On river cross-sectional change in the Niger Delta

Geomorphology 34 Ž2000. 111–126 www.elsevier.nlrlocatergeomorph

Technical Note

On river cross-sectional change in the Niger Delta T.K.S. Abam ) , W.O. Omuso RiÕer Engineering Research Group, Institute of Geo-sciences and Space Technology, RiÕers State UniÕersity of Science and Technology, P.M.B. 5080, Port Harcourt, Nigeria Received 10 September 1996; received in revised form 12 November 1999; accepted 19 November 1999

Abstract A network of dominantly distributary river systems dissects the superficial deposits of the Niger Delta comprising alluvial sediments. Changes in river cross-sections are instigated mainly by bank failures, fluctuations in discharge, and bed degradation by fluvial processes. The relative importance of factors causing river cross-sectional change was ranked, based on a deterministic sensitivity technique involving partial differentiation of soil properties, flow characteristics, and geometrical parameters of the river channels. Analysis suggests that steep bank inclination and high flow velocityrdischarge are the major causes of cross-sectional change, while interlocking of soil grains is the major erosion-restraining factor. Sensitivity coefficients were used further to generate susceptibility indices, indicating the vulnerability of channel cross-sections to change. Based on this, the risks of channel cross-sectional change were compared at different sites. q 2000 Elsevier Science B.V. All rights reserved. Keywords: river cross-section; Niger Delta; erosion

1. Introduction Changes in river cross-section are caused by several factors. These factors can be broadly classified into three, namely: Ž1. fluid-flow related factors, Ž2. soil-related factors, and Ž3. geometrical factors. The actions and inter-relationships of these factors have been variously interpreted. A qualitative evaluation of these factors, in which the magnitude of the forces acting on the river bank

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Corresponding author.

is 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 Ž1982.. Thorne Ž1978. also recognised various forces on a channel bank during his study of River Severn in the United Kingdom. First, he recognised that soil material may be entrained from the bank and transported downstream. Second, he recognised that the flow may scour the bed at the base of the bank Žincreasing bank angle and height. to bring about gravitational failure of an intact bank. Hooke Ž1979. and Charlton Ž1982. also noted these observations as the two main processes driving riverbank retreat. A widely accepted notion is that rivers scour at the narrow sections and deposit materials thus re-

0169-555Xr00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 5 5 5 X Ž 9 9 . 0 0 1 2 9 - 4

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T.K.S. Abam, W.O. Omusor Geomorphology 34 (2000) 111–126

moved at the next wide section downstream ŽPeterson, 1986.. This action causes the wide sections to fill up and occasionally leads to the attack of channel banks. The Netherlands Engineering Consultants ŽNEDECO. Ž1980., on the other hand, considered the problem of cross-sectional changes on the basis of equality between inflow and outflow of water and sediment from a given cross-section. The divergent approaches used by these workers suggest an absence of a common understanding of cross-sectional changes. Consequently, it has remained difficult practically to predict future river cross-sections for different reaches and locations accurately. The reason for this difficulty is partly due to the probabilistic nature of some of the factors, such as variable sediment load, engineering properties of the surrounding soils, and seasonal variability of flow velocity and discharge. Because of the present inability to predict accurately the future changes

in river cross section, utilization of rivers for navigation cannot be effectively carried out. This paper therefore, examines the cross-sections of the Niger Delta river system and places them in perspective, to develop a simple basis for evaluating changes in river cross-section.

2. The river systems of the Niger Delta The Niger Delta is situated in the coastal sedimentary basin area of southern Nigeria ŽFig. 1.. It covers an area of more than 36,270 km2 . Asseez Ž1974. ascribed the formation of the delta to the structural movement of the earth’s crust and the activities of fluvial processes of erosion and sedimentation. This led to the establishment of an extensive sedimentary flat criss-crossed by several distributary rivers and creeks — the Nun, Forcados, and Orashi rivers

Fig. 1. Major rivers and creeks in the Niger Delta.

T.K.S. Abam, W.O. Omusor Geomorphology 34 (2000) 111–126

113

Table 1 Physical characteristics of some rivers in the Niger Delta SrN

Name of river or creek

Length Žkm.

Width of water channel Žm.

