DISSERTATION

ADJUSTMENT AND ERROR ANALYSIS FOR CONTROL NETWORK FOR DAM DEFORMATION MONITORING BY GPS BY OKELIGHO MIKE IRUOGHENE DEPARTMENT OF CIVIL ENGINEERING UNIVERSITY OF BENIN NIGERIA DECEMBER, 2007 1 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, ³dams´ 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 2 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 3 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 4 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 5 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. 6 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. 7 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. 8 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 ³Sadd el ± kafara´, which in Arabic means ³Dam 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. 9 In the Mongol period, about 1280 AD, a new type of dam known as arch dam was built and it was called ³Kebar´. 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 10 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 11 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 µsaddle¶ through which the reservoir would otherwise escape. 12 ± 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. 13 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 ³rock 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 ³solid´ or ³hollow´. 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 14 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 ³flying 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. 15 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 ³crib´ and the ³plank´ 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 16 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) 17 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 AGBA DAM AJIWA DAM TYPE Embankment Embankment dam LOCATION Kwara State Kaduna State USE 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 ASA DAM ASEJIRO DAM AUKWIL DAM AWON DAM BAGAUDA DAM BOSO DAM Concrete Embankment Embankment Embankment Embankment dam Embankment Kwara State Oyo State Plateau State Oyo State Kano State Kaduna State CHALLAVA DAM DOMA DAM Embankment dam Embankment Bauchi State Plateau State DUDURUN WARWADA DAM DWATAIN MA DAM Embankment dam Kano State Embankment dam Kaduna State 18 NAME EDE DAM TYPE Embankment LOCATION Oyo State USE Irrigation / Water Supply Irrigation / Water Supply EJIGBO DAM Embankment Oyo State Irrigation / Water Supply EKORUDE DAM Embankment Oyo State Irrigation / Water Supply Irrigation / Water Supply ELEIYELD DAM Embankment Oyo State Irrigation ESA ODO DAM Embankment Oyo State Irrigation / Fishery Irrigation GAKATARI DAM GARI DAM GORONYO DAM GRANYI HOUSE DAM GUBI DAM GUSAU DAM Embankment Embankment Embankment Embankment dam Sokoto State Water Supply Kano State Sokoto State Plateau State Water Supply Irrigation / Water Supply Irrigation / Recreation and Fishery Water Supply Embankment Embankment Bauchi State Zamfara State GUZY GUZY DAM Embankment dam Kano State Irrigation / Recreation and Fishery Water Supply HEGWAI DAM Embankment Niger State 19 NAME IBRAHIM IDAHU DAM IKERE GORDA DAM IKPOBA DAM IWO DAM JEBBA DAM KARARA DAM TYPE Embankment dam LOCATION Kano State USE Irrigation Supply and Water Embankment dam Sokoto State Water Supply Embankment Embankment Embankment Embankment Edo State Oyo State Niger State Kano State Water Supply Water Supply Power Generation Water Supply, Fishery and Irrigation Power Generation KAINJI DAM Embankment dam Niger State KAFIN ZAKI DAM KANGIMI DAM KARAYA DAM KARHI CHRIR DAM KIRI DAM KOGIN GIRI DAM KURBAN DAM Embankment dam Embankment Embankment Embankment dam Bauchi State Kaduna State Kano State Kano State Irrigation /Water Supply Irrigation /Water Supply Fishery and Water Supply Water Supply Embankment Embankment dam Embankment Adamawa State Plateau State Kaduna State Water Supply Water Supply 20 NAME LAMINGA DAM LANG TANG DAM LIBERTY DAM TYPE Embankment Rockfill LOCATION Plateau State Plateau State USE Water Supply Water Supply Water Supply Embankment and Plateau State Rock dam Embankment dam Abuja LOWER USUEEN DAM MADA DAM MAGADA DAM MAIRUWA DAM MARECHI DAM Water Supply Embankment Embankment Embankment Embankment Plateau State Kano State Kaduna State Kano State Kano State 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 MOH AYUBA DAM Embankment dam OBA DAM OFOO DAM OJIRAMI DAM OKENE DAM OMAE DAM OPEKI ERUWA DAM Embankment Embankment Embankment Concrete Embankment Embankment dam Oyo State Niger State Edo State Kogi State Kano State Oyo State 21 NAME ORISA DAM OSHUN DAM OTIN DAM OYAN DAM