Ijciet 10 01_058

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 10, Issue 01, January 2019, pp. 640-650, Article ID: IJCIET_10_01_058
Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=10&IType=01
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication Scopus Indexed
IMPACT OF CAVITATION WITHIN
THE HOMOGENOUS SOIL UNDER HYDRAULIC
STRUCTURE ON FORMULATION OF THE SEEPAGE
QUANTITY AND UPLIFT PRESSURE
Jaafar S.Maatooq*
PhD, Professor of hydraulic structures, IAHR member, Civil Engineering Department,
University of Technology, Baghdad, Iraq.
Dhurgham M.Abdulhasan
M.Sc. student, water and hydraulic structure, Civil Engineering Department, University of
Technology, Baghdad, Iraq.
Correspondence Author
ABSTRACT
This study aims to investigate the effect of single cavity when it presence at a
specific location within the homogenous soil, on the behavior of seepage and uplift
pressure under a hydraulic structure. The results are analyzed to introduce
deterministic formulae for calculating the amount of seepage and the uplift pressure
head. The work was done in three stages by using experimental investigation; the first
stage includes 36 models of 75mm in diameter cavity, while the second and the third
stages includes eight models for each with 100mm and 34mm diameter of cavity,
respectively. The results shows that, when the cavity presence at the left side its impact
was positive on the seepage behavior. While the influence was changed to a negative
impact when the cavity presence at the right side, except at some specific locations. The
statistical software has been employed to generate the two deterministic formulae, and
the results of multiple regressions are checked by statistical indices for the purpose of
recognizing the reliability of the proposed formulae.
Keywords: seepage quantity; uplift pressure; cavity; homogenous soil; deterministic
formulae.
Cite this Article: Jaafar S.Maatooq and Dhurgham M.Abdulhasan, Impact of
Cavitation within the Homogenous Soil under Hydraulic Structure on Formulation of
the Seepage Quantity and Uplift Pressure. International Journal of Civil Engineering
and Technology, 10(01), 2019, pp. 640–650
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=10&IType=01

Jaafar S.Maatooq and Dhurgham M.Abdulhasan
1. INTRODUCTION
One of the serious challenges in the field of hydraulic structures is the seepage and the uplift
pressure problem created under these structures. Therefore, many researchers have addressed
the issue of seepage and uplift pressure under hydraulic structures using different
methodologies and study cases. While the state of arts about the subject of the presence of
cavity in the soil and its impact on the behavior of the seepage is still in its early stages. The
presence of cavities below hydraulic structures will certainly have a direct effect on seepage
process. Such effect is directed on the quantity of seepage and the amount of uplift pressure.
Maatooq et al. (2014) introduced the empirical formula for calculating the amount of seepage
under a sheet pile wall based on the result of the experimental work with presence of cavity.
The equation was developed based on the results of 33 models. Abdallah (2017), by the
experimental work investigated the influence of cavities on the stability of dam during water
flow. The results identified the best location of sheet pile in the case of the presence of cavity
at different locations vertically and horizontally.
2. EXPERIMENTAL WORK
The seepage tank was used for laboratory experiments, Figure 1 Illustrates the components and
dimensions of this tank, where this dimensions have been selected to be in consistent with the
adoption of the previous studies (e.g., Shayan and Tokaldany, 2014; Nassralla and Rabea,
2015; Alghazali and Alnealy, 2015). Figure 2 is the image illustrate the model No.3 when the
cavity located at X/L=0, Y/L=0.2. Eleven piezometers are set down the base of the dam model
to read the uplift pressure, all these piezometers are fixed to the manometers board by
transparence flexible acrylic tubes. In this study the cavity problem was treated within two-
dimensional (X-Y axis), because the length of cavity was adopted to be as the width of a
seepage tank.
Figure (1) Components and dimensions of seepage tank

