CN114912067B - Seepage inversion analysis method for single-layer geomembrane seepage-proof dam - Google Patents

Abstract

The present invention relates to a leakage inversion analysis method for a single-layer geomembrane anti-seepage dam, and belongs to the field of water conservancy engineering seepage. The leakage of geomembrane defects is divided into dispersed defect leakage and concentrated defect leakage. The dispersed defect leakage is approximately calculated according to the uniform distribution of defects, and the concentrated defect leakage is regarded as free outflow through the orifice and is calculated using the orifice outflow method. For the calculation of concentrated defect leakage, if there are two different water depth monitoring data between adjacent defects along the elevation, two sets of leakage equations are established and the elevation and area size of the concentrated leakage defect are determined by joint solution. If there are new defects between two adjacent different monitoring water depths, the elevation and area size of the concentrated leakage defect are solved by establishing a leakage equation and a partial differential equation of the leakage amount to the water level. Finally, the elevation and area size of all concentrated defects at different elevations are solved according to the leakage monitoring data of all different water levels. The method is simple, accurate and efficient.

Description

A seepage inversion analysis method for single-layer geomembrane anti-seepage dam

Technical Field

The invention relates to a leakage inversion analysis method for a single-layer geomembrane anti-seepage dam, and belongs to the field of water conservancy engineering seepage.

Background technique

Geomembrane has good tensile strength, high impact strength, anti-permeability, acid and alkali resistance, heat resistance, weather resistance, wear resistance and other characteristics. It is widely used in river dams, reservoirs, water diversion tunnels, roads, railways, airports, underground, underwater and other engineering anti-seepage. The permeability coefficient of a good quality geomembrane is generally very low, at the order of ^10-13 ~ ^10-15 m/s, and can basically be regarded as an impermeable layer. However, due to the influence of the production process and laying process of the geomembrane, some defects are generally caused, such as: local bonding of the weld is not solid, damage caused by construction and transportation, puncture during construction, tearing caused by uneven settlement of the foundation, local puncture caused by water pressure, etc. These defects will cause abnormal leakage of the geomembrane during water storage. Abnormal leakage of geomembrane will not only affect the benefits of the reservoir, but also affect the safety of the dam.

At present, geophysical exploration methods are generally used to detect leakage anomalies in geomembrane anti-seepage dams, such as high-density electrical method, geological radar, tracer method, etc.

The high-density electrical method uses the change in soil and rock resistivity caused by the change in moisture content in the soil and rock to indirectly infer the location and distribution of leakage. Therefore, based on the apparent resistivity profile of the dam body, combined with the geological conditions and the structural characteristics of the dam body, the distribution of hidden dangers and their approximate shape and size can be inferred. This method can only roughly determine the location of the leakage, but cannot determine the size of the leakage area, and cannot detect leakage below the groundwater level.

Geological radar uses electromagnetic waves to propagate in rock and soil media. When they encounter interfaces where underground media properties change, they will be reflected. Based on parameters such as the time delay, shape, and spectrum characteristics of the reflected signal, the depth of the geological body, the structure of the medium, and its properties are inferred. The disadvantage of this method is that the reflected wave is easily disturbed or the reflected wave energy is weak, resulting in unclear wave group continuity and structural information, affecting the accuracy of detection. At the same time, the detection of the size and location distribution of the leakage area is not accurate enough.

The tracer method is to inject tracers into the leakage inlet upstream of the dam and monitor the leakage outlet downstream of the dam to determine the connectivity of the water flow and the location of the leakage channel. This method requires multiple tests at different locations to determine the location of the leakage, which is not efficient and the determination of the size and location of the leakage area is also relatively rough.

Therefore, there is an urgent need for a method that can accurately and efficiently determine the location of geomembrane leakage.

Summary of the invention

The invention provides a leakage inversion analysis method for a single-layer geomembrane anti-seepage dam, which can realize rapid, efficient and economical search for the geomembrane leakage position and area.

The leakage of geomembrane is mainly caused by defects in the geomembrane. The leakage of geomembrane defects can be divided into scattered defect leakage and concentrated defect leakage. Scattered defects are small defects formed during transportation and construction, which are random and uniform. Concentrated defects are mainly caused by the tearing and puncture of geomembrane formed during the construction process. They are large in size, unevenly distributed, accidental and localized.