TYPE Concrete Embankment Embankment Concrete and embankment dam Concrete Rock and embankment dam Embankment Embankment Embankment dam LOCATION Kwara State Osun State Oyo State Ogun State USE Water Supply Water Supply Water Supply Power generation, Water Supply and Fishery Water Supply Water Supply OYUN DAM PANKOHIN DAM Kwara State Plateau State PEDA DAM RAWALI DAM RUWAN KENTA DAM SAGOMA DAM Kano State Bauchi State Kano State Irrigation / Fishery Water Supply Imagination / Fishery Embankment Kaduna State Imagination / Water Supply Water Supply Power generation Water Supply Water Supply Irrigation / Water Supply SHEN DAM SHIRORO DAM SOBI DAM TENTI DAM TIGA DAM Embankment Embankment Embankment Embankment Embankment Plateau State Niger State Kwara State Plateau State Kano State 22 NAME TUDUN WADA DAM UNGANKANO DAM WATARI DAM ZARIA DAM ZOBE DAM ZURU DAM TYPE Embankment dam LOCATION Kano State USE Irrigation, Water Supply, Fishery and Recreation. Water Supply Embankment dam Niger State Embankment Embankment Embankment Embankment Kano State Kaduna State Kaduna State Sokoto State 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. ³Tailing 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 23 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 ³Johnstown 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 ³seismic 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 ³sinkhole´ 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. ³Landslides´ 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. ³Mudflows´ (or debris flows) are rivers of rock, earth, and other debris saturated with water. An ³avalanche´ 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. ii. Elastic compression of the foundation and the underlying soil. 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. (3rd 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 xt 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. 7[weight x (residual)2] is to be a minimum. For n observations; w1r12 + w2r22 + w3r32 + - - - - - - -- - + wnrn2 is to be a minimum. Thus ---------------- (2.2) [r1 r2 r3 - - - - - - - rn] w1 0 0 0 ---------0 r1 r2 ----(2.3) w2 0 - - - - - -- - - 0 0 0 0 - - - - - - - - wn rn or rT Wr is to be a minimum 43 where µresidual¶ it the difference between the value (x) of one the measurements and the most Probable value reliability, or precision; the arithmetic mean ( x ) 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, ³ 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, ³Monitoring 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 ³Observation 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 ³ 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 ³Galileo´ instead of the abbreviation µGPS¶ 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: R= x2 y2 z2 --------------------------------(3.1) If the error in R, due to clock bias (delay time) is HR and is a constant throughout, then R HR is; 57 R1 + R= R2 + R= R3 + R= R4 + R= [(X1 - Xp) + (Y1 - YP) +(Z1 - ZP) ] [(X2 - Xp) + (Y2 - YP) +(Z2 - ZP) ] [(X3 - Xp) + (Y3 - YP) +(Z3 - ZP) ] [(X4 - Xp) + (Y4 - YP) +(Z4 - ZP) ] 2 2 2 2 2 2 2 2 2 2 2 2 ---------------(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 Har Antenna are A hain ser position atellite positions p emeris pse ora ge ub rame Identity oft are Tracking Acquisition Fig 3.1 Af ame tal GP receiver. A ter the signal is digitized, so tware is used to process it. Acquisition means to ind the signal o a certain satellite. The tracking program is used to ind the phase transition o the navigation data. In the conventional reviver, the acquisition and tracking are per ormed by hardware. rom the navigation data phase transition, the sub rames and navigation data can be obtained. Ephemeris data and pseudoranges can be obtained rom the navigation data. The ephemeris data are used to obtain the satellite positions. inally, the user position can be calculated or the satellite positions and the pseudoranges. (T I, 2005) 3.5 GP T RMINOLOGY (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 ³by 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 deformation REQUIREMENTS: measurement A successful must meet GPS the ± based system 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 µtruth¶. 