Effect of sediment gradation on scour by symmetric crossing jets: an experimental investigation Open Access

diameter of the pipe

acceleration due to gravity

total discharge in the main pipe

distance between the jets crossing point and the water surface

velocity of the jets

equivalent single pipe having a cross-sectional area equal to the total cross-sections of two jet pipes

particle size

densimetric particle Froude number

tailwater depth

ending location of the ridge relative to the hole origin

length of the scour hole

width of the scour hole

maximum depth of the scour hole

water density

sediment density

water dynamic viscosity

one of the dimensions of the scour hole

crossing angle between the jets

vertical angle of the jet

sediment non-uniformity parameter

One of the main concerns of the dam hydraulic structures is the scouring. For the dissipation of the flow energy from the dam, we use the plunge pools. The jet impingement to the river bed may lead to the scour hole, which gradually becomes large enough to endanger the dam structure. This could be problematic for the dam stability; hence, this issue needs to be addressed. The scour may lead to severe damage to a dam or its neighboring structures. The symmetric crossing jets in the dam orifices are commonly used to waste the jet energy, the scouring can occur downstream of these structures. Therefore, an accurate prediction of the scour formed by these kinds of jets is essential.

The majority of the previous research pertains to the single jet, and few studies have been conducted on the scour by crossing jets. Pagliara et al. (2006) conducted experiments to understand the two-dimensional scour of a single jet. It was observed that the densimetric Froude number had the main role in the plunge pool scour. Pagliara et al. (2008) studied the laboratory 3D scour of the plunge pool based on a previous study and developed its results for the 3D state. Pagliara et al. (2009) conducted experiments by investigating the effect of air entrainment on the scour to develop relationships for describing the main scour geometric features and longitudinal scour profiles. Pagliara & Palermo (2008) conducted a laboratory study to understand the hydraulics of the two-dimensional scour with protective structures; it was observed that the existence of the structure is a limiting factor for the development of the scour length, leading to a deeper hole. Pagliara et al. (2010) conducted a study to investigate the hydraulics of 3D scouring with protective measures; the results showed that the protective structure made the scour more complicated and led to the different types of scour holes. Research on employing protective measures for the scour reduction can also be seen in other hydraulic structures (Karami et al. 2011, 2017; Daneshfaraz et al. 2019).

Kartal & Emiroglu (2022) studied the scour topography by oblique plunging jets with circular nozzles. The topographic changes, maximum scour depth, volume of scour hole and upstream and downstream slopes of scour hole were studied. The results showed that the impingement angle and the densimetric Froude number influenced the scour form. Palermo et al. (2021) applied a theoretical method to the scour process by plunging jets. Their study focused on the time-evolution process and the equilibrium configuration for a wide range of hydraulic structures. They concluded that the scour at small scale is consistent with that at large scale. Taştan et al. (2016) investigated the effect of the thickness of the non-cohesive sediment layer on the depth of the scour caused by a water jet; the results indicated that the scour depth increases with the bed-sediment layer thickness. Chen et al. (2022a) conducted research on the scour of sand beds by submerged vertical jets with various jet diameters, distances, and velocities. They observed similar scour profiles in the asymptotic state, and models for temporal prediction of scour depth were proposed. Chen et al. (2022b) studied the scour morphology of submerged oblique jets with time. They investigated the effects of the flow velocity and water depth on the scour hole dimensions, and concluded that the scour depth, length, and width at the initial stage of scour formation changes suddenly.

