JP2020094461A - Waterway formation block and waterway structure - Google Patents

Abstract

To provide a waterway formation block which has a function similar to that of a waterway existing in nature and in which construction of a waterway structure is easy.SOLUTION: A block for forming a waterway structure used as an open ditch or a culvert comprises a pair of flat side walls 2, a plurality of water passage holes 3 formed in a state of being dispersed in the plane direction of the side wall 2 and penetrating the side wall 2, at least two connecting members 4 provided between the pair of side walls 2 to connect the pair of side walls 2, and at least two protrusions 6 projecting from the side wall 2 and/or the connecting member 4 outside the block and in the vertical direction. In the waterway forming block 1, the side wall 2 and the connecting member 4 are rigidly joined to each other, and at least the side wall 2 and the connecting member 4 have rigidity higher than that of reinforced concrete.SELECTED DRAWING: Figure 1

Description

The present invention relates to a water channel forming block having a function similar to that of a water channel existing in nature and easy to construct a water channel structure, and a water channel structure using the block.

BACKGROUND ART Conventionally, a permeation drainage type gutter block that permeates water flowing through a water channel into surrounding soil and drains it is known.
Specifically, for example, "for drainage gutter with holes and basin" disclosed in JP-A-2005-9279 (Patent Document 1) and "for rainwater infiltration-type gutter" disclosed in JP-A-9-4039. Block" (Patent Document 2), "Water-permeable U-shaped groove" disclosed in Japanese Patent Laid-Open No. 7-252869 (Patent Document 3), and Japanese Patent Application No. 63-79886 (Japanese Utility Model Publication No. 2-5479). "Gutter for groundwater reduction" (Patent Document 4) and the like are known.

On the other hand, in the permeation drainage type gutter block as disclosed in each of Patent Document 1 to Patent Document 4 as described above, in the soil on the outer surface side of the gutter block, usually, It is known that water flows in the same direction as the flow direction of water.
In addition, the concrete that constitutes the gutter block generally does not have water permeability. Therefore, when the amount of water flowing through the gutter block is increasing, the amount of water flowing in the region on the outer surface side of the gutter block also increases. Therefore, when the flow rate of water in the gutter block increases due to heavy rain or the like, scouring may occur on the outer surface of the gutter block, and in the worst case, the gutter block may be bare on the ground.

As a prior art capable of coping with such a situation, there is, for example, Patent Document 5.
Patent Document 5 discloses an invention relating to a permeable water channel having a drainage/water retention capacity improved by providing a permeable layer around the permeation type water channel member under the name of "permeable water channel".
The permeable channel disclosed in Patent Document 5 includes a permeable channel member including a plurality of walls including a pair of side walls and having a water-permeable port that allows drainage and water supply to and from the outside, and an osmotic channel member. In an osmotic channel provided with an osmotic layer which is provided outside and permeates water discharged from a water permeable port, the osmotic layer puts a granular material in a water permeable bag body and restrains the movement of the granular material. It is characterized in that a large number of bladder members are stacked or arranged side by side.
According to the invention disclosed in Patent Document 5 having the above-mentioned configuration, it is possible to prevent consolidation and compression of the permeation layer due to repeated inflow and outflow of the permeation water between the permeation type water channel member and the permeation layer, and to suppress ground subsidence. This can prevent damage to the permeable channel.
Further, according to the invention disclosed in Patent Document 5, it is required by considering the drainage/water retention capacity of the permeation type water channel member and the permeation layer together without increasing the cross-sectional area of the permeation type water channel member. It is possible to secure drainage and water retention capacity. As a result, the labor and cost for manufacturing the permeation type water channel member can be reduced.

The present inventor is not directly related to the present invention, but in the past, JP 2000-54344 A (Patent Document 6), JP 2004-324398 A (Patent Document 7), and JP 2014 -21313 (Patent Document 8), JP-A-2015-1335024 (Patent Document 9), and JP-A-2018-21342 (Patent Document 10) are invented.

JP 2005-9279 A JP, 9-4039, A JP, 7-252869, A Microfilm of Jitsugan Sho 63-79886 (Jitsukaihei 2-5479) JP, 2005-76206, A Japanese Patent Laid-Open No. 2000-54344 JP, 2004-324398, A JP, 2014-20013, A JP, 2015-135024, A JP, 2018-21342, A

In the case of the invention disclosed in Patent Document 5 as described above, it is difficult to closely attach the water-permeable bag body containing the granular material to the outer surface of the permeation-type water channel member, so that the water flowing through the permeation-type water channel member is prevented. However, there was a possibility that the permeation type water channel member could not be dispersed smoothly in the horizontal direction.
Further, in the case of the invention disclosed in Patent Document 5, it is inevitable that the water-permeable bag containing the granular material deteriorates with the passage of time.
Therefore, when the water-permeable bag that contains the granular material deteriorates and breaks with the lapse of time, there is a risk of scouring on the outside of the permeation-type water channel member. In this case, there is a concern that the physical connection between the permeation type water channel member and the surrounding granular material is broken, and as a result, the permeation type water channel member may not exhibit its intended function.
Therefore, in the case of the invention disclosed in Patent Document 5, there is a problem that it is difficult to permanently exhibit its function in the water channel once formed.

The present invention has been made in response to such conventional circumstances, the construction is easy, it is possible to prevent scouring from occurring on the outer surface side of the water channel, and to control the flow velocity of water flowing on the outer surface side of the water channel. An object of the present invention is to provide a water channel forming block that can be reduced and can be used permanently, and a water channel structure using the same.

