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12 February 2021 Effectiveness of a New Drainage System for Decreasing Erosion in Road Hillslopes
María Fernández-Raga, Iván García-Díez, Julian Campo, Julio Viejo, Covadonga Palencia
Author Affiliations +

Water is one of the most important erosive agents in roadside hillslopes. When these are built with ineffective drainage systems, erosion occurs, reducing road’s service life. However, these systems are not receiving the appropriate importance, given their strategic value. Therefore, a new drainage system called ‘branched’ is proposed in this study. Its technical and economic feasibility is compared with those of the traditional system, which consists of drainages with lines that follow maximum hillslope, to assess differences in relation to erosion, construction and maintenance costs, and service life. Different parameters were analysed, such as the average velocity of water (mm−1) running through the channels, its average specific energy (kJ), and its drag force (N). A scale model was constructed and used to test these factors before implementing it in natural terrain for testing it under field conditions. According to the theoretical and measured results, these factors were lower in the branched drainage than in the traditional one (from 24% to 34% in speed, from 37% to 60% in energy, and from 51% to 73% in force). The service life of hillslopes with a branched system of up to 0.5 m high and 1:2 grade is significantly longer than in those with a traditional drainage. Although the initial economic expense for the construction of the branched system is higher (∈3534/m3 as opposed to ∈2930/m3 for the traditional one), its maintenance cost will be lower than the traditional one (∈1230/m3 per year for the branched one as opposed to ∈1332/m3 per year for the traditional one). Consequently, under our experimental conditions, the proposed drainage will be profitable from the eighth year of construction, saving on the road maintenance in the following 15 years of service life.


Water is considered one of the most erosive agents on the roads and their adjacent hillslopes.1,2 Water erosion in hillslopes is a complex process that has been studied in numerous studies3,4 not only because of the environmental impact produced by soil loss5,6 but also because of the risks that could result from this loss, such as the pollution mixed with the water flowing down the hillslope,7,8 the expositions of humans to these pollutants,9 or the occurrence of landslide phenomena.10 Many exposed subsurface soils on eroded sites tend to be more erodible than the original soils because of their poorer structure and lower organic matter. And the steeper and longer the hillslope of a field, the higher the risk of erosion, due to the greater accumulation of runoff. Indeed, the consolidation of small fields into larger ones often results in longer hillslope lengths with increased erosion potential due to the increased velocity of water, which permits a greater degree of scouring (carrying capacity for sediment).3 In fact, the study of transport networks affected by erosion problems is gaining awareness as a very important topic in the scientific community.1114

To study erosion processes on the adjacent hillslopes of the roads, it is necessary to assess those factors that have been defined in the literature as the dominant ones: hillslope angle and length,1417 soil composition,18,19 hydraulic characteristics,20,21 soil moisture,2224 precipitation intensity and frequency,2527 vegetation cover,22,28,29 and connectivity30 of the channels of the drainage systems.

In Spain, this problem affects 166 003 km of roads with an annual investment in maintenance of up to ∈1058 million (2016).31 In the light of sustainable development, a coordinated multiscale policy should improve the effectiveness of mitigation of environmental degradation,32 which would consist of works made with environmentally friendly materials and with designs that increase the resistance and duration (to minimize contamination during repairs).32 However, traditional road design protocols lead to less dedication to innovative designs and more effort to maintenance. This maintenance expense is mainly dedicated to the cleaning of ditches and hillslope stabilization as a consequence of erosion. Due to these processes, accumulation of material in the channels of the drainage systems and in the roadside ditches is generated, as well as their flooding and hillslope instability that results due to the falling of stones.3337 All these factors may lead to landslides under certain conditions and may create serious problems such as the destruction of roads or the endangerment of human lives.3841

To minimize soil losses and to protect the hillslopes, different technical solutions can be applied.42 The selection of these solutions depends mainly on the economic resources available and the morphological, geological, and climatological conditions of the area. The most common technical solutions in Spain are concrete piles or screens with metal bolts, breakwater walls, concrete or gabion walls, geotextile or anchored triple-torsion metal mesh lining, drains and sub-drains, hydroseeding,43 concrete-ditch lining, and downspouts. However, all these measures mean an extra cost in the works, so in most of the Spanish road hillslopes only a superficial compaction of the removed soil takes place. After the eventual removal of topsoil and scarification of the surface, the re-compaction of the soil is done to a depth of about 15 to 20 cm, depending on the stability conditions. There are even cases where for temporary or economic reasons, it is not possible to compact the terrain, but after the first rain some land furrows arise, following lines of maximum hillslope. This system full of furrows, with soil compacted or not, but with lines of maximum hillslope will be called ‘traditional drainage system’. This lack of hillslope protection measures increases soil erosion as the terrain altered by humans is much more susceptible to be eroded.44

Another important parameter to take into account is the design of the hillslope and its coronation ditch (when this is planned to be built). This coronation ditch is always recommended because it is part of the drainage system and leads to the evacuation of water in an orderly manner, that is to say, directing the water strategically to avoid the creation of canals due to the concentration of water in the most vulnerable areas. This ditch is located at the top shoulder of the hillslope, and it collects and evacuates the water coming from its upper part towards the natural channels. The absence of this construction could mean the beginning of unwanted rills and ephemeral gullies along the hills. The precipitation which falls onto the hillslope tends to concentrate in certain evacuation channels also on the surface of the hillslope, which may coincide with areas of poorly resilient terrain, and if there is not an evacuation route for this water, it can also cause rock dragging and landslides in the more susceptible areas depending on the occurring conditions, such as sufficient land use, soil attributes like high organic matter content that leads to stronger soil aggregates, soil moisture, saturation, hillslope, and speed of vegetal covering. Sediment yield may then be increased in the road construction works and can lead to high maintenance costs. However, most of these problems could be avoided with an efficient drainage system that evacuates water in the least erosive possible way.30

Based on this, the design of a new drainage system is proposed. It is called ‘branched drainage’ and intends to minimize the erosion effects on the hillslopes, and consequently the maintenance costs. In this study, a comparison has been made between the traditional channels that follow maximum hillslope lines and the proposed branched drainage system to evaluate their technical viability, as well as the different production of sediments in both cases and the economic viability of the proposed new design in relation to the traditionally employed one. This can be used to evaluate the interest of proposing the new drainage system for new road and path works, which means influencing thousands of kilometres of road hillslope. The new drainage system is a great innovation in the traditional work on roads, given the lack of major advances in recent years and the lack of enough attention given to the prompt removal of water from many roads.

