# Reduction of Seepage Risks by Investigation into Different Lengths and Positions for Cutoff Wall and Horizontal Drainage (Case Study: Sattarkhan Dam)

Authors: Widodo Brontowiyono; Ali T. Hammid; Yasir M. Jebur; Ahmed Q. A. S. Al-Sudani; Dhameer A. Mutlak; Masoud Parvan
Journal: Advances in Civil Engineering
 (2022)

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## Abstract

Seepage from the earth dam’s body reduces the amount of water in the dam’s reservoir and threatens its stability. In this paper, the earth-type Sattarkhan Dam on the Aharchai River has been investigated. In this regard, the SEEP/W model from the GeoStudio 2018 software suite was used for modeling. This study examines the effects of various lengths and positions of cutoff wall and horizontal drainage on seepage, uplift pressure, and exit gradient. Increasing the length of the cutoff wall reduces seepage in both sections, with a more significant effect on Section 2; it also decreases the uplift pressure and the exit gradient. Changing the position of the cutoff wall has a significant effect on seepage fluctuations in Section 1 but has no effect on seepage in Section 2; in positions 2 to 7, the uplift pressure values are nearly identical, and the exit gradient is most significant at position 1 and least at position 2. Increasing the horizontal drainage’s length increases seepage, reduces uplift pressure, and increases the exit gradient. The closer proximity of the horizontal drainage position to the dam’s core increases seepage and decreases uplift pressure and exit gradient. Finally, it is concluded that the construction of a cutoff wall and horizontal drainage with appropriate lengths and positions reduces risk and improves the stability of earth dams.


