university of nigeria...2.1 physico-geographical conditions of the niger delta 2.2 climate of the...
TRANSCRIPT
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University of Nigeria Research Publications
TAMUNOENE, K.S Abam
Aut
hor
PG_PhD_88_6711
Title
STABILITY OF RIVER BANKS IN THE NIGER DELTA
Facu
lty
PHYSICAL SCIENCE
Dep
artm
ent
GEOLOGY
Dat
e
DECEMBER,1995
Sign
atur
e
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LI
STABILITY OF RIVER BANKS IN THE NIGER DELTA
TAMUNOENE K. S. ABAM
~ G / ~ h . ~ 1 8 8 / 6 7 1 1
, DEPARTMENT OF GEOLOGY UNIVERSITY OF NIGERIA
NSUKKA
December, 1995
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STABILITY OF RIVER BANKS IN THE NIGER DELTA
TAMUNOENE K. S . ABAM PG/Ph.D/88/6711
T'FESIS SUBMITTED TO THE DEPARTMENT OF GEOLOGY, FACULTY OF PHYSICAL SCIENCES IN FUWmLMENT OF THE REQUIREMENTS FOR THE AWARD OF IHX DEGREE OF DOCTOR OF RHILOSOPHY IN ENGINEERING GEOLOGY OF THE UNIVERSITY OF NIGERIA, NSUKKA
December, 1995
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CERTIFICATION
Mr. Tcvnunoene K.S. Abam, a post graduate student in the Department of Geology, University of Nigeria, Nsukka has satisfactorily completed the requirements for the award of the degree of Doctor of Philosophy (Ph.D. Engineering Geology).
The work embodied in this thesis is original and has not been submitted in part or full for any other diploma or degree of this or any other University.
.-- I Prof. C.O. Okogbue (Supervisor) Department bf Geology University of Nigeria Nsukka \
Prof. E.G. Akpokodje (External Examiner)
) -.A f -
Prof. C.O. Okogbue Head of Department Department of Geology University of Nigeria Ns~~kka
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ABSTRACT
Processes of bank failure and erosion in the Niger Delta have been
characterised, leading to the identification of common factors affecting
the distribution of instability of river banks.
The rates of bank recession depend on season, soil type, stratigraphy,
bank height and inclination, The direction and rate of channel water
level fluctuation, flow velocity and relative location along the river
system have also been shown to have significant influence on bank
recession rates.
Bank failure events are episodic in nature and are concentrated at the
early stages of lowering of channel water level and are mainly caused
by the sensitivity of the banks to removal of passive resistance. High
ground 'water level accentuates seepage erosion which reduces bank
stability. Bank erosion occurs where ever the average channel flow
velocity is greater that 0.5 m/sec. However, banks with height greater
than 5 m and incfimtion steeper than 65" experience accelerated
recession. Depending on the part of the bank exposed to erosion, soil
removal can increase or decrease bank stability against rotational
failure.
Soil type and stratigraphy are identified as the major parameters that
determine the mechanism of bank failure. Stratified banks with
underlying sand strata easily developed overhangs which failed by
cantilever or sliding mechanisms depending on the overhang height.
Non cohesive banks were eroded piece-meal while cohesive banks
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failed by mainly rotational mechanisms along the slip surface with a
factor of safety equal or less than unity at the highest water level. To
realistically predict the behaviour of river banks, the method of
stability evaluation must recognise the dynamic nature of the
controlling factors. The back analysis technique when combined with
knowledge of operating processes can lead to an interpretation of bank
development processes.
Analytical and quantitative methods, including charts, were developed
to facilitate the analysis of river bank stability+ The stability charts for
rotational failure of partidy submerged banks considered
l~ornogeneous soils and give conservative results. A model of river
bank profiles based on shear strength was described. The model which
can be applied to both homogeneous and stratified banks gives
reasonably good fit when cornpcved to natural river banks.
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ACKNOWLEDGEMENT
I am indebted to Prof. C.O. Okogbue for supervising this work and for
his numerous contibutions to this research. I am also grateful to Profs.
John KniU, P.R. Vaughan, Drs. M.H, de-freitas, M. Rosenbaum, G.
Evans and G. Wharton all of the University of London, U.K. for their
active support and assistance at the initial stage of this research. I a m
very grateful to the Institute of Flood, Erosion, Reclamation and
Transportation (IFERT) of the Rivers State University of Science and
Technology, for placing her data bank at my disposal.
My special thanks go to the Association of C o m n w e a l t h Universities
for their Academic Staff Scholarship and to the Rivers State University
of Science and Technology, Port Hcucourt, for their financial support
towards the fieldwork aspect of this research.
I acknowledge with thanks the helpful advice of senior academics and colleagues including Profs. Mosto Onuoha, C.O. Ofoegbu, D.M.J.
Fubara, C.S. Teme and Drs. Uma Kaln, L. Mamah and H. Ezeigbo. I a m
sincerely grateful to Mr. N.I. Thomas for typing this work.
Finally, I wish to express my sincere thanks to Engr. E.A.J. George and
my family for inspiring me to complete this work and especially to my
wife Mrs. Barbara Kingdom-Abarn for the inconveniences she had to
endure in the course of this work.
T.K.S. ABAM December 1995
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TABLE OF CONTENTS
Certification
Abstract
Acknowledgement
List of Figures
List of Tables
List of Appendices
CHAPTER ONE : Introduction
ProbIem
Objectives
Scope of the Study
Previous work
Fluvial aspects of bank stability
.The probSem of changing water level
Bank morphoIogy
Effective s&ss in partially saturated soils
CHAPTER TWO: Characteristics of the Study Area
2.1 Physico-geographical conditions of the Niger delta
2.2 Climate of the Niger delta and its effects on bank morphology
2.3 Distribution of soiI types in the Niger delta
CHAPTER THREE: Review of SIope Stability Analysis
3.1 Analysis of translational mechanism of failure
3.2 Analysis of rotational mechanism of failwe
ii
iii
v
xi
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The friction circle method
The methods of slices
Other methods of stability analysis for rotational failure mechanism
Analysis of wedge mechanism of failure
Toppling mechanism of failure
Analysis of riverbank overhangs
Shear nmechanism of failure
Beam mechanism of fialure
Tensional mechanism of fialure
Probabilistic methods of analysis
CHAPTER FOUR: Research Me thodology
4.1 Introduction
4.2 Field measurements
4.3 Labor&ry tests
4 4 Analysis of riverbanks \
CHAPTER FIVE: Results
Field measurements
Water level
Riverbank profiles
Flow velocity
Vane shear strength
Results of pore pressure measurement using standpipe piezometer
Laboratory test results
Particle size distribution
Moisture contents and consistency lilntts
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5.2,3 Bulk density 5.2.4 Shear strength
5,2.5 Permeability
CHAPTER SIX: Discussions 113
Seasonal distribution of bank failure
Areal distributoion of bank failure
Analysis of factors affecting riverbank stability
Influence of channeI water level
Influence of reIative location in river system
Influence of bank height
Influence of shear strength
Influence of unit weight
Influence of ground water IeveI
Influence of sim~dtaneous variation in bank height, water 'Ievel, unit weight and pore pressure 135 AnaIysis of processes of riverbank development and recession ' 140 Analysis of seepage erosion of alluvial river banks 140
Analysis of bank faiIure and recessiona1 mechanism 148
Determination of the roIe of fluvia1 erosion processes 179
Remedial rn-easures for riverbank stabilisation in the Niger delta 181
CHAPTER SEVEN: Development of stability charts and riverbank profile models 184
7.1 Introduction 184
7.2 RotationaI failure of partially submerged riverbank 186
7.3 Riverbank profile model deveIopment 194
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Model development
Application of the model
Comparison between model prediction and field observation of riverbank profile
Design of stable riverbank profiIes
CHAPTER EIGHT: Summaries, Conclusion and Recommendations
Summaries
ConcIusions
Recommendations
References
Appendices
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LIST OF FIGU'RES
Map showing the study area in relationship to Nigeria and Africa I1
Major rivers and creeks in the Niger DeIta 13
Montly variations in rainfaII, evaporation and temperature in the Niger delta 14
Distribution of annual rainfall in the Niger delta 16
A typical evapotranspiration anc concurrent precipitation graph for the Niger delta 17
Map showing dedirnentary environments and morphological features of present day Niger delta complex and adjacent areas
Borehole records from various geomorphic soil groups
Modified distribution of major soil groups in the Niger delta
Analysis of translational failure mechanism and it's modofication for tension crack
'Principle of the friction circle method of stability analysis
Geomeh.y.of lagarithrnic spiral slope failure mode \
Method of slices for rotational slope stability analysis
Geometrical considerations and correction factor for Janbu's method
Conditions for sliding and toppling of a block on an inclined plane
Shear failure mechanism
Beam failure mechcdsm
Tensional failure mechanism
Map of the Niger delta showing drainage pattern and study sites
Water gauge system
Typical velocity profiIe in a river channel
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Monthly variation of water level at selected locations along River Niger and its distributaries
Variation in water level in Opobo town
Monthly variation in water level at a typical tidal boundary (Peremabiri) in the Niger delta
Regional stratigraphic models of riverbank in the study area
Riverbank profiIes in the study area (June, 1988)
Changes in riverbank profile at Agbere
Changes in riverbank profile at Kaiama
Changes in riverbank profile at Yenagoa
Velocity profiles across Nun river at Agbere
Velocity profiles across Nun river at Agbere
Velocity profiles across River Nun at Sagbagreya
Velocity profiles across Oguobiri Creek near Amassoma
Velocity profiles across Egbedi creek
Vertical velocity profiles during a tidal cycle
Standpipe piezometer readings at three river bank sites near Opobo
',
Typical particle size distribution of soils in study area
Particle size distribution curves for some sites in the Niger delta
Particle size distribution of composite riverbak at Kaiama
Particle size distribution of composite riverbank at Agbere
