ADJUSTMENT AND ERROR ANALYSIS FOR CONTROL NETWORK FOR DAM DEFORMATION MONITORING

BY GPS

BY

OKELIGHO MIKE IRUOGHENEDEPARTMENT OF CIVIL ENGINEERING

UNIVERSITY OF BENIN NIGERIA

DECEMBER, 2007

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CHAPTER ONE

1.0 INTRODUCTION

A dam is a barrier across flowing water that obstructs, directs or

retards the flow thereby forming an artificial lake as a reservoir of water.

There are numerous variants, some reservoirs are formed on relatively flat

land by building long dams to encircle the required areas, and others are

built to store materials other than water. In South African English, “dams”

can also refer to the reservoir rather than the structure. Dams can be formed

by human agency, natural causes, or by the intervention of wildlife such as

beavers.

Construction of large engineering structures such as dams, bridges and

high – rise buildings is essential for the growth and development of a nation.

However, when excessively loaded and / or serviced, such structures are

subjected to deformation, potentially causing loss of lives and properties.

Therefore, the safety of these structures demand continual monitoring and in

– depth analysis of the structural behaviour, based on a large set of variables

that contribute to the deformation. In fact, the deformation itself forms the

most important parameter to be monitored. (www.cee.engr.ucdavis.edu).

Operating and maintenance personnel must be knowledgeable of the

potential problems that can lead to failure of a structure. These people

regularly view the structure and, therefore, need to be able to recognize

potential problems so that failure is avoided. If a problem is noted early

enough, the structural Engineer in charge can be contacted to recommend

corrective measure, and such measures can be implemented. Acting

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promptly may avoid possible dam failure and the resulting catastrophic

effect on downstream areas.

Modern researchers are increasingly turning to high – precision GPS

positioning as a critical tool in their efforts to analyze structural

deformations. GPS networks are usually established for the purpose of

analyzing a particular structure and observations are made periodically over

an epoch of a few years.

These observations taken on the structure and its surrounding area are

processed, evaluated and analysed for determining the rate, magnitude and

nature of the deformation.

1.1 PROJECT SITE

The Ikpoba dam is located, spanning from Okhoro to Teboga, along

the Ikpoba river running through Egor and Ikpoba – Okha local government

areas in Benin City, Edo State. It is situated on the sandy coastal plain,

which covers the central part of Edo State and some 360km due east of the

popular Lagos State of Nigeria. Elevation within the centre of the town; as

well as along the periphery of the city; range from about 75m in the

southeast to about 90m in the northeast.

It is earth dam, supported at the sides with rip – rap, with a river flow

all year round. Its level of water is the same at all time during the year with

just minor variation. The geological terrain is tertiary while the foundation is

pile. It covers a catchment area of 1.07 x 106 m2. The dams is 610m long

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with a height, at crest level, of 35m above mean sea level. It has a spillway

length (weir) of 60m and an emergency spillway length of 4m.

The dam has a reservoir capacity of 1.5 x 106 m3, Backwash reservoir

capacity 1368 m3. It is the main source of water supply for the city with

water production per pump day of 34080m3. The water supply design

capacity is 90000m3 / day serving an estimated population of 1.0 million

people at design.

The dam was impounded first in 1975 and commissioned October,

1987. At present, problems associated with the reservoir are over silting and

growth of weeds over the years.

(Edo State Urban Water Board, 2007).

1.2 AIMS AND OBJECTIVES

Dam’s construction represents a major investment in the basic

amenities of humans. It requires great funding, so much that it is almost

always government and international bodies the sponsor the Project. Apart

from this colossal financial input, its usefulness to its immediate community

cannot be overemphasized. It is therefore imperative that the structures are

constantly monitored for structural health.

The main objective of this Project is to carry out a study on ensuring

the continuing safety of engineering structures, particularly dams, that pose a

great hazard to the populace if neglected. Checks should be made

periodically when the reservoir is full and when at minimum level.

Knowledge of potential failure signs of the dam and the effect of static and

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dynamic loading will give useful information on its safety as well as

construction of new dams.

This Project work is also aimed at examining, the GPS method for

monitoring deformations and carrying out adjustment and analysis of results

and errors from measurements, access the accuracy and the usefulness of the

method with a view to adaptation to other dams and structures.

The aims and objectives of this work is providing a reliable GPS

monitoring method for a typical dam; carrying out computation, adjustment

and error analysis of results, with a view to preventing dams from

unexpected and abrupt failure and its after – effect on the populace.

1.3 PROBLEM DEFINITION

The safety of large engineering structures as dams, demand

monitoring of their deformation patterns as well as that of their

surroundings.

Dams are very useful to an economy. Lives are benefited from dams

because it; Provides water supply for domestic uses and irrigation purposes,

improves navigation and flood control, generates hydroelectric power,

creates reservoir of water for industrial uses, recreation, wildlife, tourism as

well as containing effluent from industrial sites.

However, dams could also be damaging to the environment. On

sudden failures, the reservoir water flood can change ecosystems, drown

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forests and wildlife, cause loss of agricultural lands and regulate river flows.

There are also adverse social effects because human populations are

displaced and not satisfactorily resettled. The most pressing damage,

however, is the loss of lives. Statistics reveal that bout 100 000 lives are lost

annually by floods from failed dams in the world (World Commission on

Dams, 2002). Also, reconstruction cost is high and sacrificial to other

economic sectors.

It is therefore of great importance, socially and economically, that

dams are monitored periodically. Maintenance personnel must therefore

select a conventional monitoring method to be used for their dams.

The Global Positioning System has proven to be of very high precision

in measuring position coordinates anywhere on the globe. Therefore, its

application to dam monitoring cannot be overemphasized. Its computation

and analysis is a bit rigorous and therefore requires careful techniques in

mathematical methods of adjustment and error analysis of the results

obtained.

1.4 SIGNIFICANCE OF STUDY

A monitoring programme for a dam is of utmost importance. This

Project study Provides methods to determine and be able to predict the

safety level of the dam at both maximum and minimum loading. It Provides

ways that owners and maintenance personnel can be made aware of the

prominent types and causes of failures and their tell – tale signs. This study

is important in comparing the anticipated performance of a dam with the

operational performances.

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This Project study is significant in increasing the knowledge of, the

behaviour of dams and its foundation, deformation and different monitoring

methods available, the GPS in general and its application to structural

health. The study also finds significance in helping to ascertain the accuracy

of the GPS monitoring method, which is achieved by adjustment and error

analysis.

This knowledge is priceless for research and subsequent works of

similar nature.

1.5 SCOPE OF STUDY

This Project work will involve monitoring for deformation using the

Ikpoba river dam as case study. Existing control monuments will be

examined for any defects and where there are defects, the monuments

involved will be reconstructed in accordance with specification.

Consideration will be given to the high precision differential GPS

instruments for the monitoring on a sound geometric control network. A

reference receiver will be deployed to a known GPS control point at Benin

Technical College road, while two others will be deployed to the rovering

points around the dam site.

There are eleven control points and ten movement points will be

provided along the dam crest. Three-dimensional coordinate of all the points

will be obtained by means of the GPS. Adjustments will be carried out using

the least squares adjustments technique. On completion of adjustment, error

analysis will be carried out.

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1.6 RESEARCH LIMITATIONS

This project study is actually a major research that requires some time.

Deformation in structures normally occurs at an infinitesimal rate and in

other to actually obtain real deformation data for analysis, the research

would require some years of study of the dam structure. However, the

Project work is for an academic session of about nine months. Also the

author is still an undergraduate and as such, his devotion even in the

inadequate time is not maximized. This research is therefore limited in time

and scope.

There are also financial limitations. To carry out a proper Project

research will require some financial input. Location and placement of

movement points on the dam; purchase and / or rent of instrumentation /

equipment, which is quite high; payment to personnel throughout the work

period and other incidental expenses are among these financial input. As

there is no external sponsorship, apart from resources input from the Project

supervisor, this is therefore a limitation.

The GPS equipment that gives the accuracy required are sophisticated

and expensive. It is therefore hectic to obtain them, as they are hardly

available in this part of the world. This research also has a limitation in

obtaining equipment.

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CHAPTER TWO

LITERATURE REVIEW

2.0 HISTORY OF DAMS

Around 2950 – 2750 B.C the ancient Egyptians built the first dam

known to exist. The dam was called the “Sadd el – kafara”, which in Arabic

means “Dam of the Pagans”. The dam was 11.28m tall, 106.07m wide at the

crest and 80.8m at the bottom. The dam was made of rubble masonry walls

on the outside and filled with 100, 000 tons of gravel and stone. A limestone

cover was applied to resist erosion and wave action. The structure failed

after a few years and it was concluded that overflow was the cause of the

failure. (YANG, 1999). The poor workmanship from a hasty construction

led to the failure. The dam was not watertight and water flowed through the

structure quickly eroding it away. As the water overflowed the crest, it

quickly eroded away the dam.

The second known dam to be built was an earth dam called (Nimrod’s

Dam” in Mesopotamia around 2000 BC. The dam was made watertight, with

a core wall and filled with an impervious centre made of clays.

Nimrod’s dam was built north of Baghdad (in today’s Iraq) across the Tigris

and was used to prevent erosion and reduce the threat of flooding. As the

dam was built of earth and wood, it is difficult to ascertain the exact

characteristics of the dam.

About 100 AD, the Romans were the first civilization to use concrete

in constructing dams. The dam at Ponte di San Mauro has a great block of

concrete among its remains.

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In the Mongol period, about 1280 AD, a new type of dam known as

arch dam was built and it was called “Kebar”. It is located near the ancient

town of Quam and stands 25.9m high, 54.86m long at the crest and has a

radius of curvature of 38.1m.

In the seventeenth century, the Spaniards were on vanguard of dam

construction in Europe and all other civilization generally. A Spaniard wrote

the first book on designing dams in 1736. Some known dams built in that

era are the Almendralejo dam in Spain and the Meer Allum dam at

Haidarabad in India (YANG, 1999).

It is the same Spaniards that took the art of dam building to the

Americans. The Jesuit fathers in California constructed the old mission dam

across the San Diego River in 1770. The dam was only 1.5m tall and made

of masonry and mortar. (YANG, 1999).

During the second half of the nineteenth century, California

experienced a sudden increase in population and residents began to market

water. Dams during this era were primarily private ventures. Most dams

constructed in the earlier part of this period were of earth and rock. At the

turn of the mid – century, as technology improved, large concrete dams

emerged.

A known example is the crystal springs dam, built in 1888 near the San

Andreas Fault. The crystal springs dam withstood the 1906 San Francisco

earthquake with little damage. The arch dam design also emerged in

California at the end of the century.

The Colonial masters brought dam construction into Africa. Notable

among dams constructed by the colonial lords are the Aswan dam in Egypt

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and the Kariba dam on the Zambia / Zimbabwe border. The British began

construction of the first Aswan dam in 1899 and lasted until 1902. It is a

gravity dam, 1900m long and 54m high. Because of continual overflow, a

second major dam was constructed about 6km upriver (the Nile). The Aswan

high dam also known as As – Sad Al’ – Aali began construction in 1960 and

ended in 1964. It is 3600m in length and 111m high. The Russians

constructed this enormous rock and clay dam. (en.wikipedia.org ).

The Kariba dam in the Kariba gorge and Zambia is one of the largest

dams in the world at 128m high and 579m long. The British constructed this

double curvature arch dam between 1955 and 1959. (en.wikipedia.org)

In West Africa, there is the Akosombo dam in Ghana. It is 660m high.

366m base width and 114m high. It was constructed between 1961 and

1965. There is also the Kainji dam in Nigeria. The Kainji main dam is a dam

across the Niger River. Its construction began 1964 and was completed in

1968. The dam is 85.5m high with a lake of 24km breadth at its widest point

and 8,04km long. Most part of the structure is made from earth, but the

centre is built of concrete. (en.wikipedia.org).

The single busiest decade of dam commissioning in Africa was 1985

– 1995. Africa can boast of about 1272 large dams with about 53% for

irrigation and 20% for water supple of the single purpose dam. In Nigeria,

there are three major dams; the Kainji dam, the Jebba dam built in 1985 and

the Shiroro dam built in 1990, all for hydroelectric power generation.

(YAQUB, 1999)

The Cahora Bassa dam in Mozambique is the tallest in Africa, at

171m and next is the World Bank – sponsored Katse dam in Lesotho at

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155m high. It was constructed (the latter) in 1995. The Kariba dam is the

largest in Africa by reservoir capacity. (TSIKOANE, 1995).

2.1 TYPES OF DAMS

The essential parameters that regulate dam dimensions and elevations

are;

– Length of dam

– Height of dam

– Width of dam at base

– Volume of earth in embankment

– Top of dam elevation

– Peak elevation

– Probable maximum flood spillway elevation

– Elevation where storage begins

Dams are classified based on different criteria. According to height, a

large dam is higher that 15m and a major dam is over 150m in height.

Alternatively, a low dam is less than 30m, a medium – height dam is

between 30m and 100m while a high dam is over 100m high.

Dams may be classified according to their functions:

– A SADDLE DAM: It is an auxiliary dam constructed to confine the

reservoir created by a primary dam either to permit a higher water

elevation and storage or to limit the extent of a reservoir for increased

efficiency. Such an auxiliary dam is constructed in a low spot or

‘saddle’ through which the reservoir would otherwise escape.

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– A COFFERDAM: Is a usually temporary barrier constructed to

exclude water from an area that is normally submerged. They are used

to allow construction on the foundation of permanent dams, bridges

and similar structures. When the Project is completed, the cofferdam

may be demolished or it may be retained for maintenance purposes

– A CHECK DAM: Is a small dam designed to reduce flow velocity and

control erosion.

– A WING DAM: Is a structure that only partly restricts a waterway,

creating a faster channel that resists the accumulation of sediments.

– A DRY DAM: Is designed to control flooding. It usually holds back

no water and allows the channel to flow freely except during periods

of intense flow that would otherwise cause flooding downstream.

– A DIVERSIONARY DAM: Is a structure designed to divert all or a

portion of the flow of a river from its natural course.

– A SPILLWAY: Is an important section of the dam designed to pass

water from the upstream side of a dam to the downstream side.

Spillways have floodgates designed to control the flow through the

spillway. (en.wikipedia.org.)

Dams are classified based on structure and choice of material used for

their construction. They are mainly embankment and concrete dams.

There are also timber and steel dams.

2.1.1 EMBANKMENT DAMS:

They are made from inorganic particulate materials excavated from

the earth’s surface local to the dam site and used more or less as excavated.

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Embankment dams rely on their weight to hold back the force of water.

They are subdivided into earthfill and rockfill dams, although many

embankment dams contain both types of fill. Further sub – divisions can be

made, according to material used to make the water – proof element, e.g.

central clay core, sloping clay core or upstream membrane of asphalt or

reinforced concrete. ROCKFILL DAMS are embankments of compacted

free – draining granular earth with impervious zone. The earth utilized often

contains a huge percentage of large particles hence the term “rock fill”.

(SHERARD, 1973). An example is the NEW MELONES DAM in

California, USA (en.wikipedia.org)

2.1.2 CONCRETE DAMS:

Concrete dams are made from a carefully selected and processed

harder fraction of concrete, bound together and strengthened by hydraulic

cement. They are subdivided according to their mechanism for attaining

stability.