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## Body

## 1. Introduction

Engineers and geotechnical specialists are interested in constructing earthen dams [1]. Due to their high environmental compatibility and ability to be constructed on a softer bed, these types of dams have been widely used in Iran [2]. The dam’s construction creates a significant hydraulic gradient upstream of the dam relative to downstream. This increases the likelihood that water will seep into the dam and move downstream [3]. Seepage control methods should reduce the amount of water seepage and minimize the risk of damage from slope instability, washout, or scouring of refined grains [4].The following are methods for reducing seepage in the body and foundation of an earth dam: (a) use of the core with very low permeability in the dam body; (b) use of the blanket on the upstream surface; (c) use of the cutoff wall in the dam foundation; (d) use of the grout curtain in the foundation; and (e) use of a layer with very low permeability at the bottom of the reservoir [5, 6]. Due to economic factors, cutoff walls are currently trendy. Water seepage downstream of dams can be observed in the form of increased humidity, soil softening, and increased vegetation, as well as increased spring discharge and rising groundwater piezometric levels [7, 8].For earth dams, using the cutoff wall is one way to seal the dam. Given that the construction of this cutoff wall affects the seepage and stability of the earth dam, its proper placement and length are among the most important factors to consider [9]. Using the SEEP/W model, the current study investigates the position and various lengths of the cutoff wall to improve the sealing of the earth dam. Different states of cutoff wall and horizontal drainage curtains in earth dams have been studied in order to increase the efficiency of dams and reduce the damage caused by seepage. Different states of cutoff wall and horizontal drainage and their effects on changes in uplift pressure and the piping phenomenon have been studied. As a result, the position and different lengths of cutoff wall and horizontal drainage for various situations have been determined.First, the required data and information were obtained from the Regional Water Company of East Azerbaijan Province; then, modeling was conducted using the SEEP/W model in the GeoStudio software [10]. In the continuation of the study, the desired outputs from the model are extracted, and the outcomes are discussed. The first step in numerical simulation is selecting an appropriate numerical model for the subject. Due to the capabilities of the SEEP/W model in seepage simulation, this model has been utilized in the current study. The SEEP/W model is one of the GeoStudio software models that can simulate the flow in the soil environment under all possible conditions using the finite element method [11, 12].Seepage paths in earth dam bodies, foundations, and abutments are affected by a variety of factors, including (a) embankment cracking caused by subsidence or displacement of foundations and abutments; (b) ineffective filters and drains; (c) improper connection of embankment to foundation or embankment to abutments; (d) permeable or soluble materials in the embankment; and (e) the presence of an alluvial layer or permeability in [36, 37].Failure of dams and their foundations is caused by the problems and adverse effects of seepage; these effects include (A) high and uncontrolled exit gradient, (b) piping, (c) uplift or breaking of the slope due to seepage forces, (d) exit of large volumes of water, and (e) uplift force effects [15]. Excess and uncontrolled gradients will cause soil particles to float at the dam's base. Soil leaching may occur if the hydraulic gradient in the water seepage section increases downstream from the slope of the dam body [16]. Initially, the fine grains leach; as these particles leach, the soil's resistance to flow decreases, and the hydraulic gradient rises. As the hydraulic gradient increases, coarse grain particles are leached, and soil erosion accelerates, forming dam tunnels [17]. Due to seepage from the dam body, water may emerge from the downstream surface at high elevations, followed by dam failure. Due to seepage, a substantial amount of water may permeate downstream from the dam’s body and foundation, rendering it economically unjustifiable [18]. The most critical design consideration is the influence of uplift force on the stability of a structure and its foundation. Dam designers must have a realistic understanding of the flow conditions to detect the resulting forces [19].Seepage analysis is required to determine the values of seepage flow, pore water pressure, uplift pressure, hydraulic gradient control, and scouring phenomena. Darcy initiated severe soil studies on seepage in 1856 [20, 21]. Darcy conducted sand-based experiments and presented the results as an empirical law. Darcy’s law remains the foundation of seepage studies. Combining Darcy’s law and the continuity equation yields (1) as the fundamental relation of steady-state flow seepage in a three-dimensional state [22, 23].(1)kx∂2h∂x2+ky∂2h∂y2+kz∂2h∂z2=0,where h is the piezometric height, kx is the permeability coefficient in the x-direction, ky is the permeability coefficient in the y-direction, and kz is the permeability coefficient in the z-direction.Researchers have investigated seepage and its effects on earthen dams using various models and software. Mansuri et al. [24] investigated the effects of different locations and angles of the cutoff wall under a hypothetical dam on the uplift pressure. According to the findings, cutoff wall inclination reduces the uplift pressure. Mortazavi and Soleimani [25] by investigating the seepage from an earthen dam discovered that if the cutoff wall is positioned at the dam’s base, it will be more effective at reducing seepage, and the exit hydraulic gradient will be approximately three-fourths of the critical hydraulic gradient. Nourani et al. [26] used a numerical model to find the optimal location of vertical drains in gravity dams. The result showed that the optimal location of vertical drains is not constant; as the distance between vertical drains increases and the diameter of the drain decreases, the optimal location of vertical drains moves downstream. Hekmatzadeh et al. [27] examined the impact of four cutoff walls on the stability and dependability of diversion dams against the boiling phenomenon. Increasing the shear resistance parameter of the surface between the soil and the barrier decreased the probability of dam failure, while increasing the horizontal coefficient of the earthquake significantly increased the likelihood of failure. Al-Mansori et al. [28], by investigating seepage in the earthen dam, concluded that the clay core significantly reduces the seepage and the existing gradient. Testing the effect of the anisotropy ratio on seepage revealed that an increase in the (kx/ky) ratio increases the amount of seepage. Toumi and Remini [29], by evaluating the geology and hydrogeology of the water leakage in Hammam-Grouz Dam, concluded that sealing materials are the most appropriate technique. Having the same characteristics as waterproofing areas and adapting adequately to their geological formations, assigning sealing works to a highly qualified subcontractor is crucial to achieving satisfactory sealing results for the structure to function correctly. Hassan et al. [30] analyzed the transient seepage and slope stability of sandy and extremely silty sand soils. According to the numerical results, fine particles increase pore water pressure and decrease FOS. The design and maintenance of dikes are contingent on the surrounding hydraulic conditions, dimensions, and soil types. Fine-particle, noncohesive materials were preferred. According to the literature review, various researchers have studied seepage in earthen dams. The main difference between this study and other research is the current study’s comprehensive approach; different parameters, including seepage, uplift pressure, and maximum exit gradient, have been investigated.The current study investigates the steady-state condition of an earth-fill dam (Sattarkhan Dam). The seepage values in two sections, the uplift pressure below the dam core and the maximum exit gradient at the dam claw, are extracted. Various states associated with varying lengths and positions of the cutoff wall and horizontal drainage have been evaluated to investigate these values. Detailed descriptions of the models under consideration are provided in the following sections. Figure1 depicts the overall structure of this investigation. Analyzing the desired parameters can reduce the risks associated with earthen dams. These risks include the unintended reduction of water in the dam lake, the formation of cracks and dam failures, the dam’s overturning, and the formation of piping phenomena within the dam.Figure 1
General structure of the study.Figure2 shows the locations under review, including Sections 1 and 2 (to investigate seepage), under the dam core (to investigate uplift pressure) and the dam’s claw (to exit gradient investigation). These parameters were selected to investigate the various causes of seepage and failure in earthen dams and to provide a comprehensive perspective to the readers of this article. In numerous studies, only one of the desired parameters was examined. All three parameters were examined simultaneously because the phenomena of uplift pressure and piping are closely related to percolation and percolation-influencing factors. In addition, each of the mentioned parameters generates a unique type of failure, necessitating a concurrent examination due to their close relationship. Due to the extensive use of cutoff walls and drains in Iran’s earthen dams, the current study has investigated the cases mentioned.Figure 2
The studied locations. (a) Section1. (b) Section 2. (c) Under the dam core. (d) Claw of the dam.
(a)(b)(c)(d)It is necessary to reduce the dam’s risk because of its high cost and fundamental role in meeting various needs. Therefore, maintaining the dam’s stability and minimizing the water that escapes behind it are crucial. The present study’s novelty resides in examining various associated parameters (including seepage, uplift pressure, and maximum exit gradient). The current study’s objective is to examine the effect of various lengths and positions of the cutoff wall and horizontal drainage on the parameters mentioned above, thereby reducing seepage risks.