Range of moisture content in major soil groups in the study area
Comparison of sediment shearing resistance paraIIeI and perpendicular to stratification
Result of triaxial test on specimens from Ndoni area
Result of triaxial test on specimens from Kaiama
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Result of cyclic triaxial test showing changes in strain, axial stress and pore presswe on samples from Opobo area
Monthly distribution of bank failures in the study area
A comparison of water level changes and bank failure frequency in the Niger Delta
Graphical relationship between bank heights and inclination
Comparison of shear strength profile in Ndoni and Agbere of the Niger delta
A comparison of rainfall and bank failiue distribution in the Niger delta (1988)
Correlation of bulk unit weight with factor of safety of river banks
Predicted monthly variation of factor of safety of a riverbank
F1o.t~ nets after a given interval of time during recession of flood water in Ekole creek
'. '~ariatikh of hydraulic gradient with time in two riverbanks along Ekole creek
Variation sf flow rate with time in two river banks along Ekole creek
Variation of seepage force with time in two riverbanks along Ekole creek
Riverbank section within the light grey fine silty clay soil group in the Niger delta
AnaIysis of rotational failiue caused by recession of flood water
Riverbank overhang section in Okrika
Analysis of rotational failwe caused by infiltration
Rotational bank failure caused by tree of large biomass
Analysis of transIationa1 failure caused by oversteepening due to erosion
Analysis of muItiple retrogressive bank faiIure
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Interpretation of riverbank failure process at Yenagoa
Illustration of criteria for interpreting bank stability
Analysis of criteria for recognising bank recession caused by erosion
Effect of local eroslon on. the stability of a riverbank against mass failure
A comparison of water table profiles in alluvial channel banks and earth dams
Stabili ty charts for partially submerged alluvial riverbanks
Stability charts for partially submerged alluvial riverbanks
Stability charts for partially submerged alluvial riverbanks
Equilibrium profile of a river bank
Comparison between observed and calculated bank profile
Comparison between observed and calculated bank profile c7 t Akinima
Relationship between bank inclination and stability number for various conditions of bank stability
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LIST OF TABLES
Physical characteristics of some rivers in the Niger delta
Srunmary of physical and environmental characteristics of the major soil groups (modified from Akpokodje, 1987)
Classification and characteristics of soil slope instabilities (modified from Rib and Liang 1978) Water level variation in parts of the Niger delta for 1988
Average river discharge from selected cross-sections at different periods (Data from IFERT, 1983)
Summary of in-si tu vane shear strength results Summary of sensitivity classificati~n in soil groups in the study area
Maximum reduction in shear strength due to disturbance of soils in the Niger delta
Summary of natural moisture contents of soils in the study area
Summary of consistency limits of soils in the study area
~ u m m a j of plasticity index and linear shrinkage of soils in the stud area Y Summary of bulk density of soils in the study area
Summary of direct shear test results in LGTSC-3 soil group
Summary of angles of internal friction and cohesion of soils derived from undrained triaxial shear tests
Summary of permeability of soils in the study area
Monthly record of riverbank variables in Kaiama
Approximate exit hydraulic gradient and flow rates calculated from flow nets
Summary of results for test against seepage erosion criterion
Results of riverbank anaIysis and field observation of banks
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Sensitivity coefficients of some factors affecting a partially submerged alluvial riverbank
Soil properties at different depths on a channel bank
Soil properties of an overhang
Sensitivity coeficients of variables affecting rotational beam failure of overhang
Hypothetical soil properties of a stratified riverbank
Appendix 1
Appendix 2
Appendix 3
Appendix 4
Appendix 5
Appendix 6
Appendix 7
Appendix 8
LIST OF APPENDICES
Depth to Neutral Axis
BASIC computer programme to calcrdate factor of safety of partially submerged bank using Bishop's simplified method
BASIC computer programme for calculating factor of safety against any of the three mudes of overhang failure of banks and sensitivity coefficients Plane shear failure analysis modified for partial submergence
BASI? computer programme to calculate factor of safety against plane shear failure of parfially submerged bank
A flow chart for generating stability chart parameters for partially submerged slopes
A flow chart for generating stability chart parameters for overhang failure in riverbanks
A BASIC computer programme for generating stability chart parameters for partially submerged slopes based on Bishop's simplified method
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1.1 PROBLEM
Each year a vast amount of property and arable lcmd are lost as a resrdt
of river bank failure in various parts of the world. In 1988, for example,
the damage to property and arable land caused by bank failures in the
Niger delta was estimated at one hundred and six million ncaira
(Ministry of Works and Transport, Flood and Erosion Division 1991).
Bank fCdures also lead to a continuous adjustment of channel geometry
and this affects the utility of the rivers by man and increases the level of
risk in the commercial development of the rivers.
An essential reqeement towards reducing the losses arising &om the
instability of river banks is an understanding of the processes and
mechanisms of the failures and procedures for identifying instability.
Consequently, the main objectives of this study are to:
(i) locate and describe geographical occurrences of river bank
fcdures.
(ii) investigate the causes of river bank instability, identify and
critically evaluate some of the modes of failure and retreat of the
river beds.
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(iii) develop analytical and qunntita tive methods including charts to
facilitate analysis of river bark stability.
1.3 SCOPE OF THE STUDY
Most studies of river bank inshbility have dealt with individual bank
failures or with those associated with a specific project and me thus not
able to give a regional interpretation of the causes of bank failure. The
consideration of river bank fail~ues on a regional basis has the
advantage of developing a broad overview of the distribution of bank
instability and the common factors affecting their occurence.
In order to achieve the above objectives, i t was considered nec- to
study the distribution . . patterns and engineering properties of the , .
geolgical materials making up the river banks. The influence of factors . \
such as geologic, ;tratigraphic and climatic features of the environment,
ground water and seepage, fluvial processes as
inundation were also investigated. On the basis
and adys i s the contributions of various factors
well as frequency of
of field observations
to the distribution of
river bank failure were assessed. Simplified methods of bank stability
evduation using stability charts were investigated for partially
submerged riverbanks. A criterion for seepage erosion of river banks
was also investigated.
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1.4. PREVIOUS WORK
There is a vast amount of literahue on the stability of slopes but only a
few of these deaf strictly with river banks. These include: Thorne (1978))
Ponce (1978), Edil and Vallejo (1980)) Ilagerty et d (1981) and Thorne
and Torvey (1981). Other Literature on slope stability which relate to
riverbanks are those concerned with earth dams under conditions of
changing reservoir IeveI. Some of these are Feltenius (1936), Bishop
(1952), Janbu (1954) and Morgenstern (1963). Previous work on various
aspects of river processes and bank instability are discussed beIow.
1.4.1 Huvial Aspects of Bank Stability
There are many, factors which govern the forces that cause bank ',
instability. Char1 ton (1982) grouped these factors into two classes,
namely, those associated directly with the fluid flow in the channel and
those associated with conditions exterior to the channel. The fluvial
factors which affect bank, stability include, fluid flow velocity,
boundary shear stress, fluid lift force, secondary currents, fluctuating
discharge, migration of meander pattern in dynamic equilibrium,
fluctuating sediment discharge, changes in river Ievei, obstructions
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deflecting CLIIT~ILLB L U W ~ U B cl and river traffic or wind with wave
generating capacity.
A qualitative evaluation of these factors in which the magnitude of the
forces acting on the river bank are expressed as a percentage of the
tractive force exerted on the bed of the channel by the flowing water
was provided by Simon and Li (1982). Thorne (1978) also recognised
various forces on a bank during his study of River Severn in the U.K.
First he recognised that soil material may be entrained directly from the
bank and transported downstream. Second, he recognised that the flow
may scour the.bed at the base of the bank (increasing bank angle and
height) to bring about gravitational. failure of an intact bank. These \
observations were later noted by Hooke (1979) as the two main river
bank processes.
1.4.2 The Problem of Changing Water Level:
One major feature of river channels is the periodic inundation of the
banks. The fluctuation of water level in a river channel leads to a
continuous adjustment in the balance of forces on the river bank. Desai
and Sherman (1971) showed, from an investigation of unconfined
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seepage in sloping banks subjected to the effects of changing river stage
that, among other factors, pore pressures were induced within the earth
mass due to seepage. Several recorded cases of earth dam failures in
draw-down situations have been attributed to the role of undissipated
pore pressures. According to Vaughan (1987) undissipated pore
pressures arising from varying river stage or draw-down are hardly
correctly estimated. This is because for a fal l in river level, the free
water or the phreatic surface in the earth bank lags behind the f&ng
level of water in the river and this complicates the problem of stability
as it is.;then generally difficult to compute such a free water surface.
