One-dimensional double-penetration model construction method considering soil macroporous membrane flow characteristics

Abstract

The invention relates to a one-dimensional double-penetration model construction method considering soil macropore membrane flow characteristics, and belongs to the technical field of hydrological modeling and soil science, and the method comprises the following steps: S1, constructing a control equation of an actual infiltration rate and a macropore channel opening degree; s2, constructing a flux control equation of the soil matrix under the condition of considering the water content of the soil; and S3, under the condition of considering the soil water content, constructing a control equation of the macropore channel flux. According to the model, soil macropore membrane flow characteristics are considered, the conditions of whether macropores are opened and the opening degree are quantified, and the functions of transferring moisture and supplying surrounding matrixes of a soil macropore channel are divided.

Description

Technical Field

[0001] The invention belongs to the technical field of hydrological modeling and soil science, and in particular relates to a one-dimensional dual permeability model construction method considering soil macropore membrane flow characteristics. Background Art

[0002] In nature, macropores are widely present in soil due to biological activities (such as roots, earthworms, insects) or physical processes (such as dry-wet cycles, freeze-thaw effects). Although they only account for 1% to 3% of the total porosity of the soil, their channel structure can quickly transfer surface materials (such as water, pollutants, etc.) to deep soil or groundwater layers, profoundly affecting regional water balance, pollution control and prevention, etc.

[0003] As the functions and effects of macropores have gradually attracted attention, a series of one-dimensional dual-permeability infiltration models have been developed. Dual-permeability models are a general term for a type of model in which both the soil matrix and macropores have water transport functions. The soil matrix transfers water slowly, while the macropores transfer water quickly. There is water exchange between the macropores and the matrix. Commonly used models include HYDRUS-1D, MACRO, and RZWQM.

[0004] The above models use the Richard equation, the motion wave equation or the Poiseuille equation as the control equation for macropore flow simulation, which can only approximately simulate the soil flux process and cannot describe the characteristics of macropore membrane flow movement. Therefore, the existing one-dimensional dual permeability model cannot simultaneously meet the needs of scholars for accurate flux simulation and accurate description of physical processes. Summary of the invention

[0005] The one-dimensional dual permeability model construction method considering the soil macropore membrane flow characteristics of the present invention solves the problem of lack of physical mechanism in describing the macropore flow physical process in the existing model technology.

[0006] In order to solve the above technical problems, the present invention adopts the following solutions:

[0007] The one-dimensional dual permeability model construction method considering the soil macropore membrane flow characteristics includes the following steps:

[0008] S1: Construct the governing equation between the actual infiltration rate and the opening degree of the macropore channels;

[0009] S2: Considering the soil water content, the flux control equation of the soil matrix is ​​constructed;

[0010] S3: Construct the governing equations for macroporous channel flux considering soil moisture content.

[0011] Furthermore, step S1 includes the following steps:

[0012] S1.1: Analyze soil matrix and macropore channel infiltration rates;

[0013] The infiltration rate of the soil matrix is ​​described by Darcy's formula, which is:

[0014]

[0015] Where H is the surface recharge head; h is the soil negative pressure head; K(θ) is the unsaturated hydraulic conductivity; d is the seepage propagation distance; I m is the infiltration rate of the soil matrix;

[0016] I s It is determined by the water transfer capacity of the macropore channels themselves and is not affected by the soil moisture content and its changes. The formula is:

[0017]

[0018] Where M is the macropore surface area; L u is the thickness of the film flow; g is the acceleration of gravity; v is the kinematic viscosity of water; I s is the infiltration rate of the macroporous channel;

[0019] S1.2: Analyze the actual infiltration rate and the degree of opening of macropore channels;

[0020] When the surface recharge rate R≤I m , all water is transferred downward through the soil matrix, and macropore channels play no role;

[0021] When I m <R≤I s +I m When the remaining water that satisfies the soil matrix infiltration rate is fully transferred downward through the macroporous channels;

[0022] When R>I s +I m When the macropore channels are fully open, the excess water will flow out in the form of surface runoff and will not infiltrate downward; it can be expressed as:

[0023]

[0024] Where f0 is the opening degree of the macropore channel; I represents the actual infiltration rate.