## 2. Materials and Methods

This section presents the studied dam’s specifications first, followed by the numerical methods, software, and model. Finally, the dam’s initial model is investigated.


### 2.1. Case Study

In the current study, the Sattarkhan Dam is considered a case study; the Aharchai River is situated within the dam. This river flows south of the city of Ahar before reaching the Aras River and, ultimately, the Khazar Sea. The geographic location of Sattarkhan Dam is shown in Figure3. With the construction of the Sattarkhan Dam, while controlling and regulating the surface flows of the Ahrachai River, a portion of the agricultural lands downstream of the dam was supplied with the necessary water, and the city of Ahar was supplied with potable water. The average annual flow of the Ahrachai River at the dam site is 92 million cubic meters, with a catchment area of 950 square kilometers. Construction of the SattarKhan Dam began in 1994 and was completed in 1997. The SattarKhan Dam is made of Earth. Figure 4 shows the dam’s various components. Also, to give an overview and more understanding of the physical characteristics of the dam, the general physical characteristics of SattarKhan Dam are presented in Table 1.Figure 3
The geographic location of SattarKhan Dam.Figure 4
Different components of Sattarkhan Dam.Table 1
General physical characteristics of Sattarkhan Dam.
Physical characteristics of the damDescriptionDam typeEarth damUsage of damProviding water for a portion of the agricultural lands downstream of the dam and drinking water in Ahar cityHeight of dam1459 meters above sea levelWidth of dam350 metersMaximum water level1451 meters above sea levelDam capacityThe reservoir’s normal water level volume is 135 million cubic meters, and its useful volume is 120 million cubic metersType of spillwayLateral free overflow with valveThe permeability of materials used in SattarKhan Dam is shown in Table2. Also, the values related to the specifications of other dam components are presented in Table 3. Kx and ky represent the permeability along axes 1 and 2, respectively; ρ is the density, E is the modulus of elasticity, C is the stickiness, φ is the friction angle, Ψ is the expansion angle, and υ is Poisson’s ratio in Tables 2 and 3.Table 2
The permeability values of SattarKhan Dam materials.
Type of the materialKx (m/s)Kx/kyCore1 × 10−80.1Cutoff wall2 × 10−71.0Shell1 × 10−50.1Drainage3 × 10−31.0Filter1 × 10−41.0Top layer5 × 10−61.0Bottom layer1 × 10−61.0Table 3
Characteristic values of SattarKhan Dam materials.
Type of the materialρkg/m3EN/m2C (KPa)φΨυCoreCD20301 × 107453700.3CU20301 × 107653300.3UU20301 × 107801000.3Shell21001 × 108040100.3Drainage and filter15602.5 × 10703600.3Top and bottom layers22001 × 10107505080.3