Material and Methods


Scaled model and field experiments

Two models were used to carry out the experimental tests. The first one is a model built in the laboratory at a scale of 1:100, made up of 2 exactly equal sides, in which the strata of a generic mountain in Spain can be observed; it has a breakwater in the lower stratum (15 m in power), gravel in the middle stratum (15 m in power), and earth in the upper stratum (10 m in power). Move to the sub-base of the road composed of selected soil (1.5 m thick) and the base composed of artificial gravel of 50 cm thick and hot asphalt mix of 20 cm thick. The sides of the model and its front have the most characteristic hillslope of the Spanish linear works with a hillslope of 30°45 and presents a representation of each of the 2 drainage systems to compare: the traditional and the branched one. Constant laminar flow rate is achieved thanks to a pump installed on the crest of the hillslope, with an AQUANIQUE FP 750 680 L/h pump (Figure 1D) in both cases.

Figure 1.

(A) Scale model of the 2 drainage systems studied: (B) traditional and (C) branched design and (D) pump AQUANIQUE FP 750 680 L/h.


To describe the hydraulic cycle, water is pumped from a tank below the coronation ditch so that, through the installed transversal drainage works, the water can reach both drainage systems that are installed on the hillslope in a parallel way.

A second model was built on a natural hillslope of the Monteleón Urbanization (42°39′00″N and 05°36′00″W), duplicating all the dimensions of the model (width, height, and length), but maintaining the same hillslope as the one in the model. In this way, it is possible to analyse the effect that the scale could have on the results. The soil selected was sandy loam and has a content of clay of 16%, with thick and weak granular structure, and soft structure. The top layer has few quartzite stones of 75 mm (7%), not altered. Many roots are medium, fine and very fine. This texture is complementary to the model experiments that are done in polyvinyl chloride (PVC) and in pure clay. This study was carried out in Leon (province of Leon), located in the region of Castilla y Leon, in the north-west of Spain (Figure 1). This is a transition zone between the 2 main climate areas in Spain: the continental and the Mediterranean areas. The precipitation is about 556 mm46 at about 840 m above sea level. Leon has a continental climate with long and cold winters and warm summers, but the main feature is a very irregular seasonal regime, which is greatly influenced by the Mediterranean climate. The rainiest seasons are spring and autumn, more precisely the months of April, May, and mid-December. Summer droughts are very common, with sporadic storm events, often with hail.47

The tests must be carried out under reproducible conditions, that is, with equal humidity and atmospheric pressure, and alternately in each drainage channel. To reduce possible accidental errors (eg, by manipulating the timer to measure times and calculate speeds), 30 tests are performed on each of the drainage systems.

Technical feasibility

In this article, with technical feasibility we refer to the determination of the factors that affect the erosive capacity of water. To achieve this value, different parameters that characterize the erosive power of the water are presented for both drainage systems such as the water average velocity, its average specific energy, and its drag force. All of these variables were calculated first theoretically and then experimentally to be sure that the experimental data collected were within the expected range.

First, a theoretical estimation of the mean velocity of water was done using the Manning equation48:


where S is the hillslope of the channel by 1 (m/m), n is the coefficient of resistance of the material (s−1), and Rh is the hydraulic ratio of the channel (m).

The average specific energy of the fluid (E) was calculated in metres of water column (m) with the following equation49:


where ‘v’ is the mean velocity of the water (m s−1) and ‘g’ is the gravitational constant of 9.81 m s−2.

The drag force was obtained from the following equation50:


where ‘Fa’ is the drag force (N), and ‘Cd’ is the drag coefficient for a particle in water. When Re (Reynolds number) is higher than 1000 and constant, Cd is approximately 0.5.51 All the experiments have Re > 1000 because the temperature, density, and viscosity of the water are constant.

A’ is the largest cross-sectional area depending on the drainage system (m2), ‘ρ’ is the density of the water (999.97 kg m−3), and ‘v’ is the mean velocity of the water measure in the experiments. The detailed computations and results can be consulted in full at data set from the University of León.52

First, the theoretical computations were performed to evaluate these characteristic parameters in both drainage systems. A detailed bibliographic review was carried out to find out how various authors advise the use of scale models as a method to simulate the processes occurring when water flows on a hillslope.5356 Therefore, a scale model 1/100 was constructed because it allows its easy handling and mobility.

Figure 1 shows the 2 drainage systems used: the traditional one, formed by a rectangular ditch that is usually used in the construction of roads, and the branched drainage, which is formed by 2 lateral ditches (perpendicular to the road direction) and central zigzag-shaped branches that drain into the lateral constructions. Both drainage systems were able to store the same volume of water. A 1:2 hillslope angle was selected because it is the angle recommended by the Spanish road regulations,57,58 besides being the most commonly used.55 To reduce the construction’s cost of the model, widely available materials such as PVC, silicone, and clay were used. These materials are impermeable, so simulation in this study would only simulate the runoff processes without representing the infiltration ones. This fact does not prevent the use of the model that has been used to represent conditions of saturated soil, where the runoff processes are dominant and the infiltration also decreases with increasing hillslope angle.23

After the construction of the model, velocity tests were started. These tests consisted of calculating the time it takes for a drop of water to travel the distance from the starting point of the drainage system to its end. Four drops of dye were poured into each of the tests, as shown in Figure 2. The chronometer was started when the first drop of the dye touched the water and stopped when the last drop of the dye reached the end of the system.

Figure 2.

Photographs of the tests performed for the calculation of the average water velocity over the traditional system on polyvinyl chloride (left) and the branched drainage on clay (right).


As the length of the drainage systems is known, the velocity was calculated using the elapsed time measured according to the following formula59:


where ‘v’ is the mean velocity of the water (m s−1), ‘e’ is the length of the channel (m), and ‘t’ is the travelled time (s). From the average velocity of the water, its average specific energy and drag force were calculated in both drainage systems.

