STABILITY AND SEEPAGE OF EARTH DAMS WITH TOE FILTER ...

Journal of Engineering Science and Technology Vol. 16, No. 5 (2021) 3712 – 3725 © School of Engineering, Taylor’s University

3712

STABILITY AND SEEPAGE OF EARTH DAMS WITH TOE FILTER (CALIBRATED WITH ARTIFICIAL NEURAL NETWORK)

ASMAA ABDUL JABBAR JAMEL1,*, MUATAZ IBRAHIM ALI2

1Collage of Engineering, Civil Engineering, Tikrit University, Iraq 2Collage of Engineering, Civil Engineering, Samara University, Iraq

*Corresponding Author :[email protected]

Abstract

Earth dams are important facilities and taking care of the safety of these facilities against seepage and the stability of its upstream slope is very important, and the change in the upstream head has an effect on the distribution of pressures and deformation inside the dam body and thus its stability. This research relies on the use of an artificial neural network model, linked to the Geo-Studio results, to show the effect of the amount of seepage inside the earth dam body with the toe filter used to demonstrate its effect on reducing the seepage inside the dam body, in addition to estimating the safety factor of the upstream dam slope. The study consisted of two streams; Steady state flow, and unsteady state flow for upstream head. The results obtained empirical equation for estimating the seepage inside the dam body in the case of constant and variable flow, with a correction factor (99.2) and (99.7), respectively, in addition to equations for estimating the stability of the upstream slope for the constant and variable flow conditions and with the correction factor (98.1) and (95.8), respectively. The neural network model was also obtained to represent the output models for both types of flow with a high degree of accuracy ranging from (97.8) to (99.2).

Keywords: ANN, Factor of safety, Seepage, SEEP/W, SLOP/W.

mailto:[email protected]

Stability and Seepage of Earth Dams with Toe Filter (Calibrated with . . . . 3713

Journal of Engineering Science and Technology October 2021, Vol. 16(5)

1. Introduction The earth dams are usually less rigid and therefore more likely to collapse as a result of the seepage in it. seepage reduction the stability of the upstream slope. Also as a result, the waves are formed at the surface of the water due to the wind, and these waves will hit the front face of the earth dam, sometimes causing the collapse of the slope of the front of the dam. Many researchers have gone to study the effect of these risks in several methods in their studies, such as using artificial neural network (ANN) and finite element method (FEM) to determine the amount of discharge through a specific earth dam, with variable input included a change in the water height at upstream and downstream of the dam, while the outputs included the values of piezometric pressure, which established accurate results by ANN [1]. Both ANN and the ANSYS software were used to find the maximum amount of stress hydrodynamic pressures due to earthquake, where the results had a high data accuracy, by taking into account the effect of soil, dam and reservoir [2].

Studying the effect of soil strength factors on the values of the factor of safety for slope using the ANN and SLOP/W software, where the results showed that increasing safety factor values when the values of cohesion, internal friction angle and water level increased [3]. Also, number of researchers have also adopted the use of the SEEP/W program to study the characteristics of leakage in earth dams with horizontal filters at the upstream or downstream of the earth dam or without filter, with zone, and cut-off wall [4-9]. Many researchers have been based on the use of the neural network to determine the effect of the performance of the upstream reservoir level and hydropower reservoirs statistical analysis [10, 11]. A group of researchers conducted the studies of the stability of the earth dams using SLOPE / W to find the lowest safety factor for the slopes of the downstream earth dam, and dams under the impact of earthquakes [12-16].

Therefore, since most of the previous studies were for a specific model of dams, and previous studies did not broadly adopt the toe filter effect, the current study is based on the use of Geo-studio software, which its depend on the finite element method, to study the seepage discharge inside the earth dams having a toe filter for maintaining the seepage line within the body of the dam to reduce the risk of collapse of the earth dam, and to obtain its effect on the factor of safety for the upstream slope of the earth dam in the case of steady and unsteady flow. And it relied on finding general equations to find drainage and safety factors to take advantage of them without the need to re-analyse the dam within finite element programs. Based on these results, the artificial neural network (ANN) was promote to study the effect of these variables, and indicating the importance of each variable adopted in the study. Also, extraction of mathematical relationships to find the discharge values and factor of safety for the upstream slope using the neural network model (ANN) and the nonlinear regression equations.