Examples of the research on the scour due to multiple jets can be mentioned. Latifi et al. (2018) studied the scour from the free-falling jet combined with a bottom outlet; the results were compared with the single jet, which demonstrated that the combined jet led to the lower scour depth and ridge height. Pagliara et al. (2011) investigated the scour by two crossing jets utilizing a uniform sediment sample with a geometric standard deviation of 1.17. They observed that at all crossing angles the scour depth decreases with increasing the tailwater depth. Pagliara & Palermo (2013) studied the 3D scour by the two aerated crossing jets; they observed that the air in the jets changes the scour shape. Pagliara & Palermo (2017) studied the effect of vertical non-crossing jets by locating the virtual crossing point beneath the bed; they concluded that the virtual crossing point is an essential parameter in the scour shape. Pagliara et al. (2012) analyzed the impact of vertical jets colliding at different angles and provided relationships to predict the main parameters of the scour geometry, including the maximum scour depth, scour hole length and scour hole width. Li et al. (2006) studied the impact of multiple jets on the scour formed downstream of the Xiluodu power plant on the Yangtze River. A hybrid model combining physical and numerical models was used to simulate the velocity field with several jets. The scour characteristics downstream of the river bed were predicted and analyzed by jets based on the characteristics of the calculated velocity field. Lencastre (1982) studied both hydraulic and scour profiles in the presence of crossing jets. He used a method based on the momentum equation, and his experiments were conducted only for jets in different vertical positions. Uyumaz (1988) conducted a study to investigate the scour downstream of the vertical gate caused by simultaneous flow from the top and under the gate; it was observed that the scour length and depth are lower when the water simultaneously flows from the top and under the gate. Mehraein et al. (2012) conducted experiments by colliding a circular wall jet and a vertical jet. They investigated the effect of dimensionless parameters on the scour hole dimensions. It was observed that the scour depth decreases with increasing the tailwater depth and the horizontal distance between the two jets.

The related studies that considered the non-uniform sediments in the hydraulic structures can also be mentioned: Mih & Kabir (1983) investigated the impingement of submerged water jets on non-uniform bed material using experimental and theoretical analysis. They proposed relationships for the scour geometry (cleaned depth, cleaned width, armored depth, and scoured depth). Ghodsian et al. (2012) presented the results of local scour by free-falling jets utilizing four non-uniform sediments, The median size for all the sediment samples was equal but the non-uniformity was varied. They observed that by increasing the geometric standard deviation, the scour hole dimensions decreases, and by using d₉₀ instead of d₅₀ in the densimetric Froude number a better correlation with scour hole parameters was obtained. Okhravi et al. (2022) stated the results of a laboratory study on the effects of sediment gradation on the scour at single and pile group. They used non-uniform and uniform bed samples, the results showed that the sediment gradation effect becomes less after increasing the flow shallowness. Also the scour depth decreases with increasing the sediment non-uniformity. Pandey et al. (2019) analyzed the scour process experimentally in armored streambeds for the circular pier using non-uniform gravels. They developed a graphical approach for the computation of scour depth. Pandey et al. (2021) studied the temporal variation of scour depth around a vertical spur dike, it was concluded that the scour depth varies by non-uniformity of sediment and decreases with increasing the non-uniformity. Guillén-Ludeña et al. (2017) studied the effect of the sediment gradation on morphodynamics of open channel confluences. They used uniform and non-uniform sediments, the results showed a high topographic gradient in the morphology of the bed with non-uniform sediments. Tan et al. (2020) analyzed the maximum scour depth below culverts by considering the sediment non-uniformity effect, using a wide range of data sets, they found that a simple linear equation can be employed to estimate the scour depth.

Özyaman et al. (2021) investigated the scour around spur dike experimentally, they used uniform and non-uniform bed samples. The results revealed that the scour depth and volume in the non-uniform case is lower than for the uniform case.

To the author's knowledge, there is no research on the symmetric crossing jets scour from the perspective of bed sediment gradation, and the present research seems to be the first investigating the impact of non-uniform sediment mixtures on the scour due to the impingement of the crossing jets. The current research aims to study the effect of three non-uniform sediment samples on the 3D scour morphology due to symmetric crossing jets. Since the bed particles in the rivers are naturally made up of non-uniform sediments, this novel research is conducted in this direction. The dimensionless equations are developed for the scour estimation by considering the sediment non-uniformity parameter. The vertical angle of the jets was kept constant at 45°, and the angle of crossing jets was considered three values of 30°, 70°, and 110°. The distance between the jet crossing point and the tailwater level was also taken two positive values above the water level. To predict the maximum depth of scour hole, the scour hole length, the scour hole width, and the ending location of the downstream ridge, different regression models were fitted and models with the best estimation accuracy in terms of the error criteria are presented.