To analyse whether the substrate modified the velocity, tests were carried out on a bed of clay moulded on the model with 3 mm of thickness. Finally, to evaluate the scale effects, tests were repeated in full scale on the loamy-clay soil of a hillslope located at 42°39′00″N, 05°36′00″W. The same hillslope angle of the model and a length of 0.5 m were used in these tests (Figure 3).

Figure 3.

Sampling in natural terrain: (A) detail of the traditional and branched drainage system and (B) detail of the slope and the system from its front.


Soil loss tests

To evaluate the soil’s erodibility of the hillslopes under both drainage systems, sediment collection tests were carried out. They consisted in collecting the soil entrained by the runoff water under controlled laminar flow in both drainage systems by means of filters, which were afterwards compared.

Thus, clay was moulded above the PVC channels in the model. A constant flow of 5 × 10−4 m3 s−1 was allowed to flow through both systems. At the end of each channel, a filter was installed and sediments were collected every 20 minutes for each corresponding period of time (Figure 4A). The filters were recollected after 80 minutes because before that time, the clay on the filters was negligible. This sampling was repeated 5 times in a row. The filters were then allowed to dry completely in a place without sunlight, at a constant temperature of 7°C, for 10 days. After this time, the pigments of the clay eroded by water and deposited on the filter could be observed. The method of comparing photographs using histograms of the filters with clay sediments was selected for this analysis. This is an objective method that is well suited to the goals of the experiment.60 The use of the gravimetric method has been ruled out because, on some occasions, the amount of clay collected on the filters was so small that it was very difficult to measure it exactly. The photographs of the filters were made with a Nikon D2X camera (shutter: 1/60, aperture: F4.2, focal length: 50 mm) at a height of 0.65 m with the aid of a tripod. Each of the photographs had a size of 4288 × 2848 pixels.

Figure 4.

Collection of filters for the soil loss tests in both drainage systems: (A) model and (B) natural terrain.


The software Adobe Photoshop CC 2015 was used for the treatment of the images, extracting the colorimetric histograms of each filter and comparing both the colour intensity and its dispersion. With this information, the evolution of erosion in each of the drainage systems was compared over time.

After performing these experiments in the model and to determine whether the scale influenced the sediment delivery, a field test was carried out on natural terrain. Measurements of each drainage system were adjusted to double in hillslope length than those used in the model. The experiment done with each drainage system was similar in hillslope and flow volume and discharge, but collecting the filters only once after 20 minutes of constant water flow under laminar regime over designs simulating both drainage systems in natural terrain because from the very beginning some soil was deposited on the filters. Ten sediment filters were collected for each system (Figure 4B). The number of tests performed was 2 times higher than the test performed with clay, due to the increased variability in the samples collected as a consequence of the greater possibilities of infiltration and sample losses. In this case, the method selected for the analysis of the filters was gravimetric. Each filter was weighed dry before field installation and then weighed with the collected sediment after being dried in an oven for 24 hours at 105°C (accuracy ± 0.1 mg).

Statistical analysis

Normality of the data was tested using Kolmogorov-Smirnov tests,61 and homogeneity of variances was tested using the Levene test.62 For the parametric analysis, differences in the studied variables (water average velocity, average specific energy, and drag force) between systems were established through an analysis of variance (ANOVA) test63 and confirmed a posteriori with Tukey tests.64 For non-parametric analysis, differences were determined by Mann-Whitney U test65 (M-W). In all the cases, results were considered to be statistically significant at P < .05. All statistical analyses were carried out using IBM SPSS Statistics 21.


Economic feasibility tests

Finally, to estimate the service life of both drainage systems, 10 tests were carried out measuring the time until the hydraulic structure loses the preferential channelling capacity and water evacuation, that is, when clay cover disappears in more than 5 cm from the drainage system. This experience was then repeated at full scale on the natural terrain by measuring the time required by each structure to lose 10 cm of soil. Ten tests were also performed on each system.

After estimating the service life of both drainage systems and considering the damages generated through time in both of them, an approximate calculation of the construction and maintenance costs of each system can be made. The initial investment, conservation costs, and execution time were determined depending on the factors such as hillslope angle and length, soil texture and composition, existing construction methodology, and available economic and labour resources. To calculate the costs of the construction and maintenance of both drainage systems, common parameters have to be established, which was a hillslope with a 1:2 angle and 25 m in length, built with clay loam textured soil by a foreman and a labourer. The cost of the initial investment of the traditional system, and of its annual maintenance, was estimated using the generic price database published by the Ministry of Public Works and Transport,66 and the software Presto. The approximate costs of the initial investment of the branched system were estimated by adding, to the initial investment of the traditional system, the economic expenses generated by the extra machinery and human resources needed for this construction of greater detail. For the estimation of maintenance costs in the branched system, it was taken into account that this design requires less maintenance because of the lower soil erosion generated and the increased resistance over time.


Technical feasibility

First, the theoretical velocity was calculated in PVC, clay, and natural terrain for both systems. The results obtained (2.26 and 1.58 m s−1 in PVC, 0.995 and 0.69 m s−1 in clay, and 0.754 and 0.525 m s−1 in natural terrain for traditional and branched systems, respectively) showed that over all cases, the velocity in the branched model was 30% lower than in the traditional one. Differences are even higher when the values of specific energy (between 38% and 60%) and drag force (about 52%) were calculated.

Table 1 shows the average velocity of the water, its average specific energy, and its drag force in both drainage systems, calculated experimentally using the travel time of the dye drops. Values are presented for the tests carried out in PVC and clay models. It can be observed that in the traditional drainage, a higher average velocity is obtained, which implies a higher specific energy and a higher drag force of the water. This difference is significant at 99% for all the experiments performed in PVC and clay, being always higher in the former than in the latter.

Table 1.

Experimental values of the average velocity of the water (m/s), the specific energy (water column in metres), and the drag force (N) obtained for the tests on PVC, clay, and natural terrain.


