EP4339374A1 - Pouring structure, hydraulic dam provided with same - Google Patents

Abstract

The invention relates to an overflowing structure (1), comprising an upstream facing (2), which obstructs the flow of water and an upper surface (4) threshold crest. The invention is characterized in that the upper threshold surface (4) has at least one bump (41) and at least one depression (42) in at least one plane (Pyz) of width, parallel to the transverse direction (Oy ) and in the vertical direction (Oz) and/or in at least one horizontal plane (Pxy), parallel to the horizontal direction (Ox) and to the transverse direction (Oy).

Description

The invention relates to a structure or an overflowing body, as well as a hydraulic dam provided therewith.

One field of the invention concerns flood spillways, overflow thresholds, overflows, overflow gates and valves, for example for a hydraulic dam or the like.

One of the major safety issues linked to the operation and monitoring of dams concerns the risk of flooding. The vast majority of dams are equipped with a flood spillway device which limits the maximum water level of the reservoir. There are several families and types of evacuators. Among them, we will find profiled thresholds. On these structures, the water is evacuated by overflow. There is a standardization of the profile of these thresholds which depends on the design flow which corresponds to the optimal operation of the spillway. This flow rate is associated with a water level upstream of the threshold which is called design load. When this flow rate is exceeded, the risk of separation of the water vein is significant. Once the separation of the water vein is observed, the flow over the threshold becomes unstable. Its instabilities are damaging to the structure and/or mechanical parts.

The document US-A-3,464,210 concerns a dam whose upper edge is in the shape of a saddle with a concave slope and thus indicates a desire to break the regularity of the oscillations of the water.

The document FR-A-725 373 describes a dam having a spill plate having wedge-shaped elements terminating at the top of the crest of the dam to give the body of water and indicates that it is desired thereby to give an undulating shape to the body of water and prevent vibrations of the water vein.

The document CN-B-111 042 072 describes a spillway, the upper end of which has overflow openings in the shape of an inverted isosceles trapezoid.

The geometries known by these documents have drawbacks.

These known geometries allow aeration of the overflowing sheet to ensure that the air which surrounds the freely falling jet of water is close to atmospheric pressure. Thus the risk of the jet flapping is almost eliminated.

The overflow sheet is the free-falling jet of water formed downstream of a threshold which may resemble a waterfall. Under certain conditions, air currents that form under the overflowing water table can cause the water table to flap. These air currents are due to a pressure difference between atmospheric pressure (found above the water table) and the depression which forms below the water table. By aerating the water table using the documents mentioned above, the atmospheric pressure is reduced below the water table and the intensity of the air currents is significantly reduced.

However, the geometries known by these documents do not provide throughput performance.

In particular, we seek to increase the flow rate which passes over the threshold compared to the known documents mentioned above, without there being any separation.

Detachment is characterized by the presence of a volume of air between the upper surface of the sill and the water.

An objective of the invention is to obtain a spilling structure, as well as a hydraulic dam equipped with it, where the admissible flow rate through the threshold before separation is increased to widen the normal operating range of the threshold.

• la surface supérieure crête de seuil étant plus en haut que parement amont et étant située en aval du parement amont,
• la surface supérieure crête de seuil redescendant vers l'aval,
• la surface supérieure crête de seuil s'étendant le long d'au moins une direction transversale de largeur, qui est perpendiculaire à au moins une direction horizontale de longueur allant du parement amont vers l'aval et qui est perpendiculaire à une direction verticale de hauteur,
• caractérisé en ce que
• la surface supérieure de seuil présente au moins une bosse et au moins un creux dans au moins un plan de largeur, parallèle à la direction transversale de largeur et à la direction verticale de hauteur et/ou dans au moins un plan horizontal, parallèle à la direction horizontale de longueur et à la direction transversale de largeur.

For this purpose, a first object of the invention is an overflow structure, comprising an upstream facing, which obstructs the flow of water, and an upper surface, threshold crest,

• the upper surface of the threshold crest being higher than the upstream facing and being located downstream of the upstream facing,
• the upper surface crest of sill descending towards downstream,
• the upper threshold crest surface extending along at least one transverse direction of width, which is perpendicular to at least one horizontal direction of length going from the upstream facing to the downstream and which is perpendicular to a vertical direction of height ,
• characterized in that
• the upper threshold surface has at least one bump and at least one depression in at least one plane of width, parallel to the transverse direction of width and the vertical direction of height and/or in at least one horizontal plane, parallel to the horizontal direction of length and the transverse direction of width.

Thanks to the invention, the hydraulic performance of the overflow structure is improved. This new geometry shifts upwards the point of separation of the water vein in the height - flow law and thus makes it possible to increase the admissible load without separation. The invention makes it possible to increase the maximum admissible flow rate discharged by the upper surface of the threshold without observing a separation of the overflowing water blade, that is to say without air coming into view. engulf between on the one hand the overflowing blade and on the other hand by the upper surface of the threshold the runner located downstream of it.

In particular, the invention makes it possible to increase the admissible flow rate without separation compared to the works known from the documents mentioned above. The invention makes it possible to better adhere the flow against the surface compared to the works known from the documents mentioned above.

In particular, the invention is such that it makes it possible to increase by at least 20%, or even by at least 50% or more than 100%, the admissible flow rate without separation, compared to a standard threshold of constant profile following the transverse direction of width.

These improvements are notably provided by the fact that, according to one embodiment of the invention, in each longitudinal vertical plane, parallel to the horizontal direction of length and the vertical direction of height, the upper threshold surface corresponds to a homothety , having a prescribed variable ratio of homothety, which is non-zero and which depends on the width coordinate of the upper threshold surface in the transverse direction of width, relative to a basic profile of prescribed shape in one of the vertical planes longitudinal, the prescribed variable ratio of homothety being increasing going from a hollow to a bump along the transverse direction of width.

According to one embodiment of the invention, the prescribed variable homothety ratio is curved at least with a continuous derivative along at least the width coordinate.

According to one embodiment of the invention, the upper threshold surface has, in the at least one horizontal plane on an upstream side of the upper threshold surface, a curve, which comprises the at least one bump and the at least one hollow and which has at least a continuous derivative.

According to one embodiment of the invention, the base profile comprises a determined downstream reference point, the transformation of which by the homothety along the width coordinate is located on a rectilinear segment downstream of the upper surface threshold crest , the rectilinear segment downstream of the upper threshold crest surface being parallel to the transverse width direction.

According to one embodiment of the invention, the rectilinear downstream segment of the threshold crest upper surface is formed by an end edge of the threshold crest upper surface.

According to another embodiment of the invention, the rectilinear downstream segment of the upper threshold crest surface is connected to another downstream surface.

According to one embodiment of the invention, the upper threshold surface has alternating bumps and hollows along the transverse width direction in the width plane, and/or in the horizontal plane.

According to one embodiment of the invention, the bumps, which are close to each other, have vertices, which are spaced apart, along the transverse direction of width, by a spacing distance, which is greater than or equal to 0.6 times a prescribed width value and which is less than or equal to 1.4 times the prescribed width value.

According to one embodiment of the invention, the hollows, which are close to each other, have low points, which are spaced apart, along the transverse direction of width, by a spacing distance, which is greater than or equal to 0.6 times a prescribed width value and which is less than or equal to 1.4 times the prescribed width value.

According to one embodiment of the invention, the prescribed variable ratio of homothety or z(x,y) / z(x,0) is sinusoidal between the bumps, which are close to each other and/or between the recesses, which are neighbors of each other as a function of a width coordinate of the upper threshold surface along the transverse width direction.

• où z(x,0) est un profil de base de forme prescrite convexe dans un plan vertical longitudinal prescrit (POxz), parallèle à la direction horizontale de longueur et à la direction verticale de hauteur,
• A(y) est une première fonction de hauteur, qui est continue, supérieure à zéro et inférieure ou égale à 0,5,
• f(y) est une deuxième fonction, qui est continue, qui varie suivant la coordonnée y et qui est supérieure ou égale à -1 et inférieure ou égale à 1.

According to one embodiment of the invention, the upper threshold surface has a coordinate z(x,y) in the vertical direction of height,
the coordinate z(x,y) depending on the x coordinate of the upper threshold surface (4) in the horizontal direction of length and depending on the y coordinate of the upper threshold surface in the transverse direction of width, according to following equation: $$\mathrm{z}\left(\mathrm{x}\mathrm{,y}\right)=\mathrm{z}\left(\mathrm{x}\mathrm{.0}\right)\left(1+\mathrm{HAS}\left(\mathrm{y}\right).\left(1+\mathrm{f}\left(\mathrm{y}\right)\right)\right)$$

• where z(x,0) is a basic profile of prescribed convex shape in a prescribed longitudinal vertical plane (POxz), parallel to the horizontal direction of length and the vertical direction of height,
• A(y) is a first height function, which is continuous, greater than zero and less than or equal to 0.5,
• f(y) is a second function, which is continuous, which varies according to the y coordinate and which is greater than or equal to -1 and less than or equal to 1.