Height from water level to ground level at dry season

Slope of river

Station

1 2 3 4 5 6 7 8

Nun Forcados Sagbama Ekole Egbedi Orashi Ndoni Taylor

195 196 39 78 38 306 42 95

425 518 218 270 180 210 160 100

9.5 8.5 7.3 5.9 6.2 7.3 5.8 11.1

2 = 10y5 NrA 1.23 = 10y4 NrA NrA 6 = 10y5 1.16 = 10y3 NrA

Kaiama Patani Tungbo Yenagoa Egbedi Mbiama Ndoni Okobiri

being the major ones ŽFig. 1.. Others that have significant lengths include Sagbama and Ase rivers, Bomadi and Nikoro creeks, Aroh creek, Oreri creek, Taylor creek, Ekole creek, Egbedi creek, and Brass rivers. Table 1 summarises average lengths, widths, and depths of a few of the major rivers and creeks. These rivers have more distributaries than tributaries. Consequently, they are narrower in width in their

lower reaches. They have many meanders and variations in width. The river water level varies during the year in response to the seasonal rainfall distribution. The water level rises soon after the onset of the rainy season in April and reaches a peak in about the first half of October. During this period, the rate of channel water rise varies slightly but averages 0.083

Fig. 2. A comparison of water level and bank-failure frequency in the Niger Delta Ž1998..

114

T.K.S. Abam, W.O. Omusor Geomorphology 34 (2000) 111–126

mrday. From the second half of October, the water level begins to fall, attaining a minimum value towards the end of AprilrMay of the following year. The average rate of fall of water level during recession is relatively rapid Ž0.25 mrday. compared to the rate of rise and the ease of flow of water through the soils as indicated by the permeability of this

predominant soil type Ž3.2 = 10y7 m sy1 . in the area. 3. Factors affecting channel cross-sectional change While a great many factors affect river channel cross-section directly, others affect it indirectly by

Fig. 3. Velocity profiles in selected river cross-sections ŽIFERT, 1988..

T.K.S. Abam, W.O. Omusor Geomorphology 34 (2000) 111–126

115

Fig. 3 Ž continued ..

their influence on the more relevant factors. The most important variables were listed by Peterson Ž1986. and include bed and bank resistance to flowing water, flow velocity and discharge, longitudinal slope, sediment load, geology, and anthropogenic activities.

4. Bank failure input to cross-sectional changes Bank erosion and retreat occur in many ways, primarily as a result of one or a combination of the following: Ži. removal of soil particles from the bank surface continuously over a period of time,

Žii. sequential failures of small segments of bank material, and Žiii. failure of a single large segment of bank material.

In these processes, bank failure is influenced by the mechanical properties of the in-situ bank material, river water level, bank height and inclination ŽThorne, 1978.. The most common cause of bank failure arises from the attack of river flow at the toe of a bank. As the toe erodes and the eroded material is carried away by the flow, the bank progressively steepens to where it becomes unstable and fails either as a series of successive small failures or as a large failure of a single large segment of the bank.

116

T.K.S. Abam, W.O. Omusor Geomorphology 34 (2000) 111–126

Hagerty et al. Ž1981., Thorne Ž1978., and Abam Ž1997. have described and analysed a wide range of mechanisms associated with alluvial bank failures. These studies have also identified locations and conditions in river systems favouring particular mechanisms of bank failure. For example, whereas rotational failures are common in high banks, cantilever or overhang failures are frequently observed in low banks Žwith height less than 4.6 m.. The frequency of bank failure, and hence, of recession rates are also higher for high banks. Rotational failures, apart from being the most common mechanism of bank retreat in the Niger Delta, also involve a larger material displacement in a single incident, compared to the other mechanisms. Bank failures introduce localised changes to channel geometry. However, when widespread, bank failures can affect the flow regime in a river system. The incidence and frequency of bank failure episodes are closely related to the location of the cross-section Žbend or crossing. and to the variation of river water level. For the recession rates recorded in the Niger Delta, the combination of excess pore pressures created by a recession rate far in excess of permeability, and loss of passive support trigger bank failures. Consequently, there is a concentration of bank failure episodes following the loss of this passive resistance. The relationship between channel water-level variation and the distribution of bank failures is illustrated in Fig. 2. The concentration of bank failure episodes immediately following flood recession suggests that riverbanks are very sensitive to the removal of passive resistance. This sensitivity appears to be more pronounced during the early stages of recession in water level, particularly in high and steep banks. The relatively high bank-failure frequency on the rising limb of the water level is due to the combined effect of the removal of pore water suction and increased soil unit weight. Many bank failures in the Niger Delta Žup to 78%. are located on the concave bends of rivers at points just downstream of the maximum curvature. The higher velocities and eddies at the bends scour and steepen the banks ŽCrickmay, 1960; Bathurst, 1979., thus increasing their vulnerability to collapse after the passive support from the high water level is lost or is by increased gravitational motive force.