[0025] Furthermore, step S2 includes the following steps:

[0026] S2.1: The one-dimensional Richard equation is used to describe the water flow in the soil matrix. The recharge effect of the macroporous channel on the soil matrix is ​​written into the control equation in the form of source and sink terms. The flux control equation of the soil matrix is:

[0027]

[0028] In the formula, θ is the soil moisture content, D(θ) is the diffusion coefficient, z is the depth, and θ S is the saturated water content; it does not consider the ability of macropores to store water, but only expresses the function of macropores to quickly transfer water and replenish the matrix;

[0029] S2.2: Construct the flux control equation for the matrix region considering the soil moisture content;

[0030] When the soil matrix reaches saturated water content θ S When the gradient difference disappears, the macroporous channel only plays the role of quickly transferring water, and the source and sink terms in the soil matrix area water control equation disappear; at this time, the flux control equation of the soil matrix is:

[0031]

[0032] Further, step S3 includes the following steps:

[0033] S3.1: Governing equations for water flux through macroporous channels recharging the soil matrix, taking into account soil water content;

[0034] The finite volume method is used to divide the one-dimensional soil profile into multiple equidistant soil bodies along the depth direction, with a distance of ST. Each soil body is denoted as a unit. Each unit is numbered from top to bottom. The current unit is denoted as i; the previous unit is i-1; the next unit is i+1; the water flux from the previous unit i-1 into the current unit i is denoted as The water flux discharged from unit i to the next unit i+1 is The water flux of the macroporous recharge matrix is

[0035] Calculated using Darcy's formula and Calculated using the first-order diffusion formula The specific formula is as follows:

[0036]

[0037] Among them, θ i-1 ,θ i ,θ i+1 are the water contents of units i-1, i, and i+1, respectively;

[0038] h i-1 、h i 、h i+1 is the negative pressure head of units i-1, i, i+1;

[0039] fi is the activation ratio of macropores when entering unit i;

[0040] The water content θ of the soil unit determines whether macropore lateral recharge exists, so The specific expression is as follows:

[0041]

[0042] S3.2: Governing equations for macroporous channel fluxes considering soil water content;

[0043] The flux at the bottom of cell i depends on the macropore flux entering from cell i-1 and the matrix absorption of cell i. Therefore, the macropore channel flux q at the bottom of cell i is S i The formula is:

[0044]

[0045] Furthermore, g = 9.8 m / s 2 ; v = 1.0 × 10 -6 m 2 / s.

[0046] Beneficial effects:

[0047] 1. The present invention is a one-dimensional dual permeability model construction method that takes into account the characteristics of soil macropore membrane flow, while meeting the needs of scholars for accurate flux simulation and accurate description of physical processes, and has a strong physical foundation.

[0048] 2. In the one-dimensional dual permeability model of the present invention, the conditions for whether the macropores are open and the degree of opening are accurately quantified, which can be applied to the simulation of infiltration processes with different surface recharge intensities.

[0049] 3. In the present invention, based on the water content of the soil matrix, the functions of the soil macropore channels in transferring water and replenishing the surrounding matrix are further divided.

[0050] 4. The present invention uses the finite volume method to provide discrete flux formulas for unit soil matrix flux transfer and macropore flux transfer, which is beneficial to the code implementation of the one-dimensional dual permeability model. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 The algorithm flow chart of the one-dimensional double permeability model considering the macroporous membrane flow characteristics of the present invention;

[0052] Figure 2 The infiltration and outflow simulation results and the soil profile moisture change process diagram when the water head is -6cm; Figure 2 (a) is the simulation result of infiltration and outflow when the water head is -6 cm; Figure 2(b) is the diagram of soil profile moisture change process when the water head is -6cm;

[0053] Figure 3 The infiltration and outflow simulation results and the soil profile moisture change process diagram when the water head is -1cm; Figure 3 (a) is the simulation result of infiltration and outflow when the water head is -1 cm; Figure 3 (b) is a diagram showing the change process of soil profile moisture when the water head is -1 cm. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are 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.