– GRAVITY DAMS: These are the simplest because they rely on their

own weight due to the gravitational force to oppose the overturning

moment caused by the pressure of the reservoir water on their upstream

faces. Stability is secured by making it of such a size and shape that it

will resist overturning, sliding and crushing at the toe. The dam will not

overturn provided the resultant forces falls within the base. Gravity dams

are either “solid” or “hollow”. The solid ones are more widely used

though the hollow dams are more economical as they require less

concrete, although their foundation requirement is more critical. The

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GRANDE DIXENCE DAM in Switzerland is the tallest gravity dam at

285m (en.wikipedia.org). It is also the third tallest dam.

– BUTTRESS DAMS: The concrete buttress dam also uses its weight to

resist the water forces. However, it is narrow and has buttresses at the

base or toe of the dam on the downstream side. These buttresses may be

narrow walls extending out from the face of the dam, much like the

“flying buttresses” supporting cathedral walls or a single buttress rather

like a short dam may be built along the width of the toe of the dam.

ITAIPU DAM on the border of Brazil and Paraguay has double buttress

main dam. (wikipedia.org)

– ARCH DAMS: The arch dam has a cross section that is narrow in width,

but, when viewed from above, it is curved so the arch faces the water and

the curve looks downstream.

This design uses the properties of concrete as its strength. Concrete is

known to be very strong in compression but weak in tension. The arch

dam uses the weight of the water behind it to push against the concrete

and close any joints; the force of the water is part of the design of the

dam. The arch – gravity dam is a combination of the arch type and

gravity dam. While multiple – arch dams combine the technology of arch

and buttress designs. The INGURI DAM in Georgia, of the former

USSR, is the tallest arch dam in the world at 272m (en.wikipedia.org)

and fourth in world.

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2.1.3 TIMBER AND STEEL DAMS:

Timber dams were widely used in the early part of the industrial

revolution and in frontier areas due to ease and speed of construction. Two

common types were the “crib” and the “plank” dams. Timber crib dams

were erected of timber or dressed logs in the manner of a log house, and the

interior filled with earth or rubble. The heavy crib structure supported the

dam’s face and the weight of the water. Timber plank dams employed a

variety of construction methods utilizing timbers to support a water –

retaining arrangement of planks.

Steel dams were an experiment to determine if a construction

technique could be devised that would be cheaper than concrete but stronger

than timber. Steel dams utilized steel plating and load bearing beams. The

technique failed on experimentation. (BLAKE, 1989)

2.2 EARTHFILL DAMS

Earthfill dams, also called earthen, rolled – earth or simply earth

dams, are constructed of well-compacted earth. They are dams built almost

entirely from one type of fill, with no provision for either a less pervious

core or more stable shoulders. A homogenous earth dam is entirely

constructed of one type of material but may contain a drain layer to collect

seep water. A zoned – earth dam has distinct parts or zones of dissimilar

materials, typically a locally plentiful shell with a watertight clay core.

Modern zoned – earth dam embankments employ filter and drain zones to

collect and remove seep water and preserve the integrity of the downstream

shell zone. Rolled earth dams may also employ a water – tight facing or core

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in the manner of a rock – fill dam. An interesting type of temporary dam

commonly used in high latitudes is the frozen – core dam, in which a coolant

is circulated through pipes inside the dam to maintain a water – tight region

of permafrost within it.

Examples of major earth dams include; the ROGUN DAM in Russia which

is the tallest dam in the world at 330m, the NUREK DAM in Tajikistan

which is the second tallest at 300m (Department of Irrigation Engineering,

KU, Thailand, 1997), the OROVILLE DAM which is the tallest in the

United States at 231m and the KREMASTA DAM in Greece which is the

largest earth dam in Europe at 160m high and 456m crest length. Some earth

dams in Nigeria include the KAINJI DAM with a height of 85.5m, the

SHIRORO DAM, TIGA DAM and the IKPOBA DAM.

Studies carried out by the department of Environmental protection in

Pennsylvania, USA, shows that dams in the world comprises 58% earthfill,

11% concrete / masonry, 10% store masonry, 3% rockfill and 18% for the

others.

(SHERARD, 1973)

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2.3 DAMS IN NIGERIA

The major dams in Nigeria and their purposes of construction are

tabulated below;

TABLE 2.1: DAMS IN NIGERIA

NAME TYPE LOCATION USE

AGBA DAM

AJIWA DAM

ASA DAM

ASEJIRO DAM

AUKWIL DAM

AWON DAM

BAGAUDA DAM

BOSO DAM

CHALLAVA DAM

DOMA DAM

DUDURUN WARWADA DAM

DWATAIN MA DAM

Embankment

Embankment dam

Concrete

Embankment

Embankment

Embankment

Embankment dam

Embankment

Embankment dam

Embankment

Embankment dam

Embankment dam

Kwara State

Kaduna State

Kwara State

Oyo State

Plateau State

Oyo State

Kano State

Kaduna State

Bauchi State

Plateau State

Kano State

Kaduna State

Water Supply

Water Supply and Irrigation

Water Supply

Water Supply

Water Supply

Water Supply

Irrigation and Fishery

Water Supply and Irrigation

Water Supply

Irrigation and Water Supply

Fishery, Irrigation and Water Supply

Water Supply and Irrigation

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NAME TYPE LOCATION USE

EDE DAM

EJIGBO DAM

EKORUDE DAM

ELEIYELD DAM

ESA ODO DAM

GAKATARI DAM

GARI DAM

GORONYO DAM

GRANYI HOUSE DAM

GUBI DAM

GUSAU DAM

GUZY GUZY DAM

HEGWAI DAM

Embankment

Embankment

Embankment

Embankment

Embankment

Embankment

Embankment

Embankment

Embankment dam

Embankment

Embankment

Embankment dam

Embankment

Oyo State

Oyo State

Oyo State

Oyo State

Oyo State

Sokoto State

Kano State

Sokoto State

Plateau State

Bauchi State

Zamfara State

Kano State

Niger State

Irrigation / Water Supply

Irrigation / Water Supply

Irrigation / Water Supply

Irrigation / Water Supply

Irrigation / Water Supply

Irrigation

Irrigation / Fishery

Irrigation

Water Supply

Water Supply

Irrigation / Water Supply

Irrigation / Recreation and Fishery

Water Supply

Irrigation / Recreation and Fishery

Water Supply

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NAME TYPE LOCATION USE

IBRAHIM IDAHU DAM

IKERE GORDA DAM

IKPOBA DAM

IWO DAM

JEBBA DAM

KARARA DAM

KAINJI DAM

KAFIN ZAKI DAM

KANGIMI DAM

KARAYA DAM

KARHI CHRIR DAM

KIRI DAM

KOGIN GIRI DAM

KURBAN DAM

Embankment dam

Embankment dam

Embankment

Embankment

Embankment

Embankment

Embankment dam

Embankment dam

Embankment

Embankment

Embankment dam

Embankment

Embankment dam

Embankment

Kano State

Sokoto State

Edo State

Oyo State

Niger State

Kano State

Niger State

Bauchi State

Kaduna State

Kano State

Kano State

Adamawa State

Plateau State

Kaduna State

Irrigation and Water Supply

Water Supply

Water Supply

Water Supply

Power Generation

Water Supply, Fishery and Irrigation

Power Generation

Irrigation /Water Supply

Irrigation /Water Supply

Fishery and Water Supply

Water Supply

Water Supply

Water Supply

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NAME TYPE LOCATION USE

LAMINGA DAM

LANG TANG DAM

LIBERTY DAM

LOWER USUEEN DAM

MADA DAM

MAGADA DAM

MAIRUWA DAM

MARECHI DAM

MOH AYUBA DAM

OBA DAM

OFOO DAM

OJIRAMI DAM

OKENE DAM

OMAE DAM

OPEKI ERUWA DAM

Embankment

Rockfill

Embankment and Rock dam

Embankment dam

Embankment

Embankment

Embankment

Embankment

Embankment dam

Embankment

Embankment

Embankment

Concrete

Embankment

Embankment dam

Plateau State

Plateau State

Plateau State

Abuja

Plateau State

Kano State

Kaduna State

Kano State

Kano State

Oyo State

Niger State

Edo State

Kogi State

Kano State

Oyo State

Water Supply

Water Supply

Water Supply

Water Supply

Water Supply

Irrigation / Fishing

Irrigation / Water Supply

Irrigation / Water Supply

Fishery / Water Supply and Reaction.

Water Supply

Irrigation / Water Supply

Water Supply

Water Supply

Irrigation / Water Supply

Water Supply

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NAME TYPE LOCATION USE

ORISA DAM

OSHUN DAM

OTIN DAM

OYAN DAM

OYUN DAM

PANKOHIN DAM

PEDA DAM

RAWALI DAM

RUWAN KENTA DAM

SAGOMA DAM

SHEN DAM

SHIRORO DAM

SOBI DAM

TENTI DAM

TIGA DAM

Concrete

Embankment

Embankment

Concrete and embankment dam

Concrete

Rock and embankment dam

Embankment

Embankment

Embankment dam

Embankment

Embankment

Embankment

Embankment

Embankment

Embankment

Kwara State

Osun State

Oyo State

Ogun State

Kwara State

Plateau State

Kano State

Bauchi State

Kano State

Kaduna State

Plateau State

Niger State

Kwara State

Plateau State

Kano State

Water Supply

Water Supply

Water Supply

Power generation, Water Supply and Fishery

Water Supply

Water Supply

Irrigation / Fishery

Water Supply

Imagination / Fishery

Imagination / Water Supply

Water Supply

Power generation

Water Supply

Water Supply

Irrigation / Water Supply

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NAME TYPE LOCATION USE

TUDUN WADA DAM

UNGANKANO DAM

WATARI DAM

ZARIA DAM

ZOBE DAM

ZURU DAM

Embankment dam

Embankment dam

Embankment

Embankment

Embankment

Embankment

Kano State

Niger State

Kano State

Kaduna State

Kaduna State

Sokoto State

Irrigation, Water Supply, Fishery and Recreation.

Water Supply

Imagination & Fishery

Recreation

Irrigation

Irrigation & Water Supply

(OBI, 2005).

2.4 FAILURES OF DAMS

Dam failures are of great concern because of the destructive power of

the flood that would be released by the sudden collapse of the dam.

“Tailing dam” which sometimes store toxic materials may pose additional

dangers, an example in Omai tailing dam in Guyana, which failed in 1995

releasing slurries of cyanide. The record of dam failures in succeeding years

provides a useful, if somewhat, melancholy, study. These failures indicate

definitely that the main reasons have been;

(a) Failure to Provide adequate spillway capacity: Spillway capacity is

determined from anticipated catchment area runoff influenced, just a

little, by geological conditions. A recorded disastrous failure of a dam

caused by inadequate spillway capacity and topping of the earth fill

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was of SOUTH FORK DAM in Pennsylvania in 1889. The released

mass of water swept down the valley causing what is often referred to

as the “Johnstown Flood” with a death toll of about 2000 lives.

(TSCHEBOTARIOFF, 1973).

(b) Defective foundation – bed conditions: This is essentially geological,

although it varies considerably from one case to another. A known

example was the ST. FRANCIS DAM in San Francisco, USA. After

its complete construction in 1926, the dam failed in 1928. It was

found that some of the foundation rock lost all its strength when

saturated. It had a death toll of 426 lives. Just about 30 years later, the

MALPASSET DAM in France collapsed killing 344 people. Its

failure was later found to be caused by substantial shear

displacements of the rock below the foundations and at the left

abutment.

(c) Faults in construction methods: Wrong construction can obviously

lead to failure. For example, in adequate compaction or use of wrong

type of construction materials which may lead to internal erosion or

piping failures of embankment dams. This is what happened at the

TETON DAM failure in Idaho, USA in 1976.

(d) Land slides which fall into storage reservoir, sending a wave of water

over the top of the dam can cause failure or the dam may survive but

the flood still occurs devastating the downstream valley. This is what

happened at the VAJONT DAM in Italy, 1963.

(e) Earthquakes can certainly cause damage to dam but complete failure

of a large dam due to earthquake damage is rare.

24

(f) There are also seepage failures especially in earth dams. All earth

dams have seepage resulting from water permeating slowly through

the dam and its foundation. If uncontrolled, it can progressively erode

soil from the embankment, or its foundation, resulting in rapid failure

of the dam.

(LEGGET and HATHEWAY, 1988)

Dam failures are generally catastrophic if the structure is breached

or significantly damaged. Routine monitoring of seepage from drains in,

and around larger dams is necessary to anticipate any problems and

permit remedial action to be taken before structural failure occurs. Most

dams incorporate mechanisms to permit the reservoir to be lowered or

even drained in the event of such problems.

Some failed dams and causes of failure include;

– VAL DI STAVA DAM: This dam located in Italy failed in 1985 when a

tailings dam above the village it’s located failed. The cause was due to

poor maintenance. The drainpipe in the upper dam sagged under weight

of sediment and allowed water to escape leading to poor damage.

Pressure built up on the bank because of this poor drainage, which

eventually reached a critical point causing the bank to liquefy. The

tailings from the upper dam then flowed into the lower dam causing

failure due to immense pressure.

– LAWN LAKE DAM: This earth dam at Colorado in USA failed in 1982

due to deterioration of lead caulking used for connection between the

outlet pipe and gate valve. The resulting leak eroded the earth fill and

progressive piping led to failure of the embankment.

25

– OPUHA DAM: This 29m high dam in Canterbury, New Zealand failed in

1997 due to the heavy flood from a heavy rainfall of 3 days during its

construction.

– CAMARA DAM: Located in Paraiba, Brazil, this 50m high dam failed in

2004 due to excessive rainfall and flooding causing overtopping after two

years of construction.

– SHAKIDOR DAM: It is located in Pasni, Pakistan. This 25m high dam

failed in 2005 after are week of violent rainfall. The dam overtopped.

– AAKRA KOR DAM: Located in Belutschistan in Pakistan, the small

dam failed also in 2005 after two days of rainfall. Inadequate spillway

capacity caused the failure of the dam.

– KA LOKO DAM: It is situated in Hawaii in USA. It failed in March

2006 after intense and unusual rainfall. The spillway capacity was not

enough.

2.5 FAILED DAMS IN NIGERIA

Historical records of dams in Nigeria have not revealed any dam

incident, which has resulted in a national disaster. However, some dams

have shown signs of distress, which may cause failure and if not attended to,

would degenerate into a dam disaster. Some of the embankment dams in

Nigeria, which have either failed or have developed serious signs that lead to

a failure, are;

26

2.5.1 TIGA DAM: This dam is located in Kano State along the Kano

River. It is designed for irrigation and water supply with a height of

48m. It was discovered that the dam was at a risk of disaster due to

longitudinal cracks that is being developed on parts of the dam’s crest

PROfile and undulating distortions had occurred on parts of the

upstream slopes. Hence the dam could no longer function safely under

its design conditions.

2.5.2 BAGAUDA DAM: It is a 22m high embankment dam located in

Bagauda, Kano State. It was constructed in 1970. In 19986, there was

a Probable cause of failure due to a slide, which PROgressed from the

crest to the dam stream at a section of the dam as a result of

embankment failure.

