydraulic relations well. Roughness is divided into grain and form (considered as all non‐grain sources) components. Form roughness is the dominant component, accounting for about 90% of the total roughness of the system (i.e., form roughness is on average 8.6 times as great as grain roughness). Of the various quantitative and qualitative form‐roughness indicators observed, only the sorting coefficient (σ = D₈₄/D₅₀) correlates well with form roughness. Copyright © 2008 John Wiley & Sons, Ltd.     

Experimental study of extreme shear stress for shallow flow under simulated rainfall

The raindrop impact and overland flow are two major factors causing soil detachment and particle transportation. In this study, the turbulent characteristics of the shallow rain‐impacted water flow were investigated using a 2‐D fibre‐optic laser Doppler velocimetry (FLDV) and an artificial rainfall simulator. The fluctuating turbulent shear stress was computed using digital data processing techniques. The experimental data showed that the Reynolds shear stress follows a probability distribution with heavy tails. The tail probability increases with an increase of rainfall intensity or raindrop diameter, and it decreases with an increase of Reynolds number. A modified empirical equation was derived using both the raindrop diameter and rainfall intensity as independent variables to provide a better prediction of the Darcy‐Weisbach friction coefficient f under rainfall conditions. Copyright © 2009 John Wiley & Sons, Ltd.     

A full-scale study of Darcy-Weisbach friction factor for channels vegetated by riparian species

In this article, an open channel flow resistance equation, deduced applying dimensional analysis and incomplete self-similarity condition for the flow velocity distribution, was tested using measurements carried out in a full-scale channel equipped with three types of riparian plants (Salix alba L., Salix caprea L. and Alnus glutinosa L.). In the experimental channel, having banks lined with boulders, the vegetation branches were anchored in a concrete bottom. For each species, the measurements were carried out with plants having different amounts of leaves, different plant density and plant area index. The relationship between the scale factor Γ of the velocity profile and the Froude number was separately calibrated by measurements carried out without and with vegetation. The component of Darcy-Weisbach friction factor corresponding to the riparian vegetation f_v was calculated as the difference between the measured friction factor value (channel grain roughness + vegetation) and that calculated for the channel without vegetation in the same hydraulic conditions. Using these f_v values, the relationship between the scale factor Γ and the Froude number was calibrated. In this last relationship, a scaling coefficient a varying with the investigated vegetation type was introduced. This coefficient, as expected, gives the highest friction factor values for vegetation having branches with leaves. The theoretical flow resistance law, coupled with the relationship for estimating the Γ function having a scaling coefficient different for each investigated vegetation type, allowed an accurate estimate of the Darcy-Weisbach friction factor (errors less than or equal to 20% for 82.6% of the investigated cases). Finally, for the investigated vegetation species that are characterized by a condition with few leaves or leafless, the scaling coefficient a resulted strongly related to the bending stiffness. This analysis demonstrated that the highest Darcy-Weisbach friction factors correspond to vegetation species characterized by the highest values of bending stiffness. The friction factor values calculated for this last condition are characterized by errors that were less than or equal to ±20% for 90.6% of cases.     

A low‐dimensional physically based model of hydrologic control of shallow landsliding on complex hillslopes

Hillslopes have complex three‐dimensional shapes that are characterized by their plan shape, profile curvature of surface and bedrock, and soil depth. To investigate the stability of complex hillslopes (with different slope curvatures and plan shapes), we combine the hillslope‐storage Boussinesq (HSB) model with the infinite slope stability method. The HSB model is based on the continuity and Darcy equations expressed in terms of storage along the hillslope. Solutions of the HSB equation account explicitly for plan shape by introducing the hillslope width function and for profile curvature through the bedrock slope angle and the hillslope soil depth function. The presented model is composed of three parts: a topography model conceptualizing three‐dimensional soil mantled landscapes, a dynamic hydrology model for shallow subsurface flow and water table depth (HSB model) and an infinite slope stability method based on the Mohr–Coulomb failure law. The resulting hillslope‐storage Boussinesq stability model (HSB‐SM) is able to simulate rain‐induced shallow landsliding on hillslopes with non‐constant bedrock slope and non‐parallel plan shape. We apply the model to nine characteristic hillslope types with three different profile curvatures (concave, straight, convex) and three different plan shapes (convergent, parallel, divergent). In the presented model, the unsaturated storage has been calculated based on the unit head gradient assumption. To relax this assumption and to investigate the effect of neglecting the variations of unsaturated storage on the assessment of slope stability in the transient case, we also combine a coupled model of saturated and unsaturated storage and the infinite slope stability method. The results show that the variations of the unsaturated zone storage do not play a critical role in hillslope stability. Therefore, it can be concluded that the presented dynamic slope stability model (HSB‐SM) can be used safely for slope stability analysis on complex hillslopes. Our results show that after a certain period of rainfall the convergent hillslopes with concave and straight profiles become unstable more quickly than others, whilst divergent convex hillslopes remain stable (even after intense rainfall). In addition, the relation between subsurface flow and hillslope stability has been investigated. Our analyses show that the minimum safety factor (FS) occurs when the rate of subsurface flow is a maximum. In fact, by increasing the subsurface flow, stability decreases for all hillslope shapes. Copyright © 2008 John Wiley & Sons, Ltd.     

Comment on “Overland runoff erosion dynamics on steep slopes with forages under field simulated rainfall and inflow by C. Li and C. Pan”

Managing sloping landscapes to control soil erosion processes due to rainfall and runoff is a relevant problem, especially when the vegetation is absent or sparse. The aim of this paper was to investigate the applicability of a theoretically resistance law for overland flow under simulated rainfall, based on a power-velocity profile, using field measurements carried out by Li and Pan for three plots with planted forage species (Astragalus adsurgens, Medicago sativa and Cosmos bipinnatus).The relationship between the velocity profile parameter Γ, the flow Froude number and the rain Reynolds number was calibrated using the data by Li and Pan. The obtained overland flow resistance law was also verified by independent field measurements carried out by Li and Pan in the same plots with the same forage species subjected to three different treatments (intact grass control IG, no litter or leaves NLL (only the grass stems and roots were reserved) and only roots remaining OR). The theoretical approach and the measurements carried out in the investigated conditions allowed to state that a) the Darcy-Weisbach friction factor can be accurately estimated using the proposed theoretical approach, b) the Darcy-Weisbach friction factor varies with rainfall intensity and c) for the investigated forage species, the vegetation treatment (IG, NLL, OR) does not significantly affect the flow resistance in laminar regime.