Finite Element Analysis Method for Automatic Water Conduction of Water Conduit in PC-PRB

Abstract

The present invention provides a finite element analysis method for realizing automatic water diversion of a water diversion pipe in a PC-PRB, including: determining the water diversion flow rate of the water diversion pipe based on the length of the water diversion pipe, the permeability coefficient, the water flow cross-sectional area, and the groundwater head at the starting point of the water diversion pipe and the center point of the water distribution layer; constructing a finite element equation group based on solving the seepage problem, and determining the coefficient matrix formula according to the finite element equation group; after the water diversion pipe is introduced into the target PC-PRB model, based on the SOR iterative solution method, the water flow calculation is performed according to the coefficient matrix formula; the water flow calculation includes constructing the finite element equation of the water inlet node of the water diversion pipe under the condition of stable flow and the groundwater head at the starting point of the water diversion pipe and the center point of the water distribution layer under the condition of unsteady flow; based on the water flow calculation, considering the single point injection scenario and the planar injection scenario, the parameters of the coefficient matrix formula are adjusted to realize the finite element analysis of the automatic water diversion of the water diversion pipe in the PC-PRB. The present invention can realize the automatic water diversion function of the pipeline.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical simulation, and in particular to a finite element analysis method for realizing automatic water conduction of a water conduit in a PC-PRB. Background Art

[0002] In recent years, numerical simulation methods have gradually become an indispensable and important method in the field of groundwater research because they can effectively, flexibly and at low cost analyze the laws of groundwater flow and solute transport. Using numerical simulation methods, the changes in the temporal and spatial distribution of groundwater flow fields and contamination plumes before and after the installation of permeable reactive barriers (PRBs) can be evaluated on a long time scale, and the effects of different input parameters on the remediation effect of PRBs can be analyzed, thereby providing an effective reference for the design, life assessment and optimization of PRBs. Visual MODFLOW has become the most commonly used simulation software to guide the application design of PRBs because of its simple solution method, wide range of adaptability, good visualization ability and strong compatibility.

[0003] However, Visual MODFLOW also has some limitations, as follows:

[0004] (1) The automatic water diversion (water quantity and water quality) function of the pipeline cannot be realized;

[0005] (2) The phenomenon that the permeability and reaction activity of PRB active fillers decrease with operating time is not taken into account. Summary of the invention

[0006] In order to overcome the deficiencies of the prior art, the object of the present invention is to provide a finite element analysis method for realizing automatic water conduction of water conduits in PC-PRB.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A finite element analysis method for realizing automatic water diversion of a water diversion pipe in a PC-PRB, comprising:

[0009] Determine the water diversion flow rate of the diversion pipe based on the length, permeability, water flow cross-sectional area of ​​the diversion pipe, and the groundwater head at the starting point of the diversion pipe and the center point of the water distribution layer;

[0010] Constructing a finite element equation system based on solving the seepage problem, and determining a coefficient matrix formula according to the finite element equation system;

[0011] After the flow guide pipe is introduced into the target PC-PRB model, water flow calculation is performed according to the coefficient matrix formula based on the SOR iterative solution method; the water flow calculation includes constructing a finite element equation of the water inlet node of the flow guide pipe under steady flow conditions and the groundwater head at the starting point of the flow guide pipe and the center point of the water distribution layer under unsteady flow conditions;

[0012] Based on the water flow calculation, considering the single point injection scenario and the surface injection scenario, the parameters of the coefficient matrix formula are adjusted to realize the finite element analysis of the automatic water diversion of the water conduit in the PC-PRB.

[0013] Preferably, the formula for the water diversion flow rate of the guide pipe is:

[0014]

[0015] Among them, Q p is the water diversion flow rate, K p is the permeability coefficient of the flow guide tube; A p H is the water flow cross-sectional area of ​​the guide pipe; b , H e are the starting point b of the diversion pipe and the center point e(x e ,y e ) at groundwater head, x e is the horizontal coordinate of the center point e of the water distribution layer, y e is the ordinate of the center point e of the water distribution layer; L p is the length of the guide pipe, which is the distance from the starting point b of the guide pipe to the center point e of the water distribution layer; P is the head difference coefficient, P = K p A p / L p .