2.5.3 OJIRAMI DAM: The dam was located in Igarra in Edo State. It

failed in the 1980’s because of carelessness of the workers at night.

They failed to open the sluice gate for the excess water to flow

downstream when the dam had retained more than the design capacity

from the runoff as the area experienced heavy rainfall. As a result of

the large hydrostatic force acting on the dam which is greater than it

could resist, water flowed into the reservoirs and after accumulation, it

eroded the fill around the structure which eventually led to the over

flooding of the dam.

2.5.4 GUSAU DAM: This is located in Zamfara State and was used for

irrigation and water supply. The dam collapsed in September, 2006

after heavy flooding due to the heaviest downpour ever recorded in

the area, which had fallen for the previous two days. The accident

27

occurred after sluice gates failed to function, causing the water to

overwhelm the dam, says the dams operator, the Zamfara water board.

40 people were killed and about 500 homes destroyed.

2.5.5 ZOBE DAM: This dam is located in the Kaduna River in Kaduna

State. It is built for irrigation and water supply with a height of 19m

and reservoir capacity of 177 million m3. The incident of failure

occurred in 1983 and the failure was traced to the occurrence of

significant seepage along the downstream toe about two months after

the impounding. The seepage increased with the rise in reservoir level

and piping developed which led to failure due to internal erosion.

2.6 MOVEMENTS IN STRUCTURES

All structures on earth are subject to movement. These movements

could be very small and rendered negligible or it could be just noticed or

even easily noticed. The earth underneath or the weight of the structure itself

either causes the movement of structures. The Civil Engineer has to have an

idea as to the movement expected in a structure of any magnitude.

2.6.1 GROUND MOVEMENTS / EARTH MOVEMENT

The general subject of ground movement is patently one of great

importance, not above because of the trouble and expense caused by

unexpected earth movements during civil engineering construction but also

because of possible loss of life through such movements of completed works

or even untouched natural ground – catastrophes that civil engineering can

28

sometimes avert. The Civil Engineer should therefore be concerned with the

causes of landslides and the problem related to stability of earth slopes.

The basic factor in all consideration of earth movement is that the

earth’s crust is composed of ordinary solid materials, which react to the

stresses induced in them generally in a manner similar to structural

materials, which may be tested in a laboratory. It is a reminder that the

principal cause of all minor ground movements, such as landslides and rock

falls, is the action of gravitational attraction functioning in the usual way. As

an example, a mass of rock detached in some way from the bedrock of

which it has been a part will not be held in position by mysterious means if it

is in unstable statical equilibrium. Minor movements are therefore the result

of instability of part of the earth’s crust, and to a large extent they are subject

to the ordinary laws of mechanics.

Major earthquakes usually cause large earth movements, which is a

sudden yielding of a part of the earth’s crust to strains set up in it by an

adjacent are, which lacks balance or equilibrium. Volcanic activities can also

cause ground movements. Earth movements of this type and magnitude are

generally restricted to certain parts of the world that have come to be known

as the “seismic areas”. However, it must be emphasized the actual earth

movements are not the result of earthquakes, on the contrary, they are the

cause of the quakes that follows. Human activities as modification of land,

erosion, vibrations (from machinery) and traffic also causes ground

movements.

29

– Ground Subsidence: This is a vertical displacement of ground that

accompanies earthquakes in addition to the main earth movement

responsible for the quake.

A “sinkhole” is a type of natural subsidence, which occurs when

superficial unconsolidated material subsides into holes formed in

underlying rock, which has been eroded in some way, often by solution

in ground water.

There is also artificial subsidence caused mostly by humans like miming

subsidence.

– Mass movements: This is the movements of bodies of soil, bed rock,

rock debris, soil or mud which usually occur along step – sided hills and

mountains become of the pull of gravity. This slipping of large amounts

of rock and soil is seen n landslides, mudslide etc. “Landslides” occur

when masses of rock, earth or debris move down a slope. They may be

very small or very large, and can move at slow to very high speeds.

However, slow movement is also seen in the gradual downhill creep of

soil on gently sloping land. “Mudflows” (or debris flows) are rivers of

rock, earth, and other debris saturated with water. An “avalanche” is a

sudden flow of a large mass of snow or ice down a slope or cliff.

(www.fiu.edu).

– Rock falls: These are usually more under stable than other types of earth

movements. They occur when a mass of rock becomes detached from

surrounding bedrock in some, position will permit.

(LEGGET, 1962)

30

2.6.2 FOUNDATION SETTLEMENT

Settlement is the sinking of a structure due to compression and

deformation of the underlying soil.

Foundation settlement may be caused by;

i. Elastic compression of the foundation and the underlying soil.

ii. Plastic compression of the underlying soil

iii. Repeated lowering and rising of the water table in loosed granular soil

tending to compact the soil. With an already dense soil, this change in

the water table level will loosen the material. Also expansive clay will

absorb water easily and hence will expand thereby causing cracks of

structures.

iv. Vibration from a nearby plant, which causes settlement of granular soil.

v. Seasonal volumetric changes of expansive clays i.e. shrinkage and

swelling

vi. Presence of a deep excavation close to the foundation

vii. Consolidation of weak clay soil underlying the foundation.

Elastic / Initial settlement is that which occurs immediately on

application of load on foundation. It occurs rapidly, within hours or days the

load is applied.

Primary consolidation settlement is a time – dependent deformation

that occurs in saturated or partially saturated soils. Such soils have low

permeability and are slow to dissipate their pore water.

Secondary consolidation is also a time – dependent deformation of a

smaller magnitude and is speculated to be due to the plastic deformation of

31

the soil, as a result of some complex colloid chemical processes usually

known as creep.

(KAYODE – OJO, 2007)

2.7 DEFORMATION MODES

There are various modes or ways that deformation can occur. The

three principal modes of deformation are elastic deformation, plastic

deformation and viscous deformation.

2.7.1 ELASTIC DEFORMATION:

In an elastic medium, the station is instantly and totally recoverable.

Stress is directly proportional to strain, the constant of proportionality being

the Young’s modulus. Poisson’s ration is the inverse ratio between strain in

the direction of applied stress and the induced strain in a perpendicular

direction. Young’s modulus and Poisson’s’ ration are known as elastic

constants.

For a geologic body to exhibit elastic characteristics defined by only

one value of the elastic constants each, it must be isotropic, homogenous and

continuous. Most rocks and rock masses are to some extent anistropic, in

homogenous and discontinuous and are termed quasi – elastic, semi – elastic

or inelastic. In fresh intact specimen, deformation varies with rock type as

related to mineral hardness, grain bonding and fabric.

Soils are essentially inelastic, but demonstrate pseudoelastic

properties under low stress levels as evidenced by initial stress – strain

linearity. Elastic deformation, however, is immediate and in many soil types,

32

it does not account for the total deformation occurring over long time

intervals because of the process of consolidation.

2.7.2 PLASTIC DEFORMATION:

Materials exhibiting plastic behaviour undergo permanent and

continuous deformation when the applied stress reaches a characteristic level

and in geologic materials, this can occur in several modes including pure

compression, consolidation, expansion and shear.

Pure compression occurs when sand particles are packed more tightly

together decreasing the void space, when fissures close in intact rock, or

when joints close in a mass. Because rock masses are often discontinuous,

they may undergo an initial plastic deformation as fractures close, then an

elastic deformation of intact blocks, followed by additional plastic

deformations.

Consolidation is the slow process of compression under applied load

that occurs as water is extruded from the voids of clay soils.

Expansion occurs as an increase in volume from swelling or from

plastic extension strain. Soils and rocks containing active clay minerals have

an affinity for absorbing water and swelling, heavily over consolidated soils

and rock masses containing residual stresses undergo plastic extension

straining upon a decrease in confining stresses.

2.7.3 VISCOUS DEFORMATION AND CREEP:

In a viscous material the rate of deformation is roughly proportional to

the applied stress. Creep is a time – dependent deformation wherein strains

occur beyond elastic compression, consolidation or shear at a constant stress

level below failure. Most rocks exhibit both immediate and delayed

33

deformation under applied stress and are there termed visco elastic. Hard

rocks exhibit creep as the network of cracks increases in length and intensity

under relatively high deviator stresses. Creep may occur also in foliated rock

masses containing residual stresses, when stress – relieved by excavation

(HUNT, 1986).

2.8 DEFORMATION MONITORING

All large engineering structures are susceptible to movements, which

may or may not be within design specifications. As the consequences of

failure are severe, monitoring of structures commences in the early stages of

construction, when it is important to validate assumption made at the design

stage, particularly regarding foundation seepage control. At the completion

of the structure, monitoring is applied to access structural stability and

behaviour and continues at the stage of the structure’s first loading so that

the safe establishment can be closely observed. Thereon, long – term

monitoring of operational behaviour and regular measurement of stress

states is maintained, to ensure each component of the structure is functioning

as intended.

The structural and geotechnical information needed to access a

structure’s stability is primarily obtained with instrumentation systems that

may vary for different monitoring purposes. The desirable characteristics of

these systems include proven durability and robustness, simplicity of

maintenance and use, provision of regular and reliable data sets, and

minimal personnel requirements for the collection of data.

34

Although many different types of structures exist, the bulk of

instrumentation systems installed are aimed at monitoring these key

precursors to failure: ground water pressure, chemical properties of the soil,

pressure and stresses within the ground or structure itself, surface

displacements on the structure or the surrounding bedrock. With respect to

deformation properties, no two structures are identical and thus the

performance conclusions of one cannot be extrapolated to that of another.

For this reason, each structure should be monitored regularly with a number

of instruments.

(www.ejge.com).

2.9 DEFORMATION MONITORING METHODS

The measuring techniques and instrumentation for deformation

monitoring have traditionally been categorized into two broad groups

according to the disciplines of professionals who use the techniques. These

are the geodetic surveys; which include conventional (terrestial)

photogrammetry, satellite and some special techniques (interferometry,

hydrostatic leveling, alignment etc; and the geotechnical and structural

measurements of local deformation using laser, tiltmeters, strainmeters,

extensometers, joint – meters, plumblines, micrometer etc.

2.9.1 GEODETIC METHODS:

Geodetics surveys, through a network of points interconnected by

angle and / or distance measurements, usually supply a sufficient

35

redundancy of observations for the statistical evaluation of their quality and

for a detection of errors. They give global information on the behaviour of

the deformable structure. Geodetic surveys have traditionally been used for

relative deformation measurements within the deformable object and its

surroundings. Conventional terrestrial surveys are labour intensive and

require skillful observers. Geodetic surveys with optical and electromagnetic

instruments (including satellite techniques) are always contaminated by

atmospheric refraction, which limits, their positioning accuracy to about

+1ppm to +2ppm (at standard deviation level) of the distance. New

developments in three – dimensional coordinating systems with electronic

theodolites may Provide relative positioning in almost real time to an

accuracy of + 0.05mm over distances of several meters. The same applies to

new developments in photogrammetric measurement with solid state

cameras (CCD sensors). Under the geodetic methods are;

(a) Survey Network Method: This includes; leveling for determination

of changes in elevation of monitoring points, lateral displacement

determination by offset measurement from a line of sight by use of

the theodolite and measurement of range changes between known

observation pillars or targets by electronic distance metres (EDMs).

Optical leveling requires first or second order accuracy in dam

monitoring. All conventional survey activities rely on optical

techniques to make measurements to known points. In monitoring, a

number of reference or control points located well away from the

zone of the ground movement are required. Otherwise, the control

points themselves may also be affected by surface motion. These

36

control points are best to be located in sound bedrock. Fully

automated robotic total stations can now be installed on dams to

monitor the position of a number of reflectors with varying elevations

at resolution between 0.5 to 7 seconds of are and 1 – 2mm in range.

Recent advances in this technology include motorized reflectorless

total stations and theodolites with accuracies between 1.5 – 5 seconds

of arc.

(b) Terrestrial Laser Scanning Method: Laser scanners have received

attention due to the number of measurement benefits including three

dimensional, fast and dense capture; operation without the mandatory

use of targets and permanent visual record. A disadvantage, however,

may be the difficulty to assess some fixed benchmarks on the surface

of the deforming area, unless they are special targets that can be

recognized by the accompanying software. In contrast to survey

network methods where small targets are desired to minimize

pointing error, much larger structured planar targets (e.g. spheres,

cones) are used in laser scanning. In order to profit in an optimal way

from the dense observations, it is favourable to model surface

deformation, rather than trying to detect deformation of single points.

The simplest means is the use of signalized – point measurements. A

number of predefined targets are placed on the deforming object and

repeated scans are acquired in each deflection epoch. The estimated

coordinates of the target in each epoch are compared against the zero

– load case and the deformation vectors are computed. (3 rd IAG /

12tth FIG. Symposium, Baden, 2006).

37

(c) The GPS Method: The Global Positioning System is a satellite based

positioning system. GPS receivers derive the range to a satellite by

computing the time offset between the code received from the

satellite and an identical code generated internally inside the

receiver’s hardware. GPS receivers can achieve a much greater

accuracy by first, relying on the measurement of the raw phase of the

incoming signal from the satellite and second, applying a technique

known as relative positioning. With GPS, the line – of – sight

dependency for survey observation is removed and this has altered

the practices of the survey community. Permanent GPS networks

offer the highest accuracies and temporal resolution. It also has

advantages that measurements can be taken during night or day and

under varying weather conditions making it economical and time

saving as well as the personnel requirements is very minimal.

2.9.2 GEOTECHNICAL ENGINEERING METHOD:

The geotechnical measurements give very localized and very

frequently, locally disturbed information without any check unless

compared with some other independent measurements. Geotechnical

instruments are easier to adapt for automatic and continuous monitoring than

conventional geodetic instruments. (US Army Corps of Engineers, 2002)

The main disadvantage of most dam geotechnical measuring systems

is that observations are restricted to the pre – designed locations where the

instrumentation has being installed. The same locations must be measured

separately in the horizontal and vertical components. Geotechnical

38

monitoring techniques can be especially effective in areas on a slope where

the mode of deformation motion has been previously identified. However,

for general stability monitoring, where potential regions of failure on steep

slopes or structures may not be evident, geotechnical methods are limited

(e.g. Green and Mikkelsen, 1986). It is infeasible to install a large number of

geotechnical sensors over all parts of a potentially unstable dam structure.

Geotechnical monitoring instruments include; extensometers, inclinometers,

piezometers, pressure cells, settlement cells, soil strainmeters and goodman

jacks. (www.gage-technique.demon.co.uk)

2.9.3 STRUCTURAL ENGINEERING METHOD:

This method is similar to the geotechnical engineering method.

However, in this method, the instruments are embedded into or beside the

structures and they monitor changes in tilt, level and gauge of the structure

on loading. The structural engineering monitoring instruments include;

tiltmeters, crackmeters / jointmeters, load cells, tape extensometers, liquid

level system, strain gauges, track monitoring, Bassett convergence and beam

sensors. (www.gage-technique.demon.co.uk)

2.9.4 FIBRE OPTICS METHOD:

Fibre optics measuring systems are potential new methods of

monitoring deformation. The attractiveness of theses monitoring method lies

in the advantages price of optical fibre, the possibility to use the fibre as a

measuring sensor of hundreds of metres in length, and the possibility to

implement the monitoring automatically either as a continuously operating

39

solution or a method that gives an alarm signal. It also has an advantage of

lesser personnel.

