CN114896897B - A method for calculating the breakdown time of double-layer composite liner based on GMDH neural network - Google Patents

Abstract

The invention discloses a method for calculating breakdown time of a double-layer composite liner based on a GMDH neural network, and belongs to the field of environmental geotechnical and deep learning. In the calculation stage, the breakdown time of the common working condition of the single-layer composite liner is calculated by using an analytic solution formula or a numerical simulation method, the relation between the breakdown time and the influence factors thereof is calculated by using a GMDH neural network on the basis of the calculation, a simplified formula of the breakdown time calculation is obtained, and the result is checked by using another part of data, so that a simplified and accurate calculation formula is obtained. And the double-layer composite liner is subjected to layering consideration according to the existing simplified formula, and the relation between the total breakdown time and the layering breakdown time of the double-layer composite liner is obtained, so that the result is objective and accurate, and the calculation is convenient.

Description

A method for calculating the breakdown time of double-layer composite liner based on GMDH neural network

Technical Field

The present invention mainly relates to the fields of environmental geotechnical engineering and deep learning, and in particular to a method for calculating the breakdown time of a double-layer composite liner based on a GMDH neural network.

Background Art

The liner system is an important component of the anti-pollution barrier system. It is an important barrier to prevent the diffusion of leachate and is the key to ensuring the safe service of the landfill. In modern landfills, it is usually necessary to set up a liner system at the bottom of the landfill, and the composite liner system is the most common bottom liner system currently used in landfills. The composite liner system mainly includes the following two types: one is a composite liner layer consisting of a geomembrane (GMB) and a compacted clay liner (CCL); the other is a composite liner consisting of a GMB, a geosynthetic bentonite liner (GCL) and a soil layer (AL). The most typical composite liner type specified in the relevant standards and specifications of landfills in my country is a composite liner layer consisting of a GMB and a 0.75m thick CCL. Among them, the GMB layer in the composite liner is a very effective anti-pollution barrier for non-organic pollutants (such as heavy metal ions), while the CCL layer is a good diffusion barrier for organic and inorganic pollutants in leachate. However, a large part of domestic landfills have caused significant pollution to the surrounding water or soil. This is mainly due to the high content of kitchen waste in China's landfills, large leachate production, high pollutant concentration, easy clogging of the drainage layer, and the leachate water level often reaching more than 1/3 of the landfill height. At this time, the single-layer liner system can no longer meet the anti-seepage requirements of the landfill. Therefore, the current national standard "Technical Specifications for Sanitary Landfill Treatment of Municipal Waste" GB50869 stipulates that double-layer composite liners are required for the following four situations: (1) areas with high land development density, weak environmental carrying capacity, or small environmental capacity, fragile ecological environment, etc. that require special protection; (2) landfills with a landfill capacity of more than 10 million ^m3 or a service life of more than 30 years; (3) sites with a base natural soil layer permeability coefficient greater than ^10-5 cm/s, small thickness, and high groundwater level; (4) dedicated independent storage areas of mixed landfills.

The most important evaluation condition for whether the selected liner structure can meet the use requirements is its breakdown time. At present, some scholars in my country have proposed an analytical solution for the breakdown time of a single-layer composite liner structure. However, in engineering applications, the analytical solution is relatively complex to calculate and is expressed in the form of an implicit function, which requires data inversion and is inconvenient to use. In addition, there is currently no method for calculating the breakdown time of a double-layer composite liner. It is difficult to define the anti-seepage effect of the liner structure in actual engineering applications. Therefore, it is very necessary to propose a method for calculating the breakdown time of a double-layer composite liner suitable for engineering design.

Summary of the invention

The purpose of the present invention is to provide a method for calculating the breakdown time of a double-layer composite liner based on a GMDH neural network, which is of great significance for designing double-layer composite liners in domestic landfills and evaluating their anti-fouling capabilities.

