The Journal of Engineering Research (TJER), Vol. 15, No. 2 (2018) 114-123
DOI: 10.24200/tjer.vol15iss2p114-123
Evaluation of Actual Creep Length Under Heading up
Structures Aprons
M.A. El Mollaa, N.Y. Saadb,*, and G.S. Ezizahb
a Civil Engineering Department, Higher Technological Institute, Cairo, Egypt.
b Irrigation and Hydraulics Department, Faculty of Engineering, Ain Shams University, Cairo, Egypt.
Received 13 January 2016; Accepted 26 November 2017
Abstract : In this paper a 2D finite element model (SEEP2D) is implemented to study the actual head
loss along the sheet piles fixed at the ends of an apron of a heading up structure. Different scenarios
for the thickness of the pervious layer under the apron, the length of the apron and the depths of the
upstream and downstream sheet piles are studied. Results show that assuming the outer and inner
faces of the sheet piles have the same weight for estimating the creep length while designing aprons
of hydraulic structures is weak. Design equations for the actual head loss along the outer and inner
faces for both the upstream and downstream sheet piles are driven. These equations can be used as a
tool in the practical design for aprons of heading up structures formed on pervious soil and provided
with upstream and downstream sheet piles at its ends.
Keywords: SEEP2D; Seepage; Heading-up structures; Sheet piles; Creep length.
اهلياكل فوق مئزرتقييم طول الزحف الفعلي
ب، غادة س عزيزة ب،*يوسف سعد .نيفني ،أحممد علي املوىل
لدراسة الفقدان الفعلي للقمة (SEEP2D) احملدود الطبقة التحتيةيتم تطبيق منوذج لعنصر البحثية،يف هذه الورقة :امللخص
سيناريوهات خمتلفة لسمك الطبقة دراسة ويتمالعلوية اهلياكلاملتواجدة على طول أكوام االطبقات املثبتة يف نهايات مئزر
النتائج أن االفرتاض بأن روتظه .والسفليةوطول املئزر وكذلك أعماق أكوام الطبقات العلوية املئزر،القابلة لالخرتاق حتت
طول الزحف املقدر عندما يكون تصميم مآزر اهلياكل نفس وزناألوجه اخلارجية والداخلية ألكوام الطبقات هلا
للقمة على طول األوجه اخلارجية والداخلية للخسارة الفعليةويتم عمل معادالت التصميم .ضعيفهو إفرتاض اهليدروليكية
هذه املعادالت كأداة يف التصميم العملي ملآزر ترتكز على ستخداما والسفلية. وميكنلكل من أكوام الطبقات العلوية
.نهاياتها العلوية والسفلية يفومزودة بأكوام من الطبقات لالخرتاق،هياكل متكونة على تربة قابلة
.طول الزحف ،مرتاكمةطبقات ،هياكل علوية ،تسرب :الكلمات املفتاحية
* Corresponding author’s email: neveen_yousif@hotmail.com
mailto:neveen_yousif@hotmail.com
M.A. El Molla, N.Y. Saad, and G.S. Ezizah
115
Notations
The following symbols are used in this paper.
d1 Depth of upstream sheet pile (L);
d2 Depth of downstream sheet pile (L);
hO1 Head lost along the outer face of upstream sheet pile (L);
hO2 Head lost along the outer face of downstream sheet pile (L);
hI1 Head lost along the inner face of upstream sheet pile (L);
hI2 Head lost along the inner face of downstream sheet pile (L);
g Gravitational acceleration (L/T2);
H Head difference between upstream and downstream the apron (L);
K Hydraulic conductivity of the homogeneous pervious stratum (L/T);
L Horizontal distance between the upstream and downstream sheet
Piles (L);
P1 Head at point (1) (L);
P2 Head at point (2) (L);
P3 Head at point (3) (L);
P4 Head at point (4) (L);
P5 Head at point (5) (L);
P6 Head at point (6) (L);
T Thickness of pervious stratum under the apron (L);
ρ Density of seeping water (M/L3);
Evaluation of Actual Creep Length Under Heading up Structures Aprons
116
1. Introduction
Seepage is one of the most important factors
that affects the stability of a heading-up
structure. Using sheet piles under the aprons of
heading-up structures increases the percolation
length, decreases the hydraulic gradient, and
hence provides more safety against piping and
uplift under the apron of a structure. Figure (1)
represents the concept of creep length and
hydraulic gradient diagram.