2. Materials and Analytical Program

2.1. GEO studio GEO Studio is an application based on use of finite elements identified in the solution of the problem. This program used automatic distribution of mesh elements. So, the current study has been adopted elements of the form of the quadrant and triangular

3714 A. A. J. Jamel and M. I. Ali


element, the node exceeds 3955 and the number of elements beyond the 3788, while the global size distance about 1m.

In order to analyse the flow within the earth dam using the sub-program SEEP/W for getting seepage through an earth dam having a toe filter, see Fig. 1.

For estimating the safety factor for the stability of the upstream dam is based on the sub-program SLOP/W. SLOP/W use limit equilibrium, which is one of the most common methods for the analysis of stabilized slopes. This method is based on a mechanical study of potential failures and finding an amount representing the factor of safety of this slope surface. Based on the division of the slip surface of the failure into segments and by trial and error on a number of forms of surface failure in order to obtain a critical situation for this slope surface and represented the factor of safety. Using this program will give us a set of attempts to get a critical slip surface, Fig. 2 shows the trial and error for the slip surface in SLOP/W, and Fig. 3 shows the critical slip surface.

Fig. 1. Earth dam with toe.

Fig. 2. Trails for a critical slip surface.

Fig. 3. Critical slip surface.

2.2. Numerical models setup The current study is based on an earth dam with a toe filter as shown in Fig. 4, and for two flow case models; the first is the steady state flow for constant upstream head during the study time period. Thus, the value of the discharge is obtained throughout



the body of the dam (S.Q) and the factor safety for the upstream slope of the dam (S.FS) is found in the steady state.

Fig. 4. Earth dam with toe filter (Current Study model).

The second model represents the unstable flow of water, which is the increase of the water height at the upstream head by 2m from its original level within one day. Thus, both discharge (U.Q) and factor of safety (U.FS) are calculated for unsteady state.

For the steady flow state, three different values were adopted for the upstream slope of the dam U/S= (3, 2.5, 2.25), upstream head h= (20, 25, 30) m, the coefficient of permeability 𝐾𝐾𝑦𝑦

𝐾𝐾𝑥𝑥= 𝐾𝐾 = (0.5, 1, 2) and the length of the toe filter Lf= (20, 22, 24) m,

thus obtaining 81 different cases for the first model (steady state flow). While the second model (unsteady state flow), included all the above variables were adopted for a first model plus to another variable which is the increase in the water upstream head by 2m (h+2m=H2) at time period equal to one day, the effect of this variable produce 81 cases, to extract the effect of this increase in the water level on the discharge and the factor of safety over time (T) and until the discharge get its steady state flow again. Thus, it can be said that the variables adopted for the study of both steady and unsteady flow are as indicated by Eqs.(1) and (2).

� 𝑆𝑆.𝑄𝑄𝑆𝑆.𝐹𝐹𝑆𝑆� = 𝑓𝑓�𝑈𝑈 𝑆𝑆⁄ , ℎ,𝐵𝐵, 𝐿𝐿𝑓𝑓 ,𝐾𝐾� (1)

� 𝑈𝑈.𝑄𝑄𝑈𝑈.𝐹𝐹𝑆𝑆� = 𝑓𝑓�𝑈𝑈 𝑆𝑆⁄ , ℎ,𝐵𝐵, 𝐿𝐿𝑓𝑓 ,𝐾𝐾,𝐻𝐻2,𝑇𝑇� (2)

3. Results and Discussion

3.1. Steady state flow The effect of the steady state flow condition on the discharge values through non homogenous earth dam with toe filter and on the factor of safety for the upstream slope is illustrated in Figs. 5-8.

Figure 4 shows the increase of amount in discharge value when increasing the permeability coefficient. This increase is about 6% when increasing K from 1 (as homogeneous soil) to K= 2 (non-homogeneous soil with vertical permeability, higher than horizontal permeability), and up to 7.5% increase in discharge value when increasing the K from 0.5 (vertical permeability less than horizontal) to k=1 (homogeneous soil). The amount of increase in drainage when changing K from 0.5 to 2 is about 13.2%. Thus, the effect of increasing vertical permeability leads to an



increase in the discharge value at a higher rate than the effect of horizontal permeability. It is also noticed increasing the amount of discharge by increasing the amount of upstream head and increasing discharge by increasing the slope of the dam, and by about 2% when increasing the upstream slope (U/S) by 0.05. Figure 5 shows the increasing the length of the toe filter will increase the discharge rate by 0.12-0.16%, where the presence of the toe filter will ensure the flow of water inside the dam, but will increase seepage amount with increasing toe filter length.