5. Flow velocity Particle erosion and entrainment is possible only when flow velocity exceeds a certain threshold. The applicability of this rule in the Niger Delta was demonstrated by the Netherlands Engineering Consultants ŽNEDECO. Ž1980.. This threshold velocity is dependent mainly on particle characteristics such as specific gravity, shape, and size. Entrainment of particles in cohesive soils is usually more difficult than in rounded granular soils ŽHooke, 1979. because of the action of inter-particle forces. Within the channel, flow velocity varies depending on location and depth, and on the season in the year. Results of systematic study of flow velocity variation in the Niger Delta are very few, outdated, and lack the desired detail ŽNetherlands Engineering Consultants ŽNEDECO., 1961.. Flow velocity measurements by the Institute of Geo-sciences and Space Technology ŽIGST. at four pre-selected locations, Agbere, Sabagreia, Oguobiri, and Egbedi, form the basis for relating flow velocity to cross-sectional change. The Flomate model 2000 current meter was used in each case. The survey boat for the measurement was anchored properly at the fixed position to avoid drifting. The length of the cross-section was determined before velocities were measured in segments of equal length. At each point, the current meter was lowered into the water and the velocities were measured at 0.2, 0.6, and 0.8 of the total depth. In

Table 2 Variation in percentage distribution of discharge between Rivers Forcados and Nun Survey period

Forcados River Ž%.

Nun River Ž%.

1953r1954 1959r1960 1978 1979 1980 1981 1982 1983 1984 1985–1997 1998

55 60 55 55 55 55.01 54 55.01 55 No data 46

45 40 45 45 45 49.99 45.01 44.99 45 No data 54

T.K.S. Abam, W.O. Omusor Geomorphology 34 (2000) 111–126

addition, the velocities at 1.0 m below water surface, midway, and 1.0 m above riverbed, were measured. These values are aggregated and averaged to arrive at a segment velocity. At Agbere, four sets of average flow velocities were measured across the river ŽFig. 3a. over a period of 4 months between July and October 1983. As expected, segment flow velocity increased with higher water levels. The averaged cross-sectional velocity was consistently higher than 0.75 m sy1 for water levels greater than half bank-full. The flow velocities at Sabagreia ŽFig. 3b. showed wider variations in time and across the channel due to the geometry of the channel. Higher velocities occurred near the concave or outer banks Žat bends.,

117

where they also scoured and transported debris from bank failures. Towards the inner bank, the velocities were reduced to an average of about 0.25 m sy1 . At Oguobiri, average flow velocity varied with time from 0.41 m sy1 on July 7 to a peak of 1.09 m sy1 on October 5 ŽFig. 3c.. The flow velocity fell thereafter to 0.7 m sy1 by October 10. At Egbedi creek, the flow velocity was somewhat evenly distributed across the channel ŽFig. 3d. with the maximum velocities occurring during the peak floods. Flow velocity estimates close to riverbeds based on the logarithmic distribution of the vertical velocity profile gave values consistently greater than 0.2 m sy1 , a critical value suggested by the Netherlands Engineering Consultants NEDECO Ž1980. to be the

Fig. 4. Morphological changes in sand bar location, shape, and size between 1953r1963 and 1980.

118

T.K.S. Abam, W.O. Omusor Geomorphology 34 (2000) 111–126

threshold above which particle entrainment can be expected. This implied that the channel bed was mobile, and the cross-section was dynamic.

6. Discharge, sediment flow, and morphological dynamics The bulk of the discharge into the Niger Delta is routed principally through Rivers Forcados and Nun,

and less significantly through Orashi River. The discharge into the Niger Delta and its distributaries between the Forcados and Nun Rivers for selected years from 1953r1954 to 1998 is given in Table 2. This shows a declining discharge due to the impoundments of upstream dams. In response, the flood plains of the Niger Delta have shrunk in size, resulting in the alteration of channel configuration. Related to the discharge is the sediment transport. Whereas the Forcados River predominates in sedi-

Fig. 5. River cross-sectional changes in selected locations.

