river dynamics lecture 1 for handout...river dynamics example 6 determine the combined effects of a...

River Dynamics

Equilibrium and Downstream Hydraulic Geometry

Channel Stability Analysis

Channel Stabilization and Submerged Vanes

Taiwan, November 1-2, 2016A. Jacob Odgaard

Quiz

Where?

Quiz

What’s the problem?

Quiz

Why do we have a problem?

How can we fix it?

Quiz

Dredging is one way to fix it.

Quiz

Is dredging the best solution?

Quiz

It happens only once. Right?

Quiz

Wrong!

Equilibrium / stability Problem

One year later:

Still dredging

Kaoping River2016

Kaoping River2004

Kaoping River2004

Kaoping River2005

Kaoping River2005

Kaoping River2006

Kaoping River2010

Kaoping River2010

Kaoping River2016

Kaoping River2004 & 2016

Kaoping River2013

Kaoping River2014

Channel Equilibrium and Downstream Hydraulic

Geometry

River Morphology

Zone 1: Channels are generally unstable and braided

Zone 2: Channels are relatively stable and meandering

Zone 3: Channels are unstable and braided

River Morphology

Zone 1: Erosional/degrading zone, runoff production, sediment source

Zone 2: Transport zone of water and sediment, near-equilibrium between inflow and outflow of water and sediment

Zone 3: Depositional/aggrading zone of runoff delivery and sedimentation

River Morphology

Kosi River, Nepal

River Morphology

Kosi River, Nepal

At Chatra looking upstream

River Morphology

Kosi River, Nepal

At Chatra looking downstream

River Morphology

Kosi River, Nepal

Aerial View

River Morphology

Zone 2 Challenges

Abutment scour at Bulls Bridge over Rangitikei River, New Zealand (Raudkivi and Ettema 1985, ASCE)

Zone 2 Challenges

River Equilibrium?

Depends on time scale and point of view:

Geological: No river can be considered in exact equilibrium no matter how long a time scale

Engineering: A river is in equilibrium if it has not changed its characteristics notably ina number of years, seasonal changesbeing disregarded, and if it is not likely to change its characteristics in a subsequent time period (f.ex., project life)

River Equilibrium?

Engineers prefer that rivers or river segments are in equilibrium both before construction and after.

How can we tell whether this river reach is in equilibrium? Explain in homework

River Equilibrium (Answer)

At equilibrium, the cross-sectional geometry may locally change; but over a given time period the deposition volume within a river reach must equal the erosion volume. From a river engineering point of view, the time period is typically the projected life of an infrastructure project

River Equilibrium (Alluvial)

– A river bend is in equilibrium when rate of erosion on outside equals rate of deposition on inside point bar.

– Hence, a migrating river bend can be in equilibrium

– If bend is migrating laterally and/or longitudinally, plan form is unstable

Formative/Dominant Discharge

Constant discharge at which river adjusts itself and reaches same equilibrium as that developed by annual sequence of discharges

Bank-full flow is usually used for determining equilibrium downstream hydraulic geometry.


General observations:

• Water and sediment discharge increase in the downstream direction

• Width and depth increase in the downstream direction• Slope and grain size decrease in the downstream

direction (grain size decreases exponentially)

How do the variables and their relationship to one another vary with distance downstream?

What are the dimensions of an equilibrium channel?


Assume similarity:

Bank full discharge relates to geometric variables in the same manner along entire reach

Why is this a reasonable assumption?


Dimensions of an equilibrium channel:

b = b(x, z+d)

Dependent variables:

U, d, z, b, A, Q, Qs

all functions of x and t

Assumed known variables:

, , , , ∆,

.

∆


Empirical (Regime) relationships, by Kennedy (1895), Lacey (1929), and Blench (1969):

V = mean velocity in feet per second

R = hydraulic radius in feet

A = cross-section area in square feet

P = wetted perimeter in feet

S = slope

Q = design discharge in cubic feet per second

= silt factor

Where did S come from? Assumptions?


Regime Relations in metric units:

.

.

. / /


Pierre Julien (1995) Engelund-Hansen (1967)


Example 1:

Given:Bank-full discharge Q = 104 cubic meters per second, median grain size 0.056 m

Find (1) channel slope S at which the bed material will be at

incipient motion(2) stable width and depth at this slope

Solution Strategy ?


Example 1:

Solution Strategy: Use appropriate regime formulas


Example 1:


Example 2:

Given:Bank-full discharge Q = 104 cubic meters per second, median diameter 0.0056 m

Find:Stable slope at which the bed material will be at incipient motion

Stable width and depth at this slope

River Equilibrium (Alluvial)Example 1:

Given:

Bank-full discharge Q = 104 cubic meters per second, median grain size 0.056 m

Find:

Stable slope at which the bed material will be at incipient motion


Example 2:

Given:

Bank-full discharge Q = 104 cubic meters per second, median diameter 0.0056 m

Find:

Stable slope at which the bed material will be at incipient motion



Example 2 (D = 0.0056 m):

Slope larger or smaller?

Width larger or smaller?

Depth larger or smaller?

Velocity larger or smaller?

Discussion:

River Equilibrium (Alluvial)Example 2:


What would happen to downstream geometry if in Example 2 we increase slope without changing grain size?

