JP4866146B2 - Simulation method of particle movement in sand recycling - Google Patents

Description

  The present invention relates to a method and the like that can simulate the movement of earth and sand thrown into the seabed after dredging in sand recycling at the seabed and the like, and can determine the earth and sand throwing position.

  When an artificial structure such as a port facility is installed on the beach or estuary coast, the flow of the tide changes, and the nearby coastline and the seabed are eroded, and the shaved earth flows into the port facility and accumulates. May occur. Even if such deposition occurs, it is possible to recover the state before the erosion or deposition occurs (sand recycling) by reducing the accumulated earth and sand to an eroded place at any time. However, when the eroded place is a relatively shallow sea bottom such as a shallow sea, the earth and sand transport ship cannot approach the eroded place and the earth and sand cannot be directly input.

  In such a case, an attempt is made to continuously transfer the seabed dredging and the objects to be crushed by a fixed sand bypass system consisting of a fixed pump and a pressure-feed pipeline, belt conveyor, etc., without using a sediment carrier. Is known (see, for example, Non-Patent Document 1). However, the facilities are large and expensive, and the coastal landscape is greatly affected.

Therefore, instead of directly throwing the earth and sand into the eroded place, the earth and sand can be put in by the earth and sand transport ship, and the earth and sand are thrown into a place upstream of the tide of the eroded place, and then eroded by the flow of the tide. There has also been proposed a method for allowing earth and sand to move naturally to the designated place. However, it is very difficult to determine exactly where to put earth and sand. For example, a field survey is carried out in advance on the state of movement of earth and sand due to the flow of tide using fluorescent sand, and the place where the earth and sand is introduced is determined based on the result. However, this investigation must be done by trial and error, and requires a lot of time and effort, so the number of investigations is practically limited. Therefore, the actual situation is that it is quite difficult to accurately determine the input location.
"Export Sand Bypass system", published by Queensland Government, [Search January 5, 2006], Internet <http://www.transport.qld.gov.au /Home.nsf/index/sandbypasssystem>

  The present invention can accurately simulate the subsequent movement of the sand and sand by the beach flow when the sand dredged from the sedimentation place of the seabed is put in a place different from the eroded place, and the optimum position of the sand and sand can be determined. It is an object to provide a method and the like.

  A first aspect of the invention is a method for simulating particle movement in sand recycling, the step of setting terrain conditions, wave conditions, and initial conditions of the particles where the sand recycling is performed, and the terrain conditions and the wave conditions. Calculating a plane wave field and a beach flow field at the location from the conditions; calculating an external force field applied to the particles from the plane wave field and the beach flow field; and And a step of calculating a moving position by a stochastic process.

  Here, it is preferable that the initial condition includes that the plurality of particles aggregate to form a shape in which a plurality of moving layers are stacked. Furthermore, it is preferable that a step of determining the movement possibility of the particles from the external force field and the initial condition is provided, and the movement position is calculated when the movement possibility is affirmed.

  A second aspect of the invention is a program for causing a computer to execute any one of the above simulation methods.

  In sand recycling, there is no need to conduct on-site investigations with fluorescent sand, and simulation can be repeated as many times as necessary, so that it is possible to accurately determine the earth and sand input position suitable for sand recycling.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a schematic diagram of the shape formed by the actual earth and sand 1 introduced into the earth and sand loading position of the seabed 2, FIG. 1 (1) is a side view, and (2) is a top view. The earth and sand are deposited in a shape like a bowl with a diameter of 2R and a height of H. Sediment is gradually transported from the surface by the beach current, and the sediment is returned to the target erosion position.

  However, since it is difficult to handle the calculation with the shape as it is, for simplification, it is considered that the earth and sand thrown into the seabed has a flat cylindrical shape composed of N particles as a whole. FIG. 2 is a diagram schematically showing a side surface of the cylinder 10 in which the shape of the earth and sand is idealized. Then, the overall height of the cylinder 10 is Δh, the diameter is 2r, and the cylinder 10 is regarded as a stack of thin layers. The earth and sand is a single thin layer having a thickness δs including Ns particles from only the upper surface of the cylinder. I think that it is transported and moved to the beach flow by the moving layer.

