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Finite element analysis of the se ods. Cakir [12] sophisticated a numerical model for the two-dimensional groundwater flow using the collocation method. For the purpose of comparison, they prepared a MATLAB program with the FDM. Quanshu and Ji- anjun [13] adopted a numerical simulation method for leakage analysis and investigated the influence of core and other factors by comparing the leakage area under dif- ferent conditions. Mansuri and Salmasi [14] focused on the effectiveness of using horizontal drainage and cutoff wall in reducing seepage flow from a heterogeneous earth dam. For this purpose, they investigated the effect of var- ious horizontal drainage lengths and shear wall depths on seepage under the earth dam at different locations of the foundation. Sakhmarsi et al. [15] investigated the in- fluence of cutoff wall depth, position, and permeability properties on seepage in the homogeneous earth-fill dams using SEEP/W computer software. Yuan and Zhong[16] used the weak-form quadrature element method for the analysis of three-dimensional unconstrained seepage problems. Zhang et al. [17] proposed a moving kriging mesh-free method with Monte Carlo integration to deter- mine the phreatic surface while investigating the seepage analysis. Khassaf and Madhloom [18] found the quanti- ty of seepage that occurs in soil dams with the effect of changing the core permeability and the core thickness of a core region by using the FEM SLIDE V.5.0 software. Ze- wdu[19], calculated the amount of the seepage occurring in the Koga earth-fill dam body and foundation using the finite element-based PLAXIS 2D software. Taghvaei et al. [20] prepared numerical modeling of earth dam in different clay-sand compositions using SEEP/ W software and validated it with experimental results. In their paper, Doaaand Molla [21] aimed to determine the effect of the existence of the sheet pile as well as its height and location on the total seepage discharge and velocities through the dam’s cross-section. Sanayei and Javdanian [22] developed a new analytical solution for steady seepage from dams with nonsymmetric boundary conditions. Non-sym- metrical boundary conditions for two-dimensional cases Figure 1. Flow of water through saturated pervious soil beneath a hydraulic structure metrical boundary conditions for two-dimensional cases

Figure 1 Finite element analysis of the se ods. Cakir [12] sophisticated a numerical model for the two-dimensional groundwater flow using the collocation method. For the purpose of comparison, they prepared a MATLAB program with the FDM. Quanshu and Ji- anjun [13] adopted a numerical simulation method for leakage analysis and investigated the influence of core and other factors by comparing the leakage area under dif- ferent conditions. Mansuri and Salmasi [14] focused on the effectiveness of using horizontal drainage and cutoff wall in reducing seepage flow from a heterogeneous earth dam. For this purpose, they investigated the effect of var- ious horizontal drainage lengths and shear wall depths on seepage under the earth dam at different locations of the foundation. Sakhmarsi et al. [15] investigated the in- fluence of cutoff wall depth, position, and permeability properties on seepage in the homogeneous earth-fill dams using SEEP/W computer software. Yuan and Zhong[16] used the weak-form quadrature element method for the analysis of three-dimensional unconstrained seepage problems. Zhang et al. [17] proposed a moving kriging mesh-free method with Monte Carlo integration to deter- mine the phreatic surface while investigating the seepage analysis. Khassaf and Madhloom [18] found the quanti- ty of seepage that occurs in soil dams with the effect of changing the core permeability and the core thickness of a core region by using the FEM SLIDE V.5.0 software. Ze- wdu[19], calculated the amount of the seepage occurring in the Koga earth-fill dam body and foundation using the finite element-based PLAXIS 2D software. Taghvaei et al. [20] prepared numerical modeling of earth dam in different clay-sand compositions using SEEP/ W software and validated it with experimental results. In their paper, Doaaand Molla [21] aimed to determine the effect of the existence of the sheet pile as well as its height and location on the total seepage discharge and velocities through the dam’s cross-section. Sanayei and Javdanian [22] developed a new analytical solution for steady seepage from dams with nonsymmetric boundary conditions. Non-sym- metrical boundary conditions for two-dimensional cases Figure 1. Flow of water through saturated pervious soil beneath a hydraulic structure metrical boundary conditions for two-dimensional cases

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In seepage problems, boundary conditions are used to solve the main differential equation of seepage. Boundary conditions are related to initial conditions and different flow patterns of the system. The boundary conditions do not depend on time under steady-state flow conditions. In this study, upstream and downstream levels are defined as constant head boundary conditions in order to model the seepage through the considered dams. A seepage line may be formed at the downstream region of the dam. Bound- ary conditions for seepage problems of the embankment dam with tailwater in the downstream region are given in Figure 2. Figure 2. Seepage and boundary conditions in an embankment dam
In seepage problems, boundary conditions are used to solve the main differential equation of seepage. Boundary conditions are related to initial conditions and different flow patterns of the system. The boundary conditions do not depend on time under steady-state flow conditions. In this study, upstream and downstream levels are defined as constant head boundary conditions in order to model the seepage through the considered dams. A seepage line may be formed at the downstream region of the dam. Bound- ary conditions for seepage problems of the embankment dam with tailwater in the downstream region are given in Figure 2. Figure 2. Seepage and boundary conditions in an embankment dam
Figure 3. Geometry and material properties of the dam Firstly, time indepented seepage phenomenon has been investigated in the homogeneous isotropic fill dam body. The material and geometrical properties are given in Fig- ure 3.