Because of this difficulty, Morgenstern (1963) estimated slope stability \
dming draw-down by assuming that the pore pressure ratio B given
by:
where du = induced pore pressure
d a = change in stress
is unity and that no dissipation of pore pressure occurs. Desai (1972)
used the finite element technique to develop a procedure which
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allowed the evaluation of an approximate free surface for gradual (and
sudden) draw-down in river banks and this provided data for more
precise stability analysis. However, because of variability in soil
properties for example, such rigorous approaches to bank stability
analysis may not necessarily be superior to the more common and
simplistic approach based on records of bank failure.
The historical records approach was used for the Ohio River by
Hagerty et al(1981) who concluded that bank failure and erosion on the
Ohio River was complex and episodic. They suggested that the
princip,al erosional mechanism was bank material removal by tractive
forces during flood events and internal erosion of bank materials by \
bank discharge following flood.
1.4.3 Bank Morphtrl ogy
Because bank erosion is not uniform, the bank face can take vcuious
and sometimes complex geometrical forms. Thorne and Torvey (1981)
described some bank face morphology as resembling cantilevers. Such
complex morphologies are common in large river net-works such as the
Niger Delta where Okagbue and Abcm (1986) have described failure
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mechanisms of river banks as complex; ranging from simple slip failure
in high banks to shearing and toppling in low banks (less than 2.5m in
height). Okagbue and Abam (1986) further determined that the slip
circle model of stability evaluation described by Bishop (1955) was only
adequate for bank heights exceeding 3.5 m.
1.4.4 Effective Stress in Partially Saturated Soils
The occurence of complex slope Forms may be traced to the nature of
the soil and the effect of the e~wironment on the soil behaviour. By
exposing bank materids to long spells of dry season, high levels of
moisture deficit, can be created (Zurich 1985). This imparts partial
saturation to the soil where the void spaces are occupied both by water
and by air. For such par t icy saturated soils, Bishop (1955) found that
Terzaghi's equation for effective stress may be modified to read as
follows:
= u - [Ua - X (Ua- UiLI)] 1.2 where (T = total stress
Ua = pore air pressure U,,, = pore water pressure X = fraction of unit, of cross-setional area of soil
occupied by water. This parameter is related to the degree of saturation and by implication soil suction
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For saturated soils X = I, and for dry soils X = 0. Fredlund e t al. (1978) investigated the contribution of suction
to the shear strength and discovered that suction can be most
conveniently expressed in terms of cohesion C by:
where C, = suction or apparent cohesion of the soil Ct = true cohesion of the soil
A combination of equation 1.2 and 1.3 would thus lead to a more general expression for shear strength in the form:
> _ . L ' - \
In unsaturated soils, shear deformation has a significant effect
on soil strength. According to Lumb (1975) dilatant shearing of soils increases suction, while campre$sive shearing decreases
suction.
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2.1 I'IIYSICO - GEOGRAPHTCAL CONDTTIIONS OF THE NIGER DELTA
The Niger delta is situated in the coastal sedimentary basin area of
Southern Nigeria (Fig. 2.1). It covers an area of 36,270 km2 constituting
roughly 3.9% of the land area of Nigeria. Its formation is attributed
primarily to the structural movement of the earth's crust and the
operations of physic0 - geographical processes of erosion and
sedimentation (Short and Stauble, 1967; Whiteman 1982). This led to
the establishment of nn extensive s&hentary flatf criss-crossed by
several rivers and creeks, the Nun River and Forcados River being the :,
two principal rivers (fig. 2.2). \
The River Niger bifurcates near A m a b i r i into the Nun and the
Forcados which flowed westward as the main stream of the Niger. The
Forcados gave rise on it's left side to the Sagbama River, the Bomadi
Creek and the Nikoro Creek. The Forcados River is joined from the
right by the Ase River, the &ow Creek and the Oreri Creek.
The Nun River on the other hand is joined by the Taylor Creek from it's
left and bifurcates into the Ekole Creek, which debouches into the Brass
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River. The Egbedi Creek takes off from the right of the Nun. After
some 2-4 krn in its meandering course, it meets the Sagbama River, a
left distributary of the Forcados.
River Orashi is joined by Ndoni Creek near Aboh and gives rise to
Egorobiri Creek, Saka creek and Kugbo Creek. The rivers have varying
lengths and widths. Table 2.1 summcvises the length, width and height
of some of the rivers and creeks.
TabIe (2.1) Physical characteristics of some rivers in the Niger
Name of River or. creek" 1
Width of water
channel Cm)
Nun Forcados Sagbama
Ekole Egbedi Orashi
Ndoni
Height from water level to ground at dry
season (m)
Slope of River
2 104 N/A
1.23 x lo4
N/ A N/ A
6 x 1.16 x 10"
Station
Kaiama Pa tani
Tungbo Y enagoa Egbedi Mbiama
Ndoni
The Nun and the Forcados have more distributaries than tributaries,
consequently, they are narrower in width in their lower reaches
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G L/ L F O F G U I N E A
Fig. 2.1 May showing the study area in relationship to Nigeria an
Africa
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(NDECO 1961). They have many meanders and variations in width,
attributable to the modest slope (averaging 6.3 x l o 5 at Bomadi), and
slow speed as well as the effect of tides.
2.2 CIirnate of The Niger DeI fa and it's Effects on Bank Morphohgy
The Niger delta is characterised by two distinctive seasons, namely: dry
season (November to March) and wet season (April to October), (fig.
2.3). The dry season is generally characterised by fairly high
temperatures usually greater than 26°C and a low monthly average
rainfall usually less than 200 mm. The combination of high . ., ,
temperhres and low rainfall resulted in high evaporation (monthly . \
average of about500 mm). The excessive evaporation results in the
depletion of soil moisture, shrinkage and finally soil cracking.
At the inception of the wet season, the average rainfall in the delta
increases gradually and reaches a peak (up to 500 mm/month) in Jdy.
A slight decrease is normally experienced from August to October . The
rainfall drops sharply in November (fig. 2.3). As a result of the high
rainfall during the wet season, soil moisture is recharged.
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Fig. 2.2 Major Rivers and Creeks in the Niger Delta
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RAINFALL 450 EVAPORATION 1
#
--*' @.??ahfoil ( m m l A Ewaporatlon ( m m )
( m m 1 wo 1 ( A 1 PORT HARCOURT ff Temp(bC3 A
TEMP.
[OC
I 1 1 I I I I I 1 4 J F M , A M J J A S O N 0
T I M E I m o n t h s )
Fig. 2.3 Monthly varia t i o m in rainfall, evaporation and te~nperatrrre in
the Niger Delta (Data from IFERT, 1988)
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The mean annual rainfall is reduced farther away from the coast Line
(fig. 2.4). Consequently, the areas south of Opobo, and the estuaries of
the Pennington River are the wettest areas in the Niger Delta with
about 4,000mm annual average rainfall, while the middle Delta has
3,000mm and the upper delta 2 ,000m.
The alternation of dry and wet season causes the soils in the Niger
Delta to undergo volume changes without necessarily being subjected
to any external load. Such v o l ~ m e changes =arise from changes in the
soils water content (fig. 2.5) and thus effective stress (Head, 1986). h
the field, large volume changes are manifested as shrinkage and tension ' , %
cracks within the acfected soils . When the duration of the dry season is '?
long, extensive dessication occurs leading to partial saturation of the
soil and the development of a net-work of shrinkage cracks which
extend over large areas, producing a blocky structure in the soil
(W olman 19.59).
The wetting of compact or stiff partially saturated soils results in
softening arising mainly from reduction in cohesion with little effect on
the angle of internal friction (Bishop and Henkel, 1967)
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Fig. 2.4 Distribution of atmud rainfall in the Niger Delta (BERT 1983)
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0
PRECfPlTATlON /EVAPORATION ( m m )
Avwaqe monthly precipitation and evaporation ( 1960 - 198 0 ) Port Harcourt . I
Fig. 2.5 A typical evapotranspiration and conc~vren t precipitation
graph for the Niger Delta (IFERT 1988)
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2.3 Distribntion of Soil Types in the Niger Delta
The principal geomorphic soil groups in the Niger delta were described
by Short and Stauble (1967). Those described included the coastal plain
sands, meander belt, fresh water and back swamp deposits (fig. 2.6).
Others are mangrove sw~vnp and .abandoned coastd beaches. These
soil groups are differentiated by their mode of origin rather than by
their engineering properties. Typical vertical soil profiles obtained
from boreholes drilled within the different geomorphic soil groups are
presented in fig (2.7).
Based on diffe~ences in engineering behaviour, Akpokodje (1987)
reclassified the soils in the Niger delta into four major groups namely: i
(I) Reddish brown sandy clay loam soil of low to medium plasticity
(RBSCL-I); (2) Brown sandy clay of mednm to high plasticity (BSC-2);
(3) Light grey, slightly organic, fine sand and silty day (LGFSC-3); and
(4) dark organic/peaty clay of high to extremely high plasticity
(DOPC-4). Following extensive fieldwork in the area, the writer has
refined this classification in both geographical extent and composition
as shown in fig 2.8.