In the theoretical values, there are no standard deviation values because there is only 1 value of velocity. Abbreviations: ANOVA, analysis of variance; PVC, polyvinyl chloride.

These differences between the 2 systems on the model were also evidenced in field studies in the natural terrain. The average velocity of the dye drop was 0.146 ± 0.007 m s−1 in the traditional drainage and 0.090 ± 0.006 m s−1 in the branched one (39% lower). Thus, differences in velocity, energy, and drag force were significant at 99%.

Soil loss

Photographs of the 10 filters with collected sediments were taken according to the procedure described in section ‘Technical feasibility’. The study of their colorimetric histograms was focused on red because it was the predominant band in the clay. This allowed a cleaner analysis that was dedicated only to the searched values.

Filters collected during the first hour contained very little clay (Figure 5). Therefore, the first filter analysed corresponded to 80 minutes, where sediments were only observed in the traditional system. In the branched drainage, the first sediments were collected 40 minutes later, at 2 hours. The clay accumulation became more evident over time, and even small clay aggregates were present after 140 minutes in the traditional drainage filter and after 160 minutes in the branched one. The greatest change in the former appeared between 120 and 140 minutes, and in the latter between 140 and 160 minutes, coinciding with the appearance of clay aggregates.

Figure 5.

Photographs and colorimetric analyses of the filters collected in the soil loss test of the traditional system (left) and in the branched drainage system (right) when the tests were carried out in the clay model.


On the contrary, data from soil loss tests performed on natural terrain at real scale are non-parametric, and according to the Mann-Whitney U test there are no significant differences between the collected weights (Table 2). In addition, it can be stated that over time, the branched drainage system showed less erosion (lower sediment transport).

Table 2.

Kolmogorov-Smirnov tests of the average weight of filters with sediment collected from traditional and branched drainage systems, on dry and wet days.


Tests were carried out on natural terrain at real scale. Mann-Whitney and ANOVA test values were obtained. Abbreviation: ANOVA, analysis of variance.

A different response was observed between dry days (without rain on previous days) and wet days (after rain on previous days) on field experiments. Tests carried out on wet days showed the highest difference in sediment production between drainage systems, with the amount being collected from the traditional one being much larger. Based on this, it is possible to expect a better performance of the branched drainage in climates with higher probability of precipitation. However, much more tests with different meteorological conditions have to be performed to confirm this hypothesis.

Economic feasibility

Both drainage systems presented different erodibilities according to the results of the 20 service life tests performed. The scale model of the traditional system needed 18 cycles of 20 minutes each to present severe structural damage, whereas the new branched drainage withstood up to 24 cycles. Accordingly, it is assumed that the service life of a road hillslope with traditional drainage would be approximately 20 years, whereas the same hillslope under a branched drainage design would last up to 25 years, with both service life periods being significantly different (at 99%).

It was also detected that the damages occurred in different areas of both systems: in the upper part in the traditional drainage, under the coronation ditch, whereas in the branched one, damages occurred in the changes in direction (Figure 6).

Figure 6.

(A) Last stage of the service life of the traditional system and (B) noticeable erosion on the branched drainage.


When the 20 tests were carried out on natural terrain at real scale, there was a small decrease in the service life difference between the 2 systems, although significant differences were still found (P < .05). Table 3 shows the estimated service life of both drainage systems in the scale model on clay and in the natural terrain at real scale. It can be observed that the branched system withstood 128 minutes more, in average, than the traditional one, which corresponds to an increase of about 3 years. However, a higher number of tests are necessary to be able to define accurately how long this service life would be extended. Comparisons could not be made because there are no authors who have experimented with the branched design due to its originality.

Table 3.

Kolmogorov-Smirnov tests on the estimated service life of the traditional and branched drainage systems in the scale model on clay and in the natural terrain at real scale.


Table 4 shows the execution time, the initial investment for construction, the maintenance cost, and the estimation of the service life for both drainage systems. To compare their cost, maintenance expenses of each year were added to the initial investment made in year 0. After 8 years, the costs of implementing both systems would be approximately ∈4.35/m3. From this moment, the higher costs of the initial execution of the branched system would be amortized by the annual savings related to the lower maintenance expenses required (Figure 7). Therefore, the branched drainage would become profitable during the remaining 15 years of service life.

Table 4.

Execution time, initial investment for construction, maintenance cost, and estimation of the service life of both drainage systems.


Figure 7.

Accumulated expenses during years. Each line represents the sum of the expenses in the construction plus the maintenance.


All the results have been carried out under controlled conditions so that both drainage systems had to be protected from the same erosive capacity. However, we know that the conditions in field conditions change a lot because they are influenced by changes in precipitation, overland flow, infiltration, or extreme events. Nonetheless, only small modifications have been applied in field studies because the tests were carried out over a month, and in that month the natural precipitation was not used for sampling but it did cause the soil to be sometimes dry and sometimes wet. We performed 30 trials to have a sufficient number of data for statistical analysis.

When comparing the traditional system with the branched one, it should be born in mind that the former has a number of advantages such as greater hydraulic capacity, shorter drainage time, and lower initial investment. On the contrary, the latter is able to reduce the average water velocity and dragging capacity, minimizes erosion, and has a longer service life.


According to the obtained results, the theoretical average velocity of water was higher than the one obtained experimentally with the scale model in PVC. This may be due to the fact that the theoretical calculations were done using the Manning’s general equation for open channel hydraulic, which does not take into account localized load losses or regime changes that occur along the drainage systems and can vary the water velocity drastically. Problems in applying this equation to a runoff model have been reported elsewhere.67

When exploring the data acquired from the PVC model, the water velocity in the branched system is much lower than that in the traditional one. This velocity is reduced as a result of the energy dissipation caused by the changes in fluid direction of the new drainage proposed. This decrease has been heightened by the increase in the water surface tensions with the walls of the new geometry. Besides this, it was necessary to use much more silicone to join the higher number of joints in the channels of the branched system model. According to Arakawa,68 the use of silicone could result in the increase in water friction with the channel and, therefore, a decrease in its average velocity.

