A method for calculating equivalent permeability coefficient of damaged geomembrane based on statistical theory

Abstract

The application discloses a kind of equivalent permeability coefficient calculation method of damaged geomembrane based on statistical theory, comprising the following steps: on-site inspection and sampling of damaged geomembrane, washing and shade drying in laboratory, classification marking and counting the number of different size defects, design geomembrane defect distribution table, calculate the overall area and defect area of damaged geomembrane and average defect rate, obtain the leakage of damaged geomembrane according to geomembrane defect seepage flow calculation formula, and calculate the equivalent permeability coefficient of damaged geomembrane.The application can realize the rapid calculation of the permeability coefficient of damaged geomembrane, effectively fill the blank of the permeability coefficient estimation and quantitative evaluation of defect leakage of damaged geomembrane.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of civil engineering materials, in particular to a damaged geomembrane equivalent permeability coefficient calculation method based on statistical theory. BACKGROUND

[0002] With the rapid development of composite geomembrane and construction technology, the number of water conservancy projects and underground landfill projects using composite geomembrane for seepage prevention is gradually increasing. Geomembrane or geomembrane and other geosynthetic materials are used as seepage prevention layer to control the seepage of dam body or foundation. However, defects may exist in the production, transportation and construction of geomembrane, especially in the construction process. The existence of defects will greatly reduce the seepage prevention performance of geomembrane, making it difficult to meet the needs of engineering seepage prevention. How to estimate the seepage quantity of damaged geomembrane and calculate its equivalent permeability coefficient has positive significance for quantitative evaluation of geomembrane seepage prevention performance. The existing geomembrane defect seepage estimation only stays at the qualitative analysis level, and lacks quantitative calculation of equivalent permeability coefficient of damaged geomembrane. Therefore, a new technical solution is urgently needed to complete the quantitative calculation of damaged geomembrane defect seepage and realize the rapid and accurate calculation of equivalent permeability coefficient of damaged geomembrane. SUMMARY

[0003] The technical problem to be solved by the present application is to provide a damaged geomembrane equivalent permeability coefficient calculation method based on statistical theory to solve the above-mentioned problems of the prior art. The average defect rate of the damaged geomembrane in the study area is calculated by using the weighted probability statistical analysis method. The seepage flow rate of different aperture defects is estimated by using the geomembrane defect seepage flow rate calculation formula proposed by Giround. The seepage flow rate of damaged geomembrane in different partitions is obtained by summation. Based on the equivalent principle of seepage flow rate, the equivalent permeability coefficient of damaged geomembrane is calculated.

[0004] To solve the above-mentioned technical problems, the technical scheme adopted by the present application is as follows:

[0005] A damaged geomembrane equivalent permeability coefficient calculation method based on statistical theory, specifically comprising the following steps:

[0006] Step 1, geomembrane site inspection and sampling: lifting the geomembrane overlying structure on site, and inspecting and sampling the geomembrane after lifting is completed; sampling the geomembrane samples at different elevations, regions and lap joints;

[0007] Step 2, damaged geomembrane indoor cleaning and air drying: washing the geomembrane samples obtained by site sampling with clean water, and cleaning the surface soil and particles with a soft brush for more than 3 times, and then laying the geomembrane on the laboratory for air drying;

[0008] Step 3, damaged geomembrane defect classification marking and statistics: sequentially paving the damaged geomembrane in different areas, classifying the defects into four aperture specifications according to the damage degree, and marking and counting the number of defects one by one;

[0009] Step 4, design and manufacture of geomembrane defect distribution table: the statistical table should include the partition label of geomembrane of each damage degree, the number corresponding to each aperture defect, the overall area of each damaged geomembrane, the defect area and the corresponding defect rate, the average defect rate and other data;

[0010] Step 5, estimation of damaged geomembrane leakage: using the geomembrane defect seepage flow calculation formula derived by Giround to estimate the seepage flow of each aperture defect, and then summing to obtain the leakage of damaged geomembrane in each partition;

[0011] Step 6, calculation of equivalent permeability coefficient of damaged geomembrane: based on the equivalent principle of seepage flow, the Darcy seepage calculation formula is used to inversely calculate the equivalent permeability coefficient of damaged geomembrane.