However, not all of the earth and sand contained in the moving layer is transported in unit time, so the moving layer is further divided into two upper and lower layers, and the upper layer 11 moves particles by the beach current during unit time. However, it is assumed that the layer is composed of particles that remain in the cylinder 10. The number of moving particles is N ₀ . Whether or not the cylinder 10 remains is determined based on the position after the movement. On the other hand, the lower layer 12 is a layer composed of particles that begin to be affected by the beach current after Δt. Further, the lowest layer 13 is not yet affected by the beach current and is considered as a layer of particles that are not moving. That is, FIG. 2 is a schematic diagram showing the state of the cylinder 10 at the time when the unit time Δt elapses from a certain time. Note that the unit time Δt may be determined as appropriate, specifically 1 minute, 1 hour, or 1 day. In this example, the calculation is performed with Δt set to 30 minutes.

  The soil and sand introduced in this way are regarded as a collection of N particles having a cylindrical shape, and a simulation is performed by obtaining a trajectory in which each particle is transported to the beach flow. However, since the beach current works in the same manner for all the particles of the earth and sand that have been input, simply calculating the trajectory of each particle along the beach current makes the cylinder 10 As a result, the result is merely a translation in almost the same form, which is far from the actual situation of earth and sand movement. This is because the beach current obtained by averaging in a relatively coarse unit block for calculation convenience cannot express the fine random flow that occurs in the actual flow, and it is also affected by scattering due to particle collisions, etc. Because it cannot be reflected.

Therefore, in obtaining the trajectory of each particle, a stochastic process including a random diffusion factor as shown in FIG. 3 is used. FIG. 3 is a diagram illustrating the position vector X ^{n + 1} of the same particle position vector after unit time Δt, where X ⁿ is the position vector of a particle at a certain time. Here, assuming that the velocity vector for particle transport by the beach current is Us, the position vector after unit time considering only Us is Y ^{n + 1} obtained by adding UsΔt to X ⁿ . A vector at a position obtained by adding the diffusion vector af (θ) to this is defined as X ^{n + 1} . That is, the following equation (1) is established.
X ^{n + 1} = X ⁿ + UsΔt + af (θ) (1)

Here, f (θ) is a unit vector pointing in a random direction (θ) using a uniform random number, and plays a central role in a stochastic process in which the trajectory of particles is stochastically determined. It is also a directional distribution function that determines the direction of the vector af (θ) serving as a diffusion factor around the end point of UsΔt. a is a moving distance per unit time by a stochastic process (diffusion), and is defined by the following equation (2) using the particle diffusion coefficient D and the unit time Δt.
a = (2DΔt) ^1/2 (2)

The diffusion coefficient D is based on the assumption that the sea area to be calculated is in the wave breaking band, the mixing distance is proportional to the wave height H, and the representative velocity is proportional to the bottom orbital flux amplitude Um, which is the amplitude of the disturbance caused by the wave. Then, what was defined by the following formula (3) was used. The bottom orbit flux amplitude Um can be determined from the wave field and topographic conditions.
D = 0.003UmH (3)

  By including such a diffusion factor af (θ), it becomes possible for each particle to randomly walk and also to vary the moving direction of the particle for each particle, and reflect the actual state of earth and sand movement. It became possible. The velocity vector Us of the particles is in the same direction as the average velocity vector Uc due to the beach current, and the length is 1% of Uc (Us = 0.01 Uc).

  Based on the above model, the movement simulation of earth and sand thrown into the seabed is performed as follows. FIG. 4 is a diagram showing a schematic flow of simulation. The simulation will be described using an example in which the simulation is performed by a computer. When the process is started, first, the terrain condition of the sea area to be processed is input (step S10). The topographic conditions include the position and shape of existing coastlines and harbor facilities, topography and water depth of the seabed near the coastline, soil quality of the seabed, and the like.

  FIG. 5 shows a schematic diagram of the sea area input in an actual simulation example. This is a plan view of the Tokai Port in Ibaraki Prefecture, and the sea area where a plurality of contour lines 22 are drawn is expanded in the upper part of the drawing of the quay 32, and the port 20 surrounded by jetties 31 and 32 on the left side of the drawing. Is provided. In the following, because the sediment on the seabed near the quay 32 on the right hand side of the port 20 is eroded by the beach current (roughly flows from the right to the left of the drawing) and accumulates in the port entrance 21 and the port 20, A case where it is desired to reduce this to an eroded portion will be described as an example.