Giroud concluded from the statistical analysis of actual measured data that there is one defect for every 4000m2 of construction defects. The equivalent aperture of the defect is generally 1-3mm, up to 5mm in special parts, and up to 10mm due to some accidental factors. Therefore, the leakage of geomembrane dispersed defects can be approximately calculated based on the uniform distribution of defects.

When geomembrane is used as an anti-seepage measure, the concentrated defect leakage of the dam body can be regarded as free outflow through the orifice and can be calculated using the orifice outflow method.

The specific scheme of the present invention is: a leakage inversion analysis method for a single-layer geomembrane anti-seepage dam, characterized in that: the geomembrane defect leakage is divided into dispersed defect leakage and concentrated defect leakage, the dispersed defect leakage is approximately calculated according to the uniform distribution of defects, and the concentrated defect leakage is regarded as free outflow through the orifice and is calculated using the orifice outflow method;

For the calculation of concentrated defect leakage, if there are two different water depth monitoring data between adjacent defects along the elevation, two sets of leakage equations are established and solved jointly to determine the elevation and area size of the concentrated leakage defect; if there are new defects between two adjacent different monitoring water depths, the leakage equation and the partial differential equation of the leakage amount and the water level are established to solve the elevation and area size of the concentrated leakage defect jointly, and finally the elevation and area size of all concentrated defects at different elevations are solved based on the leakage monitoring data of all different water levels.

The calculation method of scattered defect leakage is as follows:

In the formula: Q _Fd —— leakage of dam slope geomembrane defects, unit: m ³ /s, dQ _Fd —— differential leakage of dam slope geomembrane defects; η——defect coefficient, taken as 1.9635×10 ^-10 ~1.7671×10 ^-9 , average 7.854×10 ^-10 , special case take 4.9087×10 ^-7 ; μ—discharge coefficient, taken as 0.60~0.70; g——gravitational acceleration, unit: m/s ² ; H——reservoir water depth, unit: m; l——elevation of dispersed defects, unit: m; dl——differential of dispersed defect elevation; θ——inclination angle of geomembrane laying; c——length of contact between water surface and geomembrane when water depth is l, unit: m.

The calculation method of concentrated defect leakage is as follows:

Concentrated seepage equation of dam slope

Where: h——the height of the concentrated defect, in m; A——the area of the concentrated defect, in ^m2 ; H——the depth of the reservoir, in m;

Step 1: Select a water level with a normal leakage value as the initial value;

Step 2: Take the nth leakage monitoring data, Q _cdn —— the nth leakage volume, H _n —— the water depth at the nth monitoring, h _n —— the elevation of the nth defect, assign an initial value to h _n , take H _n-1 , H _n-1 —— the water depth at the n-1th monitoring;

Step 3: When calculating, first use formula (5) to calculate the current iteration _An , and then use formula (6) to calculate the current iteration _hn ; n = 1...p, p is the total number of monitoring times;

Using formula (2), the nth monitoring leakage satisfies

Combining equation (3) and equation (4), we can get

Where: A _i ——the area of the ith concentrated defect, in m ² ; h _i ——the height of the ith concentrated defect, in m;

In formula (5) and formula (6), It is approximated by monitoring data, taking

Through experiments, we can approximately take λ=0.60~1.00. For the value of _H0 water level, we can approximately take the appropriate position without leakage below the first concentrated defect. The appropriate position is the position of approximately 1 times the average water level difference; μ—discharge coefficient, which is taken as 0.60~0.70;

Step 4: Take the average value of the iteration value of h _n obtained by formula (6) and h _n in formula (5) as the calculated value of hn for this iteration;

Step 5: Determine whether to proceed to the next round of iteration: first calculate the difference between the calculated value of h _n in this round of iteration and the calculated value of h _n in the previous round of iteration. If the difference is less than the allowable value, the iteration of the nth leakage monitoring data can be stopped. Otherwise, return to Step 3 to continue the iterative calculation until the difference between the two calculated values h _n is less than the allowable value. In the next round of iterative calculation, the value of h _n in formula (5) is the calculated value of h _n in this round of iteration. When n = 1, that is, hn = h ₁ , the initial value of h ₁ in the first iterative calculation can be taken as H ₀ ;

Step 6: Take the n+1th leakage monitoring data, Q _cd(n+1) —— the n+1th leakage volume, H _n+1 —— the water depth during the n+1th monitoring, and use formula (8) to determine whether there are new defects in the n+1th leakage monitoring:

