Estimating Seepage Quantity through Homogenous Earth-Fill Dam with Horizontal Drainage Using Different Methods

Abstract

Seepage is the main cause of failure of earthen dams; to prevent this failure, excessive seepage problems should be controlled. In this study, lowest seepage quantity through homogenous earth dam with horizontal filter by different methods was estimated. SEEP/W code in (GeoStudio software 2012) and (Slide software 6.025) was used to investigate 972 models with various upstream and downstream face slopes, horizontal filter lengths, free boards, top widths, dam heights and permeability coefficients. Results showed that, comparing the seepage rates obtained from Slide and GeoStudio softwares has average differences of ratio of seepage discharge to permeability coefficient and filter length (q/kL) was less than 2%. Furthermore, nonlinear empirical equation was developed using (SPSS 22) program. The comparison of seepage quantity measured by SEEP/W and Slide versus its quantity calculated from empirical equations gave a coefficient of determination (R 2 = 0.815, 0.788) respectively. Multilinear perceptron (MLP) was used as suitable type of artificial neural network (ANN) with a base structure (5-4-1) in which 75% of data sets were for training and 17.2% were for testing. The quantity of seepage predicted by ANN compared with obtained seepage rates from SEEP/W and Slide has (R 2 =0.923, 0.942) respectively. Finally, the average percent of errors of empirical equation, Slide Program and ANN was 15.814%, 8.519% and 1.060% respectively. This means that, seepage quantities obtained from ANN was more accurate than other methods may be due to different ways of analysis.

Full text

ZANCO Journal of Pure and Applied Sciences
The official scientific journal of Salahaddin University-Erbil
https://zancojournals.su.edu.krd/index.php/JPAS
ISSN (print ):2218-0230, ISSN (online): 2412-3986, DOI: http://dx.doi.org/10.21271/zjpas
RESEARCH
PAPER
Estimating Seepage Quantity through Homogenous Earth-Fill Dam with
Horizontal Drainage Using Different Methods
Jehan M. Sheikh Suleimany1, Bruska S. Mamand2
1,2Department of Dams & Water Resources Engineering, college of Engineering, Salahaddin University- Erbil ,Kurdistan Region,
Iraq
A B S T R A C T
Seepage is the main cause of failure of earthen dams; to prevent this failure, excessive seepage problems should be controlled. In
this study, lowest seepage quantity through homogenous earth dam with horizontal filter by different methods was estimated.
SEEP/W code in (GeoStudio software 2012) and (Slide software 6.025) was used to investigate 972 models with various upstream
and downstream face slopes, horizontal filter lengths, free boards, top widths, dam heights and permeability coefficients.
Results showed that, comparing the seepage rates obtained from Slide and GeoStudio softwares has average differences of ratio of
seepage discharge to permeability coefficient and filter length (q/kL) was less than 2%. Furthermore, nonlinear empirical equation
was developed using (SPSS 22) program. The comparison of seepage quantity measured by SEEP/W and Slide versus its quantity
calculated from empirical equations gave a coefficient of determination (R2 = 0.815, 0.788) respectively.
Multilinear perceptron (MLP) was used as suitable type of artificial neural network (ANN) with a base structure (5-4-1) in which
75% of data sets were for training and 17.2% were for testing. The quantity of seepage predicted by ANN compared with obtained
seepage rates from SEEP/W and Slide has (R2=0.923, 0.942) respectively.
Finally, the average percent of errors of empirical equation, Slide Program and ANN was 15.814%, 8.519% and 1.060%
respectively. This means that, seepage quantities obtained from ANN was more accurate than other methods may be due to
different ways of analysis.
KEY
WO
R
D
S:
Homogenous dam; Seepage quantity; Horizontal filter; SEEP/W; Slide software.
DOI: http://dx.doi.org/10.21271/ZJPAS.32.1.2
ZJPAS (2020) , 32 (1);7-18 .
1. INTRODUCTION
Earth dams are important structures used as
artificial reservoirs consists from impervious
compacted layers of soils for its core and
permeable materials on their upstream and
downstream faces to be safe against sliding and
overturning forces. Seepage is the quantity of
water through an earth dam starts from upstream
of the reservoir level to the downstream toe of the
dam. The upper surface of this stream of
percolating water is known as the phreatic surface.
For the purpose of controlling this phenomenon in
the dam, different types of filters should be
designed. The Laplace equation which governs
water seepage cannot be solved analytically,
except for cases with very simple and special
boundary conditions. In the literature reviews, the
numerical example that proposed equations is
simple to use; hence the designers may find these
equations as an additional check to their design by
the conventional flow net method (Chahar, 2004).
While, a series of tests and different drain sizes
including different filter thicknesses and lengths
were applied to a physical model of an
embankment dam to check the stability in steady
and transient seepage conditions using a number
of piezometers and pressure sensors (Malekpour et
* Corresponding Author:
Jehan M. Sheikh Suleimany
E-mail: jehanmohammed.sheikhsuleimany@su.edu.krd
Article History:
Received: 07/04/2019
Accepted: 18/09/2019
Published: 25/02 /2020

