Design of Diversion Weirs: Small Scale Irrigation in Hot Climates [1 ed.]

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Wiley Series in Water Resources Engineering The 1992 'International Conference on Water and the Environment: Issues for the 21st Century' served as a timely reminder that fresh water is a limited resource which has an economic value. Its conservation and more effective use becomes a prerequisite for sustainable human development. With this in mind, the aim of this series is to provide technologists engaged in water resources development with modern texts on various key aspects of this very broad discipline.

Professor J .R. Rydzewski Irrigation Engineering Civil Engineering Department University of Southampton Highfield SOUTHAMPTON S095NH UK

Design of Diversion Weirs Small Scale Irrigation in Hot Climates

Rozgar Baban

JOHN WILEY & SONS Chichester • New York • Brisbane • Toronto • Singapore

Copyright © 1995 by John Wiley & Sons Ltd, Baffins Lane, Chichester, West Sussex PO19 IUD, England National Chichester (01243) 779777 International (+44) 1243 779777

All rights reserved. No part of this book may be reproduced by any means, or transmitted, or translated into a machine language without the written permission of the publisher. Other Wiley Editorial Offices

John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, USA Jacaranda Wiley Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Canada) Ltd, 22 Worcester Road, Rexdale, Ontario M9W lLl, Canada John Wiley & Sons (SEA) Pte Ltd, 37 Jalan Pemimpin #05-04, Block B, Union Industrial Building, Singapore 2057

British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN O 471 95211 7 'Typeset in 10/12pt Times by Laser Words, Madras, India Printed and bound in Great Britain by Redwood Books, Trowbridge, Wiltshire

To my daughter Wanausha who has seen less of me, because of the nature of my work, than both of us would like, and to the children of all the expatriates.

Contents Acknowledgements Preface

xi xiii

Part 1 INTRODUCTION 1

Site Investigation

5

1.1 Introduction 1.2 Social and Economic Aspects 1.3 Technical Considerations 1.3.1 Location of the weir 1.3.2 Type of structure 1.3.3 Topographic survey 1.3.4 Soil investigation 1.3.5 Hydrological data

5 5 6 7 8 9 9 9

Part 2 TOPOGRAPHIC SURVEY

11

2

13

Topographic Survey of the Construction Site 2.1 Fixing Benchmarks 2.2 Topographic Survey of the Project Area 2.3 Location of the Weir

Part 3 SOIL INVESTIGATION 3

Soil Investigation 3.1 3.2 3.3 3.4 3.5

Objectives of the Investigation Soil Profile under the Foundation Soil Classification Permeability of the Foundation Soil Unit Weight, Angle of Internal Friction and Cohesion of Soil

13 14 14 17 19 19 20 20 21 21

viii

Contents 3.6 Conclusion 3.7 Reference

Part 4 HYDROLOGICAL ANALYSIS 4

Hydrological Analysis 4.1 4.2 4.3 4.4 4.5 4.6 4.7

Introduction Maximum Design Discharge Mean River Discharge in the Design Minimum River Discharge The Design Discharge Frequency Analysis of Flood Records Theoretical Frequency Distribution 4.7.1 The Gumbel distribution 4.7.2 Confidence limits of the distribution 4.7.3 Log Pearson type III distribution 4.8 Measurement of Peak Discharge by the Slope-Area Method 4.9 References

Part 5 HYDRAULIC ANALYSIS OF SURFACE FLOW 5

Surface Flow Analysis 5.1 Introduction 5.2 General Design Consideration of the Weir 5.2.1 Crest elevation 5.2.2 Length of the weir 5.2.3 Shape of the weir 5.3 Discharge over Weirs 5.3.1 WES-standard weir 5.3.2 Horizontal broad crested weir 5.4 Water Profile at the Weir Site 5.4.1 Water profile downstream of the weir 5.4.2 Water profile upstream of the weir 5.5 Determination of the Tail Water Depth 5.6 Flow Through Sluice Gates 5.6.1 Design requirements 5.6.2 Discharge through sluice gates 5.7 Flow Between Piers 5.8 Canal Head Regulator 5.8.1 Open intake 5.8.2 Design of culverts 5.9 Design of De-silting Basin 5.9.1 Dimension of the basin 5.9.2 Cleaning time of de-silting basin

22 22 23 25 25 25 26 29 29 31 33 34 35 37 40 43

45 47 47 47 47 48 49 49 51 56 58 59 72 80 81 81 83 83 84 85 85 89 89 90

Contents

Ix 5.10 Automatic Discharge Control Intake 5.10.1 The design procedure 5.11 Trashrack Losses 5.12 References

Part 6 UPLIFf PRESSURE UNDER WEIR FOUNDATION 6

Uplift Pressure Under Weir Foundation 6.1 Introduction 6.2 Methods of the Seepage Analysis 6.2.1 Bligh's creep theory 6.2.2 Lane's weighted creep theory 6.2.3 Flow nets 6.2.4 Khosla's theory of independent variables 6.2.5 Analytical method 6.3 Energy Dissipators and its Effect on the Apron Length 6.4 Protection Work for the Structure 6.4.1 Length of the protection work 6.4.2 Size of riprap stones 6.4.3 Thickness of the layers 6.4.4 Grain size distribution of the filter materials 6.5 References

Part 7 SEDIMENT CONTROL DEVICES 7

Sediment Control Devices 7.1 King's Vanes 7.1.1 The design procedure 7.2 Vortex Vane 7.2.1 The simplified design procedure 7.3 Tunnel or Silt Platform 7.3.1 The design criteria 7.4 Vortex Tube 7.4.1 Determination of the head Joss 7.4.2 The design procedures 7.5 Tunnel Type Extractor in Main Canal 7.5.1 The design criteria 7.5.2 The design procedures 7.6 Settling or De-silting Basin 7.7 Design of the Escape Canal 7.7.1 The design procedure 7.8 Open Weir on Seasonal River 7.8.1 Design of the weir 7.8.2 Operation of the weir 7.9 References

91 91 94 95

97 99

99 100 100 101 103 108 118 118 120 121 122 123 123 126

127 131

132 133 134 136 139 139 142 145 148 151 151 153 155 157 159 166 168 168 169

Contents

X

Part 8 STRUCTURAL ANALYSIS OF DIVERSION WEIRS AND THE INTAKE STRUCTURES 8

Structural Analysis of Diversion Weir and Intake Structures 8.1 Main Weir 8.1.1 Acting forces on weir 8.1.2 General stability conditions 8.1.3 Critical cases to be considered 8.1.4 Weirs constructed non-monolithically with the foundation 8.1.5 Weirs constructed monolithically with the foundation 8.1.6 Design of the weir and apron 8.2 Design of the Retaining Walls 8.2.1 Active pressure in cohesionless soil 8.2.2 Cohesive soils 8.2.3 Passive force on the retaining wall 8.2.4 Stability analysis of retaining walls 8.3 Structural Design of Intakes 8.3.1 Bridge-type intakes 8.3.2 Circular culverts 8.4 Constructions Joints 8.5 References

Part 9 FINANCIAL ANALYSIS OF CONSTRUCTING WEIRS 9

Financial Analysis of Constructing Weirs 9.1 Cost of the Structure to the Farmers 9.2 Selection of the Weir Construction Materials 9.3 Reference

Index

171

175 175 175 178 180 180 184 187 193 193 197 198 198 200 200 205 213 214 215 215 217 217 220 224 225

Acknowledgements I would like to thank Mr Clive Chapman, chief technical advisor of the first phase of Institutional Support to Irrigation Development (ISID) project in Dar es Salaam, Tanzania, who initially proposed the idea and encouraged me to write this book. Thanks to Mr R. Temu, project coordinator, Mr P. Riddell, senior irrigation advisor and staff of the second phase of ISID. Without their assistance and encouragement this book could not have been written. I would also like to thank staff of the design section of Irrigation Department in Dar es Salaam, who assisted in producing the drawings. My thanks to Mrs Goodwin and Mrs Eva Mutahangarwa who assisted in producing the book manuscript. Special thanks to Professor J. R. Rydzewski at Southampton University whose continuous encouragement and constructive criticism made it possible to produce this book.

