THE FLOW BETWEEN ARMOR ELEMENTS AND ITS INFLUENCE ON EROSION OF THE SAND BASE

Robert Booij and Roland Jansens

Delft University of Technology, Faculty of Civil Engineering and Geosciences

Correspondence: R. Booij, P.O. Box 5048, 2600 GA Delft, The Netherlands

Tel.: +31 15 27 845 82; fax: +31 15 27 859 75; E-mail: r.booij@ct.tudelft.nl

Abstract: Around structures erected on sandy beds in rivers and coastal areas the bed often has to be protected from scouring by armor layers, consisting of relatively large rocks. Classical design rules lead to conservative and expensive multi-layer armoring, a so-called geometrically closed armoring. To reduce the high expenses of this kind of protection a so-called geometrically open armoring, consisting of a single layer of large rocks, is often preferred nowadays. In most predictive models it is assumed that the mean flow and the shear stress above the armor layer penetrate in the pores between the armor elements and that this penetrated flow is responsible for the erosion of the sand bed below the layer. However, the relatively thin armor layer these models predict, does not always suffice for a protection of the sand bed in practice. Measurements of the flow velocities in the pores between armor elements in a flume using the laser-Doppler technique suggest a completely different driving mechanism for the pore flow and hence a different erosion mechanism.

Two flow situations were examined: A situation with a steady ambient main flow above the armor layer and a situation with surface waves and a zero average main flow velocity above the armor layer. In both cases the mean pore flow was found to be driven by the pressure gradients in the armor layer, which are induced by the pressure gradients in the flow above the layer. Pressure gradients associated with a surface slope, with waves, or with large turbulent structures play a dominant role. Below waves the erosion of the sand bed appears to depend on the maximum pore flow and the locally generated small-scale flow structures, which detach the sand grains from the bed. Below steady flow the upward displacement of the detached sand particles through the armor layer is a bottleneck for erosion. Here large-scale velocity fluctuations in the armor layer, due to large-scale turbulence in the main flow, transport the sand particles into the flow above. The knowledge obtained will ultimately lead to different design rules. 

Keywords: erosion, sand bed,armoring, geometrically open, pore flow,waves,large-scale turbulence

1    INTRODUCTION

In coastal areas and rivers, cover layers consisting of rocks or other armor elements are applied locally to protect the underlying sandy bed from erosion. Armor layers are used:

● as bed defense in rivers                         ● around piers

● around and under breakwaters and groynes        ● downstream of sluices

● at the toe of dikes and banks                       ● as "falling aprons"

The dimensions of the rocks used and the thickness of the cover layer are chosen such that the underlying sand bed is shielded from the eroding currents and waves. A relatively safe armoring, so-called geometrically closed armoring, consists of several layers of rocks of different dimensions, such that the rocks in a layer cannot escape through the holes between the rocks in the next higher layer. As a rule a factor of 5 or less between the diameters of the stones of successive layers is used, see Figure 1. To reduce the very high expenses of this way of armoring a single layer of large rocks, so-called geometrically open armoring, is often tried nowadays, however with varying success at best (Schiereck et al, 2000).

Fig. 1    Geometrically closed and open armouring

In models used for the design of rock beds it is generally assumed that a direct coupling exists between the main flow above the armor layer and the flow through the porous armor layer. The main flow turbulence and hence the mean velocity profile are supposed to penetrate to a distance of only a few element diameters into the armor layer. Beyond this distance only a small depth-independent pore velocity would remain, corresponding to an almost vanishing shear stress. In most erosion models the prediction of the erosion of the sand base depends on the bed shear stress. The resulting very small shear stress at the sand bed below the armor elements would then be insufficient for substantial erosion of the sand bed. This would suggest that in general a relatively thin single armor layer would suffice for a safe armoring.

To investigate the flow in pores between armor elements and its influence on the erosion of the sand base, measurements of the fluid velocity and its fluctuations inside the armor layer were executed. Two different flow situations above the armor layer were examined: first, a situation with surface waves but with a zero average flow, and second, a situation with steady flow. In both situations several flow cases were investigated with different wave periods and different water heights respectively. The velocity measurements in the pores were executed using a laser-Doppler velocimeter (LDV). As the LDV requires transparency of the water, the velocity measurements could not be combined with erosion experiments. Therefore the sand bed was replaced with a concrete bottom of about equal roughness during the velocity measurements. Moreover the velocity measurements were executed at critical flow conditions concerning the onset of erosion. The critical flow conditions for the different cases were obtained from former measurements with an armored sand bed.