T.K.S. Abam, W.O. Omusor Geomorphology 34 (2000) 111–126

119

Fig. 5 Ž continued ..

ment supply to the western front of the delta, the Nun River largely controls sediment supply to the eastern delta. The bedload transported through the Niger Delta consists largely of medium sand that amounts to 0.31 = 10 6 m3 ŽNetherlands Engineering

Consultants NEDECO, 1961.. Although this amount has drastically changed over the years, the bulk of the sediments that eventually reaches the delta front has predominantly been through Forcados River ŽOyegun, 1993; Abam, 1995.. Beets Ž1989. ascribed

T.K.S. Abam, W.O. Omusor Geomorphology 34 (2000) 111–126

120

the reason for the preferential discharge through Forcados to the position, shape, and size of the sand bar at the Niger bifurcation into the Nun and Forcados. The quantity of sediments discharged through the delta is normally at a maximum during the period from September to October and lowest from December to May. This is because of the increased competence of the rivers consequent on the large discharge ŽNiger Delta Environmental Survey, 1995.. The location, shape, and size of these sandbars are altered periodically in response to the morphological dynamics of the reach, and this intrinsically determines the distribution of discharge into the river tributaries. Fig. 4 is essentially a comparison of the sand bar scenarios at the Niger river bifurcation into Nun and Forcados between 1953r1963 and 1980, which are responsible for the observed discharge distribution trends. The change in discharge distribution between the rivers Nun and Forcados observed in the survey of 1998 appears to be associated with the dredging in 1993 of a 2.5 km section of the river Nun, from Asamabiri to Odoni ŽNiger Delta Environmental Survery, 1998.. The dredging exercise deepened the channel cross-section and introduced higher flow velocities; and although the channel width was narrower, the discharge was considerably higher than the Forcados. The switch in discharge function, which gives River Nun an edge over the

Forcados will certainly be accompanied by morphological changes whose extent is yet to be assessed.

7. River cross-sections All the river cross-sections investigated ŽFig. 5. revealed irregular riverbed profiles, which are constantly changing with time in response to the processes of erosion and deposition. Measuring the area between successive bed profiles across a unit river length and multiplying by an appropriate factor assessed the changes in bed profile. The resultant changes in bed profile were then translated into volumes of eroded or deposited materials by considering a unit horizontal thickness in the cross-section. Results obtained ŽTable 3. suggest that 546 m3 of bed sediments were eroded from Agbere cross-section between July 18 and September 11 as mean velocity increased from 0.5 to 0.9 m sy1 . By October 17, peak flow had passed and mean velocity had dropped to 0.7 m sy1 . Although sedimentation had commenced at this time, much of the eroded material had been replaced. By October 28, the mean flow had reduced further to 0.6 m sy1 with a corresponding material deposition amounting to 338 m3 on the riverbed, leaving only 78 m3 of the bed material unreplaced in comparison to the July river bed profile.

Table 3 Erosion and sedimentation activities in selected stations Location

Date

Average velocity Žm sy1 .

Agbere

18r7r83 11r9r83 17r10r83 28r10r83 9r7r83 5r9r83 7r10r83 18r10r83 7r7r83 2r9r83 5r10r83 19r10r83 9r7r83 5r9r83 8r10r83

0.5 0.9 0.7 0.6 0.6 0.95 1.10 0.9 0.5 0.78 1.25 0.85 0.6 0.83 0.93

Sabagreia

Oguobiri

Egbedi

Area between successive profiles Žm2 .

Volume of materials affected Žm3 .

Predominant type of activity

Rate of change of average velocity Ž=10y2 m sy2 .

10.5 2.5 y6.5

546 130 338

erosion erosion sedimentation

0.76 y0.56 y0.91

4.5 0.4 y8

306 27.2 544

erosion erosion sedimentation

0.63 0.47 y1.8

6 14 13

288 672 624

erosion erosion sedimentation

0.51 1.42 y2.86

6 5

48 40

erosion erosion

0.4 0.3

T.K.S. Abam, W.O. Omusor Geomorphology 34 (2000) 111–126

In Sabagreia, the period of increased discharge witnessed erosion of 306 m3 sediments. The extent of erosion increased between September 5 and October 7 as flow velocity and the discharge further increased. However, by October 18, about 544 m3 of bed materials was deposited, elevating the riverbed beyond the July level. The river cross-section at Oguobiri recorded a similar pattern of erosion with increased flow velocity. In this case, a total of 960 m3 of bed sediments was eroded between July 7 and peak flood on October 5. However, rapid sedimentation was experienced following flood recession. By October 19, only 2 weeks after peak flow, as much as 624 m3 of eroded material had been replaced. Egbedi creek showed a pattern consistent with other cross-sections, but involved smaller material quantities because of the relatively smaller size of the cross-section.