Preface In most developing countries, it is now realized that the most important factor in the success of agricultural sector economy is the sustainability of irrigation projects. Experience in developing countries, especially in Africa, has shown in the last two decades, that large parastatal agricultural projects are declining because of mismanagement and lack of maintenance. Therefore, the government and international donor agencies are now concentrating on rehabilitating traditional and developing small scale irrigation projects. Following this agricultural development strategy, the need for hundreds of small diversion weirs became apparent. The policy of the governments and donor agencies concerned is to finance construction of weirs and leave other structures and canal network for the farmers themselves to implement under supervision of national and international experts. It is hoped that this book would assist irrigation/civil engineers in designing the structure without needing to consult other specialized subject books. The book covers hydrological, hydraulical and structural aspects of the design.

Part l Introduction

Introduction In recent years many parts of the world, especially African coun­ tries, have suffered from drought, a term which is an unspecific and relative one. There is no one acceptable definition of drought, so one can separate the decline of agricultural sectors as a result of shortage of rainfall from those that occur as a result of mismanaging avail­ able water resources and an increase of the rural population. The problems of water resources mismanagement and fast population growth have long been recognized and concerned international and national authorities are attempting to bring them under control and hope one day to be successful. It is the problem of shortage of readily available water for irrigation that this book is devoted to. Hopefully it will assist irrigation engineers in many developing countries to solve some water shortage problems which are by default attributed to drought. In most developing countries, especially Sub-Saharan Africa, irri� gation engineers observe that farmers are suffering from shortage of water not because of its unavailability, but mainly because of the lack of skills to make it available at the time and place required. While in some countries, for example in Yemen, farmers for centuries used groundwater for irrigation from hand dug wells, sometimes up to 40 m deep, in many African countries, once a river's water level drops to a little below its banks, farmers become desperate for irri­ gation water and crops fail. Many African rivers are seasonal but with adequate discharges to develop small irrigation schemes. However, since the farmers in most of these regions have no knowledge or finance or both, to be able to divert the water to agricultural lands, the river flow is not used. Some farmers do construct in places diversion weirs from tree trunks and stones, but these are unreliable and have to be rebuilt after each flood. In the past decade, governments of many developing countries, international developing agencies and NGOs have realized that an effective method to tackle the problem of food shortage is by helping small scale irrigation schemes and rehabilitating the traditional ones. In many cases, if farmers could be helped to control the water level

4

during the wet seasons, by constructing simple but reliable diversion weirs, the food shortage and resulting hardship could be solved. Diversion weirs and canals head regulator form the most important component of irrigation projects, especially in smallholder schemes. At present, in the majority of the ongoing irrigation schemes in Africa, all the farmers need and ask for is diversion weirs to secure irrigation water. Farmers themselves are willing to carry out the other project components and many of the governments and donor agencies rightly finance only the head regulator. The diversion weir, although apparently a simple structure across a river, is a piece of engineering w9rk which needs careful design and thorough hydrological, hydraulic and structural analysis. The view of collapsed hydraulic structures, including diversion weirs, in smallholder irrigation schemes is not uncommon, yet its design can be so simplified that an average university graduate civil engineer would be able to carry it out. The writer from his own experience in several developing countries has found that most national engi­ neers are reluctant to design even a very small structure. This is not because of a lack of engineering background but rather because of a lack of design experience and the knowledge of how to link together various civil engineering subjects and use them in the design. For this reason, international experts are frequently called upon to carry out the design, even if the structure serves areas as small as 100 ha. Obviously once the design is carried out by international consul­ tants the structure's cost increases manyfold and the scheme may be unfairly rejected on economic grounds. Usually, when the design is given to international consultants, it implies that the project implementation will be delayed. This is because of the usual complication in recruiting consultants, mobiliza­ tion of the personnel and conflicting views of the engineers involved in the design. For instance, one consultant may recommend construc­ tion of the structure from gabions and the other may recommend the use of reinforced concrete (RC). Unfortunately in many cases local factors are ignored and consequently the farmers lose faith in the project authority and become demoralized. The above mentioned situation which prevails in most, if not all developing countries, creates the need for a book to be used by design irrigation engineers. This book contains all the technical subjects required by the designer without needing too many refer­ ence books, which are usually not easily available in the developing countries. Although the materials presented in this book are meant to be used in the design of small diversion weirs, no distinction has been made between large and small ones, since the design principle in both cases is the same. However, it should be noted that this book is strictly concerned with diversion weirs which have shallow raft foundation.

Introduction

1n

l Site Investigation 1.1

INTRODUCTION

The, need for constructing a diversion weir in a specific location is usually realised through repeated requests of a group of farmers to the local authorities, to solve some of the problems which usually follow the deterioration of an irrigation scheme's main canal. Wher­ ever a group of farmers actually have problems maintaining a main canal intake, it can be observed that they themselves have tried in traditional ways to construct temporary diversion structures. Such attempts to maintain the intake are a good indication of the need to construct a diversion structure. Visiting a proposed location for the structure and questioning the farmers about their living condi­ tions reveal many social and economic factors which have to be considered before any investment is committed to the project. The following are some essential preliminary investigations which must be carried out, before construction of a diversion weir is recommended.

1.2

SOCIAL AND ECONOMIC ASPECTS

The project planner and the designer, during the first investigations, seek answers to a few questions which are crucial for deciding the scheme's feasibility. These questions are: 1. Coherence of the farming society. The existence of a developed social system is an essential element of the project feasibility. Constructing a structure in an area where the majority of the population are nomads and do not have strong bonds with agricultural lands is definitely unjustifiable. Experiences in many developing countries show that, whenever decisions for constructing a vital irrigation scheme are taken for other than socio­ economic reasons, the result always has been a total failure. There­ fore, it is important to discover that there is already in the area a farming community, though on a small scale and that they have a

Sffe Investigation

6

system of cooperation, be it on the tribal and traditional basis or a more developed organization such as a water user's association. The existence of a kind of farmer's organization indicates that the scheme, when it is built, is likely to be operated and well main­ tained by the farmers. It also indicates the possibility of the project cost recovery, if so required by the government. Through their own organization and tradition, annual taxes can be collected and used for the capital recovery, operation and maintenance costs. Initially a strong farmer organization may not exist, but a nucleus for such an organization must be there. Nowadays many weirs in developing countries are constructed by farmers themselves. Therefore mobilization of the workforce is a serious task which is to be carried out by the farmers' represen­ tative. It is therefore important to find out whether such a farmer organization exists or not. 2. Will the proposed structure create any conflict? One sensitive issue in constructing weirs is the water rights of the downstream water users. Farmers and the local authorities need to be questioned again and again to establish the water rights and a plan should be drawn to evaluate these rights quantitatively. The water rights at the structure directly affects the design of the main canal intake and the size of the irrigated area. The structure may force the local community to relocate their bathing place and livestock watering point. Its location may be a sacred place of the local community. In some rehabilitated irriga­ tion schemes, the farmers need to change their irrigation habits, for example, from day only to day and night irrigation, in order to expand the irrigated area. 3. The need for miscellaneous structure. Constructing diversion weirs, sometimes with a little extra cost, can make the farmer's life a lot easier. For example, providing a foot bridge, and a washing bay. Constructing a washing bay where a structure constructed on a seasonal river is almost a necessity. If it is not provided, in dry seasons the apron is used as a washing platform and deep ditches are dug downstream of the cut-off walls to bail out water. This causes a serious piping problem in flood seasons. The above issues must be discussed with the farmers and points of conflict should be avoided.

