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This is to certify that the

thesis entitled

Groundwater Flow and Quality
Behind an Anti-salt Dam in lower
Casamance Senegal (West Africa)

presented by

Boubacar Barry

has been accepted towards fulfillment
of the requirements for

M . S. degree in Agricultural Engineering

 

 

 

Date 11—11—91

 

0-7639 MS U is an Affirmative Action/Equal Opportunity Institution

 

LmRA-RY
Michigan State
University

r- *- “~._.__

 

 

PLACE IN RETURN BOX to remove this checkout from your record.

TO AVOID FINES return on or before date due.

   

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU Is An Affirmative Action/Equal Opportunity Institution
crtclrcwuna-D:

Groundwater rlow end Quelity
Behind en Anti-eelt Den.in Lower

Ceeenence Senegal (fleet.h£rice)

BY

Boubacar Barry

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

MASTER OF SCIENCE
in
Agricultural Engineering
Department of Agricultural Engineering

1991

ABSTRACT
GROUNDWATER FLOW AND QUALITY
BEHIND AN ANTI-SALT DAM IN LOWER
CASAMANCE SENEGAL (WEST AFRICA)
BY

Boubacar Barry

For many years, the Casamance was a food self-sufficient
region. Recently, this region has experienced foods deficits
because of the persistent drought. Given the shortage of
rainfall over the last several years and the increasing
accumulation of salt, the number of abandoned mangrove paddy
fields is multiplying throughout the region. Along the tidal
portion of the river basins one can observe a tendency towards
increased salinity of the river bed and increased salinity of
the underlying water table. Because of the shortage of
available fresh water for leaching the salt out of these
fields, site development (polders, anti-salt dams, drainage)
has become the only solution to the salt intrusion problem
since the early 1970's. Today, more than 20 anti-salt dams
have been built in the Casamance region, and rice production
has substantially increased. The present study focusses on
groundwater flow and quality in a typical valley of the Lower
Casamance region. A groundwater simulation model, using the
finite element approach for evaluating water movement in the
aquifer, is developed. Recommendations for improved
management strategies for irrigation behind anti—salt dams are

also formulated.

  

ID— l "‘1!

Approved

 

V

Major Professor Date

Approved WWM» ll/lg/f/

Department Chairperson Date

A la Memoire de mon Pere

Seigneur, Fasse que les portes du Paradis
lui Soient Ouvertes

AMEN

Ton Fils

iv

ACKNOWLEDGMENTS

I would like to give special thanks to Dr. V.F. Bralts,
who served as my advisor. I greatly appreciated his support,
and patience in helping me in my research. I would also like
to thank the members of my Committee. Special thanks go to
Dr. J. L. Posner for guiding my research at home in Senegal,
to Dr. J. Bingen for giving the opportunity to study at this
wonderful university.

In addition I want to thank my family, Maguette, Tafsir,
and Iba my lovely wife and beautiful kids, and my new found
Michigan friends, Aliou, Rabi, Jon, Martin, Jim and Mark
Pires, who helped me in more ways than they will ever known.
Last but not least, special thanks to my mom who gave never

ending support and encouragement through my frantic hours.

TABLE 03' CONTENTS

Page

LIST OF TABLES ................................. . ............ ix
LIST OF FIGURES .............................................. x
LIST OF ABREVIATIONS ........................................ xi
I . INTRODUCTION ............................................ l
A. Background .................................... I . . . . 1

B. Scope and Objectives .............................. 6

II . REVIEW OF LITERATURE AND THEORY ......................... 7
A. Irrigation and Drainage ........................... 7

1. World ......................................... 7

1 . 1 . Advanced Technology .................... 11

1 . 1 . 1 . Sprinkler Irrigation ........... 11

1 . 1 . 2 . Surface Irrigation ............ 12

1.1.3. Trickle Irrigation ............. 13

1 . 2 . Cost ................................... 14

1.3. Drainage ............................... 14

1 . 4 . Human Resources ........................ 15

2. Africa ....................................... 16

3.Sahel .......................................... 18

3 . 1 . Traditional Labour Intensive Systems . . .22
3 . 2 . Natural Flood Irrigation ............... 24

3.3. Recessional Irrigation ................. 24

vi

Page

3 . 4 . Controlled Flood Irrigation ............ 24
3.5. Total Control .......................... 25
3 . 6 . River Basin Development .............. . . 25
4. Senegal ...................................... 25
5 . Lower Casamance ........... - ...... . ............ 32

B. Hydraulics of Groundwater and Solute Transport. . .41

1 . Equation of Groundwater Flow ................. 41
1 . 1 . Steady-State Saturated Flow ............ 42
1 .2 . Transient Saturated Flow ............... 45
2. Solute Transport ............................. 50

I I I . RESEARCH METHODOLOGY

A. Research Approach ................................ 55
B. Experimental Method .............................. 56
1 . Site Description ............................ 56

1 . l . Climate and Hydrology ................. 56

1.2. Soil .................................. 57

1 .3 . Experimental Network .................. 6O

2. Piezometric Tests ........................... 61

2 .1 . Principle of LeFranc Test ............. 61

2 .2. Principle of Slug Test ................ 68

2.3. Field Data Collection ................. 7O

2 .4 . Data Analysis ......................... 71

C. Computer Simulation .............................. 74

1. Groundwater Flow and Solute Transport

vii

Page

Simulation .................................. 74

IV. RESULTS AND DISCUSSIONS ............................... 88
1 . LeFranc Test Results ........................ 88

2 . Slug Test Results ................ . .......... 91

3. Comparison between LeFranc Test and

Slug Test, ............. . ..................... 92

4 . Estimation of Groundwater ................... 94

4 . 1 . Fresh Water Flow Rate ................. 96

4 .2. Salt Water Flow Rate ....... . ......... 97

5 . Groundwater Flow Model ...................... 98

5 . 1 . Model Description .................... 105

5 .2 . Model Validation ..................... 107

6. Discussion ................................. 110

V. CONCLUSIONS AND RECOMMENDATIONS ....................... 116
APPENDIX A: Model Validation ............................. 118
APPENDIX B: Computer Program Listing ..................... 138
APPENDIX C: Simulation Results ........................... 143
LIST OF REFERENCES ......................................... 149

viii

LIST OF TABLES

Table Page

1. Gross irrigated areas by continent ............. 9
2. Distribution of irrigated areas over the

African regions ............................... 17
3. Area to be irrigated in the Sahelian Region

by Kindell Consult ............................ 23
4. Estimated values of hydraulic conductivity

by LeFranc test ............................... 9O
5. Slug test results ............................. 91

6. Comparison between LeFranc test and Slug test.92

A—l. Actual head values by Segerlind (1984)
and simulated head using the developed

numerical .................................. 118
A-2. Pressure heads simulation results .......... 120
A-3. Observed pressure heads .................... 127
A-4. Geographic coordinates ..................... 132

ix

LIST OF FIGURES

Figure ' Page
1. Major regions of Africa ............................ 2
2. Map of Senegal's rivers ............................ 5
3 Evolution of rice production in Lower Casamance...33
4 Typical toposequence in Lower Casamance ........... 40
5. Mass fluxes in a unit volume of saturated soil:

After Gray (1973) ................................. 43
6. Map of Kamoubeul River's Watershed ................ 58
7. Experimental network .............................. 62
8. Apparatus for LeFranc test ........................ 65
9. Spatial distribution of hydraulic conductivity....89

10. Variogram of hydraulic conductivity values ........ 95

11. Observed piezometric heads 02/03/87 ............... 99

12. Observed piezometric heads 04/14/87 .............. 100

13. Observed piezometric heads 06/30/87 .............. 101

14. Groundwater salinity 02/03/87 .................... 102

15. Groundwater salinity 06/30/87 .................... 103

16. Finite element mesh for Katoure Valley ........... 104

17. Model validation ................................ 109

18. Plot of simulated versus observed heads 02/03/87.111

19. Plot of simulated versus observed heads 04/14/87.112

20. Plot of simulated versus observed heads 06/30/87.113

tigure Page
C-l. Topographic maps of Katoure Valley ................ 143
C-2. Three-dimensional map of Katoure Valley ........... 144
C-3. Predicted piezometric heads by the developed

computer model for the Katoure Valley for

February 03, 1987 ................................. 145
C-4. Predicted piezometric heads by the developed

computer model for the Katoure Valley for

April 14,1987 .................................... 146
C-5. Predicted piezometric heads by the developed

computer model for the Katoure Valley for

June 30, 1987 ..................................... 147

C-6. Characteristic curve for slug test ................ 148

xi

LIST OF ABREVIATIONS

CIID : Commission International des Irrigations et
Drainages. (International Commission on Irrigation
and Drainage).

CILSS : Comite Interetats de Lutte contre la Secheresse

dans le Sahel. (Interstate Commitee for Drought

Control in Sahel).

CNRS : Centre National de Recherches Scientifiques.
(National Center for Scientific Research).

FAO : Food and Agriculture Organization.

IRAT : Institut de Recherches en Agronomie Tropical.
(Research Institute for Tropical Agronomy).

ISRA : Institut Senegalais de Recherches Agricoles.
(Senegal Agricultural Research Institute).

NBA : Niger Authority Basin.
NGO : Non-Government Organization.

OMVG : Organisation pour la Mise en Valeur du Fleuve Gambie.
(Operation for the Development of the Gambia River).

OMVS : Organisation pour la mise en Valeur du Fleuve
Senegal.

(Operation for the Development of the Senegal River) .

ORSTOM : Office de Recherche Scientifique et Technique
d'outre Mer. (Office of Overseas Scientific and
Technical Research).

SAED : Societe d'Amenagement et d’Exploitation des Terres du
Delta. (Delta Canal Development Corporation).

SODAGRIZ : Societe de Development Rizicole. (Rice

Development Company).
SODEFITEX : Societe de Development de Fibres Textiles.
(Textiles Development Company).
SOMIVAC : Societe de Mise en Valeur Agricole de la
Casamance . (Casamance Agiculture Development Co.)
USAID : united States Agency for International Development.

xii

I. INTRODUCTION

A" BACKGROUND.

The West African country of Senega1_(Fig.l) is primarily
an agricultural country. In 1980, agriculture accounted for
28 percent of the GNP and provided employment for 80 percent
of the economically active population. The most important
agricultural product in Senegal is peanuts, the mainstay of
the economy.

In recent years, cereal production in Senegal has not
been sufficient to meet consumption needs. Currently, there
is a deficit of about 200,000 tons of cereal grains each year.
For decades Senegal has exported groundnut and imported rice
to cover its food deficit. During the late sixties and early
seventies, due to the rapid growth of urban areas, the failure
of food production, the disruption of peanut production, the
instability of world prices, and the Sahelian drought, the
country has become painfully aware of its dependence on
imported food, namely rice. Since 1977, due to a generalized
drought, Senegal has imported.:more than 600,000 tons of
cereal. At the present time, domestic rice production covers
only 15 to 30 percent of the country’s needs every year.

Because of economic instability arising from the combined

        
 

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factors of heavy dependence on imported food and unstable
rainfall patterns, irrigation and full water control systems
along the major rivers have become a main priority for the
Government of Senegal.

Although most of the irrigation systems have been built
in the Senegal River Valley (Fig.2),.an ambitious program of
soil and water management has developed during the early
1980’s in the Lower Casamance region to improve food
production.

Site developments in Lower Casamance have considerably
increased during the last decade primarily because of the
drought situation. Today, more than 20 dams have been built
in the region in order to protect the paddy fields against
sea water intrusion during the high tides of the dry season,
and to store fresh water during the rainy season. It is
estimated that more than one third of the paddy fields were
abandoned in this region because of the high salinity of the
soil and water table. The fresh water retained behind the
dams helps to leach the salt out of the paddy fields and
facilitates rice growth after reclamation of the abandoned
paddy fields.

The rainfall shortage and the problem of salinization
have affected not only the polders but also the most

productive paddy fields located curthe first level terraces.

In most of the valleys where small anti—salt dams have been
built, rice production has substantially increased. Perhaps
the best example of this increase is the Katoure Valley where,
for more than one decade, the paddy fields affected by the
salt were abandoned. Only two years after the construction
of the dam, the average rice paddy yield in those same fields
was 3.5 tons per hectare. However, many problems still remain
to be solved” In many paddy fields located essentially in the
lower lands, the water table rises fast at the beginning of
the rainy season when its salinity is already very high. In
some cases, the water table salinity reaches levels twice that
of sea water, which is 35 g/l. Most of the salt is not taken
out of the system. Rather, it is diluted as the reservoir
fills up with fresh water. With the reduced amount of
precipitation each year, the water table salinity tends to
rise fast reaching a concentration that can be detrimental to
the paddy plant’s growth. This situation can lead to a big
loss in grains production, mainly when there is no more fresh
water stored.in the reservoir and (evapotranspiration is high.

Since 1984 many studies have been conducted by the
research teams of ISRA and ORSTOM in site developments where
anti-salt dams were already built.

The following analysis of groundwater management will

focus on the Katoure valley where the first anti-salt dam was

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built in 1984.

The Katoure site is representative of the Lower.
Casamance region from a soil and hydrologic point of view.
The social impact and economical aspects of the dam have also
been studied recently, and both show a need for defining
strategies for water management, especially during years with

rainfall shortage.

8. SCOPE AND OBJECTIVES.

The overall goal of this study is to increase crop
production and economic returns to farmers in the Lower
Casamance region of Senegal. This goal will be achieved
through an improved understanding and management of anti-salt
dams.

The specific objectives of this thesis are to

1. study the groundwater flow and quality in a typical

valley of the Lower Casamance region.

2. develop a groundwater simulation model for

evaluating water movement in the aquifer.

3. evaluate improved management strategies for

irrigation behind anti—salt dams.

II. REVIEW 0? LITERATURE AND TREOR!

.A. IRRIGATION.AND DRAINAGE

The following section consists of a review of irrigation
methods used around the world and those specifically employed
in the Sahel region of Africa.

1. werld.

Worldwide irrigation has expanded dramatically in this
century. In 1900 there was about 40 million hectares, and
today we find.approximately 270 million hectares of irrigation
on 18 percent of the cultivated land. Irrigation provides
approximately one third of the world’s food.

The international rate of irrigation development in the
19603 averaged almost 6 million hectares a year (FAO 1986).
The moSt rapid growth has occurred in India where, in the
19603, the gross area expanded from about 28 million to 37
million hectares, and today it is about 55 million hectares.
In the 19805, the worldwide rate of growth has declined
slightly because of economic recession, adverse terms of trade
for agriculture, and. new emphasis on rehabilitation and
modernization of existing systems. Reliable figures are not

available, but the current rate of growth has probably fallen

to about 4 million hectares a year. Table 1 shows growth in
irrigation development by continents since the middle of the
century.

In general the objectives of irrigation development
have been either to achieve self sufficiency in food and fiber
or to maximize economic efficiency in the use of land and
water. The former objective is essentially the developing
country's and the latter the developed country's. It is
interesting to reflect on some of the factors that have
influenced the pattern of growth in irrigation and drainage
over the fifty years.

From the middle of this century new technologies that had
remained latent during World War II were applied to
agriculture throughout the world. At the same time, large
investments were made in irrigation, particularly in
countries such as India, Sudan, Egypt, and Pakistan where
there has been an established tradition in irrigated crop
production. As a result, grain production rose about 3
percent a year in the period from 1950 to 1973 (FAO, 1986).
Of the new technologies, the most dramatic in its effect was
the introduction of new crop varieties in the late 19603, the
so-called "Green Revolution."

A second event which affected agricultural production and

the value of irrigation and drainage was the oil crisis of

1973 with its second wave in 1979. The rise in oil prices
contributed to a rapid decline in the growth rate of grain
production from about 3 percent to 2 percent in the period
from 1973 to 1977, and in recent years it has fallen toward 1
percent. Regions with poor climates and soils are the

most affected as we see from the present situation in Africa.
The underlying reason is that high oil prices mean high input
costs, so areas with marginal yields fall out of production.