Impact of Cavitation within the Homogenous Soil under Hydraulic Structure on Formulation of
the Seepage Quantity and Uplift Pressure
Figure (2) Model No.3 when cavity located at X/L=0, Y/L=0.2
2.1. Soil and Cavity
To represent the porous medium, granular material (sand) passing from the sieve no.14 and
retained on the sieve no.200 was used, with the diameter of the particle that 50% of a sample's
mass is smaller than it (d50) equal to 0.4 mm. The constant head permeable test was performed
and the result of coefficient of permeability (k) was equal to 8.07×10-4
m/s. To represent the
cavity, pieces of polyvinyl chloride (PVC) pipe at 34mm, 75 mm and 100mm in diameter was
used. The pipe is drilled randomly with a diameter of 1.5 mm over each surface area to allow
the flow to seep inside. The surface then was covered with a semi permeable lid to prevent
entering the sand particles inside with the seeping water. The cavity was placed to extend across
the width of the tank model.
3. DIMENSIONAL ANALYSIS
The technique used in the present study is referred to as Buckingham -π- Theory (Featherstone
and Nalluri, 1995). This method attempts to reduce the number of parameters which affect the
problem by combining some variable to form non-dimensional parameters instead of observing
the effect of individual variables. Nine independent variables as shown in Eq. (1) having an
effect on a seepage flow as a dependent variable shown in the following functional
relationship:-
q ƒ (X, Y, D, H, L, ρ, μ, g, k) (1)
Where:
X is the horizontal distance between center line of the dam and center of the cavity it take a
positive sign when a cavity located at the right side and a negative sign when the cavity located
at the left side, Y is the vertical distance between the base level of the dam and the center of
cavity, D is the diameter of the cavity, L is the length of the dam base, H is the head of the
water, ρ is the mass density of the water, μ is the fluid dynamic viscosity, g is the specific
gravity, k is the hydraulic conductivity and q is the unit discharge of seepage flow.
By selecting a common variables (ρ, k, D) as repeating variables and using the
Buckingham's theorem, the number of dimensionless groups is (n-m=7), where; n is a number
of variables, and m is a number of dimensions. As a consequence of this;
Upstream part
Middle
Downstream
Cavi Sheet

ƒ (π1, π2, π3, π4, π5, π6, π7) = 0 (2)
With the help of the π-theorem the following π-terms are produced;
π1= , π2= , π3= , π4= , π5= , π6= , π7=
Selecting the term that representing the seepage quantity as a dependent variable, the
functional relationship may be written as:-
π1= ƒ (π2, π3, π4, π5, π6, π7) (3)
The procedure of combination and elimination some parameters that have the same
influence are followed, besides excluding the term that represent the Reynold’s number (π2)
and Froude number (π3) from the context of the impact. The excluding reason is because these
parameters are not relied upon as indicators in flow through porous mediums where the
Reynolds number can be neglected because of the manner of seepage flow under the structure
is laminar (Re< 1) (Harr, 1962& Hassan and K.N.Kadhim, 2018). Since the Froude number is
an indicator of the surface flow, this term could be eliminated without any appreciable
influence on the seepage quantity. The final functional relationship may be written as;
= ƒ (H/D, X/L, Y/L) (4)
4. DESCRIPTION OF TESTING PROCEDURE
Work has been done on three stages the first stage includes 36 models with using the cavity of
75mm in diameter. Readings from the first stage were analyzed and the results indicated the
best and the worst locations with respect to the quantity of seepage and the uplift pressure.
Accordingly, eight locations were selected to develop the experiments of the second and third
stages. At these stages, cavities of 100 mm and 34 mm are used respectively to test the effect
cavity size on the quantity of seepage and the uplift pressure. All experiments were performed
under a constant head, H = 150 mm. The experiment of each model ends when the flow
becomes steady (the amount of seepage does not change with time). Table (1) lists the details
of the locations and diameters of the cavity for the 53 models undertaken.
Table (1) Details of the locations and diameters of the cavity
Model
No.
D
(mm)
Model
No.
D
(mm)
1 75
No
Cavity
No
Cavity
No
Cavity
28 75 2 -0.4 0.08
2 75 2 0 0.08 29 75 2 -0.4 0.2
3 75 2 0 0.2 30 75 2 -0.4 0.4
4 75 2 0 0.4 31 75 2 -0.6 0.08
5 75 2 0 0.7 32 75 2 -0.6 0.2
6 75 2 0.25 0.08 33 75 2 -0.6 0.4
7 75 2 0.25 0.2 34 75 2 -0.6 0.7
8 75 2 0.25 0.4 35 75 2 -0.95 0.08
9 75 2 0.4 0.08 36 75 2 -0.95 0.2
10 75 2 0.4 0.2 37 75 2 -0.95 0.4
11 75 2 0.4 0.4 38 100 1.5 -0.95 0.2
12 75 2 0.6 0.08 39 100 1.5 0.6 0.2
13 75 2 0.6 0.2 40 100 1.5 0.6 0.08
14 75 2 0.6 0.4 41 100 1.5 -0.95 0.08