• D₁ est la distance entre les sommets des bosses, qui sont voisines l'une de l'autre,
• D₂ est la distance entre les points bas des creux, qui sont voisins l'un de l'autre, $$\mathrm{d}=\left|{\mathrm{x}}_2-{\mathrm{x}}_1\right|,$$
  
  • x₁ est la coordonnée x minimale ou maximale en valeur absolue pour le profil z(x,0),
  • x₂ est la coordonnée x du profil z(x,0), qui est différente de x₁ et qui est définie de telle sorte que z(x₂,0) = z(xi,0).

According to one embodiment of the invention, D ₁ ≤ 10.d and/or D ₂ ≤ 10.d, where

• D ₁ is the distance between the vertices of the bumps, which are close to each other,
• D ₂ is the distance between the low points of the hollows, which are close to each other, $$\mathrm{d}=\left|{\mathrm{x}}_2-{\mathrm{x}}_1\right|,$$
  
  • x ₁ is the minimum or maximum x coordinate in absolute value for the profile z(x,0),
  • x ₂ is the x coordinate of the profile z(x,0), which is different from x ₁ and which is defined such that z(x ₂ ,0) = z(xi,0).

According to one embodiment of the invention, 0 <A(y) ≤ 0.5.

où λ_k est une distance d'écartement, qui est prescrite le long de la direction transversale de largeur et qui associée à chaque couple de bosses voisines et/ou de creux voisins.According to one embodiment of the invention, the first function A(y) is equal to a prescribed constant A, positive and non-zero, the second function f(y) is defined between the bumps, which are close to one of the other and/or between the hollows, which are close to each other, by $$\mathrm{f}\left(\mathrm{y}\right)=\mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">cos</figure-callout>}\left(2\mathrm{\pi }{\mathrm{y/\lambda }}_{\mathrm{k}}\right),$$

where λ _k is a spacing distance, which is prescribed along the transverse width direction and which is associated with each pair of neighboring bumps and/or neighboring hollows.

According to one embodiment of the invention, the spacing distance λ _k is different between several pairs of neighboring bumps and/or neighboring hollows.

According to one embodiment of the invention, the spacing distance λ _k is identical between several pairs of neighboring bumps and/or neighboring hollows.

According to one embodiment of the invention, the second function f(y), which is continuous, which varies according to the coordinate y and which is greater than or equal to -1 and less than or equal to 1 height is chosen from at least one of the following functions: a slot function, a sum of a maximum of 10 slot functions, a periodic function, a sum of a maximum of 10 sinusoidal functions, a sum of a maximum of 10 sinusoidal functions out of phase with each other, a piecewise function defined by hyperbolic cosines, a piecewise function defined by hyperbolic cosines on at least one interval between two bumps, an elliptic function on at least one interval between two bumps, a Bézier curve with 20 control points at most over at least one interval between two bumps, at least one semi-circle over at least one interval between two bumps, at least one arc of a circle over at least one interval between two bumps, a polynomial of degree less than or equal to 20 over at least one interval between two bumps, a piecewise function defined by polynomials of degree less than or equal to 10 over at least one interval between two bumps, a function by a maximum of 15 pieces defined by polynomials of degree less than or equal to 10 on at least one interval between two bumps.

According to one embodiment of the invention, the first function A(y) is chosen from at least one of the following functions: a continuous function of class C1, a continuous function of class C2, a continuous function of class Cn, with n being an integer greater than or equal to 3, a continuous function of class Cinfini, an elliptic function over at least one interval between two bumps, a Bézier curve with at most 20 control points over at least one interval between two bumps, at least one semi-circle on at least one interval between two bumps, at least one arc of a circle on at least one interval between two bumps, a polynomial of degree less than or equal to 20 on at least one interval between two bumps, a function by pieces defined by polynomials of degree less than or equal to 10 on at least one interval between two bumps, a function by a maximum of 15 pieces defined by polynomials of degree less than or equal to 10 on at least one interval between two bumps.

According to one embodiment of the invention, the basic profile z(x,0) of prescribed convex shape in a prescribed longitudinal vertical plane, parallel to the horizontal direction of length and the vertical direction of height is chosen from at least one of the following functions: a convex continuous function, a continuous function of class C1, a continuous function of class C2, a continuous function of class Cn, with n being an integer greater than or equal to 3, a continuous function of class Cinfini, a elliptical function on at least one interval between two bumps, a Bézier curve with at most 20 control points, at least one semi-circle, at least one arc of a circle, a polynomial of degree less than or equal to 10, a function by pieces defined by polynomials of degree less than or equal to 10, a function by a maximum of 15 pieces defined by polynomials of degree less than or equal to 10.

According to one embodiment of the invention, the basic profile of prescribed convex shape in the prescribed longitudinal vertical plane, parallel to the horizontal direction of length and the vertical direction of height, comprises a downstream section in the form of a prescribed decreasing curve extending from an upper end of the base profile downstream, and at least one upstream section, which extends from the upper end of the base profile upstream and which is formed by at least one arc of circle, the downstream section and the section downstream having a continuity of their tangent one after the other at the level of the upper end.

According to one embodiment of the invention, the downstream section in the form of a prescribed decreasing curve has the coordinate z(x,0) = -0.5.x ^1.85 in a reference frame having as its origin the upper end of the profile for x ≥ 0 in the direction from upstream to downstream.

According to one embodiment of the invention, the basic profile of prescribed convex shape in the prescribed longitudinal vertical plane, parallel to the horizontal direction of length and the vertical direction of height, comprises a Bézier curve with 4 control points of prescribed coordinates in the prescribed longitudinal vertical plane.

où P₀, P₁, P₂, P₃ sont les 4 points de contrôle de coordonnées prescrites dans le plan vertical longitudinal prescrit (POxz), la courbe de Bézier étant définie dans un repère ayant pour origine une extrémité supérieure (40) du profil (z(x,0)) de base, t est un paramètre variant de 0 à 1.According to one embodiment of the invention, the Bézier curve with 4 control points is: $$B\left(t\right)={\left(1-\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="imgf0009.png"\; state="\{\{state\}\}">t</figure-callout>}\right)}^3\cdot {\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">P</figure-callout>}}_0+3\cdot {\left(1-\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">t</figure-callout>}\right)}^2\cdot t\cdot {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="imgf0003.png,imgf0006.png"\; state="\{\{state\}\}">P</figure-callout>}}_1+3\cdot \left(1-t\right)\cdot {\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">t</figure-callout>}}^2\cdot {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_2+{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="imgf0009.png"\; state="\{\{state\}\}">t</figure-callout>}}^3\cdot {\mathrm{<figure-callout\; id="3"\; label="P"\; filenames="imgf0009.png"\; state="\{\{state\}\}">P</figure-callout>}}_3$$

where P ₀ , P ₁ , P ₂ , P ₃ are the 4 control points of prescribed coordinates in the prescribed longitudinal vertical plane (POxz), the Bézier curve being defined in a reference frame having for origin an upper end (40) of the basic profile (z(x,0)), t is a parameter varying from 0 to 1.

-0.2818 ± 20% et $\frac{z}{H_{D0}}=-0.150\pm 20\%$

, P₁ a pour coordonnées : $-0.2818-0.2\cdot 0.2818\le \frac{x}{H_{D0}}\le -0.2818+0.2\cdot 0.2818$

et -0.12 ≤ $\frac{z}{H_{D0}}\le 0.2$

, P₂ a pour coordonnées $-0.2\le \frac{x}{H_{D0}}\le 0.5$

et $-0.05\le \frac{z}{H_{D0}}\le 0.3$

, P₃ a pour coordonnées : $0.7-0.2\cdot 0.7\le \frac{x}{H_{D0}}\le 0.7+0.2\cdot 0.7$

et -0.0904 - 0.2 · 0.0904 ≤ $\frac{z}{H_{D0}}\le -0.0904+0.2\cdot 0.0904$

, les coordonnées étant exprimées en mètre,
où H_D0 est une valeur minimum prescrite de charge de dimensionnement, . $$0.097-0.2\cdot 0.097\le A\le 0.097+0.2\cdot 0.097,$$

$$1.34-0.2\cdot 1.34\le {\lambda }_k\le 1.34+\mathrm{0,2}\cdot \mathrm{1,34}\mathrm{.}$$

According to one embodiment of the invention, P ₀ has the coordinates: $\frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}=$

-0.2818 ± 20% and $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}=-0.150\pm 20\%$

, P ₁ has the coordinates: $-0.2818-0.2\cdot 0.2818\le \frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}\le -0.2818+0.2\cdot 0.2818$

and -0.12 ≤ $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}\le 0.2$

, P ₂ has coordinates $-0.2\le \frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}\le 0.5$

And $-0.05\le \frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}\le 0.3$

, P ₃ has the coordinates: $0.7-0.2\cdot 0.7\le \frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}\le 0.7+0.2\cdot 0.7$

and -0.0904 - 0.2 · 0.0904 ≤ $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}\le -0.0904+0.2\cdot 0.0904$

, the coordinates being expressed in meters,
where H _D0 is a minimum prescribed design load value, . $$0.097-0.2\cdot 0.097\le \mathrm{HAS}\le 0.097+0.2\cdot 0.097,$$

$$1.34-0.2\cdot 1.34\le {\lambda }_k\le 1.34+0.2\cdot 1.34\mathrm{.}$$

According to one embodiment of the invention, the vertical distance between the top of the bump and the bottom point of the hollow in the height direction is less than 50% of a threshold thickness, which is a horizontal distance, taken according to the direction of length, between a vertical end edge of the upstream facing and a vertical end edge of the upper threshold surface.

