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Rivers originate from mountains and hills, pass through valleys, plains and wetlands and then exit to the sea. A drainage basin can simplistically be divided into three zones: headwaters (an upper erosional zone of sediment production), transfer zone (a middle zone of sediment transport with simultaneous erosion and deposition), and depositional zone (and a lower zone of sediment deposition) (Figure 4-1). The actual situation is often more complex, because local geological controls or other factors can produce local depositional zones in the upper basin or local erosional zones in the lower basin.

Figure 4-1 Drainage Basin Zones

Source: Living in the Environment, 1990

The longitudinal profile of the river system tends to flatten through time by degradation in the upper reaches and aggradation in the lower reaches (Figure 4-2). In most natural systems this process is slow enough to be of little engineering concern. However, where the river system or catchment has been interfered with historically, profile flattening may proceed at noticeable rates. In some channelization projects, response of this type has been dramatic.

Figure 4-2 Typical Longitudinal River Profile

Source: Ohio DNR, undated

4.3.1 Headwaters (Mountain Torrents)

These are high-velocity river on steep slopes, often exhibiting a sequence of drops and chutes controlled by large boulders, fallen timber, etc. They are also commonly referred to as Production Zones, through the source of sediment that they can provide for the downstream part of the river.

Erosion and deposition are sometimes confined to severe flood events. Some mountain torrents on very steep slopes are subject to the phenomenon of “debris flows” or “debris torrents” whereby under severe flood conditions the bed becomes fluid and a virtual avalanche of boulders and gravel runs down the mountainside.

Non-alluvial channels have highly developed meanders in solid rock valleys and may have degrading beds. Many mountain rivers are classified as non-alluvial.

4.3.2 Transfer Zone

This zone is effectively a transitional zone between mountain torrents and alluvial fans. Stream velocities decrease as the river channel slope also decreases. The sediment sizes also decrease and meanders start to form.

4.3.3 Depositional Zone (Alluvial Fans)

Alluvial fans generally occur where a stream emerges from a mountain valley onto relatively flat land. They are depositional features typically characterized by alluvial materials and unstable multiple channels subject to frequent shifts or

“avulsions.”

4.4 River Geomorphology

Scientists, engineers and water resource managers are faced on how to work with rather than against nature. Engineers working on flood defense, land drainage, channel stability and navigation interest should balance the design with environmental and other considerations. The need to balance the needs of different interests, sometimes conflicting, makes it essential to take a multifunctional approach. Engineers seek to solve river–related problems while retaining those natural forms and features that allow rivers to transmit the inputs of water and sediment, support diverse habitats and provide a pleasing landscape for river centered recreation. Hence, a comprehensive and reliable morphological analysis and classification system form the essential basis to sound engineering geomorphology. The following section gives brief geomorphological principles.

Most alluvial channels exhibit a natural instability that results in continuous shifting of the river through erosion and deposition, formation and destruction of islands, development of oxbow lakes, and formation of braided channel sections.

The degree of channel instability varies with hydrologic events, bank and bed instability, type and extent of vegetation on the banks, sediment mobility and floodplain use.

Rivers have inherent dynamic qualities by which changes continually occur in the channel position and shape. Changes may be slow or rapid, but all streams are subjected to fluvial forces that cause changes to occur. In these streams, banks erode, sediments are deposited, and islands and side channels form and disappear in time.

River mechanics involves identifying the physical characteristics and understanding the relationship of the actions and reactions of fluvial forces tending to effect change in channel and floodplain morphology. This knowledge enables us to estimate the likely morphological change for river channels and floodplains as a result of fluvial forces, which assists when planning and maintaining the built environment. The potential effect of these dynamic systems

on public infrastructure such as highways and bridges should be identified and understood.

A brief introduction to river geomorphology is provided in the following sections.

More detailed descriptions and information is available in references (such as Thorne C R, Hey R D , Newson M D, 1999 and Melville & Coleman, 2000). Further discussion on sediment processes are also provided in these references, together with the FCSEC guideline for Sabo Engineering.

