DOI: https://doi.org/10.62204/2336-498X-2023-1-18

THE METHOD OF CALCULATING THE EFFECT OF DAMPING

OF THE WAVE HEIGHT OF THE FLOW BY THE VEGETATION

IN FLOODPLAIN AREAS OF BRIDGE CROSSINGS

Olena Slavinska,

 Doctor of Technical Sciences, Professor,
National Transport University, Ukraine
elenaslavin9@gmail.com; ORCID: 0000-0002-9709-0078,

Andrii Bubela,

Doctor of Technical Sciences, Professor,
National Transport University, Ukraine
 bubelaandrey@ukr.net; ORCID: 0000-0002-5619-003X,

Liudmyla Bondarenko,

Candidate of Technical Sciences, Assistant Professor,
National Transport University, Ukraine
luda_bond@ukr.net; ORCID: 0000-0002-8239-065X,

Annotation.  To solve the applied problems of road and bridge construction, a method of calculating the effect of damping of the flow wave height by the vegetation on floodplains is given. To achieve the necessary effect of extinguishing dangerous waves, the parameters of the strip of shrub plantings are substantiated. The proposed method is implemented in the form of engineering formulas for determining the degree of reduction of wind waves during their passage through thickets on floodplain areas of open water flows in the zone of influence of bridge crossings.

Keywords: wind waves, floodplains, effective shrub height, approach embankment, bridge crossing.

Introduction. The forms of unsteady flow in open channels are diverse, but the most characteristic type for rivers is a displacement wave. During the movement of displacement waves, in particular flood waves, significant volumes of water can be carried downstream and there is always a change (increase or decrease) in flow rates. Accordingly, the zone of influence of the bridge crossing extends not only to the riverbed, but also to the floodplain.

The floodplain is a complex system. The geomorphometry of floodplain areas is characterized by the presence of significant vegetation, silt from previous floods and floods and determines the genetic dissimilarity with the riverbeds. The surface of the floodplain is mostly covered with vegetation, varying in thickness and size of thickets, which affects the flow capacity of the floodplain [1-3]. The removal of vegetation under the bridge crossing is not possible, as it can lead to significant negative environmental consequences – erosion of the banks, the development of deformations at the bottom of floodplains and on embankments approaching bridges. Plant elements lead to additional vortex formation, the development of resistance to the movement of water flow, the distribution of velocities in which depends on the density of vegetation and its height. Accordingly, the processes of the development of deformations in floodplain areas depend on the cohesive qualities of bottom soil particles and on the distribution of vegetation, which reduce their intensity [4, 5].

The objective of the study.

The displacement wave in open watercourses can take different forms. If the level increases during the movement of the wave, then the wave is positive, if the level decreases, the wave is negative [6]. A forward wave (positive or negative) moves downstream, a reverse wave moves upstream (against the current). A direct positive wave that carries an increase in water flow downstream is usually called a filling wave. The reverse positive wave, which occurs, for example, in the upstream when the drop shields of the dam are completely or partially closed or the turbines are stopped, is called a support wave. The backwater wave carries the decrease in flow up the river. A direct negative wave is called a tidal wave; its occurrence can be caused, for example, by a decrease in costs in the upper reaches of the river (during the period of flood subsidence), and in the downstream by a decrease in the passage of water through buildings. The reverse negative wave is called an outflow wave; it arises in the upstream of the dam with an increase in the passage of costs through the structures, spreads up the river and carries with it an increase in costs.

The front of a wave is its leading edge that moves up or down, and the main part of it is the body of the wave. Positive waves usually have a relatively steep front, while negative waves have a gentle one. When the wave front passes, the change in the hydraulic elements of the flow is quite rapid, but within the body it is slow. The propagation of a wave, in particular its front, occurs at wave speed, but not every wave in a river flow propagates at this parameter.

The speed of movement of flood waves on large rivers is determined not only by the hydraulic parameters of the formed filling wave, but also by the conditions of its formation and transformation when passing through the channel and floodplains, where part of the water accumulates, especially from the frontal part of the flood, which leads to a decrease in the speed of movement of the actual front. On the other hand, the wave is fed by lateral tributaries that replenish the volume of the wave throughout the entire body or part of it.

Practical significance of the obtained results. To solve the applied problems of road and bridge construction, a method implemented in the form of engineering formulas for determining the degree of reduction of wind waves during their passage through thickets on floodplains of open water streams is given.

As part of this approach, the effective height of the shrub is first determined by the formula:

,                                                    (1)

where H – depth of flooding of the floodplain, m;

h – estimated wave height, m.

Next, the effective height of the shrub  is compared with the actual height of the thickets    . If the effective height of the vegetation is less than the actual height of the thickets , then the effect of damping the wave in the shrubbery will be                 achieved;

if            then it is necessary to provide for the planting of a shrub of greater height.

If there are gaps in the shrub, the percentage of thicket density decreases in proportion to the area of the gaps:

,                                    (2)

where  is the area of the gaps, %;

– percentage of thicket density, %.

The percentage of thicket density can be determined according to methodical recommendations [7] depending on the diameter of the main trunks and their number per 1 m2 of thicket area.

The height of the wave in the wave system of the calculated storm, after it passes through the strip with vegetation, will be reduced to:

,                                               (3)

where P is the percentage of wave height damping, %.