To transfer water, an electro pump with a maximum discharge of 10 l/s was used. The water was supplied to the jet pipes by a 2-inch pipe. A valve before the flow meter was used to adjust the discharge. Two pipes with circular cross-section were used for the crossing jets. The inner diameter of the jets is D = 2.2 cm. Some experiments were carried out with a single jet as reference tests to compare its resulting scour with the crossing jets. The pipe diameter of the single jet (D) was defined based on the criterion by Pagliara et al. (2011), equal to the diameter of an equivalent single pipe (⁠⁠) having a cross-sectional area equal to the total cross-sections of two jet pipes which is estimated as that becomes ⁠. The flow was divided equally between the two jet pipes. The flow discharge in the main pipe was measured by a Yokogawa (ADMAG AE) electromagnetic flowmeter with a precision of ±0.5%, which could measure the discharge between 0.138 l/s and 4.9 l/s. Figure 1(b) and 1(c) depicts a schematic view of the experimental setup and the scour in detail.

The channel was filled from the sediments, which were 30 cm thick. To achieve a horizontal surface, the bed material surface was carefully leveled before each experiment. For the tests, the crossing angle of the jet pipes was adjusted by the jet holder mechanism. The surface of the sediments was covered with an aluminum sheet; the channel was gradually filled with water. The flow rate and the tailwater level were adjusted. Then, the distance of the jets crossing point from the water surface was changed with the jet base. Then, the aluminum sheet was removed, and the experiment was started. After completion of each test, the hinged gate was gradually lowered until the water was completely drained. Then, the longitudinal and transverse scour profiles at the maximum depth section were measured using a laser distance meter with the precision of ±2 mm by installing it on a movable metal frame providing it to move in the longitudinal and transverse direction of the channel. In Table 1, the range of variations of each parameter in the experiments can be seen.

Table 1

Range of parameters

Parameter .	.	.	.	.
Value	30–110	5–10	3–9	1.3–1.75

Parameter .	.	.	.	.
Value	30–110	5–10	3–9	1.3–1.75

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Different researchers considered the scour hole equilibrium time differently; in Pagliara et al. (2011), the asymptotic stage was equal to 40 minutes. The equilibrium time by Aderibigbe & Rajaratnam (1996) was between 6 and 50 hours. In this study, it was found that 1 hour would be enough for the test period. Also, it was visually observed that the particles in the scour hole do not exit the hole after this period.

The scour hole itself is almost circular in the plan view; this circular shape is similar to those stated by other studies on the single jet (Pagliara et al. 2008; Kartal & Emiroglu 2022). Some of the particles inside the hole are suspended by floating forces and are deposited on the downstream wall of the hole and fall back into the hole due to slippage. So the slope of the downstream wall of the hole is not constant and in some experiments is step shaped. This step is located in the lower part of the wall when and in the upper part of the wall when ⁠. The floor of the hole also has a roughness in some places due to the deposition of suspended particles after the pump cessation.

In both conditions of S = 5 and 10 cm at the tailwater depths of h₀ = 3 and 6 cm, the slope of the upstream wall is steeper than the slope of the downstream wall; by increasing the tailwater depth to h₀ = 9 cm, the slope of the downstream wall becomes steeper almost equal to that of the upstream wall.

At the medium tailwater level (⁠⁠) in all the bed materials, the ridge has a crest instead of a plateau (Figure 5(c)); and the side ridges are created from the hole mid-section onward. At as the distance of the jet crossing point from the water surface increases to ⁠, the scour hole dimensions and the ridge become larger in all three bed materials.

In type B material at ⁠, the side ridges are composed of fine particles. The floor of the hole and the downstream wall are widely covered with coarser materials (armor layer), which extends up to 6 cm away from the ridge crest, and in this 6 cm reach, fine and coarse particles cover the wall. The suspended fine particles are deposited around the outer perimeter of the ridge by passing the ridge (Figure 5(c)). In type C material at ⁠, the scour mechanism is almost similar to B material, but the armor layer is more evident with a darker color.