[0055] See Figure 1 , a one-dimensional dual permeability model construction method considering the soil macroporous membrane flow characteristics, including the following steps:

[0056] S1: Construct the governing equation between the actual infiltration rate and the opening degree of the macropore channels;

[0057] The specific steps include:

[0058] S1.1: Analyze soil matrix and macropore channel infiltration rates;

[0059] On the soil surface, water infiltrates downward in two ways, namely, soil matrix infiltration and macropore channel infiltration, using I m represents the infiltration rate of the soil matrix, I s Represents the infiltration rate of macroporous channels.

[0060] The expression formula is as follows:

[0061]

[0062] Where H is the surface recharge head; h is the soil negative pressure head; K(θ) is the unsaturated hydraulic conductivity; d is the seepage propagation distance; I m It is described by Darcy's formula;

[0063] I s It is determined by the water transfer capacity of the macropore channels themselves and is not affected by the soil moisture content and its changes;

[0064] M is the macropore surface area; L u is the thickness of the film flow;

[0065] g is the acceleration due to gravity, g = 9.8 m / s 2 ;

[0066] v is the kinematic viscosity of water, v = 1.0 × 10 -6 m 2 / s, this value is the kinematic viscosity of water at 20°C, refer to page 4 of the book "Hydraulics (Second Edition)".

[0067] S1.2: Analyze the actual infiltration rate and the degree of opening of macropore channels;

[0068] Under different surface recharge conditions, whether the macropore infiltration channels are open and the degree of opening will be affected.

[0069] When the surface recharge rate R≤I m , all water is transferred downward through the soil matrix, and macropore channels play no role;

[0070] When I m <R≤I s +I m When the remaining water that satisfies the soil matrix infiltration rate is fully transferred downward through the macroporous channels;

[0071] When R>I s +I m When the macropore channels are fully open, excess water will flow out as surface runoff and will not infiltrate downward.

[0072] Therefore, the actual infiltration rate I and the degree of macropore channel opening f0 (range 0-1) are expressed as follows:

[0073]

[0074] S2: Considering the soil water content, the flux control equation of the soil matrix is ​​constructed;

[0075] The specific steps include:

[0076] S2.1: Construct the flux governing equations for the soil matrix;

[0077] During the process of soil water infiltration, the forces acting on the water movement in the soil matrix and macroporous channels are different. The soil matrix is ​​affected by capillary force and gravity, while the film flow in the macroporous channel is affected by gravity and pipe wall friction, moving downward in the form of laminar water film and replenishing the soil matrix around the pipe wall.

[0078] As the water film moves downward and is absorbed, the activation degree (f(z)) gradually decreases with depth. Here, the one-dimensional Richard equation is used to describe the water flow movement in the soil matrix. The recharge effect of the macroporous channel on the soil matrix is ​​written into the control equation in the form of source and sink terms. Then the flux control equation of the soil matrix is ​​as follows:

[0079]

[0080] Where θ is the soil moisture content, D(θ) is the diffusion coefficient, z is the depth (upward is the positive direction), θ S is the saturated water content. The second term on the right side of the control equation (i.e., the source-sink term) is the water supplied to the soil matrix by the macropore channel. It should be noted that the one-dimensional double permeability model does not consider the ability of macropores to store water, but only expresses the function of macropores to quickly transfer water and replenish the matrix.

[0081] S2.2: Construct the flux control equation for the matrix region considering the soil moisture content;

[0082] During the movement of macroporous membrane flow, membrane flow has two main functional effects: one is to quickly transfer water to the deep soil, and the other is to replenish the soil matrix around the macroporous wall. The basic principle of the latter is the lateral diffusion of water, that is, there is a water potential gradient difference between the saturated water at the tube wall and the surrounding unsaturated soil matrix. Macroporous flow will play two functions only when and only when the gradient difference exists; when the soil matrix reaches the saturated water content θ S When , the gradient difference disappears, the macroporous channel only plays the role of quickly transferring water to the deep soil, and the source and sink terms in the water control equation of the soil matrix area disappear. The specific expression is:

[0083]

[0084] S3: Construct the governing equation of macroporous channel flux considering soil moisture content;

[0085] The finite volume method refers to a method for numerically solving partial differential equations. The core idea is to divide the solution domain into multiple finite control volumes (grid cells), and then calculate the change of flux in each cell through the conservation equation in integral form.