4.4.1 Stream Types

A general overview of different stream types are provided in Table 4-1.

Table 4-1 Stream Types

Stream Types Sinuosity Index Example Figure

Straight <1.05

Sinuous 1.05 to 1.5

Meandering >1.5

Source: Geocaching, 2009

Sinuosity provides an indicative measure of the stream type. It is measured by the stream length divided by the valley length, as indicated in Figure 4-3.

Figure 4-3 Sinuosity

Source: AMWS, 2007

4.4.2 Straight Streams

Straight channels are sinuous to the extent that the thalweg usually oscillates transversely within the low flow channel, and the current is deflected from one

side to the other. The current oscillation usually results in the formation of pools on the outside of bends while alternate bars, resulting from deposition, form on the inside of the bends.

In alluvial channels, straight stream may only be a temporary condition particularly in sandy channel rivers that are prone to erosion/deposition of mobile sediments. Aerial photography and topographic maps may reveal former locations of the channel and potential directions of further movement.

4.4.3 Braided Rivers

Braiding is caused by mass bank failure (slumping) as well as large quantities of sediment load that is either deposited or remain where the stream is unable to transport. Deposition occurs when the supply of sediment exceeds the stream’s transport capacity. As the streambed aggrades from deposition, the downstream channel reach develops a steeper bed slope. Multiple channels develop on the flatter upstream slope as additional sediment is deposited within the main channel.

The aggraded material may be deposited within the channel to form bars that may build over time to become islands supporting vegetation. At the flood stage, the flow may inundate most of the bars and islands, resulting in the complete destruction of some and reworking of others. A braided stream is generally unpredictable and difficult to stabilize because the channel changes alignment rapidly, is subject to continual degradation and aggradation, and is very wide and shallow even during flooding.

4.4.4 Meandering Streams

A meandering stream consists of winding channel planform with alternating S-shaped bends (Figure 4-4). In alluvial streams, the channel is subject to lateral movement through the formation and destruction of bends (Figure 4-4). Bends are formed by the process of erosion and scouring of the banks on the outside of bends and by the corresponding deposition of bed load on the inside of bends to form point bars. The point bar constricts the bend and causes erosion in the bend to continue, contributing to the lateral migration of the meandering stream (Figure 4-5).

Figure 4-4 Meandering Stream Processes (Source: Ohio DNR, undated)

Source: Ohio DNR, undated

Meandering streams can experience processes such as avulsion and meander cut-off where the stream experiences a wholesale shift in alignment. This commonly occurs when the channel breaks its banks in alluvial rivers with expansive floodplains. The out of bank flows rework the floodplain and short circuit meanders, creating oxbow lakes, or occupy secondary flowpaths. After a cutoff is formed, the stream gradient is steeper; the stream tends to adjust in response to the increase in stream power.

Prediction of the rate and direction of the meander movement can be difficult. A review and comparison of historical mapping and aerial photographs can assist, together with local knowledge and observations. Complex morphological modeling, requiring detailed physical and hydrological data, can also be undertaken to predict the movement.

Meandering streams and rivers with bridge crossing present challenges as the rivers are highly rich in mobile sediment and unpredictable channel planform.

Likewise, highway embankments which may form part of flood mitigation scheme do present the same and similar challenges. Careful consideration is required when works are proposed in the vicinity of type of rivers as they may be flood prone.

4.4.5 Sedimentation Transport

The concept of sediment transport is provided in Annex B.

4.5 Open Channel Flow

Design analysis of both natural and artificial channels proceeds according to the basic principles of fluid mechanics. They are namely: continuity, momentum and energy and are applied in open channel flow. Several important open channel flow concepts and relationship are described in the succeeding sections.