1.3

TECHNICAL CONSIDERATIONS

A design engineer who visits the site, for the first time is seeking answers to the following vital questions, which directly affect the design.

on

Technical Considerations 1.3. l

7

Location of the weir

Initially, it is difficult to decide on the location of the proposed structure without having topographic maps of the project area and layout of the river course. However, by walking along the river up and downstream of the location where the existing intake is or where the farmers believe it is an appropriate location, it is possible to identify a few places for the proposed structure. The engineer, at this stage, considers the following factors in selecting the structure site.

Location of the irrigated area If the selected structure site is too far away from the agricultural land

which it serves, it means a long main canal is required, and hence the need for a high capital investment. On the other hand, if the site is too close to the proposed land, some of the area in the upper reach of the main canal cannot be commanded. In a situation like this, the design engineer should carry out a rough economic analysis to determine the economic merits of the two possibilities, although the economic factor is not always the decisive one. In many cases, the engineer finds himself in a dilemma between considering only the technical and economical factors, or sacrificing some of these to fulfil all the farmers' wishes. In many traditional irrigation projects, it is hard to convince farmers, who may have been cultivating lands in an area for generations, to move to the tail of the canal, on the ground that the rehabilitated scheme does not irrigate their lands. If such a problem is encountered, probably the best advice is to consult the village council and the local authority who may succeed in persuading them to accept what is best for the whole community.

Stability of the river bank and dimensions of the structure This factor affects the cost of the structure directly and its operation performance indirectly. River banks are usually unstable in shallow reaches where its cross-section is wide. This implies that a larger and costlier structure is needed in this site than when it is built on a narrower and a more stable section. In a shallow, wide section of a river, where the flow is sluggish, the velocity is less than that in a smaller cross-section, and hence there is a higher rate of silt accu­ mulation in the shallow section. This latter fact, of course, affects the performance of the structure and also increases its maintenance cost. The design engineer, if possible, . chooses a location for the structure where the river is straight, has stable banks and no deposit islands are found in the river. When a straight reach cannot be found, the weir should be built on the outside bank of a bend where the river, even at its minimum discharge, can supply the main canal with adequate water and where the sedimentation is less.

8

Site Investigation

1.3.2 Type of structure By the structure type is meant, type of the construction materials used, and its shape. In developed countries, probably the major deci­ sive factor in selecting the construction materials and shape of the structure is the economic factor. However, this is not necessarily the case in the developing countries, especially when the beneficiaries provide labour. On the first site visit, the design engineer usually investigates the following. 1. What construction materials are available in the locality and their prices? 2.

What other materials are used for construction, which are not available in the local market and what would be their costs, if imported?

3. Is there a shortage of any construction material in the market? If yes, what are they and what is the average waiting time to obtain an order? 4.

Is it possible to hire construction machinery in the locality? Where is the nearest machinery rental station and what are the rates?

5.

What is the availability of skilled labour in the area? For the kind of job in mind can skilled labourers be recruited in the area and what are the average wages?

6.

What will be the construction period? Diversion structures are usually constructed in dry seasons, when the river is dry or at its lowest level. In developing countries, where construction technology is not usually sophisticated, the construction period should be limited, as much as possible, to the dry season. This factor in many cases surpasses all other factors in selecting the structure type.

The answers to the above questions usually give the design engi­ neer sufficient information to decide what materials should be used and what construction technology followed. However, in construct­ ing large structures, the result of geotechnical investigation may be a very important factor in selecting the shape and construction mate­ rials of the structure, although in the case of small diversion weirs, this is very unlikely. Another important factor in choosing the structure type is the implementation method. If the project is implemented by farmers themselves one naturally opts for low cost materials and low tech­ nology. On the other hand, if it is constructed by contractors, the economy of the structure may be the only decisive factor.

Ji

10n

Technical Considerations

9

1.3.3 Topographic survey Once the weir location and alternative locations are decided upon, the designer then needs to view the cross-sections and profile of the river at these sections. The farm topography is obviously very important, to find the highest spot on the land. This data is extremely important where the land is very flat. It is most likely that at this stage no topographic map is available; therefore to begin with, a few spot levels are taken to assess whether a weir at the proposed locations can command the area or not. When the engineer is doing this check he must not just consider the gradient required for the gravitational flow, but also all the loss through gates, culverts and other structures. It may therefore not be possible for the designer to .carry out the design, unless he has an idea about the canal network. This may not be so much the case where the weir location is several kilometers upstream from the proposed farm and it is sufficiently high so that the gradient for the gravitational flow and losses through the structures will never be a problem. The designer should remain on the site until he knows the area well and is able to write down for the surveyor what kind of survey and what degree of precision are required. The topographic survey required is explained in more detail in Chapter 2.

1.3.4

Soll Investigation

In the first site visit and when a few locations are proposed for the structure, the engineer should also visually test the soil and describe its physical properties. Shallow pits should be dug for initial descrip­ tion of the soil profile and to ascertain the groundwater level at the weir site. The purpose of this preliminary investigation is to recom­ mend the type of tools to be used and tests required to be carried out. It should also be ascertained what facilities are available in the nearest soil laboratories. These observations will help the team in charge of the soil tests in selecting the right tools and equipment when they visit the area. Chapter 3 describes the soil investigations required to design and construct the structure.

1.3.5

Hydrological data

Hydrological data is required at the project area to obtain, after their analysis, the design discharges. The design discharges, maximum and minimum values, are important figures which are used by the

Site Investigation

10

designer to size the structure. To design the canal network, the mean discharge of the river is also needed. During the first visit to the area one would find out if any meteorological station and river gauging station are available near the scheme or not. Farmers living in the area can give invaluable information on the highest and lowest flood levels they have experienced. Chapter 4 explains in detail all the data and analysis required for designing diversion weirs. Since the site visit can be a very costly operation, especially when international personnel are involved and the site is located in a remote area, it is very important for the technical team to be well prepared in terms of required specialists and logistic support. The · first technical team to visit the area should consist of the following: • • • • • •

design engineer, construction engineer, a chief surveyor, a hydrologist, an agricultural economist, a sociologist. a a

These are in addition to the farmers' representative and local authorities.

m

Part 2 Topographic Survey

2 Topographic Survey of the Construction Site Experience in constructing weirs shows that, technically speaking, although a topographic survey of the weir site is not a complicated operation, due to lack of experience of the designer and surveyors it can drag on and turn into a costly operation. It often happens in developing countries that a survey team leaves its base to carry out the task in a remote area and once it has returned, after spending a few days on the site, the engineer realizes he does not have suffi­ cient data to carry out the design. Since, in general, in new, small and rehabilitating irrigation schemes the budget is tight, this chapter briefly explains what type of survey is required for designing the structure and its implementation.

2.1

FIXING BENCHMARKS

A permanent benchmark is needed near the weir site not less than 50 m away from the structure's location, in a place where it will not be covered by debris during the construction. If the weir supplies water to lands on both sides of the river, two benchmarks should be fixed, one for each side. The benchmarks, if possible, should be linked to the national grid system and their reduced levels should be related to the mean sea level. However, this is not crucial and time should not be wasted waiting for information from the agency in charge of the land survey. Connection of the benchmarks to the national grid system can be done at any time. Temporarily, the benchmark should be given an assumed reduced level. If two bench­ marks are fixed, the reduced level of one of them is assumed and the level of the other is related to it. However, if the proposed irrigated area is already surveyed, the reduced level of the benchmarks at the weir must be related to the ones in the field. A benchmark is preferably made of concrete with a steel peg in the middle, precast or cast in place. There is always a tendency by children or some people in the project area to pull the benchmarks

14

Topographic Survey of the Construction Sffe

out for various reasons. Therefore, a benchmark must be strong and too heavy for a single person to pull out.