The present invention is achieved through the following technical solutions:

A method for calculating the breakdown time of a double-layer composite liner based on a GMDH neural network specifically comprises the following steps:

S1: Based on the migration of pollutants in a single-layer composite liner, a mathematical model of pollutant migration is constructed;

S2: Based on the mathematical model of contaminant transport, an analytical solution for calculating the contaminant breakdown time of a single-layer composite liner is obtained;

S3: Based on the analytical solution of the calculation of the breakdown time of pollutants in a single-layer composite liner, the GMDH neural network is used for modeling, and the analytical solution is simplified to obtain the simplified fitting formula;

S4: Use numerical simulation methods to perform stratification of the double-layer composite liner and determine the distribution coefficient of each layer;

S5: Calculate the breakdown time of the double-layer composite liner based on the distribution coefficients of each layer obtained in step S4 and the simplified fitting formula obtained in step S3.

Furthermore, the mathematical model of pollutant migration described in step 1 is:

In the formula: _Dg represents the diffusion coefficient of pollutants in geomembrane; _Cg represents the concentration of pollutants in geomembrane; _Ds represents the effective diffusion coefficient of pollutants in compacted clay liner; _Cs (z,t) represents the concentration of pollutants in compacted clay liner; _va represents the Darcy flow velocity in the composite liner; _vs represents the seepage velocity in the compacted clay liner; _Rd represents the retardation factor of the compacted clay liner; z represents the vertical migration distance of pollutants.

Furthermore, in step S2, the parameters in the pollutant migration mathematical model are determined according to the type of pollutants migrating in the composite liner, the boundary conditions of the pollutant migration mathematical model are determined according to the site conditions, and the analytical solution for calculating the pollutant breakdown time of the single-layer composite liner is solved according to the boundary conditions.

Furthermore, the step S3 comprises:

(3-1) Constructing a training data set: Based on the analytical solution of the single-layer composite liner pollutant breakdown time calculation, the single-layer composite liner breakdown time corresponding to different landfill water heads, composite liner layer thicknesses, permeability coefficients, and diffusion coefficients is calculated to obtain the breakdown time of the single-layer composite liner under common working conditions and its corresponding parameter combination;

(3-2) constructing a GMDH neural network model, using one or more of the initial concentration of leachate pollutants in a part of the training data set, the Darcy velocity of pollutant migration, the Peclet number of the geomembrane, the Peclet number of the compacted clay liner, the hydrodynamic diffusion coefficient, and the diffusion coefficient of pollutants in the geomembrane as input parameters of the GMDH neural network model, using the breakdown time or the breakdown time factor as the output, training the GMDH neural network model, and obtaining a fitting formula for input-output;

(3-3) Select the remaining training data set to verify the accuracy of the fitting formula until the fitting formula error meets the requirements and the training is terminated.

Furthermore, the step S4 comprises:

A numerical model of the double-layer composite liner used on site was established, and the numerical simulation method was used to calculate the overall breakdown time of the double-layer composite liner and the breakdown time of each layer after stratification under different water head values. The total breakdown time calculation formula is as follows:

Where: T represents the total breakdown time of the double-layer composite liner; _Ti represents the breakdown time of the i-th single-layer composite liner; _αi represents the breakdown time distribution coefficient of the i-th single-layer composite liner;

The linear regression method was used to calculate the distribution coefficient of each layer until the error was within an acceptable range.

Furthermore, the step S5 is specifically as follows: obtaining the parameters of each layer in the double-layer composite liner to be calculated as the input of the simplified fitting formula, calculating the breakdown time of each layer respectively, and taking the sum of the products of the breakdown time of each layer and the distribution coefficient of each layer as the total breakdown time of the double-layer composite liner.

Compared with the prior art, the present invention has the following beneficial effects:

The present invention simplifies the calculation of the breakdown time of a composite liner by using a neural network method, which can obtain a simplified formula that is convenient for engineering calculations while ensuring the reliability of the calculations, and can better simplify the calculations during landfill design; the present invention proposes a method for layered processing and calculating the breakdown time of a double-layer composite liner, which provides a way of thinking for defining the anti-seepage effect of the liner structure in actual engineering applications.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart of a method for calculating the breakdown time of a double-layer composite liner according to an embodiment of the present invention.

FIG. 2 is a calculation model of the case of the present invention.