2    EXPERIMENTS

The fluid velocity and its fluctuations inside the armor layer were measured in a flume of the Laboratory of Fluid Mechanics of the Delft University of Technology with the following dimensions: length 12m, width .5m and height .7m. The LDV used was a 2-dimensional, reference beam, tracker system from Delft Hydraulics. Optical access to a cavity in the armor layer was established by guiding the laser beams of the LDV between the armor elements through narrow tubes. The configuration of the measuring cavity was fixed by gluing armor elements around the tubes. The ends of both tubes were guided through holes drilled in the stones (see Figure 2).

Fig. 2    Measuring pore in armor layer

In this way the cavity could be displaced and rotated without leading to accidental changes in the direct surroundings of the measuring volume of the LDV (Jansens, 2000). The equivalent cube diameter, D_n50 = (M₅₀/r)^1/3, of the rocks, used as armor elements in the experiments, was 20 mm. The typical diameter of the sand below these armor elements was 0.10 mm. The ratio of over 200 between the two diameters makes it a geometrically open armoring.

3    EXPERIMENTS BELOW WAVES

The set-up for the measurements in the situation with surface waves without mean velocity is given in Figure 3.

Fig. 3    Set-up for measurements below waves

Two wave gauge meters were used to measure the deviation from the mean surface level (MSL). An electromagnetic velocity meter (EMV) was used to measure the orbital velocity above the armor layer simultaneous with the LDV velocity measurements in the pores. Measurements were executed for different orientations of the measuring cavity, for different depths of the cavity in the armor layer and for different wave heights. To investigate the erosion mechanism, measurements were executed for different wave periods, T, at the corresponding critical wave heights. These critical wave heights, H, at which the sand bed starts eroding were determined in a previous investigation by Halter (1999). The different flow and bed parameters were taken equal to those of Halter (see table 1).

Table 1    Critical wave cases

4    EXPERIMENTS BELOW STEADY FLOW

It proved impossible to obtain a sufficient velocity over the armor layer for erosion of the sand bed using a steady free surface flow. Therefore the water flow was covered by a lid in the form of a caisson around the measuring section. In fact the flow geometry in this situation is that of a channel flow over the armored sand bed. The flow is driven by a pressure difference over the length of the caisson, which is hereafter expressed as a hydraulic gradient. Measurements were executed for different hydraulic gradients and for different depths of the measuring cavity in the armor layer. To investigate the erosion mechanism measurements were executed for different water heights below the caisson, h, at the corresponding critical hydraulic gradients. These critical gradients, i, at which the sand bed starts eroding, were determined in a previous investigation (van Os, 1998), and are given in table 2.

Table 2    Critical steady flow cases 

5    RESULTS

The main flow is found to penetrate only about 1½ stone diameters into the armor layer. Beyond this depth the measured pore velocities become independent of the depth in the armor layer. Consequently the shear stress vanishes. The driving force of the remaining pore flow is the pressure gradient, which is equal to the pressure gradient above the armor layer. This pressure gradient can be due to a hydraulic gradient, to surface waves or to large-scale turbulence structures in the main flow. Pressure fluctuations connected with small-scale turbulent structures in the main flow will vanish at short distance and will consequently only have influence on the flow between the highest armor elements.

The magnitude of the measured pore velocity is low, of the order of 30 to 50 mm/s. The Reynolds number of the pore flow is therewith too low for the flow to become turbulent. That does not mean that the flow resistance will be linear. The re-circulation regions that are present because of the strongly varying pore dimensions will lead to a quadratic flow resistance. All flow cases measured show high frequency velocity fluctuations with an intensity of about half the mean pore velocity. Because of the low value of the Reynolds number this cannot be due to turbulence in the pores, but may be connected to velocity fluctuations due to vortices detached from re-circulation regions and in wakes behind the armor elements. However the length of the measuring volume of the used LDV is about 15 mm, which is of the order of the dimension of the cavity. Hence measured particles may cross the measuring volume at different velocities, leading to velocity fluctuations in the measurements. This “measuring volume noise” is indistinguishable from real velocity fluctuations. For the resolution of the small-scale fluctuations in the pore flow and the determination of the velocity field in a pore a LDV with a shorter measuring volume, e.g. a side scatter system, is required.