In order to achieve the above-mentioned object, a water channel forming block which is a first invention is a block for forming a water channel structure used as a culvert or a culvert, and a pair of flat plate side walls and a plane direction of the side walls. A plurality of water holes which are arranged in a dispersed state and are formed through the side walls; at least two connecting members which are interposed between the pair of side walls to connect the pair of side walls; Or at least two protrusions that are provided outside the block and in a vertical direction from the connecting member, and the side wall and the connecting member are rigidly joined, and at least the side wall and the connecting member have rigidity higher than that of reinforced concrete. It is characterized by having.
In the first aspect of the invention having the above structure, the sidewalls are erected on the left and right side surfaces of the water channel to be formed, and act as retaining walls for the water channel.
Further, the water passage holes formed on the side walls have an effect of freely moving water from the soil arranged on the left and right of the water channel to the hollow portion side of the water channel or the opposite direction.
Furthermore, the connecting member is interposed between the pair of side walls and acts as a support member and a spacer for the pair of side walls. In addition, the connecting material has a function of accommodating and holding a bottom surface forming material (granular body, crushed stone, gravel, etc.) arranged on the bottom side of the water channel in the void. Further, the connecting material has an effect of hindering the flow of the bottom surface forming material to the downstream side.
Further, when the water channel structure is formed using the water channel forming block according to the first aspect of the present invention, water flows in the hollow portion of the water channel forming block and its surroundings. Therefore, the connecting member of the water channel forming block according to the first aspect of the invention is arranged so as to block the flow of water in the water channel. Therefore, when the water channel structure is formed by using the first aspect of the invention, the connecting material acts as a resistor for the water flowing on the bottom side of the hollow portion and reduces the flow velocity.
In the first aspect of the invention, since the side wall has the plurality of water passage holes, the flatness of the surface of the side wall is impaired. Therefore, when the water channel structure is formed using the first invention, the flow velocity of water flowing on the surface of the side wall is also reduced.
As described above, according to the first invention, the flow velocity is suitably reduced on the surface of the waterway forming block, so that when the waterway structure is formed by using the first invention, the surface of the waterway forming block ( In particular, it has an effect of suppressing scouring on the outer surface side).
Then, in the first invention, at least the side wall and the connecting material have rigidity higher than that of reinforced concrete, and the side wall and the connecting material are rigidly joined, so that the first invention can be used permanently. It has the effect of imparting sufficient strength.
Further, the protrusion acts as an anchor when the first invention is buried in the soil. In addition, the protrusion also acts as a resistor for the water flowing around the connecting member when the water channel structure is formed using the first invention. Therefore, the protrusion has an action of reducing the flow velocity of water flowing around the connecting member when the water channel structure is formed by using the first invention.

A waterway forming block that is a second invention is the above-described first invention, and in any water passage hole, the occupied area S ₁ of the inner side surface opening of the side wall is the occupied area S ₁ of the outer side surface opening of the side wall. It is characterized by being smaller than ₂ .
The second aspect of the present invention has the same function as that of the first aspect of the invention described above, as well as a function to prevent an intruding object (such as earth and sand) from the outer side opening of the water passage hole formed in the side wall on the inner side surface. It has the effect of making it difficult to pass to the opening side. Thus, when a new water channel structure is formed using the second invention, it has an effect of suppressing the inflow of earth and sand or the like into the water passage portion (in the hollow portion of the water channel formation block).

A waterway forming block which is a third invention is the above-mentioned first or second invention, wherein the minimum value of the interval between the water passage holes is equal to or more than the minimum value of the thickness of the side wall, and the connecting material is , The minimum thickness in the horizontal direction is greater than or equal to the minimum thickness of the sidewall, and the minimum height in the vertical direction is greater than or equal to 1.25 times the minimum thickness of the sidewall. It is characterized by that.
According to the third aspect of the present invention, in addition to the same action as the first or second aspect described above, the distance between the water passage holes and the size of the connecting member in the width direction and the thickness direction are as described above. Has the effect of adjusting the balance of the strength in the horizontal direction and the vertical direction of the structural members forming the water channel formation block. That is, according to the third aspect of the invention, the water channel forming block has a desired strength in both the horizontal direction and the vertical direction.
Further, in the third invention, the vertical thickness of the connecting member is set to be 1.25 times or more the minimum value of the thickness of the side wall, so that the bottom surface disposed on the bottom side of the hollow portion of the water channel forming block is It has the effect of increasing the holding effect (effect of impeding flow) of the forming material.
Further, in the third aspect of the invention, since the connecting member is arranged so as to block the flow of water, the effect of reducing the flow velocity of water flowing around the connecting member is increased as the vertical thickness of the connecting member increases. Get higher
As a result, according to the third aspect of the invention, as compared with the above-described first or second aspect of the invention, it is possible to more reliably prevent scouring from occurring around the connecting material side of the water channel forming block. Have.

A fourth aspect of the invention is a waterway structure according to any one of the first to third aspects of the invention, in which a groove formed by excavating the ground and a connecting member arranged vertically downward are housed in the hollow portion of the groove. A solid body provided with a water channel forming block and a group of solids interposed between the inner wall of the groove and the side wall of the water channel forming block, and arranged adjacent to the water passage hole of the water channel forming block. The object is characterized in that it can be inserted into the water passage hole but cannot pass through the water passage hole.
The fourth invention specifies the culvert formed by using the first to third inventions (blocks for forming a water channel) as a product invention.
In the fourth invention having the above-mentioned configuration, the groove has an action of housing the water channel forming block (any one of the first to third inventions) in its hollow portion. Further, the water channel forming block has the same operation as that of the first to third inventions. Further, the solid matter interposed between the inner wall of the groove and the water passage hole of the water channel forming block is for moving the water in the soil around the groove into the water channel forming block or in the opposite direction. Acts as a flow path. The solid matter also acts as an anchor for fixing the water channel forming block to the inner wall of the groove.
Furthermore, in the fourth aspect of the invention, the flatness of the outer surface of the side wall is also impaired by inserting the solid matter into the water passage hole. As a result, in the fourth invention, the flatness of the side wall is impaired by providing the water passage hole, and the solid matter is inserted into the water passage hole, whereby the flatness of the outer side surface of the side wall is improved. As a result, the effect of reducing the flow velocity on the outer surface of the side wall is more reliably exhibited. As a result, scouring of the outer surface of the side wall of the waterway formation block according to the fourth aspect of the invention is suppressed.
In addition, the solid matter group acts as a filter that prevents the earth and sand around the groove from flowing into the hollow portion of the channel forming block. Further, the solid matter acts as a resistance body of water flowing on the outer surface side of the water channel forming block, and has an action of reducing the flow velocity thereof.
Therefore, according to the fourth aspect of the present invention, both the inside of the hollow portion of the water channel forming block and the outer surface side thereof can be used as water passage portions, and the flow velocity of the water flowing in the hollow portion of the water channel forming block is It has an effect of always and surely reducing the flow velocity of water flowing on the outer surface side of the water channel forming block.
Furthermore, in the fourth aspect of the present invention, since scouring is unlikely to occur on the outer surface side of the water channel formation block, it is possible to prevent physical division between the water channel formation block and the inner wall of the groove that houses the water channel formation block. Have an effect. Therefore, it has an effect of providing a water channel structure in which water permeability in the fourth invention is not easily impaired with the passage of time.