15 75 2 0.6 0.7 42 100 1.5 1.3 0.4
16 75 2 0.7 0.08 43 100 1.5 0.7 0.4
17 75 2 0.7 0.2 44 100 1.5 0.25 0.08
18 75 2 0.7 0.4 45 100 1.5 0 0.7
19 75 2 0.95 0.08 46 34 4.4118 -0.95 0.2
20 75 2 0.95 0.2 47 34 4.4118 0.6 0.2
21 75 2 0.95 0.4 48 34 4.4118 0.6 0.08
22 75 2 1.3 0.08 49 34 4.4118 -0.95 0.08
23 75 2 1.3 0.2 50 34 4.4118 1.3 0.4
24 75 2 1.3 0.4 51 34 4.4118 0.7 0.4
25 75 2 -0.25 0.08 52 34 4.4118 0.25 0.08
26 75 2 -0.25 0.2 53 34 4.4118 0 0.7
27 75 2 -0.25 0.4 - - - - -
5. RESULTS
Regarding to the analysis the results of seepage quantity are listed in Table (2) as the percentage
"increase" or "decrease" relative to the base quantity "without cavity test" which denoted as M1
test. The data in the Table (2) are obtained based on the following formula;
±%∆q= × 100 (5)
Where, %∆q is the percentage of reducing or increasing the amount of seepage quantity
when the cavity is presence compared with the quantity of seepage of "without cavity test".
The "+" sign in Table 3 refers to increase and vice versa. The qc is the seepage quantity which
recorded with the presence of a cavity, and the qM1 considered the base quantity of seepage for
M1 test. As demonstrated by Table (2), when the cavity presence with D=75mm at the left side
of the X- axis, the recorded quantity of seepage is generally less than the base quantity at most
locations. While reverse situation occur at the right side. From Table (2) it can be see that, the
highest increasing in percentage of seepage was recorded when a cavity of 75mm diameter
presence at X/L= 1.3, Y/L= 0.4, where the amount of seepage increased up to 118% in
comparison with M1. At the same location when the diameter of cavity changed from 75mm to
100mm and 34mm the percentage of increasing in the amount of seepage in comparison with
M1 decreased from 118% to 21.8 % and 14.54% respectively. While the best decreasing in the
percentage of seepage was registered when a cavity of 75mm diameter presence at X/L= 0.6
and for a three embedded depths Y/L= 0.08, 0.2, and 0.4, at which the amount of seepage
decreased up to 80% in comparison with M1. At the same location when diameter of cavity
changed from 75mm to 100mm and 34mm the trend of the advantage has been revised. These
results give an indication that the size of cavity has an important effect on the amount of
seepage, but it however, does not have a specific trend, where the impact is depends basically
on the location of the cavity.