The analysis of the model on clay pointed to pronounced differences between both systems, albeit to a lesser extent. It is probably due to the effects of a higher vorticity produced by a generalized friction along the entire surface of the canal,69,70 which caused a decreased velocity. In addition, another aspect to take into account would be the greater depth of the branched drainage compared with the traditional one (with the objective of keeping the same hydraulic capacity in both systems). Some authors have stated that the greater the depth, the greater the vorticity.71

When these analyses were performed in the natural terrain at real scale, differences between the 2 systems were also important like the ones found in the experiment with PVC and clay (around 25%-35% more velocity in the traditional drainage than in the branched one, in both clay and natural terrain). However, the values of velocity detected between the clay and the terrain experiments were a bit larger than those in the terrain. These differences were probably due to the influence of the scale of the experiment and also because of the scarce water infiltration of the model. However, in a clay loamy soil, part of the water could infiltrate and modify the results widely.22 There are authors who do not agree with this statement, indicating that infiltration does not affect the velocity of surface water.72 Moreover, another aspect that changes considerably is the presence of a coronation ditch on the top of the model hillslope and its lack in the natural terrain.44 This aspect modifies the distance between streams of both systems, which is an essential aspect for landslides, which in turn varies their erodibility.73

Human error, when measuring, must also be taken into account, especially in the measures carried out on a small space as the scale model. The mistake that can be made in the reaction time with respect to the total time of measurement can mean a high percentage. However, it should be noted that all measurements were always made by the same researcher, and in all cases they coincided in pointing to a significant velocity decrease in the branched system. It is also necessary to bear in mind the higher difficulty of differentiating colours in a darker background flow (ie, clay) or in a more turbulent one (ie, natural terrain) due to irregularities of the terrain. Despite these difficulties, differences were always significant at 99%.

Based on the erosion tests, sediment yield from the traditional system was higher than from the branched one. This can be related to the wider drainage channel of the former that enables a greater entrainment of fine particles.74 Another explanation to this difference was suggested by Kanjanakaroon et al,75 who found that the deeper the channel, the easier the head-cut erosion development. However, in this study, although the water level is deeper in the proposed branched system, its erosion yield was lower. This means that the protection produced by the new geometry of the branched design is higher than the effect of its deeper channel.

When comparing the sediment yields measured in the natural terrain, it is possible to think that there is an influence produced by small variations in very local hillslope angles (due to irregularities in the terrain). However, they would be negligible in any case according to Kanjanakaroon et al,75 who stated that there are no significant differences between the sediment yields of a hillslope whose angle was modified from 1:1 to 1:1.5 or 1:2.

Sediment yield in the clay channel was higher after about 2 hours. This fact is not in agreement with the results of other authors who stated that the highest sediment yield occurs at the onset of rainfall episodes.25 However, it may be related to the protective effect of clay in which significant erosion is produced only after a hole is opened in the drainage.76

Erosion in the clay loamy soil was much higher77 in both drainage systems. The first type of erosion that occurred was the sheet erosion that was responsible for detaching and delivering the most superficial particles of sand due to small collapses in the upper canals that carry the water, which produce a small amount of water which could flow freely down the hillslope into the field experiment. This laminar erosion was not collected or assessed in this study because our interest was within the drainage systems only. Then, rill erosion was produced within the channels of the drainage systems, removing sand and clay particles. This erosion was detected thanks to the abundant collection of particles and sand retained in the filters and transporting pebbles, boulders, and, finally, larger stones. These processes were partially observed in the natural terrain experiments, although due to the small number (10 in each drainage system) and short duration of such tests, it was not possible to quantify their magnitude.

Finally, regarding the study carried out on the estimation of service life and economic feasibility of the branched system, the increased resistance detected throughout all the experiences performed supports strongly the new design. This resistance could be explained by the marked decrease in water velocity caused by the hydraulic jumps and vorticity associated with the branched pattern.70 This effect could also be responsible for the delay in the production and transport of sediment in this system.

In the traditional drainage, the breakdown occurred in the upper part of the system, probably because of a small hydraulic jump that originated in the joint of the coronation ditch with the hillslope drainage (Figure 6), which is the more sensible zone of this design.78 Despite this finding, some authors degrade the hydraulic jump height and the water velocity as the main causes of this erosion, highlighting soil composition as the key responsible.18

On the contrary, the breakdown in the branched system could be observed at the intersections, resulting in collapsed zones on the sides of the zigzag (Figure 6). This erosion could be produced by water friction against the perimeter, which is the origin of the shear layer and the source of vorticity.79 These erosion zones would vary in intensity depending mainly on the scale size and their behaviour as viscous or Newtonian fluid,80 the channel depth,26 or the regime type.81

It should be noted that in any of the 2 drainage systems studied, it was observed that breakdown happened from the base of the hillslope as several authors have stated.82,83 In addition, the results could vary between the scale model and the natural terrain tests, because in the former there was an upstream ditch, whereas in the latter, water was not channelled.44 This fact modified the length between streams, which in turn varied the susceptibility to erosion and hillslope landslides.73

As discussed by Salbego et al,84 the use of preventive measures to protect road hillslopes from erosion is 30% more economical than applying passive or emergency measures a posteriori. Accordingly, the use of the branched drainage, instead of the traditional one, can be considered a preventive measure against erosion in road hillslopes. This new design would need a higher initial investment, but its lower maintenance costs together with its longer service life make his system a very suitable and cheaper measure to be used in the construction of road networks.

Indeed, there is room for improvements in this research. The next step will be the analysis of subsurface lateral flow and infiltration, which was not analysed in this experiment. The aim of this article was to design a drainage system that generates less erosive impact, and this objective has been completed. The design of an experiment with infiltration would have introduced a greater number of variables that would have made the comparison of both drainage systems very difficult, due to the enormous variability in the infiltration existing in the studied soil. However, an experiment is underway to design another model which will allow a new comparison, this time taking into account these lateral flow and infiltration effects, and whose results could then be adapted to field experiments.

Another interesting question that we would be able to answer in the future would be how these 2 drainage systems will behave under extreme events, but the design of the possible method to carry out these stress tests is something that is still in the validation phase, with experts to select the best way to test it.