[0016] Preferably, the coordinates of the center point e of the water distribution layer and the formula for the groundwater head at the center point e of the water distribution layer are:

[0017]

[0018] Among them, p1, p2, and p3 are the three nodes of the β unit, A is the area of ​​the water distribution layer, and N b is the number of water distribution layer units, x p1 , x p2 , x p3 are the x-axis coordinates of each corresponding node, p1 ,y p2 ,y p3 are the y-axis coordinates of the corresponding nodes, H p1 , H p2 , H p3 is the water head at each corresponding node.

[0019] Preferably, the formula of the finite element equation group is:

[0020]

[0021] The above formula can be written in simple form:

[0022] [a]{H}={b}

[0023] Where [a] is the coefficient matrix, H is the node head to be determined, b is the source and sink term, m is the number of nodes with unknown concentration, and N is t is the number of time steps after discretizing the time domain.

[0024] Preferably, after the flow guide tube is introduced into the target PC-PRB model, water flow calculation is performed according to the coefficient matrix formula based on the SOR iterative solution method, including:

[0025] Under steady flow conditions, when the pumping well is located at the starting point b of the diversion pipe, the pumping flow rate is equal to the diversion flow rate Q of the diversion pipe. p When the finite element equation of the water inlet node of the guide pipe under the stable flow condition is established, the formula of the finite element equation of the water inlet node of the guide pipe is: Among them, b b is the source and sink term corresponding to the finite element equation established with the starting point b of the flow guide pipe as the node;

[0026] H b and H e The coefficients are placed in the coefficient matrix and compared with H b , H e The original coefficients are combined to obtain the updated coefficients; the formula for the updated coefficients is: in, Indicates that the value on the right side of the equal sign is assigned to the left side, a b,b and a e,b are respectively the required water head H b , H e The corresponding coefficient;

[0027] Under the condition of unsteady flow, recalculate the starting point b of the diversion pipe and the center point e(x e ,y e ) is calculated by Among them, H b k+1 , H b k , H e k+1 , H e k are the water heads at points b and e at the end of time steps k+1 and k, respectively, and the update coefficient is obtained; the formula for the update coefficient is:

[0028] Preferably, based on the water flow calculation, considering the single point injection scenario and the planar injection scenario, the parameters of the coefficient matrix formula are adjusted to realize the finite element analysis of the automatic water diversion of the water conduit in the PC-PRB, including:

[0029] The differential equations of the water movement problem and the pollutant migration problem are constructed; the formula of the differential equation of the water movement problem is: The differential equation for the pollutant migration problem is formulated as: Among them, H is the required water head; E is the water storage coefficient; K x , K y are the first permeability coefficient component and the second permeability coefficient component respectively; b is the thickness of the aquifer; t is the time variable; C(x, y, t) is the concentration of the pollutant to be determined; R d is the retention factor; n is the effective porosity; D x , D y are the first hydrodynamic diffusion coefficient component and the second hydrodynamic diffusion coefficient component respectively; u x 、u y are the first groundwater velocity component and the second groundwater velocity component respectively; C b is the pollutant concentration in the injected water Q; k is the first-order reaction rate constant; A is the injection area; δ(x-x b ,y-y b ) is the pulse function; δ A is an impulse function. When (x, y)∈A, δ A =1; when When A =0;

[0030] In the single-point injection scenario, a finite element equation of the injection point is established according to the newly added terms of the differential equation of the water movement problem and the differential equation of the pollutant migration problem, and a coefficient matrix is ​​adjusted according to the finite element equation of the injection point;

[0031] In the planar injection scenario, finite element equations of the water injection point are established according to the newly added terms of the differential equations of the water movement problem and the differential equations of the pollutant migration problem, and the coefficient matrix is ​​adjusted according to the finite element equations of the water injection point.