Table (2) Percentage of increase and decrease in amount of seepage due to different cavity locations
Model No. ±∆q% Model No. ±∆q% Model No. ±∆q% Model No. ±∆q%
2 ˗ 36.3 15 ˗ 59 28 + 20 41 + 10.9
3 ˗ 40 16 ˗ 23.6 29 ˗ 23.6 42 + 21.8
4 ˗ 52 17 + 21.8 30 + 56.3 43 + 20
5 + 23.6 18 ˗ 38.2 31 + 23.6 44 -5.45
6 ˗ 9.1 19 ˗ 25.5 32 + 16.3 45 0
7 0 20 ˗ 7.2 33 + 12.7 46 + 38.18
8 ˗ 45.5 21 ˗ 30.9 34 + 9.1 47 + 9.09
9 ˗ 76.3 22 ˗ 10.9 35 + 49 48 -1.81
10 ˗ 71.8 23 ˗ 52.7 36 + 1.8 49 + 5.45
11 ˗ 74.5 24 + 118 37 + 1.8 50 + 14.54
12 ˗ 80 25 ˗ 9.1 38 -1.8 51 + 27.27
13 ˗ 80 26 ˗ 36.3 39 - 27.27 52 + 51
14 ˗ 80 27 + 16.3 40 +10.9 53 + 45.45
The same procedure was followed in the analysis of the uplift pressure and the results are
listed in Table (4) according to the following formula;
±%∆H= ×100 (6)
Where, %∆H is the percentage of reducing or increasing the quantity of the uplift pressure
head when the cavity is presence as compared with the result of the “without cavity test". The
“+" sign refers to increase and vice versa, the Hc and the HM1 are at the same context as defined
for the parameters of Eq.6. The negative effect was a dominant feature of the cavity when it
presence at diameter 75mm, on the amount of uplift pressure head, except at the five locations
as identified in the Table (3). The highest amount of the uplift pressure head at the first stage
is recorded when the cavity located at X/L=0.7, Y/L=0.4 where the uplift pressure increased
about 126% in comparison with M1. At the same location when diameter of the cavity changed
from 75mm to 100mm the amount of uplift pressure decreased up to 11.09%. While with the
smaller diameter of the cavity the amount of uplift pressure head increased to 90.36% for the
same location. The minimum amount of the uplift pressure head which registered at the first
stage was when the cavity presence at X/L=0, Y/L=0.7 where the uplift pressure decreased
about 55.8 % in comparison with M1. At the same location when diameter of cavity changed
from 75mm to 100mm and 34mm the amount of uplift pressure increased up to 70.9 % and
61.27 % respectively in comparison with M1.
Table (3) Percentage of increase and decrease in head reading due to different cavity locations
Model No. ±∆H% Model No. ±∆H% Model No. ±∆H% Model No. ±∆H%
2 ˗ 14.2 15 + 68.9 28 + 101.8 41 ˗ 6.72
3 + 38.7 16 + 82.3 29 + 67.3 42 + 53.09
4 + 74.7 17 + 14.3 30 + 16.5 43 ˗ 11.09
5 ˗ 55.8 18 + 126 31 + 4.2 44 + 170.9
6 +53 19 + 101.5 32 + 78.4 45 + 70.9
7 ˗ 47.3 20 + 92 33 + 99.3 46 + 77.63
8 + 43.6 21 + 68.2 34 ˗ 50 47 + 77.81
9 + 70.3 22 + 55.3 35 + 64 48 + 77.45
10 ˗ 14.5 23 + 28.9 36 + 44.5 49 + 73.63