A waterway structure which is a fifth invention comprises a waterway formation block and a waterway formation block according to any one of the first to third inventions, which are arranged on a mounting surface formed by excavating the ground. An embedding soil to be embedded, and a group of solids interposed between the water channel forming block and the earth embedding, adjacent to the water passage forming block, the water passage hole or the gap between the connecting members. The solid matter placed is characterized in that it can be inserted into the water passage hole or the void, but cannot pass through the water passage hole or the void.
The fifth invention specifies the underdrain formed by using the first to third inventions (blocks for forming a water channel) as a product invention.
In the fifth aspect of the invention having the above structure, the placement surface acts as a support base for the water channel forming block (any one of the first to third aspects). Further, the water channel forming block has the same operation as that of the first to third inventions.
Further, the solid matter interposed between the embedding soil and the water passage holes of the water channel forming block or the gaps between the connecting members acts as an anchor for hanging the water channel forming block particularly on the embedding soil.
Further, in the fifth invention, since the water channel forming block is provided with the water passage holes and the voids between the connecting members, the flatness on the outer surface thereof is impaired, and the voids between the water passage holes and the connecting members are provided. The solid matter is inserted into the outer surface of the water channel forming block to impair the flatness of the outer surface of the water channel forming block, and the fluidity of water on the outer surface of the water channel forming block is reduced. As a result, scouring on the outer side surface of the water channel forming block according to the fifth aspect of the invention is suppressed.
In addition, the solid matter group also acts as a filter for preventing the buried soil around the water channel forming block from flowing into the hollow portion of the water channel forming block.
Furthermore, the solid matter acts as a resistance of water flowing on the outer surface side of the water channel forming block, and has the action of reducing the flow velocity thereof.
Therefore, according to the fifth aspect of the invention, both the inside of the hollow portion of the water channel forming block and the outer surface side thereof function as an integrated water channel, and at that time, the water channel forming block and the buried soil disposed around the water channel forming block. It has the effect of preventing the physical division between and.

A waterway structure which is a sixth invention is the above-mentioned fourth or fifth invention, and is provided between the inner wall of the groove or the burying soil and the solid group, and the average particle of the solid group. It is characterized in that it is provided with a granular material layer made of a granular material having an average particle diameter smaller than the diameter.
The sixth invention having the above-mentioned configuration has the same operation as the operation according to the above-mentioned fourth or fifth invention. In addition, 6th invention, the inner wall of a groove, or the earth for burying, and the granular material layer interposed between the solids group are earth and sand etc. which comprise the inner wall of a groove, or burying earth, It acts as a filter that prevents it from flowing into the gaps between the solids.
As a result, in the sixth invention, as compared with the above-mentioned fourth or fifth invention, the earth and sand forming the inner wall of the groove or the burying soil is more likely to flow into the hollow portion of the water channel forming block. It has an effect of surely preventing.

According to the above-described first invention, both the inside of the hollow portion of the water channel forming block and the outer surface side thereof can be used as the water passage portion, and at the time of water passage, the outer surface of the water channel forming block is It is possible to surely reduce the flow velocity of flowing water, and it is possible to provide a water channel forming block in which scour is unlikely to occur on the outer surface of the water channel forming block during water passage.
Therefore, when the waterway structure is formed using the first invention, the amount of water that exceeds the volume in the hollow portion of the waterway formation block can be made to flow, and the physical properties of the surrounding soil and the waterway formation block can be increased. It is possible to provide a water channel structure that can maintain a stable connection state.
Therefore, according to the first aspect of the present invention, it is possible to provide a water channel structure that can be permanently used as a permeation drainage type water channel.

According to the second invention, the same effect as the above-described first invention is obtained. In addition, the second aspect of the invention more reliably prevents the sediment, gravel, etc., which are arranged outside the waterway formation block, from flowing into the hollow portion of the waterway formation block, as compared with the first invention. can do.
Therefore, when a water channel structure is formed using the water channel forming block according to the second aspect of the present invention, the inflow from the outer surface side of the water channel forming block reduces the water permeability in the hollow portion of the water channel forming block. Can be suitably suppressed.
Therefore, according to the second aspect of the present invention, it is possible to provide a water channel structure in which clogging due to soil or the like flowing in from the outside during water passage is unlikely to occur. As a result, it is possible to reduce the labor and cost of maintenance when the water passage structure according to the second aspect of the present invention passes water.

According to the third invention, in addition to the same effect as the above-described first or second invention, the horizontal and vertical sizes of the side wall and the connecting member in the water channel forming block are set to be equal to the thickness of the side wall. Sufficient strength can be imparted to the water channel formation block by setting it to the minimum value or more.
Further, in the third invention, the vertical thickness (composition) of the connecting members is set to be larger than the thickness of the side wall, so that the connecting members are accommodated in the gap between the connecting members in the water channel structure using the third invention. It is possible to enhance the holding effect of the bottom surface forming material.
Further, in the third invention, water flows both in the hollow portion and on the outer side surface of the water channel forming block. Therefore, in the third aspect of the invention, the effect of reducing the flow velocity of the water flow around the connecting material of the water channel forming block is enhanced by setting the vertical thickness (composition) of the connecting material to be larger than the thickness of the side wall. You can
As a result, when the water channel structure is formed by using the third aspect of the present invention, it is possible to preferably prevent scouring on the vertically lower side of the water passage portion.
Therefore, according to the third aspect of the present invention, the physical connection state with the surrounding soil (particularly the vertical direction) can be more reliably maintained during water passage, and the water passage function is unlikely to deteriorate for a long period of time. A canal structure can be provided.