  Next, wave conditions off the beach, which are the origins of the beach current that carries the loaded earth and sand, are set (step S20). Wave conditions measure what kind of waves have occurred in a predetermined period offshore on the beach, and statistical wave height, period, wave direction, etc. of waves analyzed by the spectral method etc. based on this data. Contains data.

  Next, initial conditions for N particles representing the earth and sand to be introduced are set (step S30). Since the simulation is performed assuming that the N particles are input to the test input position 40 in FIG. 5, the initial condition includes the position coordinates of the test input position 40. In addition, as described above, it is considered that these N particles have a flat cylindrical shape shown in FIG. 2. As initial conditions, the depth data of each particle in the cylindrical shape (immediately after the injection) Data indicating the buried depth of each particle on the basis of the height of the upper surface of the cylinder.

  Next, the plane wave field of the target beach is calculated from the set topographic condition and wave condition (step S40). A plane wave field consists of a scalar field in which the time-averaged wave energy distribution in the vicinity of the beach is calculated and a vector field in which the wave direction is calculated. It is calculated from the terrain condition of the beach through the energy balance equation. The actual calculation is performed by a normal numerical method in which the sea area is divided into a plurality of unit areas and the differential equations are discretized.

  Next, the beach flow field is calculated (step S50). The beach flow field is a vector field that specifies the speed (velocity) and direction (flow direction) of the beach flow averaged for each location near the target beach. First, from the plane wave field obtained earlier, the values of wave height and wave direction averaged over time are obtained for each beach location in consideration of wave height attenuation due to breaking waves. Assuming these average wave heights and wave direction distributions, the coastal flow field assumes the boundary conditions of the offshore boundary and the lateral boundary based on the radiation stress. In addition, assuming a friction term on the seabed, the calculation is performed using a nonlinear long wave equation. For example, when the coast extends in the left-right direction with respect to the drawing as shown in FIG. 5, the side boundary is the boundary when the range in the left-right direction is determined in order to enable actual calculation. Means.

  As for the specific formulas and calculation methods for calculating the wave field and the beach flow field, here, Shinzo Shimizu, Takahiro Kumagai, Nobuo Mimura, Jun Watanabe, “Three-dimensional beach transformation long-term considering shoreline changes. Prediction Model ", Coastal Engineering Papers, Vol. 41, pp. This is performed in accordance with mathematical formulas and calculation methods described in 406-410, published by Japan Society of Civil Engineers (1994).

  Next, paying attention to a certain particle i (i = 1), an external force field applied to the particle i at t = Δt is calculated (step S60). Specifically, the bottom shear stress, which is an external force applied to the particle i, is extracted from the plane wave field and beach flow field obtained previously, and the ratio of the bottom shear stress and the stability force represented by the weight of the particle in water Calculate a certain number of Shields. It should be noted that the bottom shear stress to which the particles are moved naturally changes depending on the position of the particles on the seabed, such as whether they are inside the cylinder or outside the cylinder.

  Next, it is determined whether or not the focused particle i can be moved by the beach current (step S70). There are two criteria for determination, and if both are satisfied, it is determined that the particle i can move. The first criterion is whether or not the number of shields of particle i exceeds a predetermined limit number of shields. If so, the particle i can move because the bottom shear stress causing the motion of the particle exceeds the stability of the particle. The second criterion is whether or not the buried depth of the particle i in the cylindrical shape is smaller than the thickness δs of the moving layer. In the case of being small, the particles i can move because they are positioned sufficiently on the surface of the cylindrical shape. If both are satisfied, the flow proceeds to step S80, and if either or both are not satisfied, the flow proceeds to step S90. In addition, when the particle | grains i are moving outside from cylindrical shape with progress of time, it determines that it can move.

  In step S80, when the particle i is movable, the moving position of the particle i at t = 0 + Δt is calculated. In calculating the movement position, the above equation (1) is used, and the movement position is calculated by a random walk considering diffusion. The particles i move in a zigzag manner according to random numbers while roughly following the beach current. As a result, the movement trajectory varies from particle to particle, so that the actual movement of the earth and sand particles can be reproduced fairly accurately.