[0086] Here, the one-dimensional soil profile is divided into multiple equidistant soil bodies along the depth direction, the distance is denoted as ST, and each soil body is denoted as a unit; each unit is numbered from top to bottom; for each soil body, its flux change includes soil matrix flux transfer and macropore channel flux transfer.

[0087] The specific steps include:

[0088] S3.1: Governing equations for water flux through macroporous channels recharging the soil matrix, taking into account soil water content;

[0089] The current unit is recorded as i; the previous unit is recorded as i-1; the next unit is recorded as i+1; the water flux from the previous unit i-1 to the current unit i is recorded as The water flux discharged from unit i to the next unit i+1 is The water flux of the macroporous recharge matrix is

[0090] Calculated using Darcy's formula and Calculate q using the first-order diffusion formula abs i , the specific formula is as follows:

[0091]

[0092] Among them, θ i-1 ,θ i ,θ i+1 are the water contents of units i-1, i, and i+1, respectively;

[0093] h i-1 、h i 、h i+1 is the negative pressure head of units i-1, i, i+1;

[0094] f i is the activation ratio of the macropores when entering unit i.

[0095] In calculation and When , the average hydraulic conductivity of adjacent cells is used to calculate the vertical flux.

[0096] As described in S2.2, the water content θ of the soil element determines whether macropore lateral recharge exists, so q abs i The specific expression is as follows:

[0097]

[0098] S3.2: Governing equations for macroporous channel fluxes considering soil water content;

[0099] The flux at the bottom of unit i depends on the macropore flux entering from unit i-1 and the matrix absorption of unit i. According to the macropore flux recharge condition in S2.2, the macropore channel flux q at the bottom of unit i can be written as S i , the formula is:

[0100]

[0101] Using C language, the algorithms of step S1, step S2 and step S3 are constructed into a one-dimensional double penetration model code and packaged into an .exe file for easy reference by the SCE-UA calibration algorithm.

[0102] Test verification:

[0103] See Figure 2 and Figure 3 In the invention, the infiltration and outflow processes of the tension infiltration experiment with negative pressure head of -6 cm and -1 cm are simulated respectively. The SCE-UA is used to calibrate the optimization model parameters, and the objective function is the average NSE coefficient (NSE) of the predicted items of the infiltration process and outflow process and the measured data. Average ), the specific calculation method is:

[0104] NSE Average =(NSE Infiltration +NSE Outflow )

[0105]

[0106] In the formula, X0 is the observed value, X m is the analog value, is the average value of measured data.

[0107] Specifically, during the simulation, the 25 cm soil profile was divided into five soil layers for moisture flux calculation, and the inflow, outflow and profile moisture change processes were recorded and compared with the measured process.

[0108] Using SCE_UA, the parameter calibration results based on the objective function are shown in Table 1.

[0109] Table 1 Parameter calibration results

[0110]

[0111] In the table, K s is the hydraulic conductivity of the saturated area, α and β are the parameters of the soil moisture characteristic curve; θ r is the wilting water content; θ S is the saturated water content of the soil.

[0112] When the water head is -6 cm, the macroporous channels are not activated and do not play the role of transferring water and replenishing the surrounding soil matrix. The simulation results are as follows: Figure 2 The NSE value of the cumulative infiltration process is 0.998, the NSE value of the cumulative outflow is 0.999, and the average NSE value reaches 0.9985.

[0113] When the water head is -1 cm, the macroporous channels are fully activated, playing the role of transferring water and replenishing the surrounding soil matrix. The simulation results are as follows: Figure 3 As shown in the figure, the NSE value of the cumulative infiltration process is 0.984, the NSE value of the cumulative outflow is 0.985, and the average NSE value reaches 0.9845, which proves that the model is highly reliable.

[0114] Based on the above ideal embodiments of the present invention, the relevant staff can make various changes and modifications without departing from the technical concept of the present invention through the above description. The technical scope of the present invention is not limited to the contents of the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A one-dimensional dual permeability model construction method considering the soil macroporous membrane flow characteristics, characterized in that: The following steps are involved: S1: Construct the governing equation between the actual infiltration rate and the opening degree of the macropore channels; S2: Considering the soil water content, the flux control equation of the soil matrix is ​​constructed; S3: Construct the governing equations for macroporous channel flux considering soil moisture content.