2.2

TOPOGRAPHIC SURVEY OF THE PROJECT AREA

It is assumed that the irrigated area is surveyed and a contour map prepared. If the land is adjacent to the weir the design cannot be carried out without having this map or spot levels covering the lowest part of it. However, if the proposed irrigated land is very much downstream of the weir location, even if no contour map is available, a few spot levels in the area are sufficient for the design purpose. In designing a weir part of the data required is the design discharge of the main irrigation canal. This can only be estimated if the irrigated area and the cropping pattern are known. The cropping pattern is usually decided on social, economic and soil type basis, while the size of the irrigated area is based on the availability of land and the water resources. The availability of land is estimated from the topographic map of the area and the water resources from the hydrological study of the river, as is shown in Chapter 4. If the extent of the proposed irrigated area is not known, the surveyors should lay out a traverse to draw a boundary of the land and to take spot levels in the field. A contour map of the project site covering location of the structure to a scale 1:5000 or 1:10000 is ideal.

2.3

LOCATION OF THE WEIR

At the proposed location of the structure the survey required is as follows: 1. Layout of the river. The extent which the survey should cover depends on the size of the structure. About one kilometer up and downstream of the structure's location is sufficient for the purpose. 2. The topographic survey should extend 250 m to both sides of the river. 3. Cross-section of the river at each 50 m in straight reaches of the river and at 25 m in bends. The first two cross-sections up and downstream of the structure should not be more than 25 m apart. 4. A contour map of an interval not larger than 1 m for the land, 0.50 m for the river bed and of 0.25 m near the structure. 5. Layout of the river stretch surveyed should be drawn to a scale not larger than 1:2000. The weir location for a distance 50 m up and downstream of the structure to be drawn to a scale not larger than 1:200.

Lo

lte

Location of the Weir

15

6.

The horizontal and vertical scale of the river cross-sections must be the same and must not exceed 1:50 or 1:100 depending on the size of the river.

For the task explained above, apart from one or two 50 or 100 m measuring tapes, ranging roads, pegs, one level and one theodo­ lite, one usually doesn't need sophisticated surveying instruments. The first reconnaissance of the project area should discover whether the area requires to be cleared of bushes or not and accordingly preparations should be made for that. The time required to finish the survey obviously depends on the size of the river and season of the year; whether it is dry or wet, and the density of the bush in the surveyed area. A minimum of one day and a maximum of five working days is a reasonable time scale to carry out the outlined survey.

Part 3 Soil Investigation

3 Soil Investigation 3.1

OBJECTIVES OF THE INVESTIGATION

Soil specialists carry out the investigation in response to the designer's request. The designer should realize that soil investigation is an expensive operation requiring transportation, equipment and manpower. To reduce the cost, the designer must try to collect all the existing data relevant to the design. The data should be studied carefully to decide what can be achieved without soil tests, by making realistic assumptions and what cannot be done without it. It happens very often in developing countries, the moment a decision to construct a structure is made, soil specialists in the government and academic institutions show a great interest in the investigations and rush to carry them out without consultation with the designer. The result is usually a nice bound report with an expen­ sive bill which may not be of any use in the design. Soil investigation should be carried out for a purpose rather than as routine work of the project implementation. The designer first of all should list what data he needs for the design. In the case of designing hydraulic structures, as will become clear in the subsequent chapters, the data given in Table 3.1 will be needed for the purposes indicated. The question that needs to be asked at this stage is: do we really have to carry out geotechnical investigations to obtain the design data given in Table 3.1? If the proposed construction oper­ ation involves only a relatively small investment, as is the case in constructing small diversion weirs, the designer cannot afford to include more than a small number of exploratory holes and a few soil classifications in the investigation. The lack of accurate infor­ mation concerning the subsoil conditions can be compensated by the use of a liberal factor of safety in the design (Terzaghi and Peck, 1967). In the following, the design data given in Table 3.1 is briefly examined to conclude what types of soil tests are required to be carried out on the site and in the laboratory and what can be avoided.

Soll Investigation

20 Table 3.1

Required soil data for the design of hydraulic structures

Data

Purpose

to detect impermeable and soft layers under the foundation to estimate engineering properties of the soil estimate safe exit hydraulic gradient at the downstream toe of the foundation design filter under riprap 3. Permeability to estimate seepage rate under the foundation estimate the uplift pressure to calculate lateral pressure on 4. Unit weight, angle internal friction, and cohesion of the retaining walls, estimate the soil bearing capacity soil to estimate settlement of the structure 5. Compressibility and coefficient of consolidation of soil layers 1.

Soil profile under the foundation 2. Soil classification

3.2 SOIL PROFILE UNDER THE FOUNDATION Soil profile under the foundation of structures is required to reveal the depth of impermeable and soft layers. In designing the founda­ tion of heavy structures, e.g. a large weir with a bridge for heavy vehicles on the top, investigating the soil profile is necessary to assess settlement of the construction and the allowable pressure on the soil layers. For such a case, soil and geotechnical specialists should be consulted. The depth to which the investigation is to be carried out depends on the load and dimensions of the foundation. In small diversion weirs, it is hardly necessary to investigate the soil below 3 m, even if it carries a small foot-bridge. The designer would like to discover a hard rock base near the river bed to make the cost of the investigation worthwhile by eliminating construction of an expensive stilling basin for the structure. When construction of small weirs are concerned, the investigation usually does not require more than a set of hand operated augers. Sophisticated drilling equip­ ment is expensive and in remote, underdeveloped areas is not usually available in the locality.

3.3 SOIL CLASSIFICATION Soil classification and grain size distribution of the foundation soil are needed for (i) selection of safe hydraulic gradient at the downstream edge of the structure's foundation; (ii) design of filter for under riprap wherever it is used; (iii) estimating roughly the

1n

Unit Weight, Angle of Internal Friction and Cohesion of Soll

21

engineering property of the soil such as coefficient of permeability. In Chapter 6 the use of this information in the design is explained. To decide whether site or laboratory tests are required to obtain the design data, one should initially assume some likely undesirable properties of the soil and roughly design the structure for these properties. Later a second design should be carried out for a set of assumed better soil properties. If the cost difference between the two designs is substantial and greatly exceeds the cost of the site and laboratory tests, the tests should definitely be carried out.

3.4 PERMEABILITY OF THE FOUNDATION SOIL Permeability is of significant value in the determination of seepage and uplift pressure under the foundation of hydraulic structures. It is needed when a numerical model or the flow net method is used for the flow analysis under the foundation. However, where the design of small weirs is concerned, usually simplified methods are used which assume homogeneous soils and do not require the use of the soil permeability to determine the uplift pressure. The amount of water flow from upstream to downstream of a weir is not the designer's concern. The permeability is related to the type of soil and its grain size distribution. In Chapter 6 an estimate of the permeability for different types of soils is given.

3.5 UNIT WEIGHT, ANGLE OF INTERNAL FRICTION AND COHESION OF SOIL Here again, it is the cost of the work which decides whether the field and laboratory tests should be carried out for determination of the soil properties or whether to rely on some realistic assumptions. It is known that the active soil pressure of a soil which has both cohesion and friction is smaller than that of a purely frictional soil. Therefore when a retaining wall is designed, if it is assumed that the backfill soil of the structures' wing walls is cohesionless, the design will be safer than that which results from a soil which has both cohesion and the friction. The assumption made may lead to an increase in the dimension of the wall and hence the cost of its construction. In the case of designing a small structure where the height of the walls rarely exceed six metres, the increased cost will be much less than the cost of the soil tests. Small hydraulic structures usually do not collapse because the pressure of the foundation is more than the bearing capacity of the soil. They collapse due to the scour of the foundation or the differ­ ential settlement. Small weirs built on rigid foundations result in a very small contact pressure: it hardly needs to be checked against the soil bearing capacity. However, the contact pressure should be

Soll Investigation

22 Table 3.2 Proposed allowable bearing values for rafts on sand

Max. Type of soil 1. Loose 2. Medium 3. Dense 4. Very dense

N

Settlement 25 mm Qn (t/m2 )

50

7-25 25-45 >45

*

N

Settlement SO mm Qn (t/m2 )

50

14-50 50-90 >90

Max.