### 2.2. Numerical Methods

Because the differential equations of seepage cannot be solved analytically except in exceptional cases and with elementary boundary conditions, numerical methods for seepage analysis have become widespread in recent years and provide more precise results than other methods. Finite Element Methods, Finite Differences, and Boundary Element Methods are standard numerical methods for solving the flow equations [31, 32].


#### 2.2.1. Finite Element Method

The Finite Element Method is a numerical instruction for solving differential equation-described physical problems. This method is distinguished from other numerical methods by two characteristics: (a) An integral formulation is used to generate a system of algebraic equations and (b) in this method, continuous smooth functions are employed to approximate unknown quantities [33, 34].


#### 2.2.2. SEEP/W Model

SEEP/W is one of Geostudio’s models based on the finite element method [35]. The model is a specific analytical technique that can model the flow in saturated and unsaturated states. This model’s ability to simulate flow in an unsaturated environment has resulted in more realistic conditions than other models. In soils, the permeability coefficient of materials and the volume of water depend on the change in pore water pressure [36]. SEEP/W treats these relationships as continuous functions and computes them, whereas many other modeling systems cannot do so [37]. The general steps of modeling are presented in Figure 5.Figure 5
The general steps of modeling.Finally, we prepare the model for Finite Element analysis by dividing the plotted areas into more minor elements. The type of mesh can be selected from the Mesh menu. To achieve more precise results, a length of 2 m was considered for the elements in this study.


## 2.1. Case Study

In the current study, the Sattarkhan Dam is considered a case study; the Aharchai River is situated within the dam. This river flows south of the city of Ahar before reaching the Aras River and, ultimately, the Khazar Sea. The geographic location of Sattarkhan Dam is shown in Figure3. With the construction of the Sattarkhan Dam, while controlling and regulating the surface flows of the Ahrachai River, a portion of the agricultural lands downstream of the dam was supplied with the necessary water, and the city of Ahar was supplied with potable water. The average annual flow of the Ahrachai River at the dam site is 92 million cubic meters, with a catchment area of 950 square kilometers. Construction of the SattarKhan Dam began in 1994 and was completed in 1997. The SattarKhan Dam is made of Earth. Figure 4 shows the dam’s various components. Also, to give an overview and more understanding of the physical characteristics of the dam, the general physical characteristics of SattarKhan Dam are presented in Table 1.Figure 3
The geographic location of SattarKhan Dam.Figure 4
Different components of Sattarkhan Dam.Table 1
General physical characteristics of Sattarkhan Dam.
Physical characteristics of the damDescriptionDam typeEarth damUsage of damProviding water for a portion of the agricultural lands downstream of the dam and drinking water in Ahar cityHeight of dam1459 meters above sea levelWidth of dam350 metersMaximum water level1451 meters above sea levelDam capacityThe reservoir’s normal water level volume is 135 million cubic meters, and its useful volume is 120 million cubic metersType of spillwayLateral free overflow with valveThe permeability of materials used in SattarKhan Dam is shown in Table2. Also, the values related to the specifications of other dam components are presented in Table 3. Kx and ky represent the permeability along axes 1 and 2, respectively; ρ is the density, E is the modulus of elasticity, C is the stickiness, φ is the friction angle, Ψ is the expansion angle, and υ is Poisson’s ratio in Tables 2 and 3.Table 2
The permeability values of SattarKhan Dam materials.
Type of the materialKx (m/s)Kx/kyCore1 × 10−80.1Cutoff wall2 × 10−71.0Shell1 × 10−50.1Drainage3 × 10−31.0Filter1 × 10−41.0Top layer5 × 10−61.0Bottom layer1 × 10−61.0Table 3
Characteristic values of SattarKhan Dam materials.
Type of the materialρkg/m3EN/m2C (KPa)φΨυCoreCD20301 × 107453700.3CU20301 × 107653300.3UU20301 × 107801000.3Shell21001 × 108040100.3Drainage and filter15602.5 × 10703600.3Top and bottom layers22001 × 10107505080.3