Table 1. Gross irrigated areas by continent
(million hectares). (Source: FAO 1986)

 

 

 

 

 

 

 

 

.=_.._.____=_....._..-—=—-—---=-.----Ti
Regions 1950 1960 1970 1986
Europe (incl. part USSR) 8 12 20 29
Asia (incl. part USSR) 66 100 132 164
Africa 4 5 9 13
North America 12 17 29 34
South America 3 5 6 9
Australia and Pacific '1 1 2 2
Total 94 140 198 271

 

 

 

 

 

 

 

In many countries where irrigated land represents a high
proportion of the total cultivated land, the available water
resources are approaching the economic if not the physical
limits of exploitation. This applies to India, Sri Lanka, the
southwestern United States, Egypt and Sudan. There are small
island countries like Mauritius and arid zone countries like

Somalia and Botswana that need irrigation but have a very poor

10

distribution of water resources in relation to irrigable land.
Possible options in regions of water shortage are to :

(a) construct more storage reservoirs,

(b) undertake major interbasin transfers of water,

(c) better integrate use of ground and surface

waters,

(d) economize on present water use by raising water

management standards of irrigation efficiencies.

In some countries, the correct solution is to undertake
most, if not all, of these measures as part of a long term
investment program, taking into account that some of them are
longer term than others. This is indeed the policy being
followed by countries such as India and Mauritius.

The improvement of irrigation efficiency is the most
vital requirement of our time. A survey by CIID has shown
that in surface irrigation systems, application efficiencies
vary from 35 to 75 percent and conveyance efficiencies from 30
to 90 percent. The overall efficiencies fall mostly between
10 to 50 percent. Many large surface systems in Asia have
efficiencies in approximately the middle of these ranges or
about 30 percent compared with about 37 percent efficiency in
some developed countries. By contrast, countries with more
advanced drip systems have overall efficiencies of about 60
percent. However, such advanced systems are mainly applicable
to industrialized countries or where crops of high value are

grown.

11

1.1. Advanced Technology.

New irrigation technology plays an important part in the
achievement of better irrigation efficiency. In countries
with advanced technologies, water use per hectare is about
half that of the less advanced technologies.

Rapid increases in energy costs and the continual
competition for limited water resources have been the impetus
for continuing research to develop new irrigation systems and
improve technology. Advanced technology includes the use of
surface irrigation sprinklers, microsprinklers, and drip
irrigation. Recently, more attention has been given to
subsurface systems and to subsurface drip systems that inject

water into the root zones with great efficiency.

1.1.1 Sprinkler Irrigation.

The development of electronics in the 19603 and
microprocessors in the 19703 advanced this irrigation method
to one of the most efficient and reliable irrigation methods
available today. Further improvements using the concepts of
low-pressure drop tube and micro-basins developed by Lyle and
Bordovsky (1983) are under way. For example, with these
improvements, they reported irrigation efficiencies of
greater than 95 percent with a linear model system. Heerman
et al. (1984) adapted computer control and optimization
technology tn) center-pivot systems. Similar advances have

been made in water distribution, measurement, and technology

12

for system control. In developing countries, most irrigation
projects still performed well below their potentials.
(Plusquellec, 1985). Improvements can be made without highly
sophisticated technology. For example, Plusquellec emphasizes
that not all automation of water control needs to be

computerized.

1.1.2. Surface Irrigation.

Surface irrigation has been used for centuries. Major
technological advances in other fields have been used to
improve technology for surface irrigation. For example, the
adaptation of laser controls to land leveling equipment in the
mid 19703 had a major impact on technology for leveling
basins. With laser-control equipment, 4 to 8 hectare basins
can be leveled so that 85 percent of the soil surface is
within 15 mm of the mean elevation. Irrigation efficiencies
of 70 to 100 percent are now being achieved with level basins
(Dedrick et al., 1982).

Surge flow, or cycling the flow to irrigation furrows, is
a technique developed in the late 19703 to increase the
advance of water in furrows with a given amount of water.
This has made it possible to reduce runoff and improve
irrigation uniformity on many soils.

The commercial development of automatic equipment using
low cost valves and electronic controllers has played a major

role in the development of this technology. Another new

13

method of controlling water delivery to furrows is a method
called "cablegation" (Kemper et al., 1981). It has enabled
the automatic and uniform distribution of flow to individual

furrows.

1.1.3. Trickle Irrigation.

Trickle irrigation technology, often called drip
irrigation or microirrigation, has advanced greatly during the
past two decades (Bucks et al., 1982). These systems, when
properly designed, installed, and operated, can provide
excellent control of irrigation water (Bralts et al., 1987).
Plugging of emitters has been a major problem, but filtration
and chemical treatment of water minimize these problems.

Evapotranspiration for most close-growing crops is
essentially the same with these systems as*with other systems.
However, decreases in seasonal evapotranspiration of 10 to 15
percent can be achieved with buried, widely spaced trickle
lines because of reduced evaporation.

These modern technologies are rapidly penetrating the
developed countries where the cost of water is usually charged
by volume. They are unlikely to penetrate the developing
world until a more realistic tariff structure is adopted for

water.

1.2. Cost.

Irrigation is a high cost form for agricultural

14

development, and big projects have long lead times from
project inception to full development.

Costs vary widely throughout the world depending on the
type of system, water source costs, size of project, and
available resources for construction. The lowest cost of new
majdr irrigation systems are found in Asia, particularly in
India, where the surface systems cost from $2,000 to $4,000
per hectare. Inn other countries where projects are large
enough to provide economy of scale, costs are around $5,000
per hectare.

In regions where projects are small and where there has
been no long tradition for irrigation, costs are often $10,000
per hectare and more. The higher range of costs is typical of
most of sub-Saharan Africa. There, irrigable land is found in
small scattered entities, which results in not only a high
average cost of development, but also a higher cost of
infrastructure for transportation, marketing, and supplies

that must be improved as part of the project costs.

1.3. Drainage.

In drainage development, statistics are very limited.
However the majority of growth in drained areas has been in
Europe and North America. The pattern has shifted in recent
years to other regions, including the Soviet Union, China,
Pakistan, Bangladesh, and the Middle East, where the old

irrigation systems are suffering from waterlogging. In some

15

regions of the world such as Bangladesh and Cambodia, poor
drainage and. flooding represent the :main constraints on
agricultural production.

The development of corrugated plastic tubing in the 19603
greatly changed subsurface drainage technology. About 90
percent of the drain tubing being installed today is plastic
instead of clay tile.

The adaptation of laser control to drain installation in
the 19603 also advanced.this technologyu .Advances in drainage
technology have greatly reduced the cost of drainage, but
design techniques and criteria for subsurface drainage of
irrigated land have not changed. Today new techniques are
being initiated in humid regions. These techniques include
controlling drainage outflow and using the same system for

subirrigation.

1.4. Human Resources.

Of the 271 million hectares of irrigated land in the
world, 75 percent are in developing countries. Many of these
countries suffer from shortages of varying degrees in human
resources with trained management capability. Even where
there is an adequate supply of technical resources, management
resources may be lacking in many sectors. There is an urgent
need for training in management technology and irrigation

management in particular.

16

2. Africa.

.Africa has not developed irrigation to the same extent as
other developing areas, namely Asia. Only a little more than
0.3 percent of the 2,818 million hectares covered by FAO's 51
African member nations is currently irrigated. By contrast,
India which has only about one tenth of the surface area of
Africa, irrigates nearly five times as much land.

The development of irrigation in Africa has also been
very concentrated. The 13 million hectares that are currently
irrigated amount to about 5 percent of the land in Africa with
permanent and temporary crops. One in every 20 of Africa's
cropped hectares is irrigated. However, in Egypt, 98.6
percent of the cropped area is irrigated. About one half of
Africa's irrigated area is in Egypt and Sudan. Two other
countries, Madagascar and Nigeria, account for a further 20
percent of the irrigated area (FAO, 1986).

The extent to which areas are developed is not uniform
throughout. the continent. Most of what could be described as
"formally organized" irrigation -typically medium- or large-
scale projects - occurs in Egypt and Sudan. This kind of
irrigation covers about two thirds of the irrigated area. The
other one third is traditional, small-scale irrigation in
which simpler technologies are used and where there is often

only a partial control of the irrigation water. This form of

irrigation is somewhat more widely spread;

17

yet, 81 percent of

small scale irrigation occurs in just five countries.

The distribution of the irrigated area over Africa’s

major regions is shown in Table 2.

Table 2. Distribution of irrigated area over the African

region.

(Source: FAO 1986.

Refers to the total

irrigated area in 51 FAO Mamber Countries)

 

 

 

 

 

 

 

 

Regions Irrigated Area % of Total
. (1000
hectares)

llMediterranean and arid 4192 47

North Africa

Sudano Sahelian Africa 2242 25

Humid and sub-humid west 937 10

Africa

Humid Central Africa 18 -
irSub-humid and mountainous 1147 13

East Africa

Sub-humid and semi arid 433 5

Southern Africa

Total 8969 100

 

 

 

 

 

The value of irrigation in Africa.is easily demonstrated.
Although irrigation occupied only 6.5 percent of 124 million
hectares of cultivated land in 43 countries during 1970 -
1980, it provided 20 percent of the value of all the
agricultural crops grown

in those countries. Irrigation

increased.the value of agricultural production per hectare by

18

more than three times.

The need to expand irrigation in Africa arises from the
present .food and agricultural crisis, which has been
developing for several decades. As the FAO study "African
agriculture: the next 25 years" (1986) recently reported,
there has been a widespread decline in per capita food
production in Africa. Because Africa's population is likely
to double over the next 25 years, a failure to take steps
needed to halt this deterioration "could lead to a situation
in which half of Africa's people would be dependant on food
imports and food aid from developed countries... and to
widespread famine with destabilizing consequences both in and
outside Africa".

Such a result is by no means inevitable. African soils
can be made productive with good management, and the use of
more and improved inputs such as seeds and fertilizer. Other
measures include halting soil erosion, improving fertility,
and adopting agricultural policies that will provide African

farmers with the incentive they need to grow more.

3. Sahel.
The term "Sahel" refers to a climatic zone encompassing
the lands immediately south of the Sahara which receive

between 100 to 200 and 500 to 600 mm of rainfall per year

19

(authors differ in their specification of the zonal limits).
In the Sahel zone the risk of inadequate rainfall is so great
that unless farmers have access to at least supplemental
irrigation they will experience frequent crop failures.

Politically , the Sahel region consists of a chain of
former French.African nations stretching in a band across the
southern margins of the Sahara from Senegal to Sudan. In
sequence from west to east there is Cape Verde (islands
offshore Senegal to the west), Senegal, Gambia, Mauritania,
Mali, Burkina Faso, Niger, the northern portion of Nigeria,
Chad, and even part of Sudan (Fig.1).

The heavy rainfall received in the highlands of Guinea
drains north towards the Sahara rather than south towards
the ocean. Thus, the Niger and Senegal Rivers traverse
hundreds of kilometers of semi-arid land carrying water
derived from far-distant highland sources.

The fossil (600 and 40,000 years ago) and subsurface
drainages are the remnants of wetter periods that the Sahel
enjoyed” While no longer carrying surface flow, these
drainages may yet contain substantial subsurface storage
suitable for tubewell extraction.

In Sahelian Africa, water control has played.a relatively
minor part in agricultural development. This has been limited

historically to traditional small scale irrigatitwiin.drought-

20

prone areas and.the reclamation of small swamplands. .However,
in recent decades there has been.a move toward the development
of larger schemes, usually for the commercial production of
crops such as sugarcane, cotton and rice.

Irrigated farming is as yet poorly developed in the
Sahel. In 1976 there was full or nearly total water control
for only 80,000 hectares, less than 1% of the total cultivated
lands. An additional 150,000 hectares were irrigated with
partial water control.

Irrigation was first introduced by the French Colonial
.Administration quite some years ago with the first large scale
total water control development dating back to the 19303 in
the Office du Niger. The aim then was to develop cash crops
especially cotton, using modern agricultural techniques.

These projects were later added to with less expensive,
partial water control elements to be used to pmoduce food
grains for local consumption.

After independence, the Sahelian Governments wanted to
further develop irrigated farming, with emphasis on rice
production, but have not been able to rapidly undertake new
installations.

There are undoubtedly several explanations for the
current slow rate of irrigation development:

(a) up to now the Sahel has obtained its food through

21

extensive, traditional, dryland farming without
costly investments. This has been supplemented by
flood recession crops grown along the major rivers.
Irrigated farming was not considered essential for
food production.

(b) a certain number of irrigation projects were not
resounding successes and all profits accruing to the
community were far too small to cover any new
installation investment costs. In some cases, not
even the operating and maintenance costs could be
recuperated and some installations have deteriorated.

(c) projected crop yields per hectare are in general
considerably smaller than the planners predicted.

(d) lack of trained personnel mainly for management
staff, and high cost of intra-Sahelian transport of
materials and goods.

Notwithstanding these handicaps, irrigated crops have
already contributed substantially to feeding the Sahel. In
1975-1976, nearly 40% of the rice consumed in the Sahel was
produced using modern irrigation, 20% from rain-fed or flood
recession cultivation and only slightly over 40% was imported
(Club du Sahel, 1979).

The Sahelian countries already rely heavily on irrigation

for their rice supply, and since consumption is increasing,

22

they will either have to develop irrigated agriculture or
become increasingly dependent on foreign imports.

The last drought demonstrated the importance of hydro-
agricultural installations with total water control as a
guarantee for food production. Installations with partial
water control proved to be far more vulnerable to the effects
of drought, since shallow river waters only suffice to
irrigate a small part of the prepared lands. This has
encouraged the Sahelian Governments to emphasize the
development of irrigated agriculture and accelerate plans for
the development of major river basins.

Table 3 gives the estimate areas to be irrigated in
several Sahelian countries.

The irrigation systems encountered in the Sahel
Region are very diverse. The most frequent found systems are
the Traditional, Natural Flooding, Recessional, Controlled
Flooding, Total Control, and Basin Control systems. The

following is a description of these methods.

3.1 Traditional Labour Intensive Systems
Three important traditional systems that are found in the
Sahel are Calabash irrigation, Shaduf irrigation, and Dallou

irrigation.

23

Table 3. Area to be irrigated in the Sahelian Region by

Kindell Consult. (1,000 hectares).

 

 

 

 

 

 

 

 

 

Countries 1976 1982 1990 2000 ‘
Gambia 1.5 9.5 14 19.7
Burkina Faso 7.7 21.3 58.8 104
Mali 107 125* 160* 132*
Mauritania 1.4 15 30 70
¥Niger 4.8 17.5 33 52.5
Senegal 96 33.3* 83.5* 160*
llChad 5.8 23.8 49.3 71.8

 

 

 

 

 

 

* These figures comprise new land developments and
rehabilitation of existing perimeters.
irrigation.

(a) calabash.irrigation: a.hand.delivery of water onto
a field. It is found in scattered isolated areas throughout
the Sahel with usually vegetables being the dominant crop
grown.

(b) Shaduf irrigation: a traditional water lifting
device that has probably diffused into the area from the Nile
Valley. The shaduf comprises a log-suspended rod with a
bucket at one end and a weight at the other allowing water to
be lifted and swung around for depositing into irrigation
channels.

(c) Dallou irrigation: inot a widely practiced system.
Water is lifted by oxen from wells that are 4 to 5 meters

deep, and distributed throughout the plot by channels.

24

3.2. Natural Flood Irrigation.

Two types of natural flood irrigation occur in the Sahel.

(a) flood Plain Irrigation: in flood plain areas of
rivers and streams where annual flooding occurs, rice is quite
often planted. Rice is usually sown at the beginning of the
rainy season and allowed to germinate before the arrival of
the floodwater. This system is risky and the rate of success
is not high.

(1)) Depressional Irrigation (Baa-fonds) : another type of
natural flood irrigation is often carried out in depressions
where the water 'table rises during’ the rainy season to

inundate the depression.

3.3. Recessional Irrigation (Culture de Decrue).

In areas of natural flooding a common practice is to
plant crops such as sorghum as the floodwater recede.
Throughout the utilization of residual soil moisture the plant
survives until the arrival of the rainy season. The plant
matures with the onset of the rainy season and is harvested

before the rising waters inundate the field.

3.4. Controlled Flood Irrigation.

This type of irrigation permits the regulation of the
rise of floodwater to 5 cm per day for floating rice and 3 cm
per day for paddy rice. In some area, small submersible dykes

are built around plots to inhibit the rapid rise of flood

25

waters. With the application of more modern technology,
dykes, canals, and sluice gates have been constructed to
control and drain the water from perimeters and protect the
crop from rice eating fish. Such a system provides greater

reliability to the farmer for a successful crop.