According to the fourth aspect of the invention, it is possible to provide a water channel structure that can be used as a water passage both inside the hollow portion of the water channel forming block and on the outer surface side thereof. In addition, in the fourth aspect of the invention, the physical contact between the waterway formation block and the surrounding soil is unlikely to occur. Therefore, even if the water level suddenly rises due to a heavy rain, it is possible to maintain the water permeability of the water channel structure and to allow water that exceeds the volume in the hollow part of the water channel forming block to flow without any problems. You can
Further, in the fourth aspect of the invention, a strong engagement relationship is provided between the water channel forming block and the solid material group disposed around it, and the soil disposed around the water channel forming block over time. Is formed, which makes the fourth invention more difficult to break.
Therefore, in the fourth invention, the longer it is used, the higher the structural stability thereof becomes, and thus the permanent use becomes possible.
Further, in the fourth invention, since water can freely flow in and out of the surroundings or in the opposite direction, a part of the water gathered in the waterway structure, which is the fourth invention, at the time of increasing the water flow into the surrounding soil. The water can be made to flow in the flow path direction of the fourth invention while being discharged.
As a result, by increasing the construction area of the waterway structure according to the fourth aspect of the invention, it is possible to mitigate the rapid rise in water level in the river arranged downstream of the waterway structure. Therefore, the fourth invention is also useful as a flood control technique.
Further, in the fourth aspect of the invention, the inside of the hollow portion of the waterway forming block can be in a state of rich undulations, and thus it is optimal as a habitat for aquatic organisms. As a result, according to the fourth aspect, it is possible to contribute to conservation of the natural environment.

According to the fifth aspect of the invention, it is possible to provide a water channel structure that can be used as a water passage both inside the hollow portion of the water channel forming block and on the outer surface side thereof. In addition, in the fifth aspect, the physical contact state between the water channel forming block and the surrounding soil is unlikely to occur. Therefore, even if the water level suddenly rises due to a heavy rain, it is possible to maintain the water permeability of the water channel structure and to allow water that exceeds the volume in the hollow part of the water channel forming block to flow without any problems. You can
Further, in the fifth invention, a strong engagement relationship is provided between the water channel forming block and the solid group arranged around the block along with the passage of time, and the soil arranged around the block. Is formed, which makes the fourth invention more difficult to break.
Therefore, in the fourth invention, the longer it is used, the higher the structural stability thereof becomes, and thus the permanent use becomes possible.
Further, in the fifth invention, since water can freely flow in and out of the surroundings or in the opposite direction, a part of the water collected in the waterway structure which is the fifth invention at the time of increasing the water flow into the surrounding soil. The water can be made to flow in the flow path direction of the fifth invention while being discharged.
As a result, by increasing the construction area of the waterway structure according to the fifth aspect, it is possible to mitigate a rapid rise in water level in the river arranged downstream of the waterway structure. Therefore, the fifth invention is also useful as a flood control technique.
Furthermore, according to the fifth aspect, erosion of the surrounding buried soil (soil) can be suppressed like a naturally formed water channel, so that the flow path does not change over time. Therefore, according to the fifth aspect, there is also an effect that the formation position and scale of the water channel can be continuously maintained.

According to the sixth invention, the same effect as the effect according to the fourth or fifth invention is obtained. In addition, the sixth aspect of the present invention further prevents the soil arranged on the outer side of the water channel forming block or the buried soil from flowing into the hollow portion of the water channel forming block, as compared with the fourth or fifth aspect. It can be surely prevented.
As a result, according to the sixth aspect, it is possible to prevent clogging due to the earth and sand, gravel, or the like flowing in from the outside, or the embedding soil.
Therefore, according to the sixth aspect of the invention, there is an effect that the labor and cost required for the maintenance of the water channel can be reduced.

It is the perspective view which looked at the waterway formation block concerning the embodiment of the present invention from the perpendicular upper side. It is the perspective view which looked at the waterway formation block concerning the embodiment of the present invention from the perpendicular lower side. (A) It is a top view of the block for waterway formation which concerns on embodiment of this invention, (b) It is a front view (rear view) of the block for waterway formation, (c) It is a bottom view of the block for waterway formation. Yes, (d) is a side view of the same waterway formation block. 1 is a vertical cross-sectional view of a water channel structure (clearwater) according to a first embodiment of the present invention. FIG. 5 is a schematic diagram of a cross-sectional view of the water channel structure (mull) shown in FIG. 4. It is a sectional view of a waterway formation block concerning an embodiment of the present invention. FIG. 5 is a vertical cross-sectional view of a water channel structure (underdrain) according to a second embodiment of the present invention.

A water channel forming block according to an embodiment of the present invention and a water channel structure using the block will be described with reference to FIGS. 1 to 7.
FIG. 1 is a perspective view of a water channel forming block according to an embodiment of the present invention as viewed from a vertically upper side. Further, FIG. 2 is a perspective view of the water channel forming block according to the embodiment of the present invention as viewed from the vertically lower side. Further, FIG. 3(a) is a plan view of the water channel forming block according to the embodiment of the present invention, (b) is a front view (rear view) of the water channel forming block, and (c) is the water channel. It is a bottom view of a formation block, and is a side view of the (d) same channel formation block.
As shown in FIGS. 1 to 3, the water channel forming block 1 according to the present embodiment is made of a material having rigidity higher than that of reinforced concrete, for example, and is used for forming a water channel structure used as a culvert or a culvert. It is a block that can be.
Such a water channel forming block 1 according to the present embodiment is, for example, as shown in FIGS. 1 to 3, arranged in a pair of flat plate side walls 2 and in a state of being dispersed in the plane direction of the side walls 2. In addition, a plurality of water passage holes 3 formed penetrating the side walls 2, at least two connecting members 4 that are interposed between the pair of side walls 2 and connect the pair of side walls 2, It is provided with at least two projections 6 which are provided on the outer side of the water channel formation block 1 from the end surface and project in the vertical direction.
Further, in the water channel forming block 1 according to the present embodiment as described above, the side wall 2 and the connecting member 4 are rigidly joined. That is, the side wall 2 and the connecting member 4 form a rigid frame structure.
Further, a gap 5 is formed between at least two connecting members 4 provided between the pair of side walls 2.

In addition, in the watercourse forming block 1 according to the present embodiment, the protrusion 6 mainly functions as an anchor when the waterway forming block 1 is installed, and is not a supporting leg portion. For this reason, the protrusions 6 are located outside the water channel forming block 1 at arbitrary positions on the vertical surface, and more preferably, on the outer side of the water channel forming block 1 and at positions separated from each other in the vertical surface. It suffices if at least two protrusions 6 are provided. There is no particular problem even if the projection 6 according to the present embodiment does not allow the water channel forming block 1 to be self-supporting.
1 to 3, the projection 6 is described as an example in which the projection 6 is provided to project from the end face of the side wall 2 outside the water channel forming block 1 and in the vertical direction. Two or more protrusions 6 may be provided on the connecting member 4, or two or more protrusions 6 may be provided on both the end surface of the side wall 2 and the connecting member 4.
Further, as shown in FIG. 7 which will be described in the latter part, when the water channel forming block 1 according to the present embodiment is used by arranging the connecting member 4 on the vertically upper side, outside the water channel forming block 1, Further, the projection 6 may be provided on the end face of the side wall 2 on the side where the connecting member 4 is not arranged in the vertical direction (not shown). In this case as well, the projections 6 act as anchors for fixing the water channel forming block 1 to the surrounding soil 13 and the mounting surface 15.
In the case where the hollow portions of the two water channel forming blocks 1 according to the present embodiment are opposed to each other to form a cylindrical structure and used, when the water channel forming block 1 is installed, the water channel forming block 1 is placed on the vertical side. It is desirable to provide the projection 6 on the surface to be arranged.
This is because if the projections 6 are provided so as to project in the horizontal direction, the work of disposing the solids 8 on the left and right side surfaces of the water channel forming block 1 becomes complicated.