## 2.2. Numerical Methods

Because the differential equations of seepage cannot be solved analytically except in exceptional cases and with elementary boundary conditions, numerical methods for seepage analysis have become widespread in recent years and provide more precise results than other methods. Finite Element Methods, Finite Differences, and Boundary Element Methods are standard numerical methods for solving the flow equations [31, 32].


### 2.2.1. Finite Element Method

The Finite Element Method is a numerical instruction for solving differential equation-described physical problems. This method is distinguished from other numerical methods by two characteristics: (a) An integral formulation is used to generate a system of algebraic equations and (b) in this method, continuous smooth functions are employed to approximate unknown quantities [33, 34].


### 2.2.2. SEEP/W Model

SEEP/W is one of Geostudio’s models based on the finite element method [35]. The model is a specific analytical technique that can model the flow in saturated and unsaturated states. This model’s ability to simulate flow in an unsaturated environment has resulted in more realistic conditions than other models. In soils, the permeability coefficient of materials and the volume of water depend on the change in pore water pressure [36]. SEEP/W treats these relationships as continuous functions and computes them, whereas many other modeling systems cannot do so [37]. The general steps of modeling are presented in Figure 5.Figure 5
The general steps of modeling.Finally, we prepare the model for Finite Element analysis by dividing the plotted areas into more minor elements. The type of mesh can be selected from the Mesh menu. To achieve more precise results, a length of 2 m was considered for the elements in this study.


## 2.2.1. Finite Element Method

The Finite Element Method is a numerical instruction for solving differential equation-described physical problems. This method is distinguished from other numerical methods by two characteristics: (a) An integral formulation is used to generate a system of algebraic equations and (b) in this method, continuous smooth functions are employed to approximate unknown quantities [33, 34].


## 2.2.2. SEEP/W Model

SEEP/W is one of Geostudio’s models based on the finite element method [35]. The model is a specific analytical technique that can model the flow in saturated and unsaturated states. This model’s ability to simulate flow in an unsaturated environment has resulted in more realistic conditions than other models. In soils, the permeability coefficient of materials and the volume of water depend on the change in pore water pressure [36]. SEEP/W treats these relationships as continuous functions and computes them, whereas many other modeling systems cannot do so [37]. The general steps of modeling are presented in Figure 5.Figure 5
The general steps of modeling.Finally, we prepare the model for Finite Element analysis by dividing the plotted areas into more minor elements. The type of mesh can be selected from the Mesh menu. To achieve more precise results, a length of 2 m was considered for the elements in this study.


## 3. Results and Discussion

In this section, the software’s results are evaluated and discussed. Different lengths and positions of the horizontal drainage and cutoff wall are investigated for this purpose. Investigated are the seepage parameters that pass through the two desired body sections: the values related to the uplift pressure below the core and the exit gradient at the dam’s toe.