At high tailwater level (⁠⁠) and ⁠, all scour ridges have crests. In type B material, the fine particles are depleted from the hole at the early stages; while the coarse particles are suspended. Coarser sediments settle on the downstream wall and slip into the hole. Fine particles can be seen around the ridge. On the hole floor and on the downstream wall, the armor layer is formed. Side and downstream ridges are composed of a mixture of fine and coarse particles; the maximum thickness of the armor layer reaches 9 cm on the hole floor, which gradually diminishes towards the crest. In type C material, with a high tailwater level, the mechanism is the same as for B material, but the maximum thickness of the armor layer decreases to 6 cm (Figure 5(d)).

Figure 6 compares the longitudinal profiles, it can be observed that at low and medium tailwater depths, by increasing the non-uniformity parameter, the scour hole depth increases. As can be seen from Figure 6(a)–6(c), the ridge height increases with the increase of the tailwater level in all three bed materials. At the medium and high tailwater depth, the ridge height decreases with sediment non-uniformity. From Figure 6(c), it can also be seen that at high tailwater depth (⁠⁠), the amount of scour hole depth in three bed materials is very close to each other, namely the effect of sediment gradation is marginal in this condition.

In ⁠, both the scour hole and the ridge are more stretched than the at all the tailwater depths. As can be seen from Figure 7, the shape of the hole is elliptical (almond-shaped), which is due to a longer jet length (lj) before entering the water. A similar elliptical form of the hole has been observed in the single jet experiments with low jet impingment angles (Pagliara et al. 2008).

By increasing the tailwater depth, the size of the ridges is diminished due to the energy dissipation of the jet. Parts of the suspended sediments are deposited on the downstream wall of the hole, and slide into the hole and other particles are removed from the hole.

At low tailwater depth ⁠, in both S = 5 and 10 cm, in the early minutes of the experiment with the expansion of the downstream ridge, several consecutive dunes with low height with equal distance from each other and parallel to the outer curvature of the ridge are formed on the surface of the downstream ridge. As the ridge expands, the dunes also gradually migrate downstream, the dunes also cause a wavy current on the ridge surface. These dunes are flattened and disappear before reaching the mid-test due to shear stress imposed by the flow.

As can be seen from Figure 7(a)–7(c) in type A material in ⁠, and low tailwater level ⁠, the downstream ridge outer perimeter has a smooth curvature, while in bed materials B and C, the ridges have sharp edges. The side ridges are not the same, and the right ridge is far ahead compared to the left. At the suspended particles do not exist within the hole during the test. The hole floor is not fully armed and has a mixture of fine and coarse grains. Coarse particles are moved by rolling motion. On the surface of the downstream ridge, most of the particles are coarse-grained materials. The left ridge is composed of fine particles and the right one is a mixture of fine and coarse sediments. The downstream wall of the hole is armed, but not entirely. From Figure 7, it is found that at the low and medium tailwater levels, when the hole is out of symmetry, the ridge also becomes asymmetric, so the deviation of the hole to one side causes the ridge to deviate to the opposite side, for example, if the hole has swerved to the right, its ridge tends to the left.

For the present study, it is concluded that at the crossing angle of ⁠, whatever the bed materials are exposed to the higher flow intensity, the scour shape tends to be non-symmetric. For example, in the case of the high tailwater level and low Froude number, the materials are less exposed to the erosive force of the jet, therefore, the form of the scour is symmetrical.

By increasing the non-uniformity of the sediments at low tailwater depth, the scour shape tends to be more asymmetric. At low tailwater depth, the scour shapes in B and C materials are similar to each other, having a dagger-shaped ridge with sharp edges in its nose, while the ridge in A material has a smooth curvature around itself (Figure 10). Side ridges at low tailwater level are not the same, and one side is bigger than the other side. At low tailwater level from the early minutes of the test, the scour ridge starts to grow non-symmetrically in B and C materials.

At the low and medium tailwater levels ⁠, the ridges have formed almost flat with no crest, but at high tailwater level ⁠, a crest is visible. The more is the tailwater depth; the smaller is the scour size. Similar to the angle of ⁠, at ⁠, there are no suspended particles circulating inside the hole, and due to the horizontal velocity component of the radial flow, the suspended particles are transported out of the hole.