[0032] Preferably, in the single-point injection scenario, the finite element equation of the water injection point is established according to the newly added terms of the differential equation of the water movement problem and the differential equation of the pollutant migration problem, and the coefficient matrix is ​​adjusted according to the finite element equation of the water injection point, including:

[0033] According to the newly added terms of the differential equation of water movement problem, the finite element equation of injection point j = e is established; when the finite element equation of injection point j = e, the source and sink terms WI It is expressed as:

[0034] Among them, δ(x-x e ,y-y e ) is the pulse function, b is the source and sink term, N i and N e are the basis functions defined for the i and e nodes respectively;

[0035] Assuming that e is a node of the β unit, we get the formula

[0036] According to the formula get And according to W i,e Determination coefficient matrix;

[0037] According to the newly added terms of the differential equation of the pollutant migration problem, a finite element equation of j=e is established, and a stable migration formula and an unstable migration formula are constructed; the stable migration formula is W b,e =-Q; the unstable migration formula is

[0038] The coefficient matrix is ​​adjusted according to the established finite element equation of j=e, the stable migration formula and the unstable migration formula.

[0039] Preferably, in the planar injection scenario, the finite element equation of the water injection point is established according to the newly added terms of the differential equation of the water movement problem and the differential equation of the pollutant migration problem, and the coefficient matrix is ​​adjusted according to the finite element equation of the water injection point, including:

[0040] According to the new terms in the differential equation of water motion problem, W is established. i,j The calculation formula of W i,j The calculation formula is And according to W i,j Determination coefficient matrix;

[0041] According to the new terms of the differential equation of the pollutant migration problem, a stable migration is established. b,j The calculation formula of and the a of unstable migration b,j The calculation formula of stable migration a b,j The calculation formula is: Unstable migration b,j The calculation formula is

[0042] According to the stable migration b,j The calculation formula of and the a of unstable migration b,j The calculation formula adjusts the coefficient matrix.

[0043] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0044] The present invention provides a finite element analysis method for realizing automatic water diversion of a water diversion pipe in a PC-PRB, including: determining the water diversion flow rate of the water diversion pipe based on the length of the water diversion pipe, the permeability coefficient, the water flow cross-sectional area, and the groundwater head at the starting point of the water diversion pipe and the center point of the water distribution layer; constructing a finite element equation group based on solving the seepage problem, and determining the coefficient matrix formula according to the finite element equation group; after the water diversion pipe is introduced into the target PC-PRB model, based on the SOR iterative solution method, water flow calculation is performed according to the coefficient matrix formula; the water flow calculation includes constructing a finite element equation of the water inlet node of the water diversion pipe under a stable flow condition and the groundwater head at the starting point of the water diversion pipe and the center point of the water distribution layer under an unsteady flow condition; based on the water flow calculation, considering the single point injection scenario and the planar injection scenario, the parameters of the coefficient matrix formula are adjusted to realize the finite element analysis of the automatic water diversion of the water diversion pipe in the PC-PRB. The present invention can realize the automatic water diversion (water quantity and water quality) function of the pipeline. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0046] Figure 1 A flow chart of a method provided by an embodiment of the present invention;

[0047] Figure 2 A schematic diagram of a finite element mesh unit β and its nodes provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0048] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0049] The object of the present invention is to provide a finite element analysis method for realizing automatic water diversion of a water conduit in a PC-PRB, which can realize the automatic water diversion (water quantity and water quality) function of the pipeline.

[0050] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0051] Figure 1 A flow chart of a method provided by an embodiment of the present invention, such as Figure 1 As shown, the present invention provides a finite element analysis method for realizing automatic water conduction of a water conduit in a PC-PRB, comprising:

[0052] Step 100: determining the water diversion flow rate of the diversion pipe based on the length, permeability, water flow cross-sectional area of ​​the diversion pipe, and the groundwater head at the starting point of the diversion pipe and the center point of the water distribution layer;

[0053] Step 200: constructing a finite element equation system based on solving the seepage problem, and determining a coefficient matrix formula according to the finite element equation system;

[0054] Step 300: After the flow guide pipe is introduced into the target PC-PRB model, water flow calculation is performed according to the coefficient matrix formula based on the SOR iterative solution method; the water flow calculation includes constructing a finite element equation of the water inlet node of the flow guide pipe under steady flow conditions and the groundwater head at the starting point of the flow guide pipe and the center point of the water distribution layer under unsteady flow conditions;

[0055] Step 400: Based on the water flow calculation, considering the single point injection scenario and the surface injection scenario, the parameters of the coefficient matrix formula are adjusted to achieve finite element analysis of automatic water diversion of the water conduit in the PC-PRB.

[0056] Specifically, this embodiment can achieve the following functions:

[0057] 1. Realize the removal or interception of pollutants by PRB.

