1

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

Marwadi Education Foundation Group of Institution

Rajkot

Gujarat Technological University, Ahmedabad

Under the Guidance of

Assistance professor

Ms. Bahnisikha Das

2

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

3

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.

4

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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AEIOU

Empathy Mapping Canvas

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Ideation Canvas

Product Development Canvas