In describing the function and effect of the water channel formation block 1 according to the present embodiment, first, a water channel structure (crater) according to the first embodiment of the present invention will be described with reference to FIGS. 4 and 5.
FIG. 4 is a vertical cross-sectional view of the water channel structure (clearwater) according to the first embodiment of the present invention as seen from the direction of blocking the flow channel. In addition, FIG. 5 is a schematic view of a vertical cross-sectional view of the water channel structure (mull) shown in FIG. The same parts as those shown in FIGS. 1 to 3 are designated by the same reference numerals, and the description of the structure will be omitted.
As shown in FIG. 4, the water channel structure 7 (mercury 7A) according to the first embodiment mainly includes a groove 9 formed by excavating the ground, a water channel forming block 1 housed in a hollow portion of the groove 9, The solid material 8 group is provided between the inner wall 9a of the groove 9 and the side wall 2 of the water channel forming block 1.
Further, in the water channel structure 7 according to the first embodiment as shown in FIG. 4, it is possible to insert the solid matter 8 particularly adjacent to the water channel 3 of the water channel forming block 1 into the water channel 3 in particular. However, the one having an outer diameter size that cannot pass through the water passage hole 3 is used.
In addition, in the water channel structure 7 according to the first embodiment as described above, the plurality of solids 8 are also stored in the voids 5 between the connecting members 4 in the water channel forming block 1. Therefore, in the water channel structure 7 according to the first embodiment illustrated in FIG. 4, the plurality of solids 8 housed in the voids 5 between the connecting members 4 are bottom surface forming materials of the water channel structure 7.

In the water channel forming block 1 according to the present embodiment, as shown in FIGS. 1 to 3 described above, a plurality of water passage holes 3 are formed in a state of being dispersed in the plane direction of the side wall 2, and at the bottom side thereof. Has a plurality of connecting members 4 arranged in parallel. Therefore, the water channel forming block 1 as a whole does not have water impermeability, and water can freely enter and leave the hollow portion (see FIG. 5).
That is, in the water channel structure 7 according to the first embodiment, as shown by the arrow in FIG. 5, the water retained in the soil around the groove 9 is the solid 8 and the water passage hole 3 of the water channel forming block 1. And penetrates into the hollow portion of the water channel forming block 1 through. Further, in the water channel structure 7 according to the first embodiment, the water in the hollow portion of the water channel forming block 1 is dispersed in the soil around the groove 9 via the water passage hole 3 and the solid matter 8.
Further, in the water channel structure 7 according to the first embodiment, both inside the hollow portion of the water channel forming block 1 and on the outside surface side thereof (mainly the area in which the solid matter 8 is disposed) function as water passage portions.
That is, in the water channel structure 7 according to the first embodiment, the water channel forming block 1 is not a water blocking wall, but is a structure for separating a fast flow region and a slow flow region in the water passage portion.
Further, in the water channel structure 7 according to the first embodiment, the flow velocity of water flowing in the hollow portion of the water channel forming block 1 is higher than the flow velocity of water flowing on the outer surface of the water channel forming block 1. This is because in the water channel structure 7 according to the first embodiment, the group of solids 8 arranged on the outer surface of the water channel forming block 1 acts as a resistor for flowing water.

Further, in the water channel structure 7 according to the first embodiment, water flows on the outer surface of the water channel forming block 1 due to its structure, so that the solid bodies 8 do not move along with the water flow. Need to be devised.
In view of such circumstances, in the water channel structure 7 according to the first embodiment, the solid 8 disposed adjacent to the water channel 3 formed in the side wall 2 of the water channel forming block 1 is replaced by the water channel 3. It is specified as the one that can be inserted into and cannot pass through the water passage hole 3. Further, it is desirable that the solid matter 8 arranged adjacent to the water passage hole 3 has an outer size that protrudes from the water passage hole 3 when inserted into the water passage hole 3.
In this case, the solid matter 8 inserted into the water passage hole 3 forms an engaging structure with the solid matter 8 around it, and as a result, between the inner wall 9a of the groove 9 and the outer surface of the water channel forming block 1. It is possible to hinder the movement of the group of solid objects 8 interposed. Then, the solid matter 8 inserted into the water passage hole 3 also acts as an anchor that prevents the movement of the water channel forming block 1 according to the present embodiment.
In addition, the solid matter 8 inserted into the water passage hole 3 acts as a resistor for reducing the flow velocity of the water flowing on the outer surface side of the water channel formation block 1.
Therefore, according to the water channel structure 7 according to the first embodiment, it is possible to prevent scouring from occurring on the outer surface side of the water channel forming block 1.
As a result, even when the amount of water flowing through the water channel structure 7 according to the first embodiment is large, the water channel forming block 1 is not exposed by the water flowing on the outer surface side of the water channel forming block 1, The physical connection of the soil around it can be maintained.