Numerical methods (Finite Element, Finite
Difference, Boundary Element and Total
Variation Diminishing Method ) can be used to
solve seepage problems with different degrees of
complexities and accuracies Harr (1962); Serge
Leliavsky (1965); U.S. Army Corps of Engineers
(1986). Ahmed and Ellboudy (2010) carried out
a number of numerical analysis to study the
influence of different sheet pile configurations
on the seepage losses, the uplift force on the
apron, and the exit gradient at the end of the
apron. They concluded that driving a sheet pile
under a hydraulic structure that surrounds the
downstream floor apron from all sides, has
greatly reduced the exit gradient at the end toe
of the floor. However, this was accompanied
with some increase in the uplift force. Ahmed
(2011) studied different sheet piles
configurations and flow through canal banks.
Kamble et al. (2014) described the potential of
different approaches such as geological and
geotechnical methods, dam instrumentation,
geophysical methods, tracer techniques, nuclear
logging and mathematical modeling for
monitoring, detecting and analyzing seepage in
hydraulic structures.
Three dimensional modeling techniques (3D)
have recently been attempted to study seepage
beneath and around hydraulic structures for
different purposes. Eftekhar and Barani (2013)
used SEEP3D to pinpoint the best locations of
cutoff walls. They revealed that a cutoff wall
installed at the lower toe of the structure
eliminates piping and the one located at the
upper toe reduces the uplift pressure. Guerra et
al. (2012) suggested that complex junctions in
levee systems (i.e. 90 degrees bend in the levee
alignment as well as a box culvert through the
levee) should be studied using 3D models.
Koltuk and Iyisan (2013) compared between the
2D and 3D modeling techniques in studying a
rectangular shaped cofferdam taking into
account the vertical anisotropy of the permea-
bility of soil layers. He concluded that the
difference between the values obtained from 2D
and 3D analysis decreased with increasing the
length to width ratio of the cofferdam. Gad et al.
(2016) conclude that 3D simulations are
essential in studying seepage under large dams
especially in complicated 3D configurations and
lateral heterogeneity.
El Tahan and ElMolla (2013) used the electric
analogue method to investigate models of
hydraulic structures' aprons provided with two
equal cutoffs. They investigated the efficiency of
both faces (outer and inner) of these cutoffs.
They concluded that the estimation of the
percolation length under the hydraulic structure
must consider a weighted length factor for
various faces of the cut-offs.
SEEP2D is a finite element program that has
been applied in many researches to study
seepage and has proved to be an efficient tool
for seepage analysis (Ozkan 2003; Noori and
Ismaeel 2011; Anas 2012; Aboulatta et al. 2014).
ElMolla (2001) used SEEP2D to investigate
seepage under the aprons of heading up
structures provided with a single cut-off.
In this paper, SEEP2D is used to investigate
the actual head loss along the sheet piles fixed at
the ends of an apron of a heading up structure
formed on a pervious soil. Equations of the
relation between head loss along both faces
(outer and inner) of upstream (U.S.) and
downstream (D.S.) sheet piles and the involved
variables will be driven to be used in creep
length designing purpose which, to the best of
the authors’ knowledge, has not been covered in
the literature yet.
Figure 1. Line of creep and hydraulic gradient
diagram (after Serge Leliavsky, 1965).
M.A. El Molla, N.Y. Saad, and G.S. Ezizah
117
In this study sensitivity analysis for the
variables involved in the problem as well as
different scenarios for the thickness of pervious
layer under the apron, the length of the apron,
the depths of the upstream and downstream
sheet piles, and the hydraulic conductivity are
studied.