Suleimany. J. and Mamand.B/ZJPAS: 2020, 32 (1): 7-18
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ZANCO Journal of Pure and Applied Sciences 2020
al., 2012). Seepage and Stability of earth dam
were analyzed Using Ansys and GeoStudio
Softwares, the significant difference of two
programs is related to safety factor deducted that
Ansys answer is more acceptable (Kamanbedast
and Delvari, 2012).
The other investigation performed the numerical
simulation to find the effect of horizontal drain
length and cutoff wall on seepage and uplift
pressure in heterogeneous earth dam (Mansuri and
Salmasi, 2013). The case study on ''Hub'' earthen
dam located on (Karachi city-Pakistan) also
investigated. SEEP/W simulation compared with
field observations for seepage analysis.
Calibration of the material properties is made on
the basis of minimization of error while
comparing observed hydraulic heads with the
simulated ones (Arshad and Babar, 2014).
Alnealy and Alghazali (2015) analyzed of seepage
under hydraulic structures using Slide program.
Single and multi- layers soils and its effect on
structures with inclined cut-off were studied.
Casagrandi and Dupuits assumptions were
analyzed to estimate seepage through
homogeneous earth dam without filter (Jamel,
2016). Çalamak et al. (2016) investigated the
suitability and the effectiveness of blanket and
chimney drains in earth fill dams for various
properties of the drainage system. (Irzooki, 2016)
was used SEEP/W code to run on homogenous
earth dam models with horizontal toe drain, a new
equation was found for computing the quantity of
seepage. (Omofunmi et al., 2017) reviewed on
effects and control of seepage through earth-fill
dams. San Luis dam used to evaluate the
unsaturated and transient seepage analysis in
which pore-water pressures at failure and
progression of the phreatic surface through the
fine-grained core for drawdown stability analyses
(Stark et al., 2017).
The goal of this research is to examine the
capabilities of different software’s that estimate
the lowest quantities of seepage to verify the
accurate and optimum one.
2. THORETICAL CONSIDERATION
As clearly explained by Harr (1962), there were
many different assumptions for determining the
seepage quantity as explained below:
 Dupuit's Assumptions: Both discharge
quantity and free surface are independent of
the slopes of the dam. The discharge (per unit
width) through any vertical section of the dam
for the condition of tail water at potential
seepage face are shown in Figure (1-a).
 Schaffernak & Van Iterson: The first
approximate method that accounts for the
development of the surface of seepage
considering an earth dam on an impervious
base shown in Figure (1-b) with no tail water.
 L..Casagrande's: Recommended that point
Do shown in Figure (1-c) instead of point D be
taken as the starting point of the line of
seepage (Do is 0.3∆ from point D at the
upstream reservoir surface). The actual
entrance condition is then obtained by
sketching in the arc DF normal to the upstream
slope and tangent to the parabolic free surface.
 Pavlovsky's Solution: Considered the dam
divided into three zones as shown in figure (1-
d). The upper section (I) bounded by the
upstream slope and y-axis, the central section
(II) by the y-axis and a vertical line through
the discharge point of the free surface and the
lower section (III) by the latter vertical line
and the downstream slope. The streamline in
zone (I) are known to be curvilinear (dotted
curves cd); however, Pavlovsky assumed that
they may be replaced by horizontal streamline
of almost equivalent length (ed) then assuming
purely horizontal flow in zone (I).