According to one embodiment of the invention, the horizontal distance between the vertices of two bumps neighboring each other is less than 2 times a threshold thickness, which is a horizontal distance, taken along the length direction, between a vertical end edge of the upstream facing and a vertical end edge of the upper threshold surface.

A second object of the invention is a hydraulic dam comprising at least one overflow structure as described above.

• La figure Fig. 1A représente une vue schématique en coupe verticale de côté d'un seuil d'ouvrage déversant suivant l'état de la technique.
• La figure 1B représente une vue schématique en coupe verticale de côté d'un seuil d'ouvrage déversant suivant l'état de la technique dans le cas d'un décollement de nappe.
• La figure 2 représente une vue schématique en perspective d'un ouvrage déversant suivant un premier exemple de réalisation de l'invention.
• La figure 3 représente une vue schématique en perspective d'un ouvrage déversant suivant le premier exemple de réalisation de l'invention de la figure 2, montrant en niveaux de gris la valeur de la vitesse d'écoulement de l'eau.
• La figure 4 représente une vue schématique en coupe verticale d'un profil de base de forme prescrite à partir duquel est réalisé un ouvrage déversant suivant le premier exemple de réalisation de l'invention des figures 2 et 3.
• La figure 5A représente une vue schématique en perspective suivant un premier angle de vue d'un ouvrage déversant suivant un (autre) premier mode de réalisation de l'invention.
• La figure 5B représente une vue schématique en perspective suivant un deuxième angle de vue d'un ouvrage déversant suivant le premier mode de réalisation de l'invention.
• La figure 5C représente une vue schématique en perspective suivant un troisième angle de vue d'un ouvrage déversant suivant le premier mode de réalisation de l'invention.
• La figure 6A représente une vue schématique en perspective suivant un premier angle de vue d'un ouvrage déversant suivant un (autre) deuxième mode de réalisation de l'invention.
• La figure 6B représente une vue schématique en perspective suivant un deuxième angle de vue d'un ouvrage déversant suivant le deuxième mode de réalisation de l'invention.
• La figure 6C représente une vue schématique en perspective suivant un troisième angle de vue d'un ouvrage déversant suivant le deuxième mode de réalisation de l'invention.
• La figure 7A représente une vue schématique en perspective suivant un premier angle de vue d'un ouvrage déversant suivant un (autre) troisième mode de réalisation de l'invention.
• La figure 7B représente une vue schématique en perspective suivant un deuxième angle de vue d'un ouvrage déversant suivant le troisième mode de réalisation de l'invention.
• La figure 7C représente une vue schématique en perspective suivant un troisième angle de vue d'un ouvrage déversant suivant le troisième mode de réalisation de l'invention.
• La figure 8 représente un débit en ordonnée en fonction d'un rapport dimensionnel de la charge hydraulique sur le seuil en abscisses d'une part pour un ouvrage suivant le premier exemple de l'invention des figures 2, 3 et 4 et d'autre part pour un seuil standard de l'état de la technique.
• La figure 9 représente une vue schématique en perspective d'un ouvrage déversant suivant un deuxième exemple de réalisation de l'invention.
• La figure 10 représente une vue schématique de face d'un ouvrage déversant suivant un quatrième mode de réalisation de l'invention.
• La figure 11 représente une vue schématique de dessus d'une ligne passant par les sommets d'un ouvrage déversant suivant le quatrième mode de réalisation de l'invention.
• La figure 12 représente une vue schématique en coupe de profil d'un ouvrage déversant suivant le quatrième mode de réalisation de l'invention.
• La figure 13 représente vue schématique en coupe de profil d'un ouvrage déversant suivant une variante du quatrième mode de réalisation de l'invention.
• La figure 14 représente une vue schématique en coupe horizontale, vue de dessus, d'une partie de l'ouvrage déversant suivant le premier exemple de réalisation des figures 2 et 3 et suivant le deuxième exemple de réalisation de l'invention de la figure 9.
• La figure 15 représente un débit en ordonnée en fonction d'un rapport dimensionnel de la charge hydraulique sur le seuil en abscisses pour un suivant le deuxième exemple de réalisation de l'invention de la figure 9.

The invention will be better understood on reading the description which follows, given solely by way of non-limiting example with reference to the figures below of the appended drawings.

• The figure Fig. 1A represents a schematic vertical sectional side view of an overflow structure threshold according to the state of the art.
• There Figure 1B represents a schematic view in vertical section from the side of a threshold of an overflowing structure according to the state of the technique in the case of a sheet separation.
• There figure 2 represents a schematic perspective view of an overflowing structure according to a first embodiment of the invention.
• There Figure 3 represents a schematic perspective view of a spilling structure according to the first example of embodiment of the invention of the figure 2 , showing in grayscale the value of the water flow speed.
• There figure 4 represents a schematic view in vertical section of a basic profile of prescribed shape from which a spilling structure is produced according to the first example of embodiment of the invention of figure 2 And 3 .
• There figure 5A represents a schematic perspective view from a first angle of view of a spilling structure according to a (another) first embodiment of the invention.
• There Figure 5B represents a schematic perspective view from a second angle of view of an overflowing structure according to the first embodiment of the invention.
• There Figure 5C represents a schematic perspective view from a third angle of view of a spilling structure according to the first embodiment of the invention.
• There Figure 6A represents a schematic perspective view from a first angle of view of a spilling structure according to a (another) second embodiment of the invention.
• There Figure 6B represents a schematic perspective view from a second angle of view of a spilling structure according to the second embodiment of the invention.
• There Figure 6C represents a schematic perspective view from a third angle of view of an overflowing structure according to the second embodiment of the invention.
• There Figure 7A represents a schematic perspective view from a first angle of view of a spilling structure according to a (another) third embodiment of the invention.
• There Figure 7B represents a schematic perspective view from a second angle of view of an overflowing structure according to the third embodiment of the invention.
• There Figure 7C represents a schematic perspective view from a third angle of view of an overflowing structure according to the third embodiment of the invention.
• There figure 8 represents a flow rate on the ordinate as a function of a dimensional ratio of the hydraulic load to the threshold on the abscissa on the one hand for a structure following the first example of the invention of figures 2 , 3 And 4 and on the other hand for a standard threshold of the state of the art.
• There Figure 9 represents a schematic perspective view of an overflowing structure according to a second embodiment of the invention.
• There Figure 10 represents a schematic front view of an overflow structure according to a fourth embodiment of the invention.
• There Figure 11 represents a schematic top view of a line passing through the vertices of an overhanging structure according to the fourth embodiment of the invention.
• There Figure 12 represents a schematic profile sectional view of an overflowing structure according to the fourth embodiment of the invention.
• There Figure 13 represents a schematic view in profile section of an overflowing structure according to a variant of the fourth embodiment of the invention.
• There Figure 14 represents a schematic view in horizontal section, seen from above, of a part of the spilling structure according to the first example of realization of the figures 2 And 3 and according to the second example of embodiment of the invention of the Figure 9 .
• There Figure 15 represents a flow rate on the ordinate as a function of a dimensional ratio of the hydraulic load to the threshold on the abscissa for a following the second example of embodiment of the invention of the Figure 9 .

To figures 2 to 15 , the overflowing structure 1 comprises an upstream facing 2 and an upper surface 4 threshold crest, which is located downstream relative to the upstream facing 2 in the horizontal direction Ox of length going from upstream to downstream. In these figures are also represented the vertical direction Oz of height, oriented from bottom to top, and the horizontal transverse direction Oy of width, which is perpendicular to the horizontal direction Ox of length going from the upstream facing 2 to the upper surface 4 crest of threshold and is perpendicular to a vertical direction Oz of height. The upper surface 4 threshold crest descending downstream. The overflow structure 1 may include another downstream surface which is connected downstream of the upper surface 4 threshold crest. The overflowing structure 1 may also not include any other downstream surface connected downstream of the upper surface 4 threshold crest. The upstream facing 2 (and the other downstream surface when present), are further down than the upper surface 4 threshold crest. The upstream facing 2 serves to obstruct the flow of water, to retain the water up to a certain height delimited by the upper surface 4 threshold crest. When the water located on the side of the upstream facing 2 exceeds the upper surface 4 threshold crest, the water overflows towards the downstream of the upper surface 4 threshold crest. The upper surface 4 threshold crest then accompanies the fall of water from upstream to downstream. The upper surface 4 threshold ridge extends at least along the horizontal transverse direction Oy of width.

The overflow structure 1 according to the invention can be part, for example, of a flood spillway, an overflow threshold, a spillway, an overflow valve, an overflow valve, which can be part of a hydraulic dam or other. For example, the discharge structure 1 according to the invention could be part more generally of a basin, where there can be a discharge of water, such as for example a discharge basin of a nuclear power plant for electricity production, or a factory basin, or in a water distribution network, such as for example a storm overflow.

