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Experimental Investigation to Evaluate Different Parameters
of Empirical Infiltration Model for Rajkot Soil and
Mathematical Validation of the Same
A PROJECT REPORT
Submitted By
NIRAJ MEHTA
ROHAN HARIYANI
JAYDEV BALDANIYA
SULTAN BADI
In fulfilment for the award of the degree
Of
BACHELOR OF ENGINEERING
In
Civil Engineering

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Marwadi Education Foundation Group of Institution
Rajkot
Gujarat Technological University, Ahmedabad
Under the Guidance of
Assistance professor
Ms. Bahnisikha Das

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Marwadi Education Foundation Group of Institution
Civil Engineering

CERTIFICATE
Date:
This is to certify that the dissertation entitled Experimental Investigation to
Evaluate Different Parameters of Empirical Infiltration Model for Rajkot Soil
and Mathematical Validation of the Same has been carried out by Niraj Mehta,
Rohan Haryani, Jaydev Baldaniya, Sultan Badi under my guidance in
fulfilment of the degree of Bachelor of Engineering in Civil Engineering (7th
Semester) of Gujarat Technological University, Ahmedabad during the
academic year 2015-2019.
Guides:

Head of the Department

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ACKNOWLEDGEMENT

We express our sincere thanks and gratitude to our guide “Ms. Bahnisikh Das”
who guided us through various stages of our work and it is due to our guide’s
support and help that we have been able to make steadfast progress in our
project.

Whenever we faced any difficulty our guide readily and promptly helped us and
her guidance helped us find solutions to difficulties coming in our path.
Throughout our work our guide encouraged us whenever we were stuck and
thus we have been able to make this progress in our project.

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Abstract
The constant infiltration rates of soil under different soil conditions are
calculated at Rajkot district. Experimentation work is carried out on various
soils samples to determine its properties. The double ring infiltrometer is used
for measurement of infiltration rate. The study aims to determine constant
infiltration rates of the soils under different soil conditions and comparing it
with the with the infiltration rates obtained by Kostiakov, Modified Kostiakov,
and Horton’s models. The values of various constants of the models are
calculated by mathematical and graphical approach. For getting best fitting
model for particular soil and soil condition, the results obtained from various
infiltration models are be compared with observed field data and graphs are
drawn. The parameters to be considered for best fitting of model were
correlation coefficient and standard error. New infiltration model will be
developed using different methods and comparison of its result will be done
with field data.
Keywords: Infiltration, Infiltration rate, Infiltration models, soil condition.

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List of Tables
Table: 1 Field Data…………………………………………………………17
Table: 2 Constants of different models……………………………………………………21
Table: 3 Infiltration rates from different models……………………………………..21

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List of Figures
Fig.1 Graphical presentation of field data………………………………………….17
Fig.2 Graph for Horton’s model……………………………………………….18
Fig.3 Graph for Kostiakov’s model……………………………………………19
Fig.4 Graph for Modified kostiakov’s model………………………………….20
Fig.5 Infiltration in clay soil…………………………………………………..22
Fig.6 Cumulative Infiltration In clay soil………………………………………22

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Table of Contents
1. Chapter – 1 Introduction……………………………………………………8
1.1 General………………………………………………………………….8
1.2 Factors affecting Infiltration……………………………………………9
1.3 Objectives of Research work ………………………………………….10
1.4 Methodology …………………………………………………………..10
2. Chapter – 2 Literature Review ………………………………………………11
3. Chapter – 3 Infiltration Models……………………………………………..16
3.1 HORTON’S MODEL……………………………………………….16
3.2 KOSTIAKOV MODEL……………………………………………..16
3.3 Modified Kostiakov…………………………………………………17
4. Chapter – 4 Study area, Data collection and analysis………………………18
4.1 Study Area…………………………………………………………..18
4.2 Data collection………………………………………………………19
4.3 Data Analysis and comparison………………………………………19
5. Chapter – 5 Results and conclusion………………………………………….22
5.1 Values of different parameters of infiltration models………………22
5.2 Calculated infiltration rates from Different infiltration models…….22
5.3 Graphical presentation of comparison of field data with models…..23
6. Chapter – 6 Conclusion……………………………………………………..24
7. References …………………………………………………………………25
8. Canvas Sheet ………………………………………………………………26