2. Dimensional Analysis
In the present study, all the variables involved
in the problem can be expressed as (Refer to Fig.
(2)):
F (H, d1,d2,L,T,k,r,g,P1,P2,P3,P4, P5,P6 = 0 (1)
where: H = Head difference between upstream
and downstream the apron; d1 & d2 = depth of
upstream and downstream sheet pile
respectively; L = Horizontal distance between
the upstream and downstream sheet piles; T =
Thickness of pervious stratum under the apron;
K= Hydraulic conductivity of the homogeneous
pervious stratum under the apron; ρ= Density
of seeping water; g = Gravitational acceleration;
P1, P2, P3, P4, P5, P6 = Head at points(1,2,3,4,5,6).
Applying Buckingham's π Theorem, the
relationship between the above different
variables can be presented as follow:
0)
h
h
,
h
h
,
H*g
k
,
d
T
,
T
L
,
d
d
(
2I
2O
1I
1O
22
1 (2)
where
32
21
1
1
PP
PP
h
h
I
O
(3)
and
54
65
2
2
PP
PP
h
h
I
O
(4)
hO1/ hI1 = the ratio between the head loss along
the outer face and the inner face of the U.S sheet
pile, and hO2/hI2 = the ratio between the head
loss along the outer face and the inner face of
the D.S sheet pile.
3. Description of the Model
The SEEP2D software was developed by the
United States Army Engineer Waterways
Experiment Station to model a variety of
problems involving seepage. The governing
equation used in this model is the Laplace
equation. Laplace equation is the governing
differential equation for two dimensional,
steady state incompressible, isotropic flow in
the xy plane which is
0
y
h
x
h
2
2
2
2
(5)
where h is the head at any point in the flow
domain.
Transient or time varying problems and
unconfined plan view (aerial ) models cannot be
modelled using SEEP2D. SEEP2D allows for
different hydraulic conductivities along the
major and minor axes (anisoropic conditions) to
be defined. Heterogeneous models can be
created by specifying different values of
hydraulic conductivity for the elements
representing the different layers or regions.
Post-processing includes contouring of the total
head (equipotential lines), drawing flow vectors,
and computing flow potential values at the
nodes. These values can be used to plot flow
lines together with the equipotential lines (i.e.
flow nets). The phreatic surface can also be
displayed (SEEP2D Primer 1998).
Figure 2. The variables involved in the problem.
Evaluation of Actual Creep Length Under Heading up Structures Aprons
118
In a typical modelling problem involving the
SEEP2D software, a series of tasks are
performed in a specific sequence as follows: 1.
Mesh generation 2. Setting boundary
conditions; 3. SEEP2D execution; and 4. Post-
processing the output.
4. Model Application
The dimensions for different variables as
recommended from a previous study Ezizah et
al. (2000) are as follows:
d1 = (0.2 to 0.6)*L, d2/d1 = (0.7 to 0.2) , H/L =
(1/2, 1/3, 1/6, 1/8) , d1/T = (0.1 to 0.5) or T=
1.5L.
The model consists of a heading up structure
formed on a pervious homogeneous isotropic
soil layer with thickness T (T=15, 22.5,30, 60 m).
Two values of head difference (H) between U.S
and D.S the structure are considered (H=3, 7 m).
The apron of the structure is of length L (L=10,
15, 20 m) and provided with two sheet piles at
its ends driven to depths d1 and d2, where d1 is
the depth of the U.S sheet pile (d1= 3,4,5,6 m)
and d2 is the depth of the D.S sheet pile (d2=1.5,
2.5 m).
Figure (3) shows a finite element mesh used
for one of the simulations. Figure (4) shows a
Sample of flow net obtained from SEEP2D
(SEEP2D output).
4.1 Boundary Conditions
All external edges of the problem were
modelled as impermeable boundaries including
the upstream and downstream edges and the
bottom of the problem. The apron of the
hydraulic structure was also modelled as
impermeable boundary. All upstream nodes of
the structure in the canal bed were allocated a
prescribed head (H) (H=3 or 7 m). Nodes in the
canal bed downstream of the structure were
assigned a prescribed head value of zero.