Theoretical results pointed out that in the branched drainage, the average velocity of water was lower, and therefore its specific energy and drag force were also lower than in the traditional system. This result was confirmed in tests carried out in a scale model built on PVC, on clay, and, to a lesser extent, in the natural terrain. In both drainage systems studied, the longer the time that water flows, the more erosion occurs. Nevertheless, in the traditional one, the first clay aggregates started being eroded at 2 hours, whereas in the branched one, sediments appeared at 2 hours and 20 minutes. These sediments were delivered off-site to filters used to collect them 40 minutes later in the latter than in the former. Therefore, the higher resistance to erosion of the branched drainage is more noticeable the longer the water flows. In the experiments performed in the natural terrain, mean velocity of the water, its specific energy, and dragging force in the branched drainage were also lower than in the traditional system. Accordingly, sediment yield in the latter was higher than in the former. A slight influence of the environmental humidity has been found in the gravimetric tests. A greater number of experimental tests will be needed to obtain definitive values. If water flows over clay, the estimated service life of the branched drainage may be 5 years longer than that of traditional drainage or about 3 years on natural terrain. Although the initial investment of the branched design is higher than the one of the traditional system, its construction is economically feasible in hillslopes with a hillslope angle of 1:2, being profitable from the eighth year, which can represent economic savings in the following 15 years of service life. Consequently, the use of the proposed branched drainage, instead of the traditional one, can be considered a preventive, very suitable, and cheaper measure to be used in the construction of road networks. It is recommended to carry out further complementary experiments that consider the impact of lateral flows and extreme events in the comparison of both drainage systems.

Author Contributions

María Fernández-Raga: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Supervision, Visualization,Writing - original draft, Writing - review & editing. Iván García Díez: Conceptualization, Data curation, Formal analysis, Investigation, Writing - original draft. Julian Campo: Writing - original draft, Writing - review & editing. Julio Viejo: Funding acquisition, Investigation. Covadonga Palencia: Formal analysis, Investigation, Writing - review & editing.



Guerra AJT , Fullen MA , Jorge MDO , Bezerra JFR , Shokr MS . Slope processes, mass movement and soil erosion: a review. Pedosphere. 2017;27:27–41. Google Scholar


Palancar-Penella M. The water framework directive. Critical commentary [in Spanish]. Eng Territ. 2007;80:88–95. Google Scholar


Norman LM. Ecosystem services of riparian restoration: a review of rock detention structures in the Madrean archipelago ecoregion. Air Soil Water Res. 2020;13:1–13.doi: Google Scholar


Rodrigo Comino -J , Giménez Morera -A , Panagos P , Pourghasemi HR , Pulido M , Cerdà A . The potential of straw mulch as a nature-based solution for soil erosion in olive plantation treated with glyphosate: a biophysical and socioeconomic assessment. Land Degrad Dev. 2020;31:1877–1889. doi: Google Scholar


Fernández-Raga M , Fraile R , Keizer JJ , et al. The kinetic energy of rain measured with an optical disdrometer: an application on splash erosion. Atmos Res. 2010;96:225–240. doi: Google Scholar


Fernández-Raga M , Palencia C , Keesstra SD , et al. Splash erosion: a review with unanswered questions. Earth-Sci Rev. 2017;202:268–275. doi: Google Scholar


Kumar Rajneesh Kumar V , Sharma A , Singh N , et al. Assessment of pollution in roadside soils by using multivariate statistical techniques and contamination indices. SN Appl Sci. 2019;1:842. doi: Google Scholar


Vargas-Pineda OI , Trujillo-González JM , Torres-Mora MA. Supply–demand of water resource of a basin with high anthropic pressure: case study Quenane-Quenanito Basin in Colombia. Air Soil Water Res. 2020;13:1–10. doi: Google Scholar


Brevik EC , Slaughter L , Singh BR , et al. Soil and human health: current status and future needs. Air Soil Water Res. 2020;13:1–23. doi: Google Scholar


Stanley T , Kirschbaum DB. A heuristic approach to global landslide susceptibility mapping. Nat Hazards. 2017;87:145–164. Google Scholar


Hearn G. Managing road transport in a world of changing climate and land use. Proc InstCivil Eng. 2016;169:146–159. Google Scholar


Hearn GJ , Shakya NM. Engineering challenges for sustainable road access in the Himalayas. Q J Eng Geol Hydroge. 2017;50:69–80. Google Scholar


Petrucci O. The assessment of damage caused by historical landslide events. Nat Hazard Earth Sys. 2013;13:755–761. Google Scholar


Sofia G , Tarolli P. Automatic characterization of road networks under forest cover: advances in the analysis of roads and geomorphic process interaction. Rendiconti Online Soc Geol Ital. 2016;39:23–26. Google Scholar


Keramaris E. Effects of inclined impermeable bed on the turbulent characteristics of the flow using particle image velocimetry. J Turbul. 2015;16:540–554. Google Scholar


Lin GF , Chang MJ , Huang YC , Ho JY. Assessment of susceptibility to rainfall-induced landslides using improved self-organizing linear output map, support vector machine, and logistic regression. Eng Geol. 2017;224:62–74. Google Scholar


Masumian A , Naghdi R , Zenner EK. Effectiveness of water diversion and erosion control structures on skid trails following timber harvesting. Ecol Eng. 2017;105:370–378. Google Scholar


Babazadeh H , Ashourian M , Shafai-Bajestan M. Experimental study of headcut erosion in cohesive soils under different consolidation types and hydraulic parameters. Environ Earth Sci. 2017;76:438. Google Scholar


Keramaris E. Turbulent structure in uniform inclined open channel flow over different rough porous beds. Int J Sediment Res. 2017;32:45–52. Google Scholar


Di Stefano C , Ferro V , Palmeri V , Pampalone V . Measuring rill erosion using structure from motion: a plot experiment. Catena. 2017;156:383–392. Google Scholar


Hadadin N. Variation in hydraulic geometry for stable versus incised streams in the Yazoo River basin – USA. Int J Sediment Res. 2017;32:121–126. Google Scholar