3.5. Total Control.

The introduction of full water control systems throughout
the construction of dams, dykes, canals, drains, and sluice
gates provides a dependable supply of water and allows
drainage of leveled plots. Both gravity flow systems and pump
systems are found in the Sahel countries, but, because of
management and social problems, they have never fulfilled

expectations.

3.6. River Basin Development.

Currently, there is the development of interstate river
basin authorities on the Senegal (OMVS), Gambia (OMVG), and
Niger (NBA). A problem which may develop with the growth of
the river basin authorities is the emphasis upon
transportation and, power generation to the detriment of

irrigation.

' 4. Senegal.

In years of normal rainfall, cereal imports represent

about one third of the country’s needs (consumption 850 to

26

920,000 tons; imports 260 to 330,000 tons each year).
Imported cereals are mainly rice and wheat, (Ediafric, 1978).
In view of the large deficit, it is clear that every effort
must be made to free production from uncertainties due to
climatic variation in order to increase productivity. Large
scale irrigation extension is dependent upon the creation of
regulated.storage on the Senegal, Gambia.and.Casamance rivers.
In the absence of such storage reservoirs, it has been
possible to develop only small areas of modern irrigated
agriculture.

The Government of Senegal has made a commitment to the
expansion of irrigation as a mean of increasing food
production. Agriculture is delegated to various regional
development organizations.

SAED is the largest organization which is responsible for
the development of irrigation in the Senegal River Valley. In
other areas agricultural development is under the direction of
various organizations which usually have a division that
oversees irrigation development. SOMIVAC, SODEFITEX, SODAGRI
have been created for the sole purpose of increasing cereals
production, especially rice, through the development of
irrigation. There are also smaller actions such as
"Groupements Villageois or Organisations Paysannes" backed by
Non-Governmental Organisations such as Peace Corps,
Volontaires du Progres, Terre des Hommes etc., where

development is at a smaller scale. All these institutions

27

have their own administration, extension study, and
programming services.

The priority of the Government of Senegal is development.
The irrigation perimeters have been in the development of
large scale total water control systems. However, high
development costs, difficulty'in organizing farmers, and heavy
recurrent costs plus a desire to decentralize management have
resulted in a new interest in small-scale irrigation
development.

The approach at present appears to be a continued effort
to expand the total water control systems, especially in the
Senegal River Valley (Fig.2) and also to provide support and
assistance to small scale development wherever feasible.
Irrigation development is located in five regions of Senegal:
The Senegal River valley, Delta area, Anambe Basin, Lower
Casamance Region, and Niayes Region.

Irrigation has been practiced by many people and the
prevalent systems in Senegal include:

(a) traditional hand watering

(b) natural flood irrigation

(c) total water control system.

The Senegal River Basin, which has the highest potential
for irrigation development, lies within different climatic
zones, resulting in extreme fluctuations in rainfall.

In the northern part of the Basin, the average annual

rainfall of 300 mm is limited to the months of July through

28

September. In the southern portion of the Basin, the average
annual rainfall of 2000 mm occurs from May until October.
Annual variations in rainfall are also extreme, especially in
lower reaches of the River. Variations in annual stream flow
are great and reflect the variations in annual precipitation.

The seasonal characteristics of the rainfall determine
the Senegal River’s floodplain configuration, consisting of a
single flood wave moving down the River. The floodplain is
inundated annually between Bakel and St Louis. As the flood
moves through the Middle Valley and Delta region, it becomes
significantly altered.as peak flows decrease due to floodplain
storage, evaporation and infiltration losses. ‘With the end of
the annual rains, the flood gradually recedes. At the end of
the dry season (April to mid-June), flows decrease during
most years to approximately 10 cu m/sec. at Bakel.

The Lower Senegal Valley is seriously affected by soil
and. water table salinity mainly because of the drought in the
Sahel Region. during the last two decades. This salinity with
chloride, sulphate, sodium and magnesium of ancient neutral
marine origin interfered, later on, with potential acidity of
the mangrove.

Agriculture is the most important activity in the region
and rice is becoming the most dominant crop since the
construction of two dams at Diama and Manantaly and the
establishment of new irrigated perimeters. It is estimated

that 250,000 hectares can be irrigated within the next decade.

29

The Diama Dam located in the Delta of the Senegal River
is to prevent salt water intrusion in the river and to provide
a fresh water supply for irrigation in the Delta area.
Irrigation development in much of the delta could encounter
problems involving salinity and.drainage, with resulting costs
for development and operation.

The Manantaly Dam is located about 1,200 km upstream from
the Atlantic Ocean. It is designed to permit a year-round
irrigation of 225,000 hectares of land between Manantaly and
St. Louis and.a year-round flow of 100 cu m/sec. in excess for
irrigation and other requirements to provide water depths
needed for navigation. The Dam should also provide the
production of 800 gigawatt-hours per year of electricity.

Two major types of irrigation schemes have been
implemented along the Senegal River since 1973: large and
small scale irrigated perimeters. Both systems are served by
pumping water from the Senegal River or one of its old

channels.

4.1. Small-Scale Perimeters.

These perimeters are characterized by small areas of 15
to 20 hectares of heavy clay soil, an average of 20 hectares
per village perimeter and 15 to 20 farmers. The perimeter is
close enough to the River in order to facilitate the water
pumping" but at the same time should. not be subject to

flooding. Clearing, stumping, and construction are done

30

collectively by farmers but canal network design, pumping
station construction, and equipment are financed by the
government. Each individual farmer is responsible for the
leveling and construction of his own plot.

Land preparation is done in June exclusively with
traditional hand hoe or shovel and without pre-irrigation to
soften the soil. Fertilizers and yield varieties are often
used by farmers. The average yield lies between 3.5 to 5.0

tons per hectare.

4.2. Large-Scale Perimeters.

Large scale perimeters mainly located in the Delta area
are characterized by an area between 100 to 10,000 hectares.
Each perimeter is provided with heavy equipment (ie.,
tractors, combines) and large pumping stations (more than 240
hp). The perimeter is divided into holdings of 0.5 to 3.0
hectares each and is fed by a canal capable of irrigating 10
hectares.

The pumping stations and irrigation network are built and
maintained by the government which also decides on the crop to
be planted, the varieties to be grown and the agricultural
calendar.

Land preparation, seeding, and threshing are done
mechanically. Land preparation requires deep plowing every
three to four years and offset and cross-harrowing in

intervening years. Seeding is mechanized, but weeding and

31

harvesting are done manually. The main problem other than
soil and.ground water salinity is the scarcity of labor during
the peak periods of the years, especially during the
harvesting period.

The average yield is 2.5 tons of paddy rice per hectare.
By mid 1977 SAED had.brought 9600 hectares under irrigation in
the Senegal valley and delta area.) Since then, substantial
progress has been made.

Under the direction of SODEFITEX and SODAGRI, there were
in the late 19803 10,000 hectares of modern irrigation systems
in operation in eastern Senegal and Casamance. The irrigated
perimeters are located mainly in the Anambe Basin. Water
behind the Anambe Dam is distributed by gravity onto the rice
fields by a well designed system of canals. The two main
irrigated crops are rice and corn.

In the Niayes region, there are large quantities of
subsurface water at relatively shallow depths. Traditional
well gardening has been practiced for centuries, but reliance
on wells has significantly increased since the drought of the
early 19703, particularly for the dry season. Farmers using
traditional technology are usually able to produce between 25
to 40 tons/ha of vegetables. Although gardens vary greatly in
size depending on factors such as cropping season, family
size, recharge rate, depth of water table and amount of land
in dryland crops, most plots are small, less than 1/10 to 1/3

hectares, with a minimum of one well for every 1,500 to 2,500

32

square meters.

5. Lower Casamance.

For'many years, the Lower Casamance region was a food
self-sufficient region. In recent decades, this region has
experienced food deficits.

Because of the Sahelian drought during the last two
decades, the annual amount of rainfall in the Casamance region
has decreased from 1,500 mm to less than 1,000 mm. The most
striking fact is that during the period from 1966-1980, there
was greater than 20% reduction in rainfall, and over the
period of 1980-1984 the average was even lower (Fig 3).

Since the Lower Casamance region is generally' considered
marginal for mangrove rice, a reduction of 20 to 30% in
rainfall has been even more disastrous for yields. With
insufficient rainfall, there is inadequate leaching of the
polders and as the salt level increases the production of rice
becomes nearly impossible.

Geographically, the saline portion of the Casamance River
estuary extends 220 km into the country; salt water regularly
rises as far as 130 km inland. Salt content reaches its
maximum level in June and its minimum level in October. The
salinity at Ziguinchor varies between 19 and 37 grams of salt
per liter.

Apart from the Casamance River, there are 5 major basins

in the Lower Casamance. All of them are subject to the sea

33

Rice Production
Bignona (North)

Thousands

 

35

 

 

 

 

- Rainfall (mm) - Rice area (ha)
m Rice production (MT)

Figure 3. Evolution of rice production in Lower Casamance.

 

34

water effects of the river, and the maximum amplitude of the
tide is approximately one meter. Since the topography of the
region is quite flat, all of the backwaters (marigots and
bolons) are also affected by salt over much of their length.

Another result of the level landscape is a lack of runoff
in the watershed. On average, only 6% of rainfall in the
Lower Casamance goes into runoff (Harza Engineering, 1981) and
thereby helping to leach mangrove rice fields. Given the
shortage of rainfall over the last several years and the
increasing accumulation of salt, the number of abandoned
mangrove rice fields is multiplying all over the Casamance
Region.

Along the tidal portions of the river basins, we can
observe not only a tendency towards increased salinity of the
river bed itself, but also a serious tendency toward increased
salinity of the underlying water table.

This salinization process occurs at the end of the rainy
season as a result of high tides, hence feeding the water
table. Consequently, not only the polders, but also the rice
fields located on the first level of terraces are affected by
the rainfall shortage and the problem of salinization.

Irrigation and drainage have been practiced in the Lower
Casamance by farmers for centuries. The traditional Diola
system for reclaiming mangroves is based on the judicious use
of the movements of the tide. In the absence of free water,

farmers managed to leach the salt from their fields without

35

lowering the pH. This result was obtained by allowing a
continual readmission of salt water during the dry seasonr In
years of abundant rainfall, this type of field can produce as
much as 3 tons of paddy,rice per hectare with no fertilizer
and, in many cases, no weeding. The double dyke system, which
makes it possible to tap all the resources of the mangrove
(wood, charcoal, fish, pasturage, rice farming), is well
adapted.but requires a great deal of labor. Given the last 15
years of low rainfall and the flight of young people toward
the cities, the future of mangrove rice cultivation is in
question (Schillinger, 1978).

Site development (polders, drains, anti-salt dams) in the
Lower casamance focuses on the desalinization of the soil by
means of fresh water retention and partial exclusion of
brackish water. The difficulty encountered in these systems
involves finding a reasonable balance between the exclusion of
saline water and the drying out of the soil, which may provoke
a drastic decline in pH.

The low level of rainfall in recent years has
dramatically reduced the amount of fresh water available for
leaching the salt out of these fields, thus diminishing the
benefits of site development.

Nevertheless, after monitoring the Medina polder for five
years, Beye (1977) was able to reach some very important
conclusions:

(a) for the polders which were gravity drained, the

36

shallow drainage system spaced at a distance of 20
m (57% clay) and blocking the entry of brackish
water resulted in the leaching of 50% of the salt in
the upper layer (0-20 cm deep). Unfortunately, in
years of little rainfall, the salt content in the
polders quickly rose again.

(b) with respect to the pH level, the drainage system
allowing the entry of saline water every 5 days
during the off-season in order to avoid ‘total
drying out of the soil proved to be the best. The
pH held steady around 6.5.

These results and those obtained by Marius and Cheval
(1980) at Tobor and Guidel show that site development
(drainage) converts the surface horizons from acid sulfate
soil to a para-acid sulfate soil and, with more fresh water
(greater rainfall levels, fresh water retention dykes), the
polders could become viable for rice production. That is why
the Government of Senegal has recently started up an important
soil and water conservation program in Casamance in order to
improve rice production in the region. The construction of
small anti-salt dams in most of the valleys remains the
primary objective.

It is estimated that a total of 100,000 hectares could.be
irrigated in the Casamance area and the planned growth is
3,000 hectares per year. Most of the potential for irrigation

is located in the Lower Casamance region along the main

37

tributaries: Bignona: 12,000 hectares, Baila: 34,000

hectares, Kamobeul: 32, 000 hectares and, Guidel: 1, 500
hectares.
Unlike the National Programs of Soil and Water

Conservation, which are designed for large watersheds of
several hundreds of square kilometers, and sophisticated water
control systems, the small anti-salt dams are built and
managed by peasants of one, or, at the very most, a group of
three villages. These programs are less ambitious and
directed towards small watersheds not larger than several
hundreds of hectares. Most of the rice fields are not
strongly affected by the salt. The main problem encountered
there is keeping a sufficient depth of water in the plots
during the whole growing season.

The anti-salt dam consists of a dyke and one or two
reinforced concrete structures. The dyke is 400 to 1,000
meters long, 4 to 6 meters wide at the bottom, and 2 to 4
meters on the top. The height varies between 1.5 to 2.5
meters. In many cases, the dyke is built entirely by the
farmers of one, or at the very most 3, villages which share
the land on both sides of the dam. In general a road which
crosses the entire watershed is used as a foundation. This
may also present the advantage of facilitating the access to
many villages during the rainy season, mainly during the
floods.

The reinforced concrete structure located in the affluent

38

bed, consists of two or four gates (1.5 meter wide); each of
which is designed to have a rectangular weir 20 centimeters_
high and 60 centimeters wide at the bottom.

In order to retain water behind the dam, the peasants
must close the gates by installing two lines of planks on the
weir, and fill the spaces between them with mud. The planks
are placed one on top of the other. The number of planks
depends only on the farming calendar. Each plank i3 20
centimeters in height and.slightly longer than the gate width.

At the beginning of the rainy season, farmers put in
place two or three planks to retain. a certain amount of water
which will inundate the lowest rice fields and dissolve the
salt. Water will then be flushed out by removing the planks.
This type of operation has to be done as many times as needed
to get good conditions for growing rice, in many cases, until
mid—July when they start plowing their plots.

After the rice transplanting operation, which begins
mid-August, farmers put in place more planks in order to
retain more water as the rainy season ends. Only after big
storms is excess 'water released to avoid flooding the plants.
During the dry season, the gates remain closed; sea water is
not admitted.

Because of a poor water management program behind the
anti-salt dams, many conflicts have arisen between farmers
throughout the entire Lower Casamance. The rice fields close

to the dams are flooded too fast because of their lower

39

position on the toposequence, especially at a time when the

plants are not robust enough to support a long submersion.
During the same period of time the rice fields located at the
terraces need a certain depth of water to maintain good
conditions for rice growth.

In accordance with the location of their plots on the
toposequence, farmers. decide whether or not to release a part
of the water stored in the reservoir. Often, there is no
agreement among landowners, or a final decision is made too
late. Sometimes the problem of how much water to release from
the reservoir can be more complicated, as in when paddy fields
downstream from the dams do not get enough water to leach the

salt out.

40

.oocoEmmmo nosoq ca

mucosvwmomou Hmoflame

 

.v wusoflm

 

41

B. HYDRAULICS OF GROUNDWATER.AND SOLUTE TRANSPORT.

The term groundwater is usually reserved for the
subsurface water, which occurs beneath the water table in
soils and geological formations that are fully saturated.

Groundwater constitutes an important component of water

resource systems, supplying water for domestic use, industry,

and agriculture.

1. Equations of Groundwater Flow.
The basic law of flow is Darcy’s law. It is valid for

groundwater flow in any direction in space, and is stated as

follows:
=_ db
0 mar (11
_Q____ db
a K3: (2)
where:

K = hydraulic conductivity or coefficient of permeability

[L/T]

42

volume flux or flow rate [IR/T]

A cross section [LN

v specific discharge [L/T]
dh/dl = hydraulic gradient [L/L]
When combined with the continuity equation, a partial
differential equation is the result for:

(a) steady-state saturated flow,

(b) transient saturated flow,

1.1. Steady -State Saturated Plow.

Consider a unit volume of porous media such as that shown
in (Fig.5). Such an element is called an elemental control
volume. The law of conservation of mass for steady-state flow
through porous medium requires that the rate of flow into an
elemental control volume be equal to the rate of fluid mass
flows out of any elemental control volume. The equation of
continuity that translates this law into:mathematical form.can

be written, with reference to (Fig.5), as:

_a(PVx) _a(pvy) -a(sz) =0 (3)
6x aY dz

 

where p is the fluid density.