4.2 Calibration and Verification of the
Model
Experimental readings of a previous study El
Tahan and ElMolla (2013) were used to calibrate
the model to choose a reasonable cell size and
check that the input data were entering
correctly. Three different mesh cell sizes were
Figure 3. Sample of SEEP2D mesh.
Figure 4. Sample of flow net obtained from SEEP2D (SEEP2D output).
M.A. El Molla, N.Y. Saad, and G.S. Ezizah
119
used in order to calibrate the model in an
attempt to match the experimental data. Then
Mesh would be generated as smaller mesh cell
sizes were chosen around and between the two
sheet piles in order to accurately show the
changes in head when using sheet piles. The
experimental study includes two equal sheet
piles under the apron of the heading up
structure.
Two values of H were used H= 3, 6 m, L was
taken 15 and 20m while d1 and d2 were taken
5m.
Figure (5) illustrates a sample of the model
calibration using the chosen best cell size, which
represents the head readings at points P1 to P6.
It is obvious that there is a good matching
between the experimental readings and the
numerical model.
Using the calibrated mesh size, the model is
verified by another set of electric analogue
experimental readings (AboulAtta et al. 2010).
The length of apron L= 19m, the depth of the
U.S and D.S sheet pile d1= 5m, d2= 2.5m. Two
values for H (3, 7.5m) were used. Figure (6)
illustrates a sample of the model verification,
which represents the head readings at points P1
to P6. It is obvious that there is a good matching
between the experimental readings and the
numerical model.
4.3 Sensitivity Analysis
Sensitivity analysis was carried out in order
to find the most effective parameters for
different variables. From the sensitivity analysis
it is noticed that the variables which have the
biggest effect on the head loss ratio along the
upstream sheet pile are the thickness of
pervious soil layer under the apron (T) and the
depth of U.S sheet pile (d1).
For the D.S sheet pile, it is noticed that the
thickness of pervious soil layer under the apron
(T) and the depth of downstream sheet pile (d2)
have the biggest effect on the results. Moreover,
the head difference H and the hydraulic
conductivity K have negligible effect on the
ratio of the head lost along the faces for the both
sheet piles.
Figure 5. Sample of model calibration H= 6m, L= 20m, d1 & d2= 5m.
Figure 6. Sample of model verification H= 7.5 m, L= 19 m, d1 = 5m, d2= 2.5m.
Evaluation of Actual Creep Length Under Heading up Structures Aprons
120
Figures (7) and (8) show the effect of each
variable on the ratio between the head loss
along the outer face and the inner face of U.S
and D.S sheet piles respectively (hO/ hI).
5. Results Analysis
The readings obtained from SEEP 2D are
investigated and analyzed in order to determine
the effect of changing the length of apron, the
thickness of soil layer and the depths of
upstream and downstream sheet piles on the
ratio between the head loss along the outer and
the inner faces for both the upstream and
downstream sheet piles.
Plotting the head loss ratio along the outer
face and the inner face for the U.S sheet pile
((hO1/ hI1) against the depths ratio of U.S and the
D.S sheet pile (d1/d2) for different values of
(T/d2) is shown in Fig. (9). It is noticed that
(hO1/ hI1) decreases with the increase of the ratio
between (d1/d2) for all (T/d2) values. So, the
efficiency of the inner face of the U.S sheet pile
improves by 8-16% with increasing the ratio
d1/d2. Also, it is obvious that the ratio of (T/d2)
is directly proportional to (hO1/ hI1). That means
the efficiency of the inner face of U.S sheet pile
improves by decreasing the values of T/d2.
Moreover, changing T/d2 affects hO1/ hI1 values
for bigger values of d1/d2 than smaller ones.
From Fig. 9, it was found that the best relation
between (hO1/hI1) and (d1/d2) is given by linear
equation with correlation equal R (R measures
the strength of the relationship between
variables):
Figure 7. Effect of each variable on the ratio (hO1/hI1).
Figure 8. Effect of each variable on the ratio (hO2/hI2).