8. Discussion Channel cross-sections change with time and are affected mostly by discharge, sediment load, and bank failure episodes. The discharge of an alluvial river influences its form not only because of the magnitude of the discharge, but also because of the integrated effects of its constant fluctuation. During rising flood stages, the thread of maximum velocity shifts towards the center, where it deepens the river channel. However, at falling stages, the destabilising role of undissipated pore pressure combines with the erosive work of the thread of the greatest velocity that is close to the concave bank. This is the reason that the majority of bank-failures in the Niger Delta occur on the falling stage of floods. Deposition, on the other hand, is determined by the amount and character of the particles comprising the sediment. Generally, low flow velocities are characterised by deposition in the river cross-section. The configuration and geometry of meandering channels are thus determined by the pattern of erosion and deposition. The prediction of when and where future crosssectional change will occur, and the extent of such changes is very uncertain because of the many inter-

121

acting and frequently complex factors involved. However, expressing the risks of cross-sectional change quantitatively in terms of susceptibility indices, could indicate river cross-sections most predisposed to change. To do this, it is necessary to formulate a mathematical relationship for the factors affecting cross-sectional change.

9. Mathematical formulation of factors affecting river cross sectional changes Many of the factors responsible for channel cross-sectional changes are inter-related although such inter-relationships have hardly been expressed quantitatively. This is partly because of the complex nature of the relationship and the absence of data to enable appropriate correlation to be carried out. Perhaps, the most elaborate representations of these factors were by Yan Ž1986. who identified the hydrodynamic force as the main erosive component of flow. This force was expressed as: Pd s g W Co H q D H 4 Õ

2

sin2a 2g

Ž 1.

where D H s wave height Žalso given as Õ 2 brrg .; H s flow height; Õ s flow velocity; g s acceleration due to gravity; B s width of channel; t s radius of curvature; g W s unit weight of water; a s inclination of bank; and Co s coefficient. As described by Carson Ž1971. for initiation of particle motion, erosion will be effected only when this hydrodynamic force exceeds the shear resistance of the soils. In theoretical terms, this implies that a factor of safety against erosion FS e by hydrodynamic process over a unit area of the channel can be defined by comparing the hydrodynamic force to the shear resistance of the soil, thus:

t FS e s

Pd

 2 H q B4

Ž 2.

where t s shear resistance of soils on channel wall; Pd s hydrodynamic force. The shear resistance of the soil is determined by Coulomb’s shear strength relationship. Consequently, Eq. Ž2. can be expressed in full using the

T.K.S. Abam, W.O. Omusor Geomorphology 34 (2000) 111–126

122

modified Coulomb’s shear strength relationship for the soils in contact with the fluids as follows: FS e s

C q  g z y u4 tan f Ž 2 H q B .

½

g W Co H q

Õ2B rg

5

Õ

2

rock slopes was applied in this case. In the present circumstance, this technique requires partial differentiation of the factor of safety against erosion by hydrodynamic force with respect to each of the variables. The resulting sensitivity coefficients are presented in Appendix A. These sensitivity coefficients may be normalised to achieve relative sensitivity coefficients whose values fall between 0 and 1 in order to facilitate comparison. To do this, each of the sensitivity coefficients is divided by:

Ž 3.

sin2a 2g

where C s cohesion; g s soil unit weight; f s angle of internal friction; and z s soil depth affected by hydrodynamic force. The use of the modified Coulomb’s shear strength relationship is justified by its provision for pore pressure, a phenomenon that is commonly responsible for bank-failures. By this equation, the impact of wetting and sudden loss of passive support through rapid flood recession, which is a crucial factor of bank instability can be evaluated. Alternatively, the same equation may be re-expressed in terms of discharge by multiplying both numerator and denominator by the flow depth H as follows: FS e s

½

2

g W Co H q

QÕ rg

5

Õ

2

sin2a

.

dF

2

dF

2

dF

2

½ 5 ½ 5 ½ 5 ½ 5 q

q

dF

q

2

2

dF

2

dF

2

½ 5 ½ 5 ½ 5 ½ 5 ½ 5 ½ 5 q

dF

q

dD

2

dF

q

dOw

2

dt

0.5

q

da

Ž 4.

dg

dÕ

dF

dB

q

q

df

dC

2

C q  g z y u4 tan f Ž 2 H q BH .