### 3.1. The Effect of Different Lengths of Cutoff Wall

This section investigates the effects of various cutoff wall lengths on various parameters. For this purpose, the location of the heel dam core has been considered, and different lengths of 0, 5, 10, 15, and 20 meters have been studied (the numbers used to check the length of the cutoff were chosen depending on the depth of the foundation’s upper layer). For each case, distinct seepage values in Sections1 and 2 are extracted and compared. The values of the uplift pressure and the exit gradient are extracted and compared. Table 4 displays the initial values of total seepage, average uplift pressure, and exit gradient (0 m).Table 4
The values of the parameters in the initial state.
ParameterValueTotal seepage from Section1 (m3/s/m2)0.019899Total seepage from Section2 (m3/s/m2)0.017735Average uplift pressure (MPa)502.35Exit gradient0.96888Figure6 shows the percentage of changes in the total seepage of various lengths of the cutoff wall compared to the state without the cutoff wall. According to Figure 6, it is evident that as the length of the cutoff wall increases, seepage decreases, and the amount of reduction in Section 2 relative to the state without the cutoff wall is greater than in Section 1.Figure 6
Percentage reduction of total seepage through Sections1 and 2.As the cutoff wall length increases, the average uplift pressure decreases. Figure7 shows the average changes in uplift pressure based on the percentage difference between the cutoff wall and no cutoff wall.Figure 7
Percentage reduction of average uplift pressure.Increasing the length of the cutoff wall has reduced the exit gradient. Figure8 also shows the changes in the exit gradient compared to the no cutoff wall.Figure 8
Percentage of exit gradient changes.


### 3.2. The Effect of Different Positions of the Cutoff Wall

To investigate the effect of different positions of the cutoff wall, the width of the dam core is divided into 8 points with equal distances from each other, so that the first point is at the heel of the core and the last point is at the toe of the core. Also, cutoff walls with a length of 10 meters have been considered and compared for all situations (a length of 10 meters was considered when attempting to select a typical size for cutoff walls). Table5 presents the values of total seepage, average uplift pressure, and exit gradient at point No. 1. Also, the different positions considered for the cutoff wall are presented in Table 6.Table 5
The values of the parameters in point no 1.
ParameterValueTotal seepage from Section1 (m3/s/m2)0.019689Total seepage from Section2 (m3/s/m2)0.017499Average uplift pressure (MPa)560.13Exit gradient0.96423Table 6
Different positions of the cutoff wall (considering the length of 10 meters of the cutoff wall).
Position no.Distance from the heel of the core (m)1025310415520625730836Figure9 shows the seepage changes in Sections 1 and 2. Position No. 5 in Section 1 has the most changes. Also, moving the position of the cutoff wall did not have much effect on the amount of seepage from Section 2.Figure 9
Percentage of changes in total seepage in Sections1 and 2.Figure10 shows the average change in uplift pressure relative to point 1. According to Figure 10, it is clear that the amount of uplift pressure has increased in all cases. Also, the increase in point No. 8 is more than in other points.Figure 10
Percentage increase in average uplift pressure.Figure11 shows the reduction of the exit gradient in different positions of the cutoff wall. According to Figure 11, in position 2, the maximum decrease occurred, and in position 5, the lowest decrease in the exit gradient occurred.Figure 11
Percentage reduction of exit gradient in different positions of the cutoff wall.


### 3.3. The Effect of Different Lengths of Horizontal Drainage

This section investigates the effect of various horizontal drainage lengths on seepage parameters from Sections1 and 2, as well as uplift pressure and exit gradient. From the dam’s toe, horizontal drainage lengths of 30, 60, 90, 120, 150, and 182 meters are considered for this purpose (the numbers used to determine the length of the drain were chosen according to the width of the dam’s downstream shell).Figures12–14 show the results of the changes relative to the initial condition (Table 3). Figure 12 shows the variations in total seepage through Sections 1 and 2. As shown in Figure 12, the highest seepage of Section 1 occurred during 182 meters of drainage and the highest seepage of Section 2 occurred during 150 meters of drainage.Figure 12
Percentage of seepage changes in Sections1 and 2.Figure 13
Percentage of changes in average uplift pressure.Figure 14
Percentage change of exit gradient in different cases of horizontal drainage length.Figure13 shows the average change in uplift pressure below the dam core. According to Figure 13, with increasing horizontal drainage length, the values of uplift pressure decrease.Figure14 shows the exit gradient changes in different horizontal drainage length cases. According to Figure 14, it is clear that the amount of exit gradient at the dam toe is much less than in other cases, in the case without drainage. Also, the exit gradient values are almost the same in other cases.