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Chapter – 1 Introduction
1.1 General
Infiltration is the movement of water into the soil from the surface. The water is
driven into t he porous soil by force of gravity and capillary attraction. First the
water wets soil grains and then the extra water moves down due to resulting
gravitational force. The rate at which a given soil can absorb water at given time
is called infiltration rate and it depends on soil characteristics such as soil
texture, hydraulic conductivity, soil structure, vegetation cover etc.the
infiltration plays an important role in generation of runoff volume, if infiltration
rate of given soil is less than intensity of rainfall then it results in either
accumulation of water on soil surface or in runoff. The different soil conditions
affect the soil infiltration rate. Compacted soils due to movement of agricultural
machines have a low infiltration rate which is prone to runoff generation.
Infiltration will be maximum at the beginning and it decays exponentially and
gets a constant value. There will be a decrease in infiltration rate day by day due
to the saturation of the soil whereas on the first day the infiltration rate will be
more because soil will be dry in condition.
Infiltration of water into the soil has important impact in the overall functioning
of the variable land based activities. Two factors can greatly undermine
availability of water for crops which is impervious layer and ground water table.
The former might be due to excess infiltration which mostly a function of soil
characteristic get through the later may be largely due to the deposit of clay that
can create crust below the surface. The study of infiltration comes in many
hydrological problems like runoff estimation, soil moisture budgeting and for
planning of irrigation. Infiltration has an important place in the hydrological
cycle.

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1.2 Factors affecting Infiltration
Factors affecting infiltration depends on both meteorological and many soil
properties. These are
i. Texture
The liquid moves very quickly in large pores of sandy soil than it does through
small pore in clayey soil.
ii. Clay mineralogy
Some types of clay may develop cracks as they are dry. These kinds of cracks
may rapidly conduct water to the sub-surface once and the seal shuts down once
the soil becomes wet.
iii. Vegetation
Soil covered with vegetation has grater infiltration than the barren land .Because
of the bacterial activities, dense forest may have good infiltration rate than
sparsely planted crops.
iv. Antecedent Moisture content
Infiltration mainly depends on the presence moisture content in the soil. When
compare to first day the second day will have lesser infiltration rate because soil
becomes saturated on the first day.
v. Human activities
When vegetation was done or a grass covering barren land has the high
infiltration rate. Whereas the other side the construction work, over gazing of
pastures and playgrounds reduce infiltration capacity of the area considerably.

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1.3 Objectives of Research work
The objectives of the study are
• To determine the infiltration rate of soil.
• To determine the infiltration rates using Horton’s, Kostiakov and
Modified Kostiakov model.
• To compare the observed infiltration rates with the calculated infiltration
rates.
• To develop new Infiltration model.
• To compare data of developed infiltration model with field data.
1.4 Methodology

Literature review related to infiltration.
Measurement of infiltration rates of soil
Determination of infiltration rate using various
mathematical models
Determination of various soil property of study
area
Development of new infiltration model ;
mathematical validation of the same.

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Chapter – 2 Literature Review

1) Experimental Study For Determination Of Infiltration Rate Of Soils In
Field Using Double Ring Infiltrometer
Volume: 212CE4486, 2014
Author: Amreeta Champatiray
The infiltration rate is expressed in term of volume of water poured per ground
surface per unit of time. Soil erosion, surface runoff ; ground water recharge
are affected by this process. At a certain moment the maximum infiltration rate
can be indicated by the infiltration capacity of soil. Infiltration of water into the
soil can be determined by a simple instrument called Double ring infiltrometer.
To spread the water vertically after infiltration we use double ring infiltrometer.
Double ring infiltrometer is better than single ring infiltrometer. In single ring
infiltrometer the water will spread horizontally ; vertically both, from which
water will not move only towards the ground water but using double ring
infiltrometer the water will penetrate in one direction that is towards the ground
water without much wastage of water.
2) The Effect of soil moisture on infiltration as related to runoff and
recharge.
Hydrology Symposium No. 6, November 1967
National Research Council of Canada
Author: Don M. Gray and D. I. Norum
The paper provides a general outline of the mechanics of the infiltration
process.In the discussions, specific attention is given to the quantitative
influence of the initial soil moisture content as it affects both the infiltration rate
and the amount of infiltration of frozen and unfrozen soils.