Figure 6 shows the effect of the factor of safety of the upstream slope, when increasing the water height by 5m, the safety factor decreases by 0.4%. Also, the decrease of inclination of upstream by 0.05% leads to a decrease of about 10.4% in the safety factor. The effect of the amount of permeability on the reduction in factor of safety between 0.4-1.5%. While the effect of the length of the filter is shown in Fig. 8, which shows the decrease in amount of the factor of safety with values ranging from 0.11-0.19, when increasing the length of the filter 2 m.

Figure 5. Variation of seepage

through earth dam, U/S=3. Figure 6. Variation of seepage through earth dam, Lf=20 m.

Fig. 7. Variation of factor of

safety (upstream slope), Lf=20 m. Fig. 8. Variation of factor of safety

(upstream slope), U/S=3.



3.2. Unsteady state flow In the case of unsteady flow, which is represented by an increase in the water level by 2m during a period of one day, Fig. 9 shows the increase in the amount of discharge inside the dam body as a result of the increasing in upstream level, and its effect in the long term and until the flow returns to its stable state which may reach a period exceeding 4000 days. Also noted that increase the length of the filter will increase the discharge with time.

Figure 10 shows the amount of the initial increase obtained by the factor of safety when increasing the height of water by 2m, this increase is estimated by about (10%) when increasing the time from 0 days to end of the first day, and then the factor of safety tend to decline during the time until reaching the steady state with a safety factor of 6% less than the safety factor at the start time.

Figure 11 shows the performance of the toe filter during the first seven days of the unstable flow and the reduction in the safety factor at the rate of 0.36-0.15 per day. It is also noticed that increase the length of the toe filter will increase the amount of the safety factor for the unsteady state flow.

Fig. 9. Variation of seepage through earth dam with time (U.Q).

Fig. 10. Initial variation of factor of safety (upstream slope) with time

(U.FS), Lf=22 m.

Fig. 11. The performance of the toe filter with time on (U.FS).



4. Empirical Nonlinear Equation Based on the data extracted for both steady and unsteady flow conditions by the Geo-Studio software, 70% of these data were randomly assigned to meet the requirements of an integrated of output data to find general empirical equations to extract both the discharge and factor of safety of the earth dam, and then verify these equations using the remaining 30% of the results are for the purpose of verifying the performance of these equations, as shown in Figs. 12-15. Equations 3 and 4 are proposed equations to calculate the discharge amount (S.Q) and the safety factor (S.FS) respectively, in the case of steady flow. While Eqs. (5) and (6) represent the state of unsteady flow (U.Q) (U.FS), respectively.

𝑞𝑞 �𝑚𝑚3𝑑𝑑𝑑𝑑𝑦𝑦𝑚𝑚� = 0.004 ∗ 𝑈𝑈/𝑆𝑆0.0535 ℎ1.535 B−0.342 𝐿𝐿𝑓𝑓0.433 K0.108 (3)

𝐹𝐹. 𝑆𝑆 = 34.113 ∗ 𝑈𝑈/𝑆𝑆1.145 ℎ0.39 𝐵𝐵−0.979 𝐿𝐿𝑓𝑓−0.015 𝐾𝐾−0.014 (4)

𝑞𝑞 �𝑚𝑚3𝑑𝑑𝑑𝑑𝑦𝑦𝑚𝑚� = 0.003 ∗ 𝑈𝑈/𝑆𝑆0.057 ℎ0.409 𝐵𝐵−0.357 𝐿𝐿𝑓𝑓0.441 𝐾𝐾0.109 𝐻𝐻21.175 𝑇𝑇0.012 (5)

𝐹𝐹. 𝑆𝑆 = 286.641 ∗ 𝑈𝑈/𝑆𝑆1.638 ℎ−7.688 𝐵𝐵−1.99 𝐿𝐿𝑓𝑓−0.005 𝐾𝐾−0.017 𝐻𝐻28.732 𝑇𝑇−0.01 (6)

Fig. 12. The performance

of Eq. (3) (S.Q). Fig. 13. The performance

of Eq. (4) (S.FS).

Fig. 14. The performance

of Eq. (5) (U.Q). Fig. 15. The performance

of Eq. (6) (U.FS).

Figures 12-15 show a high compatibility between the results extracted by the proposed equations and extracted by the Geo-Studio program by approaching the



application on the line at angle of 45°. Later Table 5 will show the statistical criteria extracted from these suggested equations.