### 3.4. The Effect of Different Positions of Horizontal Drainage

This section investigates the effect of different horizontal drainage positions on the seepage parameters of Sections1 and 2, as well as the uplift pressure and exit gradient. The length of 30 meters of horizontal drainage at various distances from the dam (the drain was 30 meters long due to the width of the dam’s shell downstream and the common length selection), including 0 meters, 30 meters, 60 meters, 90 meters, 120 meters, and 152 meters, must have been evaluated and compared for this purpose. Table 7 presents the different positions considered for horizontal drainage.Table 7
Different positions of horizontal drainage (with a length of 30 meters of horizontal drainage).
Position no.Distance from the dam toe (m)1023036049051206152Figures15–17 show the results of the changes compared to the initial state (Table 3). Figure 15 shows the changes in total seepage. According to Figure 15, the amount of total seepage has increased in all positions except position number 6 of Section 2.Figure 15
Percentage of changes in total seepage through Sections1 and 2.Figure 16
Percentage reduction of average uplift pressure in different positions of horizontal drainage.Figure 17
Percentage reduction of exit gradient in different positions of horizontal drainage.Figure16 shows the average uplift pressure reduction in different horizontal drainage positions. As the drainage position approaches the dam core, the amount of uplift pressure below the dam core decreases.Figure17 shows the exit gradient reduction in different horizontal drainage positions. According to Figure 17, the exit gradient in position 1 is much higher than in other positions due to the placement of the dam toe on the drain.


## 3.1. The Effect of Different Lengths of Cutoff Wall

This section investigates the effects of various cutoff wall lengths on various parameters. For this purpose, the location of the heel dam core has been considered, and different lengths of 0, 5, 10, 15, and 20 meters have been studied (the numbers used to check the length of the cutoff were chosen depending on the depth of the foundation’s upper layer). For each case, distinct seepage values in Sections1 and 2 are extracted and compared. The values of the uplift pressure and the exit gradient are extracted and compared. Table 4 displays the initial values of total seepage, average uplift pressure, and exit gradient (0 m).Table 4
The values of the parameters in the initial state.
ParameterValueTotal seepage from Section1 (m3/s/m2)0.019899Total seepage from Section2 (m3/s/m2)0.017735Average uplift pressure (MPa)502.35Exit gradient0.96888Figure6 shows the percentage of changes in the total seepage of various lengths of the cutoff wall compared to the state without the cutoff wall. According to Figure 6, it is evident that as the length of the cutoff wall increases, seepage decreases, and the amount of reduction in Section 2 relative to the state without the cutoff wall is greater than in Section 1.Figure 6
Percentage reduction of total seepage through Sections1 and 2.As the cutoff wall length increases, the average uplift pressure decreases. Figure7 shows the average changes in uplift pressure based on the percentage difference between the cutoff wall and no cutoff wall.Figure 7
Percentage reduction of average uplift pressure.Increasing the length of the cutoff wall has reduced the exit gradient. Figure8 also shows the changes in the exit gradient compared to the no cutoff wall.Figure 8
Percentage of exit gradient changes.


## 3.2. The Effect of Different Positions of the Cutoff Wall

To investigate the effect of different positions of the cutoff wall, the width of the dam core is divided into 8 points with equal distances from each other, so that the first point is at the heel of the core and the last point is at the toe of the core. Also, cutoff walls with a length of 10 meters have been considered and compared for all situations (a length of 10 meters was considered when attempting to select a typical size for cutoff walls). Table5 presents the values of total seepage, average uplift pressure, and exit gradient at point No. 1. Also, the different positions considered for the cutoff wall are presented in Table 6.Table 5
The values of the parameters in point no 1.
ParameterValueTotal seepage from Section1 (m3/s/m2)0.019689Total seepage from Section2 (m3/s/m2)0.017499Average uplift pressure (MPa)560.13Exit gradient0.96423Table 6
Different positions of the cutoff wall (considering the length of 10 meters of the cutoff wall).
Position no.Distance from the heel of the core (m)1025310415520625730836Figure9 shows the seepage changes in Sections 1 and 2. Position No. 5 in Section 1 has the most changes. Also, moving the position of the cutoff wall did not have much effect on the amount of seepage from Section 2.Figure 9
Percentage of changes in total seepage in Sections1 and 2.Figure10 shows the average change in uplift pressure relative to point 1. According to Figure 10, it is clear that the amount of uplift pressure has increased in all cases. Also, the increase in point No. 8 is more than in other points.Figure 10
Percentage increase in average uplift pressure.Figure11 shows the reduction of the exit gradient in different positions of the cutoff wall. According to Figure 11, in position 2, the maximum decrease occurred, and in position 5, the lowest decrease in the exit gradient occurred.Figure 11
Percentage reduction of exit gradient in different positions of the cutoff wall.