DETAILED DESCRIPTION

The following will take the calculation of the breakdown time of a double-layer composite liner in a wrinkled state as an example, and combine with the accompanying drawings and tables to further illustrate and describe the present invention. The technical features of each embodiment of the present invention can be combined accordingly without conflict.

Step 1): Construct a mathematical model of contaminant migration in the composite liner:

In the formula: _Dg is the diffusion coefficient of pollutants in geomembrane; _Cg is the concentration of pollutants in geomembrane; _Ds is the effective diffusion coefficient of pollutants in compacted clay liner; _Cs (z,t) is the concentration of pollutants in compacted clay liner; _va is the Darcy flow velocity in the composite liner; _vs is the seepage velocity in the compacted clay liner; _Rd is the retardation factor of the compacted clay liner; z is the vertical distance of pollutant migration.

The boundary conditions of the single-layer composite liner are as follows:

C _s (z,0)＝0 (3)

C _g (0) = C ₀ S _gf (4)

Where: C ₀ —— initial concentration of leachate pollutants (mg/L); S _gf —— distribution coefficient between geomembrane and connected medium pore fluid; L _g —— geomembrane thickness (m); _ns —— porosity of compacted clay liner.

Step 2): Calculate the analytical solution for the single-layer composite liner contaminant breakdown time

According to the boundary conditions, the analytical solution formula for the pollutant breakdown time of a single-layer composite liner can be obtained as follows:

Where: C _b ——contaminant breakdown concentration at the bottom of the anti-fouling barrier (mg/L); C ₀ ——initial concentration of pollutants in the leachate (mg/L); _va ——Darcy velocity in the composite liner (m/s); S _gf ——partition coefficient between the pore fluid of the geomembrane and the connected medium; _PLg ——geomembrane Peclet number; _PLs ——compacted clay liner Peclet number; D ——hydrodynamic diffusion coefficient (m ² /s); D _g ——diffusion coefficient of pollutants in the geomembrane (m ² /s); L _g ——geomembrane thickness (m); L _s ——compacted clay liner thickness (m); _vs ——seepage velocity (m/s); t _b ——indicative pollutant breakdown time (year); _TR ——time factor; erfc(.)——complementary error function.

Step 3): Simplify the breakdown time formula of single-layer composite liner

According to common working conditions, 2096 sets of data are used to train the GMDH neural network. In this embodiment, during the training process, β ₁ =log ₁₀ ( _PLg ), β ₂ =log ₁₀ ( _PLs ), As input parameter, the time factor _TR is used as output. The following simplified formula is obtained:

β ₁ =log ₁₀ ( _PLg ) (16)

β ₂ =log ₁₀ ( _PLs ) (17)

Wherein: α ₁ , α ₂ , α ₃ , β ₁ , β ₂ , β ₃ — calculation coefficients of simplified formula, dimensionless; the meanings and units of other parameters are the same as those in the analytical solution formula of pollutant breakdown time of single-layer composite liner.

Table 1 is the training situation of the simplified formula of the present invention, and Table 2 is the test situation of the simplified formula of the present invention. As shown in Tables 1 and 2, according to the existing analytical solution model combined with the actual working conditions, a total of 1260 sets of training data and 836 sets of verification data were simulated. The data fitting degrees of both are relatively high, 0.88 and 0.92 respectively, and the relative errors are only 10.87% and 10.14%, which meet the engineering requirements of errors within 20%. And the arrays with relative errors greater than 20% account for 14.69% and 10.05% respectively, which account for a relatively small proportion. The GMDH simplified formula can still maintain a relatively high accuracy under so many training and verification arrays, which shows that it has a high reliability, and the simplified formula itself is not complicated, and the coefficients contained are all calculated through basic functions, and it has good applicability in engineering.