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 y Aim for a balanced distribution of known stations over the network. y Try to include loops in the network, keeping in mind that the lesser the number of stations in a loop, the better the reliability. y 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: y Absolute and relative standard ellipses. y A ± posteriori standard deviations of observations. y A ± posteriori standard deviations of stations. y Minimal Detectable Bias (MDB) of observations. y Minimal Detectable Bias (MDB) of known stations. y Bias to Noise Ration (BNR) of observations y 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. 73 Start Initial design of network formulation of m ill hypothesis Quality control for design PRECISIO N: (relative) standard ellipses and criterion circles a posteriori standard deviations RELIABILITY: Internal : M DB External : BNR Criteria Y End N Im provements 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: y Free network adjustment y Constrained adjustment 74 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 µperfect¶ 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; y The least squares adjustment will produce the best possible result; y The statistical testing checks the result in order to make it µerror ± free¶; y The precision and reliability parameters quantify the quality of the result. 76 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 y Using dual frequency GPS receivers. Coordination of the chosen points form first order control pillars in static differential mode. y A minimum of four satellites is to be observed concurrently during data logging. y GDOP value during observation at the end of each session should not exceed 5. y All computation options available during the processing of baseline observations are to be applied consistently throughout data reduction Procession. y Detail of all the processing procedure must be in line with technical specification on baseline processing, least square adjustment and datum transformation. y 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 y 4 Leica GPS 300 series with accessories y 4 Tripods y 2 Sheated machetes y 2 Operational vehicles. Data acquisition in the field was done with three units of ³Leica 300´ GPS Systems and their corresponding accessories. The ³Leica 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 ³Wild Tripods´ were used for mounting the GPS receivers. Also, a Laptop Computer equipped with ³SKI 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. y The rovering points observed were named and identified as requirement. 81 y Duration of satellite observations was 1 hour. y GDOP for the points, except the point 2si, all through observations were below 5.0. y 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: 15o Auto select 4 seconds. Automatic GMT + 1 15 seconds Minimum Elevation Mask Minimum no. of SVs Measurement Sync Time Satellite Heath Time Zone Sampling Rate ± - 82 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 ³Microsoft Windows´ based software also from ³Leica 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; y Cut ± off angle y Tropospheric model y Ionospheric model y Solution type y Ephemeris y Data used y Phase Frequency y Code Frequency : : : : : : : : 15 degrees Hopfield No model Standard Broadcast Use Code and Phase Automatic Automatic 83 y Limit to resolve ambiguities y A priori rms y Sampling rate for static y Phase processing y Cycle slip detection : : : : : 20km 10mm Use all Automatic Phase check and loss lock flag y Phase measurement rms : 10mm 5 9 minutes y Update rate for kinematic (epoch) : y Min. time to fix ambiguity L1 only : Other things worthy of note during the reduction are; y All applicable ambiguities were resolved for all the baselines during processing. y 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. y Coordinate transformation was done with ³Geodetic 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 ³Fundamentals of GPS Receivers´; the general from for the equations for finding user position from GPS satellites is 84 i where i (xi - xu)2 1,2,3 and 4 (yi - yu) (zi - zu) bu ----------------- (4.1) 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; pi (xi - xu) xu (xi - xu) 2 (yi - yu ) yu (zi - zu ) 2 u bu ---------------- (4.2) (yi - yu ) (zi - zu ) 2 pi (xi - xu) xu ((yi - yu) yu (zi - zu ) zu pi - bu bu --------------(4.3) In this equation; Hxu, Hyu, Hzu and Hbu 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 Hxu, Hyu, Hzu and Hbu 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 Hxu, Hyu, Hzu and Hbu 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; 85 Hp1 H p2 H p3 H p4 where Ei1 = xi ± xu , pi ± bu = E11 E12 E21 E22 E31 E32 E41 E42 Ei2 = yi ± yu , pi ± bu E13 E23 E33 E43 1 1 1 1 H xu H yu H zu H bu ---- (4.4) Ei3 = zi ± zu pi ± bu The solution to the matrix equation is; -1 H xu H yu H zu H bu 4.4 = E11 E12 E21 E22 E31 E32 E41 E42 E13 E23 E33 E43 1 1 1 1 H p1 H p2 H p3 H p4 -----(4.5) 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. 