Seepage Analysis Equations for Zoned Earth Fill Dams with an Inclined Core

Many embankments dams’ failure had been reported due to constant and transient seepage and side slope scouring and sliding developed during rising and falling of reservoir water table. In order to stop water from reaching the downstream slope, a great lot of study has been done on seepage analysis and dam stability. To clear out drains and impermeable middle drains are used to lower the phreatic line and disperse excessive pore water strain. One of the widely used approaches, which are frequently time-consuming and require specific equipment may be used to analyze seepage for the glide method and decide how tons water seeps from the dam's frame.

The aim is to discuss the results obtained from the observation to identify the change in water seepage quantities, phreatic line shape and stability of the dam with the different changes that were made to the dam, core and filter.

Furthermore, the purpose is also to increase brief estimation empirical equations for both the seepage discharge amount and the height of water stage out of the variety shapes of the significant core by using the use of statistical techniques of a couple of nonlinear regressions. Dams are indispensable structures for storing water supplies, facilitating irrigation needs, controlling floods, and producing electricity. However, dam screw ups may have catastrophic repercussions, bringing about lack of human lifestyles, property harm, and environmental degradation. One of the primary reasons of dam failure is seepage, which transpires when water percolates via the dam's frame and foundation. Seepage can lead to erosion, instability, and in the end, the fall apart of the dam. Consequently, it's miles actually critical to because it must be predicting seepage to make sure the safety and balance of dams. Seepage exam is a crucial detail of dam format and operation. Traditional methods for seepage examination are often complex, time-consuming, and require specialized equipment. These methods may not be feasible for all dam undertakings, especially for small or medium-sized dams. Furthermore, the precision of seepage exam is relatively reliant at the first-class of enter records, which can be tough to reap in exercise. The accurate prediction of seepage is indispensable for ensuring the safety and stability of dams. Seepage examination can help identify potential issues and prevent dam failure. Moreover, seepage examination can optimize dam layout and operation, reducing the risk of seepage-related problems and enhancing the dam's overall performance.