6    CRITICAL FLOW RESULTS

The measured pore velocities at critical conditions below waves are almost equal in cases B, C and D (see table 3). For this comparison the pore velocity below waves is ensemble-averaged, meaning here that the velocity in equal phases of the wave cycle is averaged. In table 3 the maximum value of the ensemble-averaged pore velocity, u, and the intensity of the fluctuations of the pore velocity, u′, as obtained from the measurements are given. Estimates of Jansens (2000) of the velocity required to destabilize the individual sand grains lead to the same order of magnitude (~ 40 mm/s). Considering the uncertainty in the estimated value, the expected variation of the pore velocity around the armor elements and the uncertainty in the intensity of the real velocity fluctuations, the measured pore velocity appears sufficient for the onset of erosion. It can be concluded that below waves the pore flow driven by the pressure gradient connected with the surface slope determines the erosion. Case A deviates slightly. This is probably due to a slightly incorrect value of the critical wave-height, H, as measured by Halter. The short, steep waves in this case easily lead to such an error. Moreover, this being an error is plausible, as only in this case the orbital velocities measured by Halter are 25% lower than the computed ones.  

Table 3    Critical wave loading

The measured mean pore velocities at critical conditions below steady flow are not equal in the different cases (see table 4), suggesting that in this situation the mean pore velocity does not solely determine the onset of erosion. In this situation fluctuations with a large time-scale are observed, as can be seen from the auto-correlation function R(τ) in Figure 4.

Fig. 4    Autocorrelation coefficient of velocity fluctuations

The time-scale T of these fluctuations grows with the water depth, showing that these fluctuations are caused by pressure gradients connected with large-scale turbulent structures in the main flow. The intensity of the large-scale pore velocity fluctuations u″ and their time-scale T are given in table 4. The combination of the fluctuations and the mean pore flow is sufficient for erosion but their values do not give a simple explanation of the same onset of erosion in all cases. It should be realized that for erosion of the sand bed the sand has to be removed through the armor layer. In the uniform flow through the armor layer below a steady flow this can be done by large-scale velocity fluctuations, that move the sand grains over a vertical distance comparable to the thickness of the armor layer or at least of the individual armor elements. Indeed the product L of the intensity of the large-scale fluctuations and their time scale is equal in all cases, leading to the conclusion that the pore flow fluctuations due to large-scale turbulence can determine the erosion (Booij et al, 1998). (It should be noted that the critical condition requires the erosion of a few grains over the armor layer, so the tails of the probability distributions of u″ and T determine the distance covered, leading to much higher distances than L). In the wave situation the varying pore flows apparently to remove the sand grains.

Table 4    Critical steady flow loading

7    CONCLUSIONS

(1) The feasibility to measure pore velocities in a scale model opens the possibility for a more fundamental investigation into filter behavior and bed stability. The results discussed here show that the obtained knowledge will ultimately lead to different design rules.

(2) The main flow penetrates only about 1½ stone diameters into the armor layer. Beyond this depth the pore flow is driven by pressure gradients above the armor layer. These gradients can be due to a hydraulic gradient, the presence of surface waves or large-scale turbulence structures in the main flow. Beyond 1½ stone diameters the measured pore velocities are independent of the depth in the armor layer.

(3) In the situation of surface waves and zero average flow the maximum values of the horizontal pore velocity at critical wave loading are equal for all cases. This demonstrates that this maximum pore velocity determines the onset of erosion for this condition.

(4) In the situation of steady flow the mechanism of erosion is more complicated. Here the upward displacement through the armor layer is an additional bottleneck. This displacement appears to be executed by large-scale fluctuations corresponding with large-scale turbulence in the main flow.

(5) For the resolution of the small-scale fluctuations in the pore flow and the determination of the velocity field in a pore a LDV with a shorter measuring volume, e.g. a side scatter system, is required.

References

Booij, R., et al, The influence of pressure fluctuations on the flow between armour elements, Proceedings 26^th International Conference On Coastal Engineering, Copenhagen, 1998, pp 1898-1905.

Halter, W., The behaviour of erosion filters under the influence of wave loads (in Dutch), MSc thesis, Delft University of Technology, February 1999.

Jansens, R., The penetration of waves in a filter layer (in Dutch), MSc thesis, Delft University of Technology, November 2000.

Os, P. van, Hydraulic loading on a geometrically open filter structure (in Dutch), MSc thesis, Delft University of Technology, January 1998.

Schiereck，G.J., et al, Filter erosion in coastal structures, Proceedings 27^th International Conference On Coastal Engineering, Sydney, 2000, to appear.