43

l /%—a°°i:

 

 

 

 

 

 

, _
:l x f
l I, A:

-1. one) '
... z-s—L... A: — ,1-.-_=-11—»..12<am..
x .I'
I,
o // Ay

 

 

 

Figure. 5. Mass fluxes in a unit volume of saturated soil:
After Gray (1973).

44

If the fluid is incompressible, p(x,y,z) is constant
and the p’s can be removed from Eq.(3). Even if the fluid is.
compressible and p(x, y, z) is not constant, it can be shown
that terms in the form pam,/8x are much greater than terms
in the form map/ax both of which arise when the chain rule
is used to expand Eq.(3). In either case, Eq.(3) simplifies

to:

av av 6v
?7- 7?! 7f— 0 ( )

Substitution of Darcy’s law for v“ \Q, and v; in Eq.(4)

yields the equation of flow through an anisotropic saturated

porous media:

8 an a an a

an =
a; (KXTX) +33; (Ky-a?) +3-2- ) 0

”(=33 (5)

For isotropic media, K,==Ig = K; if the media is also
homogeneous, then K(x,y,z) is constant. Equation (5) then
reduces to the equation of flow for steady-state flow through

a homogeneous, isotropic media:

45

8212+ 3212 + 8?}: =0
‘63? 377 ‘5? (6)

Equation (6) is known as Laplace’s equation. Its solution
is a function of h in terms of x, y, and 2 that describes the
value of the hydraulic head (h) at any point in a three-
dimensional flow field. A solution to Eq.(6) allows us to
produce a contoured equipotential map of h and, with the
addition of flowlines, a flow net.

In a two-dimensional flow field, for example, in the x2-
plane, the central term of Eq.(6) would drop out and the
solution would be a function of h in terms of x and 2 (ie.,

h(x,z)).

1.2. Transient Saturated Flow.

The law of conservation of mass for transient flow in a
saturated porous medium requires that the net rate of fluid
mass flow into an elemental control volume be equal to the
time rate of change of fluid mass storage within the element.
With reference to (Fig.3), the equation of continuity takes

the form:

_ a (pm) _ 8 (my) _ 39v.) = a (pn)
dx dy dz dt (7)

 

46

where n is the porosity of the aquifer.

Expanding the right hand side, Eq. (7) is:

_ 8 (pvx) _ a (pvy) _ 3 (9") gm 39+ an (8)
3x BY ‘_?fi?—' ‘3? pifi?

The first term on the right-hand side of Eq.(8) is the
mass rate of water produced by an expansion of the water under
a change in its density p. (The second term is the mass rate
of water produced by compaction of the porous medium as
reflected by the change in its porosity n. The first term is
controlled by the compressibility of the fluid B and the
second term by the compressibility of the aquifer a. The
change in p and the change in n are both produced by a change
in h, and the volume of water produced by the two mechanisms
for a unit decline in head is EL, where S, is the specific
storage given by S, = :g(a + Bn). The mass rate of water
produced (time rate of change of fluid mass storage) is S,

ah/at, and Eq.(8) becomes:

_a(pv,)_a<pv>_8(pv.>_ 3h 9
dx dyy dz $853? ( )

 

47

Expanding the terms on the left-hand side by the chain
rule and recognizing that terms of the form pdeax are much
greater than terms of the form map/3x allows us to eliminate

p from both sides of Eq. (9) . Inserting Darcy’s law we obtain:

a an a an a

an an
.3; (Xx-33’ +37 (Kym?) +33 (10)

“=72" =23?

This is the equation of flow for transient flow through
a saturated anisotropic porous medium. If the medium is

homogeneous and isotropic, Eq.(lO) reduces to:

3212 + 6212 + 8222 = 3.. ah (11)
"A? 37’ 7)? 7'3?

or, expanding S;

am 82h 8212 = pg(a+nB) an
ax2+ ay2+ 3:2 K .3? (12)

 

48

Equation (12) is known as the diffusion equation. The
solution h(x,y,z,t) describes the value of the hydraulic head
at any point in a flow field at any time. .A solution requires
knowledge of the three basic hydrogeological parameters, K, a,
and n, and the fluid parameters, a and B.

For the special case of a horizontally bounded aquifer of
thickness b, S = S,b and T = Kb, and the two-dimensional form

of equation (12) becomes:

821: + 321: = s an
‘6? "a7 7?? (13)

The solution h(x,y,t) describes the hydraulic head at any
point on a horizontal plane through the horizontal aquifer at
any time. This solution requires knowledge of the aquifer
parameters 8 and T.

For the special case of a horizontally unbounded aquifer
(Phreatic Aquifer), T = Kb, where b is the aquifer saturated
thickness, and Q,the specific yield. &,is defined as the
volume of water, an unconfined aquifer releases from storage
per unit area of aquifer per unit decline in water table.

S ne, where ne is the effective porosity of the

Y

aquifer.

The technique of analysis of groundwater flow is a four—

49

step process, involving:
1. examination of the physical problem,
2. replacement of the physical problem by an
equivalent mathematical expression,
3. solution of the mathematical problem with.the accepted
techniques of mathematics,
4. interpretation of the mathematical results in terms of
the physical problem.
Mathematical models based on the physics of flow usually
take the form of boundary-value problems. To fully define a
transient boundary-value problem for subsurface flow we need
to know:
1. the size and shape of the region of flow,
2. the equation of flow within the region,
3. the boundary conditions around the boundaries of the
region,
4. the initial conditions in the region,
5. the spatial distribution of the hydrogeologic
parameters that control the flow,
6. a mathematical method of solution.
If the boundary-value problem is for a steady-state
system, requirement (4) is removed.
The method of solution can be categorized roughly into

five approaches:

50

1. solution by inspection,
. solution by graphical techniques,

2
3. solution by analog model,
4. solution by analytical mathematical techniques,
5

solution by numerical mathematical techniques.

2. Solute Transport.

The common starting point in the development of
differential equations to describe the transport of solutes in
porous materials is to consider the flux of solute into and
out of a fixed elemental volume within the flow domain.

The physical processes that control the flux into and out of
the elemental volume are advection and hydrodynamic
dispersion. Loss or gain of solute mass in the elemental
volume can occur as a result of chemical or biochemical
reactions or radioactive decay.

Advection is the component of solute movement attributed
to transport by the flowing groundwater. The rate of
transport is equal to the average linear velocity, v, where
v = v/n, v being the specific discharge or Darcy’s velocity,
and n the porosity.

Hydrodynamic dispersion, or spreading phenomena, is an
irreversible process. It canlxaa.mechanical dispersion which

dominates at a high velocity or a diffusion at a very low

51

velocity. However, in many cases, or as a first
approximation, the fluxes due to hydrodynamic dispersion are
much smaller than those due to advection, for example, for

saturated flow:

IqCI >| nDh°VC| (14)

where: c = solute concentration [M/Lfi
q = total flux [L3/L2T]
n = porosity

Dh== hydrodynamic dispersion coefficient [IF/T].

Under such conditions, polluted groundwater bodies move
in the aquifer along the pathlines of the water itself, at the
velocity of the latter. In the absence of adsorption,
sources, and. sinks, the pollutant balanced. equation for

saturated flow, 9=n , reduces to:

Bnc=_ ,
W V Cq (15)
q=nv

For the simple casecmfaihomogeneous nondeformable porous

52

medium vn = O , and an/at = O , Eq.(15) reduces to:

ac: _ ,
372' V'VC CV v (16)

For steady flow of an incompressible fluid in a

homogeneous nondeformable porous medium, vuV == 0, Eq.(16)
becomes:

3c__ 'V

‘d? V C (17)

In a two-dimensional flow in the xy-plane, Eq(l7) takes

the form:

ac=_v ac_v 8c
3? ”'32—: ’3? (18)

The solution of Eq.(18) which is a linear hyperbolic
partial-differential equation in the three independent

variables (x, y, t), can be rewritten in the form:

53

ac dc v8c+v3c
‘3? “in? v'?? ”a? (19)

It can be represented, at least in principle, by lines of
constant concentration, called characteristics. Along such a

characteristic, the variation of c vanishes:

8c acd ac
dc ‘3?““3-0'” 'a-dy'0 (20)

The statement dc/dt = 0 means that the concentration of
an observed fixed particle does not change with time as it
travels in the considered domain. For the above reason, dx =
V5 dt, and dy ==Vg dt. This means that the direction of the
characteristic coincides with that of the flow, namely that of
the streamline.

Similar to the models of saturated flow problems, the
complete model of a pollution problem consists of the
following items:

1. specification of the geometrical configuration of

the closed surface that bounds the problem area
with possible segments at infinity,

2. vspecification of the dependent variables of the

54

pollution problem (i.e., the concentration, c(x,t))
of the specific constituent or constituents under

consideration.

III. RESEARCH METHODOLOGY

.A. RESEARCH APPROACH.

Based upon the need for an improved understanding of the
engineering and management aspects of the anti-salt dams, the
following approaches are proposed for achieving the objectives
of this research:

Objective: 1. To study the groundwater flow and quality
in a typical valley of the Lower Casamance
region.

The approach to be followed under this objective will be

to describe and measure the groundwater flow and quality of a
typical valley in the Lower Casamance region in Senegal. For
this study, the Katoure valley will be used because of the
availability of hydrologic and soils data. Field data have
been collected for more than six years.

Objective: 2. To develop a groundwater simulation model
for evaluating water movement in the
aquifer.

The approach to be used under this objective will be to

develop a finite element model for evaluating groundwater
movement in a mono layered aquifer. Data from the Katoure

valley site will be used to verify the model.

55

56

Objective: 3. To evaluate improved management strategies

for irrigation behind anti-salt dams.
An,evaluation and discussion of the results of the
simulation model will be made so that recommendations for

improved management parameters can be formulated.

B. EXPERIMENTAL‘MITBODS.

1. Site Description.

The Katoure site is located 5 km Southwest of Ziguinchor
(Fig. 6). The watershed area is about 95.6 square kilometers
(BCEOM - IRAT 1970). The Katoure river is an affluent of the
Kamoubeul River which itself is the most important affluent of

the Casamance River.

1.1. Climate and Hydrology.

Like the whole sub-humid.west African region, the climate
is sub-Guinean characterized by two distinct seasons:

1. a dry season from November to May,

2. a rainy season which extends from June to October.

The average rainfall in Ziguinchor prior to 1965 measured
around 1,600 mm. Seventy percent of the time the highest
total monthly rainfall (one third of the annual total) was
recorded in the month of August, 20 percent of the time in

September, and 10 percent of the time in July. The calculated

57

potential evapotranspiration (class A pan) is about 1,300 mm
per year at Ziguinchor.

During the rainy season the water balance prepared by
Schillinger (1978) shows a major surplus only during the
months of July, August, and September. Beginning in October,
periods of drought appear frequently creating a negative
balance.

Because of its very low relief and current rainfall
deficit, the hydrology of the watershed is under the influence
of the sea water intrusion. Salt water frequently flows as
far as 30 km from the confluence of the Katoure River,
creating an acute salinization problem in the rice fields
located on the river plain. Above the river plain we have
areas which are fed by run off coming from the plateau and a
rise of the water table. During the period from August 15 to
October 1, these soils often benefit from the underground
water, which gives local rice cultivation a particular

character.

1.2. Soil.
The nature of the soils depends on the soil’s position in
the topographical sequence.
On the plateau, the soil is sandy loam with a sandy

surface. Two types predominate:

58

 

 

Watershed Limit

 

 

 

 

 

 

 

 

~

,- -7-“;q:vu.:t.fif TTT

(‘Izcg' [.1 g" .‘|lee-I.e e-cvfi. o”.
l W’Néflymfi-Mig' = Roads
5 17 I I v a
P.” 3 . ':%ihib. +94 Border between Senegal and Guinea Bissa
gJi |IL | } fifial .
. U a I f ..o.:.: I Anti-Salt Dam
' I M ' (may)

‘ l ‘4.’

i. him 'l I M133
E FE! O'.”.u ._ |'_ l , Upperland (Plateau)
._ _A7‘-flll‘l’l.| 15:}..7Lgif'fihn‘. v.;l"::‘-

___ “ ,__- ' .

 

 

 

[ Ibhcltus 0030- o I 10-
fl

Figure 6. Map of the Kamoubeul River’s watershed

59

(a) red, low base status iron soil with a higher clay

content in the B horizon,

(b) ferrugineous, leached tropical beige soils found

in the central well drained uplands.

Along the inland valley and the river itself, there can
be found a sandy zone (50 to 80% sand) that is temporally
flooded during the rainy season. The dominant types are the
Gray water-bearing soils, well known as transition soils
between the plateau and the alluvial plain.

The upstream portion of these soils is often abandoned
because underground water no longer rises to the same level
after more than 10 years of drought. The middle portion is
used occasionally for rice cultivation of direct seeded rice;
the lower portion, which includes the fringes of the alluvial
plain, is also used for rice, either by direct seeding or by
transplanting.

The inland valley is dominated by mineral hydromophic
soils, characterized by a fine texture (48% clay) and high,
natural fertility. These soils, located upstream of the
alluvial plain, are not affected by the salinity problem.
They are often surrounded by a sandy upper terrace of 0.5 to
1 meter in altitude above the average level of the river,
while the altitude of the upper terraces ranges between 2 to

6 meters.

60

The alluvial plain is mainly dominated by two types of
soil, both affected by salinity and acidity problems:
(a) para-acid sulfate soils which can be classified as
Loamy-clayey acid soils,
(b) acid sulfate soil which contains 80% sand.
Both types of soils are the result of alluvial infilling
which followed the great Ogolian regression, and plateau

colluvium.

1.3. Experimental Network.

The Katoure Dam is 440 meters long and designed to
protect 780 hectares against the intrusion of saline water
during the daily tides. It is located next to the village of
Katoure, 15 km from the mouth of the river. The dike was
entirely built by farmers of three villages who own lands in
the valley. The dike is 440 meters long, 2.60 meters wide on
the top, 5.0 meters at the bottom, and the average height is
about 1.5 meters.

A reinforced concrete structure with four gates is built
in the river bed. Each gate is 1.50 meters wide and designed
with a rectangular weir.

A network of 98 piezometers was installed on 100
hectares located on both sides of the dam; 80 hectares behind

the dam and 20 hectares upstream (Fig.7). The depth of the

61

piezometers varies between 6.0 and 12.0 meters.

2. Piezometric Tests

Two methods have been used in order to determine the

hydraulic conductivity of the aquifer.

(a) The LeFranc Test, named after a French geologist, is
based on the realization of a permanent flow
regime. This test is a variant of the absorption
test. This test has been done on 98 piezometers.

(b) The Slug Test has been performed on 42 piezometers

in order to validate the results of the previous

test .

2.1. Principle of LeFranc Test

This test consists of creating a variation of head either
by injection or by pumping into a cavity with a known
diameter. A pipe screened on one end is introduced to the
cavity. The screened part of the pipe is 1.5 meters long and
should be entirely located under the watertable.

From a tank, water is poured into the piezometer through
a length of rubber tubing (Fig.8). The overflow is collected
in a beaker. A quasi permanent flow regime is reached when
the difference between the volume of water from the tank and

the overflow becomes constant over a period of time.

62

 

 

‘\ ‘o' :3."

. \/
0 ' -\‘.’-\_/
o I'

O

‘1“ lull-n
. )5'0-‘OI
V‘

'6‘! H

0
0
O 0 U
.' 0 U
o : °°
\ 0 x 0
“new: J °
.j}
I:
L
o Piezometer .
II
. .- - t
oriezometcre Le:r:nc .es:
- Infiltration Test a 70L513’c1cts \\_\ ,
' Double rzng Infiltrat:on Tcs: (Htxle ' 'w ”9 ’w"
»——I Neutron Probe and Sense Ceszmetc: Tesq
_ \

       

_V

 

 

Figure 7.

Experimental network.

 

63

Then, the inflow water is stopped and the drawdown measured
every 15 seconds during the first 20 minutes and every 5
minutes during the next 40 minutes.