According to the invention, figures 2 to 15 , the upper surface 4 threshold ridge comprises, along the horizontal transverse direction Oy of width, one (or more) bump 41 and one (or more) hollows 42. Thus, the upper surface 4 threshold ridge may comprise a ( or more) bump 41 and one (or more) hollows 42 in one (or more) plane Pyz of width, parallel to the transverse direction Oy of width and to the vertical direction Oz of height, as shown in particular in figures 2 to 15 . The upper surface 4 threshold crest may also include one (or more) bump 41 and one (or more) hollows 42 in (or more) one (or more) horizontal plane Pxy, parallel to the horizontal direction Ox of length and to the transverse direction Oy of width, as shown in particular in figures 2 to 15 .

Thus, the upper threshold surface 4 may comprise an alternation of bumps 41 and hollows 42 along the transverse direction Oy of width in the plane Pyz of width, and/or in the horizontal plane Pxy.

We describe below the laws which govern a spilling structure according to the state of the art, with reference to the figures 1A And 1B , in an example where the upper surface 4 threshold crest is rectilinear and horizontal along the transverse direction Oy of width.

In the state of the art, as shown in the Figure 1A , for a water height H above the upper surface 4 threshold crest upstream of this, that is to say on the side of the upstream facing 2, we can observe a separation (shown by the reference DEC at Figure 1B ) of the water vein according to the Figure 1B , when the flow rate Q of water above the upper surface 4 threshold peak becomes greater than a design flow rate Q _D and when this height H of water becomes greater than a prescribed value H _D of design load (H > H _D ) or 1.1 times this prescribed value H _D of design load (H > 1.1.H _D ). This DEC separation of the water vein significantly degrades the performance of the upper surface 4 threshold peak. In the event of separation, depressions at the water/upper surface interface 4 threshold peak appear. This DEC separation can lead to a flapping of the water table which is detrimental to the stability of the structure.

To the Figure 1B , this DEC separation of the water vein is the fact that the trajectory of the lower sheet of the water jet pouring downstream of the upper surface 4 threshold crest is at a non-zero vertical distance above the surface downstream 30.

où L est la largeur de la surface supérieure 4 crête de seuil le long de la direction transversale Oy de largeur, g est l'accélération de la pesanteur et C_d est un coefficient de débit.The general law of flow rate of water flows submerged on the upper surface 4 threshold crest gives this flow rate Q of water according to an increasing function of the height H of water above the upper surface 4 threshold crest upstream of this (height - flow law), according to the following equation: $$Q={\mathrm{<figure-callout\; id="2"\; label="VS\; d\; L"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">VS</figure-callout>}}_{d}L\sqrt{2{\mathit{<figure-callout\; id="3"\; label="gH"\; filenames="imgf0009.png"\; state="\{\{state\}\}">gH</figure-callout>}}^3}$$

where L is the width of the upper surface 4 threshold crest along the transverse direction Oy of width, g is the acceleration of gravity and C _d is a flow coefficient.

The flow coefficient C _d is variable as a function of the height H. Thus the higher the flow coefficient C _d , the more the flow rate Q is increased or otherwise the higher the performance of the upper surface 4 threshold peak.

Generally speaking, the flow coefficient C _d can be given by the following equation: $${\mathrm{VS}}_d=0.495{\left(\frac{H}{H_D}\right)}^{0.12}$$

We therefore have, when the flow rate Q of water above the upper surface 4 threshold peak is equal to the design flow rate Q _D , the flow coefficient C _d which is equal to 0.495.

The invention makes it possible to increase the prescribed value H _D of design load, from which the DEC separation is observed. This new geometry shifts upwards the point DEC of separation of the water vein in the height - flow law and thus makes it possible to increase the admissible load without separation (= prescribed value H _D of design load) between 5% and 25%, which is equivalent to an increase in the design flow rate Q _D without separation of at least 50%.

The upper threshold surface 4 according to the invention makes it possible to create water vortices and local water depression zones upstream of the hollows 42 and water confinement zones upstream of the bumps 41, which tends to flatten the flow of water upstream against this upper threshold surface 4, which increases the prescribed value H _D of design load. Thus, thanks to the invention, the overflowing structure can be better protected from a surge of water.

According to one embodiment of the invention, in particular in the first example of embodiment of the invention, represented in figure 2 , 3 And 4 and in the second embodiment of the invention, represented in Figure 9 , in each vertical longitudinal plane Pxz, the upper surface 4 of the threshold (and possibly the downstream part of the surface of the upstream facing 2, connected to the upper surface 4 of the threshold) is constructed by an equalization with respect to a base profile C = z(x,0), which has a prescribed shape in a determined longitudinal vertical plane POxz base, with a prescribed variable ratio of homothety H _D /H _D0 = z(x,y)/z(x,0) along the width coordinate y of the upper threshold surface 4 along the transverse width direction Oy. This prescribed variable ratio of homothety H _D /H _D0 = z(x,y)/z(x,0) is non-zero and is a prescribed function, depending on the width coordinate y of the upper threshold surface 4 in the transverse direction Oy of width. The prescribed homothety ratio H _D /H _D0 = z(x,y)/z(x,0) is therefore different in several longitudinal vertical planes Pxz, spaced from each other along the transverse direction Oy of width. The prescribed variable ratio of homothety H _D /H _D0 = z(x,y)/z(x,0) increases going from a hollow 42 to a bump 41 along the transverse direction Oy of width. The prescribed variable ratio of homothety H _D /H _D0 = z(x,y)/z(x,0) decreases going from a bump 41 to a hollow 42 along the transverse direction Oy of width.

According to one embodiment of the invention, represented in figures 2 to 15 , the prescribed variable ratio H _D /H _D0 of homothety or z(x,y) / z(x,0) is curved at least with a continuous derivative (C1 continuous) on the coordinates. Consequently, the upper threshold surface 4 is without protruding edges.

According to one embodiment of the invention, represented in figure 2 , 9 And 14 , the upper threshold surface 4 has, on an upstream side 45 of the upper threshold surface 4, a curve Cxy, which is formed by the bump(s) 41 and the hollow(s) 42 in the horizontal plane(s) Pxy . The Cxy curve has at least a continuous derivative in the horizontal Pxy plane(s). The upstream side 45 is located upstream relative to the top of the upper threshold surface 4 in each plane Pxz. The upstream side 45 is located upstream relative to the upper end 40 of the base profile (C, z(x,0)) in the plane POxz. Consequently, the bump(s) 41 and the hollow(s) 42 propagate in the horizontal Pxy plane(s) and are also present in the horizontal Pxy plane(s). This characteristic allows the flow to be increased without separation.

According to one embodiment of the invention, represented in figure 2 , 3 And 9 , the basic profile C or z(x,0) has a downstream point (x1 at the figure 4 ) determined reference, whose transformation by the homothety along the width coordinate y is located on a downstream rectilinear segment 31 of the upper surface 4 threshold peak. The segment 31 is downstream relative to the rest of the upper surface 4 threshold ridge. The downstream rectilinear segment 31 of the upper surface 4 threshold crest is parallel to the transverse direction Oy of width. This makes it possible to have a reference point for the center of the homothety, which can be located on a three-dimensional line along the direction Oy but is not located in the downstream rectilinear segment 31.

The downstream rectilinear segment 31 of the upper surface 4 threshold ridge can be formed by the end edge 31 of the upper surface 4 threshold crest (previous case without other downstream surface).

In another embodiment, the rectilinear downstream segment 31 of the upper surface 4 threshold crest is connected to another downstream surface (previous case with the other downstream surface).

According to one embodiment of the invention, represented in figures 2 , 3 , 5A to 7C , 9 And 14 , the prescribed variable ratio of homothety H _D /H _D0 = z(x,y)/z(x,0) is periodic along the transverse direction Oy of width. The prescribed variable homothety ratio H _D /H _D0 = z(x,y)/z(x,0) can be periodic according to a prescribed repetition width λ (period or wavelength) along the transverse direction Oy of width. Thus, points 411 of the same height (along the vertical direction Oz of height) of each of the pairs of two consecutive bumps 41 along the transverse direction Oy of width have the same constant spacing distance between these two points 411, this constant spacing distance being equal to the prescribed repetition width λ, as shown in Figure 7A . Likewise, according to one embodiment of the invention, points 421 of the same height (along the vertical direction Oz of height) of each of the pairs of two consecutive hollows 42 along the transverse direction Oy of width have the same distance constant spacing between these two points 422, this constant spacing distance being equal to the prescribed repetition width λ, as shown in Figure 7C .

