# Analysis of Permeability Stability of Mask Dam Considering Geomembrane Defects

**Abstract:** In order to study the seepage characteristics of low cost textured geomembrane defects in the reservoir water level and the stability of the upstream dam slope, the finite element analysis model of the damaged textured geomembrane factory price was established by Geo-slope software, and the damaged parts of the aquaculture geomembrane manufacturers were The damage dimensions were analyzed for seepage elements and stability. The results show that the higher the high quality aquaculture geomembrane damage location is, the larger the size is, the higher the immersion line is, the larger the leakage is, but the latter is obviously less than the former; when the reservoir water level falls to the low price aquaculture geomembrane damage elevation, there is an immersion line. The sudden change of “mutation”; the initial stability safety factor becomes smaller as the aquaculture geomembrane manufacturers defect position becomes higher and the size becomes larger, and the safety factor generally decreases first, then tends to be stable, but after the reservoir water level elevation There is a sudden rise in the low cost textured geomembrane defect. The research results provide a reference for the stability evaluation and treatment of the mask dam during operation.

**Keywords:** textured geomembrane factory price defect; reservoir water level dip; mask dam; saturated-unsaturated seepage; stability analysis

### 1. Research background

Composite low cost textured geomembrane is a kind of anti-seepage material with good anti-seepage performance, convenient construction, low cost, and strong deformation. It is widely used in the reservoir dam seepage prevention project of medium and low head. China’s representative mask dams include the Xixiayuan Earth and Rock Dam Project and the Xiangyang Pumped Storage Power Station. There are foreign Miele dams in Colombia and Olivenhain dams in the United States. However, the high quality aquaculture geomembrane is characterized by aging and breakage. According to relevant statistics, the defects are unevenly distributed in different parts of the textured geomembrane factory price. The defects of the HDPE geomembrane for sale will cause problems such as the elevation of the water level line in the dam, the expansion of the saturation zone, and a large amount of leakage. In the case of a sudden drop in the reservoir water level, the instability of the upstream dam slope is likely to occur.

Many scholars have carried out some research on the seepage characteristics of earth-rock dams considering aquaculture geomembrane manufacturers defects: Sun Dan et al. based on the saturation-unsaturation theory, numerical simulation of the influence of high quality aquaculture geomembrane defects of different parts and different sizes on seepage elements; Li Qiu et al. analyzed the anti-seepage characteristics of the HDPE geomembrane for sale of Qingyuanhu Reservoir and considered the influence of the size and location of the wholesale HDPE geomembrane damage. Shen Zhenzhong conducted an indoor test under the action of different pressure heads under the condition of composite low price aquaculture geomembrane defects. However, the research on such problems is still not perfect, especially in the case of HDPE geomembrane for sale defects, the stability study of the dam slope where the reservoir water level plummeted has not been reported. In view of this, it is necessary to discuss the seepage characteristics of the membrane dam under the damage of the textured geomembrane factory price and the stability under the sudden drop of the reservoir water level and analyze the law.

In this paper, a mask dam is taken as an example to study the seepage characteristics of low cost textured geomembrane under different damage conditions, and the variation law of safety coefficient of upstream dam slope under different decreasing rates of reservoir water level is discussed, which provides a certain evaluation for the stability evaluation and treatment of mask dam. Reference.

### 2. Seepage-slope stability coupling analysis method

**2.1 Saturated-unsaturated seepage finite element analysis theory**

The unsaturated soil Darcy’s law is written as a tensor in the form of

（1）

Where: vi is the flow velocity in the I direction; kij is the unsaturated permeation tensor; θ is a function related to the position head; his the total head; xj is the position indicator; kr is the relative water permeability; width=14, height= 14, dpi = 1010 is the saturated permeation tensor.

The continuous flow equation for porous media is

（2）

Where: xi is the position identification; ρ is the density of water; Q* is the source and sink term; n is the porosity; Sw is the saturation.

Substituting equation (1) into equation (2) and considering ρ as a constant, considering that θ and hc (pressure head) exist θ=θ(hc), k(θ)=k[θ(hc)], h=z +hc relationship (where z is the position elevation of the calculation point), you can get

(3)

Thus, the saturated-unsaturated differential equation expressed by the pressure head can be obtained as

(4)

Where: C(hc) is the water content; Ss is the unit water storage.

**2.2 Slope stability theory**

The slope stability analysis is based on the Bishop method proposed by Professor Bishop in the 1950s. The Bishop method is used to find the safety factor formula.