A distributed fibre optic system consists of an optical fibre for

temperature sensing and a measuring unit. A short laser pulse is sent into the

sensing fibre. As a result of spontaneous Raman scattering, some anti –

Stokes and Stokes photon are generated along the fibre. A fraction of these

scattered photos is captured in guided modes of the fibre and then

propagated back and detected by a fast photodetector. By measuring the

signal received at differing times after the pulse is sent and relating this to

the fibre the backscattered light came from. This is the basic operation

principle of a fibre optic temperature sensor for monitoring.

Fibre optics monitoring is particularly suitable for temperature regions

where the varying seasons result in extensive temperature differences

between soil structures and water. (ENGLUND, 1999)

2.10 CONTROL NETWORK

A control network is a set of reference points of known spatial

coordinates. The higher – order (high precision, usually miltimetre – to –

decimetre on a scale of continents) control points are normally defined in

both space and time using global or space techniques, and are used for lower

– order points to be tied into. The lower – order control points are normally

used for engineering, construction and navigation. The scientific discipline

that deals with the establishing of coordinate on points in a high – order

control network is called geodesy, and the technical discipline that does the

40

same for points in a low – order control network is called surveying. A

control point is divided into horizontal (X – Y) and vertical (Z) controls.

(en.wikipedia.org)

2.11 SURVEY ERRORS

Taking measurements is an operation, which is subject to variations

that will occur even if all the conditions remain the same during the period

of repeated measurements. These variations are caused by the fact that no

observation can be repeated exactly (except by sheer chance) because of

instrument limitations and human weaknesses in the ability to center, point,

match and read. All these variations in the elementary operations, however

small, produce corresponding variations in the resulting measurement.

Therefore, an observation or a measurement is a variable known as a random

variable (ANDERSON and MIKHAIL, 1985)

Since measurement variation is a natural phenomenon, then a

measurement will usually differ from its true value, whatever that true value

may be. The difference between a measurement and its true value is called

the measurement error. Thus if, x is a given measurement and x t is the

(unknown) true value, then the error e is given by;

e = x – xt. ---------------------------------------------------(2.1)

Error analysis refers to working on observations taken to minimize the errors

contained within. (ANDERSON and MIKHAIL, 1985)

41

2.11.1 TYPES OF SURVEY ERRORS:

The types of errors that usually occur in any survey measurement

include;

(a) Gross errors / Mistakes / Blunders: They can be of any size or nature, and

tend to occur through carelessness. Writing down the wrong value,

reading the instrument incorrectly, measuring to the wrong mark, etc; are

examples of gross errors. People, machine, weather and various other

things can cause them. Careful procedures and relentless checking of the

work deal with gross errors.

(b) Systematic / Cumulative errors: These errors are either constant or

variable throughout an operation. They are generally attributable to

known circumstances. The values of these errors can be calculated or

modeled and applied as correction to the measured quantity. Systematic

errors in the main conform to mathematical and physical laws.

Systematic errors are the most difficult errors to deal with and therefore,

they require very careful consideration prior to, during and after the

surveys.

(c) Compensating / Random errors: These are the small errors that will

usually remain in a system of measurement after all the other errors have

been removed. Random errors are assumed to have a continuous

frequency distribution and obey the law of Probability. By definition,

these errors tend to accumulate proportionally to the square root of the

number of operations involved.

(EHIOROBO, 2004).

42

2.11.2 ADJUSTMENT

Adjustment refers to the technique used by Engineers and Surveyors

in obtaining the most correct value in observations taken. Adjustment is

necessary in order to overcome the inconsistency between measurements

that results from random errors. In performing adjustments, one must take

into account the relative confidence level one has in each of the

measurements involved.

The method of least squares is the most commonly used method of

determining the most Probable values of observed quantities, assuming that

only accidental errors are present. It states that the sum of the weighted

residuals squared will be a minimum, i.e. [weight x (residual)2] is to be a

minimum.

For n observations;

w1r12 + w2r2

2 + w3r32 + - - - - - - -- - + wnrn

2 ---------------- (2.2)

is to be a minimum. Thus

[r1 r2 r3 - - - - - - - rn] w1 0 0 - - - - - - - - - 0 r1

0 w2 0 - - - - - -- - - 0 r2 ----(2.3)

0 0 0 - - - - - - - - wn rn

or rT Wr is to be a minimum

43

where ‘residual’ it the difference between the value (x) of one the

measurements and the most Probable value reliability, or precision; the

arithmetic mean ( ) is taken to be the most Probable; else it is calculated by

statistical analysis.

(BANNISTER and BAKE, 1994).

2.12 SOME DAM MONITORING WORKS

– PACOIMA DAM: Pacoima dam is located in the San Gabriel maintains,

about 5km northeast of Sylmar, California. This dam is a 113m tall

concrete arch dam that was completed in 1928. Because of their concern

about the stability of the dam, the country of Los Angeles, with the

technical support of the US Geological Survey (USGS), began

monitoring the dam using continuous GPS.

In September 1995, a system of three continuously operating GPS

receivers was deployed to monitor the displacements of Pacoima dam

relative to a stable station nearby at Fire camp 9 (2.5km away). At

Pacoima dam, the station DAM 1 was placed on the thrust block at the

left abutment of the dam, while station DAM 2 was placed near the

centre of the dam’s arch. The reference station CM P9 was placed on

stable bedrock outside of the steep – walled carryon that the dam spans.

The CM P9 GPS antenna was mounted into the slab on the bedrock.

The current system at Pacoima dam uses dual frequency P – code

GPS receivers that are commercially available. These sample all civilian

– accessible GPS observable at a rate of one sample every 30 seconds.

Data are collected on the receiver’s internal memory, then downloaded

44

using high speed moderns over regular phones lines once per day.

Starting in January 1996, data from the Pacoima dam system were

analysed daily at the USGS as a subset of the Southern California

network processing (HUDNUT and BEHR,1998).

- LIBBY DAM: In February 2002, the US Army Corps of Engineers

deployed a GPS monitoring system at Libby dam. Six GPS monitoring

stations are located along the crest of the dam to measure horizontal and

vertical deformation. A GPS reference station is located on each side of

the dam to Provide differential correction information. Processing

software collects raw measurements from all eight stations and computes

high – precision GPS solutions in real time.

The Libby dam is located in the Kootenai River in northwest

Montana, USA. It is a straight axis concrete dam composed of 47

monoliths (MLs). It has a length of 880m and height of 128.6m.

Engineers who continually analyze readings from the instrumentation

deployed on the dam manage careful monitoring effort. Besides the GPS

system, the instrumentation at Libby dam includes’ plumb lines,

jointmeters, foundation deformation meters, extensometers, uplift

pressure cells, inclinometers, concrete temperature meters, leakage

measurements and a laser alignment system.

The GPS system was installed at Libby dam to replace the

existing laser alignment system. Several of the GPS instruments were

collected with existing and reliable plumblines so that the two

45

measurement systems could be compared. The Corps uses this automated

GPS system as it provides continuous measurements from key monoliths.

These continuous data is deemed to be more valuable for

analysis than the twice – yearly laser survey, and would allow data to be

collected for true peak - loading conditions. (US Army Corps of

Engineers, 2002).

2.12.1 DEFORMATION WORKS IN THE UNIVERSITY OF BENIN

Here in the University of Benin, numerous final year Project works

have been carried out on monitoring and / or deformation especially on the

nearby Ikpoba river dam. These past Project works had some similarities

with this work but there are also marked disparities with each of them.

In 2005, AUGUSTINE ONOME OBI carried out a Project work

titled, “ A Survey Technique for Monitoring Deformation at Ikpoba River

Dam”. In that work, the author used trigonometric leveling to establish a

vertical control network with the existing monuments around the dam.

Analysis of the results were carried out and adjusted using least square

method. Accuracy standards were evaluated using the standard error of the

mean. The author concluded that the accuracy fell into third order class

specification and noticed it was because of the type of instrument used for

observation.

Also in 2005, MERIAMU DAUDA – IKHAREWORE carried out a

Project work titled, “Monitoring of Subsidence at Ikpoba River Dam Using

Geodetic Leveling Techniques”. In that work, the author carried out

structural deformation measurement of local and regional movement of the

46

dam using micro geodetic network in which both horizontal and vertical

angles were measured. Points were marked along the dam axis and the

points were coordinated from the established horizontal control. A level was

then used to carry out geodetic leveling along the marked point on the dam

axis using the three-wire method as a first – epoch measurement.

Again in 2005, PRINCE UMASABOR carried out a Project work

titled “Observation and Error Analysis in a 3 – D Control Network for

Setting Out Work”. The Project work involved the observation, error

analysis and adjustment in a 3 –D control network. A baseline consisting of

two adjoining brace quadrilaterals was chosen at the same Ikpoba dam site.

All angles and a base line were then observed by method of rounds on 4 –

zeros using a theodolite while the baseline was measured using a 100m steel

tape. The final results were adjusted using unconstrained least squares

adjustment method. The results gotten for the standard errors satisfied the

second order specification as required.

Also in 2005, EMEFIENE CHRISTOPHER carried out a Project

work titled “ Observation and Error Analysis in a Large Vertical Network

for Setting Out Monitoring of Movement in Dams”. In the Project a network

consisting of a twin braced quadrilaterals at Ikpoba dam was established.

Horizontal measurements were carried out which consisted of horizontal

angles and a baseline. Levels were then run in loops in both clockwise and

anticlockwise directions to cover two mathematical loops. After completion,

the levels were reduced and adjustment carried out by the least squares

method. The standard errors calculated satisfied third order vertical control

specification.

47

This Project work is similar to the first two highlighted with respect to

monitoring of deformation of dam. Also the latter two have similarities with

this work with respect to observation, adjustment and error analysis. There

are also individual similarities. However, the marked difference between this

Project work and all highlighted above is the introduction of highly precise

GPS monitoring for the deformation measurement. It is the first time that a

GPS monitoring technique is carried out o the Ikpoba River dam and this is

the first epoch.

48

CHAPTER THREE

3.0 GLOBAL NAVIGATION SATELLITE SYSTEMS (GNSS)

GNSS is the standard generic term for satellite navigation systems that

Provide autonomous geo – spatial positioning with global coverage. A

GNSS allows small electronic receivers to determine their location

(longitude), latitude and altitude to within a few meters using time signals

transmitted along a line of sight by radio from satellites. Receivers on the

ground with a fixed position can also be used to calculate the precise time as

a reference for scientific experiments.

As of 2007, the United States’ NAVSTAR Global Positioning System

(GPS) is the only fully operational GNSS. The Russian GLONASS is

GNSS in the process of being restored to full operation. The European

Union’s Galileo positioning system is a next generation GNSS in the initial

development phase, scheduled to be operational in 2010. China has indicated

it may expand its regional Beidou navigation system into a global system.

India’s IRNSS, a next generation GNSS is in the developmental phase and is

scheduled to be operational in 2012.

The Original motivation for satellite navigation was for military

applications. Satellite navigation allows for hitherto impossible precision in

the delivery of weapons to targets, greatly increasing their lethality whilst

reducing inadvertent casualties from mis – directed weapons. Satellite

navigation also allows forces to the directed and to locate themselves more

easily, reducing the fog of war.

49

GNSS systems have a wide variety of uses; these include; navigation

(ranging from personal hand – held devices for trekking to devices fitted to

cars, trucks, ships and aircraft), time transfer and synchronization, location –

base services such as enhanced 911; surveying entering data into a GIS,

search and rescue, geo – physical sciences, tracking devices in wildlife

control.

GNSS that Provide enhanced accuracy and integrity monitoring,

usable for civil navigation as classified as follows - GNSS – 1 is the first

generation system and is the combination of existing satellite navigation

systems, (GPS and GLONASS) with Satellite Based Augmentation Systems

(SBAS) or Ground Based Augmentation Systems (GBAS). In the United

States, the satellite-based component is the Wide Area Augmentation

System (WAAS), in Europe it is the European Geostationary Navigation

Overlay Service (EGNOS) and in Japan it is the Multi – Functional Satellite

Augmentation System (MSAS). Ground based augmentation is Provided by

systems like the Local Area Augmentation System (LAAS).

– GNSS – 2 is the second generation of systems that independently

Provides a full civilian satellite navigation system, exemplified by the

Galileo positioning system.

These systems will Provide the accuracy and in integrity monitoring

necessary for civil aviation. This system consists of L1 and L2 frequencies

for civil use and L5 for system integrity. Development is also in PROgress

to Provide GPS with civil use L2 and L5 frequencies, making it a GNSS – 2

system.

50

A GNSS may have several layers of infrastructures:

– Core Satellite navigation systems, currently GPS, Galileo and

GLONASS

– Global Satellite Based Augmentation Systems (SBAS) such as

Ommistar and Starfire.

– Regional SBAS including WAAS (US), EGNOS (EU), MSAT

(Japan) and GAGAN (India).

– Regional Satellite Navigation Systems such as QZSS (Japan), IRNSS

(India) and Beidou (China).

– Continental Scale Ground Based Augmentation Systems (GBAS) e.g.

the Australian GRAS and the US department of Transportation

National service.

– Regional Scale GBAS such as CORS networks.

– Local GBAS typified by a single GPS reference station operating Real

Time Kinematic (RTK) corrections.

The Global Navigation Systems that are currently available and / or in

the development stages include, the GPS, GLONASS, GALILEO, IRNSS,

DORIS and Compass.

The Indian Regional Navigational Satellite System (IRNSS) is a

proposed autonomous regional satellite navigational system to be constructed

and controlled by the Indian government. It is intended to Provide an absolute

position accuracy of better than 20 meters throughout India and within a region

extending approximately 1500 to 200km around her. A goal of complete control

has been stated, with the space segment, ground segment and user receivers all

51

being built in India. The government approved the Project in may 2006, with

the intention that it will be implemented within six to seven years.

China has indicated they intend to extend their regional navigational

system, called BEIDOU or DIPPER into a global navigation system; a Program

that has been called COMPASS in China’s official news agency, Xinhua. The

Compass system is Proposed to utilize 30 medium earth orbit satellites and five

geostationary satellites.

DORIS; an acronym for Doppler Orbitograph and Radio – positioning

Integrated by Satellite, is a French precision system.

(en.wikipedia.org)

3.1 GALILEO

The European Union and European Space Agency agreed on March

2002 to introduce its own alternative to GPS, called the Galileo positioning

system. The required satellites are to be launched between 2006 and 2008

and the system will be working under civilian control, from 2010. The first

experimental receivers were launched on 28th December, 2005. The receivers

will be able to combine the signals from both Galileo and GPS satellites to

greatly increase positioning accuracy.

Galileo is tasked with multiple objectives including;

(a) to provide a higher precision to all users that is currently available

through GPS or GLONASS.

(b) To improve availability of positioning services at higher latitudes

(c) To provide an independent positioning system upon which European

nations can rely even in times of war or political disagreement.

52

Named after the Italian astronomer, Galileo Galilei, the Galileo

positioning system is referred to as “Galileo” instead of the abbreviation

‘GPS’ to distinguish it from the existing United States System.