86 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 of the propagation path between SVP (satellite visibility) and k ( and in ( p m p k) or SVP ), 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; SD Km = p p Km + N Km +S p + FTKm -------------------------------(4.6) Km p where P ± is the satellite signal source p m 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. SDKm = K m + NKm +S Km + FTKm -------------------------------------(4.7) 87 vq eq vp Km e p m b k Km 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; DDkm = ppq ppq km ppq + Nkm + S km ------------------------------------------(4.8) ppq 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 S D Km . Similarly, the dot product of b with a unit vector eq in the direction of satellite q would relate to S D Km . 88 Incorporating this into the double difference equation will be; DDkm = (b.epq) P ± 1 ppq --------------------------------------------------- (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 DDcp2 DDcp3 DDcp4 = e12x e13x e14x e15x e12y e13y e14y e15y e12z e13z e14z e15z bx by bz + N1 N2 N3 P ---(4.10) 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 P is the applicable wavelength (ELLIOT, 1996) 89 4.5 THE GENERAL LEAST SQUARES EQUATIONS Two basic methods exist for the adjustment of observations by the least squares, namely; The µindirect method¶ which uses observation equations, and The µdirect 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) r12 = a12v12 + 2a1b1v1v2 + 2a1c1v1v3 ± 2a1Q1v1 +b12v2 + 2b1c1v2v3 ± 2b1Q1v2 + c12v32 ± 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]v22 + 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: xf xv1 xf xv2 xf xv3 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] [ac]v1 + [bc]v2 + [cc]v3 = [cQ] (SCHOFIELD, 1993) -------------------------------------(4.16) = 2[ac]v1 + 2[bc]v2 + 2[cc]v3 ± 2[cQ] = 0 = 2[ab]v1 + 2[bb]v2 + 2[bc]v3 ± 2[bQ] = 0 ----------------( 4.15) = 2[aa]v1 + 2[ab]v2 + 2[ac]v3 ± 2[aQ] = 0 From least squares 7r2 = minimum. Thus, squaring r1 gives 91 (b) MATRIX METHODS A more conventional approach to the general equations is from the application of matrices. Given the observation equations as; a1v1 + a12v2 + - - - - - - - - - +a1nvn ± q1 = r1 a2v1 + a22v2 + - - - - - - -- - + a2nvn ± q2 = r2 ----------------(4.17) am1v1 + am2v2 + - - - - - -- +amnvn ± qm = rm where a = coefficient of the observation equations v = corrections q = absolute terms r = the residual in matrix form the equations become r = AV ± q --------------------------------------------------------(4.18) A least squares solution is obtained by minimizing the quadratic form rTWr, i.e. rTWr = O, where W is on m x m diagonal matrix of weights. RTWr = (Av ±q)T W (Av ± q) = (VTAT ± qT) W (Av ± q) = VT (ATWA)v ±VT(ATWq) ± (qTWA)v + qTWq x(rTWr)/xv = 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) 92 (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 c1v1 + c2v2 - - - - - - - + cnvn + q3 = 0 ---------------------------(4.20) Each equation is then multiplied by an unknown correlative and may be written; 93 k1(a1v1 + a2v2 + - - - - - - - anvn + q1) + k2 (b1vn + b2v2 + - - - bnvn + qn + k3(c1v1 + c2v2 + - - - - - + cnvn + q3 = 0 From the least squares principle, [vv] = a minimum. For simplification of analysis, the total function may be written as; F = v12 + v22 - - - - - +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: xF xv1 xF xv2 = 2v2 ± 2k1a2 ± 2k2b2 ± 2k3c2 = 0 -----------------------(4.21) = 2v1 ± 2k1a1 ± 2k2b1 ± 2k3c1 = 0 xF xvn = 2vn ± 2k1an - 2k2bn ± 2k3cn = The above equations reduced to V1 = k1a1 + kab1 + k3c1 V2 = k1a2 + k2b2 + k3c2 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 K1[ac] + k2[bc] + k3[cc] + q3 = 0 ------------------------------(4.23) --------- ----------------(4.22) 94 (b) MATRIX METHODS (DIRECT) Rewriting the condition equations in more conventional terms gives; a11v1 + a12v2 + - - - - - - - + a1nvn = q1 a21v1 + a22v2 + - --- - - - - + a2nvn = q2 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) ----------------------------(4.24) 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 (HE, HN) to be applied to a set of provisional coordinates in order to render the network geometrically correct. 