According to one embodiment of the invention, represented in figure 2 And 3 , 5A, 5B, 5C , 6A, 6B, 6C , 9 And 14 , the prescribed variable ratio of homothety H _D /H _D0 = z(x,y)/z(x,0) is sinusoidal between the bumps 41, which are close to each other and/or between the hollows 42, which are close to each other as a function of a width coordinate y of the upper threshold surface 4 in the transverse direction Oy of width.

où A est une amplitude prescrite de hauteur, qui est positive et non nulle, λ est la largeur de répétition λ prescrite le long de la direction transversale Oy de largeur, y est la coordonnée de largeur de la surface supérieure 4 de seuil suivant la direction transversale Oy de largeur, H_D0 est une valeur minimum prescrite de charge de dimensionnement.According to one embodiment of the invention, represented in figure 2 And 3 , 9 And 14 , the prescribed variable ratio of homothety H _D /H _D0 = z(x,y)/z(x,0) is defined by $$H_D={\mathrm{<figure-callout\; id="0"\; label="H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">H</figure-callout>}}_D\left(1+\mathrm{HAS}\left(1+\mathit{<figure-callout\; id="2"\; label="cos"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">cos</figure-callout>}\left(\frac{2\pi }{\lambda }y\right)\right)\right)$$

where A is a prescribed height amplitude, which is positive and not zero, λ is the prescribed repetition width λ along the transverse direction Oy of width, y is the width coordinate of the upper threshold surface 4 along the direction transverse Oy of width, H _D0 is a prescribed minimum value of design load.

More generally, according to one embodiment of the invention, the bumps 41 and/or the hollows 42 may not be periodic along the transverse direction Oy of width. An example of such a non-periodic embodiment is shown in figures 10, 11 , 12 and 13 , which are views of the same work following different viewing angles, as mentioned above. To these figures 10, 11 , 12 and 13 , points B1, B2, B3, B4 are tops of bumps 41, points C1, C2, C3 are bottoms of hollows 42.

We can imagine more marked deformations in a preferred direction. Thus, the separation distance Y (represented in figure 2 ) between the bumps 41 neighboring each other (for example the spacing distance Y taken at the top of the neighboring bumps 41) along the transverse direction Oy of width can be variable, and can be greater than or equal to 0.6 times a prescribed value Y0 of width and less than or equal to 1.4 times the prescribed value Y0 of width. Likewise, the spacing distance Y between the hollows 42 neighboring each other (for example the spacing distance Y taken at the lowest point of the hollows 42) along the transverse direction Oy of width can be variable, and may be greater than or equal to 0.6 times a prescribed value Y0 of width and less than or equal to 1.4 times the prescribed value Y0 of width.

In each pair of two consecutive bumps 41 along the transverse direction Oy of width, the prescribed variable ratio H _D /H _D0 of homothety can be defined in the manner indicated above between these bumps 41 neighboring one of the 'other and/or in each pair of two consecutive recesses 42 along the transverse direction Oy of width.

The above embodiments thus apply a deformation to the upper threshold surface 4, which is propagated in a variable manner as a function of the coordinate y along the transverse direction Oy of width, as shown for example to figure 2 , 3 , 9 And 14 . We thus have an upper threshold surface 4 with a vertical profile varying along the transverse direction Oy of width.

More general embodiments of the coordinates z(x,y) of the upper threshold surface 4 according to the invention are described below, into which the embodiments described above of the figures 2 to 15 .

According to one embodiment of the invention, the upper threshold surface 4 has a coordinate z(x,y) in the vertical direction Oz of height, this coordinate z(x,y) depending on the coordinate x of the upper surface 4 of threshold along the horizontal direction Ox of length and depending on the y coordinate of the upper surface 4 of threshold along the transverse direction Oy of width, according to the following equation: $$\mathrm{z}\left(\mathrm{x}\mathrm{,y}\right)=\mathrm{z}\left(\mathrm{x}\mathrm{.0}\right)\left(1+\mathrm{HAS}\left(\mathrm{y}\right).\left(1+\mathrm{f}\left(\mathrm{y}\right)\right)\right).$$

The basic profile C = z(x,0) has a prescribed convex shape in the prescribed longitudinal vertical plane POxz, parallel to the horizontal direction Ox in length and the vertical direction Oz in height.

A(y) is a first height function, which is continuous, greater than zero and less than or equal to 0.5.

f(y) is a second function, which is continuous, which varies according to the y coordinate and which is greater than or equal to -1 and less than or equal to 1.

According to one embodiment of the invention, we define xi (represented for the first example of the figure 4 , the base profile for the second example of the Figure 9 not shown) as being the minimum or maximum x coordinate in absolute value for the basic profile z(x,0). We define x ₂ as being the x coordinate of the profile z(x,0), which is different from x ₁ and which is defined such that z(x _2,0 ) = z(x _1,0 ). We define the distance d = |x ₂ - x ₁ |. We define the distance D ₁ between the vertices 411 of the bumps 41, which are close to each other, as well as the distance D ₂ between the low points 421 of the hollows 42, which are close to each other. , such that D ₁ ≤ 10.d and/or D ₂ ≤ 10.d.

According to one embodiment of the invention, 0 <A(y) ≤ 0.5.

According to one embodiment of the invention, the first function A(y) is equal to a prescribed constant A, positive and non-zero, the second function f(y) is defined between the bumps 41, which are adjacent to one another. on the other and/or between the hollows 42, which are close to each other, by f(y) = cos (2πy/ λ _k ), where λ _k is a spacing distance Y, which is prescribed along the transverse direction Oy of width and which is associated with each pair k of neighboring bumps 41 and/or neighboring hollows 42. This embodiment therefore corresponds to the first example, represented in figures 2 And 3 and in the second example of the Figure 9 .

According to one embodiment of the invention, the spacing distance λ _k is different between several pairs of neighboring bumps 41 and/or neighboring hollows 42.

According to another embodiment of the invention, the spacing distance λ _k is identical between several pairs of neighboring bumps 41 and/or neighboring hollows 42.

Embodiments of the second function f(y), the first function A(y) and the basic profile C = z(x,0) of prescribed shape are described above.

Following the first example of embodiment of the invention at figure 4 , the basic profile C = z(x,0) of prescribed shape comprises in the basic plane POxz, several sections, which have different geometric shapes and which are connected to each other, with for example a continuity of the tangent between the sections and in sections.

A downstream section C ₀ of the basic profile C of prescribed shape extends from the upper end 40 of this profile C following a decreasing curve downstream of this upper end 40 in the horizontal direction Ox in length and downwards , that is to say in a downstream dial 43. For example, the origin O of the mark of the coordinate x of length following the horizontal direction Ox of length, of the coordinate y of width following the transverse direction Oy of width and the height coordinate z along the vertical height direction Oz, is located at the upper end 40 of the basic profile C of prescribed shape. The decreasing curve of the downstream section Co of the basic profile C of prescribed shape towards the downstream can be z = -0.5.x ^1.85 .

The downstream section Co of the basic profile C of prescribed shape can be connected upstream of the upper end 40 of the basic profile C of prescribed shape to one or more upstream sections C ₁ , C ₂ , C ₃ , connected one following the other, that is to say in an upstream dial 44. The downstream section C ₀ and the upstream section C ₁ have continuity of their tangent one following the other at the level of the upper end 40. Each upstream section C ₁ , C ₂ , C ₃ can each, for example, be in the shape of an arc of a circle. The radii of the arcs of the upstream sections C ₁ , C ₂ , C ₃ can be decreasing and with centers located higher and higher and more and more upstream, going from a section C ₁ , C ₂ , C ₃ towards the other from downstream to upstream. The arcs of a circle have a continuity of their tangent one after the other from downstream to upstream.

Thus, for example, the first upstream section C ₁ can be a first circular arc C ₁ , which is centered on a first center A ₁ and which has a first radius R ₁ , being connected to the upper end 40 of the profile Basic C of prescribed form. The second upstream section C ₂ can be a second arc of a circle C ₁ , which is centered on a second center A ₂ and which has a second radius R ₂ , being connected to the first upstream section C ₁ and being located upstream of the first upstream section C ₁ . The third upstream section C ₃ can be a third arc of a circle C ₃ , which is centered on a third center A ₃ and which has a third radius R ₃ , being connected to the second upstream section C ₂ and being located upstream of the second upstream section C ₂ .

Below, an example of the basic profile C = z(x,0) of prescribed shape is given, with the coordinates and radii expressed in proportion to the prescribed design load value H _D.

The first center A ₁ has for example coordinates x= 0 and z = -0.5. The first radius R ₁ is for example equal to 0.5. The first arc of a circle C ₁ extends in the domain of validity of the abscissa x going from -0.175 to 0.

The second center A ₂ has for example coordinates x= -0.105 and z = -0.219. The second radius R ₂ is for example equal to 0.2. The second arc of circle C ₂ extends in the domain of validity of the abscissa x going from -0.276 to -0.175.

The third center A ₃ has for example coordinates x= -0.2418 and z = -0.136. The third radius R ₃ is for example equal to 0.04. The third arc of circle C ₃ extends in the domain of validity of the abscissa x going from -0.2818 to -0.276.

Of course, the basic profile C of prescribed shape may be different from the example mentioned above, the homothety mentioned above being able to apply to any basic profile C = z(x,0) in prescribed form.

There figure 8 represents the flow rate Q (expressed in m ³ /s), calculated by a computer simulation, on the ordinate, as a function of the H/H _D0 ratio on the abscissa, on the one hand for an upper surface 4 of known standard threshold according to the figure 1 (flow rate Q represented by the points formed by small circles filled with white, surface 4 called standard threshold) and on the other hand for the upper surface 4 of the threshold of the overflowing structure following the first example of figures 2 , 3 And 4 according to the invention (flow rate Q, Q _INV represented by the points formed by small circles filled with black, surface 4 called threshold with homothetic profile).