Suleimany. J. and Mamand.B/ZJPAS: 2020, 32 (1): 7-18
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ZANCO Journal of Pure and Applied Sciences 2020
Figure 1. Assumptions of seepage quantity through earth dam (Harr, 1962).
2.1 Dimensional Analysis
Dimensional analysis is an important tool to
investigate the relationship between different
variable’s and categorize to convert them into a
smaller number of dimensionless parameters to
identify any phenomenon. In the present study, the
Buckingham's - theorem was used for evaluation
of the manner in which the variables controlled
the seepage quantity through a homogenous earth
dam. The expected factors that affecting on the
seepage quantity for a general section of
homogenous earth dam with horizontal drainage
a. Dupuit's assumptions:
  󰇛

󰇜

b. Schaffernak & Van Iterson: 󰇛󰇜󰇛󰇜
c. L..Casagrande: α
d. Pavlovsky's Solution:  
󰇛󰇜

Suleimany. J. and Mamand.B/ZJPAS: 2020, 32 (1): 7-18
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ZANCO Journal of Pure and Applied Sciences 2020
blanket as sketched in Figure (2), was defined in
Equation (1):
  󰇛 󰇜 . . . . . . . . (1)
The basic variables are (L, q and ) taken as
repeated variables in all -terms, and each of other
variables are presented in each -terms. After
performing the dimensional analysis, new
expression was found as shown in Equation (2):
  󰇡
 
󰇢 . . . ... . . . . . . . . (2)
In which the obtained dimensionless parameters
from the above equation can be defined as: 󰇛󰇜 is
the slope of the upsteam face of the dam,󰇛󰇜 is
the slope of the downsteam face of the dam,
󰇛/H) is the dimensionless ratio of the dam
freeboard to its height, (b/L) is the proportion of
top width of the dam to the span of the horizontal
blanket filter and (q/kL) ratio related to the
permeability coeffeicient of the soil with seepage
quantity and the length of horizontal blanket filter.
Figure 2. Overall sector of homogenous earth dam.
3. METHODOLOGY OF THE STUDY
Methodology of this study was conducted on the
total of 972 homogenous earth dam models. These
models includes the summation of 486 runs that
done by GeoStudio (SEEP/W code) and also 486
runs done by (Slide) software taking into
consideration the same models for each test in
both software. Different geometries of
homogenous dam were created and the material
for dam body and filter modeled with hydraulic
conductivity data point function. The details of
selected variables are shown in Table (1), in
which it consists of two different upstream and
downstream slopes of the dam and three different
values for each: dam height, filter length,
permeability coefficient, free board and top width.
As explained in Figure (3), the upstream boundary
blue nodes are designated as head boundaries with
total head equal to the water level in the reservoir.
The downstream toe is assigned a total head of 0.0
m (H = elevation). The downstream slope is
assigned a potential seepage face type of boundary
condition. Also the Slide software can be
automatically utilized by the seepage
analysis engine because it has the capability to
carry out a finite element groundwater seepage
analysis for steady state or transient conditions.
Table (1). Conducted dam section variables for both GeoStudio & Slide programs.
D/S & U/S
slope (α, θ)
Variables
1
2
3
α1= 2:1
θ1=2.5:1
α2= 2.5:1
θ2=3:1
H: Dam Height (m)
14
16
18
b: Top Width (m)
4
6
7
L: Filter Length (m)
10
20
25
FB: Free Board (m)
1
1.5
2
k: Permeability Coefficient (m/s)
1*10-4
1*10-5
1*10-6