## 3.3. The Effect of Different Lengths of Horizontal Drainage

This section investigates the effect of various horizontal drainage lengths on seepage parameters from Sections1 and 2, as well as uplift pressure and exit gradient. From the dam’s toe, horizontal drainage lengths of 30, 60, 90, 120, 150, and 182 meters are considered for this purpose (the numbers used to determine the length of the drain were chosen according to the width of the dam’s downstream shell).Figures12–14 show the results of the changes relative to the initial condition (Table 3). Figure 12 shows the variations in total seepage through Sections 1 and 2. As shown in Figure 12, the highest seepage of Section 1 occurred during 182 meters of drainage and the highest seepage of Section 2 occurred during 150 meters of drainage.Figure 12
Percentage of seepage changes in Sections1 and 2.Figure 13
Percentage of changes in average uplift pressure.Figure 14
Percentage change of exit gradient in different cases of horizontal drainage length.Figure13 shows the average change in uplift pressure below the dam core. According to Figure 13, with increasing horizontal drainage length, the values of uplift pressure decrease.Figure14 shows the exit gradient changes in different horizontal drainage length cases. According to Figure 14, it is clear that the amount of exit gradient at the dam toe is much less than in other cases, in the case without drainage. Also, the exit gradient values are almost the same in other cases.


## 3.4. The Effect of Different Positions of Horizontal Drainage

This section investigates the effect of different horizontal drainage positions on the seepage parameters of Sections1 and 2, as well as the uplift pressure and exit gradient. The length of 30 meters of horizontal drainage at various distances from the dam (the drain was 30 meters long due to the width of the dam’s shell downstream and the common length selection), including 0 meters, 30 meters, 60 meters, 90 meters, 120 meters, and 152 meters, must have been evaluated and compared for this purpose. Table 7 presents the different positions considered for horizontal drainage.Table 7
Different positions of horizontal drainage (with a length of 30 meters of horizontal drainage).
Position no.Distance from the dam toe (m)1023036049051206152Figures15–17 show the results of the changes compared to the initial state (Table 3). Figure 15 shows the changes in total seepage. According to Figure 15, the amount of total seepage has increased in all positions except position number 6 of Section 2.Figure 15
Percentage of changes in total seepage through Sections1 and 2.Figure 16
Percentage reduction of average uplift pressure in different positions of horizontal drainage.Figure 17
Percentage reduction of exit gradient in different positions of horizontal drainage.Figure16 shows the average uplift pressure reduction in different horizontal drainage positions. As the drainage position approaches the dam core, the amount of uplift pressure below the dam core decreases.Figure17 shows the exit gradient reduction in different horizontal drainage positions. According to Figure 17, the exit gradient in position 1 is much higher than in other positions due to the placement of the dam toe on the drain.


## 4. Conclusion

Increasing the length of the cutoff wall decreased seepage in both sections, with a more significant effect on Section2; it also decreased the uplift pressure and exit gradient. Changing the cutoff wall’s position significantly affects seepage fluctuations in Section 1 but has no effect on seepage in Section 2. From positions 2 to 7, the uplift pressure values are nearly identical, and the exit gradient is most significant at position 1 and least at position 2. Except for the 182 meters of horizontal drainage in Section 2, increasing the length of horizontal drainage has increased seepage in both sections; it has also decreased the uplift pressure and increased the exit gradient. Closer placement of horizontal drainage to the dam core has increased seepage in both sections, except for position 6 in Section 2, and decreased uplift pressure and exit gradient.



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*Source: 6441646-2022-09-25.xml*