*

Note: N = Number of blows per foot in standard penetration test Qn = Proposed allowable bearing capacity *= The soil requires compaction.

low enough at the foundation level and at the levels of soft soil layers underneath, if such layers exist, so that it does not cause a large settlement of the structure. In the case of flexible gabion weirs, settlement of the foundation does not create any problem. Table 3.2 gives the allowable pressure on different types of soil which causes a maximum settlement of no more than 2.5 and 5 cm, see Terzaghi (1967). The stress under the foundation on different soil strata must not exceed the allowable values given in the table. In the case of small weirs of rigid raft foundation, a 5 cm settlement does not create any major problems regarding the controlled water level upstream of the weir. In Table 3.2 it is assumed that groundwater is at or above the foundation. If the depth of rock is less than half of the raft width, the bearing capacity can be increased.

3.6 CONCLUSION The aim of the above discussion was to conclude that the soil investi­ gation should be carried out only for design purposes and only when its cost would be substantially less than the increase of the cost of the structure due to the use of a high factor of safety in the design. In designing small weirs, hand dug pits and holes made with hand operated augers are sufficient for the purpose. There would hardly be any need for holes over 3 m deep. In small irrigation schemes, the designer should always think about what soil tests need not be carried out without affecting the safety of the structure and increasing its cost.

3. 7 REFERENCE Terzaghi, K. and Peck, B. R. Soil Mechanics in Engineering Practice 2nd Edition, Wiley, New York, 1967.

Part 4 Hydrological Analysis

24

Hydrological Analysis

LIST OF SYMBOLS A Cs ETc ET0 g IN j

K L m n N

P q

Q Qd

QT

Q

R S

Se T V x .x a a

River cross-sectional area (m2) Skewness coefficient Crop water requirement (mm) Potential evapotranspiration (mm) Acceleration due to the gravity (m/s2) Net irrigation requirement (mm) Risk or probability of occurring an event in any year Frequency factor, or channel hydraulic conveyance Distance between the river cross-sections (m) Serial number of an event in a record of hydrological data arranged in a seceding or descending order Project life (year) or manning coefficient (m- 1 13 /s) Size of sample Probability of the discharge being equalled or exceeded or probability of non occurrence of an event Project water demand (1/s/ha) River discharge (m3 /s) Project water demand (m3 /s) Annual river peak flow (m3 /s) Mean of annual peak flow Hydraulic radius (m) Energy line or canal bed gradient Reduced standard deviation Return or recurrence period (year) Mean flow velocity (mis) Value of variate X Mean of Variate X Velocity distribution coefficient Standard deviation of a variate

4 Hydrological Analysis 4.1

INTRODUCTION

Hydrological data is needed in the design of a weir to deduce from its analysis a few significant figures. These figures are: the minimum, mean and maximum discharges of the river at the proposed location of the weir. To obtain these values, the flow record for as many years as possible is needed, so that one would be able to carry out the frequency analysis. However design engineers, especially in underdeveloped countries, are not always so fortunate to find a river gauging station at or near the weir location. Therefore the discharge at the weir would be estimated by correlating the river discharge at some known locations on the same river to rainfalls recorded at scattered rain gauges in the catchment and the area of the catchment. The design engineers may well deal with cases where no hydrological data can be found at all. In such cases, especially when a large structure is to be designed, the designers should seek the assistance of experienced hydrologists. However it is not uncommon that in small remote development projects the design engineer has to face the problem by himself. In the following sections, the use of the maximum, minimum, and mean river discharges in the weir design and a few techniques that are usually used in the analysis are explained.

4.2

MAXIMUM DESIGN DISCHARGE

The maximum design discharge is the peak river discharge that corresponds to a certain return period which is usually decided by the designer on economic and engineering ground. The maximum design discharge (Qmax) is used in the design, to determine the back water curve results from constructing the weir, in order to predict the highest water level that occurs, on average once every (T) years, where T is the selected return period of the discharge. The Qmax determines the water afflux on the weir and hence the height of the weir wing walls and the cross-bridge, if one

26

is to be built. It also reveals whether dykes along the river banks will be needed or not, and if needed, to what height they should be built. The designer, in the hydraulic analysis, tries to predict the water profile up and downstream of the weir at different flow magnitudes. The higher the discharge, the higher and longer the upstream surface water profile would be. However, the use of the Qmax in determina­ tion of the water profile downstream of the weir does not necessarily lead to the most critical case, since the water depth in the channel (tail water) is the controlling factor. In general, it could be said that the higher the weir crest above the apron, the more significant the Qmax value would be in the design of the downstream components of the weir, such as: length of the apron and the energy dissipators. This subject is dealt with in detail in Chapter 5.

4.3 MEAN RIVER DISCHARGE IN THE DESIGN To design the intake of the irrigation scheme's main canal, where it takes off from a diversion weir, the discharge of the main canal will be needed. In a proposed irrigation area, the discharge of the feeder canal depends on: (i) types of crops and (ii) area of the project. However, area of the project is directly linked to the availability of water in the river and the water rights downstream of the weir. The procedure for determination of the offtake canal capacity and hence the developed area is as follows: 1. The river mean discharge which has an acceptable probability of occurrence, in short periods say 10 or 15 days, should be determined. In irrigation projects, usually 80% flow reliability is taken, i.e. a flow which would be equalled or exceeded in four out of five years. Here, it is assumed that a continuous flow record is available, which unfortunately is not always the case. Obviously, the shorter the period taken, the more reliable the results one would get. 2. The water rights for the farmers downstream of the weir should be established from the water and local authorities in the project area. The maximum available water to the project in each period in the irrigation season is the calculated mean river discharge minus the downstream water rights. 3. Determine the water requirement per hectare of the project area for the crop pattern advised by the project agronomist. This value should include all the estimated losses in the field and the cp al network to the edge of the river. 4. Values of the available water calculated for each period in step 2 divided by the water requirement established in step 3 gives the maximum area which can be irrigated in a particular period.

Hydrolog/cal Analysis

Mean River Discharge In the Design

27

The smallest area in any period of the season is the maximum area which can be developed for irrigation relying on the river discharge. The above steps are illustrated by means of the following example.

Example 4.1 As a part of a large 'small holders irrigation development' project, there was a need to construct a weir on a river to divert water to an area proposed for growing rice. The constraint on the size of the area to be developed was the availability of water in the seasonal river. The local authority and the project management needed to know how large the size of the irrigated area would be (see Fig. 4.1). To answer this question, the water authority in the area was approached to obtain the river flow record near the area. The data was then analysed by the project hydrologist to determine the river mean discharge for the 80% probability of exceeding. Table 4.1 presents the methodology followed in determining the rice water requirement (Brouwer and Heibloem, 1986) and the area which could be irrigated from the river. The analysis which is shown in Fig. 4.1 reveals that the first ten days of March is the most crit­ ical period for irrigation. The designer should realize that a slight shortage of irrigation water over a short period does not neces­ sarily mean a reduction of the irrigated area. What is important is when, in the crop growing season, the water shortage occurs and for how long. The problem of water shortage may be solved POSSIBLE IRRIGATED AREA(ho)

4..-------------------------,

'l? 2.5 � -/j I; ti

2

J 1.5

; 1

2

� 0.5

Fig. 4.1 Determination of the project area and seasonal water demand

!

o .__..._._......____.__..__.__.__..__.______._..__.______._..__.....__._.....,. II III

Dec.

--j

I

111111

ll

lll

l Il

llll

· GroWf"lg Season m Decads.

n m

...... BO'!, Mean river discharge

+

--£,-lrrig. dem. A = 200ho.

-s- 1mg. dem. A= 250ho.

lrrig. dem. A =lOOha.