2. The one-dimensional dual permeability model construction method considering soil macroporous membrane flow characteristics according to claim 1 is characterized in that: Step S1 includes the following steps: S1.1: Analyze soil matrix and macropore channel infiltration rates; The infiltration rate of the soil matrix is ​​described by Darcy's formula, which is: Where H is the surface recharge head; h is the soil negative pressure head; K(θ) is the unsaturated hydraulic conductivity; d is the seepage propagation distance; I m is the infiltration rate of the soil matrix; I s It is determined by the water transfer capacity of the macropore channels themselves and is not affected by the soil moisture content and its changes. The formula is: Where M is the macropore surface area; L u is the thickness of the film flow; g is the acceleration of gravity; υ is the kinematic viscosity of water; I s is the infiltration rate of the macroporous channel; S1.2: Analyze the actual infiltration rate and the degree of opening of macropore channels; When the surface recharge rate R≤I m , all water is transferred downward through the soil matrix, and macropore channels play no role; When I m <R≤I s +I m When the remaining water that satisfies the soil matrix infiltration rate is fully transferred downward through the macroporous channels; When R>I s +I m When the macropore channels are fully open, the excess water will flow out in the form of surface runoff and will not infiltrate downward; it can be expressed as: Where f0 is the opening degree of the macropore channel; I represents the actual infiltration rate.

3. The one-dimensional dual permeability model construction method considering soil macropore membrane flow characteristics according to claim 2 is characterized in that: Step S2 includes the following steps: S2.1: The one-dimensional Richard equation is used to describe the water flow in the soil matrix. The recharge effect of the macroporous channel on the soil matrix is ​​written into the control equation in the form of source and sink terms. The flux control equation of the soil matrix is: In the formula, θ is the soil moisture content, D(θ) is the diffusion coefficient, z is the depth, and θ S is the saturated water content; it does not consider the ability of macropores to store water, but only expresses the function of macropores to quickly transfer water and replenish the matrix; S2.2: Construct the flux control equation for the matrix region considering the soil moisture content; When the soil matrix reaches saturated water content θ S When the gradient difference disappears, the macroporous channel only plays the role of quickly transferring water, and the source and sink terms in the soil matrix area water control equation disappear; at this time, the flux control equation of the soil matrix is:

4. The one-dimensional dual permeability model construction method considering soil macroporous membrane flow characteristics according to claim 3 is characterized in that: Step S3 includes the following steps: S3.1: Governing equations for water flux through macroporous channels recharging the soil matrix, taking into account soil water content; The finite volume method is used to divide the one-dimensional soil profile into multiple equidistant soil bodies along the depth direction, with a distance of ST. Each soil body is denoted as a unit. Each unit is numbered from top to bottom. The current unit is denoted as i; the previous unit is i-1; the next unit is i+1; the water flux from the previous unit i-1 into the current unit i is denoted as The water flux discharged from unit i to the next unit i+1 is The water flux of the macropore recharge matrix is ​​q abs i ; Calculated using Darcy's formula and Calculate q using the first-order diffusion formula abs i , the specific formula is as follows: Among them, θ i-1 ,θ i ,θ i+1 are the water contents of units i-1, i, and i+1, respectively; h i-1 、h i 、h i+1 is the negative pressure head of units i-1, i, i+1; f i is the activation ratio of macropores when entering unit i; The water content of the soil unit θ determines whether there is lateral recharge of macropores, so q abs i The specific expression is as follows: S3.2: Governing equations for macroporous channel fluxes considering soil water content; The flux at the bottom of cell i depends on the macropore flux entering from cell i-1 and the matrix absorption of cell i. Therefore, the macropore channel flux q at the bottom of cell i is S i The formula is:

5. The one-dimensional dual permeability model construction method considering soil macroporous membrane flow characteristics according to claim 2 is characterized in that: g=9.8m / s 2 ;v=1.0×10 -6 m 2 / s.

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