Table 1 Training status

Training array 1260 Goodness of fit 0.88 Mean relative error 10.87% Number and proportion of groups with relative error greater than 20% 185 groups, 14.68% Number and proportion of groups with relative error greater than 30% 89 groups, 7.06% Relative error greater than 50% 29 groups, 2.30%

Table 2 Test results

Validate array 836 Goodness of fit 0.92 Mean relative error 10.14% Number and proportion of groups with relative error greater than 20% 84 groups, 10.05% Number and proportion of groups with relative error greater than 30% 27 groups, 3.23% Number and proportion of groups with relative error greater than 50% 8 groups, 0.96%

Step 4): Layering of double-layer composite liner

In order to verify the rationality of the layered calculation method of the breakdown time of the double-layer composite liner, a model verification was first carried out, and the calculation model diagram is shown in Figure 2. The calculation method for the breakdown time of the double-layer composite liner is: first calculate the breakdown time of the composite liner (upper), once the composite liner (upper) is broken down, use the source concentration (C0) as the top boundary condition of the composite liner (lower) to calculate the breakdown time of the composite liner (lower). The COMSOL software was used to calculate the breakdown time of 500 groups of double-layer composite liners with different parameters in the non-simplified and simplified cases. After linear regression analysis, the upper and lower layer breakdown time distribution coefficients were obtained to be 1, that is, the total breakdown time = the breakdown time of the composite liner (upper) + the breakdown time of the composite liner (lower). After simplification, the average relative error of the calculated breakdown time is about 6.74%, which is small, so it can be considered that the layered processing is correct and effective.

Step 5): Calculate the breakdown time of the double-layer composite liner

The upper water head of a double-layer composite liner is h _w = 10m, the geomembrane folds are 100m, the leakage frequency is 1/ha, 1/2 of the fold width is 0.1m, the geomembrane thickness L _g is 0.002m, the CCL permeability coefficient K _ccl = 1.0×10 ^-10 m/s, the porosity n _ccl is 0.4, and the thickness L _ccl is 0.3m; the permeability coefficient of the leachate drainage layer (DL) is K _Dl = 1×10 ^-10 m/s, the porosity n _Dl is 0.5, the thickness L _Dl is 0.3m, and θ is 1.0×10 ^-8 m ² /s. The pollutant is chloride ion, the product of the pollutant diffusion coefficient and the distribution coefficient in the geomembrane is S _gf D _g is 1.0×10 ^-15 m ² /s, the diffusion coefficient D _ccl in CCL is 5.0×10 ^-10 m ² /s, and the diffusion coefficient D _Dl in DL is 1.0×10 ^-9 m ² /s. The calculation model is shown in Figure 2, and the calculation is performed:

Calculate the leakage rate of the upper layer of the double-layer composite liner:

_Ls ＝ _Lccl + _LDl ＝0.6m

Calculate the breakdown time of the upper layer of the double-layer composite liner:

According to the empirical formula, the breakdown time factor _TR is 0.385, so the breakdown time of the upper liner is:

The lower water head h _w = 0.3m, the geomembrane fold is 100m, the leakage frequency is 1/ha, 1/2 of the fold width is 0.1m, the geomembrane thickness L _g is 0.0015m, the CCL permeability coefficient K _ccl = 1.0×10 ^-10 m/s, the porosity n _ccl is 0.4, and the thickness L _ccl is 0.3m; the natural attenuation layer (AL) permeability coefficient K _Al = 1×10 ^-7 m/s, the porosity n _Al is 0.3, the thickness L _Al is 1.0m, and θ is 1.0×10 ^-8 m ² /s. The pollutant is chloride ion. The product of the pollutant diffusion coefficient and the distribution coefficient in the geomembrane is S _gf D _g, which is 1.0×10 ^-15 m ² /s. The diffusion coefficient in CCL is D _ccl , which is 5.0×10 ^-10 m ² /s. The diffusion coefficient in AL is D _Al, which is 6.0×10 ^-10 m ² /s.

Calculate it:

Calculate the leakage rate of the lower layer of the double-layer composite liner:

Calculate the breakdown time of the lower layer of the double-layer composite liner:

According to the empirical formula, the breakdown time factor _TR is 0.369, so the breakdown time of the lower liner is:

Therefore, the total breakdown time of this double-layer composite liner is 93.9 years.