I

!!Ill

f--May _

Table 4.1

Months

--

I

II

Eto at 80% 3.2 Prob. mm/d Growing season Crop Coeff. ETc mm/d ETc mm/decad Saturation demand mm Percolation mm/d Perco./decad mm Standing water mm Rain 80% prob. mm/decad 0 Effec. rain mm/decad 0 IN-Net Irrg. mm/decad IN mm/d q 1/s/ha Mean river Q 0.59 80% prob. cumecs Possible Irrg. area ha. Qd(lOO ha.) cumecs Qd(200 ha.) cumecs Qd(250 ha.) cumecs

March

February

January

December

1�

Irrigation water requirement in a project

April

June

May

III

I

II

III

I

II

III

I

II

III

I

II

III

I

II

III

I

II

III

3

3

2.4

3

3.2

2.9

3

2.7

3.2

2.9

2.7

3

3.2

2.5

3

3.4

3

3

3

0.03 0.06 0.6

0.65 0.65 0.65 1.15 1.15 1.15 1.04 1.95 2.08 1.89 3.45 3.11 3.68 3.02 19.5 20.8 18.9 34.5 31.1 36.8 30.2

1.04 2.81 28.1

1.04 3.12 31.2

0.67 2.14 21.4

0.67 0.67 0.5 1.68 2.01 1.7 16.8 20.1 17

200 2

2

2

2

2

2

2

2

2

2

2

2

2

2

20

20

20

20

20

20

20

20

20

20

20

20

20

20

100 25.3 5.18

18.8 1.28

13.9 0

199 121 19.9 12.1 6.39 3.88 0.75

2.06

1.49

5.9

6.2

2.3

2

6.2

7.7

4.1

6.7

0

0

2.6

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

39.5 40.8 38.9 54.5 51.1 56.8 50.2 3.95 4.08 3.89 5.45 5.11 5.68 5.02 1.27 1.31 1.25 1.75 1.64 1.83 1.61 1.28

0.78

0.39

0.27

0.47

0.57

48.1 4.81 1.55

51.2 5.12 1.65

41.4 4.14 1.33

2.43

3.32

0.85

36.8 40.1 37 3.68 4.01 3.7 1.18 1.29 1.19 3.36

0.26

0.25

322 257 1572 638 202 210 165 384 1008 595 312 2844 571 2017 353 0.13 0.15 0.12 0.13 0.12 0.16 0.64 0.39 0.13 0.13 0.12 0.18 0.16 0.18 0.16 0.27 0.25 0.26 0.25 0.35 0.33 0.37 0.32 0.24 0.26 0.24 0.31 1.28 0.78 0.33 0.32 0.3 0.39 0.33 0.32 0.33 0.31 0.44 0.41 0.46 0.4 0.97 1.6 0.41 0.3

Note: Qd is irrigation water demand for the assumed area.

:r:

"


(8.17)

= angle of internal friction of the soil. qtim2

H

pressure sz:::

�

Fig. 8.9 A typical

retaining wall and active son pressure

•i ,.\

Structural Analysis of Diversion Weir and Intake Structures

194

If the soil is partly submerged and also carries a uniform distributed surcharge, the pressure distribution will be as shown in Fig. 8.9. The coordinates of the pressure diagram can be evaluated as follows: Distance

Location

Pressure

Remarks

At the level of water table Additional active pressure at level of foot Water pressure Surcharge pressure

BC =DE EF

Kah1Ys Kah2Ys

Ys = soil density

FG Al, CK, GL

Ywh2 Kaq

Total pressure at the foot of the wall

DL

DE+ EF + FG + GL

HA=q/ys P =K a Ys (HA) P=Ka Ysq/Ys P=Ka q

The total force acting on the weir is equal to the area on the pres­ sure diagram (HDLH), and its location can be found by summing moments of all components of the diagram about a point and dividing it by the total area.

Example 8.4

In Fig. 8.9 assume the following values h1= 3 m h2 = 4 m, Ys = 1.8 t/m3 , q= 0.9 t/m2 , Ka =0.45 determine the pressure diagram, acting forces and location of the resultant.

Solution Pressure value t/m2

Distance BC = DE EF FG Al=CK=GL HA= q/Ys DL Area

0.45 X 1.80 X 3 = 2.43 0.45(1.80 - 1) X 4 = 1.44 lx4=4 0.45 X 0.90 = 0.41 0.90/1.80 = 0.50 2.43 + 1.44 + 4 + 0.41 = 8.28 Ma(t. m)

Value

All'BA IKI'I BKK'DB KLK'K

0.41 X 3 = 1.23 (2.43 X 3)/2 = 3.65 (2.43 + 0.41) X 4 = 11.36 (8.28 - (2.43 + 0.41) X 4/2 = 10.88

HIKLDH

27.12

1.23 X 3.65 X 11.36 X 10.88 X

(4 + 3/2):::;: 6.77 (4 + 3/3) = 18.23 4/2 = 22.72 4/3 = 14.51 62.23

Design of the Retaining Walls

195

H

Al= 0-41

4

--+-i.....,.-,...----#-:Tl.22 X:2.31m

D

E

Solution

L

of· example 8-3

62.23 X= -- =2.30m 27.12

Active earth pressure against rough walls In the previous section it was assumed that the back of the retaining wall is smooth. In practice, the surface will often be rough, so that Rankine's method tends to over-estimate the actual lateral pressure which would develop at failure. There are several methods for deter­ mination of active forces on rough walls, here only two simple methods are demonstrated. Engineers should refer back to text books of soil mechanics for more detail. The two methods described here are Rebhann's and Coulomb's wedge methods. The active pressure on the walls can be deter­ mined as follows (see Fig. 8.10).

Rebhann's method

1. Draw line BC at the angle (angle of shearing resistance). 2. Draw a semi-circle with BC as diameter.

Fig. 8.10

Rebhann's method for determination of active force

Structural Analysis of Diversion Weir and Intake Structures

196

3. Draw line AF at the angle (a = + 8), where 8 is angle of friction of the wall and the soil. For common construction materials it ranges between 20 and 30° . 4. Draw line FG at right angle to BC. 5. With BG as radius the arc EG is to be drawn. 6. Draw ED parallel to AF. BD is the plane of failure. 7. With ED as radius the arc DH is drawn. 8. The active force Pa = area of DEH multiplied by the unit weight of soil, i.e.

= ½o i e eccentricityportin9

l ngth ot e

pipe

d. Distributed

load oreo -Altunote 10041

Fig. 8.19 H truck loading system, live load distribution of truck wheels (ACPA, 1988) (Reproduc�d

by permission)

relative to the pipeline. Therefore live load on the pipe per linear metre can be calculated as follows: P(l +If) (8.24) Wi=---Le

Constructions Joints

213

Types of culvert pipes

Pipes of different materials such as plain concrete, reinforced concrete, corrugated steel and vitrified clays, are used for culverts, but the most common ones are plain and reinforced concrete. Plain precast pipe is much used for small culverts. For sizes over 0.60 m, the concrete should be reinforced. A safety factor of 1.50 is recommended to be applied in calculating the carrying capacity and the type of bedding.