1) If equation (8) holds true, there is a new defect between two consecutive different monitoring water depths. Return to Step 2 and iteratively calculate A _n+1 and h _n+1 until the end, and determine the height h and defect area size A of all defects;

2) If formula (8) is not true, it means that there is no new defect in the n+1th leakage monitoring. Then use formula (11) and formula (12) to correct h _n and _An of the nth defect, and take An ₊₁ = 0 and h _n+1 = H _n . Then return to Step 2 and iterate the next water depth monitoring until the end, and determine the height h and defect area size A of all defects;

If the water depth between two adjacent defects n and n+1 is H _n1 and the leakage is Q _cdn1 during the first monitoring, and the water depth is H _n2 and the leakage is Q _cdn2 during the second monitoring, then using formula (2) we can get

Combining equations (9) and (10), we can get the size A _n and height h _n of the nth defect as follows:

The beneficial effects of the present invention are: the method does not require additional equipment and facilities, and only requires leakage monitoring data at different water levels to invert the elevation and area of the defect, which is simple, accurate and efficient, and provides a new way for geomembrane leakage detection. After obtaining the defect area size and elevation, it can provide a basis for dam anti-seepage treatment.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a schematic diagram of the monitoring data of two different water depths between adjacent defects along the elevation;

Figure 2 is a schematic diagram of the situation where there are new defects between two adjacent monitoring water depths along the elevation.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

Example 1: As shown in Figures 1-2, the leakage of geomembrane defects is divided into dispersed defect leakage and concentrated defect leakage. The amount of dispersed defect leakage can be approximately calculated according to the uniform distribution of defects, and the concentrated defect leakage can be regarded as free outflow through the orifice, and is calculated using the orifice outflow method. For the case where there are two different water depth monitoring data between adjacent defects along the elevation, two sets of leakage equations are established and solved jointly to determine the elevation and area size of the concentrated leakage defect. For the case where there are new defects between two adjacent different monitoring water depths, the elevation and area size of the concentrated leakage defect are solved jointly by establishing the leakage equation and the partial differential equation of the leakage amount to the water level. Finally, the elevation and area size of all concentrated defects at different elevations are solved based on the leakage monitoring data of all different water levels.

Furthermore, the calculation method of the scattered defect leakage is as follows:

In the formula: Q _Fd —— leakage of dam slope geomembrane defects, unit: m ³ /s, dQ _Fd —— differential leakage of dam slope geomembrane defects; η——defect coefficient, taken as 1.9635×10 ^-10 ~1.7671×10 ^-9 , average 7.854×10 ^-10 , special case take 4.9087×10 ^-7 ; μ—discharge coefficient, taken as 0.60~0.70; g——gravitational acceleration, unit: m/s ² ; H——reservoir water depth, unit: m; l——elevation of dispersed defects, unit: m; dl——differential of dispersed defect elevation; θ——inclination angle of geomembrane laying; c——length of contact between water surface and geomembrane when water depth is l, unit: m.

Furthermore, the calculation method of concentrated defect leakage is as follows:

Concentrated seepage equation of dam slope

Where: h——the height of the concentrated defect, in m; A——the area of the concentrated defect, in m ² ; H——the depth of the reservoir, in m;

Step 1: Select a water level with a normal leakage value as the initial value;

Step 2: Take the nth leakage monitoring data, Q _cdn —— the nth leakage volume, H _n —— the water depth at the nth monitoring, h _n —— the elevation of the nth defect, assign an initial value to h _n , take H _n-1 , H _n-1 —— the water depth at the n-1th monitoring;

Step 3: When calculating, first use formula (5) to calculate the iteration _An , and then use formula (6) to calculate the iteration _hn ; n = 1...p, p is the total number of monitoring times, because each monitoring will detect a defect, so n represents both the number of monitoring times and the number of defects;

Using formula (2), the nth monitoring leakage satisfies

Combining equation (3) and equation (4), we can get

Where: A _i ——the area of the ith concentrated defect, in m ² ; h _i ——the height of the ith concentrated defect, in m;

In formula (5) and formula (6), It is approximated by monitoring data, taking

Through experiments, we can approximately take λ=0.60~1.00. For the value of _H0 water level, we can approximately take the appropriate position without leakage below the first concentrated defect. The appropriate position is the position of approximately 1 times the average water level difference; μ—discharge coefficient, which is taken as 0.60~0.70;