To the figure 8 , the upper surface 4 of standard threshold known according to the figure 1 corresponds to the basic C profile of prescribed form of the figure 4 , extended in a rectilinear and horizontal manner following the direction Oy of width, that is to say with the amplitude A taken to be zero in the formula mentioned above of the homothety ratio H _D /H _D0 . = z(x, y) / z(x,0).

To the figure 8 , the upper threshold surface 4 of the overflow structure according to the invention corresponds to the homothetic embodiment described above for two identical spacing distances λ, for an amplitude A = 5% of H _D0 and a distance λ d spacing = 75% of H _D0 and for a spill width (y) fixed at 1.5 m, in the formula for the prescribed variable ratio of homothety H _D /H _D0 . = z(x, y) / z(x,0).

To the figure 8 , we do not observe any separation of the water blade on the upper surface 4 of the threshold of the overflowing structure according to the invention for the abscissa H/H _D0 going up to 1.7, whereas such separation DEC of the water blade on the upper surface 4 of the standard threshold is observed for an abscissa H/H _D0 greater than 1.34.

Consequently, for the standard threshold, the flow values without separation are only valid for H/H _D0 less than or equal to 1.34. For the standard threshold, for H/H _D0 equal to 1.34 the flow rate (Q _st ) is equal to 5 m ³ /s. The maximum flow rate of the standard threshold without separation is therefore 5 m ³ /s.

There figure 8 shows that for the points having the abscissa of the ratio H/H _D0 equal to 1.67 the flow rate Q _INV of the upper threshold surface 4 of the spilling structure according to the invention without separation is equal to 7.8 m ³ /s, and is therefore increased by 56% compared to the maximum flow rate of the standard threshold without separation of 5 m ³ /s.

Following the second example of embodiment of the invention in Figure 9 , the basic profile C = z(x,0) of prescribed convex shape in the prescribed longitudinal vertical plane POxz comprises a Bézier curve with 4 control points of prescribed coordinates in the prescribed longitudinal vertical plane POxz.

où P₀, P₁, P₂, P₃ sont les 4 points de contrôle de coordonnées prescrites dans le plan vertical longitudinal prescrit POxz, la courbe de Bézier étant définie dans un repère ayant pour origine l'extrémité supérieure 40 du profil z(x,0) de base. Le plan vertical longitudinal prescrit POxz est parallèle à la direction horizontale Ox de longueur et à la direction verticale Oz de hauteur. Le paramètre t varie de 0 à 1. Le couple B(t) désigne les coordonnées x et z(x,0) du profil de base dans le plan vertical longitudinal prescrit POxz. Les 4 points de contrôle P₀, P₁, P₂, P₃ de coordonnées prescrites sont donnés par leurs coordonnées prescrites x et z dans le plan vertical longitudinal prescrit POxz. Par conséquent, la coordonnée x du profil de base dans le plan vertical longitudinal prescrit POxz est la combinaison B(t) mentionnée ci-dessus en fonction des coordonnées x des4 points de contrôle P₀, P₁, P₂, P₃. La coordonnée z du profil de base dans le plan vertical longitudinal prescrit POxz est la combinaison B(t) mentionnée ci-dessus en fonction des coordonnées z des 4 points de contrôle P₀, P₁, P₂, P₃.This Bézier curve with 4 control points can be: $$B\left(t\right)={\left(1-\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="imgf0009.png"\; state="\{\{state\}\}">t</figure-callout>}\right)}^3\cdot {\mathrm{<figure-callout\; id="0"\; label="P"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">P</figure-callout>}}_0+3\cdot {\left(1-\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">t</figure-callout>}\right)}^2\cdot t\cdot {\mathrm{<figure-callout\; id="1"\; label="P"\; filenames="imgf0003.png,imgf0006.png"\; state="\{\{state\}\}">P</figure-callout>}}_1+3\cdot \left(1-t\right)\cdot {\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">t</figure-callout>}}^2\cdot {\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">P</figure-callout>}}_2+{\mathrm{<figure-callout\; id="3"\; label="t"\; filenames="imgf0009.png"\; state="\{\{state\}\}">t</figure-callout>}}^3\cdot {\mathrm{<figure-callout\; id="3"\; label="P"\; filenames="imgf0009.png"\; state="\{\{state\}\}">P</figure-callout>}}_3$$

where P ₀ , P ₁ , P ₂ , P ₃ are the 4 control points of prescribed coordinates in the prescribed longitudinal vertical plane POxz, the Bézier curve being defined in a reference frame having as its origin the upper end 40 of the profile z( x,0) basic. The prescribed longitudinal vertical plane POxz is parallel to the horizontal direction Ox in length and the vertical direction Oz in height. The parameter t varies from 0 to 1. The pair B(t) designates the coordinates x and z(x,0) of the base profile in the prescribed longitudinal vertical plane POxz. The 4 control points P ₀ , P ₁ , P ₂ , P ₃ of prescribed coordinates are given by their prescribed coordinates x and z in the prescribed longitudinal vertical plane POxz. Therefore, the x-coordinate of the base profile in the prescribed longitudinal vertical plane POxz is the above-mentioned combination B(t) based on the x-coordinates of the 4 control points P ₀ , P ₁ , P ₂ , P ₃ . The z coordinate of the basic profile in the prescribed longitudinal vertical plane POxz is the combination B(t) mentioned above according to the z coordinates of the 4 control points P ₀ , P ₁ , P ₂ , P ₃ .

• P₀ a pour coordonnées : $\frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}=-0.2818\pm 20\%$
  
  et $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}=-0.150\pm 20\%$
  
  ,
• P₁ a pour coordonnées : $-0.2818-0.2\cdot 0.2818\le \frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}\le -0.2818+0.2\cdot 0.2818$
  
  et -0.12 ≤ $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}\le 0.2$
  
  ,
• P₂ a pour coordonnées $-0.2\le \frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}\le -0.5$
  
  et $-0.05\le \frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}\le 0.3$
  
  ,
• P₃ a pour coordonnées : $0.7-0.2\cdot 0.7\le \frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}\le 0.7+0.2\cdot 0.7$
  
  et -0.0904 - 0.2 · 0.0904 ≤ $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}\le -0.0904+0.2\cdot 0.0904$
  
  ,
• les coordonnées étant exprimées en mètre,
• où H_D0 est la valeur minimum prescrite de charge de dimensionnement, . $$0.097-0.2\cdot 0.097\le A\le 0.097+0.2\cdot 0.097,$$
  
  $$1.34-0.2\cdot 1.34\le {\lambda }_k\le 1.34+0.2\cdot 1.34.$$
  

According to one embodiment,

• P ₀ has coordinates: $\frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}=-0.2818\pm 20\%$
  
  And $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}=-0.150\pm 20\%$
  
  ,
• P ₁ has the coordinates: $-0.2818-0.2\cdot 0.2818\le \frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}\le -0.2818+0.2\cdot 0.2818$
  
  and -0.12 ≤ $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}\le 0.2$
  
  ,
• P ₂ has coordinates $-0.2\le \frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}\le -0.5$
  
  And $-0.05\le \frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}\le 0.3$
  
  ,
• P ₃ has the coordinates: $0.7-0.2\cdot 0.7\le \frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}\le 0.7+0.2\cdot 0.7$
  
  and -0.0904 - 0.2 · 0.0904 ≤ $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}\le -0.0904+0.2\cdot 0.0904$
  
  ,
• the coordinates being expressed in meters,
• where H _D0 is the minimum prescribed design load value, . $$0.097-0.2\cdot 0.097\le \mathrm{HAS}\le 0.097+0.2\cdot 0.097,$$
  
  $$1.34-0.2\cdot 1.34\le {\lambda }_k\le 1.34+0.2\cdot 1.34.$$
  

According to one embodiment, 0.01 ≤ A ≤ 0.2 and 0.5 ≤ λ _k ≤ 1.5.

• P₀ a pour coordonnées : $\frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}=-0.2818$
  
  et $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}=-0.150$
  
  ,
• P₁ a pour coordonnées : : $\frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}=-0.2818$
  
  et $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}=0.200$
  
  ,
• P₂ a pour coordonnées : $\frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}=0.2930$
  
  et $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}=0.3000$
  
  ,
• P₃ a pour coordonnées : : $\frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}=0.7000$
  
  et $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}=-0.0904$
  
  ,
• A = 0.097,
• λ_k = 1.34.