  In step S90, it is determined whether i = N is satisfied, that is, whether the calculation has been completed for all N particles. If not, the flow proceeds from step S90 to step S60, i is increased by 1 by setting i = i + 1, that is, steps S60 to S90 are executed for another particle i. This is performed for all N particles.

  On the other hand, when i = N is satisfied, since the calculation has been completed for all the particles, the flow proceeds from step S90 to step S100, and it is determined whether or not t exceeds a predetermined calculation time. . Here, the predetermined calculation time is a time for which it is determined in what period the earth and sand should be reduced after the earth and sand is charged. For example, a plan period until the end of the reduction such as one month, three months, one year, or the like is set. In this example, 40 days are set. If t does not exceed the predetermined calculation time, the scheduled reduction end time has not yet elapsed, so the flow returns from step S100 to step S60, and t = t + Δt. t is advanced by Δt, and steps S60 to S100 are executed again. This flow is repeated until the time t reaches a predetermined calculation time due to the accumulation of Δt.

  If the time t exceeds the predetermined calculation time, the scheduled reduction end time has been reached, so the flow proceeds from step S100 to step S110, and the data of the final movement positions of the N particles is shown in FIG. The process is finished after being output on the topographical map.

  Next, an example is shown in which a simulation is performed on an actual sea area. FIG. 6 shows a simulation result when 16 days have elapsed since the earth and sand (N = 100,000 pieces) were added to the test input position 40 with respect to the terrain described in FIG. In FIG. 6, the simulation results are displayed using contour lines with respect to the common logarithm of the number of particles moved to each unit section. However, when the number of sand was 0, it was set to 0 for convenience. As can be seen from FIG. 6, it can be seen that the particles are diffusing and moving from the test loading position 40 toward the lower left direction toward the drawing. FIG. 7 is a diagram showing a simulation result when 40 days have passed since the insertion under the same situation. It can be seen that some of the particles reach the quay 32 and the entrance 21 of the harbor.

On the other hand, in order to verify the validity of the simulation results, a field survey was conducted in which fluorescent sand was actually introduced at the test entry position 40 in the same sea area. FIG. 8 is a diagram showing a place where sampling was performed in the field survey. Sampling is performed at each intersection of a checkerboard-like lines in each Figure to 16 days and after 40 days from the feeding corresponding to FIGS. 6 and 7, soil was collected volume 300 cm ³ (surface area 120 cm ²⁾ at each intersection, The number of fluorescent sand contained was counted. FIG. 9 shows the results of the field survey 16 days after the introduction, and FIG. 10 shows the results of the field survey after 40 days. The survey results showed only a grid-like part. The number near the intersection is a common logarithm of the number of fluorescent sands obtained. However, when the number of sand was 0, it was set to 0 for convenience. In the field survey, a wave meter was installed offshore of the target sea area to simultaneously measure the wave conditions for use in the simulation.

  Comparing FIG. 6 and FIG. 9, it can be seen that an approximate result is obtained in that the particles diffuse and move from the test loading position 40 in the lower left direction of the drawing. Moreover, comparing FIG. 7 with FIG. 10, it can be seen that a result that is quite approximate is obtained in that some particles reach the vicinity of the entrance of the quay or harbor. Considering that the beach current used in the simulation is only an averaged macroscopic flow and does not include microscopic disturbances that directly affect particle movement, the results of FIGS. The approximation of is surprisingly high.

  Further, FIGS. 11 to 14 show simulation results when the place where the earth and sand is charged is changed. FIG. 11 is a simulation result of the situation after 16 days have passed since the earth and sand injection position is changed to the north side (left side of the drawing) from the test injection position 40 in FIG. . The point that the particles are moving to the lower left of the drawing is the same as in FIG. 6, but the particles reach the harbor entrance 21 and the quay 32 in 16 days. FIG. 12 shows the simulation result of the situation after 24 days from FIG.

  FIG. 13 is a simulation result of a situation after 16 days have elapsed since the loading position of earth and sand was changed from the loading position of FIG. 11 to a position closer to the quay. It can be seen that the particles have not reached the harbor entrance 21 but have reached the quay 32 when the 16th day has passed. Furthermore, FIG. 14 shows the simulation result of the situation after 24 days from the time of FIG. 13, that is, after 40 days from the insertion. It can be seen that the particles have not reached the harbor entrance 21 even after 40 days.