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Estuaries
i Fluuia -Mar ine a Beochta and barn Traoaltionol Environment Marina Includiog Lower Oelloic Ploin 8 CaoStai belt Mar in r Envlronmenl Fig. 2.6 Map showing morphological soil groups in present day Niger
delta Complex (Short & Stauble, 1967)
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M: nqravm worn p Gmul
Fig. 2.7 C o m p ~ i s o n of borehole records drilled at various genrnorphic
units (Data from Enmh George Associates 1990)
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These soil groups and their hydraulic properties are sumrnarised in
table (2.2). Within these major soil groups, however, other soil types
occur and this results in variability in the surface distribution and
stratification. Stratigraphic sections obtained from various borehole
logs and from exposed river bank surfaces show that generally, the soil
layers are irregularly stratified and show a tendency for coarsening
upwards. In the upper reaches of the Niger delta, the exposed river
bank faces are dominated by sandy soils while silty and clayey soils
predominate towards the coast.
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Fi. 2.8 Mo.dified distribution of major soil groups in the Niger
Delta (Modified from Akpokodje, 1987)
-
nE G E NL
1 Reddish b r o w n r a n d y c lay loam ( R B S C L - I ) IT1 Brown sandy c lay ( B S C - 2 1 1wJ Light grey to d a r k s l i g h t l y organic t i ne r a n d a n d s i l t y cloy ( L - G F S C - 3 )
Dark t o d a r k brownish o r p a n k a n d pea ty c lay of high plast ic i ty ( D O P C - i d I -. -
.-
Fi. 2.8 Modified distribution of major soil groups in the Niger
Delta (Modified from Akpokodje, 1987)
-
Table (22) Summary of Physical and Environmental Characteristics of the Major
Soil Groups (Modified from Akpokodje 1987)
Major Soil Group
Reddish brown sandy day loam RBSCL-I
Brown sandy clay BSC-2
.... . - , < Light grey slightIy .. organic fine ' sand and silt cIay LGFSC-3
Dark organid peaty day DOPC-4
In-Situ Condition
Very loose when wet to very dense when dry
- - - - - -.
Loose to dense when dry
Hard with abundant s hrinkase cracks when dry
Hard with abundant shrinkage cracks when dry but very soft to highly compressible when wet
Geologic Unit
Coastal plain sand
Coastal plain sand and Sornbrciro- Warri deltaic plain
Backswamp and fresh water swamps and meander belts
Mangrove swamps and salt water LMcksnmnps
Geomorphic and Hydraulic Properties
Dry, flat to subhorizontal land, generally rmt affected by seasonal floods, g d drainage conditions, with water table 3 5 m, marshes are scarce. Dry, flat to subhorizontal sloping land with prominent seasonal fresh water n~arshes, poor to good drainage, water table generally between 3-5 m.
Mmos t totally submerged during et season, with exception of naturaI drainage problems with seasonal and temporary flooding due to rainfall and rise in groundwater tabIe. Groundwater table generally between 0-3 m. Frequently totally submerged during high tides a n d seasonal floods; very severe drainage problems, water table genenily between 0-2 m.
-
3. REVIEW OF SLOPE STA'BTLX'IY ANALYSIS
Introduction
As a result of the need to understand and correctly predict slope
behaviour, several methods of assessing the stability of slopes have
been developed. These slope stability methods are based on five
mechanisms of failure, namely: translational, rotational, wedge,
toppling, and flow slides. Rib and Linng (1978) distinquished these
various types of slope instability (table 3.1) and suggested guidelines
for recogrusing each type in the field. Rib and Liang's guidelines have
been extended to accommodate characteristic features observed in . . I
channel bank failures. Whereas slope failures of the transla tional and .. \ \
rotational types are generally amenable to one of the simple techniques
of analysis, toppling, and flow slides have rarely been confidently
analysed in terms of a factor of safety.
3.1 Analysis of Translational Mechanism of Failure
A translational failure mechanism usually involves the displacement of
the unstable soil or rock mass along a continuous weak plannar surface
as illustrated in fig (3.1).
-
Culrnan's Method of Analysis
A method for analysing translational failure mechanism was first
suggested by Culman (1886). Hx method involves the resolution of
forces parallel and normal to the weak planner surface (fig. 3.1)
resulting in the foLlowing expressions:
where C = cohesion (kN/m2) L = length of plane of weakness (m)
W = weight of unstable soil mass (kN) O = angle of internal friction (degree) j3 = slope angle (degree)
.< - . \ . < The ratio FI/F2 is taken as a measure of the factor of safety (FS) of the
- \ slope. The slop: is considered unstable if the factor of safety is less or
equal to unity. The resolution of forces in this way implicitly assumes
that aH forces on the sliding mzss including it's gravitational weight
and forces due to the pressure of water act through the centroid of the
sliding mass. The implication of this assumption is that rotational
moments are ehinated although these contribute to instability.
Strictly, this assumption is not true for acixal slopes, but according to
Hoek and Bray (1981), the errors introduced by such moments can be
ignored without greatly altering the accuracy.
-
FI = C , L t N Tan N b
( a A N A L Y S I S OF T R A N S L A T I O N A L FAILURE
Z o = Oeplh of Tension crack Zt = Llmi t lng depth of Tentl la Z o n e
2 C ' y + T a n ( 4 5 t @/2 1
( bl CULMAN'S ANAUIS15 MODlFlEO TO TAKE A C C O U N T O F TD(SION CRPI(
Fig. 3.1 Analysis of translational fCail~u.e mechanism and its
modification for tension crack
-
f I Parts Surrounding Slide Main Scam
Has no cracks
s flow Has few cracks
tf, 1''
fiow May Rave a few cracks
f l~w; Has few cracks
[S h m l shaped at angle of rcpose
Typically has wrraeed or V-shaped upper part; is long and narrow, bare and commonly striated
-- Its concave towards slide, in some types is nearly circular and slide issues through narrow orifice Is steep and concave toward slide; may have variety of shapes in outline: nearly straight, gentle arc, circular or bottle shape
Flanks
3ave cantinubus. xrve into main ..' ;cam
steep and rregular in uppe: pa* m y bhve levels built in lower parts
Arc cumed; have steep sides
Commonly diverge in direction of movement
Parts that Wave Moved Head
Usually has none
May haw none
Commonly consists of a slump block
Is generally under wa ti? r
Body
Is mnEcal hmp of soil, equal in vrslume to head Cmsisrs of large blocks pushed along in a matrix of finer material; has flow h e s
form. Flows drainage ways a d Can make sharp turns; is very Tong compared to length Js broken into small pieces, shows flow structure
Spreads out on underwater floor
Foot
Has none
Has none
Has none
-
In a critical condition where F l / F 2 = 1, the maximum height that a
slope can sustain beyond which the translational mechanism of fadure
would be expected to occur is given by:
4G'sin u cos 0 ?'" = 1' (I - cos(p - 8 ) )
where I-IC = criticaI height of dope Y = unit weight (kN/rn3) ,O = slope angle (degree O = angle of friction (degree)
C = cohesion (kN/m2)
As the slope angle decreases, plane failure becomes much less Likely
and the Culmcm's analysis seriously overestimates bank stability
(Thorne 1978).
Correction for Tension Crack \
The non-provision for tension cracks in Culman's original relationship
may seriously d e b t its application. Tension cracks reduce the
effective length of the potential failure surface and decrease bank
stability but according to Thorne and Torvey (1981) they do not
invaLidate the stability analysis provided that the depth of tension
cracking is smcd compared with the bank height. In order to
accomodate the effect of tension, Carson (1971) considered the depth of
the zone of tension in relation to the length of the fdu re surface. The
maximum depth to which tension cracks may develop can be predicted
-
from the engineering properties of the soil (Terzaghi and Peck 1969).
Within the tensile zone, the shear strength of the soil is zero. Thus the
strength in this area can be discounted from that which would be
mobilized in a slope that has no tension crack.
3.2 AnaIysis of Rotational Mechanism of Failure
Two techniques of analysis have been applied to rotational failure
mechanisms, namely, finite element and Limit equilibrium techniques.
The finite element technique determines the normal and shear stresses
along a failure surface by considering the elastic properties of the soil
in terms of Young's modulus and poissons ratio. Although this
technique gives a useful indication of the influence of stress
distribution on the stability of the slope, it is not widely used owing \
primady to the highly ma thema tical procedures required for obtaining
solutions. Besides, the accuracy of this technique in practical problems
is not superior to those of the limit equilibrium technique (Duncan and
Wright 1980).
The Limit equilibrium methods on the other hand define stability with
respect to the limiting strength of the soil. All Limit equilibrium
methods have two principal features:
-
(1) They define the factor of safety (FS) in the same way,
in which S = shear strength and T = shear stress required to induce
equilibrium.