4.5.1 Definition & Basic Principles

4.5.1.1 Energy

As shown in Figure 4-5, the total energy at a given location in an open channel is expressed as the sum of the potential energy head (elevation), pressure head, and kinetic energy head (velocity head). The total energy at a given channel cross section can be represented as:

Equation 4-1

𝐸𝐸𝑡𝑡= 𝑍𝑍 + 𝑦𝑦 +𝑉𝑉² 2𝑔𝑔

where:

Et = total energy, m

Z = elevation above a given datum, m y = flow depth, m

V = mean velocity, m/s

g = gravitational acceleration, 9.81 m/s²

Written between an upstream cross section designated 1 and a downstream cross section designated 2, the energy equation becomes:

Equation 4-2

𝑍𝑍1+ 𝑦𝑦1+𝑉𝑉₁²

2𝑔𝑔 = 𝑍𝑍²+ 𝑦𝑦2+𝑉𝑉₂² 2𝑔𝑔 + ℎ^𝐿𝐿

where:

hL = head or energy loss between section 1 and 2, m

The energy equation states that the total energy head at an upstream cross section is equal to the total energy head at a downstream section plus the energy head loss between the two sections.

Figure 4-5 Energy Grade Line

Source: Virginia DOT, 2002

4.5.1.2 Steady and Unsteady Flow

A steady flow is one in which the discharge passing a given cross section is constant with respect to time. The maintenance of steady flow in any reach requires that the rates of inflow and outflow be constant and equal. When the discharge varies with time, the flow is unsteady.

4.5.1.3 Uniform Flow and Non-uniform Flow

A non-uniform flow is one in which the velocity and depth vary in the direction of motion, while they remain constant in uniform flow. Uniform flow can only occur in a prismatic channel, which is a channel of constant cross section, roughness and slope in the flow direction. Non-uniform flow can occur either in a prismatic channel or in a natural channel with variable properties.

4.5.1.4 Gradually Varied and Rapidly Varied Flow

Gradually varied flow is a non-uniform flow in which the depth and velocity change gradually enough in the flow direction that vertical accelerations can be neglected.

Otherwise, it is considered to be rapidly varied

4.5.1.5 Specific Energy

Specific energy, E, is defined as the energy head relative to the channel bottom (refer to Figure 4-6). If the channel is not too steep (slope less than 10%) and the streamlines are nearly straight and parallel (so that the hydrostatic assumption holds), the specific energy E becomes the sum of the depth and velocity head:

Equation 4-3

𝐸𝐸 = 𝑦𝑦 + 𝛼𝛼 (𝑉𝑉² 2𝑔𝑔)

where:

y = depth, m

α = velocity distribution coefficient V = mean velocity, m/s

g = gravitational acceleration, 9.81 m/s²

The velocity distribution coefficient is taken to have a value of one for turbulent flow in prismatic channels but may be significantly different for natural channels.

4.5.1.6 Critical Flow

Critical flow occurs when the specific energy is a minimum for a given discharge in regular channel cross sections. The depth at which the specific energy is a minimum is called critical depth. At critical depth, the Froude number has a value of one. Critical depth is also the depth of maximum discharge when the specific energy is held constant. These relationships are illustrated in Figure 4-6. During critical flow, the velocity head is equal to half the hydraulic depth. The general expression for flow at critical depth is:

Equation 4-4

𝛼𝛼𝑄𝑄² 𝑔𝑔 =

𝐴𝐴³ 𝑇𝑇

where:

α = velocity distribution coefficient Q = total discharge, m³/s

g = gravitational acceleration, 9.81 m/s² A = cross-sectional area of flow, m²

T = channel top width at the water surface, m

Figure 4-6 Specific Energy Diagram

Source: Virginia DOT, 2002

4.5.1.7 Subcritical Flow

Depths greater than critical depth occur in subcritical flow, and the Froude number is less than one. In this state of flow, small water surface disturbances can travel both upstream and downstream, and the control is always located downstream.

4.5.1.8 Supercritical Flow

Depths less than critical depth occur in supercritical flow, and the Froude number is greater than one. Small water surface disturbances are always swept downstream in supercritical flow, and the location of the flow control is always upstream.