Also, formula (3) makes it possible to determine the required percentage of wave repayment:

.                                       (4)

Figure 1 shows the results of a numerical experiment on the influence of the density of thickets on the reduction of the calculated wave height. For calculations, the diameter of the main trunks is assumed equal to 3 cm, the plane of the gaps – 30% of the total area of the floodplain. As can be seen from Fig. 1, an increase in the density of vegetation thickets accelerates the effect of wave damping on floodplain areas of open water streams.

Fig. 1. Influence of thicket density on wave damping in floodplains

of open water streams

Here are several test practical examples of the application of formulas (1)-(4).

Test example 1. Suppose that in the process of research and preliminary design, it turned out that the floodplain of the river in the wave-dangerous direction is partially overgrown with small forests. Thickets with a height of 1,5-2 m, not continuous, with a plane of gaps that is 30% of the total area of the floodplain.

In the process of dumping the flood embankment, it is assumed that the shrubbery will be removed at a distance of 20 m from the base of the embankment, and the remaining strip of shrubbery will be 40 m wide. The depth of flooding of the floodplain at a level of 0,33% – H=1,2 m; estimated wave height of 1% assurance in the system of storm waves of 50% pr assurance at the approach to the strip of small forest – h=0,4 m.

It is necessary to determine the height of the waves on the approach to the highway embankment.

In this case, the effective height of the shrub will be  which is less than the height of the shrub on the floodplain of 1,5 m. Therefore, the effect of damping the wave in the bush will be achieved.

According to surveys data, there are on average 5-6 trunks with an average diameter of 3 cm for every 1 m2 of thickets.

According to [7] the density of the bush will be 0,353, and taking into account the gaps: .

For the width of the shrub strip of 40 m, we will get a percentage of wave height damping of 28% [7].

The estimated wave height of 1% assurance after passing through a 40 m wide shrub will be: m.

Test example 2. During the design of the floodplain part of the embankment, it was established that a wave with a height of 0.1 m rolling onto the road slope is safe.

The depth of the floodplain at the level of 0,33% – H=0,9 m, the estimated wave height is of 1% assurance in the storm wave system, 50% assurance on the approach to the designed planting strip h=0,3 m. It is proposed to plant a strip of shrubs with a diameter of the main trunks of 3 cm on a width of L=60 m.

It is necessary to determine the density of shrub plantings to achieve the necessary effect of extinguishing dangerous waves.

In this case, the necessary height of the shrub is determined, not less than:  m.

In this case, the required percentage of wave damping will be: .

Thus, when  and L=60m we determine p=0,48.

Further, according to [7], when p=0,48 and a diameter of the main trunks is 3 cm, we find the number of main trunks per 1 m2 – 7 pieces.

Test example 3. The depth of the floodplain in the wave-dangerous direction beyond the level of 0.33% H=1,5 m, the calculated wave height of 1% assurance in the storm wave system of 50% assurance on the approach to the designed forest strip h=0,6 m.

According to the conditions of construction of the embankment, a wave of no more than 0,1 m should approach it.

A 2 m tall shrub with an average trunk diameter of 4 cm is available for planting.

It is necessary to determine the width of the shrub planting strip and its quantity per 1 m2 to achieve the necessary effect of damping of dangerous waves.

First, we will check the effectiveness of the height of the bush. The minimum height of the shrub should be:  m.

Thus, the height of the bush is sufficient to dampen the waves.

Let’s determine the required percentage of wave damping: .

According to [7], at  the following variants of a forest strip with boundaries are possible:

– for thickets density of 0,25% – width 100 m;

– for thickets density of 1,2% – width 40 m.

If the average diameter of the main trunk is 4 cm, then we can offer the following options for planting a shrub [7]:

– for a width of 100 m, 2 trunks/m2 are required;

– for a width of 80 m – 4 trunks/ m2;

– for a width of 60 m – 5 trunks/ m2;

– for a width of 40 m – 10 trunks/ m2.

A planting width of 40 m with the number of bushes of 10 pcs/m2 will be optimal, which corresponds to the distance between bushes in a row and between rows of approximately 30 cm.

Test example 4. The depth of the floodplain in the wave-dangerous direction beyond the level of 0,33% H=1,8 m, the calculated wave height of 1% assurance in the storm wave system of 50% assurance at the approach to the designed forest strip of the h=0,9m.

According to the conditions of construction of the embankment, a wave with a height greater than 0,05 m should not approach it.

For planting, a shrub with an average height of 2,5 m and with an average trunk diameter of 3,5 cm is available. Planting will be carried out at a density of 8 pieces per 1 m2.

It is necessary to determine the width of the forest strip to meet the established requirements.

In this case, the effective height of the shrub will be:  m.

Thus, the effect of wave damping will be achieved.

With a diameter of the main trunk of 3.5 cm and a planting density of 8 pieces per 1 m2, we find p=0,77 [7].

Next, we determine the required percentage of wave damping: .

For p=0,77 and , we get the required width of the shrub strip – 70 m.

The proposed method of calculating the effect of damping of the height of the flow wave by the vegetation on floodplain sections of bridge crossings makes it possible to solve important problems that arise during the design of highways, in particular:

1) Determination of the reduction of the estimated height of the waves after their passage through the shrub on floodplains – approaches to highway embankments;

2) Determination of the width and density of the strip of shrub plantings to achieve the necessary effect of damping of dangerous waves in floodplain areas of open streams – approaches to bridge crossings.

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