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3) Surface factors affecting the rate of intake of water by soils
SOIL SCIENCE SOCIETY PROCEEDINGS 1939
Author: F. L. DULEY
This paper is mainly focused on the effect of soil texture on infiltration.
Different soils, varying rather widely in texture and profile characteristics are
tested. Soils containing large amounts of coarse material such as sandy loams
have been compared with silt loams and clay loams as to their rate of water
absorption.
4) Green-ampt Infiltration parameters from soils data
J. Hydraul. Eng. 1983.109:62-70.
By Walter J. Rawls, 1 M. ASCE, Donald L. Brakensiek, 2 and Norman Miller3
The analysis of approx 5,000 soil horizons indicated that Green and Ampt
parameters (effective porosity, wetting front capillary pressure, and hydraulic
conductivity) could not be developed based on phases of soil order or suborder.
However, sets of average parameters are developed based on soil horizon or soil
texture class, or both. A procedure for determining the Green and Ampt
parameters based on soil properties utilizing the full spectrum of soil survey
information is outlined.

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5) Infiltration Studies Of Different Soils Under different Soil Conditions
And Comparison Of Infiltration Models With Field Data
Volume: E-ISSN0976-3945
Author: JagdaleSatyawanDagadu, Nimbalkar P.T.
The constant infiltration rates of different soils under different soil conditions
were calculated at Sangola, district solapur of Maharashtra region.
Experimentation work was carried out on black cotton, clay, and sandy soil.
Soil conditions considered for black cotton soil were compacted, ploughed, and
harrowed, for clay soil unploughed and ploughed, and for sandy soil
unploughed. The double ring infiltrometer method was used for measurement of
infiltration rate. The study aimed to determine constant infiltration rates of those
soils under different soil conditions and comparing it with the standard
infiltration rates.
6) Experimental Study on Infiltration in Guwahati Using Double Ring
Infiltrometer.
ISSN (Online): 2319-8753
Vol. 5, Issue 12, December 2016
Gayatri Das1, Mimi Das Saikia2
In this paper, an attempt has been made to find the constant infiltration rates of
different soils under different soil conditions. Field experiments were carried
out at six different sites located within Guwahati. The highest infiltration rate
obtained was 10.73cm/hr at Eastern Retreat and the lowest was 1.73cm/hr
occurred at Bonda. Soil tests have also been done to know the soil type and how
the infiltration curve varies for each soil type with respect to time.

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7) Infiltration Through Disturbed Urban Soils and Compost-Amended Soil
Effects on Runoff Quality and Quantity
Volume: EPA/600/R-00/016 December 1999
Author: Robert Pit, Janice Lantrip, Robert Harrison
This project examined a common, but poorly understood, problem associated
with land development, namely the modifications made to soil structure and the
associated reduced rainfall infiltration and increased runoff. The project was
divided into two separate major tasks: (a) Testing infiltration rates of impacted
soils, and (b) Enhancing soils by amending with compost to increase infiltration
and prevent runoff.

8) A Study on Infiltration Characteristics of Soils at Andhra University
Campus, Visakhapatnam
ISSN 2249-3131 Volume 7, Number 1 (2017), pp. 29-44
Sreejani TP1 , Abhishek D2 , Srinivasa Rao GVR3 , Abbulu Y
An attempt has been made in the present work to evaluate infiltration
characteristics of soils at Andhra University campus using a single and double
ring infiltrometer. Experimentation work is carried out at five different points in
the campus. The study is aimed at determining the constant infiltration rates of
those soils using both the infiltrometers and comparing it with the infiltration
rates obtained by Kostiakov, Philip’s, and Horton’s and GreenAmpt infiltration
models. The values of various constants of the models are calculated by
graphical approach. To get best fitting model for a particular soil condition the
results obtained from various infiltration models are compared with observed
field data and graphs are drawn with correlation coefficient and standard error
as tools.

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9) An approach toward a physical interpretation of infiltration-capacity
SOIL SCIENCE SOCIETY PROCEEDINGS 1940
Author : ROBERT E. HoRTON
INFILTRATION-CAPACITY was first defined by the author as the maximum
rate at which a given soil when in a given condition can absorb rain as it falls.
Infiltration-capacity is usually designated by f, and since f varies with time,
especially during the early part of rain, it is to be understood that the condition
of the soil and hence the infiltration-capacity, vary with time, until a certain
minimum infiltration-capacity fc is reached. Certain other factors, such as
temperature of the air, and of rain and soil surface, rain intensity, initial soil-
moisture, initial and residual rain occurring at intensities less than the
infiltration-capacity, also require consideration.