The LeFranc test does not estimate a local permeability
but an overall value, which can be very different.
Nevertheless, it is a quick and cheap test which can be easily
repeated , and it gives important indications with regard to
aquifer structure and heterogeneity. V

The mathematical resolution of this type of problem is
done by Maurice Cassan (Les Essais d’Eau dans la
Reconnaissance des Sols). The physical formulation of the
problem is as follows.

Let H be the depth of water in the tube above the
watertable, and z the depth of water at any time t. For an
interval of time dt the drawdown is dz and the flow can be

expressed by the following equation:

1=Adz
at (21)

where A is the internal cross-section of the pipe, and

dz/dt = infiltration rate.

64

The negative sign means that any change on dz implies a
head reduction.

Because the intake is long and cylindrical, it is
recommended to use the coordinates of an ellipsoid with a
focal distance equal to 1/2.

Thus Q = mKD, and equating with equation (21), we

obtain:
Adz 1
- =mKD
at (22)
where D = internal diameter of the pipe
K = hydraulic conductivity of the aquifer
m = shape coefficient. If l/D > 10 then
m = (2 n l/D) / ln(2 l/D)
l = length of the screened portion of the pipe

At t = 0, Z = H and integrating (22), we obtain:

dfz _mKD
T.{dt (23)

MKD

an=- t+Constant

 

(24)

65

 

 

 

 

 

 

Tripod
"es-em
Dealer
L/ I ‘/ -' ///’/’////
J / ////////////// '/// 4;////f/////////,>7////////////A/////x .//// / / /' / ' ' '

 

 

 

 

 

Ida

 

 

 

 

 

Figure 8. Apparatus for LeFranc test.

66

ln H = Constant.

MKD

an=-_jr_t+lnH (25)
_ =_nma>

lnz lnH "I—t (26)
Z=_1Mfl3

1n? t (27)
2:84;”

7? (28)
_mKD

Z=He fir (29)

By using loglo inscead of In, equation (29) becomes:

Z=_IMU)
231097) Tt (30)

67

2
TI (31)

_2.3A

t:

log

where A.is the internal cross section of the pipe. It is also

assumed to be equal to the cross section of the cavity.

A: n02
71 (32)
Equation (32) becomes:
=_2.31tD Z
t T—mx 1°97? (33)

If we plot in a semi log scale Z/H function of time, t, we

obtain a straight line with a negative slope(s)

8:2.3nD
ZmK (34)

The hydraulic conductivity (K) is then computed as

68

follows:

K32.3nD
43m (35)

2.2. Principle of Slug Test.

The method is initiated by causing an instantaneous
change in the water level in a piezometer through a sudden
introduction of a known volume of water or by introducing a
solid cylinder of known volume into the piezometer. The
recovery of the water level with time is then observed. The
simplest interpretation of piezometer-recovery data is that of
Hvorslev (1951). His initial analysis assumed a homogeneous,
isotropic, finite medium in which both soil and water are
incompressible.

The rate of inflow, q, at the piezometer tip at any time,
t, is proportional to the hydraulic conductivity, K, and to

the unrecovered head difference, H - h, so that

dh =FK(H-h)

= 2
q(t) HrHE (36)

where F is a factor that depends on the shape and the

69

dimensions of the piezometer intake.

Hvorslev defines the basic time lag, T” as:

Tagnr2
0 1T. (37)

When this parameter is substituted. in Eq.(37), the
solution to the resulting ordinary differential equation, with
the initial condition, h = H0 at t = 0, is:

H-h_ -c/T,

-e

H (38)

To interpret a set of field recovery data, the data are
plotted and the value of To measured graphically. I< is
determined from Eq.(38). For a piezometer intake of length
L and radius R, with L/R > 8, Hvorslev (1951) has

evaluated the shape factor, F. The resulting expression for

K is:

._. r21n(L/R)

K
2LIB (39)

 

70

For slug tests run in piezometers that are open over the
entire thickness of a confined aquifer, Cooper et al. (1967)
and Papadopoulos et al. (1973) have evolved a test-
interpretation procedure. Their analysis is subject to the
same assumptions as the Theis solution for pumpage from a
confined aquifer. Contrary to the Hvorslev method of
analysis, it includes consideration of both formation and
water compressibility. It utilizes a curve-matching procedure
to determine the aquifer coefficients T and S. The hydraulic
conductivity K can then be determined on the basis of the
relation, K = T/b. Like the Theis solution, the method is
based on the solution to a boundary-value problem that
involves the transient equation flow, Eq.(13).

Both techniques presented are quite similar in principle
and are easy to apply on field. However, they are heavily
dependent on a high-quality piezometer intake. If the
wellpoint or screen is corroded or clogged, measured values
may be highly inaccurate. On the other hand, if a piezometer
is developed by surging or backwashing prior to testing, the
measured values may reflect the increased conductivities in

the artificially induced gravel pack around the intake.

2.3. Field Data collection.

Piezometric heads were measured with an electrical device

71

every two weeks during the dry season from.November to May and
after every major storm during the rainy season. The
estimated error of the device is about 2 centimeters.

Samples of surface and subsurface water were regularly
analyzed (once per month) in order to determine the
electrical conductivity (salinity), pH, and Aluminum sulfates,
which are responsible for most of the acidity problems
encountered in mangrove lands.

Besides the field tests described earlier, samples of the
aquifer material at the location of each piezometer were
analyzed for physical and chemical properties. Soil samples
were taken from every one meter below the water table surface

to a depth of six meters.

2.4. Data analysis

The major task of the analysis was the estimation of the
average area and the optimal contouring of certain parameters
such as pdezometric heads, groundwater salinity, hydraulic
conductivity.

The estimation problem becomes strongly significant
because of the spatial variability of some soil physical
parameters, the existence of a correlation structure, and the
fact that the data contain errors in measurement since they

were collected at unequally spaced intervals.

72

The method of estimation of random fields that was used
is the so-called universal Kriging or nonstationary fields.

This method deals with estimating values of a field
parameter or linear functions of the field at a point (or
points) from a limited set of observed values.

Nonstationary is here limited to those cases where the
mean cannot be assumed constant, and it becomes necessary to
describe and account for the mean function m(u) in some
manner. An unknown nonstationary drift also implies that the
covariogram, whether semivariogram or covariance, cannot be
estimated since the residuals are unknown. Hence, estimating
the mean and estimating the covariogram are related processes.
Universal Kriging proposes a particular functional form for
modelling the mean and treats the related processes of mean
and covariogram estimation as:

1) an iterative procedure estimating first one

statistic, then the other,

2) an invocation of the theory of intrinsic random

function of order k.

Developed by Natheron and others at the Fontainebleau
School (1971), universal Kriging proposes that the mean (or
drift) can be modeled as a linear combination of v basic

functions fn as follows:

 

73

m(u)=§)vanf"(u) (40)

The basic functions are known functions, but the
coefficients, a“. where r1== 0,1,2,...pv are unknown and
have to be estimated. The iterative procedure involves
finding the best unbiased linear estimaterof the coefficients,
an, of the drift by first assuming some covariogram
structure, then forming the residuals from the estimated drift
in an attempt to reconstitute the original assumed
covariogram. The solution is obtained when the initial
assumed covariogram and the reconstituted covariogram agree.

In the present case study, the experiment consisted of
Kriging each observation point using neighboring points and
then using various measures of the difference between kriged
and known values as criteria for assessing the validity of the
assumed underlying drift and covariogram model. The original
data consisted of piezometric heads, salinity and pH of water
samples taken from each piezometer, and hydraulic conductivity
of the aquifer. Contoured maps of water table surface and
salinity are drawn and used to evaluate groundwater flow and

quality.

74

C. COMPUTIR.SIMULATION.

l. Groundwater Flow and Solute Transport Simulation

The numerical method used to simulate both groundwater
flow and solute transport was the finite element method” This
method is applied.to the time dependent flow of a confined and
isotropic aquifer, Eq (13). The same equation was used to
solve for a phreatic aquifer assuming that the Dupuit
assumption holds. A new term I is added to the general
formula in order to account for infiltration. The general

formula then becomes:

S%=-aa:-‘(T%)+%(T%)+I ’ (41)

where S denotes the storativity or specific yield depending on
whether or not the aquifer is confined, and I denotes the net
infiltration or evaporation. The assumption was made that
there is no leakage and that the boundary conditions are
assumed to be of the first or second kind. Thus, everywhere
along the boundary, either the head or the rate of water
supply is given. Unlike the steady flow case, 3¢/8t = 0,

initial conditions are needed. The initial condition at time

t = 0 was ¢ = ¢°(x,y), where ¢°(x,y) is a known function.

 

75

Equation (42) may be satisfied throughout a specified
region R in the x-y plane. Boundary conditions must be
satisfied on the boundary of that region . A general

formulation of the boundary conditions can be written as

4H. (42)
and
26.. (43)
tram qh

on 81 and. SN respectively, where S1 and. S2 are
boundary segments which together constitute the entire
boundary of the region R. On SI, the head is given while
on 52, the groundwater flux normal to the boundary is
prescribed.

The region R in which the flow takes place is
subdivided into a large number of discretized elements, in

each of which the groundwater head is then approximated by a

 

76

simple function. 'Triangular or quadrangular elements are used
because they make it possible to closely follow natural
(curved) boundaries. This kind of subdivision also
facilitates using a dense mesh in subregions of great interest
and a coarse mesh in areas where the flow is of interest.

To approximate the variation of the head within an
element the assumption was made that the head varies linearly
within each element. The piezometric surface is thus
approximated by a diamond-shaped surface, such that in each
element the head is represented by a planar surface. The
surface generated by such small planar elements, defined by
the value at the nodal point, is a continuous surface, but
slopes are discontinuous along the boundaries. The
groundwater head at a point inside an element is defined by a
linear interpolation between the value at the mesh points,
(i.e. the nodes).

Therefore, piezometric head 4) throughout the entire

region can be expressed by:

¢=1£1N1(XIY) $1 (44)

where $1 is the head at node i, and N1 is a shape

 

77

function or base function defined by
N,=1,forj=i, N,=0,forj<>i

with linear interpolation within each element.

The problem is solved by a stepwise integration in time.
The values at the end of a first time step is obtained,
starting from the initial values. (A next time step is then
made by considering the values at the end of the first time
step as the initial values for the second time step, etc.

A simple way to derive the basic algebraic equations of

the numerical method is to integrate the differential equation

(43) for t = 0 to t = At. This results in:

Gawain

a) , a) _ (45)
.3. T ) 3% .I

‘a- 3“?-

where ¢’ is the value of the head at the end of the time
interval considered, while the values of ¢ and I are
averages over the time interval. They are obtained by
integration over At.

It is now assumed that the average value of the head ¢
during the time interval can be expressed in terms of the

values at its beginning and its end in the form:

78

¢'e¢°+(1-e)¢’ (46)

where e is an interpolation constant, with 0 S e S 1.

Formula (45) states that the average value is a linear
combination of initial value and.the final one, with different
weights. For 6 = 0, the average value is equal to the final
value. For' 8 = l, the average is equal to the initial value.
In many practical cases, the transient processes are of a.
slowly decaying nature. ,This suggests that the average value
should be slightly biased towards the final value with 8 being
somewhat smaller than 0.5. The value of 8 will be an input
parameter of the computer program.

By substituting Eq (46) into Eq (45) , equation (45)

becomes:

a a (47)

Q _ 2!! - .Ji_=
82—:(T3x)+8y(T6y)+I sAtu-e) °

The time derivative has been eliminated by the process of

integrating over the time step. As a result, an equation in

 

79

terms of the average value ¢ has been obtained.

In general, the approximation will not exactly satisfy
the partial differential equation (46). Therefore, this
condition is relaxed. by requiring' that the differential
equation be satisfied only on the average, using a number of
weighting functions equal to the number of unknowns. This is
called the method of weighted residuals (Zienkiewicz, 1977).
For more convenience, the shape functions N1 are used as

weighting functions. This leads to the conditions:

.2 22 a 21> - 4:9; } (4a)
fn{[ax(Tax)+ay(T8y) +I SAt(1+E) 1N1 dxdy

where i e C to be satisfied for each value of i for which $1
is unknown. These values of i constitute a certain class,
denoted by C.

C is the class of node numbers in which the value of the
head is unknown. The values of j. for all points of the
boundary segment S1 are excluded. Transmissivity 1? is
assumed to be constant over the entire domain.

Satisfaction of Eq.(48) for all i.e C 'will lead to just
as many equations as there are unknown values (Bear and

Verruijit, 1987).

 

80

Equation (48) can be separated into three integrals

J1 ,J2 and J3

J1+J1+J1=o (49)
for all i e C
.. a 31 a 21
J1fR{-a’—‘[N1Tax]+Ty[N1Tay]}dxdy (50)
LN1_18N 6N1_18N (5 1
h.[{f£¢3[ (hr &x 8y 8y]}mb“br )
J =f{IN -——S——£NN (4) -¢’)}dxdy (52)
3 R 1 At(1'€) j 1 j j j

The summation in the second and third integrals should be

 

81

performed over all values of j from j = 1 to j = n, where
n is the number of nodes. Equation (48) is the basic equation
of the method of finite elements. Each of the three
integrals will be evaluated separately.

The first integral J}, as expressed by Eq (50), can be
transformed into a line integral along the boundary S of the
region R by the so-called divergence theorem or Gauss'

theorem. This gives:

J1=fs{N1T-%}ds (53)

where i e C.

Thus, in the integration of the right hand side, the
values of i are restricted to points located on the boundary
5,. The corresponding shape functions N1 are zero on S1
and therefore, only a contribution from the integral along 82
remains. On that part of the boundary, the value of T(8¢/8n)
is known because it represents the amount of water Q1
supplied to the system at node i.

The second integral J2 defined by Eq.(51) can be

written formally as

82

J2='§P11¢1 (54)

where the summation in the right-hand side means summation

over all elements Rp included in the R domain and where:

- may. Mia} 55
Prune; any' By] my ‘ ’

To evaluate this integral, we first note that
contributions to this integral can be expected only if element
lg contains both nodes i and j. If either node i or j do
not belong to the integral, one of the shape functions is zero
and, thus no contribution to the integral is made. Thus
restriction can be made to elements containing both nodes i
and j.

The shape functions are assumed to be linear in order to
facilitate evaluation of this integral. The mathematical
procedure is referred to (Reddy, 1984) and to (Bear and

Verruijt, 1987).

 

83

The third integral J3, defined by Eq.(52), may be
regarded as consisting of two parts. The first part is an

integral of the infiltration function I.
J1-1-- f {1N1}dx_dy (56)

where i e C.

For any particular value of i, the shape function N1 is
different from zero only in the surrounding elements. If in
all of these elements the infiltration function is assumed to
be constant, which is only a minor restriction if the elements
are sufficiently small, the integral over an element Rp
actually expresses the average of the product Igh over that
element, multiplied by the area of element.

The second part of the third integral can be written as:

J3-2=:£—

_ I
1 M15 11) («b 4:) f (N.N.}dxdy (57)

where i e C.

84

Again, it is assumed that the physical parameters are
constant. 11 complete mathematical development of the.
different integrals presented. here is done by Bear and
Verruijit, 1987.

It may be concluded that the solution of a:nonsteady flow

in an aquifer can be based on:

§(p11¢1+n11(¢1_¢g)1 =11 (58)

where the coefficients Pij and R11 are obtained when solving
numerically each of the three integrals J1,;h , j3

In order to improve the convergence when solving for
Eq.(53) we used the Gauss-Seidel method. Practical
experience with this method has shown that convergence can be
improved by multiplying the correction in each updating step
by a factor somewhat greater than 1. This means that in each
step the error is not made equal to zero; it is made to change
sign, in anticipation of future corrections.

Triangular elements lead to a certain asymmetry in most
networks, because of the diagonal in a system of squares.
This can be avoided by adding a second diagonal and an

additional node in the center. However, this leads to almost

85

twice the number of nodes and elements in the mesh. It is
more effective to compose a quadrangular element by
considering it to be the sum of four triangular ones. Thus we
will have only half as many elements, each with four nodes
instead of three. As a consequence, the matrix must be
generated in four steps for each of the composing triangles.
Because a quadrangular element is considered the sum of two
sets of two triangles, the effective transmissivity is doubled
in the process. In order to account for this effect all
transmissivity values should be reduced by a factor of 2.

A network of quadrangular elements may appear to be less
flexible than a system of triangles because it seems to be
less amenable to local refinements.