The Galileo satellites consist of 30 spacecraft at orbital attitude of

2322km. There are three orbital planes at 56o inclination. Each plane will

contain nine operational satellites an one active spare. Satellite lifetime is at

least 12 years, with mass of 675kg and body dimensions =2.7m x 1.2m x

1.1m.

There will be four different navigation services available:

– The Open Service (OS) will be free for anyone to access. Receivers

will achieve an accuracy of less than 4m horizontally and less than 8m

vertically if they use both OS bands.

– The encrypted Commercial Service (CS) will be available for a fee

and will offer an accuracy of better than 1m. the CS can also be

complemented by ground stations to bring the accuracy down to less

than 0.1m.

– The encrypted Public Regulated Service (PRS) and Safety of Life

Service (SoL) will both provide accuracy comparable to the Open

Service. Their main aim is robustness against jamming an the reliable

detection of problems within 10 seconds. (en.wikipedia.org).

3.2 GLONASS

Global Navigation Satellite System is a radio - based satellite

navigation system developed by the former Soviet Union and now operated

for the Russian government by the Russian Space Forces.

53

Its constellation was completed in 1995 but the system rapidly fell into

disrepair with the collapse of the Russian economy. Beginning in 2001,

Russia has been committed to restore the system by 2011.

A fully functional GLONASS constellation consists of 24 satellites,

with 21 operating is such that, if the constellation is fully populated, a

minimum of five satellites are in view from any given point at any given

time.

GLONASS satellites transmit two types of signal: a standard precision

(SP) signal and an obfuscated high precision (HP) signal. All satellites

transmit the same SP signal, however each transmits on a different

frequency using a 25 – channel frequency division multiple access

technique. The more accurate HP signal is available for authorized users. An

additional civil reference signal on L2 frequency is to be added with the next

generation of satellites to substantially increase the accuracy of navigation

relaying on civil signals.

The ground control segment of GLONASS is entirely located within

former Soviet Union Territory.

As of July 2007, the system is not fully available, however it is

maintained and remains partially operational. In recent years, Russia has

kept the satellite orbits optimized for navigating within her at the cost of

degrading coverage in the rest of the world. As of July 2007, GLONASS

availability in Russia was 37.7% and average availability for the whole

Earth was down to 28.8%. Meaning that, at any given time of the day in

Russia, there is 37.7% likelihood that a position fix can be calculated.

(en.wikipedia.org)

54

3.3 GLOBAL POSITIONING SYSTEM (GPS)

The Global Positioning System (GPS) is a satellite – based navigation

system made up of a network of 24 satellites placed into orbit by the United

States’ Department of Defence. It was developed in 1972 for the US navy

and air force. GPS was originally intended for military applications, but in

the 1980’s, the government made the system available for civilian use. GPS

works in all weather conditions, anywhere in the world, 24 hours a day.

There are no subscription fees or setup charges to use GPS. The GPS system

was designed to be a passive survivable continuous system, which can

Provide any user with 3 – dimensional, position, velocity and time

information.

GPS satellites circle the earth twice a day in a very precise orbit and

transmit signal information to earth. GPS receivers take this information and

use triangulation to calculate the user’s exact location. Essentially, the GPS

receivers compare the time a signal was transmitted by a satellite with the

time it was received. The time difference tells the GPS receiver how far

away the satellite is. Now, with distance measurements from a few more

satellites, the receiver can determine the user’s position and display it on the

unit’s electronic map.

The GPS (officially called NAVSTAR) system consists of a military P

– code and a civil clear acquisition (C/A) component. The P – code

providing precise positioning can be denied to unauthorized users but the

CA code is made available to any suitably equipped user. The system

consists of the space segment, control and user segments. The space segment

consists of constellation of satellites made up of 21 operational plus 3

55

unorbit spare satellites. The control segment consists of 3 ground antennae

(GAE), 5monitoring stations (MS) and pre – launch compatibility station

(PCS) and a master control station (MCS). The users segment consists of

user’s equipment (receiver), which Provides users with precise positioning

and timing information.

The satellites, which are constantly moving, orbit the earth about

12000 miles above us. They make two complete orbits in less than 24 hours

traveling at speeds of roughly 7000 miles per hour. The satellites are

powered by solar energy. They have backup batteries on board to keep them

running in the event of a solar eclipse, when there is no solar power. Small

rockets boosters on each satellite keep them flying in the correct path.

A GPS receiver must be locked up to the signal of a least three

satellites to calculate a 2 – dimension position (latitude and longitude) and

track movement. With four or more satellites in view, the receiver can

determine the user’s 3-dimension position (latitude, longitude and altitude).

Once the user’s position has been determined, the GPS unit can calculate

other information, such as speed, bearing, track, trip distance, distance to

destination, sunrise and sunset and more.

3.3.1 GPS SIGNALS AND BASIC OPERATION PRINCIPLES

GPS satellites transmit two low power radio signals, designated L1

and L2. Civilian GPS uses the L1 frequency of 1575.42MHz in the UHF

band. The signals travel by line of sight i.e. they will pass through clouds,

glass and plastic but will not go through most solid objects as buildings and

mountains.

56

A GPS signal contains three different bits of information a

pseudorandom code is simply an I.D. code that identifies which satellites it’s

receiving. Ephemeris data tells the GPS receiver where each GPS satellite

should be at any time throughout the day. Each satellite transmits ephemeris

data showing the orbital information for that satellite and for every other

satellite in the system. Almanac data, which is constantly transmitted by

each satellite, contains important information about the status of the satellite

(healthy or unhealthy), current date and time. This part of the signal is

essential for determining a position.

In GPS measurement, at least 3 satellites are required. The Procedure

involves measurement of distances (ranges) to the three satellites where Xs,

Ys, Zs position are known in other to define the users position; Xp, Yp, Zp.

The satellites transmit a signal on which the time of its departure, to, from

the satellite is modulated. The receiver in turn notes the time of arrival, tA, of

this time mark. Then the time, which it took the signal to go from satellite to

receiver, is; tA – tD, called the delay time. The measured range, R, is obtained

from R = (tA – tD) C. C is velocity of light. In GPS measurements, four

satellites are used rather than 3. The equation of position is derived from the

following. A line in space is defined by the difference in coordinates as:

--------------------------------(3.1)

If the error in R, due to clock bias (delay time) is R and is a constant

throughout, then R + R is;

57

---------------(3.2)

Where Xi, Yi, Zi (i = 1 – 4) are coordinates of satellites 1,2,3,4 and

Xp, YP, ZP, are unknown coordinates of P.

Solving the four equations for the four unknowns, eliminate errors due to

clock bias. (EHIOROBO, 2006).

3.4 THE GPS RECEIVER

The signals transmitted from the GPS satellites are received from the

antenna through the radio frequency (RF) chain the input signal is amplified

to proper amplitude and the frequency is converted to a desired output

frequency. An analog – to – digital converter (ADC) is used to digitize the

output signal. The antenna, RF chain, and ADC are the hardware used in the

receiver. (See fig 1).

58

Fig 3.1 A fundamental GPS receiver.

After the signal is digitized, software is used to process it. Acquisition

means to find the signal of a certain satellite. The tracking program is used

to find the phase transition of the navigation data. In the conventional

reviver, the acquisition and tracking are performed by hardware. From the

navigation data phase transition, the subframes and navigation data can be

obtained. Ephemeris data and pseudoranges can be obtained from the

navigation data. The ephemeris data are used to obtain the satellite positions.

Finally, the user position can be calculated for the satellite positions and the

pseudoranges.

(TSUI, 2005)

3.5 GPS TERMINOLOGY

(a) SV tracking time: Signal tracking is related to the amount of time a

given GPS satellite is in continuous view of the receiver / antenna.

59

Satellites that are just rising, setting, or are only in view for short

periods of time (less than 15 minutes) are to be suspected as unfit.

(b) Satellites – in – view: GPS satellites are more densely placed over the

mid – to – lower earth latitudes. A minimum of five satellites is

recommended for reliable GPS processing results. Generally, eight or

more GPS satellites are available at optimal observing times.

An extra satellite in view increases data redundancy and provides the

user the option to select only the highest quality data within a session.

(c) Continuous L1 / L2 Signal Lock: Maintaining continuous phase lock

on both L1 and L2 signals is a critical requirement for obtaining high

quality data. Loss – of – lock on any satellite indicates a problem with

its signal reception and tracking. If possible, only data collected from

satellites that maintain continuous lock should be used for final

baseline processing.

(d) GPS time and date: While most clocks are synchronized to Coordinate

Universal Time (UTC), the Atomic clocks on the satellites are set to

GPD time. The difference is that GPS time is not corrected to match

the rotation of the Earth, so it does not contain leap seconds or other

corrections, which are periodically added to UTC. The lack of

corrections means the GPS time remains at a constant offset (19

second) with International Atomic Time (TAI). The GPS navigation

message includes the difference between GPS time and UTC, which

60

as of 2006 is 14 seconds. Receivers subtract this offset from GPS time

to calculate UTC and specific time zone values.

(e) Dilution of Precision (DOP): GDOP and PDOP (Geometric and

Position DOP respectively) are measures of geometric and position

strength related to satellite constellation geometry and user range

error. PDOP is computed as the ratio range error to the single station

position error used in code range positioning. Both the geometry and

the number of tracked SVs are highly correlated to DOP values.

Effects of low and high DOP windows can be observed in GPS

performance result.

(f) Satellite elevation angle: This is the angle of inclination of the

satellite usually relative to the local horizon. Satellites at low

elevations generally produce low quality signals because of multipath,

refraction, attenuation and reduced antenna gain. In theory, data from

lower elevation satellites will improve satellite geometry, however

any benefit from geometry is offset by poor signal quality.

(g) L1 / L2 signal strength: Signal strength on L1 / L2 carriers are

measured by the receiver as a carrier – to – noise density (C/N) ratio.

C/N is a function of transmitter power; satellite elevation angle;

antenna gain pattern; signal attenuation; and receiver noise power.

GPS signal quality is related to the behaviour of its signal strength

profile.

61

(h) Ephemeris: This refers to a description of the path of a celestial body

indexed by time. The navigation message from each GPS satellite

includes a predicted ephemeris for the orbit of that satellite valid for

the current hour. The ephemeris is repeated every 30 seconds.

(i) Spoofing: This is the deliberate transmission of fake signals to skew

the position calculations of a GPS receiver. The spoofer mimics a

GPS satellite, rather like a pseudolite, but with disruptive intent.

(j) Anti – Spoofing: This is the encryption of the P – code signal

transforming it to Y – code that is unavailable to civilian users. Anti

spoofing prevents an encryption – keyed GPS receiver fro being

spoofed “by a bogus, enemy – generated GPS P – code signal.

3.6 DIFFERENTIAL GPS

DGPS is an enhancement to GPS that uses a network of fixed ground

based reference stations to broadcast the difference between the positions

indicated by the satellite systems and the known fixed positions. These

stations broadcast the difference between the measured satellite

pseudoranges and actual pseudoranges, and receiver stations may correct

their pseudoranges by the same amount.

The underlying premise of differential GPS is that any two receivers

that are relatively close together will experience similar atmospheric errors.

62

DGPS requires that a GOS receiver be set up on a precisely known location.

This GPS receiver is the base or reference station. The base station receiver

calculated its position based on satellite signals and compares this location

based on satellite signals and compares this location to the known location.

The difference is applied to the GPS data recorded by the second GPS

receiver, which known as the roving receiver. The corrected information can

be applied to data from the roving receiver in real time in the field using

radio signals or through post processing after data capture using special

processing software.

Real – time DGPS occurs when the base station calculate and

broadcasts corrections for each satellite as it receives the data.

(MORAG, 2003)

3.7 GPS AND DEFORMATION MONITORING

GPS surveying techniques for structural monitoring have a high

potential for reduction in manpower needed for conducting deformation

surveys. Although GPS can yield positions that are comparable to the

accuracy levels expected for conventional surveys, its use in the past was

limited because of a requirement for lengthy station occupation times.

Reduced occupation times have now been realized through the use of

specialized instrumentation and enhanced software analysis, resulting in

reliable sub – centimeter accuracy from much shorter observations. The

63

following are the basic considerations for a proper monitoring of structural

deformation with the GPS.

3.7.1 SURVEYING REQUIREMENT

a. ACCURACY: Typical accuracy requirements for deformation

surveys range between 10mm horizontally and 2mm vertically for

concrete structures, and up to 30mm horizontally and 15mm vertically

for embankment structures.

Surveying accuracy specifications are meant to ensure detection of a

given amount of movement under normal operating conditions.

Allowable survey error thresholds are related to the maximum

expected displacement that would occur between repeated

measurement campaigns. For each survey, final positioning accuracies

at the 95% Probability level should be less than or equal to one – forth

(0.25) of the predicted displacement value.

Settlement of earth and rockfill embankments decreases as a

function of time (due to consolidation). Normal vertical subsidence is

on the order of 400 mm over 5 – 10 your stabilizing phase,

PROgression most actively in the first two years. Average settlement

rates of approximately 50mm / year, up to a maximum of 140mm /

year are typical. Horizontal displacements on embankment structures

follow similar stabilizing trends with maximum displacements on the

order 90 – 100mm, occurring at peak rates of 30mm / year.

Positioning accuracies of approximately 10mm / year vertically and 5

–10 mm / year horizontally are required at the 95% confidence level.

64

b) SYSTEM REQUIREMENTS: A successful GPS – based

deformation measurement system must meet the following

performance requirements:

– The system should provide relative horizontal and vertical-positioning

accuracies comparable to those obtained from existing conventional

deformation surveys, within stated accuracy requirements of

approximately 5mm or less at the 95% confidence level.

– Station occupation times should be reduced to minutes per station

required for a typical monitoring survey in one working day.

– The system must operate with commercial off – the – shelf (COTS)

equipment having nominal power requirements. It is desired that the

system no require classified access for full performance.

– The system must collect data that conforms to Receiver Independent

Exchange (RINEX) standards for subsequent must provide redundant

observations of monitoring point positions so that reliability,

statistical assessments, and detection of outliers are enabled.

– The system must provide localized coverage over a network of survey

points that would be typically installed on project sites.

– It is desired that no specialized operational procedures be required to

initialize the system and conduct a mission. Any needed pre – mission

operations must be within the capability of the survey crew to

perform.

c) EQUIPMENT REQUIREMENTS: Only precise carrier phase

relative positioning techniques will yield accuracies sufficient for GPS

structural deformation surveys. Commercial off – the – shelf (COTS)

65

geodetic type receiver / antenna equipment has the operational

capabilities necessary for collecting high – quality carrier phase data.

A list of recommended components for such a system are as follows:

– Receiver: A geodetic quality GPS receiver must have; L1 / L2 phase

measurement capability, up – to – date firmware version, and

hardware boards, minimum of 3 – 10 megabyte internal raw data

storage.

– Antenna: At minimum, the antenna must be a dual frequency GPS

L1/L2 microstrip antenna with flat ground plane or choke ring, and

type – matched to GPS receiver.

– Transmission cables

– Power supply

– Software: processing and post – processing software.