2

dF

dw

ŽNote: the terms in the partial derivatives are defined in Appendix A.. This procedure produced the normalised sensitivity coefficients given in Table 4. Based on the absolute magnitudes of the normalised sensitivity coefficients, ranks indicating the relative importance and potential contribution of the various parameters to channel cross-sectional change were established. The ranks Ž R . are in numerically ascending orders of magnitude with the most important variable having the rank of 1 ŽTable 4..

2g

Eq. Ž4. has thus incorporated the hydrodynamic, soil properties, and geometric characteristics of the channel, into a single expression that allows further mathematical analysis. The relative importance of the constituent variables in this equation was then determined from a sensitivity analysis. A simplistic deterministic sensitivity analysis developed by Ramachandran and Hosking Ž1985. for the analysis of

Table 4 Sensitivity values for variables affecting channel cross-sectional change Variable parameter

Sensitivity coefficient

Normalised sensitivity coefficient

Sensitivity rank

Cohesion Angle of internal friction Flow velocity Radius of curvature Width of river channel Flow depth Soils unit weight Unit weight of water Bank inclination Wave height

0.163 4.12 y1.086 6.3 = 10y5 y9.53 = 10y5 y0.095 0.094 y0.633 y3.7 y0.587

0.029 0.73 y0.193 1.2 = 10y5 y1.7 = 10y5 y0.017 0.0167 y0.1125 y0.658 y0.101

5 1 3 10 9 7 8 4 2 6

T.K.S. Abam, W.O. Omusor Geomorphology 34 (2000) 111–126

123

Table 5 Susceptibility indices of channel cross-sections in some local sites LocationrParameter

Agbere

Sabagreia

Oguobiri

Egbedi

Maximum Value

Cohesion ŽkNrm2 . Angle of internal friction Ž8. Flow velocity Žmrs. Radius of curvature Žm. Width of river channel Žm. Flow depth Žm. Soils unit weight ŽkNrm3 . Unit weight of water ŽkNrm3 . Bank inclination Ž8. Wave height Žm. Susceptibility index

28 26 1.0 1650 410 10 19.0 10 85 0.27 y0.517

32 27 1.45 350 400 14 18.5 10 86 0.25 y0.194

37 15 1.20 1500 500 12.5 18.95 10 82 0.25 y0.476

48 25 0.95 1750 130 11 18.75 10 85 0.25 y0.091

48 27 1.45 1750 500 14 19 10 86 0.27

The ranks of the various parameters suggest that interlocking of grains resulting in high angles of internal friction of soils is the most important factor restraining erosion, while steep bank inclination, high flow velocity, and rapid draw-down in river water level during flood recession are the major factors promoting erosion. Although the angle of internal friction is ranked 1 by the sensitivity technique, in reality, it is cohesion that usually contributes most to shearing resistance in low banks. The assignment of the least rank to the radius of curvature of river channels is justified by the observed absence of erosion at low water in many river bends. The concentration of bank-failures at bends is therefore explained by the existence of steep banks, high flow velocities, and gravitational motive forces in this area. In spite of being ranked 4th in terms of sensitivity, the unit weight of water is practically constant unless sediment load approaches very high concentrations. Apart from ranking, the factors affecting crosssectional change, the vulnerability to cross-sectional change of various sites, was compared. By expressing the measured sensitivity coefficients of each variable at a site, as a fraction ŽFV. of the largest value of the same variable amongst the sites evaluated, indices for comparing the vulnerability of sites to cross-sectional changes was generated. FV s

Pi Pmax

Ž 5.