The same approach is used when modeling salty water
intrusion. The governing differential equation is similar to

Eq - (47), which describes groundwater flow. It can be written

as :
6 do 6 dc dc C'Co
— D — +— D — -v—-———=0 59
ax‘ “8x) 8y( Way) 8x (1-e)At ‘ ’
Where v is an average velocity of the groundwater flow and

D is the component of the dispersion tensor on both x and y

direct ions. The same finite element mesh of triangular

86

elements, and linear interpolation functions are used in this
advection-dispersion problem. The basic idea here is that the
physical variables (the piezometric head, ¢ and the pollutant
concentration, c) are defined at the nodes of a network of
triangles, and that the linear interpolation in the element is
performed by the definition of shape functions N1 Cx,y).
The groundwater head, 4) and the concentration, c are

expressed as:

(I) (my) =EN,(x.y) ()1 (60)

c(XJ) =2N1(X.y) c1 (61)

This means that the velocity, which is defined by the
derivative of the head, is constant throughout each element.
Assuming that density and viscosity are not affected by
changes in the concentration, the velocity distribution can be
solved as a separate problem, independent of the solution of

the concentration. We assume that the groundwater flow

87

problem has been solved, and that the velocity components in
all direction can be considered as known.

The finite element equation is then derived in a flow
model with a Galerkin approach. This means that the partial
differential equation (56) is multiplied by each of the shape
functions, and that the result is integrated over the domain.
Each of the surface integrals is evaluated by a summation of
integrals over triangular elements. By an appropriate
rotation of the coordinate system in an element, the X-axis
can always be made to coincide with the direction of the flow,
so that for the evaluation of the integral over a single

element can always be written in the form of Eq.(56).

IV. RESULTS AND DISCUSSIONS

Estimated values of hydraulic conductivity obtained by
applying the Lefranc test are presented in table (4) and
figure (9). These values are also compared with those
obtained using the Slug test for several piezometers where
both methods have been performed with success.

A general conclusion on both techniques, which have been
previously described in chapter III, is also drawn.

The analysis of the spatial variability of the hydraulic
conductivity is performed using a geostatistical package
(Geostat 1986), based on universal kriging and developed by
ORSTOM.

1. LeFranc Test Results.

This test has been applied with success in approximately
72 piezometers. Field data collected during the test are
presented in Appendix 'A. Estimation of local hydraulic
conductivity values are made using Maurice Cassandre’s
resolution in "les essais d eau dans la reconnaissance des
sols", (Eq (21) thru Eq (36)).

The computed values of hydraulic conductivity are
relatively small, mostly in the range between llr‘ and 10‘6
cm/sec. The smallest values were found in locations where a

relatively high level of salinity was present.

88

89

 

 

@629
9696
e
@01

.88 83
o .

 

6)
® @3.8

 

)

6
9
9

(90‘
0

® 0:631»?

.5 .
0 so ah» ‘0‘

O
0

 

G «flak

 

Scale

Figure 9. Spatial distribution of hydraulic conductivity.

90

Table 4. Estimated values of hydraulic conductivity by

LeFranc test. K .10“ (cm/sec)

 

 

 

 

 

 

-
j

Pi K' Pi K Pi K Pi K Pi K

 

 

 

 

3 74 19 180 35 77 63 330 83 20

 

4 51 20 190 36 18 65 400 85 25

l

 

5 2.5 21 190 39 100 66 350 87 190

 

6 280 22 250 40 36 68 260 88 61

 

7 280 23 5.6 43 130 70 600 89 95

 

8 500 24 94 44 96 71 190 90 34

 

9 290 25 180 45 60 72 24 92 220

 

10 320 26 7.3 47 240 73 160 93 310

 

12 150 27 150 48 240 75 91 94 17

 

13 210 28 8 50 35 76 5.7 97 230

 

14 330 29 210 55 380 77 60 98 260

 

15 230 30 52 56 80 79 380 - -

 

16 190 32 760 57 390 80 150 - -

 

17 170 33 200 61 76 81 8.9 - '-

 

18 170 34 67 62 140 82 92 - -

 

 

 

 

 

 

 

 

 

 

 

 

91

2. Slug Test Results.

This second technique was conducted in a few randomly
selected piezometers. The principles are described in chapter
III. The field data collected are then analyzed using a set
of equations (Eq 37 thru Eq 40), and the results are presented
in table (5) .

Most of the data collected at many piezometers cannot be
interpreted because of a relatively small drawdown. The curve
obtained using a log-log scale is simply a horizontal line
that cannot be superimposed on any of the characteristic

used when applying the Slug Test.

Table 5. Slug test results K 10* (cm/sec)

 

 

 

 

 

 

 

Piezometer Hydr.cond Piezometejm
Number K(cm./s) (cm./s)
23 5.6 71 190
36 20 77 35
49 220 83 20
56 71 88 65
63 290 92 180

 

 

 

 

 

 

92

3. Comparison between LeFranc Test and Slug Test.
Results obtained by both techniques at the piezometers
are quite similar. The differences between the values of

hydraulic conductivity are relatively small or even

negligible. This confirms the validity of the results
obtained by each of the two techniques, especially by the
LeFranc test, which has been conducted with success on more
than three quarters of the installed piezometers.

The fact that most of the field data collected.during the

Slug test cannot be analyzed seems to indicate that this

technique is less effective.

 

 

 

 

 

 

Table 6. Comparison between LeFranc test and Slug
test K 10“ (cm/sec.)

Piez LeFranc Slug Piez LeFranc, Slug
23 5.6 5.6 77 60 35
36 18 20 83 20 20
56 80 71 88 61 65
63 330 290 92 220 180
71 190 190 - - -

 

 

 

 

 

 

 

 

93

The spatial distribution of the hydraulic conductivity

shows that the highest values of hydraulic conductivity are
Indeed,

located in two zones within the study area (Fig 9).
‘these regions correspond to the main entrance of salt water

:into the drain and to the South-western part of the valley

zaround piezometer 73.
Geostatistical analysis of tflna hydraulic conductivity
shows that the distribution is partially random. The

esestimated or experimental variogram of the field data (Fig.
Output of the program

21.0) is compared with a spheric model.
The most important information

is presented in Appendix A.
we can obtain from (Fig. 10) is the path of the variogram, or

the best sampling distance. As it can be shown in (Fig. 10),
This means

the best sampling distance is about 80 meters.
tzfirmuat approximately half of the measurements would be enough

t:;<:> obtain a good estimation and representation of the spatial

Va xiability of the studied parameter.
resulting from the universal

The sampling distance
}<::::piging will be used later in order to define an appropriate

ItIeE: sh for ground water flow modelling using the Finite Element

Irlearthod.
The parameters required for modelling the experimental

variogram in this case-study are the drift coefficient, which

i-Si estimated at 0.6, the number of neighboring points (10

 

94

points), and the sampling distance (80 meters). The
experiment then consisted of kriging each observation using
neighboring points and using various measures between krigged
‘values and known values as criteria for assessing the validity

c>f the assumed underlying drift and covariogram models.

4. Estimation of Groundwater Flow.

Graphical techniques are used to evaluate groundwater
jEilow in the study area. This method is based on. an
interpretation of a contour map representing piezometric
heads and water salinity at several points in time (Fig. 11,
12, 13, 14, 15). The contour maps are obtained using a
Golden Software package (SURFER Version 4.1), which is based

'Eizrtong other techniques in Universal Kriging.

A Study of three contour maps representing piezometric
heads in February, April and, June (Fig. 11, 12, 13), shows
that there is no predominant flow direction for the
SEII1:‘<oundwater. On the contrary, water flows in all directions.
one of the main reasons is that the region is quite flat with
many depressions which can be seen as major evaporative zones
acting like convergency points for groundwater flows. Contour

ITIEilps of groundwater salinity are presented in (Fig 14, 15).

Superimposing both kinds of contour maps, it appears

Clearly that in February and in April salt water flows from

95

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«mm 23 g 3

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8. is: g 25.: 8 >36; g. " gumégj

 

 

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96

the river (Bolong) towards the North and pours out into a
drainage axis, which can be defined by a line connecting
piezometers 15, 30, and 23.
Fresh water (electrical conductivity < 1 mS) from the
piezometric dome in the northern part of the valley flows
1:owards the same drainage axis. As a result, we observe a
lpartial dilution of the salt water which then flows towards
-t:he south-east, and the east into a large depression that also
(czollects flows coming from 'the terraces located at the
:raorthern and eastern parts of the study area (Fig. 11, 12,
ZL13).
This depression is certainly an evaporative area that
.I:Lz:ovokes a fast increase of salinity during the dry season.
Based on Fig (12), flow rates for both salt and fresh
‘Nreaiter converging towards the large depression located at the

north-western part of the study area are computed as follows.

4.1. Fresh water flow rate.
Estimation of fresh water flow rate is based on Darcy’s
3Lmeaswy Eq (1) (Q = K Si).
Where: K = Field average of hydraulic conductivity: 2.5
10‘6 m/sec.
b = Aquifer thickness: 33 meters (B. Dieng et Le

Priol. 1986).

97

L = Average distance between equipotential lines
from the contour map of the observed
piezometric heads 04/14/87 L : 130 meters.

8 = Flow crossection: 302 *(33 = 10‘. m2.

i = Hydraulic gradient: dh/L = 0.25/130 =1.9.103.

2.5 10* m/sec. * lo‘rfi’* 1.9 10'3 = 4.7 10*

0
ll

nP/sec.

4.2. Salt water flow rate.
Estimation of salt water flow rate is much more difficult
because, theoretically, Darcy’s law cannot be applied when
‘ewaater salinity reaches a high level. One way of solving this
1;>z:oblem is to compute the equivalent fresh water for those
piezometers where high concentration of salt, mainly NaCl, is
present.
Based on the fact that values of hydraulic conductivity
are very small and that, for most parts of the valley,
€2I:z:‘oundwater is contaminated with salt intrusion with various
IL.<E:‘vels of concentration, we assume for the purpose of flow
Ilrwaaste estimation that Darcy’s law holds. This assumption is
jorawdeed a simplification of a very difficult problem.
8 = 319 * 33 = 1035 m2

0.25/271.3 = 9.2 10‘4

i

2.5 10'6 m/sec. * 10.5 m2*'9.2 10‘4 = 2.4 10*‘nP/sec.

(0
ll

 

98

Fresh water flow rate is higher than that of salt water.
Electrical conductivity values in the drainage axis are
intermediate between those of fresh and salt water; this
confirms a certain dilution of salt water.

rIn June, groundwater flow remains almost the same
:regardless of the amount of precipitation at the beginning of
the rainy season.

The depression observed in February and April still

eaxists in June and receives water from all directions.

5. Groundwater flow model.

Based on estimation of hydraulic conductivity over the
«erratire study area, an attempt to model groundwater flow using
ea. numerical procedure is made. Finite element techniques are
used to solve the basic flow equation (Eq (13)) . The computer
program is written in Quick Basic version 4.5. It is derived
iffzzrom a set of examples developed and presented by Bear and

‘i77652rruijit, 1987. A. listing' of the computer: program is
presented in Appendix B.

The finite element mesh is presented in Fig.(l6).
Several assumptions have been made, among them the Dupuit
assumption (cf. Chapter III). All elements are rectangular
and have approximately the same size. The total number of

rectangular elements is 109. The aquifer is considered to be

99

 

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103

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Figure 16. Finite element mesh for Katoure Valley.

104

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

105

infinite, homogeneous and intrinsic with a constant thickness

(33 meters) and has a field average hydraulic conductivity of

2.5 10'6

5.1. Model Description.

The program uses interactive input, with self-explanatory
input prompts. The program asks first for some geometrical
data which define the mesh. Then it asks for physical
parameters: the initial head, the infiltration rate, the
transmissivity and the storativity. If the head at node
(I) is given then the type-indicator IP (I) is set equal to 1;
if not, the value of IP (I) is set equal to -l. The program
then asks for the rate of local water supply.

All these parameters are considered constant throughout
the region. The program asks then for a value for the time
step.

The actual calculations are performed in lines 4055-5400
as follows:

5.1.1. Gonotation of Systems Matrix

When all the input data have been entered, the system
matrix {P} can be generated. This is performed in lines
3220-4040. For a particular element as indicated by the
variable J, the coordinates of the nodes are stored in the

variable XJ(I) and YJ(I): Then the coefficients 8(1) and C(I)

106

and the determinant D are calculated based on the mathematical
development of Eq (52). This then enables us to calculate the
values of the matrix {P} for element J and stores them in
the appropriate positions of the matrix, as defined by K and
II“ Note that the summation over all elements is performed.by
adding the contributions from each element consecutively to
the matrix {P}, which is initially filled with zeros.

5.1.2. Solution of Equations.

The system of equations is solved by the Conjugate
Gradient Method, in lines 4050 —5400. This method is usually
effective when it comes to computer memory requirement and
time of computation. It also allows the use of a pointer
matrix; it is very simple to account for the boundary
conditions without the need to modify the system matrix.
After completion of NI iterations, the values of F(I) are
calculated and the solution is finally printed.

As in all transient solutions, the magnitude of the time
steps deserves some special attention. Because the finite
element method is very similar to the finite difference
method, it can be expected that for a value of t: in the
range from 8 = 1/2 through a = 1, the numerical process is
unconditionally stable. This is indeed observed when the
program is executed” .Also, to obtain sufficient accuracy, it

is suggested that the first time step be of the order of

107

magnitude:

' 5(Ax)’
Al: —-2—T— (52)

where Ax denotes a characteristic measure for the mesh and
T the transmissivity. Because in the present case study the
mesh size is 100 meters and the transmissivity T = 0.25 m/day,

it follows that the first time step should be 8000 days.

5.2. Mbdsl‘Vhlidstion.

The developed numerical model was tested on an example
from Segerlind (1984). The simulated piezometric heads are
presented in Appendix A, together with the actual heads
reported by Segerlind (1984). Figure (17) shows a good
correlation between the two series of data. This
demonstrates that the developed numerical model is working
realistically.

For' this study three scenarios were ‘tested. They
represent pressure heads in February, April and, June. For
all scenarios it is assumed that there is only one given

pressure head at node (5) and an average field flow rate for

108

all elements. 'Node (5) is monitored well, located outside the
paddy fields on the side of the valley. In February, the
average flow rate is 4 10*mP/sec. and the given head is 34
meters; in April, the average flow rate is assumed to be

3 10*MP/sec. and the given head 33.50 meters. In June, the
flow rate is 2.50 10‘5nfi/sec. and.the given head 32.50 meters.
Unlike the two previous months, it is assumed that at time 't=
0 , uniform infiltration starts on the entire area of the
aquifer at a constant rate of I = 0.005 m/day.

After performing the finite element calculations, the
predicted values of pressure heads along the free surface were
compared with the observed values at the same node points and
for the same time period. Simple linear regression using
Statgraphics version 2.6 is used for all three scenarios in
order to test for the model validation. We assumed that both
observed and predicted pressure heads are random variables.
Results of the test are presented in Appendix C. They show
that there is a good correlation between the observed and the
predicted head pressures for the first two scenarios (R2,
respectively 0.89 and 0.99). For the third scenario, the test
shows that there is almost no correlation between observed and
predicted variables 18 = 0.12. Reasons for this can be found
in the set of assumptions made earlier. The assumption that

the groundwater is fresh everywhere in the area and that

Simulated Hands (In)

200

190

180

170

150

150

«o

130

120

109

 

 

 

120

I
‘140

I I I
‘150 180

Actual R” CIID

Figure 17.

Model validation.

 

200

110

infiltration is also at a constant rate all over the finite
element mesh cannot hold. The study area should be divided
into homogeneous subregions based on soil type and hydraulic
conductivity of the unsaturated zone. IBecause of the long dry
season that ends in May, the groundwater salinity is extremely
high in June, and that particular attention should be given

to establishing the equivalent fresh water head pressure.

6. Discussion.

This jpresent case study’ shows ‘that among ‘the field
techniques used, the LeFranc test is the most reliable. This
technique is easy to replicate and the results give a good
estimation of the hydraulic conductivity. However, in a
Situation like Katoure valley where we do have a salt water
intrusion and a dilution problem, a more cautious attitude
should be taken when interpreting the results. This can be
done by applying other field techniques on randomly selected
points and comparing the different results. Because of the
spatial variability of soil’s physical parameters, a
geostatistical analysis is highly necessary.