– Computer system

– Field equipment: Steel tapes, plummets, tripods, field book et

(US Army Corp of Engineers, 2002)

3.7.2 SURVEYING PROCEDURES

The objective of deformation surveys is to determine the position of

object on the monitored structures GPS has several advantages over

conventional surveys GPS is highly recommended for conducting surveys of

the reference network of stable points surrounding the project structure. The

fieldwork and procedures for GPS deformation surveys can be conducted in

ways that are very similar to conventional surveying field operations. These

include;

66

(a) FIELDWORK PREPARATION: Data collection efforts with GPS

equipment require a moderate level of planning and coordination.

Typically a GPS monitoring survey will require occupations of multiple

station points. If multiple receiver units are employed, then coordination

of different occupation sequences should be specified prior to the

fieldwork. The schedule of station occupation times is based on GPS

mission planning. Satellite constellation status and local observing

conditions are to be determined before fieldwork.

(b) FIELDWORK PROCEDURES: Data collection efforts depend on

consistent fieldwork practices. A recommended sequence of events for

each monitoring station is as follows;

– Preparation to the entire GPS equipment

– Receiver user – defined parameters e.g. data logging rate is set to one

second, P – code tracking disabled etc.

– Station data logging, includes measuring antenna height, orienting the

antenna ground plane to height, orienting the antenna ground plane to

magnetic / true north. One the receiver unit has acquired at least five

satellites; data logging using the appropriate user controls can be

initiated.

– At the end of the station observing session, the date logging function

is terminated through the user interface. Equipment is then moved to

the next station setup.

(c) DATA COLLECTION PROCEDURES: A session length of 15 – 30

minutes (L1/L2 GPS carriers phase data) is required to meet minimum

positioning accuracies using two simultaneously observed reference

67

stations. Stations are positioned relative to at least two stable reference

stations in the reference network. Simultaneous data collection at all

three stations is required. Greater redundancy can be obtained by

observing each station twice at different time periods.

A minimum of five visible satellites must be tracked at all times.

Also, at a minimum, L1 phase and CA code data must be recorded by the

receiver at specified logging rates. Specific information related to the

data collection must be noted and recorded on the appropriate log sheets.

These include: Station names, L1/L2 phase centre offsets, start and stop

times of each session, notes about problems encountered, entered

filename and antenna height.

A one second data-logging rate should be used in all data collected

for monitoring surveys. The logging rate is defined as the time interval

between each data value recorded in the receiver’s internal memory

written to an external storage device.

(US Army Corps of Engineers, 2002)

3.7.3 DATA PROCESSING PROCEDURES

A variety of software applications are available for GPS data post –

processing and adjustment. Commercial software is adequate for most GPS

monitoring surveys, with some limitations. Scientific versions are more

complex and may require auxiliary data to enable certain user – functions.

68

These higher – end packages are capable of extensive and customized

processing with robust levels of output and statistics.

Most GPS post – processing software has standard features for

loading data processing baselines. This is because different applications

generally have the same requirements for internal treatments of GPS data

and computations. GPS raw data required for post – processing are the

observation files and ephemeris files.

Computation of baselines requires the following information supplied

or edited by the use: station names specified for each endpoint of the

baseline, antenna heights in meters for both baseline stations, separate

filename for GPS data collected at each station, approximate coordinates for

each station with position quality, receiver and antenna type with known

phase center offset, and session start and stop times for each station

observation set. The results of each baseline solution are examined for

completeness and then compared to survey design specifications.

The points to note in processing multiple baselines in a monitoring

network includes; the reference network is processed before the monitoring

network in order to establish high accuracy control coordinates for each

reference station. All simultaneously observed baselines are processed

separately between each reference station that was occupied during the

survey.

All stable reference network stations are fixed with control

coordinates established by the reference network survey processing results.

Each monitoring station data file is processed baseline – by – baseline using

each simultaneously observed reference station data file.

69

Once all the data has been processed and validated, GPS baseline ties

will connect the entire surveyed network of monitoring points. All post

processed GPS solution vectors are processed using least square network

adjustment software. Final coordinates are then differenced from the

previous survey adjustment to determine the 3D displacement at each survey

station. An examination of plotted movement trends (coordinates

differences) and comparison of direction an magnitude to the maximum

expected displacement is made to summarize deformation of the structure.

Any unusual or unexpected movement trends should be traced back so that

the supporting GPS data is validated a second time.

(US Army Corps of Engineers, 2002)

3.8 SOURCES OF GPS SIGNAL ERRORS

Factors that can degrade the GPS signal and thus affect accuracy

include the following;

(a) Selective Availability: The most relevant factor for the inaccuracy of the

GPS system is no longer an issue. On May 2, 2000; the so – called

selective availability (SA) was turned off. Selective availability is an

artificial falsification of the time in the L1 signal transmitted by the

satellite. For civil GPS receivers, that leads to a less accurate position

determination.

(www.kowoma.de)

(b) Satellite geometry: This describes the position of the satellites to each

other from the view of the receiver. Ideal satellite geometry exists when

70

the satellites are located at wide angles relative to each other. Poor

geometry results when the satellites are located in a line or in a tight

grouping. The DOP values are commonly used to indicate the quality of

the satellite geometry.

(c) Atmospheric effects: There is reduced speed of propagation in the

troposphere and ionosphere. While radio signals travel with the velocity

of light in the outer space, their propagation in the ionosphere and

troposphere in slower.

(d) Clock inaccuracies and rounding errors: Despite the synchronization of

the receiver clock with the satellite time during the position

determination, the remaining inaccuracy of time still leads to an error of

about 2m in the position determination. Rounding and calculation errors

of the receiver sum up to about 1m.

(e) Relativity: According to the theory of relatively, due to their constant

movement and height relative to the Earth – centered inertial reference

frame, the clocks on the satellites are affected by their speed (special

relativity) as well as their gravitational potential (general relativity).

(f) Orbital errors: Although the satellites are positioned in very precise

orbits, slight shifts of the orbits are possible due to gravitation forces. The

orbit data are controlled and corrected regularly and are sent to the

receivers in the package of ephemeris data. Therefore, the influence on

the correctness of the position determination is rather low.

(g) Number of satellites visible: The more satellite a GPS receiver can see,

the better the accuracy. GPS units typically will not work indoors,

underwater or underground.

71

(h) Multipath effects: Multipath errors are due to reflected GPS signals from

surfaces (such as buildings, metal surfaces, hard ground etc.) near the

receiver, resulting in one or more secondary propagation paths. These

secondary – path signals, which are superimposed on the desired direct

path signal, always have a longer propagation time and can significantly

distort the amplitude and phase of the direct – path signal.

(IYIADE and OWUSU – NKASAH, 2002)

Multipath effects are much less severe in moving vehicles. When the

GPS antenna is moving the false solutions using reflected signals quickly

fail to converge and only the direct signals result in stable solutions. It was

this same multipath effect that caused ghost images on televisions with

antenna on the roof.

(www.kowoma.de)

3.9 GPS NETWORK PLANNING

The quality of a network can be assessed in terms of precision and

reliability. This valuation may take place before the start of the actual

measurements in the field, namely during the planning or design of the

network. While precision is the closeness to one another of a repeated set of

observations of the same quantity, i.e. a measure of the control over random

error, reliability is the closeness to a theoretical ‘truth’.

Usually the study of the topographic maps of the area and

reconnaissance in the field precedes the initial design. The outcome of the

initial network design depends on the purpose of the network and on related

demands on precision and reliability.

A number of general rules of thumb apply for network design:

72

Aim for a balanced distribution of known stations over the network.

Try to include loops in the network, keeping in mind that the lesser the

number of stations in a loop, the better the reliability.

Strive for network sides of approximately equal length.

When establishing a GPS network with a number of simultaneously

operating receivers (at least three), the actually planned network

configuration can be altered even after completion of the measurements in

the field.

In case of N receivers, the number of possible baselines is N (N – 1).

2

However, only a subset of (N – 1) linearly independent baselines should be

selected for computation in the raw data processing.

The output of the design computation is:

Absolute and relative standard ellipses.

A – posteriori standard deviations of observations.

A – posteriori standard deviations of stations.

Minimal Detectable Bias (MDB) of observations.

Minimal Detectable Bias (MDB) of known stations.

Bias to Noise Ration (BNR) of observations

Bias to Noise Ration (BNR) of known stations.

Based on this output, the network can further be improved until the

requirements are satisfied. The design Process can be represented by the

scheme below.

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3.10 ADJUSTMENT OF A NETWORK

From observations carried out in the field, the Surveyor will have to

compute an end result: the coordinates. When redundant observations are

available, as it should be, adjustment is required to get a unique and optimal

solution.

The adjustment of a network is usually sub – divided into two separate

steps or phases:

Free network adjustment

Constrained adjustment

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A free network can be defined as a network of which the geometrical

layout is determined by the observations only. The position, scale and

orientation of the network are fixed by a minimum number of constraints,

through the base stations. Thus, the base stations impose no extra constraints

on the adjustment solution. In a free network adjustment, the emphasis is

laid on the quality control of the observations, rather than on the

computation of coordinates. Selecting other stations to fix the position, scale

and orientation will change the coordinate, but not the statistical testing.

Having eliminated possible outliers in the observations in the free

adjustment, the network can be connected to the known stations. This does

impose extra constraints on the solution. Now the emphasis is on the

analysis of the known stations and on the computation of the final

coordinates. There are two types of constrained adjustments: absolutely

constrained and weighted constrained.

The difference between these two types is in the coordinate

computation. In an absolutely constrained adjustment the coordinates of the

known stations are kept at their original value, i.e. they do not receive a least

squares correction. An absolutely constrained adjustment is sometimes

called a pseudo least squares adjustment. In a weighted constrained

adjustment however, the known stations do receive a correction. The choice

for an absolutely or weighted constrained adjustment leaves the testing

results unchanged.

It should be noted that the quality of a network, whether already

measured or only existing as design, could be assessed in terms of precision

and reliability. By designing a network, it is possible to control the quality.

75

However, designing a ‘perfect’ network is not enough. It therefore means

that the quality control will have to include some sort of statistical testing, in

order to clear the result of possible outliers. The effectiveness of the testing

will depend on the reliability of the network. The more reliable a network is,

the higher the Probability that outliers will be detected by the testing.

In a nutshell, it can be said that for the observations of a control

network;

The least squares adjustment will produce the best possible result;

The statistical testing checks the result in order to make it ‘error – free’;

The precision and reliability parameters quantify the quality of the result.

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CHAPTER FOUR

4.0 RECONNAISSANCE

The first and very important stage of any survey Project is the

preliminary reconnaissance. Reconnaissance comprises selection,

determination of sizes and shapes of the resulting triangles (for stations), the

number of angles or direction to be observed, the intervisibility and

accessibility of stations, the usefulness of the station in later work, cost of

necessary signals and the convenience of the base line measurements are all

considered.

The Project Engineer / Surveyor studies all the available maps, survey

information and photographs of the area and undergoes onsite inspection

where he chooses the most favourable location for station. He then draws the

plan and overall network of control points and boundaries.

At the Ikpoba dam, the Project crew, headed by our Project

Supervisor, carried out the necessary reconnaissance as required. The control

points already exist. The reconnaissance started on the Okhoro wing of the

dam where there are six of the control points. Intervisibility was established

between these control points by clearing and cutting off bushes and shrubs

lying between them in each pair. This is to create access and not a necessity

for observation.

The movement points were then monumented along the dam axis. A

total of ten movement points were Provided on the dam axis. Starting at the

end of the dam axis, five of the points were placed at 100m intervals. The

other two points were marked adjacent to the crest by the spillway.

77

On the second day of reconnaissance, the work was moved to the

Teboga arm of the dam where the five already existing control points were

established.

Lines were cleared for intervisibility between theses points. The

remaining three movement points were then monumented along the dam

axis.

A plan was then prepared showing the control points and the

movement points for monumentation and record purposes.

4.1 DIFFERENTIAL GPS OBSERVATION

The GPS observation or field measurement was carried out by

differential GPS technique. The GPS observation for monitoring and

establishment of controls around the dam area was carried using three,

LEICA 300 GPS receivers with Antenna. SURVICOM SERVICES NIG

LTD provided the instrument together with the observation crew.

The control point used for the survey was the CFG113B. It is located

about 1km into and along the Benin – Technical Road just after the cattle

market. This is off the Ugbowo / Lagos Road. Three 20 GPS stations were

established within the site location.

78

Fig 4.1 LEICA GPS Controller.

Fig 4.2 LEICA GPS Antenna on tripod.

4.1.1 SCOPE OF FIELDWORK

The job required the following;

79

Using dual frequency GPS receivers. Coordination of the chosen points

form first order control pillars in static differential mode.

A minimum of four satellites is to be observed concurrently during data

logging.

GDOP value during observation at the end of each session should not

exceed 5.

All computation options available during the processing of baseline

observations are to be applied consistently throughout data reduction

Procession.

Detail of all the processing procedure must be in line with technical

specification on baseline processing, least square adjustment and datum

transformation.

Detailed description of station observed was to be produced. The

technical specification also requires that observations at the geodetic

stations shall be carried out for not less than 1 hour at 15 seconds

sampling rate.

4.1.2 PERSONNEL

The personnel consisted of the Project supervisor (the head), three

operators of the GPS equipment from the contractor’s firm, and five student

assistants working on different Project topics on the dam site.

4.1.3 EQUIPMENT

The following equipment was employed for the execution of the

fieldwork.

80

4 Leica GPS 300 series with accessories

4 Tripods

2 Sheated machetes

2 Operational vehicles.

Data acquisition in the field was done with three units of “Leica 300”

GPS Systems and their corresponding accessories. The “Leica 300” system

is a Dual Frequency GPS receiver with Geodetic Antenna for L1 and L2

signals (at 1575.422MHz and 1227.60MHz) and interactive Hand Held

Controller. The system is capable of correlating the Y – codes in L1 and L2

to obtain a time difference. By adding the difference in the time delays to the

Clear Acquisition (CA) Code measurements, a pseudo range measurement

with the same information as the actual precise (P) – code is obtained –

thereby correcting the Anti – Spoofing (AS) effect. The system also has

internal programs for dealing with the intentional manipulation of Satellite

Clock Frequency and Orbit in the Ephemeris Data (Selective Availability).

The Leica 300 is an improvement on older GPS receivers and is capable of

tracking signals in areas with obstructions like light trees.

The corresponding “Wild Tripods” were used for mounting the GPS

receivers. Also, a Laptop Computer equipped with “SKI 2.3 and SKI– PRO”

processing softwares were used during baseline processing and network least

squares adjustment.

4.1.4 METHODOLOGY

Three (20) GPS observations were carried out.

The rovering points observed were named and identified as

requirement.

81

Duration of satellite observations was 1 hour.

GDOP for the points, except the point 2si, all through observations

were below 5.0.

The window for the vertical angle of satellite observations was limited

to 15 degrees.

Data acquistion for the GPS observation began on the 11th of August

at the Okhoro arm of the dam and was concluded on the 12th of August at the

Teboga arm of the dam.

In each rovering station, the antenna was mounted on the tripod and

then properly centered to the centre point of the monuments.

The antenna was then leveled horizontally using the leveling bubble.

The equipment was then activated and the antenna oriented to the North

using the sun’s direction. The project an Job name were entered using the

controller program. Antenna height was measured per station and also

entered. The antenna offset (height of Antenna = 0.441m) was also entered.