Hasani et al. [1] investigated the Ilam earth dam, which functions a crucial clay middle, using SEEP/W to evaluate the effect of mesh kind and scale on typical flow charge. Mohammadi et al. [2] optimized the geometry of the Birjand Hesar Sangi earth dam, which features a central core, using SEEP/W. Jamel [3] used an artificial neural network (ANN) to verify the SEEP/W model's estimates of seepage quantity in a homogenous earth dam without a filter. The results were compared to the solutions provided by Casagrande and Dupuit. Khassaf and Madhloom [4] used SLIDE V.5.0 software to investigate seepage parameters in the centrally located Khassa Chai earth dam, focusing on varying core permeabilities and thicknesses. When Li et al. [5] used the ABAQUS finite element software to analyze the seepage of a clay core wall dam and the steady seepage condition under saturated-unsaturated conditions is simulated, they found out that the result from the GeoStudio software were the same as the ABAQUS. The experimental model was used to validate the numerical analysis. Shakir [6] utilized a finite element model to investigate seepage quantities and free surface positioning concerning varying core permeability, thickness, and location for a zoned earth dam with two core types: an inclined upstream core and a vertical low permeability core. Fakhari and Ghanbari [7] employed SEEP/W to test an embankment dam, considering two distinct core types: a vertical core and an inclined core towards the upstream side. They assessed the influences of reservoir water elevation, dam crest width, and primary core angle. Li and Liu [8] examined consistent-country and temporary seepage via a cored dam the use of Seep/W. Salem et al. [9] conducted experimental studies to analyze seepage through earth dams with internal cores. They examined the effects of core hydraulic conductivity, width, base thickness, and penetration on earth dams with and without internal cores. Their research combined experimental approaches and numerical simulations using SEEP/W to verify the experimental models. Using GeoStudio software, Zahedi and Aghazani [10] investigated earth-fill dams with diaphragm, vertical, and inclined core types, analyzing different slopes and geometries. Their study focused on seepage behavior through the dam body and the impact of core anisotropy. Jamel [3] used SEEP/W to research seepage volumes via a cored earth dam, thinking about varied upstream and downstream slopes for the dam and center. Kheiri et al. [11] investigated an embankment dam with center, cutoff wall and horizontal drain using SEEP/W, comparing cutoff wall placement and intensity influences on sub-dam seepage. Salmasi et al. [12] evaluated and contrasted vertical and upstream-inclined cores employing SEEP/W to simulate seepage and hydraulic gradients of a zoned earth dam presenting a clay middle. To probe numerous earthen dam seepage traits-homogeneous, zoned with transition filter and diaphragm with impermeable rock core Sazzad and Alam [13] used SEEP/W. As reported by Zedan et al. [14], the finite element approach changed into used for the cause of reading the stability of the Sharin Earthen Dam underneath various conditions the use of the Geostudio application The outcomes were that developing the permeability of the quilt layer leads to a lower in the outlet gradient and a boom within the permeability within the dam body. Finally, Aziz et al. [15] studied the effect of the shape of the middle on the stability of the lateral slope of the earth dam come to be the usage of the Slide 6 software program to take a look at the factor of protection of the lateral slopes of the dam. The results showed that with the useful resource of developing the lateral slopes of the middle and the top width of the dam, the thing of safety decreases [15]. Yousif [16] studied the seepage assessment thru Al-Adhaim dam by means of using the finite factors GeoSlope software program, he studied unique parameters that might manipulate the seepage and exit gradient inside the dam with the aid of the use of removing the middle, changing the center region, converting filters places and thicknesses. Studied the assessment achieved on Bhimdi earth dam that is a 21 m excessive (Maharashtra State) through converting one-of-a-type parameters which include changing berm width, role of clear out drains by using the use of the usage of Geo-Slope software program [17]. Both ANN and the ANSYS software program were used to find out the maximum quantity of strain hydrodynamic pressures because of earthquake, in which the consequences had an excessive records accuracy, through considering the effect of soil, dam and reservoir [18]. Evaluated the safety element inside the Karolinka dam's frame and foundation. Also, they studied the consequences of dam top on the dam's stability. The have a look at emerge as accomplished thru using the finite detail approach in Plaxis 3D software application. The acquired numerical outcomes show an exquisite agreement with the determined information [19]. Studied the behavior of seepage in the course of a homogeneous earthen dam with clay center changed into the usage of distinct engineering situations. The have a examine become finished the use of Slide v6 application. In this observe, three certainly one of a kind dam height, 3 notable upstream blanket lengths with 4 one-of-a-kind blanket thicknesses and 4 super cutoff depth were hired and the findings located out that the tempo of the drainage declined with the upstream blanket period, cutoff intensity, and blanket thickness expanded. In addition, the have an impact on of the upstream blanket period is better than the cutoff depth. During this, the price of filtering has become more advantageous with decrease pinnacle breadth of the dam [20].

His studies objectives to broaden sincere and expeditious equations for predicting seepage discharge and intensity of water emerging from the core in zoned earth-fill dams with an angled middle. The have a look at employs a statistical technique and synthetic neural networks (ANNs) to analyze the glide method and calculate seepage discharge and depth of water emerging from the core. The proposed equations can be used for the initial design and analysis of zoned earth-fill dams, minimizing the need for complicated and time-ingesting techniques. The findings of the examine can make contributions to enhancing the protection and balance of dams, preventing capacity screw ups, and optimizing dam layout and operation.

1.1 Numerical solution

Two numerical techniques have been extensively employed in stability evaluation: the Finite Difference Method (FDM) and the Finite Element Method (FEM). FDM is normally the primary numerical approach applied for fixing devices of differential equations, wherein preliminary and/or boundary values are given, and each spinoff within the governing equations is changed by using the usage of an algebraic expression formulated in phrases of field variables (e.G., pressure or displacement) at discrete spatial points, leaving those variables undefined within elements. FLAC (Fast Lagrangian Analysis of Continua), one of the set up software program applications applied in slope stability analysis, is rooted in the FDM. Despite being derived thru special methodologies, each FDM and FEM yield distinctly similar consequences.