(5)

Where: FS is the safety factor, which is obtained by iteration; c is the soil cohesion; β is the base length of the slider; W is the gravity of the soil strip; α is the inclination angle of the bottom of the strip; φ is the soil Internal friction angle; mα can be expressed as

(6)

**2.3 Seepage-slope stable coupling**

In this paper, the Seep/W module in the Geostudio analysis module is used to calculate the transient seepage field under different working conditions of the mask dam, and the different pore water pressures at each moment are introduced into the Slope/W module for transient stability analysis of the upstream dam slope environmental geomembrane for sale. The Bishop method automatically searches for the radius of the sliding surface by software to obtain the variation of the safety factor with time.

### 3. Numerical simulation of geomembrane defects

**3.1 Project Overview**

A mask dam is built on a deep overburden. The anti-seepage scheme uses the upstream dam surface to cover the composite low cost textured geomembrane and extends 40m upstream, with a textured geomembrane factory price thickness of 0.01m. The elevation of the dam foundation is 0.0m, the elevation of the dam crest is 28.0m, the slope of the upstream slope is 1:2.4, and the slope of the downstream slope is 1:1.6. The gravel is built inside the dam body, and the drainage rib is provided at the dam toe environmental geomembrane for sale. The elevation is 22.0m, the dead water elevation is 5.0m, and the downstream water level is 0.0m. A typical section of the mask dam is shown in Figure 1.

**Figure 1 Typical section of the mask dam**

**3.2 Material parameters**

The physical and mechanical parameters of various materials of the mask dam are shown in Table 1. The aquaculture geomembrane manufacturers are not easy to simulate due to its small size. The percolation calculation adopts the literature method to convert the thickness and the permeability coefficient equivalently. The low cost textured geomembrane damage simulation is carried out by the literature method, that is, the damage is given. The textured geomembrane factory price has a large permeability coefficient to simulate the strong permeable condition. The value of this paper is 10m/s.

The unsaturated permeability coefficient equation uses the Fredlund-Xing method to estimate the permeability coefficient curves and soil-water characteristic curves of various materials, as shown in Fig. 2.

**Figure 2 Soil permeability coefficient curve and soil-water characteristic curve**

**Table 1 physical and mechanical parameters of materials**

**3.3 Simulated conditions of geomembrane defects under sudden drop in reservoir water level**

Due to the randomness of the location of low price aquaculture geomembrane defects, the paper takes three schemes: upper part (18.0m elevation), middle part (12.0m elevation) and the bottom part (6.0m elevation), and combines different reservoir water level decline rates (2.00, 1.00, 0.50). , 0.25m / d, from the normal water level 22.0m elevation to the dead water level 5.0m), the size of the aquaculture geomembrane manufacturers damage is taken to a circular defect of 0.1m and 0.2m, the specific working conditions are shown in Table 2 Show.

**Table 2 calculation conditions**

**3.4 Model scope and initial and boundary conditions**

Model range: As shown in Figure 1, the model takes b point as the coordinate origin, the horizontal direction is the x-axis environmental geomembrane for sale, the vertical direction is the y-axis, the bottom of the model is taken to the -55.0 m elevation, and the left and right extensions are 50 m. Using triangle and quadrilateral elements, the entire model is divided into 1210 nodes and 1154 units. The mesh at the low cost textured geomembrane is refined, and the overall model is shown in Figure 3.

**Figure 3 overall model**

Initial conditions: The steady-state analysis results of different low price aquaculture geomembrane defects and different sizes were taken as initial conditions for transient analysis of each working condition.

Boundary conditions: As shown in Figure 1, the brief is the upstream variable head boundary to simulate the difference in the rate of decline of the reservoir water level in different operating conditions environmental geomembrane for sale. The Seep/W module of Geo-slope software provides a method for dealing with such boundary conditions wholesale HDPE geomembrane: setting the head of the upstream slope of the reservoir as a function of time. For a certain moment, when the head on the node is smaller than the elevation of the node, then The boundary flow Q=0 on the node. Kl is the downstream 0 head boundary, ba, am, ml, fgh is the impervious boundary environmental geomembrane for sale, and hijack is the free seepage boundary.

### 4. Analysis of results

**4.1 Geomembrane defect seepage field analysis**

The position of the immersion line under stable seepage in different parts of the aquaculture geomembrane manufacturers defect is shown in Fig. 4. It can be seen from Fig. 4 that the part with a large change in the elevation of the immersion line is the upstream dam slope of the mask dam environmental geomembrane for sale. Therefore, in the case of a sudden drop in the upstream reservoir water level, the unloading of the water pressure acting on the upstream dam slope easily leads to the upstream dam slope. Instability.