Liu YJ , Hu JM , Wang TW , Cai CF , Li ZX , Zhang Y. Effects of vegetation cover and road-concentrated flow on hillslope erosion in rainfall and scouring simulation tests in the Three Gorges Reservoir Area, China. Catena. 2016;136:108–117. Google Scholar


Yubonchit S , Chinkulkijniwat A , Horpibulsuk S , Jothityangkoon C , Arulrajah A , Suddeepong A. Influence factors involving rainfall-induced shallow slope failure: numerical study. Int J Geomech. 2017;17:1–13. Google Scholar


Zheng YW , Hatami K , Miller GA. Numerical simulation of wetting-induced settlement of embankments. J Perform Constr Fac. 2017;31:993. Google Scholar


Navarro-Hevia J , Lima-Farias TR , de Araujo JC , Osorio-Pelaez C , Pando V. Soil erosion in steep road cut slopes in Palencia (Spain). Land Degrad Dev. 2016;27:190–199. Google Scholar


Paik J , Escauriaza C , Sotiropoulos F. Coherent structure dynamics in turbulent flows past in-stream structures: some insights gained via numerical simulation. J Hydraulic Eng. 2010;136:981–993. Google Scholar


Woldie DW , Sidle RC , Gomi T. Impact of road-generated storm runoff on a small catchment response. Hydrol Process. 2009;23:3631–3638. Google Scholar


Persichillo MG , Bordoni M , Meisina C. The role of land use changes in the distribution of shallow landslides. Sci Total Environ. 2017;574:924–937. Google Scholar


Seutloali KE , Beckedahl HR. Understanding the factors influencing rill erosion on roadcuts in the south eastern region of South Africa. Solid Earth. 2015;6:633–641. Google Scholar


Sosa-Perez G , MacDonald L. Wildfire effects on road surface erosion, deposition, and road-stream connectivity. Earth Surf Proc Land. 2017;42:735–748. Google Scholar


Mosconi EM , Colantoni A , Gambella F , Cudlinová E , Salvati L , Rodrigo-Comino J. Revisiting the environmental Kuznets curve: the spatial interaction between economy and territory. Economies. 2020;8:74. doi: Google Scholar


Budetta P , De Luca C , Nappi M . Quantitative rockfall risk assessment for an important road by means of the rockfall risk management (RO.MA.) method. B Eng Geol Environ. 2016;75:1377–1397. Google Scholar


Moos C , Dorren L , Stoffel M. Quantifying the effect of forests on frequency and intensity of rockfalls. Nat Hazard Earth Sys. 2017;17:291–304. Google Scholar


Singh PK , Kainthola A , Panthee S , Singh TN. Rockfall analysis along transportation corridors in high hill slopes. Environ Earth Sci. 2016;75:441. Google Scholar


Yuan JK , Li YR , Huang RQ , Pei XJ. Impact of rockfalls on protection measures: an experimental approach. Nat Hazard Earth Sys. 2015;15:885–893. Google Scholar


Zhang L , Lambert S , Nicot F. Discrete dynamic modelling of the mechanical behaviour of a granular soil. Int J Impact Eng 2017;103:76–89. Google Scholar


Almeida S , Holcombe EA , Pianosi F , Wagener T. Dealing with deep uncertainties in landslide modelling for disaster risk reduction under climate change. Nat Hazard Earth Sys. 2017;17:225–241. Google Scholar


Canolu MC. Deterministic landslide susceptibility assessment with the use of a new index (factor of safety index) under dynamic soil saturation: an example from Demircikoy watershed (Sinop/Turkey). Carpath J Earth Env 2017;12:423–436. Google Scholar


Raspini F , Bardi F , Bianchini S , et al. The contribution of satellite SAR-derived displacement measurements in landslide risk management practices. Nat Hazards. 2017;86:327–351. Google Scholar


Sepulveda SA , Petley DN. Regional trends and controlling factors of fatal landslides in Latin America and the Caribbean. Nat Hazard Earth Sys. 2015;15:1821–1833. Google Scholar


Rodrigo-Comino J , López-Vicente M , Kumar V , et al. Soil science challenges in a new era: a transdisciplinary overview of relevant topics. Air Soil Water Res. 2020;13:1–17. doi: Google Scholar


Gyasi-Agyei Y. Cost-effective temporary microirrigation system for grass establishment on environmentally sensitive steep slopes. J Irrig Drain Eng. 2004;130:218–226. Google Scholar


Cao LX , Zhang KL , Liang Y. Factors affecting rill erosion of unpaved loess roads in China. Earth Surf Proc Land. 2014;39:1812–1821. Google Scholar


Suárez J. , Landslides and Slope Stability in Tropical Areas [in Spanish]. Bucaramanga, Colombia: UIS; 1998. Google Scholar


Fernandez-Raga M , Castro A , Marcos E , Palencia C , Fraile R. Weather types and rainfall microstructure in Leon, Spain. Int J Climatol. 2017;37:1834–1842. doi: Google Scholar


Fernandez-Raga M , Castro A , Palencia C , Calvo AI , Fraile R. Rain events on 22 October 2006 in Leon (Spain): drop size spectra. Atmos Res. 2009;93:619–635. Google Scholar


Manning R , Purser Griffith J , Pigot TF , Vernon-Harcourt L . On the Flow of Water in Open Channels and Pipes. Dublin: Transactions; 1890. Google Scholar


Aguera-Soriano J . Mechanics of Incompressible Fluids and Hydraulic Turbomachines, 5ª ed. Ciencia 3 .SL. EDITORIAL; 2002. Google Scholar


Russell BFRS , Whitehead AN . Newton’s Principia Mathematica (Section 7, Book 2, Proposition 37). Cambrige University Press; 1910. Google Scholar


Chanson H. , Flow Hydraulics in Open Channels [in Spanish]. Bogotá, Colombia: McGraw-Hill; 2002. Google Scholar


García-Diez I . Design and Evaluation of a New Drainage System for the Linear Works [PhD thesis]. León, Spain: University of León. Google Scholar


Bachmann D , Bouissou S , Chemenda A. Influence of weathering and pre-existing large scale fractures on gravitational slope failure: insights from -D physical modelling. Nat Hazard Earth Sys. 2004;34:711–717. Google Scholar