1.2 Analytical solution

The seepage characteristics of diverse earth dam types, such as homogeneous, zoned with transition filters, and diaphragms with impervious rock cores, had been tested by means of Sazzad and Asmaa Jamel. ANN is employed to validate the accuracy of SEEP/W model's predictions concerning the seepage amount in a homogeneous earth dam missing a clean out. The effects have been as compared to Casagrande and Dupuit's answers [13]. Abdel-Kawy discovered that the wedged-shape center is the maximum green in lowering the quantity of seepage because of factors that have an effect on the seepage discharge and the location of the loose floor [20].

1.3 Experimental studies

Irzooki and Jamel investigated the phreatic line and seepage characteristics of a homogeneous earth dam, with and without a horizontal filter, using the Hele-Shaw model. Experiments were conducted using three different viscous oils to simulate varying soil permeabilities. Each soil type was tested with three different downstream slope angles of the dam. Various runs were performed, altering upstream slope, reservoir head, and filter length. The goal was to develop an empirical equation to determine the optimal filter length for mitigating downstream cover. Results indicated that reducing upstream reservoir head, upstream slope, and downstream slope angle increased downstream cover, while reducing filter length had the opposite effect [21]. For Salem, along with other researchers, conducted experimental studies on seepage through earth dams with an internal core. They examined the impact of core permeability, width, base thickness, and penetration, both experimentally and using SEEP/W for numerical validation [9]. Additionally, El-Hazek performed experimental and numerical modeling to study the slope stability and seepage water behavior of earth-fill dams. These studies aimed to enhance the understanding of seepage dynamics and improve dam design and safety [22].

1.4 Statistical studies

It is crucial to layout and optimize the dimensions of a dam's drainage tool to ensure the downstream shell remains dry and to prevent a boom in pore water stress inside the earth dam. A numerical example proved the ease of utilization and alertness of those equations, emphasizing their utility as an additional layout test alongside popular techniques which consist of the glide net method. Mazaheri applied GeoStudio software to model Marvak earth dam with actual cloth parameters, investigating the minimal element of protection by various drainage dimensions, fabric houses, and dam slope. Through neural network schooling on statistics acquired from Marvak dam modeling, they determined the minimal trouble of safety for horizontal drainage. Their findings highlighted the massive impact of internal friction angle of drainage fabric and dam slope at the minimal issue of protection [23]. Heidari used synthetic neural networks (ANN) to model leakage from Shahrchay dam, verifying the version's accuracy. They concluded that specific physical facts approximately the dam come to be vain for the ANN version, and model verification for every piezometer turned into completed completely using multiyear static records on dam frame and water height both upstream and downstream [24].

A Group of 200 varied zoned earth fill dam models has inclined cores are established to build the required database. Halve of them has forward-inclined cores and the rest has backward-inclined cores. All dam models were created with varied ranges of properties and dimensions according to the safe boundary limits recommended for side slope stability, sliding, and scouring in embankment construction designs, Figures 1 and 2.

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Figure 1. Sketch for zoned earth fill dam models has forward inclined core

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Figure 2. Sketch for zoned earth fill dam models has backward inclined core

Table 1. Adopted dam models’ variables ranges

The aim of this study was to develop quick and simple equations for calculating seepage discharge and estimating the depth of water emerging from the inclined core in zoned earth fill dams. A database of 200 varied dam models with forward or backward inclined cores was created. These models adhered to recommended safety limits for stability. Flow analysis was conducted using Geo Studio SEEP/W and SPSS software to calculate seepage discharge and water depth for each model. The developed equations demonstrated high accuracy in predicting seepage and water depth. efficiency in predicting the seepage discharge amount and depth of water emerging from the core, with correlation coefficients of 97.3 and 89.5, respectively, when compared to other analysis methods. Overall, this study provides a simplified and efficient method for analyzing seepage in zoned earth fill dams with inclined cores, which can help in the design and construction of these types of dams to ensure their stability and safety.

The future work for this study could include the following:

1) Analysis the use of Geo Studio software program suggests a mild decrease in seepage discharge amount for the ahead-inclined middle shape as compared to the backward-inclined middle shape, with a distinction of about 0.03%.