The small values of hydraulic conductivity and
tansmissivity indicate that groundwater flow in this case
study is under the influence of vertical fluxes, like

evaporation or infiltration. Indeed, the drawdown

111

 

34.3
34..
34 7 -I
34.. -
34.5 -
34.4 "'
34.3 -
34 2 -
34.1 -

a c:
33.3 '1
33.. -1
33.7 '1
33.0 -I
33 5 -
33.4 -1
”.3 1
”.2 -‘
33.1 -

33 l I I I
33 332 334

amounted W (n) 02103107

 

 

 

I I l I I l l I l l I l I

I
335 338 34 342 344 348 348
Marv-d thud. (ID 0210337

Figure 18. Plot of simulated versus observed heads 02/03/87.

112

 

Wodlcttd mm (lD 04114107

 

 

 

 

32‘“? I I I I I I I I I
325 328 33 332 334 336 338 34 342

(bur-v.6 Md. (n) 0411418?

Figure 19. Plot of simulated versus observed heads 04/14/87.

113

 

33.7 -

35.8 -

”.3 -

35.4 -i

”a: d

3.1 -

35-

343-

Slllflttod I.“ (ll) $130!?)

34.-

 

347-

 

 

3‘-'*I I I I I I I i I I I

I I I
33 332 334 336 338 34 342

I I I I I
344 346 348

MM “do (IO WSW-7

Figure 20. Plot of simulated versus observed heads 06/30/8'7.

114

during the dry season is very important and the amount of
precipitation at the beginning of the rainy season in June
raises the watertable level very fast. It can be said,
however, that flow rates of fresh or salty water are quite
small and groundwater flbws in all directions towards some
large depressions. These depressions can be considered as
high.potential evaporative zones where, during the dry season,
intermediate values of electrical conductivity due to the
mixing of both fresh and saline water are observed.

Contour maps of groundwater salinity show that, during
the dry season, salt water intrusion from the river (Bolong)
is very important and represents a real problem for farmers
growing vegetables in the side of the valleyu Because use of
fresh water in the side of the valley is very intensive, salt
water reaches most of these gardens very quickly.

The simulation program presented in this thesis can be
used as a prediction tool for future behaviors of groundwater
flow. However, particular attention has to be given to the
fact that we do not have a homogeneous medium, at least from
a water salinity point of viewu The finite element mesh must
include as one of its criteria for homogeneous elements, soil
type and infiltration rates for the unsaturated zone. These
parameters are very important if we want to better predict

future behavior of the groundwater during the rainy season and

115

after specific storms.

The numerical model developed.can be used for evaluating
water management policies, mainly during the dry season.
Plots of the observed as well as the simulated data (Appendix
C) show that salt water intrusion happens most of the time
during that period of the year. By intensively pumping the
groundwater to irrigate the increasing area under vegetable
growing every year, farmers create a very important drawdown
that provokes salt water intrusion. As a consequence most of
the gardens on the terraces are abandoned after only one year
of exploitation. Using this numerical model one can estimate
how much water (pumping rate) should be pumped to maintain a
balance that will reduce the magnitude of the salt intrusion
and secure at least a vegetable production.

This model can also provide interesting information when
planning for future water use. Simulated piezometric heads
together with contour maps of water quality are an important
criterion in the selection of agricultural field locations
with saline water tables close to the surface and where

artificial subsurface drainage should be installed.

'V. CONCLUSIONS AND RICONNINDAIIONS

A study of groundwater flow and quality in an
ancient mangrove plain like Katoure valley was made difficult
by the complexity of encountered problems due basically to
soil heterogeneity and presence of salt water. Field
techniques for estimating soil and water parameters, as well
as methods of analyzing collected data, have to be cautiously
selected. Because of the spatial variability of soil’s
physical parameters, a geostatistical analysis is necessary.
Often, this leads to making assumptions that can sometimes
introduce significant errors.

The finite element method proved to be an excellent
tool for simulating groundwater flow and quality in such
complex media. This method is particularly flexible when
dealing with irregular'boundaries as well as important
heterogeneity problems. This is indeed the main problem one
has to solve when studying groundwater in a mangrove ecosystem
like the Lower Casamance region of Senegal.

Today, the primary issues of concern relating to future

impacts of anti-salt dams are:

1. groundwater levels,

2. groundwater contamination by sea water intrusion,

116

117

3. soil salinization as a result of salt water intrusion
and high evaporation potential,
4. flatness of the terrain which makes natural drainage

almost impossible in many locations.

The proposed numerical model developed as part of this
study already addresses most of these concerns. However, to
better estimate the real impact of the Katoure anti-salt
dam, this model has to be coupled.with one which woulderedict
groundwater quality. Therefore, by combining both models,
real perspectives for a good management decisions could be
made. This will be the key factor for the success of the
anti-salt dams policy. Today sufficient data on the Lower

Casamance region are available.

APPENDICES

APPENDIX .A

1104.1 Validation

 

 

Table A-1: Actual head values by Segerlind (1984) and
simulated head values using the developed
numerical model.

Nodes x (m) y (m) .Actual H (m) Simulated H (m)

1 0.00 0.00 200.00 200.00

2 0.00 1000.00 200.00 200.00

3 0.00 2000.00 200.00 200.00

4 0.00 3000.00 200.00 200.00

5 1000.00 0.00 180.20 180.09

6 1000.00 500.00 179.60 180.40

7 1000.00 1000.00 178.00 177.60

8 1000.00 2000.00 177.90 177.80

9 1000.00 2500.00 179.40 179.40

10 1000.00 3000.00 179.80 180.10

11 1500.00 1000.00 166.10 165.40

12 1500.00 1500.00 164.30 163.80

13 1500.00 2000.00 165.70 166.10

14 2000.00 0.00 169.00 168.50

15 2000.00 500.00 166.70 166.30

16 2000.00 1000.00 160.40 158.50

17 2000.00 1500.00 124.90 125.60

18 2000.00 2000.00 159.70 157.5019

19 2000.00 2500.00 165.10 165.00

20 2000.00 3000.00 169.30 167.80

21 2500.00 1000.00 162.00 162.10

22 2500.00 1500.00 158.90 157.80

23 2500.00 2000.00 160.80 160.60

24 3000.00 0.00- 172.50 172.40

25 3000.00 500.00 171.70 171.30

26 3000.00 1000.00 169.90 169.50

27 3000.00 2000.00 168.30 168.50

28 3000.00 2500.00 168.70 168.80

29 3000.00 3000.00 168.70 168.70

30 4000.00 0.00 185.50 185.30

31 4000.00 1000.00 184.30 184.30

32 4000.00 1500.00 183.50 183.50

33 4000.00 2500.00 179.50 179.40

34 5000.00 0.00 200.00 200.00

35 5000.00 1000.00 200.00 200.00

36 5000.00 2000.00 200.00 200.00

118

119

Table A-2: Pressure heads simulation results

 

 

gg_e Coordinates (meters) Pressure Heads (meters)
X Y 02/03 04/14 06/30
1 0 0 33.83 33.42 34.72
2 100 0 33.69 33.26 34.90
3 200 0 33.38 32.94 35.20
4 300 0 33.03 32.60 35.23
5 350 0
6 400 0 33.52 33.01 35.12
7 500 0 33.55 33.02 34.74
8 600 0 33.69 33.38 34.29
9 700 0 33.60 33.36 34.19
10 800 0 33.57 33.23 34.12
11 900 0 33.42 33.12 34.04
12 1000 0 33.43 34.14 33.94
13 1100 0 33.52 33.24 33.90
14 1200 0 33.56 33.30 34.00
15 0 100 33.95 33.60 34.73
16 100 100 33.92 33.50 34.86
17 200 100 33.64 33.22 35.21
18 300 100 33.61 33.22 35.28
19 350 100 33.72 33.26 35.25
20 400 100 33.65 33.21 35.28
21 500 100 33.72 33.12 34.82
22 600 100 33.45 33.88 34.40
23 700 100 33.44 33.25 34.20
24 800 100 33.42 33.14 34.16
25 900 100 33.40 33.01 34.15
26 1000 100 33.53 33.00 34.03
27 1100 100 3.56 33.24 34.03
28 1200 100 33.53 33.31 34.00
29 0 200 33.55 33.45 34.74
30 100 200 33.84 33.66 34.87
31 200 200 33.82 33.86 34.54
32 300 200 34.12 33.40 33.88
33 400 200 33.82 33.26 34.68
34 500 200 33.76 34.16 33.61
35 600 200 33.65 33.17 33.52
36 700 200 33.59 33.19 34.32
37 800 200 33.49 33.84 34.62
38 900 200 33.40 33.17 34.25
39 1000 200 33.50 33.95 34.06
40 1100 200 33.36 33.02 33.89
41 1200 200 33.38 33.26 34.13
42 0 300 33.35 33.60 34.76
43 100 300 33.50 33.52 35.00
44 200 300 33.81 33.80 34.82
45 300 300 33.86 33.60 34.43
46 400 300 34 25 33.44 34.76

 

120

Table A—2 (continued)

 

 

flede # Coerdineges (meters) Pressure Heads (meEers)

X Y 02/03 04/14 06/30
47 500 300 33.97 33.38 34.75
48 600 300 33.85 33.31 34.54
49 700 300 33.78 33.29 34.43
50 800 300 33.71 33.32 34.84
51 900 300 33.2 33.39 34.42
52 1000 300 33.46 33.10 -34.07
53 1100 300 33.55 33.76 34.94
54 1200 300 33.37 33.32 33.38
'55 0 400 33.07 33.67 34.90
56 100 400 33.51 34.44 33.85
57 200 400 33.88 33.58 33.85
58 300 400 33.80 33.40 34.40
59 400 400 33.60 33.52 35.05
60 500 400 33.68 33.49 35.04
61 600 400 33.85 33.44 34.87
62 700 400 33.82 33.37 34.75
63 800 400 33.80 33.47 34.60
64 900 400 33.70 33.50 34.10
65 1000 400 33.76 3.34 33.71
66 1100 400 33.73 33.29 34.94
67 1200 400 33.79 33.46 34.25
68 0 500 33.55 33.64 34.99
69 100 500 33.66 33.52 34.87
70 200 500 33.85 33.55 34.87
71 300 500 33.77 33.44 34.87
72 400 500 33.70 33.51 34.74
73 500 500 33.82 33.45 34.92
74 600 500 33.12 33.37 35.10
75 700 500 34.80 33.30 35.04
76 800 500 33.93 33.20 34.97
77 900 500 33.87 34.88 35.11
78 1000 500 33.90 33.26 34.24
79 1100 500 33.78 33.84 33.86
80 1200 500 33.60 33.70 35.17
81 0 600 33.74 33.77 35.05
82 100 600 33.44 33.55 35.14
83 200 600 33.66 33.51 35.19
84 300 600 33.70 33.41 34.11
85 400 600 33.80 33.20 34.84
86 500 600 33.55 33.41 35.13
87 600 600 33.23 33.40 3.28
88 700 600 33.40 33.40 35.26
89 800 600 33.30 33.30 35.14
90 900 600 33.30 33.01 34.67
91 1000 600 33.96 32.96 34.02
92 1100 600 34.80 32.94 34.19

 

121

Table A—2 (continued)

 

N d oordin m Pr r H d m r
X Y 02/03 04/14 06/30
93 1200 600 33.93 32 94 34.19
94 0 700 33.87 33.75 35.02
95 100 700 33.90 33.77 35.03
96 200 700 33.78 33.46 35.12
97 300 700 33.60 33.44 35.22
98 400 700 33.74 33.66 35.24
99 500 700 33.44 33.81 35.37
100 600 700 33.66 34.67 35.55
101 700 700 33.70 33.50 33.52
102 800 700 33.80 33.27 35.10
103 900 700 33.55 33.13 35.25
104 1000 700 33.23 33.18 34.18
105 1100 700 33.20 33.09 34.39
106 1200 700 33.24 33.75 34.35
107 0 800 33.37 33.71 35.06
108 100 800 34.05 33.62 35.10
109 200 800 34.13 33.52 35.19
110 300 800 33.98 33.49 35.23
111 400 800 33.90 33.61 35.23
112 500 800 33.87 33.96 35.25
113 600 800 34.11 33.53 35.35
114 700 800 34.18 33.13 35.80
115 800 800 34.07 33.38 35.40
116 900 800 33.71 33.46 34.97
117 1000 800 33.52 33.26 34.90
118 1100 800 33.57 33.00 34.42
119 1200 800 33.64 33.84 34.98
120 0 850 33.69 34.87 33.90
121 100 850 34.12 33.83 35.06
122 200 850 34.16 33.67 35.12
123 -300 850 34.12 33.62 35.20
124 400 850 34.00 33.61 35.15
125 500 850 33.96 34.00 35.24
126 600 850 34.07 33.82 35.26
127 700 850 34.34 33.49 35.63
128 800 850 33.97 33.54 35.37
129 900 850 33.60 33.58 35.02
130 1000 850 33.74 33.42 34.86
131 1100 850 34.01 33 17 34.90
132 1200 850 33.50 33 19 34.93

122

Table A-3: Observed pressure heads.

 

 

Piez. # coordinates (meters) Pressure Heads (meters)
X Y 02/03 04/14 06/30

1 150 200 , 33.83 33.56 34.13
2 100 150 34.13 33.73 34.38
3 50 150 34.10 33.77 34.59
4 50 50 33.99 33.66 33.98
5 50 250 33.85 33.77 34.33
6 150 250 34.10 33.98 34.17
7 200 450 34.01 33.87 34.17
8 50 350 33.96 33.78 34.73
9 150 500 33.73 33.50 34.00
10 100 500 33.77 33.57 34.03
11 50 550 33.82 33.66 34.94
12 100 650 33.87 33.63 33.93
13 100 700 33.13 33.85 34.10
14 200 600 33.59 33.48 33.47
15 200 650 33.94 33.67 33.62
16 150 350 33.81 33.56 33.29
17 0 350 33.95 33.77 34.61
18 300 400 33.65 33.35 34.09
19 350 350 33.99 33.65 34.02
20 40 250 33.78 33.30 33.67
21 60 350 33.79 33.41 33.87
22 650 350 33.78 33.45 33.48
23 650 500 33.74 33.39 34.46
24 700 450 33.02 33.36 34.02
25 600 450 33.89 33.61 33.63
26 550 500 33.50 33.30 33.54
27 450 500 33.81 33.66 33.54
28 450 700 34.01 33.60 34.00
29 400 600 33.25 33.25 33.71
30 350 600 33.66 33.39 33.21
31 550 750 34.46 34.10 33.21
32 500 850 33.93 33.61 33.64
33 650 600 33.70 33.43 34.36
34 600 650 33.83 33.54 33.66
35 600 800 34.42 34.17 33.46
36 700 650 33.83 33.63 33.95
37 700 700 34.19 33.87 34.73
38 700 750 34.02 33.71 33.90
39 750 750 33.34 32.97 33.83
40 750 850 33.88 33.79 34.27
41 750 700 33.90 33.58 33.27
42 800 750 33.80 33.68 34.31
43 800 650 33.71 33.52 34.58
44 900 700 33.95 33.30 34.82

45 950 700 33.36 33.14 33.68

Table A-3 (continued)

123

 

 

Piez # Coordinates (meters) Pressure Heads (meters)
46 1050 700 33.71 33.24 33.91
47 1150 700 33.72 33.43 34.03
48 1100 800 33.48 33.34 33.25
49 1200 800 33.95 33.08 32.90
50 1050 850 33.71 33.59 33.86
51 1000 800 33.15 33.58 33.62
52 900 800 33.62 33.45 34.08
53 800 800 33.59 33.15 33.22
54 800 500 33.84 33.27 33.63
55 300 150 33.74 33.39 33.64
56 300 150 33.94 34.39 33.42
57 350 50 33.84 33.44 33.62
58 400 150 33.42 33.43 33.14
59 450 150 33.70 33.95 ‘ 33.45
60 450 200 33.61 33.40 33.53
61 450 100 33.80 33.19 33.65
62 500 50 33.53 33.34 33.28
63 550 0 33.88 33.23 33.78
64 550 150 33.97 33.18 33.80
65 600 50 33.43 33.77 33.30
66 650 150 33.47 33.13 33.64
67 750 150 33.66 33.20’ 33.37
68 750 200 33.43 33.43 33.51
69 750 250 33.61 33.18 33.88
70 800 250 33.46 33.23 33.55
71 800 200 33.90 32.91 33.91
72 850 200 33.56 33.41 34.00
73 850 100 33.42 33.36 33.63
74 900 100 33.52 33.17 33.62
75 900 150 33.56 33.08 33.91
76 800 500 33.86 33.20 33.89
77 950 300 33.10 33.31 32.90
79 950 400 33.31 33.56 33.50
79 900 500 33.06 33.90 32.90
80 900 550 33.26 33.90 33.21
81 1000 550 33.11 32.70 33.79
82 1000 600 33.61 32.94 33.60
83 850 400 33.42 33.69 33.49
84 1000 150 33.82 33.03 32.84
85 1000 100 33.58 33.03 33.48
86 1000 500 33.03 32.64 33.49
87 1100 150 33.98 33.40 34.33
88 1100 300 33.97 32.73 34.11
89 1100 500 33.08 33.90 33.48
90 1200 500 33.60 33.74 33.60
91 1150 600 33.54 32.74 33.72

124

Table A-3 (continued)

 

Coordinates (meters) Pressure Heads (meters)

 

X Y 02/03 04/14 06/30
92 1050 400 34.78 33.40 33.90
93 1200 300 33.05 33.37 32.80
94 300 200 33.79 33.41 33.67
95 300 0 33.21 32.75 34.57
96 200 150 33.61 33.42 33.53
97 200 200 33.36 33.90 34.28
98 200 550 34.36 33.29 34.12

125

Table A-4: Geographic Coordinates.