Further, in the water channel structure 7 according to the first embodiment, the connecting member 4 in the water channel forming block 1 is arranged so as to block the water flow path in the water channel structure 7, and the solid matter is placed in the voids 5 between the connecting members 4. Eight groups are housed. For this reason, in the water channel structure 7 according to the first embodiment, it is possible to prevent the solid matter 8 from moving to the downstream side of the flow path during water passage, and at the same time, the plurality of solid matter contained in the connecting member 4 itself and the voids 5 thereof. The object 8 can reduce the flow velocity of the water flowing around the connecting member 4.
Therefore, in the water channel structure 7 according to the first embodiment, it is possible to preferably prevent scouring from occurring on the bottom in the hollow portion of the water channel forming block 1 and on the vertically lower surface of the connecting member 4.
Furthermore, in the waterway structure 7 according to the first embodiment, the waterflow structure 7 according to the first embodiment flows by appropriately adjusting the thickness of the layer formed of the solid 8 groups arranged around the waterway formation block 1. The flow rate of water can be changed as desired. Therefore, according to the water channel structure 7 according to the first embodiment, it is possible to provide a water channel structure having high versatility with respect to the flow rate.
Moreover, at the bottom of the hollow portion of the water channel forming block 1, the water continues to flow at a reduced flow rate, which provides an optimal environment for growing aquatic organisms.
Therefore, the water channel structure 7 according to the first embodiment can be used not only as a drainage channel or a water channel, but also can contribute to conservation of the ecosystem around the channel.

Furthermore, in the water channel structure 7 according to Example 1, as shown in FIGS. 4 and 5, the water channel structure 7 is provided between the inner wall 9a of the groove 9 and the group of solids 8 and has an average particle size larger than that of the group of solids 8. It may be provided with a granulate layer 10 of granules having a small average particle size (optional component).
In this case, when the granular material layer 10 functions as a filter and the water in the soil around the groove 9 flows into the hollow portion of the water channel forming block 1, a part of the soil becomes a solid 8 group. It has an effect of preventing the water channel forming block 1 from entering the hollow portion through the gap.
Furthermore, in the water channel structure 7 according to the first embodiment including such a granular material layer 10, water can be made to flow even in the granular material layer 10. The flow velocity of water flowing in the granular material layer 10 becomes slower than the flow velocity of water flowing in the solid substance group 8.
That is, in the water channel structure 7 according to the first embodiment, as the distance from the hollow portion of the water channel forming block 1 increases, the flow velocity of water flowing therethrough becomes slower.
Therefore, in the water channel structure 7 according to the first embodiment, the flow rate of water flowing through the water channel structure 7 according to the first embodiment can be increased by providing the granular material layer 10 in addition to the group of solids 8.

Here, the detailed structure of the water channel formation block 1 according to the present embodiment will be described in more detail with reference to FIG. 6.
FIG. 6 is a cross-sectional view of the water channel forming block according to the embodiment of the present invention. More specifically, FIG. 6 is a sectional view taken along line AA in FIG. Note that the same parts as those shown in FIGS. 1 to 5 are denoted by the same reference numerals, and the description of the configuration thereof will be omitted.
As shown in FIG. 6, in the water channel formation block 1 according to the present embodiment, in an arbitrary water passage hole 3 formed in the side wall 2, the occupying area S ₁ of the inner side surface opening 3 a of the side wall 2 is defined as follows. It may be configured to be smaller than the occupied area S ₂ of the outer side surface opening 3b (optional component).
In this case, it is possible to easily insert the solid matter 8 into the outer side surface opening 3b from the outside of the water channel forming block 1. In addition, it is possible to make it difficult for the solid matter 8 inserted into the water passage hole 3 to pass through the inner side opening 3a to the hollow portion side of the water channel forming block 1.
Therefore, by specifying the inner side surface opening 3a and the outer side surface opening 3b in the side wall 2 as described above, when the water channel structure 7 is formed using the water channel forming block 1 according to the first embodiment, the outside of the side wall 2 is formed. It is possible to facilitate the work of arranging the solid matter 8 in the.
The planar shapes of the inner side surface opening 3a and the outer side surface opening 3b in the side wall 2 are not particularly specified, but may be any shape as long as the shape does not hinder the insertion of the solid matter 8.
In addition, the planar shapes of the inner side surface opening 3a and the outer side surface opening 3b in the arbitrary water passage hole 3 may be similar (optional component). In this case, there is an advantage that the water passage hole 3 can be easily formed when the water channel forming block 1 according to the first embodiment is molded.
Furthermore, the side wall 2 provided with the water passage holes 3 may have a grid-like appearance (optional component). In this case, water can surely and smoothly flow into and out of the hollow portion of the water channel forming block 1 over the entire area of the side wall 2.

Further, as shown in FIG. 6, in the water channel formation block 1 according to the present embodiment, the distance between the water passage holes 3, more specifically, the distance between the opening edges of the adjacent water passage holes 3, , Q, a minimum thickness U of the connecting member 4 in the horizontal direction (see FIG. 3A), and a minimum thickness R of the connecting member 4 in the vertical direction (see FIG. 6). All of the above) may be set to be equal to or larger than the minimum value P of the thickness of the side wall 2 (optional component).
In this case, the strength of the water channel forming block 1 in the horizontal direction and the vertical direction can be made uniform. In this case, it is possible to avoid the water channel forming block 1 from being damaged when the solid 8 is strongly pushed into the water passage hole 3.

In addition to the above-described identification of the values of Q, U, and R in the water channel formation block 1 according to the present embodiment, as shown in FIG. 6, the minimum value of the thickness of the connecting member 4 in the vertical direction R may be set to 1.25 times the minimum thickness P of the sidewall 2 or more (optional component).
In this case, in the water channel forming block 1, the depth of the voids 5 between the connecting members 4, 4 in the vertical direction can be increased. In this case, the effect of holding the bottom surface forming material (for example, the solid matter 8 or the like) by the connecting material 4 can be further enhanced.
Further, in the water channel forming block 1 according to the present embodiment, the connecting member 4 is arranged so as to block the flow of water. Further, as described above, in the water channel structure 7 according to the first embodiment, the outer surface of the water channel forming block 1 also functions as a water passage portion. Therefore, the larger the minimum value of the thickness R of the connecting member 4 in the vertical direction is, the more easily the effect of reducing the flow velocity of the water flowing around the connecting member 4 is exhibited.
Therefore, by setting the minimum value R of the thickness of the connecting member 4 in the vertical direction to be 1.25 times or more the minimum value P of the thickness of the side wall 2, the flow velocity in the water channel structure 7 according to the first embodiment. And the effect of preventing scouring on the bottom side of the hollow portion of the water channel forming block 1 can be more reliably exhibited. Therefore, when water is passed through the water channel structure 7 according to the first embodiment, it is possible to prevent a problem in water flow due to scouring on the outer surface of the water channel forming block 1.