According to the second embodiment example,

• P ₀ has coordinates: $\frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}=-0.2818$
  
  And $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}=-0.150$
  
  ,
• P ₁ has the coordinates: $\frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}=-0.2818$
  
  And $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}=0.200$
  
  ,
• P ₂ has the coordinates: $\frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}=0.2930$
  
  And $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}=0.3000$
  
  ,
• P ₃ has the coordinates: $\frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}=0.7000$
  
  And $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}=-0.0904$
  
  ,
• A = 0.097,
• _λk = 1.34.

et $\frac{z}{H_{D0}}\le -1$

. Par exemple, le point P_r de raccordement de la courbe de Bézier peut avoir pour coordonnées $\frac{x}{H_{D0}}=-0.2818$

et -4.5 ≤ $\frac{z}{H_{D0}}\le -1$

.The Bézier curve can connect to the upstream facing 2 at a connection point P _r in the prescribed longitudinal vertical plane POxz. The point P _r corresponds to the minimum depth of deformation of the upstream facing 2.
The connection point P _r of the Bézier curve can have coordinates -0.2818 - $0.2\cdot 0.2818\le \frac{\mathrm{<figure-callout\; id="0"\; label="x\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">x</figure-callout>}}{H_D}\le -0.2818+0.2\cdot 0.2818$

And $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}\le -1$

. For example, the connection point P _r of the Bézier curve can have coordinates $\frac{x}{{\mathrm{<figure-callout\; id="0"\; label="H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">H</figure-callout>}}_D}=-0.2818$

and -4.5 ≤ $\frac{\mathrm{<figure-callout\; id="0"\; label="z\; H\; D"\; filenames="imgf0005.png,imgf0010.png"\; state="\{\{state\}\}">z</figure-callout>}}{H_D}\le -1$

.

There Figure 15 represents the flow rate Q (expressed in m ³ /s), calculated by a computer simulation, on the ordinate, as a function of the H/H _D0 ratio on the abscissa, on the one hand for an upper surface 4 of known standard threshold according to the figure 1 (flow rate Q represented by the squares filled with white, surface 4 called standard threshold) and on the other hand for the upper surface 4 of the threshold of the overflowing structure following the second example of the Figure 9 according to the invention (flow rate Q, Q _INV represented by the points formed by small circles filled with black, surface 4 called threshold with homothetic profile).

To the Figure 15 , the upper threshold surface 4 of the overflow structure according to the invention corresponds to the homothetic embodiment described above for two identical spacing distances λ, for an amplitude A = 5% of H _D0 and a distance λ d spacing = 75% of H _D0 and for a spill width (y) fixed at 1.5 m, in the formula for the prescribed variable ratio of homothety H _D /H _D0 . = z(x, y) / z(x,0).

To the Figure 15 , we do not observe any separation of the water blade on the upper surface 4 of the threshold of the overflowing structure according to the invention for the abscissa H/H _D0 going up to 2.3, whereas such separation DEC of the water blade on the upper surface 4 of the standard threshold is observed for an abscissa H/H _D0 greater than 1.34.

Consequently, for the standard threshold, the flow values without separation are only valid for H/H _D0 less than or equal to 1.34. For the standard threshold, for H/H _D0 equal to 1.34, the flow rate (Q _st ) is equal to 17 m ³ /s. The maximum flow rate of the standard threshold without separation is therefore 17 m ³ /s.

There Figure 15 shows that for the points having the abscissa of the ratio H/H _D0 equal to 2.3, the flow rate Q _INV of the upper threshold surface 4 of the spilling structure according to the invention without separation is equal to 46 m ³ /s, and is therefore increased by 170% compared to the maximum flow rate of the standard threshold without separation of 17 m ³ /s.

According to one embodiment of the invention, the amplitude of a deformation (vertical distance between the top of a bump 41 and a low point of a hollow 42) in the height direction Oz is less than 50% of the threshold thickness, which is taken in the direction Ox of length between a vertical edge 21 at the end of the upstream facing 2 and a vertical edge 31 at the end of the surface 4.

According to one embodiment of the invention, the horizontal distance between the vertices of two bumps 41 neighboring each other (or local maxima) is less than 2 times the threshold thickness, which is taken in the direction Ox of length between a vertical edge 21 at the end of the upstream facing 2 and a vertical edge 31 at the end of the surface 4.

In the embodiments of the invention, represented in figures 2 to 15 , the upstream facing 2 comprises, in top view, one (or more) concavities 22 extending downwards the hollow(s) 42 to the lower vertical edge 21 at the end of the upstream facing 2.

In the embodiments of figures 2 to 15 , the upstream facing 2 comprises or is formed by a surface parallel to the height direction Oz, which connects to the upper threshold surface 4. Thus, the upstream facing 2 comprises or is formed by a surface formed of generators parallel to the height direction Oz. This surface of the upstream facing 2 can be curved in top view, as shown in figure 2 , 3 , 5A, 5B, 5C .

In the embodiments of figure 2 , 3 , 4 , 5A, 5B, 5C , the upstream facing 2 comprises a surface 23, which is overhanging relative to the lower vertical edge 21 at the end of the upstream facing 2. This surface 23 extends downward the bump(s) 41.

The invention makes it possible to generate three-dimensional modifications of the upper surface 4 threshold peak for a spill length fixed in the transverse direction Oy of width.

Thus, the invention could also be applied to the upper surface 4 threshold crest described above, making changes of directions or zigzags in top view, to have an increased total length along these changes of directions in the plane horizontal Pxy.

Of course, the embodiments, features, possibilities and examples described above can be combined with each other or selected independently of each other.

Claims (27)

Overflowing structure (1), comprising an upstream facing (2), which obstructs the flow of water, and an upper surface (4) threshold crest, the upper surface (4) threshold crest being higher than the upstream facing (2) and being located downstream of the upstream facing (2), the upper surface (4) threshold crest descending downstream, the upper surface (4) threshold crest extending along at least one transverse direction (Oy) of width, which is perpendicular to at least one horizontal direction (Ox) of length going from the upstream facing (2) towards the downstream and which is perpendicular to a vertical direction (Oz) of height, characterized in that the upper threshold surface (4) has at least one bump (41) and at least one depression (42) in at least one plane (Pyz) of width, parallel to the transverse direction (Oy) of width and to the vertical direction (Oz) of height and/or in at least one horizontal plane (Pxy), parallel to the horizontal direction (Ox) of length and to the transverse direction (Oy) of width, in each vertical longitudinal plane (Pxz), parallel to the horizontal direction (Ox) of length and to the vertical direction (Oz) of height, the upper threshold surface (4) corresponds to a homothety, having a prescribed variable ratio (H _D /H _D0 , z(x,y)/z(x,0)) of homothety, which is non-zero and which depends on the width coordinate (y) of the upper threshold surface (4) following the direction transverse (Oy) of width, relative to a basic profile (C, z(x,0)) of prescribed shape in a (POxz) of the longitudinal vertical planes (Pxz), the prescribed variable ratio (H _D /H _D0 , z(x,y)/z(x,0)) of homothety being increasing going from a hollow (42) to a bump (41) along the transverse direction (Oy) of width. Work according to claim 1, characterized in that the prescribed variable ratio (H _D /H _D0 , z(x,y)/z(x,0)) of homothety is curved at least with a continuous derivative along at least the coordinate width (y). Structure according to any one of the preceding claims, characterized in that the upper threshold surface (4) has, in the at least one horizontal plane (Pxy) on an upstream side (45) of the upper threshold surface (4). , a curve (Cxy), which includes at least one bump (41) and at least one hollow (42) and which has at least a continuous derivative. Work according to any one of the preceding claims, characterized in that the basic profile (C, z(x,0)) comprises a determined downstream point (x1) of reference, the transformation of which by homothety along the width coordinate (y) is located on a downstream rectilinear segment (31) of the upper surface (4) threshold crest, the downstream rectilinear segment (31) of the upper surface (4) threshold ridge being parallel to the transverse direction (Oy) width. Structure according to claim 4, characterized in that the downstream rectilinear segment (31) of the upper surface (4) threshold ridge is formed by an end edge (31) of the upper surface (4) threshold crest. Structure according to claim 4, characterized in that the downstream rectilinear segment (31) of the upper threshold crest surface (4) is connected to another downstream surface. Structure according to any one of the preceding claims, characterized in that the upper threshold surface (4) has an alternation of bumps (41) and hollows (42) along the transverse direction (Oy) of width in the plane (Pyz) of width, and/or in the horizontal plane (Pxy). Structure according to claim 7, characterized in that the bumps (41), which are adjacent to each other, have vertices, which are spaced apart, along the transverse direction (Oy) of width, of a spacing distance (Y), which is greater than or equal to 0.6 times a prescribed value (Y0) of width and which is less than or equal to 1.4 times the prescribed value (Y0) of width. Structure according to claim 7 or 8, characterized in that the recesses (42), which are adjacent to each other, have low points, which are spaced apart, along the transverse direction (Oy) of width, a spacing distance (Y), which is greater than or equal to 0.6 times a prescribed value (Y0) of width and which is less than or equal to 1.4 times the prescribed value (Y0) of width. Structure according to any one of claims 1 to 9, characterized in that the prescribed variable ratio (H _D /H _D0 ) of homothety or z(x,y) / z(x,0) is sinusoidal between the bumps ( 41), which are close to each other and/or between the recesses (42), which are close to each other as a function of a width coordinate (y) of the upper surface (4 ) threshold along the transverse direction (Oy) of width. Structure according to any one of claims 1 to 10, characterized in that the upper threshold surface (4) has a coordinate z(x,y) in the vertical direction (Oz) of height,
the coordinate z(x,y) depending on the x coordinate of the upper threshold surface (4) in the horizontal direction (Ox) of length and depending on the y coordinate of the upper threshold surface (4) in the transverse direction (Oy) of width, according to the following equation: $$\mathrm{z}\left(\mathrm{x}\mathrm{,y}\right)=\mathrm{z}\left(\mathrm{x},0\right)\left(1+\mathrm{HAS}\left(\mathrm{y}\right).\left(1+\mathrm{f}\left(\mathrm{y}\right)\right)\right)$$