As can be seen from Figure 12, at shallow and medium tailwater depths ⁠, a shallow erosion can be observed downstream of the main scour hole in all the bed materials. This scouring is caused by the falling of the radial flow of the resulting jet on the downstream ridge at the angle of ⁠. This radial flow causes a secondary scour and also a secondary ridge by distributing the primary ridge, which can be seen obviously at in Figure 11(a) and 11(b). It is slightly different compared to the ridges formed at the crossing angle of ⁠. At the maximum tailwater depth ⁠, due to the dissipation of the jet's radial flow, there is no such erosion on the primary ridge.

At the high tailwater level, there are no suspended sediments. In B and C materials, the armor layer is not created perfectly and is mixed with the fine particles on the hole floor and its downstream wall. The side ridges are composed of fine and coarse particles. The scour depth has also decreased by increasing the tailwater depth to (Figure 12). Comparing the longitudinal scour profiles at the low tailwater level (⁠⁠, it can be observed that the scour depth value decreases with increasing the non-uniformity, and in A material is deeper compared to the other bed samples. Also that is the case for the erosion depth within the secondary scour hole on the downstream ridge. The height of the ridge in A material is also higher. At all the tailwater levels, the ridge-ending location in the A material is ahead of the other bed samples.

Figure 13(c) shows the scour profiles in the bed material B at the low tailwater level with and medium discharge (⁠⁠. As can be seen, the single jet has produced the lowest scour depth while the crossing jets at the have the largest scour depth with equal values. It is observed that at the low tailwater level ⁠), the crossing jets at the angle of act like the single jet in terms of the scour profile similarity. In Figure 13(d) with and ⁠, the profiles are almost similar to Figure 13(b), but the scour depth at the is lower than the single jet. The scour depth value at the and are the maximum and minimum, respectively. In Figure 13(e), the scour profiles in bed material C are shown with medium tailwater depth ⁠) and ⁠; the difference among the scour depth values is low at compared to the other conditions. It can be seen that the scour depth at is deeper compared to the others like those at the low tailwater depth condition (13a,c). The scour depths by and the single jet are very close. In Figure 13(f), with and high tailwater depth, the scour profiles at the different crossing angles are almost similar to Figure 13(d) in terms of the maximum scour depth sequence.

It is concluded that at the crossing angles of and with high tailwater level, the scouring is less than those of the and the single jet, while at the low tailwater depth, the opposite occurs.

As can be seen from Figure 14(a,c,e,g) for and ⁠, all scour features (the maximum depth of scour hole, the scour hole length, the scour hole width, and the ending location of the scour ridge), increase with increasing the densimetric Froude number at all the crossing angles and in all the bed sediment materials. At the low tailwater level, the scour hole depth and length values at crossing angles of 70°, and 110° are higher compared to (Figure 14(a) and 14(c)). From Figure 14(a), it is shown that for ⁠, the scour depth is higher in C material (green line, ⁠) but in A material (blue line, ⁠) has lower values.

From Figure 14(c) it is evident that at ⁠, the length value (⁠⁠) is higher than those of the ⁠. The trend for the ending location of the ridge (⁠⁠) (Figure 14g) is nearly similar to the scour hole length. As can be seen, in bed material A, the scour values (⁠⁠) at and are higher than the other materials. In Figure 14(b), 14(d), 14(f), 14, it is evident that in the different bed samples for ⁠, the scour dimensions values versus tailwater level have an almost upward trend namely at the minimum tailwater depth they have the lowest values; at the maximum tailwater depth, they have the highest values. While for the wider angles (⁠⁠, due to the energy dissipation of the jet, the process is inverse and the scour features decrease with increasing the tailwater depth.

The accuracy performance was evaluated in terms of the coefficient of determination (R²) and the mean absolute percentage error (MAPE). As can be seen from Table 3, the developed equations for each crossing angle can estimate the scour characteristics with approximately good accuracy (R² > 0.8). For ⁠, the R² is above 0.9 for all the scour features, but has higher errors than the other angles.