Further, as shown in FIG. 6, the vertical length T of the protrusion 6 in the water channel formation block 1 according to the present embodiment may be at least 0.8 times or more the minimum value P of the thickness of the side wall 2. This projection 6 also acts as a resistor for the water flowing on the outer surface side of the water channel forming block 1. Therefore, a longer vertical length T of the protrusion 6 is advantageous for reducing the flow velocity of water flowing on the outer surface side of the water channel formation block 1. On the other hand, if the vertical length T of the protrusion 6 is longer than necessary, the workability of the water channel forming block 1 is deteriorated. Therefore, the vertical length T of the protrusion 6 is sufficient as long as it can form an engagement relationship with the small number of solids 8 arranged adjacent to the protrusion 6. That is, the vertical length T of the protrusion 6 may be 0.8 times or more the minimum value P of the thickness of the side wall 2, but it does not have to be a value that greatly exceeds the average particle size of the solid 8 group.
However, in order to increase the amount of water flowing through the water channel structure 7 according to the first embodiment, when it is necessary to set the thickness of the group of solids 8 arranged vertically below the connecting member 4 to be large, the projection 6 The vertical length of may be set to exceed the above value.

The vertical depth D and the horizontal width W of the hollow portion of the water channel formation block 1 according to the present embodiment may be appropriately set according to the intended use of the water channel structure 7 according to the first embodiment (FIG. 6). See).
When the water channel forming block 1 according to the present embodiment is made of reinforced concrete, the minimum value P of the thickness of the side wall 2 is preferably 120 mm or more.
Further, there is no particular problem even if the minimum value P of the thickness of the side wall 2 exceeds the above value, but the larger the minimum value P of the thickness of the side wall 2 is, the heavier the weight of the water channel forming block 1 is. The workability of the forming block 1 is reduced.
The water channel forming block 1 according to the present embodiment may be made of a material other than reinforced concrete as long as it has strength and durability equivalent to that of reinforced concrete.

Finally, with reference to FIG. 7, another water channel structure (underditch) using the water channel forming block 1 according to the present embodiment will be described.
FIG. 7 is a vertical cross-sectional view of a water channel structure (underdrain) according to a second embodiment of the present invention as seen from the direction in which the flow path is blocked. The same parts as those shown in FIGS. 1 to 6 are designated by the same reference numerals, and the description of the structure will be omitted.
As shown in FIG. 7, the water channel structure 7 (the underdrain 7B) according to the second embodiment is arranged in a state in which the connecting member 4 is arranged vertically above the mounting surface 15 formed by excavating the ground. The water channel forming block 1 according to the present embodiment, the burying soil 13 for burying the water channel forming block 1, and the solid material 8 group interposed between the water channel forming block 1 and the burying soil 13 And are provided.
Further, in the water channel structure 7 according to the second embodiment, the solids 8 arranged adjacent to the water holes 3 of the water channel forming block 1 or the voids 5 of the connecting members 4 are in the water holes 3 or in the water holes 3. A material that can be inserted into the space 5 between the materials 4 but cannot pass through the water passage hole 3 or the space 5 is used.

In the water channel structure 7 (dark culvert 7B) according to the second embodiment as described above, unlike the water channel structure 7 (light culvert 7A) according to the first embodiment, it is formed between the connecting members 4 of the water channel forming block 1. The void 5 has the same action and effect as the water passage hole 3 formed in the side wall 2 of the water channel formation block 1.
Therefore, for example, the water channel structure 7 (dark conduit 7B) according to the second embodiment is formed by using the water channel forming block 1 having the same size as the water channel forming block 1 used for the water channel structure 7 (light channel 7A) according to the first embodiment. In the case of forming it, it is necessary to arrange the solid material 8 having an outer size larger than that of the solid material 8 arranged adjacent to the water passage hole 3 at a position adjacent to the void 5 between the connecting members 4 (FIG. 7). See).

The action and effect of the water channel structure 7 (dark culvert 7B) according to the second embodiment is substantially the same as that of the water channel structure 7 (light culvert 7A) according to the first embodiment. Further, while the water channel structure 7 according to the first embodiment (the culvert 7A) is installed with the hollow portion of the water channel forming block 1 open to the ground surface, the water channel structure 7 according to the second embodiment ( In the underdrain 7B), the entire water channel forming block 1 is buried in the ground, and the positions of the water channel forming block 1 in the ground are different.
For this reason, in the waterway structure 7 according to the second embodiment (underdrain 7B), the effect of providing a place for growing aquatic organisms and in the surrounding area, compared to the waterway structure 7 according to the first embodiment (drain 7A). The effect of preserving the natural environment becomes difficult to exert.
On the other hand, in the case of the water channel structure 7 (the underdrain 7B) according to the second embodiment, the water in the soil can be smoothly discharged to the outside by installing it in the soil of the wetland body, for example. As a result, according to the water channel structure 7 (underdrain 7B) according to the second embodiment, for example, a wetland can be used as a cultivated land.
In addition, by installing the water channel structure 7 (the underdrain 7B) according to the second embodiment in the valley of the mountain, the rainwater collected in the valley can be drained by flowing not through the surface of the ground but through the ground. In this case, it is possible to reduce the risk of landslides occurring in the valleys of the mountains.

In addition, the mounting surface 15 on which the water channel structure 7 according to the second embodiment is formed is usually hard impermeable ground or the like, and is not easily eroded. Therefore, in the water channel structure 7 according to the second embodiment, even when the water channel forming block 1 is simply mounted on the mounting surface 15, scouring of the bottom of the water passage portion 16 progresses with time. There is no problem that the water channel structure 7 itself collapses toward the vertically lower side.
On the other hand, when the placing surface 15 is soft and scouring may occur at the bottom of the water passage portion 16 in the water channel structure 7 according to the second embodiment, the solid matter 8 group is previously provided at the bottom of the water passage portion 16. The water channel structure 7 (the underdrain 7B) may be formed after it is laid.
Alternatively, a tubular structure in which the hollow sides of the two water channel formation blocks 1 according to the present embodiment are opposed to each other is arranged in series to form a tubular water passage portion 16, and the tubular water passage portion 16 is further formed. The water channel structure 7 (not shown) may be formed by providing a layer of the solid 8 groups so as to cover the entire outer circumference of the water passage portion 16 (the water channel forming block 1 group).
In this case, since the entire area on the outer surface side of the water channel formation block 1 (especially the area where the group of solids 8 is arranged) can be used as the water passage portion 16, it is possible to form the underdrain 7B having a large flow rate.