[0058] 2. Realize the automatic water diversion function of the diversion pipe.

[0059] Optionally, PRB removes or intercepts pollutants through adsorption, precipitation, oxidation-reduction, etc. between pollutants and reaction media. To simulate the reaction process, PRB-Trans introduces the first-order reaction kinetic equation and three isothermal adsorption modes (i.e., Henry, Freundlich, and Langmuir isothermal adsorption modes); considering that the permeability coefficient and reaction activity of PRB fillers will decrease with the running time, the permeability coefficient, decay constant, and adsorption constant can all be set as functions of the time variable.

[0060] Furthermore, the function of the pressure reducing and converging system of this embodiment is realized as follows:

[0061] (1) Water movement issues

[0062] The diversion pipe is a pipe connecting the upstream pressure relief well and the downstream buffer water distribution layer. It will directly guide the groundwater and pollutants collected in the well to the downstream water distribution layer. Since the water distribution layer is usually filled with highly permeable gravel, it can be considered that the concentration of water and pollutants introduced by the pipeline is basically evenly distributed in the water distribution area. The diversion flow rate Q of the diversion pipe p (m 3 ·d -1 ) can be calculated by the following formula:

[0063]

[0064] In the formula, K p : Permeability coefficient of the flow guide tube (m·d -1 );A p :Water flow cross-sectional area of ​​the diversion pipe (m 2 );H b , H e : are the starting point b of the diversion pipe and the center point e(x e ,y e ) groundwater head at (m); L p : Length of the flow guide pipe (m), the distance from b to e; P = K p A p / L p (m 2 ·d -1 ).

[0065] The position of the center point e of the pipeline water distribution area (x e ,y e ) and water head H e It is equal to the area-weighted average of the midpoint values ​​of each unit in the water distribution area:

[0066]

[0067] In the formula, p1, p2, and p3 are the three nodes of the β unit, such as Figure 2 As shown. A is the area of ​​the water distribution layer, N b is the number of water distribution layer units, x p1 , x p2 , x p3 is the x-axis coordinate of each corresponding node, y p1 ,y p2 ,y p3 is the y-axis coordinate of each corresponding node, H p1 , H p2 , H p3 is the water head of each corresponding node. In actual calculation, the distance (x e ,y e ) The nearest node is the center point, and the water head of this node is H e.

[0068] When solving the seepage problem, the finite element equations are as follows:

[0069]

[0070] The above formula can be written in simple form as:

[0071] [a]{H}={b};

[0072] Where: [a] is the coefficient matrix, H is the node head to be determined, b is the source and sink term, m is the number of nodes with unknown concentration, N is t In order to discretize the time domain into time steps, the coefficient matrix [a] of the finite element equations is established based on adjacent nodes, that is, the number of non-zero elements of equation j will not exceed the number of nodes adjacent to node j plus 1. The coefficient matrix [a] obtained in this way is a symmetric positive definite matrix, which is easy to solve. However, after the water diversion function of the diversion pipe is introduced, the finite element equations will change, which will affect the structure of the coefficient matrix [a].

[0073] Under steady flow conditions, when the pumping well is located at the starting point b of the diversion pipe, the pumping flow rate is equal to the diversion flow rate Q of the diversion pipe. p When , the pumping and injection effect of the well is similar to the water diversion effect of the diversion pipe. Based on this, when establishing the finite element equation of j = b (diversion pipe water inlet node):

[0074]

[0075] b b H is the source and sink term corresponding to the finite element equation established with the starting point b of the guide pipe as the node. b and H e The coefficients are placed in the coefficient matrix and compared with H b , H e The original coefficients are combined to obtain:

[0076]

[0077] In the formula, It means to assign the value on the right side of the equal sign to the left side. Taking the above formula as an example, the original coefficient a b,b After adding P, continue to use a b,b express.

[0078] At this time, the coefficient of the equation j = b is increased by node e, and the right-hand side term remains unchanged. It can be seen that after using the algorithm of pipe water diversion, since node b is not adjacent to the central node e of the water distribution area, the finite element equation of j = b adds a non-zero element of node e, which destroys the symmetric positive definiteness of the coefficient matrix of the water flow problem, and thus brings complexity to the calculation. However, the SOR iterative solution method adopted by PRB-Trans does not require the coefficient matrix [a] to be symmetric and positive definite.