Other information recorded in the GPS controller unit per station were

station name, operator name, user approximate co-ordinates, etc. The

acquisition parameters for the Leica 300 SST were set as:

Minimum Elevation Mask – 15o

Minimum no. of SVs - Auto select

Measurement Sync Time - 4 seconds.

Satellite Heath - Automatic

Time Zone - GMT + 1

Sampling Rate - 15 seconds

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Type of Job - Static

The student assistants; who were properly oriented to re – activate the

receiver and communicate to the Pupil Surveyor in case it goes off while

acquiring data; manned each GPS observation station.

Station occupation sheets were also filled with information which

included point name, short time, stop time, initial position (Latitude,

Longitude) estimate, station diagram, pillar condition remarks, sky visibility

diagrams, antenna height observed etc.

4.2 REDUCTION OF OBSERVATION

The raw data fed into the GPS controller, after complete observation

at site, was – downloaded into the laptop computer which hast he SKI2.3

software is a Leica software and was used principally for downloading the

field data from the controllers. The SKI– PRO is a “Microsoft Windows”

based software also from “Leica Geo – systems”. It has the capability of

performing least squares adjustments, coordinate transformations, importing

and exporting data to RINEX and all common CAD and GIS systems.

The processing parameters used by the software for this reduction are;

Cut – off angle : 15 degrees

Tropospheric model : Hopfield

Ionospheric model : No model

Solution type : Standard

Ephemeris : Broadcast

Data used : Use Code and Phase

Phase Frequency : Automatic

Code Frequency : Automatic

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Limit to resolve ambiguities : 20km

A priori rms : 10mm

Sampling rate for static : Use all

Phase processing : Automatic

Cycle slip detection : Phase check and loss

lock flag

Phase measurement rms : 10mm

Update rate for kinematic (epoch) : 5

Min. time to fix ambiguity : 9 minutes

L1 only

Other things worthy of note during the reduction are;

All applicable ambiguities were resolved for all the baselines during

processing.

Residuals for all the baselines were will within tolerance and the

adjustment for the whole network was done with the SKI software that

was also used for the data processing.

Coordinate transformation was done with “Geodetic Software” to obtain

local coordinates.

4.3 MEASREMENT OF PSEUDORANGE (CODE)

Referring to section 3.1.1 of this project work and using the notations

given by JAMES BAO-YEN TSUI in his book “Fundamentals of GPS

Receivers”; the general from for the equations for finding user position from

GPS satellites is

----------------- (4.1)

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where i = 1,2,3 and 4

xi, yi, zi are satellite coordinates

xu,yu,zu are unknown user coordinates

pi are the measured ranges

bu is the user clock bias error expressed in distance

The above equation has to be linearised to effect an easy solution. This can

be achieved by differentiation of the equations, giving;

---------------- (4.2)

--------------(4.3)

In this equation; xu, yu, zu and bu can be considered as the only

unknowns. This equation can best be solved by ITERATION. This is

achieved by assuming some initial values for xu, yu, zu and bu quantities.

From these initial values a new set of xu, yu, zu and bu can be calculated.

These values are used to modify the original xu, yu, zu and bu to find another

new set of solutions. This new set of xu, yu, zu and bu can be considered again

as known quantities. The process continues until the absolute values of xu,

yu, zu and bu are very small and can be neglected. The final values of xu,

yu, zu, and bu are the desired solution.

The above equation can be written in matrix form as;

p1 11 12 13 1 xu

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p2 = 21 22 23 1 yu

p3 31 32 33 1 zu ---- (4.4)

p4 41 42 43 1 bu

where i1 = xi – xu , i2 = yi – yu , i3 = zi – zu

pi – bu pi – bu pi – bu

The solution to the matrix equation is;

xu 11 12 13 1 -1 p1

yu = 21 22 23 1 p2

zu 31 32 33 1 p3 -----(4.5)

bu 41 42 43 1 p4

4.4 CARRIER PHASE EQUATIONS

The generation of both carrier phase and pseudo range (code) double

differences is the key to determining the baseline vector between the ground

and airborne platform antennas. In so doing, satellite ephemeredes must be

properly manipulated to ensure that the carrier – phase and code

measurement made at the two receiver locations are adjusted to a common

measurement time base with respect to GPS system time. (ELLIOT, 1996).

The interferometric double – difference is formed using two single

differences. Involved in this metric are two separate satellites and two

receivers, one at either end of the baseline.

Let the phase centres of two antennae be located at k and m, and b be

the unknown baseline between them. Referring to one satellite, the lengths

86

of the propagation path between SVP (satellite visibility) and k ( ) or SVP

and in ( ), in terms of fractional and integer carrier cycles is to be

obtained. The interferometric variable, the single difference (SD), is now

created by differencing the carrier – cycle propagation path lengths (SVP to

k and m). This gives;

-------------------------------(4.6)

where P – is the satellite signal source

is the transmitted satellite signal phase as a function of time

N is the unknown integer number of carrier cycles from p to k or p to m.

S is phase noise due to all sources (e.g. multipath)

F is the carrier frequency

T is the associated satellite or receiver clock bias.

For the double difference, a second satellite q, is introduced (See fig 4). For

q, the additional SV, a second SD metric can be formed.

-------------------------------------(4.7)

87

Fig 4.3 GPS interferometer (two satellites)

The interferometric double difference (DD) is now formed suing the

two SDs. Involved in this metric are tow separate satellites and the two

receivers, one at either end of the baseline, b. the DD is gotten by

differencing the SD for each satellites;

------------------------------------------(4.8)

Where the superscripts p and q refer to the individual satellites, and k

and m are the individual antennas. It now remains to relate the DD to the

unknown baseline are which exists between the two receiver antennas.

Referring again to fig 4., it is evident that the projection of the b onto

the line of sight between p and m can be written as the scalar (dot) product

of b, with a unit vector ep , in the direction of satellite p. this projection of b

(if converted to wavelengths) is . Similarly, the dot product of b with

a unit vector eq in the direction of satellite q would relate to .

88

Incorporating this into the double difference equation will be;

= (b.epq) – 1 --------------------------------------------------- (4.9)

Of the variables in the above equation, there is only one that can be

precisely measurement by the receiver and that is the carrier phase. In

actuality, then, it is the carrier – phase measurements of the receivers that are

combined to produce the DDs. The term DDcp is adopted to represent this

and implicit in its formulation is conversion to metres. The noise term will

be dropped to simplify the expression. In the end, as the carrier – cycle

ambiguity search progresses, the noise source tend to cancel. There remains

to the determined the baseline vector (b), which has three components, (bx,

by, bz), plus an unknown integer carrier – cycle ambiguity (N) associated

with each of the DDcp terms. Toward this end, four independent DD

equations, a minimum of five satellites is necessary. The transfiguration and

extension of the equation therefore becomes;

DDcp1 e12x e12y e12z N1

DDcp2 = e13x e13y e13z bx N2

DDcp3 e14x e14y e14z by + N3 ---(4.10)

DDcp4 e15x e15y e15z bz N4

Where DDcp1, for example, is the first of four independent DDs, e12

represents the differenced unit vector between the two satellites under

consideration, b is the baseline vector, N1 is the associated integer carrier –

cycle ambiguity, and is the applicable wavelength

(ELLIOT, 1996)

89

4.5 THE GENERAL LEAST SQUARES EQUATIONS

Two basic methods exist for the adjustment of observations by the

least squares, namely;

- The ‘indirect method’ which uses observation equations, and

- The ‘direct method’, which uses condition equations.

The indirect method of variation of coordinates is the most universally

used because of the ease with which it can be applied to any type of

networks; thus, a simple program suffices for all requirements.

(SCHOFIELD, 1993).

4.5.1 METHOD OF OBSERVATION EQUATIONS

As the aim of field observation is to produce the true or most probable

value (MPV) of that measurement, it follows that provided the

measurements contain only random errors, the adjustment should bring

about minimal changes in their value. The method recommended here is

therefore to assume a value for the quantity and by least squares ascertain

the correction to that quantity that will produce the MPV. It follows that if

the value assumed is as close as possible to the MPV, then the size of the

correction will be correspondingly smaller.

(a) GENERAL EQUATIONS

The observation equation is given by,

MPV – (Observed value) = Residual ---------------------(4.11)

90

Expressing the observation equations in general terms;

a1v1 + b1v2 + c1v3 – Q1 = r1

and anv1 + bnv2 + cnv3 – Qn = rn -------------------------------( 4.12)

From least squares r2 = minimum. Thus, squaring r1 gives

r12 = a1

2v12 + 2a1b1v1v2 + 2a1c1v1v3 – 2a1Q1v1 +b1

2v2 + 2b1c1v2v3 –

2b1Q1v2 + c12v3

2 – 2c1Q1v3 + Q12 ----------------------------------(4.13)

Repeating for r2 -------- rn will only change the coefficients to a2b2c2 and

anbncn. Thus summing the results and expressing the sum of the squares the

manner; [rr], one gets.

[rr] = [aa]v12 + 2[ab]v1v2 + 2[ac]v1v3 – 2[aQ]v1 + [bb]v2

2 + 2[bc]v2v3 –

2[bQ]v2 + [cc]v32 – 2[cQ]v3 + [QQ] ------------------------------(4.14)

As [rr] = f(v1, v2, v3), differentiate and equate to zero for a minimum:

f = 2[aa]v1 + 2[ab]v2 + 2[ac]v3 – 2[aQ] = 0

v1

f = 2[ab]v1 + 2[bb]v2 + 2[bc]v3 – 2[bQ] = 0 ----------------( 4.15)

v2

f = 2[ac]v1 + 2[bc]v2 + 2[cc]v3 – 2[cQ] = 0

v3

These reduce to the general from for normal equations as follow;

[ab]v1 + [bb]v2 + [bc]v3 = [bQ]

[aa]v1 + [ab]v2 + [ac]v3 = [aQ] -------------------------------------(4.16)

[ac]v1 + [bc]v2 + [cc]v3 = [cQ]

(SCHOFIELD, 1993)

91

(b) MATRIX METHODS

A more conventional approach to the general equations is from the

application of matrices. Given the observation equations as;

a1v1 + a12v2 + - - - - - - - - - +a1nvn – q1 = r1

a2v1 + a22v2 + - - - - - - -- - + a2nvn – q2 = r2

----------------(4.17)

am1v1 + am2v2 + - - - - - -- +amnvn – qm = rm

where a = coefficient of the observation equations

v = corrections

q = absolute terms

r = the residual

in matrix form the equations become

r = AV – q --------------------------------------------------------(4.18)

A least squares solution is obtained by minimizing the quadratic form rTWr,

i.e. rTWr = O, where W is on m x m diagonal matrix of weights.

RTWr = (Av –q)T W (Av – q)

= (VTAT – qT) W (Av – q)

= VT (ATWA)v –VT(ATWq) – (qTWA)v + qTWq

(rTWr)/v = 2(ATWA) v – (ATWq) – (qTWA)T = 0

2(ATWA)v = (ATWq) + (ATWTq) = 2(ATWq)

thus, the normal equations are (ATWA)v = ATWq

and the solution for V is V = (ATWA) – 1 ATWq ----------------(4.19)

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(ATWA) – 1 is the variance – covariance (var –cor) matrix

(SCHOFIELD, 1993).

4.5.2 METHOD OF CONDITION EQUATIONS

In this method, equations are formed, based on the conditions of

adjustment to be satisfied. In order to reduce the number of normal

equations, an undetermined multiplier called a correlative or Lagrangian

multiplier multiplies each condition equation. The resultant condition

equations are then combined in the least squares condition and, after

differentiation, expressed as a linear function of the correlative. Thereafter,

back – substituting into the condition equations produces a set of correlative

normal equations equal in number to the number of conditions. The

equations are solved to find the values of the correlatives, which can then be

expressed in terms of the correlations.

(SCHOFIELD, 1993).

(a) GENERAL FORM (CORRELATIVES)

Writing the condition equation in a general form:

a1v1 + a2v2 - - - - - - - + anvn + q1 = 0

b1v1 + b2v2 - - - - - - - + bnvn + q2 = 0 ---------------------------(4.20)

c1v1 + c2v2 - - - - - - - + cnvn + q3 = 0

Each equation is then multiplied by an unknown correlative and may be

written;

k1(a1v1 + a2v2 + - - - - - - - anvn + q1) + k2 (b1vn + b2v2 + - - - bnvn + qn +

k3(c1v1 + c2v2 + - - - - - + cnvn + q3 = 0

93

From the least squares principle, [vv] = a minimum. For simplification of

analysis, the total function may be written as;

F = v12 + v2

2 - - - - - +vn2 – 2k1(a1v1 + a2v2 + - - - - +anvn + q – 2k2(b1v1 + b2v2

+ - - - - - - +bnvn + q2) – 2k3(c1v1 + c2v2 + - - - - - cnvn + q3) = a minimum

Differentiating each variable in turn and equating to zero:

F = 2v1 – 2k1a1 – 2k2b1 – 2k3c1 = 0

v1

F = 2v2 – 2k1a2 – 2k2b2 – 2k3c2 = 0 -----------------------(4.21)

v2

F = 2vn – 2k1an - 2k2bn – 2k3cn =

vn

The above equations reduced to

V1 = k1a1 + kab1 + k3c1

V2 = k1a2 + k2b2 + k3c2 --------- ----------------(4.22)

V3 = K1an +k2bn + k3cn

Substituting these values into the original equations and substituting K for

k simply to emphasize the format, gives the general form for correlative

normal equations:

K1[aa] + k2[ab] + k3[ac] + q1 = 0

K1[ab] + k2[bb] + k3[bc] + q2 = 0 ------------------------------(4.23)

K1[ac] + k2[bc] + k3[cc] + q3 = 0

(b) MATRIX METHODS (DIRECT)

Rewriting the condition equations in more conventional terms gives;

94

a11v1 + a12v2 + - - - - - - - + a1nvn = q1

a21v1 + a22v2 + - --- - - - - + a2nvn = q2 ----------------------------(4.24)

am1v1 + am2v2 + - -- -- --+ amnvn = qm

or in matrix terms;

Av = q.

Introducing the weight matrix W and the vector of correlatives k,

minimizing the quadratic form vTWv gives;

V = W –1 ATk

Which on substituting in the matrix equation produces the normal equations:

(AW – 1 AT)k =q

the normal equations are solved for k, which is back – substituted to give v.

alternatively, both steps may be combined using

v = W – 1 AT (AW – 1 AT) –1q ----------------------------------------(4.25)

4.6 VARIATION OF COORDINATES

The variation of co-ordinates’ method of adjustment, which is

basically a least squares method using observation equations, is virtually the

standard method of network adjustment. (SCHOFIELD, 1993)

The method is an iterative process, which computes the necessary

coordinate corrections (E, N) to be applied to a set of provisional

coordinates in order to render the network geometrically correct.

4.6.1 OBSERVATION EQUATIONS

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The method requires the formation of an observation equation for

each and every mean observation comprising the network.

Consider the length ij in the network with an observed value of Oij.

From the provisional coordinates of i and j, computed value of Cij may be

obtained.

As the provisional coordinates of i and j will be adjusted by amounts

E and N, so the computed distance will change by an amount Lij.