2) Moreover, decreasing dam upstream slope or increasing the width of the dam crest reduces considerably the discharge to a certain extent and then its effect ceases.

3) Furthermore, the height of water emerging from the core shows a direct proportional relationship with core permeability, dam downstream slope, and core slope, while an inverse proportional relationship is observed with dam permeability, core width, and filter length. The dam height, reservoir water level, dam crest width, and dam downstream slope have little to no effect.

4) Artificial neural network model (ANN) shows that is the models group number selected (200) was enough and appropriate and correlation coefficients was greater than 95%, whilst the expected results in comparison with the determined effects for each seepage discharge and phreatic line height rising from the center.

5) Independent variables normalized importance shows that the highest influence on the seepage discharge and phreatic line height emerging from the core is for the core permeability and the dam permeability, (materials properties), more than 80% and lowest influence is for the core base distance from the upstream of the dam, less than 20%.

6) Both of the predicted equations are accurate and suitable to estimate the seepage discharge and the phreatic line peak rising from the center, and equations parameters variance analyzing has a very good correlation coefficient (r²), more than 96% for both.

7) In addition, when the results that calculated from the equations compared with those observed for new set of models (50 models) the correlation coefficients were (97.3%) for the seepage discharge (q) and (89.5%) for the phreatic line emerging from the core (Y_o), so they may be used with reassurance.

8) The equation predicting seepage discharge indicates a direct proportionality with several factors: the peak of the dam, the reservoir stage, the permeability of the dam, the upstream slope of the dam, the permeability of the center, the slope of the core, and the period of the filter out. Conversely, it suggests an inverse proportionality with the downstream slope of the dam, the crest width of the dam, the base width of the dam, the crest width of the middle, and the space from the middle base to the upstream thing of the dam.

9) The equation predicting the peak of the phreatic line emerging from the middle shows an immediate proportionality with the reservoir degree, the upstream slope of the dam, the base width of the dam, the permeability of the center, and the period of the clean out. Conversely, it indicates an inverse proportionality with the peak of the dam, the permeability of the dam, the downstream slope of the dam, the crest width of the dam, the slope of the middle, the width of the middle, and the space from the middle base to the upstream facet of the dam.

10) The results that obtained for seepage discharge from experimental and numerical models shows a good agreement with correlation factor (R2) equal to 99.4%. In general, experimental result values were less than numerical result values and differed by 3% to 18%.

11) There is a direct effect of the shape of the core and its location on the amount of water seeping from the reservoir through the body of the zoned earth fill dam. It was found that there was a decrease in the amount of seeping water when the shape of the core changed from rectangular to trapezoidal by 62% and increased to 79% when the core slope decreased from 1:0.25 to 1:0.75. While an increase in it occurred when using inclined core towards the back by 1% and increased to 43% when the core slope decreased from 1:0.25 to 1:0.75, and in the case of forward inclined by 3% and increased to 43% when the core slope decreased from 1:0.25 to 1:0.75.

12) In addition, this decreasing and increasing mentioned in past point in case of increasing core crest width to dam crest width ratio from 0.25 to 0.75 causes a decreasing about 20% in seepage for trapezoidal core shape. And an increasing about 4% for 1:0.25 slope, 17% for 1:0.5 slope, and decreasing about 5% for 1:0.75 slope in seepage for forward inclined core shape. Also causes an increasing about 3% for 1:0.25 and 1:0.5 slopes, and decreasing about 5% for 1:0.75 slope in seepage for backward inclined core shape.

13) Finally, increasing core crest width to dam crest width ratio from 0.25 to 0.75 causes a decreasing in seepage about 65% for rectangular, 47% to 34% for trapezoidal, 63% to 66% for forward, and 64% to 66% for backward core shapes and for all slopes.

14) By monitoring the stability of the dam's upstream surface during a rapid water drop in the reservoir, it was observed that the dam demonstrated high resistance to sliding. This stability was evident across all core shapes, except for a minor portion of the surface near the base in the rectangular and backward core shapes.