[0012] Further preferably, the sampling area should be not less than 5% of the total area of the study area, and the differences in the upper, middle and lower elevation positions and the section positions should be considered; the sampling area of the overlapping part should be not less than 10% of the total sampling area, so as to ensure the rationality of the field sampling.

[0013] Further preferably, in step 3, the damaged geomembrane defect classification marking classifies and counts the number of the damaged geomembrane according to four apertures of 0-2mm, 2-5mm, 5-10mm and more than 10mm, and distinguishes them by using four different marks or four different colors.

[0014] Further preferably, in step 4, the influence weight of defects of different apertures and positions on the overall defect seepage flow is considered comprehensively, and the average defect rate of the damaged geomembrane in the study area is calculated by using the weighted probability statistical analysis method based on the geomembrane defect distribution table.

[0015] Further preferably, in step 5, considering the permeability coefficient of the geomembrane underlayer and the thickness of the low-permeability soil layer, the seepage flow Q of a single damaged geomembrane defect is calculated by using the composite impermeable layer defect seepage flow calculation formula proposed by Giround, and the single geomembrane defect leakage calculation formula is as follows:

[0016]

[0017] i avg = 1 + H w / [2H s ln(R / r1)] (2)

[0018]

[0019] wherein: i avg is the average hydraulic slope; H w is the water head above the geomembrane, m; k s is the permeability coefficient of the soil layer below the geomembrane, m / s; H s is the thickness of the low-permeability soil layer below the geomembrane, m; R is the radius of the permeable area in the soil below the geomembrane, m; r1 is the radius of the circular hole above the geomembrane, m; a is the area of the hole above the geomembrane, m 2 .

[0020] The leakage amount of the damaged geomembrane in the entire study area Q is obtained by summing up the leakage amounts of the individual defects of the geomembrane. g .

[0021] Further preferably, in step 6, based on the flow equivalence principle, the equivalent permeability coefficient k g is determined using the following calculation formula:

[0022]

[0023] wherein: Q g is the leakage amount of the damaged geomembrane, m 3 / s; T g is the thickness of the geomembrane, m; ΔH is the water head difference above and below the geomembrane, m; A is the permeable area of the geomembrane, m 2 .

[0024] The present application has the following beneficial effects:

[0025] 1. The present application solves the problem of quantitative calculation of the equivalent permeability coefficient of the damaged geomembrane, and can calculate the leakage amount of the damaged geomembrane, thereby inversely calculating the equivalent permeability coefficient of the damaged geomembrane.

[0026] 2. The present application comprehensively considers the influence weight of defects of different diameters and positions on the overall defect leakage amount, and based on the overall defect distribution of the geomembrane, the average defect rate of the damaged geomembrane in the study area is calculated using the weighted probability statistical analysis method.

[0027] 3. The present application can increase the number of classified groups of the circle point marking aperture within the allowable calculation amount range, to further improve the calculation accuracy. DETAILED DESCRIPTION

[0028] Figure 1 is the principle flowchart of the present application.

[0029] Figure 2 is the defect area marking schematic diagram of the damaged geomembrane of the present application.

[0030] Figure 3 is the defect marking schematic diagram of the overlapped portion of the geomembrane of the present application.

[0031] wherein: 1. damaged geomembrane; 2. 0-2mm aperture defects; 3. 2-5mm aperture defects; 4. 5-10mm aperture defects; 5. aperture defects greater than 10mm; 6. ruler. DETAILED DESCRIPTION

[0032] The technical solution of the present application is: a damaged geomembrane equivalent permeability coefficient calculation method based on statistical theory, as shown in Figure 1 , including geomembrane site inspection and sampling, damaged geomembrane indoor cleaning and air drying, damaged geomembrane defect classification and statistics, designing a geomembrane defect distribution table, damaged geomembrane leakage estimation, and damaged geomembrane equivalent permeability coefficient calculation.