(2) They make the implicit assump tion that the same values of shear
strength may be mobilized over a wide range of strains along the slip
surface. This assumption is a weakness of the h n i t equilibrium
tecluuques since strength is strongly dependent on stmin. However in
comparison with the finite element analysis technique, the Limit
equilibrium methods do not in general requhe as much iterative
computations and as a result are widely used. The various limit
equilibrium' methods are now discussed.
3.2.1 The Ffictioh Circle Method
The ecuIiest limit equilibrium technique is perhaps the "Friction Circle"
method originally developed by Taylor (1937) for analysing circular
failures. The method considers the stability of an entire sLiding mass as
a single unit fig (3.2). At Limiting equilibrium the method assumes that
the resultant of the normal and frictional force is tangent to a
hypothetical circle "Friction Circle" &awn at the centre of the circular
surface and with radius (r) given by:
-
where R -= radius of the circular failure surface 0 = angle of int,ernal friction of soil.
The disadvantage of the "Friction Cirde'method is that it can only be
applied to a homogeneous slope with single values of cohesion and
angle of internal friction and unfortunately, most slope materids are
not homogeneous. Also, in using the friction circle method, the
distribution of forces along the failure surface must be arbitrarily
assumed. This in itself is a source of error. This difficulty is overcame
by the logarithmic spiral method in which the resultant of dl the \
normal cvld frictional forces pass though the origin of the spiral no
matter their magnitude. Consequently, when a moment is taken about
the origin, the combined effect of normal and frictional forces is nill
(Huang 1983), and only the weight and the cohesion moments need be
considered. The problem with the log spiral method, however, is that
the geometry of most failure surfaces do not bear much resemblance to
the log spiral. The log-spiral method is schematically represented in fig
3.3
-
TRIAL C I R C U L A R F A I L U R E S U R F 4 CE
Fig. 3.2 Principle of the friction circle method of stability analysis
C d T a n Q R = R o C
R = I n s t a n t r a d i u s o l 0 f r o m R W h e r e
R o t R a d l u s o t e n t r a n c e p o l n l
E x p i e = b a s e o f n o l u r o l l o p a r i t h m s
Fig. 3.3 Geometry of logarithmic spiral slope fcdrue mode
-
0.J
3.2.2 The Methods of Sfires
Unlike the friction circle m d log spiral methods, the methods of slices
involve the division of the potentidy unstable soil mass into slices (fig
3.4a) and can thus accomodate complex slope geometries, variable soil
and water pressure conditions. However, the division into slices gives
rise to intersLice forces (fig 3.4b) which may affect bank stability.
Fellenirms's Method of Slices
The Fellenius method was the earliest of the methods of slices. This
method Like the friction circle method deals exclusively with circular
failure surfaces. Here, the factor of safety is defined in terms of moment
equilibrium and is expressed numerically by:
where P V = bulk weight of soil in slice a = imlinatiorl of slice L = width of dice W = pore water pxessure at the base of she slice O = angle of internal Friction of soil
C =. cohesion of the soil
The imylication of this definition is that the factor of safety is the same
in each slice a situation which implies mutual support between
adjacent slices. To achieve equihbrium in each slice in the direction
-
normal to the base of the slice, the method further assumes that the
resultant of all forces on the sides of the slice acts parallel to the
bottom of the slice. In actuality, however, this assumption is not true
for ail slices (Whitman and Bailey 1967), and as a result, some of the
slices will not be in equilibrium. This lack of equilibrium in the balance
of forces in the slope is one source of error. The others are associated
with problem solving when large pore water pressures are developed
and for situations of deep circrdar failures. Where large pore pressures
are involved and the inclination of the slip surface is steep, the UL term
in equation (3.5) becomes greater than the W. cos (a) term suggesting
condition of net uplift at the base of the slice. The method therefore
underestimates t+e stability of natural slopes and can not thus be used
to estimate long-term stability.
Bishop's Method of Slices
The sources of error in Fellenius method are eliminated in the Bishop's
method due chiefly to the indusion of interslice forces in the equations
of equilibrium. In this method, the factor of safety is expressed by:
-
where CL = effective cohesion 0 = effective angle of internal Friction b = width of sKce U = pore water pressure ai = inclination of base of slice Xi and Xi+l are slide forces on a slice
When (Y - Xi+,) in equation 3.6 is equated to zero, the solution to the problem becomes greatly simplified and the method is then referred to
as Bishop's simplified method. Because the difference in the side forces
may not be- zero, Bishop's simplified method does not satisfy all
equilibrium conditions. Inspite of this, however, it has been shown by
severd workers '(Whitman and Bailey 1967, Duncan and Wright 1980,
Huang 1983) that the method can give satisfactory results, especially
where failure surfaces can be approximated by a circle. Bishop (1955)
compared the safety factors obtained from the simplified method with
those from the more rigorous method in which all equilibrium
conditions are satisfied. He found that the vertical interslice force could
be assumed zero without introducing significant errors (typically less
than 1%).
-
do
. - -
I
Channel Water Level
Q
Hydrostatic Pressure
( a \ CIRCULAR FAILURE MECHANISM O F f ' A R T I A w SUBMERGE0 SLOPE
( b ) FORCES ON A TYPICAL SLICE IN A CIRCULAR FAILURE MECHANISM .
Fig. 3.4 Method of slices for rotational slope stability analysis
-
Duncan and Wright (1980) also compared Bishop's simplified method
with more accurate methods. The Bishops simplified method was
shown by these workers to be accrua te within 5% of the methods which
satisfy all equilibrium conditions. Due to it's simplicity and accuracy,
the Bishops simplified method has become one of the most widely used
methods for the analysis of circular failures (Bromhead 19%). By
modrfying the distribution of unit weight below and above water level,
Bishops method cnn also effectively deal with problems of partial
submergence (fig. 3.4b). The weight of the submerged part of a slice is
computed by multiplying the bouyant unit weight of the soil by the
area of the pqrt of the slice below water level. The consideration of
partial submerg~nce in this way modifies equation (3.6) to:
1 P S = C[C'.O+ tan^(^^ + C V ~ - [J . b +
C ( W I + W 2 ) sin a sec CY
f (Xi - Xi+l))I L+tang , t ana FS
where VV1 = weight of part of sfice above water level IY2 = weight of part of slice below water level
A si~nplification of the above equation as in Bishop's simplified method leads to the expressiorl:
1 F S = [ ~ ' ~ t t a n B ( ( W ~ + W ~ ) cos a-tJ-h-sec a)]
(W1 + 1V2) sin a 3.8
-
Janbu (1957) had given a rather simplistic and approximate
approach to partial submergence in terms of total stress. Using
his approach the factor of safety of a partially submerged
homogeneous slope is expressed by:
where IVJ , ,u. are constants depending on the angle of internal friction of the soil
C = cohesiou (kN/m2) y = bulk unit weight of soil (kN/m3) y, = unit weight of water ( k ~ / m ~ ) 15 = slope height (m) H, = channel water levels (m)
3.3 Other Methods of Stability Analysis for Rotational Failure Mechanism
For slip surfaces of irregular shapes, limit equilibrium methods such as
Morges tern ilnd Price (1965), Spencer (l967), Janbu(1973) and Sarma
(1979) are usually used, The basic concept in these methods is the same,
the difference lies in the assumption of the interslice forces. Huang
(3983) noted that if both moment and force equilibrium are satisfied the
assumption of interslice force should have only small effects on the
safety factors obtained by any other method. The only problem that
would naturally zuise from analyzing irregulnr surfaces is that because
of the irregular shape of the surface, forces normal to that surface do
-
not meet at a single point. Consequently, the convenience of a single
point thro~igh which a number of force components act and are
therefore lost from a moment equation based on that point is no longer
available. The problem is eliminated in Janbu (1973) by resolving the
forces on a slice vertically and assuming the sum of the vertical forces
to be zero. This res~dts in the expression of the factor of safety as:
z(C'.b + (W - i.J . b t d r ) tan01 secZ a F S = C W . t anu I+t,nn antan 0 3.10
FS
where 10 = ccorection factor depending on soil type and dope geometry (fig. 3.5) and defined nurnericalIy as fo!lows:
for C > O m d 0 > 0; I. = 1 + 0 . 5 ( d / L - 1 . 4 ( d / ~ ) ~ ) for C = 0, = 1 + 0.31 ( d / L - ~ . 4 ( d / ~ ) ~ )
C = effectiveness cohesion (kNl/rn2) b = width of slice m)
, u = pore pressure I kx/rn2) 14' = bulk weight of slice (kN) dz = resultant interslice foi-cc jkN) '0 = angle of internal friction (clegwe) L = span of potentially unst,able soil mass (m) d = relative depth of potentially unstabIe soif mass (m)
Some of the geometrical considerations of Janbu (1973) are illustrated in
fig.(3.5a). The solution to equation (3.10) requires an iterative procedure
in which successive values of FS are substituted until;
-
Slip Surface
a ) Explanatary dlaqram of peamelrlcal mrr ldmra l i o n a tn Jan but Method
C o r r s c ? l o n toc tor char t tar dan b u i Me1 hod
0 0.2 0 3 0.4
R A T I O d j L
Fig. 3.5. Geometrical considerations and correction factor for
Janbu's method
-
The correction factor (fo) can result in an increase of 13'' in the factor of
safety (Bromhead 1986). Landslides with small (d/L) ratio are
thus more accurately analysed. In riverbank, L is generally small and
the (d/ L) ratio is often large. Therefore Janbu's method is not very
suitable for riverbanks.