5. Artificial Neural Networks (ANN) Artificial neural networks are important and preferred tools in mathematical representations because of their flexibility in dealing with data and predicting complex results. Multi-Layer Perceptron network (MLP) is a function of data which called input layer or independent layer variables to minimize the error of responses which called outputs layer, while hidden layer has units, each unit has functioned with output and input layers depends upon the network type and the user specifications which multiplied by an adaptable link weight (W) and bias.

Figures 16 and 17 show network models that have been adopted to the current study for the steady state of flow and the unsteady state, which gave high accuracy in the representation of input and output network. Tables 1 and 2 shows the estimate weight parameter where these parameters obtained for hyperbolic tangent function for hidden layer, while for output function was identified function. The following expression was expressed to calculate the output values for the advanced models, see Eq. (7).

Output = ∑ (𝑊𝑊𝑗𝑗 ∗ (𝑡𝑡𝑡𝑡𝑡𝑡ℎ (∑ (𝑊𝑊𝑖𝑖𝑗𝑗 ∗ (𝐼𝐼𝑡𝑡𝐼𝐼𝐼𝐼𝑡𝑡)𝑖𝑖)𝑚𝑚𝑖𝑖=1

𝑛𝑛𝑗𝑗=1 + Bias𝑗𝑗))) + Bias (7)

Figures 18 and 19 show the accuracy of the results extracted based on the results of the weights of the artificial neural network and the results extracted by the Geo-Studio for both steady and unsteady flow respectively. Where a high convergence was obtained in the values of the extracted results between these two methods, and this indicates the high efficiency of the artificial neural network program in visualizing the results.

Figure 20 shows variation of the mean squared error with number of epochs for training data and testing data.

Fig. 16. Steady state

neural network models. Fig. 17. Unsteady state neural network models.



Fig. 18. The performance of steady state neural network.

Fig. 19. The performance of unsteady state neural network.

Fig. 20. Variation of (MSE) with epochs for training and testing data.



Table 1. Steady state ANN weight parameter. Parameter Estimates

Discharge Parameter Estimates

Factor of Safety

Predictor

Hidden Layer 1 Output Layer Hidden Layer 1 Output

Layer

H(1:1) H(1:2) H(1:3) Q

H(1:1) H(1:2) H(1:3) F.S m3 /day/m

Input Layer

(Bias) -0.724 0.056 0.318 0.031 0.427 -0.386 U/S -0.056 0.196 0.188 -0.027 0.872 0.085

h 0.582 -0.38 0.753 0.582 -0.03 0.421 B 0.088 -0.116 -0.276 -0.13 0.48 0.029 Lf 0.159 -0.002 0.034 0.231 -0.073 -0.045 K 0.135 -0.527 -0.131 0.136 -0.003 -0.112

Hidden Layer 1

(Bias) 0.349 0.314 H(1:1) 0.98 0.388 H(1:2) -0.542 0.974 H(1:3) 0.838 1.31

Table 2. Unsteady state ANN weight parameter. Parameter Estimates

Discharge Parameter Estimates

Factor of Safety

Predictor Hidden Layer 1 Output

Layer Hidden Layer 1 Output Layer

H(1:1) H(1:2) H(1:3) H(1:4) Q m3/day/m H(1:1) H(1:2) H(1:3) H(1:4) F.S

Input Layer

(Bias) 0.718 0.509 -0.895 0.248 -0.16 -0.427 1.639 0.367 U/S -0.186 -0.224 -0.224 -0.211 -0.168 -0.215 -0.359 0.545 H -0.494 -0.563 -0.172 0.343 -0.327 0.266 -0.295 0.002 B 0.237 0.003 0.219 0.11 0.18 0.327 0.313 0.655 Lf -0.206 -0.026 -0.02 -0.001 -0.108 -0.117 0.031 -0.06 K -0.154 -0.114 -0.72 -0.091 -0.033 -0.229 0.071 0.004 H2 0.071 -0.517 0.225 0.347 -0.038 0.408 0.196 -0.03

Time (days) -0.057 0.041 -0.018 0.07 -0.111 0.103 0.884 -0.02

Hidden Layer

1

(Bias) 0.046 0.763 H(1:1) -0.892 -0.801 H(1:2) -0.309 0.629 H(1:3) -0.603 -0.984 H(1:4) 0.997 1.019

Independent variable importance The importance of the entered data in the network and measure how the output depends on it, as well as the normalized importance is also a significant value, which represents the percentage of the division of the importance of each entry to the greatest importance of input. Tables 3 and 4 show the importance of independent inputs in the case of steady and unsteady flow, respectively. It is noted that the upstream head had the greatest effect on discharge in both steady and unsteady flow, and the safety factor in steady flow. While the upstream slope is the largest effect on the safety factor in the case of steady flow, the rest of the inputs affect the output of the neural network according to the graduated ratios as it shown in the same tables.