[0033] The present application will be further described in detail below in combination with the drawings and specific preferred embodiments.

[0034] Step 1, geomembrane site inspection and sampling: the geomembrane overlying structure is lifted, the existing geomembrane is not damaged during lifting, the sampling area should be no less than 5% of the total area of the study area, and different elevation positions, different section positions, and the sampling area of the lap joint part should be no less than 10% of the total sampling area should be considered, so as to ensure the rationality of the site sampling.

[0035] Step 2, damaged geomembrane indoor cleaning and air drying: the geomembrane sample obtained by site sampling is washed with clean water, and soft hair brushes are used for appropriate washing at least 3 times or more to remove surface soil and particles, and then the geomembrane is laid out in the laboratory for ventilation and air drying until the damaged holes of 0-2mm on the geomembrane are clearly visible.

[0036] Step 3, damaged geomembrane defect classification, marking and statistics: as shown in Figure 2 and Figure 3 , the cleaned and dried geomembrane is placed in a place with sufficient light, the geomembrane is divided into regions using a marker pen, the damaged parts are classified according to four aperture sizes of 0-2mm, 2-5mm, 5-10mm and greater than 10mm, the four types of defects with different aperture sizes are marked and circled with black, blue, red and green marker pens of four different colors, and the number of each type of aperture defect is counted.

[0037] Step 4, design a geomembrane defect distribution table, count the number of different aperture defects in each region of the geomembrane into the geomembrane defect distribution statistical table, and calculate the overall area, defect area and defect rate of different damaged geomembranes, comprehensively consider the influence weight of different aperture sizes and part defects on the overall defect flow rate, and calculate the average defect rate of the damaged geomembrane in the study area by using the weighted probability statistical analysis method.

[0038] Step 5, the leakage estimation of damaged geomembrane: the leakage of different aperture defects is estimated by the formula derived by Giround, and then summed to obtain the leakage of damaged geomembrane in different partitions.

[0039] The leakage calculation formula of single geomembrane defect is as follows:

[0040]

[0041]

[0042] i avg =1+H w / [2H s ln(R / r1)] (3)

[0043] In the formula: i avg is the average hydraulic gradient; R is the radius of the permeable area in the soil under the geomembrane, m; a is the area of the hole on the geomembrane, m 2 ; r1 is the radius of the circular hole on the geomembrane, m; H w is the water head on the geomembrane, m; k s is the permeability coefficient of the soil layer under the geomembrane, m / s; H s is the thickness of the low-permeability soil layer under the geomembrane, m.

[0044] After summation, the leakage of damaged geomembrane in all regions Q g

[0045] Step 6, the equivalent permeability coefficient calculation of damaged geomembrane: since the size, number and location of damaged areas of the geomembrane are random, only the average water head is used for calculation here. Based on the equivalent principle of permeation flow, the Darcy seepage calculation formula is used to inversely calculate the equivalent permeability coefficient k g of the damaged geomembrane, and the calculation formula is as follows:

[0046]

[0047] After transformation, we get:

[0048]

[0049] In the formula: Q g is the leakage of damaged geomembrane, m 3 / s; T g is the thickness of the geomembrane, m; ΔH is the water head difference between the top and bottom of the geomembrane, m; A is the permeation area of the geomembrane (m 2 ).

[0050] The preferred embodiments of the present application are described in detail above, but the present application is not limited to the specific details of the above-described embodiments, and various equivalent transformations of the technical solutions of the present application can be made within the technical concept of the present application, and these equivalent transformations all belong to the protection scope of the present application.