3.4 Analysis of W ~ d g e Mechanism o f Failure
In the wedge mechcanism of fd~u-e , the unstable soil mass is assumed
to be approximately bound by two or three intersecting planes of
weakness. The wedge analysis gives a satisfactory estimate of the safety
factor (Lcmbe and Whitman 1969) although the method of slice ccm be
used for solution of such problems. The wedge mechanism is generdy \r
suitable o d y for blo&y soil rock masses.
The shear resistance along the segments of the failure surface is
expressed in terms of the applicable strength parameters and a safety
factor which is the same for all segments.
3.5 Toppling Mechanism of Failure
Toppling by definition is the overturning of columns or blocks of earth
mass about some fixed base. According to Zcvuba and Mencl (1969) the
-
earliest reported recognition of toppLing of geological materials in
scientific literature was probably in the 1950's. de-Freitas and Watters
(1977) reported several field examples of toppling failures. Ashby
(1971), Teme (1982) and Jarvis (1985) used physical models to study
toppling failure. Ashby's work considered the simple case of a rigid
rectangular block on a steeply dipping phne and established the
relationship between the slope of the plane and the dunensions of the
block (fig 3.6)' such that equilibrium exists when:
. .. where d-breadthofblock
h = height of block a ='dip of the base plane
when b/h > t.an a , the block is stable when tan > tan 0, sliding occurs when b/h < t,an a and 0 .: a toppling and sliding occur simultaneously
While Jarvis (1985) extended Ashby's criteria to cope with
non-rectangular blocks (produced essentially by non-parallel joints),
Teme (1982) investigated the behaviour of blocky geological materials
a ure. undergoing toppling f il
-
3.6 Analysis of Riverbank Overhangs
Thorne (1978) identified three mechanisms of failwe of bank overhangs
and proposed methods for their analysis. These mechanisms include
shear, beam and tensile f d w e of overhang soil masses (figs 3.7 to 3.9).
3.6.1 ShearMechanismof Failure
The shear failure involves displacement along a vertical plane such as
AA (fig 3.7). Such failures will be expected if the shear stress exceeds
the shear strength along AA. Numericdy this condition may be
expressed by:
wher; 1.V = weight of overhang (kN) T, = shear st-rength per unit lerlgth (kIV/m2) H = height of overhang (m) d t = depkh of crack (m)
A factor of safety against shear failure can be defined as the ratio of shear strength to the shear stress
Ts F S , = -
S s
where S, = shear stress (k8/m2). Since shear sbress is. due entirely to the weight of t,he ovehang, it can be equated to:
-
T but T3 = 9 wl~ere I-r, = compressive strength [k~/m') . Therefore
Substituting 3.14 into 3.15 yields
where Y = m i t weight of soil ( k ~ / n ~ ~ ) B = widt.h of overhang (m)
Equation 3.16 is an expression of factor of safety against overhang shear
fLdure in terms of measurable p~ammeters,
3.6.2 Beam Mechanism of Failure
Beam mechanism of failure results from the rotational moment due to
the self weight of the overhang (fig 3.8), overcoming the moment due to
cohesion along AA. In this failure mechanism, the overhang fails by
rotation of the block forward into the channel. The cohesion within the
overhang should be strong enough to preclude any form of
disintegration during this failure process.
-
GEOMETRY OF BLOCK ON INCLINED PLANE
10 2.0' 30' 4 0 5 0 60 70 80 90
BASE PLANE ANGl F 'b - nFGRFFS
Fig. 3.6. Conditions for sliding and toppling of a block on an
inclined plane af(nfter Hoek and Bray 1977)
-
( a UNFA ILED CONOlTlON ( b) SHEAR FAILURE
Fig. 3.7. Analysis of shear failure overhang (after Thcvne 1978)
C Z I Compressive Zone) "143- Nwtrol axis I
Fig. 3.8. Analysis of rotational beam (after Thorne 1978)
Fig. 3.9. Analysis of tensional failure of overhang (after Thorne
1978)
-
In the analysis of a beam mechanism of failure, Thorne (1978) used the
concept of neutral axis common to beams in structural mechanics.
Above the neutral axis, it is assumed that the overhang is in tension
while below it the overhang is in compression. An approximate
location of the neutral axis can be calculated from a Mohr-Coulomb
diagram of the soil material (Appendix I).
At the Limiting condition of a beam failure, both force and moment
equilibrium are satisfied. These conditions are expressed numerically
first by resolving forces horizontcaUy with respect to AA which results
in: , , '.
i
where Tt = tensile strength (kN/m2) T Z = length of tensile zone (nl) Tc = compressive strength (kiY/m2)
C Z = length of compressive zone (m)
and second by tCzking moments about the vertical or horizontal axis
which yields:
-
where TS, = tensile stress.
Since failure by the beam mechanism is considered to occur when the
tensile stress overcomes the tensile strength, the factor of safety against
failure may be defined as:
substituting equation 2.18 into 2.19 yields:
\
3.6.3 Tensional Mechanism of Failure
Tensional mechanism of failure occ~us across a horizontal plane such
as a bedding plane at the outer fibre below the neutral axis when the
self weight of the ccmtilever overcomes the material cohesion (fig 3.9).
At f d u r e , the part of the overhang below the weak plane is detached
and translates vertically downward. Numerically, this failure
condition is expressed (Thome 1978) by:
-
where Tr. = tensile strength (kPl/rn2) B = width of overhang (m)
Y = bulk unit weight of soil (k3/rn3) d = thickness of underpart of overhang involved in
tensional failure (rn)
A factor of safety against failure by tensional mechanism is thus
defined as:
The weakness in Thorne's analysis is the implicit assumption that the \
entire overhang is involved in the failure process. This is not correct for
soils in general and as is exemplified in the Niger delta where gradud
disintegration of overhang is common. The part of river bank overhang
that is involved in failure is determined by the location, depth and time
of development of tension crack.
3.7 Probabilistic Methods of Analysis
N1 the stability andysis methods described so far are deterministic, in
that the shear strength of soils, the loadings applied to the slope and
-
the factor of safety are assumed to have fixed values although in real
field situations, large variations in shear strength and in loading
frequently exist. The probabilistic method which evaluates the factor of
safety in terms of a probabilty of failure attempts to account for the
nahual variability in property. However, because a large number of
tests is normally required to ascertain the variability of the shear
strength, the probabilistic method is rarely used in practice and is also
considered expensive for a developing country like Nigeria.
-
4. RESEARCH M l i ~ O D O L O G Y
4.1 htrodnction
This research specifically examined bank failures along Rivers Niger,
Nun, Forcados, Orashi and h o and a few of their distributaries (fig.
4.1). These rivers traverse the entire Niger Delh and so provide a
regional perspective.
4.2 Field Measmrnents
Fieldwork to idenbfy soil types and. their spatial distribution was
carried out by land and sea routes to the study area. This led to the
modification of the engineering soil map by Akpokodje (1987).
Based on the modified engineering soil map, the Niger delta was
sub-divided into four zones. These zones correspond to the soil groups
differentiated in fig. 2.8. Typical sites were then selected from each
zone for detailed observation and measurement. These sites include
Ndoni, Akitlima, Agbere, Port Harcorut, Opobo and O w a .
The measurements carried out include soil pro+rties (cohesion, angle
of internal friction, bulk tmit weight), recession rates of riverbanks and
flow velocity. The physical process of bank erosion along a 250x11
-
Fig. 4.1 Map of the Niger Delta showing drainage pattern
-
stretch of river bank in each site was carefully observed. The
monitoring of recession was based on indicator pegs installed exactly
10m from the immediate bank at each of the sites. The pegs were
wooded stakes (50 x 50 x 300mn1) driven into the ground. A similar
approach was adopted by Hooke (1979,1980), Thorne and Tovey (1981)
and Hagerty et al (1983). The approach enabled some quantitative
measure of material removal or deposition at the site to be readily
determined.
Site inspection to locate areas of bank instability was carried out on
speed boat and by canoeing along the rivers. Active inactive bank
slides were mapped. h evaluation was made regarding the type of
failure cmd whether or not soil type played a significant role in
inducing failure. The incidence of toe erosion was assessed by
considering the seepage characteristics of the soil, while the location of
each slide was assessed by considering the l~ydrodyn&tics of the river ,'
systems. ?.
Twenty five riverbank sites within the study sea were selected for
detailed studies. The selection of each specific site was governed by the
-
presence of recent riverbank failures. However, an attempt was made
to select sites that represented alI sub-environment within the large
depositional environment of the delta to observe changes in the pattern
of erosion and bank recession. This was necessary to high-light
specific environmental influences on the problem. In some of these
sites, monitoring schemes were set up and observations made on a
regular basis during the study period.