M.A. El Molla, N.Y. Saad, and G.S. Ezizah
121
2
1
1
1
d
d
ba
h
h
I
O
(6)
where a, b are coefficients depending on T/d2.
The value of a and b are given in the Table 1.
So, the general empirical head loss equation
along the U.S. sheet pile could be presented as
follows:
2
1
2
2
1
21I
1O
d
d
184.0
d
T
006.0
d
d
d
T
005.018.2
h
h
(7)
Plotting the ratio of the head loss along the
outer and the inner face for the D.S. sheet pile
((hO2/ hI2) against the depths ratio of U.S. and
the D.S. sheet pile (d1/d2) for different values of
(L/T) is shown in (Fig. 10). It is noticed that
((hO2/ hI2) decreases with the decrease of (d1/d2)
for all values of (L/T). That means the efficiency
of the inner face of the D.S. sheet pile improves
by 1-3% with decreasing the ratio (d1/d2).
Moreover, comparing the hO2/ hI2 values at the
same depth ratio values, we can conclude that as
(L/T) values increase the ((hO2/ hI2) values
decrease by 2-4%.
From Fig. 10, it was found that the best
relation between (hO2/hI2) and (d1/d2) is given
by linear equation with correlation equal R.
Figure 9. Design chart for the ratio between the head lost along the outer and the inner faces of U.S
sheet pile.
Figure 10. Design chart for the ratio between the head lost along the outer and the inner faces of D.S
sheet pile.
Table 1. The value of a and b constants.
T/d2 6 9 10 12 15 20
a -0.16 -0.14 -0.13 -0.1 -0.11 -0.09
b 2.2 2.26 2.24 2.24 2.3 2.28
R 0.92 0.96 0.97 0.99 0.96 0.98
Evaluation of Actual Creep Length Under Heading up Structures Aprons
122
2
1
2
2
d
d
ec
h
h
I
O
(8)
where c, e are coefficients depending on L/T.
The value of c and e are given in the Table
(2). So, the general empirical head loss equation
along the D.S sheet pile could be presented as
follows:
2
1
2
1
2I
2O
d
d
016.0
T
L
181.0
d
d
T
L
027.0251.2
h
h
(9)
For the studied variables range, the ratio
(hO1/ hI1) for the upstream sheet pile ranges
from 1.55 to 2.15, and the ratio (hO2/hI2) for the
downstream sheet pile ranges from 2.08 to 2.3.
6. Conclusion
SEEP2D is implemented to study the actual
head loss along the sheet piles fixed at the ends
of an apron of a heading up structure. The
following main conclusions may be drawn:
For the U.S. sheet pile, the variables,
which have the biggest effect on the
head loss ratio along both of its faces,
are the thickness of pervious soil layer
(T) and the depth of U.S. sheet pile (d1).
For the D.S. sheet pile, the thickness of
pervious soil layer (T), the apron length
(L) and the depth of D.S. sheet pile (d2)
have the biggest effect on the head loss
ratio.
The outer and inner faces of the sheet
piles do not have the same weight for
estimating the creep length. Actually,
the creep length along the inner face of
the U.S. pile is about 55% of its
supposed value and for the D.S. pile is
about 45% of its supposed value for
most of the tests ranges.
Increasing the sheet pile depth ratio
(d1/d2=4) improves the efficiency of the
inner face of the U.S. sheet pile by 8-
16%.
The improvement of the D.S. sheet pile
efficiency by decreasing d1/d2 or
increasing L/T is small. So, it is better to
increase the sheet pile depth ratio to
improve the efficiency of the U.S. sheet
pile, although it undermines the
downstream sheet pile efficiency by
small amount.
Design equations for the actual head
loss along the outer and inner faces for
both the upstream and downstream
sheet piles are driven. These equations
may be used as a tool in practical design
for aprons of heading up structures
formed on pervious soil and provided
with upstream and downstream sheet
piles at the ends of the apron.
Conflict of Interest
The authors declare no conflicts of interest.
Funding
No funding was received for this project.
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