8.4 CONSTRUCTIONS JOINTS Constructing a weir takes days and maybe weeks regardless of its size. The occurrence of construction joints is therefore inevitable. Dealing with joints should not be difficult once one understands the forces and moments that act on members of the structure. The weir apron is usually a thick floor so designed that its weight balances the uplift pressure. If the floor is doubly reinforced, with light temper­ ature steel, a layer at the top and bottom, the joints which occur as a result of casting the concrete at different times, should not cause any structural problems. The hair cracks between the old and the new concrete will be so small that fine grains of the foundation soil do not go through. However, if the floor is not reinforced, the concrete casting must be carried out according to a prepared plan, so that the joint between the old and the newly casted concrete is straight and it must be made absolutely sure that the foundation·soil particles will not be washed away through the joint. This can be achieved either by putting a layer of flexible material in the joint fixed between concrete blocks on both side of the joint to seal it, or by putting a layer of filter under the joint and filling the joint with a flexible water-resistant material. The filter layer under the joint can be either of filter cloths, if available, or a layer of graded sand specially designed for the purpose. Construction joints in retaining walls must be handled differ­ ently from that which occurs in the floor. If the wall is reinforced, one must try to cast it in vertical strips rather than in horizontal ones, since each vertical strip can act as an individual wall. The site supervisor should estimate the quantity of work that can be achieved daily, convert it to metre lengths of the wall at its full height and put a controlled vertical joint at the end of the daily work. It is very important to seal the joint either by a flexible layer, properly designed sand filter or filter cloth at the back of the wall. The masonry walls construction joints do not create any problem since by using an appropriate mortar the old and new constructions bond together and act as one unit. Expansion joint!! in the structure depend on the type of material used in the construction. Masonry walls need a vertical joint each 12

Part 9 Financial Analysis of Constructing Weirs

Financial Analysis of Constructing Wein

216

LIST OF SYMBOLS a1, a2 A1, A 2 Ac1, Ac2 Ap B1,

Bi

Bg Cp CPI CP2 '

le

Fn Fp Fp1

G1, G2

id

L1,

Li

½> n

N

Pr

PVB qp ro

Farmers' holding area before and after the scheme (ha) Cultivated area before and after the scheme Annual depreciation and operation and maintenance costs for two alternative designs Annual capital recovery cost Gross annual benefit of the scheme less depreciation cost of the structure for two alternative designs Gross annual benefit of the scheme Construction cost of the weir Construction cost of two alternative designs of the weir Capital recovery factor Number of the beneficiary farmers Annual cost of the structure to a farmer Annual structure cost and its operation and maintenance Gross farmers' income before and after the scheme Interest rate Discount rate Economic life of the structure for two alternative designs (year) Time horizon considered in the project economic analysis (year) Delay in implementation of the project (year) Duration of the capital investment loan Price of the agricultural product Present value of benefit B Annual cost of the structure to a farmer in terms of the product Rate of manual maintenance cost as a fraction of the structures capital cost

9 Financial Analysis of Constructing Weirs In this chapter two questions that face the project planner and designer are discussed. The first one is: what will be the scheme's cost to the farmers and how it will be interpreted in terms of the farm products. This question is becoming increasingly . important in recent years, since the policy of most international developing agencies and governments, nowadays, is to encourage beneficiaries to contribute partially or fully to the construction cost of the scheme. The second question is the subject of selecting alternative designs and construction materials. In answering this question, it is assumed here that the designer has some background in project economic and financial analysis. However, where constructing small weirs is concerned, in most cases the practicality and engineering judgements are the decisive factor rather than pure economic criteria.

9.1 COST OF THE STRUCTURE TO THE FARMERS If the project authority decides that the capital investment would be recovered from the beneficiaries, the question that arises is how much each farmer should pay and for how long? Usually farmers pay in terms of their products such as rice or maize. The farmers obviously require to know their obligations quantitatively, to decide whether it is worthwhile to become a member of .the scheme or not. Therefore a simple financial analysis needs to be carried out. The following is a methodology for such analysis, which could applied. 1. Assume that the scheme's cost is Cp and this sum is to be borrowed from a development bank at an interest rate i and must be paid back by equal annual payments Ap in N years. The annual payment Ap can be calculated as the following, (Gittinger, 1982). (9.1)

218

Financial Analysis of Constructing Wein

fc

+ i) j = [ (1 + j)N - 1] (1

N

(9.2)

The capital recovery factor f c can also be obtained from Table 9.1. 2. Assume that the cultivated area after completion of the scheme is A2 and the holding area by a farmer isa2, then: Number of farmersFn =A2/a2

(9.3)

andFp =Ap /Fn

(9.4)

where FP = annual payment of a farmer towards recovery of the capital investment. 3. In addition toFP each farmer is required to pay for the operation and maintenance (0 & M) of the scheme. If the scheme is only a small weir, the O & M costs can be negligible. However, if it is assumed that the annual O & M costs are a fraction r0 of theFP then the total amount which a farmer must pay annually (Fpt) is: (9 .5)

or in one equation _ a2 Cp (l + i)N (l + r0 )i Fpt [(l + i)N - l] A2

(9.6)

4. Let price of the major product be (Pr), e.g. $/kg of rice or maize, then the quantity of the product qp to be set aside by a farmer to pay for the construction and its operation and maintenance is: (9.7)

Note: The price of the product Pr is the price at which the farmers can sell his product, usually a cash crop, at his usual place of sale. This can be the farm gate or local market. However, if the authority collects the product instead of money, Pr is the price for which the authority can sell the product. It should be noted that the transport, middle men dealers and other miscellaneous costs should be reflected in the price, since the lender is only concerned about the net amount of money received. 5. Once the farmers know how much they have to pay for the scheme, they can decide whether it is worthwhile going ahead or not. To help them further in the decision-making and to make them understand better their situation with and without the scheme, one needs to determine the farm budget before and after construction of the scheme.

Cost of the Structure to the Formers Table 9.1

219 Capital recovery factor fc

Year 2 3 4 5 6 7 8

9 10 11 12 13 14 15

16

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

39 40 41 42

43 44 45

46 47

48

49 50

Interest rate in % (i) 1.01 0.507512 0.340022 0.256281 0.20604 0.172548 0.148628 0.13069 0.11674 0.105582 0.096454 0.088849 0.082415 0.076901 0.072124 0.067945 0.064258 0.060982

0.058052 0.055415 0.053031 0.050864

0.048886

0.047073 0.045407 0.043869 0.042446 0.041124 0.039895 0.038748 0.037676 0.036671 0.035727 0.03484 0.034004 0.033214 0.032468 0.031761 0.031092 0.030456 0.029851 0.029276 0.028727 0.028204 0.027705 0.027228 0.026771 0.026334 0.025915 0.025513

1.02 0.51505 0.346755 0.262624 0.242158 0.178526 0.154512 0.13651 0.122515 0.111327 0.102178 0.09456 0.088118 0.082602 0.077825 0.07365 0.06997 0.066702 0.063782 0.061157 0.058785 0.056631 0.054668 0.052871 0.05122 0.049699 0.048293 0.04699 0.045778 0.04465 0.043596 0.042611 0.041687 0.040819 0.040002 0.039233 0.038507 0.037824 0.037171 0.036556 0.035972 0.035417 0.03489 0.034388 0.03391 0.033453 0.033018 0.032602 0.032204 39.59679

1.03 0.522611 0.35353 0.269027 0.218355 0.184593 0.160506 0.142456 0.128434 0.117231 0.108077 0.100462 0.09403 0.088526 0.083767 0.079611 0.075953 0.072709 0.069814 0.067216 0.064872 0.062747 0.060814 0.059047 0.057423 0.055938 0.054564 0.053293 0.052115 0.051019 0.049999 0.049047 0.048156 0.047322 0.046539 0.045804 0.045112 0.044459 0.043844 0.043262 0.042712 0.042192 0.041698 0.04123 0.040785 0.040363 0.039961 0.039578 0.039213 0.043493

1.04 0.530196 0.360349 0.27549 0.224627 0.190762 0.16661 0.148528 0.134493 0.123291 0.114149 0.106552 0.100144 0.094669 0.089941 0.08582 0.082199 0.078993 0.076139 0.073582 0.07128 0.069199 0.067309 0.065587 0.064012 0.062567 0.061239 0.060013 0.05888 0.05783 0.056855 0.055949 0.055104 0.054315 0.053577 0.052887 0.05224 0.051632 0.051061 0.050523 0.050017 0.04954