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ZANCO Journal of Pure and Applied Sciences 2020
Figure 3. Location of the boundary conditions of homogenous earth dam.
4. RESULTS AND DISCUSSION
The main sections of this study deal with the
effect of dimensionless parameters in regards of
homogenous dam on the seepage quantity of the
dam itself. Results of each part were concluded
separately in the following configurations:
4.1 Mesh Size Dependence
In order to test mesh dependence on the amount of
seepage discharge, four types of meshes as quads
and triangles, triangles only, rectangular grid of
quads and triangular grid of quads was
investigated. The result of each method on the
first run is shown in Table (2). The differences in
seepage quantities was a small fractions but quads
and triangles grid type was selected in all runs
because of the lowest seepage quantity.
Table (2). Seepage quantification using different grid types.
Grid Type
No. of
Elements
No. of
Nodes
Seepage
discharge (m3/s)
Quads and triangles
500
559
3.726*10-6
Triangles only
495
299
3.782*10-6
Rectangular grid of quads
497
545
3.844*10-6
Triangular grid of quads / triangles
468
512
3.799*10-6
4.2 Effect of the Thickness of Filter
In this study the thickness of filter was
investigated and compared with the dam section
assuming filter thickness as zero. For this purpose
two tests were done, first test was on the dam
section having one grid thickness of the horizontal
filter. The results of seepage quantity for 13m
reservoir head was (3.7243*10-4 m3/s) as shown in
Figure (4-a); whereas the second test of dam
section with no filter thickness gave as
(3.7375*10-4 m3/s) as a seepage quantity inside the
dam body as shown in Figure (4-b).The difference
between seepage quantities of both runs was
(1.32*10-6 m3/s) which can be ignored.
4.3 Effect of the Dimensionless Parameters on
Seepage Quantity
In this section, the effect of dimensionless
parameters that computed from SPSS was clearly
investigated. Figure (5) and Figure (6)
demonstrate the relationship between the
dimensionless parameter (q/kL) versus upstream
and downstream slopes respectively. Results
Potential
Seepage Face
Zero Pressure
Reservoir Head
Dam Height = 13 m
Base Width = 67 m
Freeboard = 1 m
Filter Length = 10 m
Top Width = 4 m
Permeability Coefficient = 0.0001 m/s

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ZANCO Journal of Pure and Applied Sciences 2020
showed that the quantity of seepage obtained from
Slide software was smaller than that of SEEP/W
for the same effecting variables on the dam. In
which the average difference of (q/kL) between
both software was 1.696%. Also, both figures
explained that seepage quantity increases as the
upstream and downstream face slopes were
increased.
Figure (7) shows the relationship between (q/kL)
and (FB/H) for Slide and SEEP/W software’s. The
effect of the freeboard on the seepage quantity
was investigated in which seepage quantity
decrease with increasing the height of freeboard
when a height of dam not more than 18m.
Figure (8) demonstrates the relation between
(q/kL) and (b/L). For the range of (b/L = 0.2 to
0.6) the seepage quantity decreases with
increasing the top width of the dam. While, it
increased with increasing length of horizontal toe
drain.
Figure 4. SEEP/W runs to explain the effect of filter thickness.
3.7243*10-4 m3/s
3.7375*10-4 m3/s
b. Filter thickness = zero
a. Filter thickness = 1m