Water Level Measurement
Channel water level was measured at eight locations I
area as shown in (fig. 4.1). The measurement of water level
commenced with the setting up of Temporary Bench Marks (TBM) and
gauge station (fig. 4.2). Thereafter the water level was measured by
reference to the scale of the gauge on a regular basis. These tasks were
carried out jointly with the Flood and Erosion Division of Rivers State
Ministry of Works and Transport, Port Harcourt. f
Riverbank Profile Measurement ',
Riverbank profiles were measured using regular surveying instruments
including a theodolite, an optical clinometer, a geological compass,
-
BENCH MARK /'
( b ) IRON
BENCH M A R K
SCALE 1- 1 : 25
WATER GAUGE
Fig. 4.2. Water Gauge System -
-
tape and ranging poles. The optical clinometer was used to estimate
average bank height and inclination where riverbcanks were
inaccessable. Because it is difficult to detect recessions with this
technique only, measurement was complimented with the use of
reference pegs (Jacob's rods) which consisted of easily identifiable thin
rods with yellow flags. The geological compass was used to measure
the inclination of bank slopes in places where the banks were
accessible. The tape was used for h e a r measurements including the
areal extent of riverbank failures.
C h m d Cross-Section Measurement
The profile of the river channel was determined by echo-sounding from
the water surface at a sufficient number of points along the breadth of
the river. Echo-sounders are electronic devices which measure the
travel t ime of accoustic waves. The principle of the echo-sounder is
based upon:
(i) water being a good medium to propagate dound waves.
(ii) sound waves being very well reflected by the riverbed.
-
During field use, the echo-sounder was callowed to hang over the side
of an out-board engine boat. As the boat travels across the river
channel the echo-sounder generates transmits accoustic waves to
the riverbed which reflects these waves. The arrival of the reflected
waves on the surface is recorded by a hydrophone. The time lapse
between transmission and reception of an accoustic pulse is a measure
of the depth to the riverbed. From these depth measurements, the
cross-sectional area of the channel can be calculated.
Flow Velocity Measurement
Flow velocities were measured using the propeller-type current meters.
The current meter was introduced into the river and readings on the
meter taken at. the surface and at least three intervals on the vertical to
the riverbed. The procedure was repeated for other verticals in the
cross-section with the same current meter. From these measurements,
a mean velocity (V) was determined using the .4rapezoidd rule
expressed numerically by:
-
where the parameters are as illustrated in a typical velocity profile (fig.
4.3).
The product of the average velocity (11) and the cross-sectional area
gives the dischc?xge.
So3 Sampling
The selection of a sampling technique in the riverbanks was determined
by the soil type and quantity desired for testing. Both disturbed and
relatively undisturbed samples were takgn for laboratory shear and
permeability tests. Here disturbance has been qualified, for even the
best s a m y h g technique causes some mechanical disturbance (Bishop
1966. Three techniques were used in obtaining relatively trndishubed
samples.
(1) A U-4 sample tube was driven by a scampler head to an
appropriate depth excavated to the surface. The tube was then cleared
up, seded and transported to the testing laboratory.
(2) The 3 8 m diameter cylindrical s m P h tubes with piston
sampler were also employed. In order to avoid the development of
-
0
'I Fig. 4.3.
f d i .
A
Typical velocity profile in a river channel
-
large tensile stresses as the sampler was prdled out, two precautions
were observed:
(i) a rest period was doeved, so that f i d i adhesion and friction
between the soil and tube codd develop.
(ii) the scvnyle tube was turned at least two revolutions to shear the
sbil at the bottom end of the tube. OnIy tubes with sufficiently sharp
and tappered cutting edges were employed in order to minimize
sample disturbance.
(3) Rectangular blocks of samples were excavated and trimmed.
This technique was applied mainly to surface sediments. Excavation
of samples was done in order to obtain samples that were minimally
disturbed and whose tested properties would very much replicate
properties of the in-situ soils. Bishop (1966) concluded that although
no specimen may be regarded as entirely undisturbed, carefdly
excavated and trimmed block samples are often the least disturbed.
Field Tests
A number of field tests were carried out mainly at locations where
collection of relatively undisturbed samples was difficult and where
-
knowledge of the soil properties was necess~wy. The field tests carried
out included: (i) field vane shear tests and (ii) field pore pressure
measurement with- stand pipe piezometer.
Field Vane Shear Test
The field vane shear test was required for the measurement of
undmined strength and the determination of the loss of sbength due to
disturbance or remoulding (sensitivity)
-
after failure in order to obtain both peak and residual shear strength
values. After each test, the vane was thoroughly cleaned of all clay
adhering to the vane surfaces. This minimised the disturbance effects
for subsequent tests.
The results obtained from the vane test were subjected to a correction
for friction losses in the system. TlGs was carried out by inserting the
torque rods to a typical test depth (but without the vane affixed) and
measuring the torque required for rotation. From the pec& and
residual values of vane shear strength, the sensitivity of the soil (SN)
was calculated using the relationship:
Peak vcme shear strengkh SN = 4.2
Residual mane shear
The values of SN were compared with standard sensitivity values,
developed by Rosenqvist (l953), thus enabling the soil to be classified
in terms of sensitivifiy. High sensitivity values ( ~ 2 . 5 ) imply that the soil
would lose strength sapidly upon disturbance. Nsq, from the vcme /
results, the maximum reduction in shear strerikth upon disturbance
(SR%) was derived using the relationship: I ,'
-
(v, - v,) . l o o S R =
%J where V,, = peak shear strength
I/, = rcsidual shear strength
Stand-Pipe Pore Pressure Measurement
The set-up for this consisted of a stand-pipe at the end of which was
fitted a porous stone. The stand-pipe was W e d with water coloured
with Potassium Permanganate dye to ensue visibility from a distance
of about 20m (at high water an observer is required to retreat about
20m for safety). The reading of the external water level and the water
level within the stand-pipe was made simultaneously at intervals of 15
minutes. However, at peak flood, observation was terminated because
external water level exceeded the water level, within the tube thus
obscuring i t .
4.3 Laboratory Tests
Laboratory tests to characterise the soils were, m k e d out. These ,
include, index tests comprising Liquid and plastic Limits and natural I.'
moisture content. Others include determination of bullc unit weight,
particle size distribution, shear strength and permeability tests.
-
Triaxial Shear Strength Tests
Shear strength tests were carried out in a txiaxial and a shear box
apparatus. The triaxlal apparatus used has a capacity of five tons and
consists of a compression load frrlme with a multi-speed drive. The
five ton capacity was considered suitable for normally consolidated
alluvial sediments.
The load and strain did gauges together with the pore pressure system
were linked with transducer and connected to a 24-channel data
logging device enabling automatic recording of readings. These
trcmducers were first calibrated to derive transducer constants which
enabled computer processing of the test results. The BS.1377: 2975, was
the standard adopted in the testing programme. Depending on the
type of test, the gear setting was adjusted to produce a suitable
machine speed as follows:
Quck undrained tests; 0.744 mm/minrrte x
Drained tests; 0.00119 mrn/minute ,
Consolidated undrained tests; 0.744 mm/dnute .
-
The direct shear test was carried out on a shear box apparatus
equipped with a drive unit, shear box carriage and a load hanger. A
specimen size measuring about 6 c m x 6 cm was used consistently. A
gear combination of 100/50, producing a machine speed of 0.372
mm/rninute was used in all the tests.
The test procedures adopted follow those specified in ASTM.3080.
Readings of the shear and vertical displacement together with the load
dial guage were recorded at intends of 1.0 minute. Where rapid
changes in deformation were noticed, the interval was reduced to
enable an accurate picture of the behaviour of the specimen to be
obtained.
Particle Size Distribution
The pca.rticle size distribution, permeability, moisture content and
Atterberg Limits were determined in accordance with the British
Standards (BS 1377,1975). K
Bulk Density x>
The density of the sediments was determined by the core cutter method
which involves measuring the mass (M) of a fixed volume of cylindrical
core samples of sod.
-
4.4 Analysis of Everbanks
Both intact and fcziled bank sections were studied and their modes of
failure assessed as either flow slides, rotational, translational, toppling
or a combination of these. The approximate area of each slide was
measured on ground and this provided a basis for assessing the overall
slide activity in a pcuticular reach of the river. On the basis of field and
analytical evidence a probable cause of instability was proposed.
After a mechanism of bank failure was id.entified, the sensitivity of the
bcmk to various factors was analysed using a deterministic technique.
Estimating The ImporE;ance Of Factors Affecting Channel Bank Failure
The imp~rt~ance of various factors czffecting the stability of channel
banks can be estimated from a sensitivity analysis. Rmachandran
-
lczrge number of tests or observations are made. Thus the reliability
approach is uneconomical, especially in a third world country like
Nigeria. For these reasons, a deterministic approach was preferred in
this study.
Using the deterministic approach, the effect on the factor of safety of
hdividual pczrarneters was determined by partial differentiation of the
factor of safety (FS) (equation 3.8) with respect to each pczrarneter. This
will result in a number of equations expressed in terms of observable
and measurable parameters such as cl~annel water level (K.), angle of
internal friction @, cohesion (C), bank height (H), and pore pressure (U).