**Figure 4: Steady immersion line position of different defect parts**

**Table 3: Stable seepage leakage and film thickness immersion line under different working conditions**

It can be seen from Table 3 that in the case of no damage to the high quality aquaculture geomembrane, the leakage and the post-film immersion line have the lowest elevation, and once the damage occurs (as shown in the lower part of the working conditions in Table 3), the leakage amount and the post-membrane immersion line elevation are respectively The increase of 223.27% and 72.41%, it can be seen that once the HDPE geomembrane for sale failure occurs, the impact on the seepage elements of the mask dam is very large. When the damage size is the same, the location of the wholesale HDPE geomembrane defect is higher, the position of the immersion line in the dam is higher, and the slope of the immersion line is steeper, which is more unfavorable for the stability of the dam; the larger the size of the environmental geomembrane for sale damage, the higher the immersion line elevation. However, the extent of the impact is not affected by the location of the defect. The leakage amount through the dam body also increases with the upward displacement of the wholesale HDPE geomembrane defect. When the maximum leakage amount occurs at the top of the low price aquaculture geomembrane, it is 68.73m3/d, and the minimum leakage amount is when the HDPE geomembrane for sale is not damaged. 11.56m3/d, the size of the wholesale HDPE geomembrane damage also has a certain impact on the leakage. The larger the size, the larger the leakage, but the impact is not great. In general, the location of the high quality aquaculture geomembrane damage to the mask dam leakage and the immersion line elevation is greater than the damage size.

The immersion line in the dam falls with a decrease in the reservoir water level. When the reservoir water level passes through the damaged part of the low price aquaculture geomembrane, there is a “mutation” in the immersion line in the dam. This is because the low cost textured geomembrane from the damaged part to the following elevation forms a complete anti-seepage system, which causes the immersion line in the dam to suddenly decrease. Here, the elevation of the post-film immersion line in working condition B-4 is taken as an example, as shown in Fig. 5. It is shown that: on the 39th day, because the reservoir water level elevation is higher than the HDPE geomembrane for sale defect elevation, there is a leakage channel of the high quality aquaculture geomembrane defect, which makes the immersion line in the dam high; on the 40th day, the reservoir water level falls below the textured geomembrane factory price defect elevation, the reservoir water level There is no leakage channel below the elevation, and the immersion line in the dam produces a “mutation” effect.

**Fig. 5 Change of post-film immersion line in working condition B-4**

**4.2 Stability analysis of upstream dam slope**

The calculation time length of different working conditions is uniformly taken as 80d, and the safety factor changes with time as shown in Fig. 6.

It can be seen that as the water level of the reservoir decreases, the safety factor of the upstream dam slope first decreases environmental geomembrane for sale, eventually reaching a stable value, and the faster the reservoir water level decreases, the more severe the safety factor decreases. The initial conditions are different, so the safety factor distribution of different working conditions is different. When the wholesale HDPE geomembrane is not damaged (condition D), the initial safety factor is the highest, which is 2.347. As the aquaculture geomembrane manufacturers damage position gradually moves up, the initial safety factor gradually changes. Small, and the larger the size of the HDPE geomembrane for sale damage, the smaller the safety factor. When the reservoir water level falls to the high quality aquaculture geomembrane damage elevation, there is a sudden increase in the safety factor. The reason is that the immersion line in the dam suddenly drops, resulting in the safety factor of the upstream dam slope becoming larger. The location of the HDPE geomembrane for sale damage also has a certain influence on the magnitude of the “mutation” of the safety factor. The lower the elevation of the damage location, the smaller the magnitude of the “mutation”, and the larger the damage size, the smaller the “mutation”.

**Fig.6 Curve of the safety factor of different working conditions with time**

### 5. Conclusion

In this paper, the Geo-slope software is used to simulate the high quality aquaculture geomembrane defects at different locations (upper, middle, lower) and different sizes (0.1m and 0.2m) for a mask dam on a deep overburden, considering different reservoir levels. The effect of the falling rate condition (2, 1, 0.5, 0.25 m/d) leads to the following conclusions:

(1) The location and size of textured geomembrane factory price defects are important factors affecting the seepage field of the mask dam. The initial immersion line elevation and leakage in the mask dam increased with the increase of the wholesale HDPE geomembrane damage position and the size of the defect, but the latter effect was significantly smaller than the former.

(2) During the process of reservoir water level decline, the internal immersion line of the dam body lags behind the reservoir water level. When the reservoir water level drops below the low price aquaculture geomembrane damage elevation, there is a “mutation” in the internal immersion line of the dam.

(3) The overall change trend of the safety factor of the mask dam is firstly decreased and then stabilized. The faster the reservoir water level declines, the more severe the safety factor changes. When the reservoir water level drops below the aquaculture geomembrane manufacturers damage elevation, the safety factor has a sharp rise. “mutation”.

(4) This paper only considers the influence of the location and size of the wholesale HDPE geomembrane damage on the seepage characteristics and stability of the mask dam. The influence of other influencing factors such as the contact between the low price aquaculture geomembrane and the underlying layer on the stability of the upstream dam slope of the mask dam remains to be determined. Further research.