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Figure 5. Relationship between (q/kL) and (tanθ).
Figure 6. Relationship between (q/kL) and (tanα).
Figure 7. Relationship between (q/kL) and (FB/H).
0.18
0.22
0.26
0.30
0.34
0.38
0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52
q/kL
tanθ
FB=1m, H=14m, tanα = 0.5, k=10-6 m/s L=10m, b=4m (GeoStudio)
L=20m, b=6m (GeoStudio)
L=10m, b=6m (GeoStudio)
L=20m, b=4m (GeoStudio)
L=10m, b=4m (Slide)
L=20m, b=6m (Slide)
L=10m, b=6m (Slide)
L=20m, b=6m (Slide)
0.18
0.22
0.26
0.30
0.34
0.38
0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52
q/kL
tanα
FB = 1m, H=14m, tanθ = 0.4, k=10-6 m/s L=10m, b=4m (GeoStudio)
L=20m, b=6m (GeoStudio)
L=10m, b=6m (GeoStudio)
L=20m, b=4m (GeoStudio)
L=10m, b=4m (Slide)
L=20m, b=6m (Slide)
L=10m, b=6m (Slide)
L=20m, b=4m (Slide)
0.18
0.22
0.26
0.30
0.34
0.38
0.05 0.07 0.09 0.11 0.13 0.15 0.17
q/kL
FB/H
tan θ= 0.4, tanα = 0.5, k=10-4 m/s L=10m, b=4m (Geostudio)
L=20m, b=6m (GeoStudio)
L=10m, b=6m (GeoStudio)
L=20m, b=4m (GeoStudio)
L=10m, b=4m (Slide)
L=20m, b=6m (Slide)
L=10m, b=6m (Slide)
L=20m, b=4m (Slide)

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ZANCO Journal of Pure and Applied Sciences 2020
Figure 8. Relationship between (q/kL) and (b/L).
4.4 Empirical Equation for Determining the
Seepage Quantity
In this section, the SPSS statistical software was
used for predicting empirical general
relationships. This relations was represented the
relating independent pi-terms which significantly
affect the seepage quantity per unit width. For this
purpose the seepage quantities that obtained from
SEEP/W and Slide software were examined in
SPSS based on the dimensional analysis pi-terms.
Two new expressions were obtained as Equation
(3) based on GeoStudio results and equation (4)
based on seepage quantities obtained from Slide
software.
  󰇛󰇜 󰇛 󰇜󰇛󰇜
󰇛
󰇜󰇛
󰇜 󰇛󰇜
  󰇛󰇜 󰇛 󰇜󰇛󰇜
󰇛
󰇜󰇛
󰇜 󰇛󰇜
The empirical equation in regards of calculated
values of seepage discharge should be compared
with the measured seepage discharges. For the
purpose of predict a best relation, non-linear
regression equations were founded. Figure (9)
shows the seepage quantities obtained from
GeoStudio and Slide program was compared with
its quantities calculated from Equations (3 and 4)
respectively. Best fitting intercept line was
selected to show a better regression depends on
high determination coefficient (R2). Eventually,
results explained that the seepage rates from
SEEP/W code versus Equation (3) gave higher
determination coefficient (R2=0.815), whereas it
was (R2=0.788) in comparison between seepage
rates from Slide software versus Equation (4).
0.18
0.22
0.26
0.30
0.34
0.38
0.24 0.3 0.36 0.42 0.48 0.54 0.6
q/kL
b/L
L=20m, tanθ = 0.4, tanα = 0.5, k=10-6 m/s FB=1m, H=14m (GeoStudio)
FB=2m, H=16m (GeoStudio)
FB=1m, H=16m (GeoStudio)
FB=2m, H=14m (GeoStudio)
FB=1m, H=14m (Slide)
FB=2m, H=16m (Slide)
FB=1m, H=16m (Slide)
FB=2m, H=14m (Slide)