where z(x,0) is the basic profile (C) of prescribed convex shape in a prescribed longitudinal vertical plane (POxz), parallel to the horizontal direction (Ox) of length and to the vertical direction (Oz) of height, A(y) is a first height function, which is continuous, greater than zero and less than or equal to 0.5, f(y) is a second function, which is continuous, which varies according to the y coordinate and which is greater than or equal to -1 and less than or equal to 1. Work according to claim 11, characterized in that $${\mathrm{D}}_1\le 10.\mathrm{d}\mathrm{And}/\mathrm{Or}{\mathrm{D}}_2\le 10.\mathrm{d},$$

where D ₁ is the distance between the vertices (411) of the bumps (41), which are close to each other, D ₂ is the distance between the low points (421) of the hollows (42), which are close to each other, $$\mathrm{d}=\left|{\mathrm{x}}_2-{\mathrm{x}}_1\right|,$$

x ₁ is the minimum or maximum x coordinate in absolute value for the profile z(x,0), x ₂ is the x coordinate of the profile z(x,0), which is different from x ₁ and which is defined such that z(x ₂ ,0) = z(xi,0). Work according to claim 11 or 12, characterized in that $$0<\mathrm{HAS}\left(\mathrm{y}\right)\le 0.5.$$

Structure according to any one of claims 11 to 13, characterized in that the first function A(y) is equal to a prescribed constant A, positive and non-zero, the second function f(y) is defined between the bumps (41 ), which are close to each other and/or between the hollows (42), which are close to each other, by $$\mathrm{f}\left(\mathrm{y}\right)=\cos \left(2\pi \mathrm{y}/{\mathrm{\lambda }}_{\mathrm{k}}\right),$$

Or
λ _k is a spacing distance (Y), which is prescribed along the transverse direction (Oy) of width and which is associated with each pair (k) of neighboring bumps (41) and/or neighboring hollows (42). . Structure according to claim 14, characterized in that the spacing distance λ _k is different between several pairs of neighboring bumps (41) and/or neighboring hollows (42). Structure according to claim 14, characterized in that the spacing distance λ _k is identical between several pairs of neighboring bumps (41) and/or neighboring hollows (42). Work according to any one of claims 11 to 16, characterized in that the second function f(y), which is continuous, which varies according to the coordinate y and which is greater than or equal to -1 and less than or equal to 1 height is chosen from at least one of the following functions: a slot function, a sum of a maximum of 10 slot functions, a periodic function, a sum of a maximum of 10 sinusoidal functions, a sum of a maximum of 10 sinusoidal functions phase-shifted from each other with respect to the others, a piecewise function defined by hyperbolic cosines, a piecewise function defined by hyperbolic cosines over at least one interval between two bumps, an elliptical function over at least one interval between two bumps, a curve of Bézier with at most 20 control points on at least one interval between two bumps, at least one semi-circle on at least one interval between two bumps, at least one arc of a circle on at least one interval between two bumps, a polynomial of degree less than or equal to 20 on at least one interval between two bumps, a piecewise function defined by polynomials of degree less than or equal to 10 on at least one interval between two bumps, a function by at most 15 pieces defined by polynomials of degree less than or equal to 10 on at least one interval between two bumps. Work according to any one of claims 11 to 17, characterized in that the first function A(y) is chosen from at least one of the following functions: a continuous function of class C1, a continuous function of class C2, a continuous function of class Cn, with n being an integer greater than or equal to 3, a continuous function of class Cinfini, an elliptic function on at least one interval between two bumps, a Bézier curve with at most 20 control points on at least one interval between two bumps, at least one semi-circle over at least one interval between two bumps, at least one arc of a circle over at least one interval between two bumps, a polynomial of degree less than or equal to 20 over at least one interval between two bumps, a piecewise function defined by polynomials of degree less than or equal to 10 on at least one interval included between two bumps, a function by a maximum of 15 pieces defined by polynomials of less than or equal degree to 10 on at least one interval between two bumps. Structure according to any one of the preceding claims, characterized in that the basic profile z(x,0) of prescribed convex shape in a longitudinal vertical plane prescribed (POxz), parallel to the horizontal direction (Ox) of length and to the vertical direction (Oz) of height is chosen from at least one of the following functions: a convex continuous function, a class C1 continuous function, a continuous function of class C2, a continuous function of class Cn, with n being an integer greater than or equal to 3, a continuous function of class Cinfini, an elliptic function on at least one interval between two bumps, a Bézier curve with 20 points of controls at most, at least one semi-circle, at least one arc of a circle, a polynomial of degree less than or equal to 10, a piecewise function defined by polynomials of degree less than or equal to 10, a function by at most 15 pieces defined by polynomials of degree less than or equal to 10. Structure according to claim 19, characterized in that the basic profile (C, z(x,0)) of prescribed convex shape in the prescribed longitudinal vertical plane (POxz), parallel to the horizontal direction (Ox) of length and at the vertical direction (Oz) of height, comprises a downstream section (Co) in the form of a prescribed decreasing curve extending from an upper end (40) of the base profile (C, z(x,0)) towards the downstream , and at least one upstream section (C ₁ , C ₂ , C ₃ ), which extends from the upper end (40) of the base profile (C, z(x,0)) towards the upstream and which is formed of at least one arc (C ₁ , C ₂ , C ₃ ) of a circle,
the downstream section (C ₀ ) and the downstream section (C ₀ ) having a continuity of their tangent one after the other at the level of the upper end (40). Structure according to claim 20, characterized in that the downstream section (Co) in the form of a prescribed decreasing curve has the coordinate z(x,0) = -0.5.x ^1.85 in a reference having as its origin the upper end ( 40) of the profile (C, z(x,0)) for x ≥ 0 in the direction going from upstream to downstream. Structure according to claim 19, characterized in that the basic profile (C, z(x,0)) of prescribed convex shape in the prescribed longitudinal vertical plane (POxz), parallel to the horizontal direction (Ox) of length and at the vertical direction (Oz) of height, comprises a Bézier curve with 4 control points of prescribed coordinates in the prescribed longitudinal vertical plane (POxz). Structure according to claim 22, characterized in that the Bézier curve with 4 control points is: $$B\left(t\right)={\left(1-t\right)}^3\cdot P_0+3\cdot {\left(1-t\right)}^2\cdot t\cdot P_1+3\cdot \left(1-t\right)\cdot t^2\cdot P_2+t^3\cdot P_3$$

where P ₀ , P ₁ , P ₂ , P ₃ are the 4 control points of prescribed coordinates in the prescribed longitudinal vertical plane (POxz), the Bézier curve being defined in a reference frame having for origin an upper end (40) of the base profile (z(x,0)), t is a parameter varying from 0 to 1. Work according to claim 23, taken in combination with claim 14, characterized in that P ₀ has coordinates: $\frac{x}{H_{D0}}=-0.2818\pm 20\%$

And $\frac{z}{H_{D0}}=-0.150\pm 20\%$

, P ₁ has the coordinates: $-0.2818-0.2\cdot 0.2818\le \frac{x}{H_{D0}}\le -0.2818+0.2\cdot 0.2818$

and -0.12 ≤ $\frac{z}{H_{D0}}\le 0.2$

, P ₂ has coordinates $-0.2\le \frac{x}{H_{D0}}\le 0.5$

And $-0.05\le \frac{z}{H_{D0}}\le 0.3$

, P ₃ has the coordinates: $0.7-0.2\cdot 0.7\le \frac{x}{H_{D0}}\le 0.7+0.2\cdot 0.7$

and -0.0904 - 0.2 · 0.0904 ≤ $\frac{z}{H_{D0}}\le -0.0904+0.2\cdot 0.0904$

, the coordinates being expressed in meters, where H _D0 is a minimum prescribed design load value, . $$0.097-0.2\cdot 0.097\le \mathrm{HAS}\le 0.097+0.2\cdot 0.097,$$

$$1.34-0.2\cdot 1.34\le {\lambda }_k\le 1.34+0.2\cdot 1.34.$$

Structure according to any one of the preceding claims, characterized in that the vertical distance between the top of the bump (41) and the low point of the hollow (42) in the direction (Oz) of height is less than 50% of a threshold thickness, which is a horizontal distance, taken along the direction (Ox) of length, between a vertical edge (21) of the end of the upstream facing (2) and a vertical edge (31) of the end of the surface upper threshold (4). Structure according to any one of the preceding claims, when they depend at least on claim 7, characterized in that the horizontal distance between the vertices of two bumps (41) adjacent to each other is less than 2 times a threshold thickness, which is a horizontal distance, taken along the direction (Ox) of length, between a vertical edge (21) of the end of the upstream facing (2) and a vertical edge (31) of the end of the surface upper threshold (4). Hydraulic dam comprising at least one overflow structure (1) according to any one of the preceding claims.

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