The final adjusted distance should equal the most probable, i.e. the

observed distance plus its residual correction (v). Thus

Cij + Lij = Oij + Vij

And lij = (Oij – Cij) + vij

Now as lij = (Ej – Ei)2 + (Nj – Ni)2

lij = (Ej –Ei)( Ej - Ei) + (Nj – Ni)( Nj - Ni) ----------------(4.26)

Lij lij

But as (Ej – Ei) = Sinij and (Nj – Ni) = Cosy

lij lij

where ij is the bearing of line ij; then,

- EiSinij - NiCosij + EjSinij +NjCosij – (O – c)ij = Vij ------(4.27)

which is the observation equation for length ij.

The observation equations can be expressed in matrix form as;

V = Ax – b

A is an m x m matrix, is a column vector of n terms, v and b are column

vectors of m terms.

m = number of observed lengths

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n = twice the number of points to be adjusted

As already shown in the matrix methods under the indirect methods;

4.6.2 PROCEDURE

For application of the variation of coordinates method to network

adjustment, first obtain Provisional coordinates for each model point of the

network. Using the Provisional coordinates compute the lengths (or other

parameters) of the observed data. These are the C values which, with their

appropriate observed (O) values, produce the b vector of m (O – C) terms.

Formulate observation equations for each and every observation. Estimate a

priori weights for the observations using the inverse of the variances and

form a diagonal weight matrix W of size m x m.

Solve the above matrices to obtain the x vector of coordinate

corrections (E, N). The corrections are applied to the Provisional

coordinates now replace the Provisional coordinates and the whole process

repeated (only the weights remain fixed), until the x vector of coordinate

corrections is sensibly zero. (SCHOFIELD, 1993)

4.7 ADJUSTMENT OF GPS OBSERVATION

Since redundancy exists in measurement networks, a method is

needed to correct the measurements to make them fit the conditions as well

as possible. The amount by which each measurement must be corrected is

called the measurement residual. The least squares adjustment method will

make the observations fit into the model by minimizing the sum of squares

97

of the observation residuals. The final measurement residuals are called the

least squares correction.

Least squares adjustment models consist of two important

components: the mathematical model and the stochastic model. The

mathematical model is a set of relations between the measurements and the

unknown coordinates. The stochastic model describes the expected error

distribution of the measurements.

(Manual of SKI– PRO Software, 2005).

4.7.1 MATHEMATICAL MODEL

Measurements are normally processed in computations to define

coordinates for survey points. Through computations, coordinates are

expressed as a function of the observations. Each computation, therefore,

defines a mathematical model. In this case, of the least squares adjustment,

the mathematical model forms a basic for the least squares adjustment.

At least squares adjustment requires the location, orientation, and

scale of the measurement network to be defined. It requires linear equations;

therefore, the model must be linearised. Usually this means that a number of

iterations is needed to reach a solution. Moreover, approximate values of the

coordinate unknowns in the adjustment are required. But approximate values

can lead to an increasing number of iterations or, in the worst case, to no

convergence at all.

98

4.7.2 STOCHASTIC MODEL

A geodetic observable, such as a direction, distance or elevation

difference, is a random or stochastic variable. A stochastic variable cannot

be described by a single and exact value because there is an amount of

uncertainty involved in the observation process. The variation in

measurements of a single quantity is modeled by assuming a normal

probability distribution. This distribution is based on the mean (U) and the

standard deviation (r) of a measured quantity. See fig 5 below.

Fig 4.4 Normal distribution curves.

The mean (U) is a mathematical representation for the best expected

value of the measured quantity. The standard deviation (r) is a measure of

the dispersion or spread of the probability, and characterizes the precision of

the measurement. The square of is called the variance.

By definition there is a 0.684 probability that normally distributed

stochastic variables will fall within a window limited by - and +. For a

window limited by – 2 and + 2, this probability is 0.954. In general, the

Probability that a stochastic variable takes a value between X1 and X2 is

99

equal to the area enclosed by the curve, and the X1 and X2 coordinates, as

shown shaded in the figure.

It is possible for two or more measurements to be correlated. This

means that a deviation in one measurement will influence the other. This

correlation between coordinates x, y and z is mathematically expressed in a

3 x 3 matrix, called a VARIANCE –COVARIANCE MATRIX.

In the data model for the survey datasets, the variance – covariance

matrix is used to express the Probability distribution for survey point

coordinates and Provide a quantitative estimate of survey point quality.

Since this matrix is symmetrical, the values of the variance – covariance

matrix can be for the survey points and coordinates.

For each measurement, a standard deviation is chosen. The value

is based on knowledge about the measurement process and experience. The

precision of the coordinates computed in the adjustment depends on the

precision of the observations and on the propagation of this precision

through the mathematical model.

(Manual on SKI- PRO Software, 2005)

x2 xy xz

Q = yx y2 yz

zx zy z2

And because of symmetry;

100

Q = x2 xy xz

y2 yz

z2

Typical Variance – Covariance Matrix

4.7.3 FORMULAE

The linearised mathematical model is expressed as follow;

y = Ax + e + a ----------------------------(4.28)

Where y = (m) vector of observations;

e = (m) vector of corrections;

A = (m x n) design matrix;

X = (n) vector of unknowns;

a = (m) vector of constants

The stochastic model is: 1

Qr = 2Q= 1 P –1

2 -------------------------------------(4.29)

Where Qr = (m x m) variance – covariance matrix;

2 = a – priori variance – of unit – weight;

Q = (m x m) weight coefficient matrix;

P = (m x m) weight matrix

The least squares criterion is:

et P e = minimum -------------------------------(4.30)

4.8 PRECISION, ACCURACY AND ERROR ANALYSIS

101

W. SCHOFIELD in his book “Engineering Surveying” highlighted

the following important facts;

– Scatter is an ‘indicator of precision’. The wider the scatter of a set of

results about the linear, the less reliable they will be compared with

results having a small scatter.

– Precision must not be confused with accuracy; the former is a relative

grouping without regard to nearness to the truth, while the later

denotes absolute nearness to the truth.

– Precision may be regarded as an index of accuracy only when all

sources of error, other than random errors, have been eliminated.

– Accuracy may be defined only be specifying the bounds between

which the accidental error of a measured quantity may lie. The reason

for defining accuracy thus is that the absolute error of the quantity to

is generally not known. If it were, it could simply be applied to the

measured quantity to give its true value. The error bound is usually

specified as symmetrical about zero. Thus the accuracy of measured

quantity x is x ex where ex is greater than or equal to the true but

unknown error of x.

– The true value of an observation can never be found, even though

such a value exists. True error similarly can never be found, for it

consists of the true value minus the observed value. Relative error is a

measure of the error inn relation to the size of the measurement. Most

probable value (MPV) is the closest approximation to the true value

that can be achieved from a set of data. Residual is the closest

102

approximation to the true error and is the difference between the MPV

of a set and the observed values.

The standard deviation () which is a numerical value

indicating the amount of variation about a central value, is the most

popular index to assess the precision of a set of observations. It

establishes the limits of the error bound within which 68.3% of the

values of the should lie, i.e. seven out of a sample of ten. Thus,

-------------------------------------------(4.31)

Similarly, a measure of the precision of the mean ( ) of a set is obtained using the

standard error (x), thus

---------------------------------------(4.32)

n is number of observations, xi is observation.

Standard error therefore indicates the limits of the error bound within which

the ‘true’ value of the mean lies, with a 68.3% certainty of being correct.

It should be noted that and x are entirely different parameters. The value

of will not alter significantly with an increase in the number of

observations, the value x , however, will alter significantly as the number of

observation increase. It is important therefore that to describe measured data

both values should be used.

103

Weights indicate the relative precision of quantities within a set. The

greater the weight, the greater the precision of the observation to which it

relates. For weighted data;

--------------------------------------------------(4.33)

Standard error (the weighted mean) =

------------------------------------(4.34)

4.9 COMPUTATION OF STANDARD ERRORS

As reduced by the SKI– PRO software, the computation of the

standard errors; for each of the x, y, z components; for baselines is

illustrated with theses two examples.

Baseline 1

Notation: CFG113B – DEFM11Si

A – Posteriori rms (o) = 0.4513

Var – Cov Matrix (Q) =

Q = +2.7084080 x 10 – 6 +1.0312500 x 10 – 7 +1.4511000 x 10 - 7

+3.6107300 x 10 –7 - 5.0238000 x 10 –8

+1.9381700 x 10 – 7

x = o = 0.4513 = 0.0007m

104

x = o = 0.4513 = 0.0003m

z = o = 0.4513 = 0.0002m

Baseline 2

Notation: CFG113B – DEFM7Si

A – posteriori rms(o) = 0.7274

Var – Cov Matrix:

Q = +6.9898100 x 10 – 7 +9.356400 x 10 – 8 +7.419600 x 10 – 8

+2.177100 x 10 – 7 - 2.497400 x 10 – 8

+1.1829300 x 10– 7

x = o = 0.7274 = 0.0006m

y = o = 0.7274 = 0.0003m

z = o = 0.7274 = 0.0003m

4.10 RESULTS

The final coordinates in WGS84 as given by SURVICOM

SERVICES NIG. LTD are as follows;

Table 4.1 Coordinates of control points in WGS 84

Point ID Baseline X(m) Y(m) Z(m)

10SI

11SI

7SI

6SI

BL5

BL1

BL2

BL6

6308271.9526

6308282.2834

6308274.3779

6208260.6580

623325.2907

623267.4114

623263.9339

623312.6525

703728.3917

703727.3408

703799.0790

703836.9325

105

1SI

RF01

4SI

8SI

9SI

BMB 1

5SI

3SI

5SI

3SI

RF10

RF09

RF08

RF04

RF02

RF07

BL3

BL7

BL4

BL8

BL15

BL9

BL16

BL10

BL17

BL11

BL18

BL12

BL19

BL13

BL20

BL14

6308275.0107

6308259.6561

6308155.3838

6308186.6260

6308190.1463

6308176.3641

6308155.0086

6308176.3718

6308154.5475

6308195.2137

6308206.7852

6308206.7852

6308218.2502

6308230.8544

6308254.0329

6308224.3550

623128.4931

623328.7345

623920.1053

624021.6763

623962.9226

623943.4109

623990.1893

623906.4774

623990.1947

623906.4641

623807.6077

623799.8040

623701.9410

623597.8111

623402.3549

623626.9156

703968.1621

703822.2221

704239.4684

703936.1223

703891.7303

703932.3815

704030.6330

704298.0938

704030.6338

704298.0229

703924.1244

703906.8687

703889.7113

703870.9568

703835.7902

703903.5099

4.11 ANALYSIS OF RESULTS

Using baselines 1 and 2 as study example, the one – dimensional

standard errors were obtained as follows;

Baseline 1:

x = 0.0007m = 0.7mm y = 0.0003m = 0.3mm

z = 0.0002m = 0.2mm

Therefore position quality = =

106

= 0.8mm

3 – D accuracy = =

= 0.8mm

Baseline 2 is also computed as above. This analysis of the standard errors

reveal that these results satisfies the first order specification which is the

quality of control network required for monitoring of dams.

4.12 TRANSFORMATION OF COORDINATES

The finished coordinates of the monitoring points were given by the

SKI– PRO software to the WGS – 84 geodetic datum. These coordinates

were then transformed using the INCAR geometry software to the Nigeian

Transverse Mercator in Minna.

GEODETIC PARAMETERS

WGS – 84 GEODETIC PARAMETERS USED

Datum – World Geodetic System 1984

Spheroid – World Geodetic System 1984

Semi – Major Axis – a = 6 378 137.000m

Semi – Minor Axis – b = 6 356 752 . 314m

First Eccentricity Squared – e2 = 0.006 694 379

Inverse of Flattening – 1 = 298. 257 233 6

f

NIGERIAN LOCAL DATUM GEODETIC COORDINATES

107

Datum – Minna

Spheroid – Clark 1880 (Modified)

Semi – Major Axis – a = 6 378 249.145m

Semi – Minor Axis – b = 6 356 514 . 870m

First Eccentricity Squared – e2 = 0.006 803 511 283

Inverse of Flattening – 1 = 293. 465 000 0

f

Projection – Transverse Mercator (TM)

Operation Zone – West Belt

Central Meridian – 8o 30’ 00” East

Latitude of Origin – 4o 00’ 00” North

Falser Easting – 6705553.983m

Falser Northing – 0.000m

Scale Factor – 0.999 75

DATUM TRANSFORMATION PARAMETERS

SHIFT TRANSFORMATION PARAMETERS

dX = +111. 916m

dY = +87. 852m

dZ = – 114 . 499m

ROTATION PARAMETERS

Rx = – 1. 875 27 sec

Ry = – 0. 202 14 sec

Rz = – 0.219 35 sec

108

SCALE FACTOR = – 0. 032 45

(GPS Report by SURVICOM SERVICES NIG. LTD, 2007)

The transformed coordinates to the Minna datum is given as;

Table 4.2 Transformed coordinates

Station Northing (m) Easting (m)CFG113B1SI2SI3SI4SI5SI6SI7SI8SI9SI10SI11SIRF1RF2RF4RF6RF7RF8

263 376. 370263 113. 179263 077. 561263 447. 512263 389. 128263 178. 697262 982. 763262 944. 052263 083. 361263 038. 966262 873. 542262 871. 856263 038. 923262 981. 549263 017. 357263 337. 668263 056. 172263 036. 481

355 504. 658357 055. 430357 881. 067357 851. 686357 865. 533357 933. 487357 251. 380357 201. 640357 964. 019357 904. 950357 263. 090357 204. 481357 904. 917357 341. 295357 537. 973357 840. 733357 567. 522357 642. 810

109

CHAPTER FIVE

5.0 CONCLUSION AND RECOMMENDATIONS

5.1 CONCLUSION

The purpose of this project was to carry out adjustment and

error analysis of an Engineering control network for the purpose of

deformation monitoring.

The Global Positioning System was used in obtaining the

coordinates of the control points. It is a satellite-based navigation

system made up of a network of 24 satellites orbiting the earth in

outer space. These satellites transmit signal information and use

triangulation to obtain the user’s position.

A total of 11 control points and 9 monitoring points were

observed by the differential GPS technique. The necessary adjustment

of the observations was carried out using the method of least squares

within the SKI-PRO processing software.

The results obtained from computation of the standard errors of

mean shows that the Global Positioning System and the associating

computer soft wares are a priceless tool for monitoring of deformation

in dams and other structures.

5.2 RECOMMENDATIONS

It is recommended that the Global Positioning System should

be top on consideration of methods for monitoring of structures. It is

therefore pertinent to call on the Government, Alumni bodies and

other relevant authorities to assist the University in purchasing GPS

110

receivers and other modern equipment for the department of civil

engineering. This will no doubt empower the students and young

graduates of this discipline. This will further make them bold, vast

and in tune with the global trend of the profession of Civil

Engineering.

It is also strongly recommended that the Government, owners

and operators of large engineering structures like dams, bridges, high-

rise buildings e.t.c; should carry out monitoring operations

intermittently to ensure stability and rectification of faults when they

occur to avoid an ensuing catastrophe.

It is especially important here in Nigeria and other developing

countries to imbibe a culture of ascertaining the structural health of

dams, bridges, telecom mast e.t.c; even as they aspire to be among the

developed nations.

111

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