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ZANCO Journal of Pure and Applied Sciences 2020
Figure 9. Comparisons of seepage rates found from GeoStudio and Slide with calculated seepage rates from
empirical equations.
4.5 Artificial Neural Network (ANN)
ANN is a nonlinear mathematical model that can
simulate arbitrarily complex nonlinear processes
that relate the inputs and outputs of any system. In
many complex mathematical problems that lead to
solving complex nonlinear equations, Multilayer
Perceptron (MLP) and radial basis function (RBF)
networks are common types of ANN that are
widely used in water resources engineering
(Parsaie and Haghiabi, 2018). In this
investigation, the MLP model was used to define
of appropriate functions, weights and bias that
should be considered. For this purpose the seepage
quantity through homogenous earthen dam
sections were collected. The datasets were divided
in to two groups as training and testing, 75% was
for training and 17.2% was for testing with 7.8%
for validation (holdout). An ANN may have
different values of input, hidden and output layers.
Therefore the base structure of this investigation
was (5-4-1) this means that: five inputs, four
hidden layers and one output. Figure (10) shows
that the accuracy of the ANN models for
calculating the seepage discharge through
homogenous earth dam. The quantity of seepage
predicted by ANN was compared with the seepage
quantity from SEEP/W and Slide software, the
determination coefficients for these relations was
R2= 0.923 and R2= 0.942 respectively. This means
that slide software gave accurate results than that
of SEEP/W code.
R² = 0.8146
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008
Seepage
discharge
calculated by eqn.
(3) (m3/s)
R² = 0.7881
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008
Seepage discharge
calculated by eqn. (4)
(m3/s)
Seepage discharge in (m3/s)
Slide Software
(SEEP/W) code

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Figure 10. Comparisons of seepage rates found from GeoStudio and Slide with calculated seepage rates
from ANN.
4.6 Comparison of Seepage Quantity by
Different Methods
Figure (11) shows the comparison between
seepage discharges obtained from different
methods. It seems that among 64 runs of each
method, the seepage quantities were divided as
group points based on the same dimensions of the
dam, reservoir level and permeability coefficient.
There are small fractions in differences between
them. In which; seepage quantities that obtained
from SEEP/W code was much greater than the
amount that obtained from slide software for the
condition of ignoring tail water at the potential
seepage face and approximated phreatic line of the
homogenous dam.
For more details on the differences in seepage
rates, the average percent of errors in each method
based on the seepage quantities obtained from
SEEP/W code was shown in Table (3). This table
demonstrates that SEEP/W seepage quantities
compared with its quantity obtained from ANN
and Slide software has the average percent errors
about 1.060% and 8.519% respectively. On the
other hand, SEEP/W quantities compared with its
quantity obtained from Equation (3) of this
investigation, it has 15.814% average errors in
seepage rates.
Eventually, the maximum seepage quantity
obtained from ANN was (6.856*10-4 m3/s) which
is less seepage rates than the quantities measured
by other methods taking into consideration of the
same affecting dimensionless parameters.
Table (3). Different % errors of seepage quantity with comparing to SEEP/W.
Seepage quantities
obtained from:
Empirical
Equation (eqn. 3)
Slide Program
Artificial Neural
Network
Average Errors:
15.814 %
8.519 %
1.060 %
R² = 0.9234
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008
Seepage discharge
by ANN (m3/s)
R² = 0.9421
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008
Seepage discharge by
ANN (m3/s)
Seepage discharge (m3/s)
(SEEP/W) code
Slide Software

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ZANCO Journal of Pure and Applied Sciences 2020
Figure 11. Comparison of seepage quantities by different methods.
5. CONCLUSIONS
The key messages of this study are the following:
1. The slight increasing in quantity of seepage
was observed with increasing the upstream
and downstream slopes of the earth dam.
2. The quantities of seepage increases with
increasing horizontal toe drain and decreasing
top width of the earth dam.
3. The seepage quantity obtained from
GeoStudio software was greater than its
quantity attained from Slide software. In
which, the average difference of dimensionless
parameter (q/kL) between Slide software and
SEEP/W code was 1.696 %.
4. The seepage rates measured by Slide software
was compared with its quantity achieved by
ANN. This relation gave a higher
determination coefficient (R2 = 0.942) than
nonlinear empirical equations found from
SPSS.
5. SEEP/W seepages compared with its quantity
obtained from ANN and Slide software has the
average percent of errors less than 1.5 % and 9
% respectively.
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0
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0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64
Seepage discharge by different
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