Dimensionless shear stress increases => bed material starts to move => channel cross section changes

How would you introduce bed-loadtransport rate?

Several bed-material transport formulas are of form

--->

Bed-Material Load Formulas

Engelund-Hansen

Formula is based on observations/measurements in Rio Magdalena, where D > 0.19 mm.

With s = 2.65:


Pierre Julien:

Validated for

Meyer-Peter Muller:

With s = 2.65,



River Dynamics

We can introduce any of the bed-material formulas into the last Regime equation (the one with tau star)

Take Julien’s first:

Take b from second equation:

River Dynamics

We get:

Interpretation: the product of slope and discharge on the right-hand side must be balanced by the product of grain size and sediment discharge on the left-hand side - known as Lane’s (1955) balance:

River Dynamics

Lane’s (1955) relationship

States that equilibrium conditions exists between hydraulic conditions on the left-hand side and sediment conditions on the right-hand side

Perturbations to one or several of the parameters in the relation will be balanced by a change in one or several of the remaining parameters.

River Dynamics

Lane’s (1955) relationship

Lane/Borland illustration (Borland 1960)

River Dynamics

River’s Response to Changes (away from Equilibrium)

Qualitative Assessment

Quantitative Assessment

River Dynamics

River Dynamics

River Dynamics

Downstream of dam

River Dynamics

River Dynamics

River Dynamics

River’s Response to Changes (away from Equilibrium)

Qualitative Assessment

Quantitative Assessment

River Dynamics

Take S from this equation and substitute in the Regime equations (left):

Julien’s Regime formula: Julien’s Sediment formula

Combined to yield

River Dynamics

River Dynamics

Or in terms of bed-material concentration

Conversion:

River Dynamics

Example 5

Estimate the equilibrium (hydraulic) geometry of an alluvial stream at a bank-full discharge of 127 cubic meters per sec with median grain size D = 0.5 mm and a bed-material concentration of 150 ppm.

Strategy:

Use the Regime formulas that include sediment concentrations

River Dynamics

Quantitative Trend Analysis:

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• Summary

– Changes in width and depth depend primarily on discharge

– Increases/decreases in water and sediment discharges exert counterbalancing effects on channel slope and the Shields parameter

– Grain-size effects are comparatively small

River Dynamics

Example 6

Determine the combined effects of a 50% decrease in water discharge (Q -) and a 200% increase in sediment discharge (Qs

+) on channel width, flow depth, flow velocity, slope, and Shields parameter.

River Dynamics

Example 7

The Jamuna River in Bangladesh conveys a water discharge of 48,000 m3/s at bank-full flow condition. At this discharge the bed-material discharge is approximately 2.6 million tons per day. Median grain size is 0.2 mm

(1) Use Julien’s regime formulas to estimate the equilibrium geometry (“downstream hydraulic geometry”) of this river.

Your answer should state depth, width, cross-sectional average velocity, slope, and dimensionless shear stress.

River Dynamics

Example 7 (continued)

(2) Field measurements at this discharge indicate a flow depth of 6.6 m, width 4,200 m, and average velocity 1.7 m/s, slope 7.5 × 10-5, and dimensionless Shields’ stress of 15.

Compare your above estimate with these field measurements and, if different, explain why there is a difference.

Characterize the river at this location (straight, meandering, or braided).

River Dynamics

Example 8

Given:

Alluvial fine sand-bed channel with bank-full width 100 m, a flow depth of 3 m, slope 1.5 m/km, and a flow velocity of 3 m/s.

Find:

Expected change in downstream hydraulic geometry if the dominant flow discharge is decreased by 50%. The bed-material size and the sediment concentration are expected to remain the same.

River Dynamics

Alternative tools for estimating channel changes:

Henderson’s (1966) and Engelund-Hansen’s (1967) approaches will be discussed next.

River Meandering and Channel Stability

will be discussed tomorrow


Equilibrium Bend Flows

Equilibrium in River Bends

Bed is sloped upward toward inner bank because of transverse bed shear stress

Super-elevation at outer bank


Most analyses consider only central portion of cross section:


Analysis is simplified by assuming linear transverse velocity profile


Depth of scour:


Example 3:



Example 4



Natural Channel Design Model

Case Study

Effect of construction of Cochiti Dam on Rio Grande River Channel

Reference:

Julien, P., Richard, G., and Albert, J. (2005). “Stream restoration and environmental river mechanics” International Journal of River Basin Management, 3:3, 191-202

Case Study

Upstream drainage area about 37,800 km2

Dam traps virtually entire sediment load from upstream

Major impact on downstream channel:• Bed degradation

• Coarsening of bed from sand to gravel

Case Study

Case Study

Case Study

Case Study

Case Study

Conclusions:

• 99% reduction in sediment concentration flowing into study area

• Degradation of up to 2 m• Sand bed became gravel bed• Width decreased by up to 76%• Channel pattern shifted from a braided, multi-

channel pattern to a meandering, single-thread pattern

• Sinuosity increased, with some bank erosion• Flood plain no longer floods at peak flows

Problems on Case Study



At-the-station geometry


river dynamics lecture 1 for handout...river dynamics example 6 determine the combined effects of a...

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