Claims

1. A method for calculating the equivalent permeability coefficient of a damaged geomembrane based on statistical theory, characterized in that: Comprising the following steps: S1, geomembrane site inspection and sampling: geomembrane site overlying structure lifting, lifting process does not damage the existing geomembrane, after lifting, the geomembrane is inspected and sampled: sampling the geomembrane samples at different elevations, regions and overlapping parts; S2, damaged geomembrane indoor cleaning and air drying: using clean water to rinse the geomembrane samples obtained by site sampling, using soft brush to wash more than 3 times, removing surface soil and particles, then laying in the laboratory for ventilation and air drying the geomembrane, until the damaged holes of 0-2mm on the geomembrane are clearly visible; S3, damaged geomembrane defect classification, marking and statistics: sequentially laying the damaged geomembrane in different regions, classifying the defects into four aperture specifications according to the damage degree, and marking and counting the number of defects one by one; S4, design and preparation of geomembrane defect distribution table, the statistical table should include the partition label of geomembrane of each damage degree, the number corresponding to each aperture defect, the overall area of damaged geomembrane, the defect area, the corresponding defect rate and the average defect rate; S5, damaged geomembrane leakage estimation: according to the permeability coefficient k of the soil layer under the geomembrane s , combined with the calculation formula of the defect seepage flow of the geomembrane derived by Giround, the defect seepage flow of each pore size under the geomembrane in different regions is estimated, and then summed to obtain the leakage of the damaged geomembrane in different partitions, and the average defect rate of each study area is weighted to obtain the overall leakage of the damaged geomembrane; S6, calculation of equivalent permeability coefficient of overall damaged geomembrane: based on the equivalent principle of permeation flow, the Darcy seepage calculation formula is used to obtain the equivalent permeability coefficient of overall damaged geomembrane.

2. The method for calculating the equivalent permeability coefficient of a damaged geomembrane based on statistical theory according to claim 1, characterized in that: The sampling area in S1 should not be less than 5% of the total area of the study area, and the upper, middle and lower positions at different elevations should be considered, and the sampling area of the overlapping part should not be less than 10% of the total sampling area, so as to ensure the rationality of the site sampling.

3. The method for calculating the equivalent permeability coefficient of a damaged geomembrane based on statistical theory according to claim 1, characterized in that: In S3, the damaged geomembrane defect classification and marking, the damaged geomembrane is classified and marked according to four aperture specifications of 0-2mm, 2-5mm, 5-10mm and more than 10mm, and four different marks or four different colors are used to distinguish them.

4. The method for calculating the equivalent permeability coefficient of a damaged geomembrane based on statistical theory according to claim 1, characterized in that: In S4, the influence weight of defects of different aperture and position on the overall defect seepage flow is considered comprehensively, based on the geomembrane defect distribution table, the weighted probability statistical analysis method is used to calculate the average defect rate of the damaged geomembrane in each study area.

5. The method for calculating the equivalent permeability coefficient of a damaged geomembrane based on statistical theory according to claim 1, characterized in that: In S5, considering the permeability coefficient of geomembrane underlayer and the thickness of low permeability soil layer, the seepage flow Q of single damaged geomembrane defect is calculated by using the formula for calculating the seepage flow of composite impermeable layer defect proposed by Giround, and the formula for calculating the seepage flow of single geomembrane defect is as follows: i avg = 1 + H w / [2H s ln(R / r1)] (2) where: i avg is the average hydraulic slope; H w is the water head on the geomembrane, m; k s is the permeability coefficient of the soil layer under the geomembrane, m / s; H s is the thickness of the low permeability soil layer under the geomembrane, m; R is the radius of the permeable area in the soil under the geomembrane, m; r1 is the radius of the circular hole on the geomembrane, m; a is the area of the hole on the geomembrane, m 2 ; The leakage amount of the damaged geomembrane in the whole study area Q can be obtained by summing up the leakage amount of individual geomembrane defects. g .

6. The method for calculating the equivalent permeability coefficient of a damaged geomembrane based on statistical theory according to claim 5, characterized in that: S6 Based on the principle of flow equivalence, the equivalent permeability coefficient k of the damaged geomembrane g The following calculation formula is used to determine: wherein: Q g L is the leakage of the damaged geomembrane, m 3 / s; T g is the thickness of the geomembrane, m; ΔH is the water head difference above and below the geomembrane, m; A is the permeation area of the geomembrane, m 2 .

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