95 4.6.1 OBSERVATION EQUATIONS 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 HE and HN, so the computed distance will change by an amount HLij. The final adjusted distance should equal the most probable, i.e. the observed distance plus its residual correction (v). Thus Cij + HLij = Oij + Vij And Hlij = (Oij ± Cij) + vij Now as lij = (Ej ± Ei)2 + (Nj ± Ni)2 Hlij = (Ej ±Ei)( HEj - HEi) + (Nj ± Ni)( HNj - HNi) ----------------(4.26) Lij lij But as (Ej ± Ei) = SinEij and (Nj ± Ni) = CosEy lij lij where Eij is the bearing of line ij; then, - HEiSinEij - HNiCosEij + HEjSinEij +HNjCosij ± (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. 96 m = number of observed lengths 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 (HE, HN). The corrections are applied to the Provisional coordinates now replace the Provisional coordinates and the whole process repeated (only the weights remain fixed), until the x vector of coordinate corrections is sensibly zero. (SCHOFIELD, 1993) 4.7 ADJUSTMENT OF GPS OBSERVATION Since redundancy exists in measurement networks, a method is needed to correct the measurements to make them fit the conditions as well as possible. The amount by which each measurement must be corrected is called the measurement residual. The least squares adjustment method will make the observations fit into the model by minimizing the sum of squares 97 of the observation residuals. The final measurement residuals are called the least squares correction. Least squares adjustment models consist of two important components: the mathematical model and the stochastic model. The mathematical model is a set of relations between the measurements and the unknown coordinates. The stochastic model describes the expected error distribution of the measurements. (Manual of SKI± PRO Software, 2005). 4.7.1 MATHEMATICAL MODEL Measurements are normally processed in computations to define coordinates for survey points. Through computations, coordinates are expressed as a function of the observations. Each computation, therefore, defines a mathematical model. In this case, of the least squares adjustment, the mathematical model forms a basic for the least squares adjustment. At least squares adjustment requires the location, orientation, and scale of the measurement network to be defined. It requires linear equations; therefore, the model must be linearised. Usually this means that a number of iterations is needed to reach a solution. Moreover, approximate values of the coordinate unknowns in the adjustment are required. But approximate values can lead to an increasing number of iterations or, in the worst case, to no convergence at all. 98 4.7.2 STOCHASTIC MODEL A geodetic observable, such as a direction, distance or elevation difference, is a random or stochastic variable. A stochastic variable cannot be described by a single and exact value because there is an amount of uncertainty involved in the observation process. The variation in measurements of a single quantity is modeled by assuming a normal probability distribution. This distribution is based on the mean (U) and the standard deviation (r) of a measured quantity. See fig 5 below. Location parameter of curve -r +r standard deviation - 2r +2r x2 x1 mean (U) 68.4% 95.4% 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 W is called the variance. By definition there is a 0.684 probability that normally distributed stochastic variables will fall within a window limited by - W and +W. For a window limited by ± 2W and + 2W, this probability is 0.954. In general, the 99 Probability that a stochastic variable takes a value between X1 and X2 is 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 W is chosen. The value W 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) W x2 Q = Wyx Wzx Wxy Wy2 Wzy Wxz Wyz Wz2 100 And because of symmetry; Q = W x2 Wxy Wy2 Wxz Wyz Wz2 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 = W2Q= 1 P ±1 W2 -------------------------------------(4.29) Where Qr = (m x m) variance ± covariance matrix; W2 = 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) 101 4.8 PRECISION, ACCURACY AND ERROR ANALYSIS W. SCHOFIELD in his book ³Engineering Surveying´ highlighted the following important facts; ± Scatter is an µindicator 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 (W) 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, _ i n 1 2 1 (xi - x) (nn - 1) 2 Similarly, a measure of the precision of the mean ( x ) of a set is obtained using the standard error (Wx), thus _ i n 1 (xi - x ) (nn - 1) n is number of observations, xi is observation. Standard error therefore indicates the limits of the error bound within which the µtrue¶ value of the mean lies, with a 68.3% certainty of being correct. It should be noted that W and Wx are entirely different parameters. The value of W will not alter significantly with an increase in the number of observations, the value Wx , however, will alter significantly as the number of observation increase. It is important therefore that to describe measured data both values should be used.   -------------------------------------------(4.31) 2 1 2 n ¡ ---------------------------------------(4.32) 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; _ i n w 1 2 wi (xi - x) (nn - 1) 1 2 Standard error (the weighted mean) w _ i n i w 1 i 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 (Wo) = 0.4513 Var ± Cov Matrix (Q) = Q = +2.7084080 x 10 ± 6 +1.0312500 x 10 ± 7 +3.6107300 x 10 ±7 +1.4511000 x 10 - 7 - 5.0238000 x 10 ±8 +1.9381700 x 10 ± 7 Wx = Wo Q11 = 0.4513 2.7084080 x 10 ¢ ¢ ¢ ¢ --------------------------------------------------(4.33) w n w 1 wi (xi - x) 2 1 2 w wi (nn - 1) ( n W 1 wi ) 1 2 ------------------------------------(4.34) -6 = 0.0007m 104 Wx = Wo Q22 Wz = Wo = 0.4513 3.61073 x 10 1.93817 x 10 -7 = 0.0003m = 0.0002m Q33 = 0.4513 -7 Baseline 2 Notation: CFG113B ± DEFM7Si A ± posteriori rms(Wo) = 0.7274 Var ± Cov Matrix: Q= 6.9898100 x 10 ± 7 9.356400 x 10 ± 8 2.177100 x 10 ± 7 7.419600 x 10 ± 8 - 2.497400 x 10 ± 8 1.1829300 x 10± 7 Wx = Wo W y = Wo Wz = Wo Q11 Q22 Q33 = 0.7274 = 0.7274 = 0.7274 6.98981 x 10 -7 = 0.0006m -7 2.177100 x 10 1.18293 x 10 -6 = 0.0003m = 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 oints in WGS 84 Point ID 10SI 11SI 7SI Baseline BL5 BL1 BL2 X(m) Y(m) Z(m) 703728.3917 703727.3408 703799.0790 6308271.9526 623325.2907 6308282.2834 623267.4114 6308274.3779 623263.9339 105 6SI 1SI RF01 4SI 8SI 9SI BMB 1 5SI 3SI 5SI 3SI RF10 RF09 RF08 RF04 RF02 RF07 BL6 BL3 BL7 BL4 BL8 BL15 BL9 BL16 BL10 BL17 BL11 BL18 BL12 BL19 BL13 BL20 BL14 6208260.6580 623312.6525 6308275.0107 623128.4931 6308259.6561 623328.7345 6308155.3838 623920.1053 6308186.6260 624021.6763 6308190.1463 623962.9226 6308176.3641 623943.4109 6308155.0086 623990.1893 6308176.3718 623906.4774 6308154.5475 623990.1947 6308195.2137 623906.4641 6308206.7852 623807.6077 6308206.7852 623799.8040 6308218.2502 623701.9410 6308230.8544 623597.8111 6308254.0329 623402.3549 6308224.3550 623626.9156 703836.9325 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: Wx = 0.0007m = 0.7mm Wz = 0.0002m = 0.2mm Wy = 0.0003m = 0.3mm 106 Therefore position quality = 2 X + 2 y = 0.72 + 0.32 = 0.8mm 3 ± D accuracy = 2 X + 2 y + 2 Z = 0.7 + 0.3 + 0.2 2 2 2 = 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. y GEODETIC PARAMETERS WGS Datum Spheroid Semi ± Major Axis Semi ± Minor Axis ± ± ± ± ± 84 GEODETIC PARAMETERS USED World Geodetic System 1984 World Geodetic System 1984 a = 6 378 137.000m b = 6 356 752 . 314m e2 = 0.006 694 379 1 = 298. 257 233 6 f First Eccentricity Squared ± Inverse of Flattening ± 107 NIGERIAN LOCAL DATUM GEODETIC COORDINATES Datum Spheroid Semi ± Major Axis Semi ± Minor Axis ± ± ± ± Minna Clark 1880 (Modified) a = 6 378 249.145m b = 6 356 514 . 870m e2 = 0.006 803 511 283 1 = 293. 465 000 0 f Projection Operation Zone Central Meridian Latitude of Origin Falser Easting Falser Northing Scale Factor ± Transverse Mercator (TM) ± ± ± ± ± ± West Belt 8o 30¶ 00´ East 4o 00¶ 00´ North 6705553.983m 0.000m 0.999 75 First Eccentricity Squared ± Inverse of Flattening ± y 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 108 Rz = ± 0.219 35 sec 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 CFG113B 1SI 2SI 3SI 4SI 5SI 6SI 7SI 8SI 9SI 10SI 11SI RF1 RF2 RF4 RF6 RF7 RF8 Northing (m) 263 376. 370 263 113. 179 263 077. 561 263 447. 512 263 389. 128 263 178. 697 262 982. 763 262 944. 052 263 083. 361 263 038. 966 262 873. 542 262 871. 856 263 038. 923 262 981. 549 263 017. 357 263 337. 668 263 056. 172 263 036. 481 Easting (m) 355 504. 658 357 055. 430 357 881. 067 357 851. 686 357 865. 533 357 933. 487 357 251. 380 357 201. 640 357 964. 019 357 904. 950 357 263. 090 357 204. 481 357 904. 917 357 341. 295 357 537. 973 357 840. 733 357 567. 522 357 642. 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, highrise buildings e.t.c; should carry out monitoring operations intermittently to ensure stability and rectification of faults when they occur to avoid an ensuing catastrophe. It is especially important here in Nigeria and other developing countries to imbibe a culture of ascertaining the structural health of dams, bridges, telecom mast e.t.c; even as they aspire to be among the developed nations. 111 REFERENCES Anderson, J.M. and Mikhail, E. M. 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