Similarly, the relative impact ŽRI. of a particular variable on the channel cross-section may be expressed as the product of the inverse of the rank and the fraction of the variables. Pi 1 RI s Ž 6. Pmax R The sum of impacts representing the combined effects of all variables on channel cross-section may then be referred to as the susceptibility index, and expressed as: N Pi 1 Si s Ý Ž 7. is1 Pmax R where N s number of parameters considered; Pi s value of ith parameter; Pmax s largest value among the Nth parameter; and R s rank. This concept was applied to four randomly chosen local sites for detailed investigation. The results, which include the calculated susceptibility indices, are summarised in Table 5. The results suggest that the channel cross sections at Agbere are the most susceptible to change, followed by Oguobiri. The suggested order of susceptibility appears to be consistent with the observed changes in river cross-section. 10. Conclusions The factors affecting river cross-sectional change are inter-related, although these have been broadly classified into three groups, namely: those related to

124

T.K.S. Abam, W.O. Omusor Geomorphology 34 (2000) 111–126

fluid flow, those related to the soils, and geometrical factors. The last two constitute bank stability determinants. The contributions and relative importance of factors affecting channel cross-sectional change were evaluated based on field measurements and the application of a deterministic sensitivity technique. This analysis produced coefficients whose magnitude also determines their relative importance to cross-sectional change. The ranking of the coefficients suggested that channel bank steepening and increased

flow velocity are the major causes of change in river cross-section, whereas inter-granular friction of soil grains was identified as the major erosion-restraining factor. Rapid drop in pool level during recession of floods compared to the soil permeability is recognised to be a major contributor to mass bank failure. The sensitivity coefficients were also applied in the determination of vulnerability of sites to erosion. This application produced indices for comparing the risks of cross-section change in different sites.

Appendix A. Deterministic sensitivity relationships for factors affecting channel cross-sectional changes Variablerparameter Cohesion

Partial derivative Numerical relationships Ž2 HqB. d FrdC Õ 2 B sin2a Co g W H q rg 2g

Angle of internal friction d Frd f

½ ½

5 5

Ž 2 H q B . g zsec 2a Co g W H q

Õ2B rg

sin2a 2g

Flow velocity

d FrdÕ

½

Co g W H q

Õ2B

Õ2

rg 4

d Frdt

½ ½

Co g W H q

½

2r2g2

d Frd B

½ ½

Õ2B

Õ2

rg

Co g W H q

Õ2B rg

sin2a

2

sin2a 2g

Õ2

Õ 3B

sin2a

rg

2g

2

sin2a

d FrdQ

½ ½

2g

2g

2g

Ž C q g 2tan u .  2 H 2 q B 4 sin2ag W Co Discharge

rg

g W Co H q

QB rg

2

2g

y Ž C q g tan u . Co g W 2 Hg q 4 Width of river channel

sin2a

sin2a

Õ B

Ž 2 H q B . Ž C q g tan u . Radius of curvature

Õ 3B

5 ½ ½ ½ 5 5 ½ 5 5 5 ½ 5 5 5

y Ž 2 H q B . Ž C q g tan u . Co g W 2 Hg q 4

5

Õ

2

sin2a 2g

Õ3 2 rg 2 2

5

sin2a

T.K.S. Abam, W.O. Omusor Geomorphology 34 (2000) 111–126

Õ 4 sin2a

½

y Ž C q g z tan u . 2Co g W Flow depth

d Frd H

d Frdg

Õ2B

Õ 2 sin2a

rg

2g

z tan u  2 H q B 4

Co g W H q

Õ2B

Õ 2 sin2a

rg

2g

Õ 2 B Õ 2 sin2a

y Ž C q g z tan u . Co H q Unit weight of water d Frdg W

Co g W H q

rg

d Frd a

Õ 2 sin2a

rg

2g

Co g W H q 2

y Ž C q g z tan u . Wave height

d Frdw

Drawdown

d Frdu

2

2

Õ B

Õ 2 sin2a cos a

rg

2g

Õ2B

Õ 2 sin2a

rg

2g

Ž2 HqB.

2

2

Co g W Õ sin a 2g

Co g W H q

Ž2 HqB.

2g

Õ2B

y Ž C q g z tan u . Co H q Bank inclination

5

2

½ ½ 5 5 ½ 5 5 5 ½½ ½ ½ 5 5 ½½ 5 5 ½ ½ 5 5 ½ 5 ½ ½ 5 5 ½ 5 Co g W H q

Soil unit weight

2 rg 2

125

Ž2 HqB.

Õ2B

Õ 2 sin2a

rg

2g

2

y Ž 2 H q B . tan u

g W Co H q

Õ2B

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