0.04909 0.048665 0.048262 0.047882 0.047522 0.047481 0.046857 22.99787

1.05 0.537805 0.367209 0.232012 0.230975 0.197017 0.17282 0.154722 0.14069 0.129505 0.120389 0.112825 0.106456 0.101024 0.096342 0.09227 0.088699 0.085546 0.082745 0.080243 0.077996 0.075971 0.074137 0.072471 0.070952 0.069564 0.068292 0.067123 0.066046 0.065051 0.064132 0.06328 0.06249 0.061755 0.061072 0.060434 0.05984 0.059284 0.058765 0.058278 0.057822 0.057395 0.056993 0.056616 0.056262 0.055928 0.055614 0.055318 0.05504 0.04377

1.07 0.553092 0.381052 0.295228 0.213891 0.209796 0.185553 0.167468 0.153486 0.142378 0.133357 0.125902 0.119651 0.114345 0.109795 0.105858 0.102425 0.099413 0.096753 0.094393 0.092289 0.090406 0.088714 0.087189 0.085811 0.084561 0.083426 0.082392 0.081449 0.080586 0.079797 0.079073 0.078408 0.077797 0.077234 0.076715 0.076237 0.075795 0.075387 0.075009 0.07466 0.074336 0.074036 0.073758 0.0735 0.07326 0.073037 0.072831 0.072639 22.85428 0.044136 1.06 0.545437 0.37411 0.288591 0.237396 0.203363 0.179135 0.161036 0.147022 0.135868 0.126793 0.119277 0.11296 0.107585 0.102963 0.098952 0.095445 0.092357 0.089621 0.087185 0.085005 0.083046 0.081278 0.079679 0.078227 0.076904 0.075697 0.074593 0.07358 0.072649 0.071792 0.071002 0.070273 0.069598 0.068974 0.068395 0.067857 0.067358 0.066894 0.066462 0.066059 0.065683 0.065333 0.065006 0.0647 0.064415 0.064148 0.063898 0.063664

1.08 0.560769 0.388034 0.301921 0.250456 0.216315 0.192072 0.174015 0.16008 0.149029 0.140076 0.132695 0.126522 0.121297 0.11683 0.112977 0.109629 0.106702 0.104128 0.101852 0.099832 0.098032 0.096422 0.094978 0.093679 0.092507 0.091448 0.090489 0.089619 0.088827 0.088107 0.087451 0.086852 0.086304 0.085803 0.085345 0.084924 0.084539 0.084185 0.08386 0.083561 0.083287 0.083034 0.082802 0.082587 0.08239 0.082208 0.08204 0.081886 22.66714

1.09 0.568469 0.395055 0.308669 0.257092 0.22292 0.198691 0.180674 0.166799 0.15582 0.146947 0.139651 0.133567 0.128433 0.124059 0.1203 0.117046 0.114212 0.11173 0.109546 0.107617 0.105905 0.104382 0.103023 0.101806 0.100715 0.099735 0.098852 0.098056 0.097336 0.096686 0.096096 0.095562 0.095077 0.094636 0.094235 0.09387 0.093538 0.093236 0.09296 0.092708 0.092478 0.092268 0.092077 0.091902 0.091742 0.091595 0.091461 0.091339 0.044595

1.1

0.57619 0.402115 0.315471 0.263797 0.229607 0.205405 0.187444 0.173641 0.162745 0.153963 0.146763 0.140779 0.135746 0.131474 0.127817 0.124664 0.12193 0.119547 0.11746 0.115624 0.114005 0.112572 0.1113 0.110168 0.109159 0.108258 0.107451 0.106728 0.106079 0.105496 0.104972 0.104499 0.104074 0.10369 0.103343 0.10303 0.102747 0.102491 0.102259 0.10205 0.10186 0.101688 0.101532 0.101391 0.101263 0.101147 0.101041 0.100946 22.43579

Financial Analysis of Constructing We/11

220

Example 9.1

A group of 160 farmers represented by their water users' association approached an agricultural development bank to loan $40 000 for constructing a weir on a river and rehabilitating the scheme's feeder canal. It is necessary to find out how much each farmer must pay annually in terms of the product, in this case it is rice, under the following conditions. Project area before the rehabilitation A 1 = 80 ha, A2 = 160 ha holding area before and after rehabilitation, a1 = 0.50 ha, a2 = 1.00 ha P = 0.20 $/kg, r0 = 2% of the capital investment, i = 3% and N = 10 years.

Solution

Annual cost of the scheme per farmer, without the farm input cost Fp,: 1.00

40 000(1 + 0.03) 10 (1 + 0.02) [(1 + 0.03) - 1] X 160

X

Fpt = ------------= 30$/f armer 10

This includes 2% annual operation and maintenance costs of the structure. In terms of the farm product q: 30 qp = - = 150 kg/farmer 0.20 If, for example, the yield before and after the rehabilitation is assumed at 1.5 and 2.5 t/ha, and the difference between the level of the farm input before and after the rehabilitation could be neglected, then the difference between the farmer's income due to the project would be as follows: Annual gross income before the project G 1 = 1500 kg/ha x 0.50 ha x 0.20$/kg = $150. If 2% of this amount is spent for some maintenance of the old canal, the gross income would be $147. Annual gross income after the project G2 = 2500 kg/ha x l.00ha x 0.20$/kg - 30 = $470. Therefore each farmer will be better off by: 470 - 147 = 323 $/year.

9.2 SELECTION OF THE WEIR CONSTRUCTION MATERIALS In small irrigation schemes the subject of selecting a design among many alternatives occasionally becomes a rather complicated matter. This is especially the case when more than one technical body is involved in the design. One may recommend alternative A and the other prefers alternative B. In between, the engineer in charge of

Selection of the Weir Constnictlon Materials

221

the project implementation becomes confused and does not know what decision should to take. Obviously, if the recommendation for selecting an alternative design is based on technical analysis, there should not be any confusion. However, when a small scale structure is to be built, usually the best structure is the one which uses local materials and expertise. An important factor to be considered is the availability of the proposed construction materials in the area and in the country. It is absurd to recommend a structure from a material which has to be imported and involves a waiting period of months or even years. It is advisable, when one deals with a small structure, not to take all the decisions purely on the economic basis, but also the psychological effect of implementation delay of the scheme on the farmers. In the section that follows, it is explained how to select a scheme on the basis of cost analysis of the alternative designs. In Fig. 9.1, two alternatives are demonstrated schematically. One of them can start immediately, since all the construction materials are available locally. The second starts some time later, because the materials need to be imported. The two designs have different economic lives, and operation and maintenance costs. In both cases the return from the scheme is assumed to be the same and the project period over which the cost is analysed is also the same, though in the second case it does not start immediately. Let, CPt , Cp2 C 1 , C2 01 , 02 Ac1Ac2 B8 B1 , B2

= capital cost of the two alternatives = annual depreciation of the alternative structures

= operation and maintenance of the structure = total annual cost = C + 0 = gross benefit of the project

= gross annual benefit of the two alternatives 1

and 2 minus depreciation of the capital investment L2 , Li = economic lives of the structure in alternative 1 and 2 Lp = the agriculture project period for the analysis (Lp = 25 to 50 years) id = discount rate PVB = present value of gross project benefit minus depreciation n = delay in the project yield

If a linear depreciation method is applied, C 1 and C2 can be deter­ mined as follows: (9.8) C2 = �2 C1 =�I' PVB1

= B1[(l + id)½ -1] id (1 + id)Lp

(9.9)

Financial Analysis of Constructing We/11

222 Lp G) >

o

3

cost � 01 1 0 & !vi 0, � Cp,1---....:.,.....---1-----+---+----+---ti-+-----f---+----l . . C, Deµrec1at1on c,

a .[

a,1 ,,1 .. L�r·,[ �

G,oss "'"" �

s,t s,i st s,t s,f s,i s,f s,t B,t A B1=Bg-(C1+01)

Net return

Lp E,------------,,/'.___-------➔ I 1-E 1 I L2 A - C p2

Cp2 n .I ._ I Storts late

-

III

0:2,,

C½"