The above-described embodiment is only a preferred solution of the present invention, but it is not intended to limit the present invention. A person skilled in the relevant technical field may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, any technical solution obtained by equivalent replacement or equivalent transformation falls within the protection scope of the present invention.

Claims (4)

1. A method for calculating the breakdown time of a double-layer composite liner based on a GMDH neural network, characterized in that it specifically comprises the following steps: S1: Based on the migration of pollutants in a single-layer composite liner, a mathematical model of pollutant migration is constructed; S2: Based on the mathematical model of contaminant transport, an analytical solution for calculating the contaminant breakdown time of a single-layer composite liner is obtained; S3: Based on the analytical solution of the calculation of the breakdown time of pollutants in a single-layer composite liner, the GMDH neural network is used for modeling, and the analytical solution is simplified to obtain the simplified fitting formula; The step S3 comprises: (3-1) Constructing a training data set: Based on the analytical solution of the single-layer composite liner pollutant breakdown time calculation, the single-layer composite liner breakdown time corresponding to different landfill water heads, composite liner layer thicknesses, permeability coefficients, and diffusion coefficients is calculated, and the breakdown time factors and corresponding parameter combinations of common working conditions of the single-layer composite liner are obtained; (3-2) Constructing the GMDH neural network model, using part of the training data set, with β ₁ = log ₁₀ ( _PLg ), β ₂ = log ₁₀ ( _PLs ), As input parameter, with breakdown time factor _TR as output, the GMDH neural network model is trained to obtain the fitting formula about input-output; where _Cb represents the breakdown concentration of pollutants at the bottom of the anti-fouling barrier, _C0 represents the initial concentration of pollutants in the leachate, _PLg represents the Peclet number of the geomembrane, and _PLs represents the Peclet number of the compacted clay liner; (3-3) Select the remaining training data set to verify the accuracy of the fitting formula until the fitting formula error meets the requirements and the training is terminated; S4: Use numerical simulation methods to perform stratification of the double-layer composite liner and determine the distribution coefficient of each layer; The step S4 comprises: A numerical model of the double-layer composite liner used on site was established, and the numerical simulation method was used to calculate the overall breakdown time of the double-layer composite liner and the breakdown time of each layer after stratification under different water head values. The total breakdown time calculation formula is as follows: Where: T represents the total breakdown time of the double-layer composite liner; _Ti represents the breakdown time of the i-th single-layer composite liner; _αi represents the breakdown time distribution coefficient of the i-th single-layer composite liner; The distribution coefficient of each layer was calculated using the linear regression method until the error was within an acceptable range; S5: Calculate the breakdown time of the double-layer composite liner based on the distribution coefficients of each layer obtained in step S4 and the simplified fitting formula obtained in step S3. 2. The method for calculating the breakdown time of a double-layer composite liner according to claim 1, wherein the mathematical model of pollutant migration in step 1 is: In the formula: _Dg represents the diffusion coefficient of pollutants in geomembrane; _Cg represents the concentration of pollutants in geomembrane; _Ds represents the effective diffusion coefficient of pollutants in compacted clay liner; _Cs (z,t) represents the concentration of pollutants in compacted clay liner; _va represents the Darcy flow velocity in the composite liner; _vs represents the seepage velocity in the compacted clay liner; _Rd represents the retardation factor of the compacted clay liner; z represents the vertical migration distance of pollutants. 3. The method for calculating the breakdown time of a double-layer composite liner according to claim 1 is characterized in that, in step S2, the parameters in the mathematical model of pollutant migration are determined according to the type of pollutants migrating in the composite liner, the boundary conditions of the mathematical model of pollutant migration are determined according to the site conditions, and the analytical solution for calculating the breakdown time of pollutants in a single-layer composite liner is solved according to the boundary conditions. 4. The method for calculating the breakdown time of a double-layer composite liner according to claim 1 is characterized in that the step S5 is specifically: obtaining the parameters of each layer in the double-layer composite liner to be calculated as the input of the simplified fitting formula, calculating the breakdown time of each layer respectively, and taking the sum of the products of the breakdown time of each layer and the distribution coefficient of each layer as the total breakdown time of the double-layer composite liner.