4.5.1.9 Froude Number

The Froude number, Fr, represents the ratio of inertial forces to gravitational forces and is defined by:

Equation 4-5

𝐹𝐹𝑟𝑟 = 𝑉𝑉

√(𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔 𝜃𝜃 𝛼𝛼)⁄

where:

α = velocity distribution coefficient V = mean velocity = Q/A, m/s g = acceleration of gravity, 9.81 m/s² d = hydraulic depth = A/T ,m

θ = channel slope angle, m/m

This expression for Froude number applies to any open channel or channel subsection with uniform or gradually varied flow. For rectangular channels, the hydraulic depth is equal to the flow depth.

4.5.1.10 Hydraulic Jump

A hydraulic jump occurs as an abrupt transition from supercritical to subcritical flow in the flow direction. There are significant changes in depth and velocity in the jump, and energy is dissipated. For this reason, the hydraulic jump is often employed to dissipate energy and control erosion downstream of structures such as highway culverts and spillways.

A hydraulic jump will not occur until the ratio of the flow depth (y1) in the approach channel to the flow depth (y2) in the downstream channel reaches a specific value that depends on the channel geometry. The depth before the jump is called the initial depth (y1), and the depth after the jump is the sequent depth (y2).

Refer to Figure 4-8.

Figure 4-7 Hydraulic Jump Diagram

When a hydraulic jump is used as an energy dissipater, controls to create sufficient tailwater depth are often necessary to control the location of the jump and to ensure that a jump will occur during the desired range of discharges. Sills can be used to control a hydraulic jump if the tailwater depth is less than the sequent depth. If the tailwater depth is higher than the sequent depth, a drop in the channel must be used to ensure a jump.

4.5.2 Flow Classification

The classification of open-channel flow can be summarized as follows:

Steady Flow

 Uniform Flow

 Non-uniform Flow - Gradually Varied Flow - Rapidly Varied Flow Unsteady Flow

 Unsteady Uniform Flow (rare)

 Unsteady Non-uniform Flow - Gradually Varied Unsteady Flow - Rapidly Varied Unsteady Flow

The steady, uniform flow case and the steady, non-uniform flow case are the most fundamental types of flow treated in most hydraulic conditions.

4.5.2.1 Steady Uniform Flow

For a steady, uniform flow, the mean velocity, V, can be computed with Manning’s equation:

Equation 4-6

𝑉𝑉 = 1

𝑛𝑛 𝑅𝑅^{2 3⁄} 𝑆𝑆^1/2 where:

V = velocity, m/s

n = Manning’s roughness coefficient R = hydraulic radius = A/P, m P = wetted perimeter, m

S = slope of the energy grade line, m/m (For steady uniform flow, S

= channel slope, m/m)

The selection of Manning’s n is generally based on observation; however, considerable experience is essential in selecting appropriate n values. Typical ranges of n values for various types of channels and floodplains is given in Table 4-2, Table 4-3, Table 4-4 and Table 4-5.

Table 4-2 Values of Manning’s Roughness Coefficient 'n' (Uniform Flow) - Natural Channels

Description Minimum Maximum

Fairly Regular Section

1. Some grass & weeds, little or no brush 0.028 0.033

2. Dense growth of weeds, flow depth greater weed height 0.033 0.040

3. Some weeds, light brush on banks 0.035 0.050

4. Some weeds, heavy brush on banks 0.050 0.070

5. Some weeds, dense trees 0.060 0.080

For trees within channel, with branches submerged at

high flood increase all above values by 0.010 0.020

6. Winding, some pools & shoals, clean (1.) 0.035 0.045

7. Winding, some pools & shoals, clean, lower stages,

more ineffective sections 0.045 0.055

8. Winding, some pools & shoals, clean, some weeds &

stones (3.) 0.040 0.050

9. Winding, some pools & shoals, clean, lower stages,

more ineffective sections, stony sections 0.050 0.060

10. Sluggish river reaches, rather weedy or with deep

pools (4.) 0.060 0.080

11. Very weedy reaches (5.) 0.100 0.150

Irregular sections, with pools, slight meander;

increase above values by about 0.010 0.020

Mountain streams, no vegetation in channel, bank steep, tree & brushes along banks submerged at high flood