Step 4: Take the average value of the iteration value of h _n obtained by formula (6) and h _n in formula (5) as the calculated value of hn for this iteration;

Step 5: Determine whether to proceed to the next round of iteration: first calculate the difference between the calculated value of h _n in this round of iteration and the calculated value of h _n in the previous round of iteration. If the difference is less than the allowable value, the iteration of the nth leakage monitoring data can be stopped. Otherwise, return to Step 3 to continue the iterative calculation until the difference between the two calculated values h _n is less than the allowable value. In the next round of iterative calculation, the value of h _n in formula (5) is the calculated value of h _n in this round of iteration. When n = 1, that is, hn = h ₁ , the initial value of h ₁ in the first iterative calculation can be taken as H ₀ ;

Step 6: Take the n+1th leakage monitoring data, Q _cd(n+1) —— the n+1th leakage volume, H _n+1 —— the water depth during the n+1th monitoring, and use formula (8) to determine whether there are new defects in the n+1th leakage monitoring:

1) If equation (8) holds true, there is a new defect between two consecutive different monitoring water depths. Return to Step 2 and iteratively calculate A _n+1 and h _n+1 until the end, and determine the height h and defect area size A of all defects;

2) If formula (8) is not true, it means that there is no new defect in the n+1th leakage monitoring. Then use formula (11) and formula (12) to correct h _n and _An of the nth defect, and take An ₊₁ = 0 and h _n+1 = H _n . Then return to Step 2 and iterate the next water depth monitoring until the end, and determine the height h and defect area size A of all defects;

If the water depth between two adjacent defects n and n+1 is H _n1 and the leakage is Q _cdn1 during the first monitoring, and the water depth is H _n2 and the leakage is Q _cdn2 during the second monitoring, then using formula (2) we can get

Combining equations (9) and (10), we can get the size A _n and height h _n of the nth defect as follows:

Embodiment 2: The present invention is described below with reference to specific cases.

A rockfill dam is simulated. The dam body is protected by geomembrane. The model dam height is 60 cm. The leakage of the geomembrane is measured at different water levels when the seepage is stable. Due to the small size of the model, the scattered leakage of the geomembrane is not considered here. The rationality of the inversion algorithm is verified by two working conditions.

Working condition 1: defect radius r = 2mm, elevation is 19.85cm.

Working condition 2: The defect radius is r=2mm, r=3mm, and r=2mm, and the elevations are 19.9cm, 28.50cm, and 40cm respectively.

The test results are shown in Table 1.

Table 1 Leakage test and inversion results

Through the inversion algorithm, it can be obtained that in working condition 1, the defect is mainly concentrated at an elevation of 19.29cm, and the defect radius is 1.98mm, which is very close to the true value. The defect size inverted at the elevation position without defects is very small, all less than 0.5mm, which can be basically ignored; in working condition 2, the error between the inverted defect elevation and size and the true value is also small, both less than 5%, and the defect size inverted at the elevation position without defects is also relatively small, only 0.75mm. The example analysis shows that the measurement result error of this method is small, and the geomembrane leakage elevation and area size can be determined quickly and efficiently.

The specific implementation modes of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above implementation modes, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims (1)

1. A seepage inversion analysis method of a single-layer geomembrane seepage-proof dam is characterized by comprising the following steps of: dividing geomembrane defect leakage into dispersed defect leakage and concentrated defect leakage, wherein the dispersed defect leakage amount is approximately calculated according to the uniform defect distribution, the concentrated defect leakage is regarded as free outflow through an orifice, and the method of orifice outflow is adopted for calculation;

for the calculation of the concentrated defect leakage, if 2 times of different water depth monitoring data exist among adjacent defects along the elevation, the elevation and the area of the concentrated leakage defect are determined by establishing 2 sets of leakage equations; if new defects exist between adjacent 2 times of different monitoring water depths, the elevation and area of the concentrated leakage defects are solved simultaneously by establishing a leakage equation and a partial differential equation of leakage quantity to water levels, and finally the elevation and area of the concentrated defects at different elevations are solved according to leakage monitoring data of all different water levels;

the method for calculating the leakage quantity of the dispersion defect comprises the following steps:

wherein: q (Q) _Fd -dam slope geomembrane defect leakage amount, the unit is: m is m ³ /s，dQ _Fd -differential leakage of defects of geomembranes of dam slopes; η -defect coefficient, 1.9635 ×10 ^-10 ～1.7671×10 ^-9 Average 7.854 ×10 ^-10 Special case is 4.9087 ×10 ^-7 The method comprises the steps of carrying out a first treatment on the surface of the Mu-flow coefficient, 0.60-0.70; g-gravitational acceleration in units of: m/s ² The method comprises the steps of carrying out a first treatment on the surface of the H, reservoir water depth, wherein the unit is: m; l-the height of the dispersion defect, in units of: m; dl—differential of dispersion defect elevation; θ—inclination angle of geomembrane laying; c, when the water depth is l, the unit of the contact length of the water surface and the geomembrane is: m;

the method for calculating the concentrated defect leakage amount comprises the following steps:

dam slope centralized leakage equation

Wherein: h- (h)-the elevation of the concentrated defects in units of: m; a, the area of the concentrated defect is as follows: m is m ² The method comprises the steps of carrying out a first treatment on the surface of the H, reservoir water depth, wherein the unit is: m;

step1: selecting the water level of a certain leakage normal value as an initial value;

step2: taking nth leakage monitoring data, Q _cdn Leakage of nth time, H _n -the water depth at the nth monitoring, h _n -the elevation of the nth defect, given h _n Giving an initial value, taking H _n-1 ，H _n-1 -the water depth at the time of monitoring for the n-1 th time;

step3: during calculation, the iteration A is calculated by utilizing the method (5) _n Then calculate the iteration h according to the formula (6) _n The method comprises the steps of carrying out a first treatment on the surface of the n= … … p, p being the total number of monitoring;

with the use of (2), the nth monitored leakage satisfies

The combined type (3) and the formula (4) can be obtained

Wherein: a is that _i -the area of the ith concentrated defect in units of: m is m ² ；h _i -the elevation of the ith concentrated defect in units of: m;

in the formula (5) and the formula (6)Obtained by monitoring data approximation

By experiment, λ=0.60 to 1.00 can be approximated for H ₀ The water level is taken to be approximately at a proper position without leakage below the 1 st concentrated defect, and the proper position is approximately at a position with 1-time average water level difference; mu-flow coefficient, 0.60-0.70;

step4: taking the iteration h of the round obtained by the formula (6) _n And h in equation (5) _n The average value of the two is used as the calculated value of hn of the iteration of the round;

step5: judging whether to perform the next iteration: first calculate the h of the iteration of this round _n Calculated value of (2) and h of the previous iteration _n If the difference is smaller than the allowable value, stopping the iteration of the nth leakage monitoring data, otherwise returning to Step3 to continue the iteration calculation until the calculated value h is calculated twice before and after _n The difference of (2) is less than the allowable value; on the next iteration, h in equation (5) _n The value is h of the iteration of the round _n Is calculated from the calculated values of (a); when n=1, i.e. hn=h ₁ H is calculated in the first iteration ₁ The initial value of H ₀ ；

Step6: taking n+1st leakage monitoring data, Q _cd(n+1) Leakage of (n+1) -th time, H _n+1 -the water depth at the n+1th monitoring, and judging whether the newly added defect exists in the n+1th leakage monitoring by using the formula (8):

1) If the formula (8) is established, a new defect exists between two adjacent different monitoring water depths, returning to Step2, and performing iterative calculation A _n+1 And h _n+1 Determining the height h and the defect area A of all defects until the process is finished;

2) If equation (8) does not hold, indicating that no additional defect exists in the n+1st leakage monitoring, correcting h of the n defect by using equations (11) and (12) _n And A _n And take A _n+1 =0 and h _n+1 ＝H _n Then returning to Step2, and iteratively performing next water depth monitoring until the water depth monitoring is finished, and determining the heights h and the defect area sizes A of all defects;

if the water depth is H in the first monitoring process between two adjacent defects n and n+1 _n1 Leakage amount is Q _cdn1 The method comprises the steps of carrying out a first treatment on the surface of the The water depth is H in the second monitoring _n2 Leakage amount is Q _cdn2 Obtainable by the formula (2)

The size A of the nth defect can be obtained by combining the formula (9) and the formula (10) _n And elevation h _n Is that