  In this way, by changing the earth and sand input position and repeating the simulation, the particles reach a place where it is desirable that the particles reach (for example, the quay 32) and reach a place where it is desirable that the particles do not reach (for example, the port entrance 21). This makes it possible to easily determine the desired input location. At that time, it is only necessary to obtain the local wave conditions by some means, and the on-site survey using the fluorescent sand on the site becomes unnecessary, so that enormous labor and cost for the on-site survey are eliminated.

  Although the embodiments have been described above, the present invention is not limited to the specific embodiments described above, and various modifications are possible. For example, in the above, a model was used in which the earth and sand thrown in was formed into a flat cylindrical shape in which thin layers were stacked. However, in the calculation, the cylinder does not have to be a cylindrical shape because it is treated as a point, such as a square or a triangle. A model having an arbitrary shape may be used. In short, there are particles that can move and particles that cannot move at a certain time t, and whether or not the particles can move out of the sediment input position during the unit time Δt even though they can move. Each can be reflected in the result.

  In calculating the plane wave field and the beach flow field, the method described in the literature is used in the above description, but other known methods may be used. In addition, the calculation of the particle trajectory using a stochastic process is not performed by randomly changing the vector direction using a uniform random number as described above, but by shifting the particle movement direction based on the beach flow direction. A probability function using an angle as an argument may be used. Further, although the diffusion coefficient is defined on the assumption of the breaking band, it may be appropriately determined for each including the breaking wave band.

  Although the present invention has been described above as a simulation method, the present invention may be a program for causing a computer to execute the simulation method. The program may be stored in a computer-readable recording medium. Here, the recording medium refers to a recording medium such as a flexible disk, a magneto-optical disk, a portable medium such as a ROM and a CD-ROM, and a hard disk incorporated in a computer system. The program may be arbitrarily divided, and the divided programs may be stored in the storage medium.

It is the schematic diagram which showed the state of the earth and sand thrown into the seabed. It is a schematic diagram of the model which idealized the input earth and sand into a cylindrical shape. It is the conceptual diagram which illustrated the calculation method of the stochastic process. It is the flowchart which showed the outline flow of simulation. It is the topographical map of the example of the sea area made into simulation object. It is the figure which showed the simulation result after 16 days passage when earth and sand are thrown into the test pouring position. It is the figure which showed the simulation result after 40 day passage when earth and sand are thrown into the test pouring position. It is the figure which showed the point which sampled the fluorescent sand when conducting the field survey. It is the figure which showed the fluorescent sand distribution at the time of passing 16 days after putting fluorescent sand into the test charging position 40. It is the figure which showed the fluorescent sand distribution at the time of 40 days having passed since the fluorescent sand was thrown into the test insertion position. It is the figure which showed the simulation result after 16 days when the earth and sand are thrown into another loading position. It is the figure which showed the simulation result after 40-day progress when earth and sand are thrown into another loading position. Furthermore, it is the figure which showed the simulation result after 16 days passage when earth and sand are thrown into other loading positions. Furthermore, it is the figure which showed the simulation result after progress for 40 days when earth and sand are thrown into another loading position.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Earth and sand thrown into the seabed 2 Seabed 10 Idealized earth and sand 11 A layer of particles 12 Δt that remains in the cylinder but starts moving in the cylinder after Δt 13 A particle that does not move after Δt Layer 20 Port 21 Port entrance 22 Contour line 30 North side jetty 31 South side jetty 32 Quay wall 40 Test entry position

Claims (4)

  A method for simulating particle movement in sand recycling, comprising: setting a topographic condition, a wave condition, and an initial condition of the particle at a place where the sand recycling is performed; and from the topographic condition and the wave condition, A step of calculating a plane wave field and a beach flow field, a step of calculating an external force field applied to the particles from the plane wave field and the beach flow field, and a moving position of the particles by the external force field by a stochastic process And a step of calculating.   The simulation method according to claim 1, wherein the initial condition includes a model in which a plurality of the particles are aggregated to form a shape in which a plurality of moving layers are stacked.   2. The method according to claim 1, further comprising a step of determining the movement possibility of the particles from the external force field and the initial condition, and the movement position is calculated when the movement possibility is affirmed. Or the simulation method of 2. A program for causing a computer to execute the simulation method according to claim 1.

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