 

 

Piez. # coordinates (meters) Elevation (centimeters)
X Y Z

1 150 200 173
2 100 150 183

3 50 150 180

4 50 50 176
5 50 250 173

6 150 250 234
7 200 450 217

8 50 350 193

9 150 500 190
10 100 500 187
11 50 550 202
12 100 650 231
13 100 700 203
14 200 600 219
15 200 650 214
16 150 350 181
17 0 350 189
18 300 400 129
19 350 350 219
20 40 250 167
21 60 350 184
22 650 350 153
23 650 500 170
24 700 450 202
25 600 450 219
26 550 500 214
27 450 500 205
28 450 700 234
29 400 600 183
30 350 600 219
31 550 750 251
32 500 850 226
33 650 600 233
34 600 650 238
35 600 800 288
36 700 650 240
37 700 700 254
38 700 750 252
39 750 750 187
40 750 850 204
41 750 700 234
42 800 750 120
43 800 650 243
44 900 700 208
45 950 700 204

126

 

 

Table A-4 (continued)
Piez # Coordinates (meters) Elevation (centimeters)
X Y Z
46 1050 700 188
47 1150 700 170
48 1100 800 134
49 1200 800 195
50 1050 850 196
51 1000 800 214
52 900 800 216
53 800 800 218
54 800 500 221
55 300 150 136
56 300 150 164
57 350 50 234
58 400 150 185
59 450 150 145
60 450 200 166
61 450 100 125
62 500 50 120
63 550 0 134
64 550 150 139
65 600 50 215
66 650 150 153
67 750 150 114
68 750 200 172
69 750 250 124
70 800 250 129
71 800 200 86
72 850 200 127
73 850 100 147
74 900 100 113
75 900 150 103
76 800 500 127
77 950 300 187
78 950 400 106
79 900 500 86
80 900 550 77
81 1000 550 92
82 1000 600 220
83 850 400 98
84 1000 150 93
85 1000 100 55
86 1000 500 146
87 1100 150 79
88 1100 300 224
89 1100 500 222
90 1200 500 148

127

Table A-4 (continued)

 

 

Piez # Coordinates (meters) Elevation (centimeters)
91 1150 600 155
92 1050 400 185
93 1200 300 138
94 300 200 156
95 300 0 182
96 200 150 170
97 200 200 191
98 200 550 226

128

Kriging Results

RESULTATS
PEP ERREUR HOY. VAR. D'ERREUR
.3 9.2249918-03 .6728318
.35 9.2249932-03 .672832
.4 9.2249968-03 .672832
.45 9.2249968-03 .672832
.5 9.2249932-03 .672832
.55 9.224998E-03 .6728319
.6 9.2249962-03 .6728318
.65 9.224992-03 .672832
.7000001 9.2249982-03 .6728318
.75 9.2249988-03 .672832
.8 9.224998-03 .672832
l-REAFFICHER * 2-SUITE
(*) (Exclusion des cas 2m-2e>2.5*£c.Type)
lFIN 2 3 4 5 6

(Zn-2e)/Ve

1.
1.
1.
1.
.125032
.106161
.08844

.071749
.055985
.041061
.026899

PHHHHHP

215292
1901

166816
145194

(Zn-2e)/Ve

(*)

1.
1.
1.
1.
1.

HIJF‘HFJF'

215292
1901

166816
145194
125032

.106161
.08844

.071749
.055985
.041061
.026899

10

' 12 9
APPENDIX B

Computer Program Listing

1000 DEFINT I-N: KEY OFF: GOSUB 9800

1100 PRINT "--- Groundwater Modeling"
1200 PRINT "--- Finite Element Method"
1300 PRINT "--- Quadrangular elements"
1400 PRINT "--- By Boubacar BARRY": PRINT

1500 DIM XJ(4). YJ(4), b(3), C(3), ks(4, 3)

. PRINT
1 0(3)

1600 DIM x(500), y(500), IP(500), f(500), Fa(500). 9(500)

1650 DIM U(500), V(500), W(500)
1700 DIM P(500, 11), KP(500, 11), NP(400, 4
1750 DIM S(400). PP(400), R(400, 11): N2 =
1800 INPUT "Number of nodes .......... "' n
1900 INPUT "Number of elements ....... "; H
1950 INPUT "Maximum error.... .......... "; E
2000 FOR 1 = 1 TO n
GOSUB 6600
NEXT 1
FOR j = 1 TO M
GOSUB 7300
NEXT J
2100 GOSUB 9800
PRINT "Present input data (Y/N) ......
2200 GOSUB 9500

IF a5 = "N" THEN 2400
2300 FOR 1 = 1 TO n
GOSUB 7900
NEXT 1
FOR j = 1 TO M
GOSUB 8600
NEXT j
2400 FOR 1 = 1 TO 4
FOR 3 = 1 TO 3
x = i + j - 1

IF K > 4 THEN K = K - 4
2500 ks(i. J) = K
NEXT j, i
GOSUB 9800
PRINT "Generation of pointer matrix'
2600 FOR 1 = 1 T0 n
KP(i, l) = i
KP(i, NZ) = 1

NEXT 1
2700 PRINT " Element ...... ";
FOR j = 1 TO M
PRINT j;
2800 FOR K = 1 TO 4
KK NP(J. K)

FOR L = 1 TO 4
LL = NP(j. L)
2900 IA = 0
FOR II = 1 T0 KP(KK. NZ)
IF KP(KK, II) = LL THEN IA = l
3000 NEXT II
IF IA = 0 THEN KB = KP(KK, N2) + 1
KP(KK, NZ) = KB
KP(KK, KB) = LL

), T(400)
11

3100 IF KB

3200 NEXT L, K,

PRINT ' PRINT
EE =

J'

.00001

3210 PRINT "Generation of system matrices'

PRINT

3220 FOR j
PRINT j;

FOR KW

ZX

Element

0:
3230 FOR 1

YJ(i)

3240 ZX

ZY
NEXT 1
ZX
ZY
3245 FOR 1 l
XJ(i)
YJ(i)
i

Z
Z

X
Y
TO
NEXT
b(1)
b(2)
b(3)
cll)
c(2)
c(3)
0(1)
0(2)
0(3)
D

3250 YJ(2)
YJ(3)
YJ(1)
XJ(3)
XJ(1)
XJ(2)
XJ(2)
XJ(3)
XJ(1)
ABS(D(1)

3203

3260

IF
DD
DE
XX

2
3270
3275 T(j) /
S(.1)/
(XJ(1)
+ XJ(3)
1XJ(1)
+ XJ(3)
(YJ(1)
+ YJ(3)

3280

3285 KY

YY =
FOR H
KK
II

FOR L
4000 KV s(Kw,
IF NP(j, KV)
L L + l

(j.

N
K (KK.
k

(I I" II II

4010

/
/
x
Y

(
(

x
a:

3

N

1 TO 11:

L

130

N2 THEN 6500

TO M

ZY

1))

= MK)
ZX + x(K)
ZY + y(K)

3

3
3
J(i) - ZX
J(i) - ZY
- YJ(3)
YJ(1)
YJ(2)
XJ(2)
XJ(3)
XJ(1)
YJ(3)
YJ(1)
YJ(2)
D(2)

- XJ(
- XJ(
XJ(
+ 0(3)

YJ(2)
YJ(3)
YJ(1)

(INN)

3) F
l) *
2) *
)

+

D < EE THEN 4040

4 * D)

4 * (1 E)
XJ(1) + XJ(2)

* XJ(3)) / 12
YJ(1) + XJ(2) * YJ(2)

* YJ(3)) / 12
YJ(1) + YJ(2)

* YJ(3)) / 12

* D)
* XJ(2)

* YJ(2)

1 T0 3
ks(Kw,

K))
Z)

L 1

)

= KP(KK. LL) THEN 4015

IF L < 4 THEN 4000 ELSE 4030

4015
4020

P(KK,
aa

LL)

+ YY

P

XX * h(K)

(KK. LL) + DD * (h(K) * b(L)
* b(L) + XY * (h(K) * C(L)
* C(K) * C(L) + h(K) * D(L)

+ C(K)
+ b(L)

* C(L))
* C(K))

131

4025 R(KK. LL) 8 R(KK, LL) + DE 4 so
4030 NEXT LL. I
4036 FOR 1 s 1 TO 3

K 8 NP(J. ks(Kfl. 1))

4“!) = «100 + D * PPU) I 12

NEXT 1
4040 NEXT Kw, J
PRINT : PRINT : PRINT
tn 8 0: RE 8 ER 3 EE

PRINT "time I"; tn

4045 INPUT "Time after next step "; tt
' it = 1
dt 8 tt - tn
IF dt <8 0 THEN 5900
4050 b 8 1 / dt
tn 8 It
PRINT ”Solution of equations”
PRINT " Iteration "; it
4055 FOR 1 8 1 TO n
0(1) 8 0
12 8 KP(i. NZ)
IF IP(1) > 0 THEN 4075
4050 U(i) 3 9(1)
FOR 3 = 1 TO 12
L 8 KP‘iu J)
4070 U(i) 8 0(1) - 9(1. J) ‘ {(L)

NEXT J
4075 V(i) = 0(1)
NEXT 1
CU = 1
FOR 1 = 1 TO n
UU = UU + U(i) ‘ U(i)
NEXT 1

4080 PRINT it:
FOR 1 = 1 TO n

H(i) = 0
12 8 KP(i. NZ)
4085 FOR j 2 1 TO 12
wIi) : wIII + (PII. J) + b t R11. J)) ‘ VIXP(1. J))
NEXT 3, i
4090 vw : 1

FOR 1 = 1 TO n
VH : VH + V(i) ' ”(1)
NEXT 1
4095 as = UU / vw
FOR 1 = 1 T0 n
IF IP(i) > 0 THEN 5100
5000 f(i) = f(i) + as ' Vii)
U(i) = 0(1) - as ' V(i)
5100 NEXT 1
Wso
FOR 1 = 1 TO n
NW : RH + U(1) ‘ C(I)
NEXT 1

5300 it = i

5100

5500

5600

5900
5950
6500

6600
6700
6800
6900
7000
7100

7200
7300
7400
7500
7600
7700
7800
7805
7810

IF

FOR 1

NEXT

JOSUB

FOR 1 =

PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT
PRINT

LPRINT USING as;
LPRINT " - f = "

132

t + 1

it <= n AND HE > EE THEN

= 1 TO n

Fa(i) =

{(1) =
i

4080

(f(i) - / (l -

Fa(i) +
Fa(i)

Fa(i)) E)

9800: as = "####.##"

1 TO n

_x=
USING as: xti);

-y= ;
I0 -x=I';
USING as; x(i);

'9.

USING as; y(i);
'0 - f = [I ;

USING as; Fa(i)
y(i)

LPRINT USING 85; Fa(i)

PRINT
PRINT
PRINT
PRINT

LPRINT

GOSUB
PRINT
PRINT

GOSUB
INPUT
INPUT
PRINT
IF a5
IF as

VEXT i
"time = "; tn
"Time = "; tn
GOTO 4045
END
END
9800
"Pointer width
GOTO 5900
9800: PRINT "Data of node "; 1:
x ......... ........ "; K(I)
" y ................. "; y(i)
Head given lY/N) .. 7 "; . GOSUB 9500
= "Y" THEN IP(i) = 1: INPUT " F ....... .......... ";
= "N" THEN IP(i) =

(N2) too small."

PRINT PRINT

RETURN

GOSUB
INPUT
INPUT
INPUT
INPUT
INPUT
INPUT
INPUT

"Node 1 .............
"Transmissivity
"Storativity.........
"Re(dis)charge .......

PRINT "Data of element ";

o
I
P
o
F
9
'

NP(j, 2
NP(j. 3
NPlj, 4
T(j)
8(3)
PPtj):

J
NP(j, 1)
)
)
)

RETURN

133

GOSUB 9800: PRINT "Node "; i: PRINT PRINT
PRINT " x ................. "; x(i)
PRINT " y ................. "; y(i)
IF IP(i) > 0 THEN PRINT " F ........... ..... "; f(i)
IF IP(i) < 0 THEN PRINT " Q ........... ..... "; q(i)
GOSUB 9400: IF as = "N" THEN GOSUB 6600: GOTO 7900
RETURN
GOSUB 9800: PRINT "Element "; J: PRINT PRINT
PRINT "Node 1 ............. "; NP(j, 1)
PRINT "Node 2 ............. "; NP(j, 2)
PRINT "Node 3 ........ ..... "; NP(J. 3)
PRINT "Node 4 .......... "; NP(j, 4)
PRINT "Transmissivity ... "; T(j)
PRINT "Storativity... ...... ."; S(J)
PRINT "Re(dis)charge........"; PP(j)
GOSUB 9400: IF a5 = "N" THEN GOSUB 7300: GOTO 8600
RETURN
PRINT PRINT PRINT "Correct (Y/N) ....... ";
as = INPUT$(1): IF as = "Y" OR as = "y" THEN PRINT "Yes": as = "Y": RETURN
IF as = "N" OR as = "n" THEN PRINT "No": as = "N": RETURN
GOTO 9500
CLS . LOCATE 1, 30, l: COLOR 0, 7
PRINT COLOR 0, 7: PRINT RETURN

END

134

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Bear J., and A. Verruijit. 1987. Modeling groundwater Flgw
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Beye, G. 1973. Bilan de cinq annees d’Etudes du Dessalement
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Bralts, V.F., D.M. Edwards and I-Pau Wu. 1987. Drip
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Bucks, D.A., F.S. Nakayama, and A.W. Warrick. 1982.
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Club du Sahel. 1979. Strategy and Programs for Drought
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Cooper, H.H., J.D. Breddehoeft, and 1.5. Papadopoulos. 1967.
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Dedrick, A.R. 1982. Level-basin irrigation. In: Advance§
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Ediafric. .1982. Etudes Economiques du Senegal. La filiere
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FAO. 1984. Agriculture: Toward 2000. Food and.Agricultural
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141

GeoStat. 1971. Universal kriging. Office de Recherche
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Harza Engineering. 1981. Hydrology Report. Agriculture
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Heerman, D.F. and D.L. Swendensky. 1984. Simulation analysis
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Hvorslev, M.J. 1951. Time lag and soil permeability in
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Kemper, W.D., W.H. Heinemann, D.C. Kincaid, R.V. Le Prion,
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Kinzelbach W. 1986. grgundwater Modelling: An Introdugtion

with Sample Programs in Basic. Elsevier, Amsterdam,
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Lyle, W. and J.P. Bordovsky- 1983. LEPA irrigation system

evaluation. Transactions of the American Society of
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Marius, C. and M. Cheval. 1980. Note sur les 8013 de la
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Papadopoulos, I.S., J.D. Bredehoeft, and H.H. Cooper. 1973.
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Segerlind, L.J. 1984. Applied Finite Element Analysis.
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Zienkiewcz, O.C. 1977. The Finite Element Method in
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