Table 3. Independent variable importance at steady state.

Parameter Discharge Factor of Safety

Importance Normalized Importance % Importance Normalized

Importance % U/S 0.033 4.6 0.357 85.4

h 0.703 100 0.418 100 B 0.049 7 0.161 38.6 Lf 0.069 9.9 0.019 4.5 K 0.146 20.8 0.044 10.5

Table 4. Independent variable importance at unsteady state.

Parameter Discharge Factor of Safety

Importance Normalized Importance % Importance Normalized

Importance % U/S 0.05 11.55 0.27 100

h 0.43 100 0.25 90.8 B 0.07 17.4 0.21 76.1 Lf 0.07 17.19 0.02 6.1 K 0.15 33.83 0.05 17.4 H2 0.16 37.51 0.08 30.3

Time (days) 0.06 14.93 0.13 48.2

6. Validating for ANN and Regression Models A series of statistical analyses on each of the proposed nonlinear regression equations, as well as to ascertain the accuracy of the artificial neural network, according to this statistical information, so Table 5 shows a set of statistical variables that represent the coefficient of correlation, mean absolute percentage error, average accuracy percentage, and relative error for ANN which show high accuracy of data compatibility for both the proposed equations model and the artificial neural network models. While Figs. 21 and 22 show the performance regression between training, validation test for discharge and factor of safety respectively, and Fig. 23 shows very low error in ANN histogram results.

Table 5. Validation ANN and non-linear regression models.

Statistical standards

Statistical values of Regression Analysis

Statistical values of ANN models

Coefficient of

Correlation (R) %

Mean Absolute

Error (MAPE)%

Average Accuracy (AA) %

Coefficient of

Correlation (R) %

Relative Error% Mean Absolute

Error (MAPE) %

Average Accuracy (AA) % Model

No. Training Testing

S.Q 99.2 2.57 97.4 99.5 1.1 0.9 2.2 97.8

S. FS 98.1 1.18 98.8 99.6 0.8 0.9 0.81 99.2

U.Q 99.7 6.4 93.6 99.8 0.3 0.3 1.22 98.8

U. FS 95.8 1.23 98.8 98 5.2 1.4 1.07 98.9



Fig. 21. The performance regression between training, validation test for discharge.

Fig. 22. The performance regression between training,

validation test for factor of safety.

Figure 23. Error histogram in ANN results.

7. Conclusions Based on the current study, a set of conclusions can be set, depending on the use of the artificial neural network and the Geo-Studio program, as follows: • S.Q increase with increasing the permeability. The effect of increasing vertical

permeability leads to an increase in the discharge value at a higher rate than the effect of horizontal permeability.

• At steady state increasing the length of the toe filter will increase the discharge rate by 0.12-0.16%.

• A time period exceeding 4000 days for takes for flow to return to its stable state. • Increasing the length of the toe filter will increase the amount of the safety factor

for the unsteady state.



• ANN shows that the upstream head had the greatest effect on discharge in both steady and unsteady flow and the safety factor in steady flow. While the upstream slope is the largest effect on the safety factor in the case of steady flow.

• High accuracy of data in both the proposed equations model and the artificial neural network models.

Nomenclatures B Dam base width, m h Upstream head, m H2 Increase in the water upstream head by 2 m K Coefficient of permeability Lf Length of the toe filter, m S.FS. Factor safety for the upstream slope of the dam at steady state

S.Q Discharge throughout the body of the dam at steady state, �𝑚𝑚3𝑑𝑑𝑑𝑑𝑦𝑦𝑚𝑚�

T Time period, (day)

U.FS. Discharge throughout the body of the dam at unsteady state, �𝑚𝑚3𝑑𝑑𝑑𝑑𝑦𝑦𝑚𝑚�

U.Q Factor safety for the upstream slope of the dam at unsteady state U/S Upstream slope of the dam Abbreviations

AA Average Accuracy ANN Artificial Neural Networks MAPE Mean Absolute Error R Coefficient of Correlation

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