Table 3

Coefficients of Equation (4) for estimation of the scour dimensions

Parameter .	.	.	.	.	.
a		0.135	1.111	0.765	0.868
b		1.093	0.929	0.984	1.156
c	30°	0.13	−0.025	0.00449	0.074
d		0.231	0.13	0.225	0.207
e		0.771	0.536	0.616	0.55
R2		0.88	0.87	0.84	0.95
MAPE(%)		5.6	3.4	4.9	2.9
a		1.393	1.656	2.682	2.591
b		0.491	0.892	0.705	0.994
c	70°	−0.298	−0.317	−0.271	−0.36
d		−0.202	0.15	−0.166	0.097
e		0.132	0.379	0.283	0.192
R2		0.87	0.94	0.86	0.94
MAPE(%)		6.3	3.6	5.5	4.3
a		0.841	2.125	2.262	2.454
b		0.704	0.847	0.783	1.104
c	110°	−0.53	−0.674	−0.413	−0.718
d		−0.481	0.222	−0.321	0.02
e		0.294	0.377	0.272	0.351
R2		0.92	0.95	0.93	0.95
MAPE(%)		10.1	6.1	6	8.8

Parameter .	.	.	.	.	.
a		0.135	1.111	0.765	0.868
b		1.093	0.929	0.984	1.156
c	30°	0.13	−0.025	0.00449	0.074
d		0.231	0.13	0.225	0.207
e		0.771	0.536	0.616	0.55
R2		0.88	0.87	0.84	0.95
MAPE(%)		5.6	3.4	4.9	2.9
a		1.393	1.656	2.682	2.591
b		0.491	0.892	0.705	0.994
c	70°	−0.298	−0.317	−0.271	−0.36
d		−0.202	0.15	−0.166	0.097
e		0.132	0.379	0.283	0.192
R2		0.87	0.94	0.86	0.94
MAPE(%)		6.3	3.6	5.5	4.3
a		0.841	2.125	2.262	2.454
b		0.704	0.847	0.783	1.104
c	110°	−0.53	−0.674	−0.413	−0.718
d		−0.481	0.222	−0.321	0.02
e		0.294	0.377	0.272	0.351
R2		0.92	0.95	0.93	0.95
MAPE(%)		10.1	6.1	6	8.8

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The relationships developed by Pagliara et al. (2011) for wider angles are presented for and ⁠, which have a low difference from the current research angles (⁠ and ⁠); therefore, their results were compared with the present study applying this research dataset. As can be seen from Table 4, generally, the prediction accuracy for scour hole depth at is lower than the other angles with R² = 0.21 and MAPE = 37.9. Also, the equations show lower accuracy compared to the empirical models of the present study.

Table 4

Formulae presented by Pagliara et al. (2011) 

.	Formulae .	R2 .	MAPE (%) .
		0.21	37.9
		0.38	12.2
		0.32	15.7
		0.93	12.6
		0.77	7.9
		0.73	19.5
		0.75	18.1
		0.62	18.5
		0.66	27.7

.	Formulae .	R2 .	MAPE (%) .
		0.21	37.9
		0.38	12.2
		0.32	15.7
		0.93	12.6
		0.77	7.9
		0.73	19.5
		0.75	18.1
		0.62	18.5
		0.66	27.7

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In the present study, the scouring process of the symmetric crossing jets with three non-uniform bed sediments having a close median diameter was investigated at three different crossing angles of ⁠,⁠, and ⁠. The effect of bed gradation was studied. The main results are summarized as below:

• For the crossing angle of at the low and medium tailwater levels, the scour hole depth increases with increasing the sediment non-uniformity.

• For ⁠, the armor layer is created in B and C materials which is thick and is perfectly created but for and ⁠, it is thin with a mix of the coarse and fine particles.

• The scour hole shape at is circular, while at and it has an elliptical form.

• At low tailwater level for and ⁠, the ridges are flat and elongated with no crest, and by increasing the non-uniformity of the sediments, the scour shapes tend to be more asymmetric.

• At the low and medium tailwater levels for ⁠, a secondary scour is formed on the downstream ridge in all the bed samples, which causes a secondary ridge to be developed.

• By comparing the crossing jets scour with the single jet, it is concluded that at the crossing angles of and with high tailwater level, the scouring is less than that of the single jet and ⁠, while at the low tailwater depth, the opposite occurs.

• The resulting jet length increases with increase in the discharge and crossing angle.

• The various new regression formulae were proposed for the estimation of the scour characteristics in which adding the sediment non-uniformity parameter in the formulae led to a better accuracy.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.