[0079] Under unsteady flow conditions, Among them, H b k+1 , H b k , H e k+1 , H e k are the water heads at points b and e at the end of time steps k+1 and k respectively. We can get:

[0080]

[0081] (2) Pollutant migration issues

[0082] For the pollutant migration problem, the pipeline water flow rate Q is calculated through water flow calculation. p At this point, the effect of the flow pipe injecting into the water distribution layer is similar to the water injection effect of the well; assuming that there are N b Units, N nd nodes, whose area is:

[0083]

[0084] The concentration of pollutants in the pumped water is equal to the concentration C at the pumping node. b , is unknown. The mass of pollutants contained in the injected water is also unknown and is equal to QC b , so both the pumping effect and the injection effect should be considered.

[0085] In the case of water wells, the differential equation of water movement problem is expressed as:

[0086]

[0087] Where, H: required water head (m); E: water storage coefficient; K x , K y : Permeability component (m·d -1 ); b: aquifer thickness (m); t: time variable (d); C(x,y,t): concentration of the pollutant to be determined (mg·L -1 );R d : retention factor; n: effective porosity; D x, D y : Hydrodynamic dispersion coefficient component (m 2 ·d -1 );u x 、u y : Groundwater velocity component (m·d -1 );C b : Pollutant concentration in injected water Q (mg·L -1 ); k: first-order reaction rate constant (d -1 );A:Injection area (m); δ(x-x b ,y-y b ) is the pulse function (δ = 1 at point b, δ = 0 at other positions); δ A is an impulse function. When (x, y)∈A, δ A =1; when When A =0.

[0088] The differential equation for the pollutant migration problem can be expressed as:

[0089]

[0090] Compared with the differential equations without considering PC-PRB, one more term is added to the differential equations for water movement and pollutant migration, where: I =Qδ A / A,W I C I =QC b δ A / A, where C b is the pollutant concentration at node b, which is also unknown.

[0091] ① Single point injection scenario: Implementing W I Function of item

[0092] At this time W I =Qδ(xx e ,yy e ). When establishing the finite element equation of the injection point j = e, the source and sink term W I It is expressed as:

[0093]

[0094] Among them, δ(x-x e ,y-y e ) is the pulse function (δ = 1 at point e, δ = 0 at other positions), b is the source and sink term, N i and N e are the basis functions defined for the i and e nodes respectively.

[0095] Assuming e is a node of β unit, we have:

[0096]

[0097] It can be seen that:

[0098]

[0099] It can be seen that Q only affects the principal elements of the j=e equation, and the coefficient matrix [a] remains unchanged.

[0100] ② Single point injection scenario: achieving W I C I Function of item

[0101] When single-point injection is used, the amount of pollutant injected at node e is QC b Therefore, the unknown quantity C needs to be considered when establishing the finite element equation of j = e. b .

[0102] For stable migration:

[0103] W b,e = -Q;

[0104] The right-hand side remains unchanged.

[0105] For unstable migration:

[0106]

[0107] It can be seen that the addition of non-zero elements at node b in the finite element equation of j=e changes the coefficient matrix [a].

[0108] ③ Planar injection scenario: achieving W I Function of item

[0109] At this time W I =Qδ A / A, it is necessary to evenly distribute the pumping flow Q to each unit in the injection area. Similar to the case of non-point source, W i,j The calculation formula is:

[0110]

[0111] For this algorithm, the coefficient matrix [a] remains unchanged.

[0112] ④ Planar injection scenario: achieving W I C I Function of item

[0113] For stable migration, the mass of pollutants obtained by unit β per unit time is I = QC bΔβ / A is equally divided among the three nodes of the β unit, and we have:

[0114]

[0115] For unstable migration, Divide equally among 3 nodes and you get:

[0116]

[0117] At this time, the finite element equation of each node in the water distribution area has an additional element, namely, the b element, and the coefficient matrix [a] has changed.