Further, in FIG. 7, the case of disposing only one water channel structure 7 (underdrain 7B) according to the second embodiment is described as an example, but the water channel structure according to the second embodiment is underground. A plurality of 7 (dark culverts 7B) may be provided in parallel (not shown). In this case, a desired number of water passage portions 16 each including one group of water channel forming blocks arranged in a tubular shape may be arranged in parallel with each other with eight groups of solids interposed (not shown).
As described above, when the water channel structures 7 (dark culverts 7B) according to the second embodiment are arranged side by side in the ground while being close to each other, the culvert 7B having a large flow rate is used to reduce the volume of voids formed in the ground. Can be formed while. Thereby, even if a natural disaster such as an earthquake occurs, it is possible to make it difficult to damage the water channel structure 7 (the underdrain 7B) according to the second embodiment.

Further, in the water channel structure 7 (underdrain 7B) according to Example 2, as shown in FIG. 7, an average particle size smaller than the average particle size of the solid bodies 8 is provided between the solid bodies 8 and the burying soil 13. The granular material layer 10 made of the granular material may be provided.
In this case, the granular material layer 10 functions as a filter to suppress the inflow of the burying soil 13 into the water passage portion 16 of the water channel structure 7 as in the case of the water channel structure 7 (the culvert 7A) according to the first embodiment. can do. As a result, it is possible to reduce the risk that the water passage portion 16 of the water channel structure 7 (the underdrain 7B) according to the second embodiment causes a problem such as clogging with the inflow material from the surroundings.
Therefore, according to the water channel structure 7 (underdrain 7B) according to the second embodiment, it is possible to provide the water channel structure 7 that is easy to maintain and can withstand permanent use.

In addition, when constructing the water channel structure 7 according to Examples 1 and 2, it is necessary to arrange the end faces of the water channel forming block 1 without a gap as in the case of installing a conventionally known gutter or a permeation drainage type gutter. Absent. That is, when constructing the water channel structure 7 according to Examples 1 and 2, and when arranging the water channel forming blocks 1 in series, there is a gap between the end surfaces of the adjacent water channel forming blocks 1. May be. In this case, between the end faces of the adjacent water channel forming blocks 1, it is possible to insert a solid substance 8 of a size that can be inserted into this gap but cannot pass through this gap. As a result, it is possible to preferably prevent the soil around the groove 9 and the burying soil 13 from flowing into the hollow portion of the water channel forming block 1 through the gap between the water channel forming blocks 1.
This means that it is not necessary to strictly face the end faces of the adjacent water channel forming blocks 1 when the water channel structures 7 according to Examples 1 and 2 are constructed on a steep slope, for example.
Further, particularly when the water channel structure 7 according to the first and second embodiments is constructed on a steep slope, for example, a step may be intentionally formed between the end faces of the adjacent water channel forming blocks 1 (optional). Optional components). In this case, since a resistor that reduces the flow velocity is formed at a desired interval in the water passage portion (for example, the water passage portion 16) having a higher flow velocity in the water channel structure 7, The effect of reducing the flow velocity of flowing water can be expected.

Further, in the water channel structure 7 according to the first and second embodiments, crushed stone is mainly assumed as the solid matter 8, but as a substitute for crushed stone, for example, one obtained by classifying crushed waste concrete or the like for a long period of time. Solids that can retain their shape over time can be used.

INDUSTRIAL APPLICABILITY As described above, the present invention can be used as both the inside and outside of the water channel forming block as the water passage portion, and at the time of use, scouring does not occur on the bottom side or the outer surface of the water channel forming block. Moreover, it is a waterway forming block capable of forming a waterway suitable for habitation of aquatic organisms and a waterway structure using the same, and can be used in fields related to agriculture, civil engineering, irrigation equipment, disaster prevention technology, and the like.

DESCRIPTION OF SYMBOLS 1... Block for forming a water channel 2... Side wall 3... Water passage hole 3a... Inner side surface opening 3b... Outer side surface opening 4... Connection material 5... Void 6... Protrusion 7... Water channel structure 7A... Mine channel 7B... Dark channel 8... Solid matter 9... Groove 9a...Inner wall 10...Particle layer 11...Water 12...Impermeable layer 13...Embedding soil 14...Impermeable layer 15...Mounting surface 16...Water passage

Claims (6)

A block for forming a waterway structure used as a culvert or a culvert,
A pair of flat side walls,
A plurality of water passage holes formed in a state of being dispersed in the plane direction of the side wall, the plurality of water passage holes being formed through the side wall,
At least two connecting members provided between the pair of side walls to connect the pair of side walls;
At least two protrusions protruding from the side wall and/or the connecting member in the vertical direction outside the block,
The side wall and the connecting member are rigidly joined,
At least the side wall and the connecting member have a rigidity equal to or higher than that of reinforced concrete, and a water channel forming block. 2. The water channel forming block according to claim 1, wherein in any of the water passage holes, an occupying area S ₁ of an inner side surface opening of the side wall is smaller than an occupying area S ₂ of an outer side surface opening of the side wall. .. The minimum value of the interval between the water holes is equal to or more than the minimum value of the thickness of the side wall,
The connecting material is
The minimum value of the thickness in the horizontal direction is greater than or equal to the minimum value of the thickness of the side wall,
The minimum value of the height in the vertical direction is 1.25 times or more of the minimum value of the thickness of the side wall, and the waterway forming block according to claim 1 or 2. A trench made by excavating the ground,
The water channel forming block according to any one of claims 1 to 3, wherein the connecting member is accommodated in a hollow portion of the groove in a state where the connecting member is disposed on a vertically lower side,
A solid group provided between the inner wall of the groove and the side wall of the water channel forming block;
The solid matter arranged adjacent to the water passage hole of the water channel forming block can be inserted into the water passage hole, but cannot pass through the water passage hole. Waterway structure. The water channel forming block according to any one of claims 1 to 3, which is disposed on a mounting surface formed by excavating the ground.
An embedding soil for embedding the water channel forming block, and a solid matter group interposed between the water channel forming block and the embedding soil,
The solid matter disposed adjacent to the water passage hole or the gap between the connecting members of the water channel forming block can be inserted into the water passage hole or the gap, but the water passage A waterway structure characterized by being unable to pass through holes or said voids. The inner wall of the groove, or the earth for burying, and a solid material group, provided with a granular material layer made of granular material having an average particle diameter smaller than the average particle diameter of the solid material group. The water channel structure according to claim 4 or 5, wherein:

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