1. Bottom of gravel, cobbles & few boulders 0.040 0.050

2. Bottom of cobbles, with large boulders 0.050 0.070

Large Stream Channels (top width greater than 30m) Reduce smaller stream coefficients by 0.10

Table 4-3 Values of Manning’s Roughness Coefficient 'n' (Uniform Flow) - Floodplains

Description Minimum Maximum

1. Pasture, short grass, no brush 0.030 0.035

2. Pasture, tall grass, no brush 0.035 0.050

3. Cultivated land-no crop 0.030 0.040

4. Cultivated land, nature field crops 0.045 0.055

5. Scrub& scattered brush 0.050 0.070

6. Wooded 0.120 0.160

Table 4-4 Values of Manning’s Roughness Coefficient 'n' (Uniform Flow) – Man-made Channels & Ditches

Description Minimum Maximum

1. Earth, straight & uniform 0.020 0.025

2. Earth bottom, rubble sides / riprap 0.030 0.035

3. Grass covered 0.035 0.050

4. Dredged 0.028 0.033

5. Stone lined & rock cuts, smooth &uniform 0.030 0.035 6. Stone lined & rock cuts, rough & irregular 0.040 0.045

7. Lined - smooth concrete 0.014 0.018

8. Lined - grouted riprap 0.020 0.030

9. Winding sluggish canals 0.025 0.030

10. Canals with rough stony beds, weeds on earth banks 0.030 0.040

Table 4-5 Values of Manning’s Roughness Coefficient 'n' (Uniform Flow) - Pipes

Description Minimum Maximum

1. Cast Iron, Uncoated 0.013 0.015

2. Cast Iron, Coated 0.012 0.013

3. Wrought Iron, Black 0.013 0.015

4. Wrought Iron, Galvanized 0.014 0.017

5. PVC, HDPE 0.009 0.013

If the normal depth computed from Manning’s equation is greater than critical depth, the slope is classified as a mild slope while a steep slope is classified as one where the normal depth is less than critical depth. Thus, uniform flow is subcritical on a mild slope and supercritical on a steep slope.

Strictly speaking, uniform flow conditions seldom, if ever, occur in nature because channel sections change from point to point. For practical purposes in most hydraulic engineering problems, however, the Manning equation can be applied to most streamflow problems by making judicious assumptions. When the requirements for uniform flow are met, the depth (yn) and the velocity (Vn) are said to be normal and the slopes of the water surface and channel are parallel. For practical purposes, in open channel design, minor undulations in streambed or minor deviations from the mean (average) cross-section can be ignored as long as the mean slope of the channel can be represented as a straight line.

4.5.2.2 Non-Uniform Flow

General

For the gradually varied flow condition, the depth of flow must be established through a water surface profile analysis. The basic principles in water surface profile analysis are where:

 Water surface approaches the uniform depth line asymptotically

 Water surface approaches the critical depth line at a finite angle

 Subcritical flow is controlled from a downstream location

 Supercritical flow is controlled from an upstream location

There are twelve (12) possible water surface profiles (see Figure 4-9) depending on the particular flow conditions. A complete discussion of water surface profile analysis is contained in most open channel hydraulics textbooks, such as Chow (1959) and Henderson (1966).

Methods of Analysis

Two methods of performing a water surface profile analysis are:

 The Direct Step method

 The Standard Step method

Both methods make use of the energy equation to compute the water surface profile. The direct step method can be used to analyse straight prismatic channel sections only. The standard step method is applicable to prismatic and non-straight channel alignments.

For a complete discussion of both refer to Open-Channel Hydraulics (Chow, 1959) or numerous other textbooks on open channel hydraulics.

The analysis of water surface profile problems is best performed by computer.

Available computer models are discussed in Section 4.10.

4.6 Closed Conduit Flow Calculations (Drainage Systems)

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