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Chapter – 3 Infiltration Models

The following infiltration models were assessed for finding best fitting model to
observed field infiltration rate data.
3.1 HORTON’S MODEL:
Named after the same Robert E. Horton mentioned above, Horton’s
equation is another viable option when measuring ground infiltration
rates or volumes. It is an empirical formula that says that infiltration starts
at a constant rate, fo, and is decreasing exponentially with time, t. After
some time when the soil saturation level reaches a certain value, the rate
of infiltration will level off to the rate fc. Horton expressed decrease of
infiltration capacity with time as an exponential decrease as
f = fc + (fo – fc) e-kt
Where,
f is infiltration capacity at any time t.
fc is final steady state infiltration capacity.
fo is initial infiltration capacity.
k Horton’s constant representing rate of decrease in infiltration
Capacity.
t is time in hours.

3.2 KOSTIAKOV MODEL:
f = ����
Where,
f is cumulative infiltration at any time t.
t is time in min.
a and b are constants

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3.3 MODIFIED KOSTIAKOV MODEL:
f = atb + c
Where,
f is cumulative infiltration at any time t.
t is time in min.
a, b and c are constants whose values depends on soil type.

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Chapter – 4 Study area, Data collection and analysis

4.1 Study Area
Marwadi Education Foundation college campus is selected for study. It is
located in Rajkot district of Gujarat. Campus is approximately 15 km far from
Rajkot city on Morbi highway. Data is collected from open ground of campus.

4.2 Data collection
4.2.1 Infiltration Data:
Double ring infiltration meter is used to collect the infiltration of soil.
Experiment was conducted on 30th July, 2018. Infiltration Data for
approximately 2 hours are collected. Data is collected until constant infiltration
is obtained. Table given below represents the infiltration rate at a time t.
Time t (mins) Infiltration rate (cm/hr)
20 0.9
40 0.6
60 0.4
80 0.3
105 0.2
130 0.1
Table: 1 Field Data

Fig.1 Graphical presentation of field data
0
0.2
0.4
0.6
0.8
1
020406080100120140
Infiltration(cm/hr)Time(min)
Field data

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4.2.2 Determination of soil type:
Liquid limit test and plastic limit test was performed to determine the soil type.
From results it is found that soil type is clay. More specifically it is clay with
high plasticity (CH type).
4.3 Data Analysis and comparison
Constants of different empirical models are determined by graphical method.
4.3.1 For Horton’s Model:
F = fc + ( fo – fc ) e-kt
where, f = infiltration capacity at any time t in cm/hr.
fc = final steady state infiltration capacity.
Fo = initial infiltration capacity.
t = time in hours.
K = Horton’s constant representing rate of decrease in infiltration

Fig.2 Graph for Horton’s model
here,fc = 0.1
fo = 0.9
slope = (-1/kloge) -1.8442 = (-1/kloge) k = 1.25
f=fc+(fo-fc)e-kt f=0.1+(0.9-0.1)e-1.25t f=0.1+0.8e-1.25t
y = -1.8442x + 1.7008
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0.11
Time(hour)
f -fc
time-hr y-axis

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4.3.2 For Kostiakov:
f=atb
From graph, equation of line is y = 0.6155x-08315
In kostiakov’s eq ,b is slope so here slope b = 0.6155
While a is antilog of intercept,
Here intercept is -0.8315. So, a=antilog (-0.8315) = 0.147
therefor,f = atb
is ,f = 0.147t0.6155
where,f = Cumulative infiltration rate (cm/hr)
t = Time elapsed (min)

Fig.3 Graph for Kostiakov’s model

y = 0.6155x -0.8315
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
00.511.522.5
log(f)
log(t)
log(f) y axis

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4.3.3 For Modified Kostiakov:
f=atb + C
Value of c from calculation,c = 0.161
From graph, equation of line is y = 0.6939x – 1.0117
In kostiakov’s eq, b is slope so here slope b = 0.6939
While a is antilog of intercept,
Here intercept is -0.8315. So, a=antilog (-1.0117) = 0.097
therefor,f = atb + c
is ,f = 0.097t0.6939 + 0.161
where,f = Cumulative infiltration rate (cm/hr)
t = Time elapsed (min)