[0118] The beneficial effects of the present invention are as follows:

[0119] (1) The present invention proposes a dynamic association algorithm for non-adjacent nodes, and realizes the automatic water diversion function of the flow guide pipe in the PC-PRB by adjusting the coefficient matrix of the finite element equation group;

[0120] (2) In view of the differences in the removal mechanisms of different pollutants in leachate by PRB active fillers, nonlinear isothermal model and first-order chemical reaction equation were introduced;

[0121] (3) Considering that the permeability and reaction activity of PRB active fillers will decrease with the operating time, parameters such as permeability coefficient, decay constant and adsorption constant can be set as functions of time variables.

[0122] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0123] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A finite element analysis method for realizing automatic water conduction of water pipes in PC-PRB, characterized in that: include: Determine the water diversion flow rate of the diversion pipe based on the length, permeability, water flow cross-sectional area of ​​the diversion pipe, and the groundwater head at the starting point of the diversion pipe and the center point of the water distribution layer; Constructing a finite element equation system based on solving the seepage problem, and determining a coefficient matrix formula according to the finite element equation system; After the flow guide pipe is introduced into the target PC-PRB model, water flow calculation is performed according to the coefficient matrix formula based on the SOR iterative solution method; the water flow calculation includes constructing a finite element equation of the water inlet node of the flow guide pipe under steady flow conditions and the groundwater head at the starting point of the flow guide pipe and the center point of the water distribution layer under unsteady flow conditions; Based on the water flow calculation, considering the single point injection scenario and the surface injection scenario, the parameters of the coefficient matrix formula are adjusted to realize the finite element analysis of the automatic water diversion of the water conduit in the PC-PRB; Based on the water flow calculation, considering the single point injection scenario and the surface injection scenario, the parameters of the coefficient matrix formula are adjusted to realize the finite element analysis of the automatic water diversion of the water conduit in the PC-PRB, including: The differential equations of the water movement problem and the pollutant migration problem are constructed; the formula of the differential equation of the water movement problem is: ; The formula of the differential equation for the pollutant migration problem is: ;in, H To seek water head; E is the water storage coefficient; K x , K y are the first permeability coefficient component and the second permeability coefficient component respectively; b is the thickness of the aquifer; t is the time variable; C is the concentration of the pollutant to be determined; R d is the retention factor; n is the effective porosity; D x , D y are the first hydrodynamic diffusion coefficient component and the second hydrodynamic diffusion coefficient component respectively; u x , u y are the first groundwater velocity component and the second groundwater velocity component respectively; C b For water injection Q Concentration of pollutants contained; k is the first-order reaction rate constant; A is the injection area; ( x-x b , y-y b ) is the impulse function; is a pulse function, when ( x , y ) A hour, =1; when ( x , y ) A hour, =0; In the single-point injection scenario, a finite element equation of the injection point is established according to the newly added terms of the differential equation of the water movement problem and the differential equation of the pollutant migration problem, and a coefficient matrix is ​​adjusted according to the finite element equation of the injection point; In the planar injection scenario, finite element equations of the water injection point are established according to the newly added terms of the differential equations of the water movement problem and the differential equations of the pollutant migration problem, and the coefficient matrix is ​​adjusted according to the finite element equations of the water injection point.

2. The finite element analysis method for realizing automatic water conduction of water conduits in PC-PRB according to claim 1, characterized in that: The formula for the water diversion flow rate of the guide pipe is: ； in, Q p is the water diversion flow rate, K p is the permeability coefficient of the flow tube; A p is the water flow cross-sectional area of ​​the diversion pipe; H b , H e The starting points of the flow guide tubes b The center point of the water layer e ( x e , y e ), x e The center point of the water distribution layer e The horizontal axis of y e The center point of the water distribution layer e The vertical coordinate of L p is the length of the flow guide pipe, and the length of the flow guide pipe is the starting point of the flow guide pipe. b To the center of the water layer e distance; P is the head difference coefficient, P = K p A p / L p .

3. The finite element analysis method for realizing automatic water conduction of water conduits in PC-PRB according to claim 2, characterized in that: The center point of the water distribution layer e Coordinates and center point of water distribution layer e The formula for the groundwater head at is: ； in, p 1. p 2. p 3 for The three nodes of the unit, A is the water distribution layer area, N b is the number of water distribution layer units, x p1 , x p2 , x p3 are the corresponding nodes respectively. x Axis coordinates, y p1 , y p2 , y p3 are the corresponding nodes respectively. y Axis coordinates, H p1 , H p2 , H p3 is the water head at each corresponding node.

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