De Schepper G , Therrien R , Refsgaard JC , He X , Kjaergaard C , Iversen BV. Simulating seasonal variations of tile drainage discharge in an agricultural catchment. Water Resour Res. 2017;53:3896–3920. Google Scholar


Eli RN , Gray DD. Hydraulic performance of a steep single layer riprap drainage channel. J Hydraulic Eng. 2008;134:1651–1655. Google Scholar


Guo JCY , MacKenzie KA , Mommandi A . Flow interception capacity of inclined grate. J Irrig Drain Eng. 2016;142:1–5. Google Scholar


Escario V . Land Clearing. State of the Art of This Technique [in Spanish]. 1981. MOPU Publication services. Google Scholar


Fomento. Spanish Ministry of Public Works and Transport. General technical specifications for road and bridge works [in Spanish]. 1976. Google Scholar


Newton I. , Philosophiæ naturalis principia mathematica typis. Geneva, Switzerland: Barrillot & Filii; 1687. Google Scholar


Camacho GE , Fierro AMB . Potential non-invasive colorimetric test for the analysis of human tears [in Spanish]. Univ Méd. 2013;54:199–208. Google Scholar


Kolmogorov A. Italian Giornale dell’Istituto Italiano degli Attuari. Gorn Inst Ital Att. 1933;4:83–91. Google Scholar


Levene H . Robust tests for equality of variances. In Olkin I , Hotelling H , eds. Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling. Stanford, CA: Stanford University Press; 1960:278–292. Google Scholar


Fisher RA. , Statistical Methods for Research Workers. Edinburgh: Oliver & Boyd; 1925. Google Scholar


Tukey JW. , Exploratory Data Analysis. Reading, MA: Addison-Wesley; 1977. Google Scholar


Mann HB , Whitney DR. On a test of whether one of two random variables is stochastically larger than the other. Ann Math Statist. 1945;18:50–60. Google Scholar


Fomento. Spanish Ministry of Public Works and Transport. General price base for platform projects [in Spanish]. 2008. Google Scholar


Nearing MA , Polyakov VO , Nichols MH , et al. Slope-velocity equilibrium and evolution of surface roughness on a stony hillslope. Hydrol Earth Syst Sci. 2017;21:3221–3229. Google Scholar


Arakawa K. Dynamic sliding friction and similarity with Stokes’ law. Tribol Int. 2016;94:77–81. Google Scholar


de Dios M , Bombardelli FA , Garcia CM , Liscia SO , Lopardo RA , Parravicini JA. Experimental characterization of three-dimensional flow vortical structures in submerged hydraulic jumps. J Hydro Environ Res. 2017;15:1–12. Google Scholar


Wang H , Leng XQ , Chanson H. Hydraulic jumps and breaking bores: modelling and analysis. Proc Inst Civil Eng. 2017;170:25–42. Google Scholar


Park MC. Behavior analysis by model slope experiment of artificial rainfall. Nat Hazard Earth Sys. 2016;16:789–800. Google Scholar


Herrera-Granados O , Kostecki SW. Experimental study of the influence of small upward seepage on open-channel flow turbulence. J Hydraulic Eng. 2017;143:06017009. Google Scholar


Fan W , Wei XS , Cao YB , Zheng B. Landslide susceptibility assessment using the certainty factor and analytic hierarchy process. J Mt Sci. 2017;14:906–925. Google Scholar


Selkimaki M , Gonzalez-Olabarria JR. Assessing gully erosion occurrence in forest lands in Catalonia (Spain). Land Degrad. Dev. 2017;28:616–627. Google Scholar


Kanjanakaroon P , Ekkawatpanit C , Wongsa S , Israngkura U , Kositgittiwong D. Effects of embankment breach position on characteristics of failure. Paper presented at: Proceedings of the 36th IAHR World Congress: Deltas of the Future and What Happens Upstream; 28 June-3 July 2015; The Hague, The Netherlands. The Hague, The Netherlands: IAHR; 2015:4714–4723. Google Scholar


Zhang Q , Zhang XF . Research on incipient motion and erosion features of artificial filling clay. Archit Eng New Mater. 2015:362–371. Google Scholar


Charru F , Mouilleron H , Eiff O. Erosion and deposition of particles on a bed sheared by a viscous flow. J Fluid Mech. 2004;519:55–80. Google Scholar


Najafi-Nejad-Nasser A , Li SS. Reduction of flow separation and energy head losses in expansions using a hump. J Irrig Drain Eng. 2015;141:9. Google Scholar


Zhang GF , Wang H , Chanson H. Turbulence and aeration in hydraulic jumps: free-surface fluctuation and integral turbulent scale measurements. Environ Fluid Mech. 2013;13:189–204. Google Scholar


Li YW , Li ZY. Numerical modelling of multi-step energy dissipation facility in rushing trough. Appl Mech Mater. 2011;94:606–612. Google Scholar


Haynes PH , Johnson ER , Hurst RG. A simple model of Rossby-wave hydraulic behavior. J Fluid Mech. 1993;253:359–384. Google Scholar


Regmi RK , Jung K , Nakagawa H , Kang J. Study on mechanism of retrogressive slope failure using artificial rainfall. Catena. 2014;122:27–41. Google Scholar


Tohari A , Nishigaki M , Komatsu M. Laboratory rainfall-induced slope failure with moisture content measurement. J Geotech Geoenviron. 2007;133:575–587. Google Scholar


Salbego G , Floris M , Busnardo E , Toaldo M , Genevois R . Detailed and large-scale cost/benefit analyses of landslide prevention vs. post-event actions. Nat Hazard Earth Sys. 2015;15:2461–2472. Google Scholar
© The Author(s) 2021 This article is distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 License ( which permits non-commercial use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access page (
María Fernández-Raga, Iván García-Díez, Julian Campo, Julio Viejo, and Covadonga Palencia "Effectiveness of a New Drainage System for Decreasing Erosion in Road Hillslopes," Air, Soil and Water Research 14(1), (12 February 2021).
Received: 10 September 2020; Accepted: 29 December 2020; Published: 12 February 2021
branched drainage
traditional drainage
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