11 + 17.8 24 + 48 37 + 25.1 50 + 81.09
12 + 26 25 + 87.8 38 + 25.45 51 + 90.36
13 + 37 26 + 3 39 + 14.18 52 + 68.18
14 + 54.2 27 + 47.1 40 ˗ 29.09 53 + 61.27
6. STATISTICAL ANALYSIS
Multiple nonlinear regression models were developed by using SPSS statistical software V.24
to simulate the experimental results. The results of 37 models were used to create two
equations, the first equation is for predicting the amount of the seepage and the second is to
predict the uplift pressure head under the dam. The results of the other 15 models were used
for verification.
6.1 Results of Statistical Analysis
The functional relationship of Eq.4 has been processed by multiple regression analysis to create
deterministic equations for the quantity of seepage. Different deterministic models have been
tested by statistical analysis and the process is rested on the following model;
Y = C + C1 X1
3
+ C2 × X2 + C3 × X3 (7)
The results of multiple regression analysis for the experimental data show that;
C = 0.0377, C1 = 0.0018, C2 = - 0.0086 and C3 = 0.0364
Therefore, the seepage quantity can be given by the following equation:
Y = 0.0377 + 0.0018 X1
3
- 0.0086 X2 + 0.0364 X3 (8-a)
The above equation can be also written in terms of design parameters as the following
equation;
= 0.0377 + 0.0018( ) 3
- 0.0086 + 0.0364 (8-b)
Five statistical indices used to check the reliability of the proposed formulae these indices
are; the coefficient of determination R2
, mean bias error (MBE), root mean square error
(RMSE), Nash Sutcliffe Efficiency Coefficient (NSEC) and the percent bias (PBIAS). The first
indicator ranges from 0 to 1, with higher values indicating less error variance, and typically
values greater than 0.5 are considered acceptable. About the second and third indices the zero
values indicate a perfect fit. While for the fourth indicator, values between zero and 1 are
generally viewed as an acceptable performance level, whereas the less than zero value indicates
an unacceptable performance. The optimal value of PBIAS is zero, whereas lower values
indicate better model simulation. When the value of PBIAS is positive this indicates a tendency
of the model for underestimation whilst negative values indicate overestimation (Moriasi et
al., 2007). Based on the above, the statistical indicators of model 8-b are; R2
=0.87,
RMSE=0.0295, MBE=0.00185, PBIAS=2.265 and NSEC=0.9091.
Figure 3 shows the predicted quantity of seepage by using Eq.8-b and comparing the results
with the measured data points. In Figure 4, the verification of the deterministic model is
illustrated with the 15 remaining of measured data. The statistical indicators of the verification
process are; R2
=0.912, RMSE=0.004, MBE=0.01713, PBIAS=18.579 and NSEC=0.9036.
Through nature of spreading the data points around the perfect line along with the results of
indices, the deterministic model of Eq.8-b can be adopted with acceptable reliability.

Figure (3) Correlation between observed and predicted for the deterministic model of Eq.8-b
Figure (4) Verification of Eq.8-b
The second equation is for the uplift pressure head. Depending on the results of the
experimental work a selection was made for the dependent and independent variables as in
following functional relationship;
= ƒ ( , ) (10)
Where; h is the average of the eleven piezometers reading which recorded with the presence
of a cavity. Different deterministic models have been tested by statistical analysis and the
process is rested on the following model;
Y = C + C1 × X1 + C2 × X2 (11)
The result of multiple regression analysis for the experimental data shows that;
C = - 0.41, C1 = 0.735 and C2 = 0.081
Therefore, the uplift pressure head can be given by the following equation:
0
0.05
0.1
0.15
0.2
0.25
0 0.05 0.1 0.15 0.2 0.25
Predictedq/kD
Observed q/kD
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Observedq/kD
Predicted q/kD

Y = - 0.410 + 0.735 X1 + 0.081 X2 (12-a)
The equation 12-a can be also written in terms of design parameters as the following
equation;
= - 0.410 + 0.735 + 0.081 (12-b)
The statistical indicators of model 12-b are;
R2
= 0.942, RMSE = 0.2468, MBE = 0.0003, PBIS = - 0.0223 and NSEC = 0.9711.
Figure 5 shows the test of prediction with the observed data when the deterministic model
of Eq.12-b is used. Also the verification was conducted using 15-data points those excluded
from creation of the deterministic model. The verification results have achieved the following
statistical indicators;
R2
= 0.85, RMSE = 0.6047, MBE = -0.0332, PBIS = -2.6922 and NSEC = 0.9137.
The spreading of data points around the perfect line is presented in Figure 6. The values of
the statistical indicators and the feature of spreading data points indicate inducement besides
over prediction. Accordingly, using model of Eq.12-b for calculation the uplift pressure head
with presence of a cavity leads to acceptable with more precaution to the safe side.
Figure (5) Correlation between observed and predicted for the deterministic model of Eq.12-b
0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1 1.5 2 2.5 3 3.5
Predictedh/D
Observed h/D