Fig.4 Graph for Modified kostiakov’s model

y = 0.6939x -1.0117
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
00.511.522.5
log(f
-c)
log(t)
log(f-c) y axis

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Chapter – 5 Results and conclusion

5.1 The values of different parameters of infiltration models

Table: 2 Constants of different models

5.2 Calculated infiltration rates from Different infiltration models

Time(min) Field Data
(cm/hr)
Horton’s
Model
(cm/hr)
f=0.1+0.8e1.25t

Kostiakov’s
(cm/hr)
f = 0.147t0.6155
Modified Kostiakov
(cm/hr)
f = 0.097t0.6939 +0.161

20 0.9 0.63 0.93 0.94
40 0.6 0.45 0.49 0.48
60 0.4 0.33 0.41 0.4
80 0.3 0.25 0.35 0.37
105 0.2 0.20 0.4 0.42
130 0.1 0.16 0.3 0.3
Standard error 0.17 0.23 0.24
Correlation
Coefficient
0.98 0.92 0.91
Table: 3 Infiltration rates from different model

Horton’s Model
f=fc+(fo-fc)e-kt

Kostiakov’s Model
f=atb

Modified Kostiakov’s
f=atb + c

K a b a b c
1.25 0.147

0.6155

0.097 0.6939

0.161

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5.3 Graphical presentation of comparison of field data with models:

Fig.5 Infiltration in clay soil

Fig.6 Cumulative Infiltration In clay soil

0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
020406080100120140
Infiltration rate (cm/hr)
Time (min)
Infiltration in Clay soil
Field data
Horton’s
kostiakov
modi. Kos
0
0.5
1
1.5
2
2.5
3
3.5
020406080100120140
Cumulative Infiltration (cm/hr)
Time (min)
Cumulative Infiltration in Clay soil
Field data
Horton’s
kostiakov
modi. Kos

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Chapter – 6 Conclusion

• From results it is seen that values of standard error and co-relation
coefficient is different for different model.
• Results from Horton’s model is most relatable to field data.
• The infiltration to the soil got constant after a short time interval due to
saturation of the soil as measurements were taken in rainy season
• From research work it was also found that soil conditions effects
infiltration rate. From the graphs of infiltration rates against time it is
found that initial infiltration rates were high and decreased with time up
to constant infiltration rate.

• From the result after analysis it was found that an infiltration models
varies. From correlation coefficient and Standard Error it was found that
Horton’s model is the best fitting model with high degree correlation
coefficient and minimum standard error.

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References:
1. ASTM.2003.D3385-9403; “Standard test method for infiltration
rate of soils in field using double ring infiltrometer”.

2. Wu, l., Pan., Robertson, M., and Souse, (1997); “Numerical
evaluation of ring infiltrometer under various soil conditions”. Soil
Sci.162:771-777.

3. M. Lilli, V.F. Bralts, P. Yinghua, L.Han and L.Tingwu, (2008);
“Methods for measuring soil infiltration,” State of art, Int J Agric &
Biol Eng. 1(1), pp 22-30.

4. G.E.Osuji, M.A.Okon, M.C.Chukwuma and I.I.Nwarie (2010)
“Infiltration characteristics of soil of soil under Selected Land Use
Practices in Owerri, South-eastern Nigeria,” Nwarie World Journal of
Agriculture Sciences 6(3), pp 322-326.

5. Tricker, A.S, (1978); “The infiltration cylinder: Some comments on
its use”. J.Hydrol (Amsterdam) 36:383-391.

6. Champatiray Amreeta “Experimental Study for Determination Of
Infiltration Rate Of Soils In Field Using Double Ring Infiltrometer”
Vol. 212CE4486

7. Jagdale Satyawan Dagadu, Nimbalkar P.T. “Infiltration Studies of
Different Soils Underdifferent Soil Conditions and Comparison of
Infiltration Models with Field Data” .Vol. E-ISSN0976-3945

8. Balraj Singh, Parveen Sihag, Diwan Singh, Study of Infiltration
Characteristics of Locally soils, Journal of Civil Engineering and
Environmental Technology, Volume 1, Number 5; August, 2014 pp. 9
– 13

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