DISSERTATION
Transcript of DISSERTATION
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)
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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)
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(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.
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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
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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.
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