For example, the effect of cohesion on the factor of safety against
rotational failure of channel bank will be given by:
d F - - L ac (rv, c W2) sin CY
To obtain the effect of pammeters which are not
equation 3.8, the equation is re-expressed in a
/
directly reflected in
way, such that the
parameter can be related to the factor of safety directly. For example,
-
to derive the effect of bank height and channel water level on the factor
of safety, the term (W, + W,) in equation 3.8 is replaced with
(H - LVL) LI; Yl + \,IfL . C* , Y2 where H = bank height
f,; = width of slice Y1 = unit weight of soil above water b e 1 Yz = unit weight of soil below water level
iVL = channel w ~ t e r level
A sensitivity coefficient for each such variable can then be obtained.
Correlation and interdependences between any factors were taken
account of by multiplying the sensitivity coefficient by an appropriate
correlation coefficient. Because the calculated sensitivity coefficients
may vary widely, it is usually convenient to normalise them+to range
beteween I and 0. This enabled graphical comparisons to be carried
out since d coefficients wiU then be of the same order of magnitude,
The method of normalisation employed expressed the relative
sensitivity ( p ) in the form: /
-
A sensitivity coefficient may be positive or negative. A negative
coefficient implies that an increased value of the variable will reduce
the factor of safety. Conversely, a positive sensitivity coefficient
suggests that an increased value of variable wiU enhance stability. The
higher the .sensitivity coefficient, the more important the variable is to
the stabiLity of the river bank. According to Akpokodje (1995) a
comparable resuIt can be achieved using step-wise multi-variate
regression analysis.
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5. RESULTS
5.1 FlXLD MEASUREMENTS
5.1,1 Water Level
A seasonal vcviation of water level was recorded for the rivers studied
in the Niger Delta. The water level began to rise soon after the on-set of
the rainy season in April and reached a peak about the f i s t half of
October (fig. 5.1). During this period, the rate of channel water rise
varied slightly and averaged 0.083 m/day. The dates at which the
water level reached its peak in 1988 varied between 15 October to 17
October (table 5.1). From the second hcdf of October, the water level
began to fall, attaining a m j n i m r m value t o ~ w d s the end of January of
the following year. Thereafter, the water level remained fairly constant
until about April of the following year. The average rate of fal l is 0.25
m/day which is approximately 3 times the rate of rise (table 5.1).
h tidal areas, e.g. Opobo, a semidiurnal tidal cycle is usually
experienced in which the water level attains two peaks and a low
within 24 hours (fig, 5.2). Two tidal seasons (the spring and neap
tides) are distinguished. The water level at sprhg tide varied over a
range of approximately 2m, whereas at neap, the tidal range is reduced . /
to about 1.2m. The durations of rise and fal l of water level in the tidal
areas are fairly equal.
-
Monthly variation of water level at selected locations dong
River Niger and its distributaries (IFERT)
-
WATER LEVEL'^.' REFERENCE
TO h lSL( rn ) 0.8
Fig. 5.2. Variation in water level in Oyobo Town (Data from
NEDECO, 1980)
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Table (5.1) Water Level Variation in Parts of the Niger Delta For 1988
Rived Maximum Grcck Wxtcr
Abovc
River Niger
River Nun
River Xun
Ki vcr Nun
EkoIe Greek
Ekole Creek
River
6 Ocr..
15 Oct.
15 Oct.
9 Oct.
17 Oct.
17 Oct .
16 Oct.
15 Jan .
20 Jan.
20 Jan.
7 Jan.
21 Jan .
21 J a n .
20 Jan.
Fate of iicc c ~ k n j/w Oct. & 30 J;m. (M/d:ry)
0.110
0.271
0.296
0.100
0 -229
0.221
0.250
At the boundary of the tidal zone with the fresh water zone, there are
periodic reversals of flow direction and water level (fig. 5.3). Between
January and August, the tidal influence on water level is significant,
with flow directions regularly reversed. From September to P-
November, the reversal of flow was no longer experienced due to the \
overwl~eelming impact of the flood water from the upstream of the river
system.
-
5.1.2 Riverbank Profiles
Measurement of riverbank profiles was carried out in locations dong
three major river routes in the Niger Delta, namely; Rivers Niger, Nun
and Orashi (fig. 4.1). The regional stratigraphy along the river routes is
as shown in (fig. 5.4). Various riverbank forms were observed (fig 5.5).
The riverbanks range in height from 1.2m to about 15m. The highest
baxk occur upstream. Towards the sea, the bank height is reduced. In
Ndoni for instance, some banks measure 15m in height whereas in the
most southerly parts of the delta, e.g. Bonny, the bcmks are generCdy
less than 3.5m in height.
A common feature of the riverbanks irrespective .. of the
sub-environment is their steep bank angles which are generally above
45 degrees. The top sections of the bank profiles are nearly always
vertical. Sometimes, the banks are obkse in inchnation as illustrated
by the slope profiles in Ndoni (fig 5.5a), Agbere (fig 5 .5~) and #-
Agudma (fig 5.5d). To a large extent, the Gank profiles me ':
geologiccaUy and stratigraphically controlled as was earlier reported by
Henkel(1867). The granular and more erodible &ata tend to be gently
inclined while the cohesive layers tend to be steeply inclined.
-
Fig.5.6. Changes in Riverbank profile at Agbere
Fig.5.7. Changes in Riverbank profile at Kaiama
Y E N A G O A
Fig. 5.3. Monthly variation in water levei at a typical tidal
boundary (Perernabiri) in the Niger Delta (IFERT)
-
Fig. 5.4 Regional stratigraphic models of riverbank in the study
area
-
The bank faces and crest are frequently cracked. Cracks as deep as
1.2m are common. Most bank faces have accu~xundations of debris
arising from bank failures. The slide areas range from 29m2 to 81m2.
The toe area of the banks are gener'dly steep (usually between 80 and
90 degrees) due to constant presence of wave activity. Profiles of three
bank sections located in Agbere, Kaicvna and Yenagoa monitored
between 15 November, 1988 and 30 November 1990 are shown in figs
(5.6-5.8). Clearly, recession is apparent in each of the banks. However
the amount of recession is uneven although these bculks are located
dong the same river, and have comparable soil type and bmk height.
This is due to differences in the soil properties, pore pressure,
seconbcuy currents and boundqr shear stress associated with the
meandering nature of the rivers.
Bank profiles appear to reflect the combined actions of all geomorphic
processes in operation in the area. A dose exahination of the
geornorphic processes in relation to bank fahure have led to the
identification of toe erosion, soil type, high current velocity as some of
the pertinent factors causing recession. Although granular and less
-
cohesive strata within bank profiles tend to be more erodible, factors
other than soil type clearly contributed to observed recession. This is
exemplified by one of the monitored bank profiles (fig, 5.7) in which
the preferential erosion of the bottom sandy strata resulted in
undermining = ~ d consequent mass failure and retreat of the bank.
5.1.3 Flow VPl~city
Flow velocity and flow depth were measured by IFERT (1983) in
Agbere, Sabagreya, Amassoma and Egbecli. Shdtaneous
measurement of velocity and flow depth was necessary to calculate
discharge as well as investigate any possible relationship between the
~ M T O variables. Discharge values cdcdated for these locations at
different times are presented in table 5.2.
At Agbere, four sets of flow velocity measurements were made across
the river cros+section (fig. 5.9). The highest velocity was recorded just
before yec& flood on 11 September 1983. Although tKe flow velocities
varied, the average flow velocity for each measurement was
consistently higher than 0.75 m/sec. ,,
-
Fig. 5.8 Changes in riverbank profile in Yenagoa
-
The result of flow velocity measurement at Sabagreya showed wide
variations in time and across the channel cross-section (fig. 5.10). The
highest velocities occur at the steep concave banks. Towards the
convex bank, the velocities are reduced at average rate of about 2.2 x
lo5 m per second. As the water level increased, the flow velocities and
discharge dso increased. Average flow velocities increased from 0.62
m/sec by 9 July to 1.10 m/sec by 7 October at peak flood and fell to
1.01 m/sec by 18 October, 1983.
At Amassoma, the average flow velocity varied with time from 0.41
m/sec by 7 July to a peak of 1.09 m/sec by 5 October (fig. 5.11). The
flow velocity fell thereafter to 0.73 m/sec by 19 October. .. Velocity
across the channel at any given t h e was however fairly constant.
At Egbedi creek, the flow velocity was somewhat evenly distributed
across the channel (fig. 5.12) with the maximum velocities occuring
during peak flood. At low water, velocity estimates obtained by timing
the displacement of floating objects show averag'e values of 0.22 m/sec.
,.'
-
DISTANCE FFlOU L E F T R l h S
Fig. 5.9. Velocity profiles a c m s Nun River at Agbere (Dah from IFERT , 1983)
-
b 9 J u l y ,983
Fig. 5.10. Velocity profiles across River Nun at Sabagreya (Data from WERT ,1983)
-
Fig. 5.11. Velocity profiles across Oguobiri Creek near hmassoma (Data from I F ~ R T ,1983)
-
I I I 1 I i I I 20 4 0 60 80 100 I 2 0 140
DISTANCE FROM L E F T BANK
Fig. 5.12. Velocity profiles across Egbedi Creek (Data from IFERT , 1983)
-
Table (5.2): Average River Discharge From Selected Cross-Sections at Different
periods (Data from IFERT, 1983)