Figure (6) Verification of Eq.12-b
7. CONCLUSIONS
After analysis the experimental data it can be concluded that, on the positive side of the model
(left side), presence of cavity with 75 mm diameter had a positive effect in terms of minimizing
the amount of seepage, except for three locations ( X/L = 0 , Y/L = 0.7 ) , ( X/L = 0.7 , Y/L =
0.2 ) and ( X/L = 1.3 , Y/L 0.4 ) where seepage increased for these locations by 23.6, 21.8 and
118% respectively as compared to the base model (M1). While at the negative side of the model
(right side) the reverse situation occur when the same cavity size presence, except for three
locations ( X/L = -0.25 , Y/L = 0.08 ) , ( X/L = -0.25 , Y/L = 0.2 ) and ( X/L = -0.4 , Y/L = 0.2
), where a decrease in seepage was recorded in these three locations by 9.1 , 36.3 and 23.6 %
respectively compared to the base model (M1). Hence, it can be concluded that the presence of
cavity in the left side does not constitute a danger to any hydraulic structure in terms of seepage
while it constitute a danger when it located at right side except for the three locations at each
side. The size of the cavity has a significant effect on the amount of seepage, however if this
effect is negative or positive it is depends on the location of cavity. In addition, regarding to h
the effect of uplift pressure head the effect in general was negative for all cavities size and for
any locations except five locations at the first stage and two location at the second stage.
Equations 9-b and 12-b can be used to predict the amount of seepage and uplift pressure
respectively.
REFERENCES
[1] Abdallah M. H. The Influence of Cavities on the Stability of Dam During Water Flow.
M.Sc. Thesis, University of Kufa, Iraq 2017.
[2] Alghazali N.O.S., Alnealy H.K.T. Experimental Study for Pizometric Head Distribution
under Hydraulic Structures. International Journal of Scientific & Technology Research,
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[3] Maatooq J.S., Laith J. Aziz, Taghreed A. Almahdee Musa. Development of Empirical
Formula for Influence of Cavities on Seepage under Sheet Pile Wall for Hydraulic
Structures. Kufa journal of Engineering Vol.5, No.2, 2014, 93-106.
[4] Harr A.E., 1962 (ed) “Ground Water and Seepage” M.C. Graw-Hill Book Company.
0
0.5
1
1.5
2
2.5
3
0 0.5 1 1.5 2 2.5 3
Observedh/D
Predicted h/D

[5] Moriasi D. N, Arnold J. G, Van L. M., Bingner R.L., Harmel R. D., Veith T. L. Model
Evaluation Guidelines for Systematic Quantification of Accuracy in Watershed
Simulations. Transactions of the American Society of Agricultural and Biological
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MNLR and CFD Simulation Approaches). (IJCIET), Volume 9, Issue 3, (Feb 2018)
[7] Nassralla T.H. and Rabea A.R.M.A. Seepage Characteristics under Hydraulic Structure
Foundation (Supported by Sheet pile) In Multi-Layers Soil. The Egyptian International
Journal of Engineering Sciences and Technology Vol. 18, No. 4, 2015, 229–238.
[8] Featherstone R.E. and Nalluri C., 1995 (3rd
ed) “Civil Engineering Hydraulics” Blackwell
Science Ltd.
[9] Shayan H.K. and Tokaldany E.A. Effects of blanket, drains, and cutoff wall on reducing
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