Figure 3. Geometry and material properties of the dam Firstly, time indepented seepage phenomenon has been investigated in the homogeneous isotropic fill dam body. The material and geometrical properties are given in Fig- ure 3.
Table 3. Seepage rate per unit width of dams with different soil properties (m?/s/m)
Table 3. Seepage rate per unit width of dams with different soil properties (m?/s/m)
From Table 2, it can be clearly seen that the highest hy- draulic head and pressure load values are in the region of the upstream part close to the foundation. The seepage quantity of dams in different situations with isotropic and anisotropic filling material properties are
From Table 2, it can be clearly seen that the highest hy- draulic head and pressure load values are in the region of the upstream part close to the foundation. The seepage quantity of dams in different situations with isotropic and anisotropic filling material properties are
Table 4. Seepage rate per unit width of dams with horizontal drain- age of different lengths (m?/s/m) Table 4 presents that the amount of seepage per unit width increases as the horizontal drainage length increases.
Table 4. Seepage rate per unit width of dams with horizontal drain- age of different lengths (m?/s/m) Table 4 presents that the amount of seepage per unit width increases as the horizontal drainage length increases.
Table 6. Seepage rate per unit width of the dam foundation (m?/s/m)
Table 6. Seepage rate per unit width of the dam foundation (m?/s/m)
Table 5. Seepage rate per unit width of the dam (m?/s/m)
Table 5. Seepage rate per unit width of the dam (m?/s/m)
Example 5 Also, for the horizontal undrained (Case 3) and horizon- tally drained embankment dams with anisotropic mate- rial, the location of the phreatic line is determined and shown in Figure 6. It can be seen in Figure 7, that the seepage line in dams with horizontal drainage is inside the dam body and it cannot cause any possible damage to the downstream re- gion due to piping. This result demonstrates the impor- tance of using the horizontal drains to control the posi- tion of the phreatic line for the stability of earthen dams.
Example 5 Also, for the horizontal undrained (Case 3) and horizon- tally drained embankment dams with anisotropic mate- rial, the location of the phreatic line is determined and shown in Figure 6. It can be seen in Figure 7, that the seepage line in dams with horizontal drainage is inside the dam body and it cannot cause any possible damage to the downstream re- gion due to piping. This result demonstrates the impor- tance of using the horizontal drains to control the posi- tion of the phreatic line for the stability of earthen dams.
Figure 6. Geometry and material properties of the dam with horizon- tal drainage
Figure 6. Geometry and material properties of the dam with horizon- tal drainage
Figure 8. Geometry and material properties of the dam for the rectangular dam body with water in the down- stream region. The geometric and material properties are given in Figure 8. The results obtained in this section are given in Table 5 and compared with those of Parsi and Daneshm [33] and Parsi [34]. They [33, 34] examine the position of the phreatic surface, which is unknown at the beginning of the solution and must be determined in an iterative process, with different theories.
Figure 8. Geometry and material properties of the dam for the rectangular dam body with water in the down- stream region. The geometric and material properties are given in Figure 8. The results obtained in this section are given in Table 5 and compared with those of Parsi and Daneshm [33] and Parsi [34]. They [33, 34] examine the position of the phreatic surface, which is unknown at the beginning of the solution and must be determined in an iterative process, with different theories.
Figure 9. Geometry and material properties of the dam
Figure 9. Geometry and material properties of the dam
Table 7. Hydraulic head and pressure load values of the dam
Table 7. Hydraulic head and pressure load values of the dam
The authors thank the Scientific Research Projects Direc- torate of Cukurova University for supporting the present study (FBA-2019-12058). Figure 10. Geometry and material properties of the dam with cutoff wall (Example 6) Table 8. Seepage rate per unit width of dams with cuttoff wall of different depths (m*/s/m) Acknowledgements In the last example, the effect of the cutoff wall shown in Figure 10 on the quantity of seepage from the dam foun- dation has been investigated. An impermeable cutoff wall with depths of 7, 8, 9, 10, 11, and 12 m has been installed at the upstream ends of the dam model. For a cutoff posi- tion at the upstream end of the dam, the rate of the seep- age discharge from the foundation in the depth of 7- 12 m, the rate of seepage discharge reduction to the base model are 28.97%, 32.43%, 35.72%, 38.85%, 41.84%, and 44.69 % respectively. From Table 8 it can be understood that the cutoff wall has a significant effect on the seepage and the seepage decreases as its length increases.
The authors thank the Scientific Research Projects Direc- torate of Cukurova University for supporting the present study (FBA-2019-12058). Figure 10. Geometry and material properties of the dam with cutoff wall (Example 6) Table 8. Seepage rate per unit width of dams with cuttoff wall of different depths (m*/s/m) Acknowledgements In the last example, the effect of the cutoff wall shown in Figure 10 on the quantity of seepage from the dam foun- dation has been investigated. An impermeable cutoff wall with depths of 7, 8, 9, 10, 11, and 12 m has been installed at the upstream ends of the dam model. For a cutoff posi- tion at the upstream end of the dam, the rate of the seep- age discharge from the foundation in the depth of 7- 12 m, the rate of seepage discharge reduction to the base model are 28.97%, 32.43%, 35.72%, 38.85%, 41.84%, and 44.69 % respectively. From Table 8 it can be understood that the cutoff wall has a significant effect on the seepage and the seepage decreases as its length increases.
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