User:Kinshh92

=Draft Page=

Draft of Bank Erosion page due 10/29/13 -->This page was deleted by an administrator.

=Final Page= Final page due 11/19/13

Bank erosion is the wearing away of the banks of a stream or river. This is distinguished from erosion of the bed of the watercourse, which is referred to as scour. Bank erosion occurs when concentrated flow removes sediment from the stream bank. Such erosion leads to sediment transport through streams and rivers.

The roots of trees growing by a stream are undercut by such erosion. As the roots bind the soil tightly, they form abutments which jut out over the water. These have a significant effect upon the rate and progress of the erosion. Stream channel erosion may be a primary contributor to total sediment yield in urbanized watersheds.

Measurement
Erosion and changes in the form of river banks may be measured by inserting metal rods into the bank and marking the position of the bank surface along the rods at different times. This simple measurement technique can be enhanced with the use of a data logger attached to a rod of photoreceptors; the logger records the voltage, which is an indication of how much of the rod is exposed.

Permissible Velocity
Permissible velocity is the maximum velocity in a stream that can occur before erosion will happen. A table of permissible velocities for common types of channels has been established by the United State Army Corps of Engineers.

These permissible velocities can be calculated using the Manning formula:


 * $$V = \frac{k}{n} {R}^{2/3} \, S^{1/2}$$

where:
 * V is the average velocity across the cross-section (length/time, ft/s, m/s),
 * k is a conversion factor equal to 1 for SI units or 1.49 for U.S. customary units,
 * n is the Manning coefficient (unitless),
 * R is the hydraulic radius (length, ft, m),
 * S is the stream slope (length/length, ft/ft, m/m)

Permissible Velocity Example
For example, consider a man-made channel with grassy earthen lining that was recently completed. The trapezoidal channel was constructed to have a bottom width of 8 ft with 3H:1V side slopes and carry a maximum depth of 1.0 ft. The channel bed slope was built with an average of 0.001 ft/ft. What is the maximum permissible velocity when the channel is bankfull at a flow depth of 1.0 ft?


 * n = 0.018 (from Table of Values of Manning's n for Excavated or Dredged Channels > Earth, straight, and uniform > clean, recently completed)
 * k = 1.49 for SI units
 * Area = (bottom width)x(flow depth) + 2*(side slope)*(flow depth)
 * A = $$(8 ft)*(1.0 ft) + 2*(3)*(1.0 ft) = 11.0 ft^2$$
 * Wetted Perimeter = (bottom width) + 2*(side slope)*(flow depth)
 * P = $$(8 ft) + 2*(3)*(1.0 ft) = 14.0 ft$$
 * Hydraulic Radius = Area / Wetted Perimeter
 * R = $$11.0 ft^2 / 14.0 ft = 0.786 ft$$
 * S = 0.001 ft/ft

Therefore,
 * $$V = \frac{1.49}{0.018} {(0.786 ft)}^{2/3} \, (0.001 ft/ft)^{1/2}$$


 * $$V = 2.23 ft/s$$

The maximum permissible velocity in the stream channel before bank erosion will occur is 2.23 ft/s.

Shear Stress
Shear stress with regards to open channel flow is the force parallel to the boundary of the stream channel and fluid. Shear stress varies over a stream cross section. This variation can be approximated for a trapezoidal channel as:

where:
 * $$\tau = \gamma {y} {S_{0}} $$ at the bottom of the channel
 * $$\tau = {0.76} \gamma {y} {S_{0}} $$ at the sides of the channel
 * $$\gamma$$ = Specific weight of the fluid (weight/volume, N/m^3, lb/ft^3),
 * $$y$$ is the depth from the water surface (length, m, ft),
 * $$S_{0}$$ is the channel slope (length/length, m/m, ft/ft)

In bank erosion, the shear stress can be used to identify the point when erosion will occur, in which case the shear stress is known as the critical shear stress.

Shear Stress Example
For example, consider the same man-made stream channel as above. The channel has a trapezoidal cross-section with bottom width of 8 ft, side slopes of 3H:1V and channel bed slope of 0.001 ft/ft. When the channel is bankfull at 1.0 ft, what is the shear stress on the side of the channel at a depth of 0.75 ft from the water surface?


 * $$\gamma = 62.43 lb/ft^3 $$, using the specific weight of water at an assumed temperature of 40°F
 * $$y = 0.75 ft $$
 * $$S0 = 0.001 ft/ft $$

Therefore,
 * $$\tau_{c} = {0.76}*{62.43 lb/ft^3}*{0.75 ft}*{0.001 ft/ft} $$
 * $$\tau_{c} = 0.036 lb/ft^2 $$

Control
Bank erosion is a natural process: without it, rivers would not meander and change course. However, land management patterns that change the hydrograph and/or vegetation cover can act to increase or decrease channel migration rates. In many places, whether or not the banks are unstable due to human activities, people try to keep a river in a single place. This can be done for environmental reclamation or to prevent a river from changing course into land that is being used by people. There are ways to try to prevent or slow these processes via stream restoration and erosion control measures. One way that this is done is by placing riprap or gabions along the bank.

Manmade channels can also be designed to prevent erosion of channel sides and bottom. This can be done by using the permissible velocity to determine channel dimensions.

Permissible Velocity Method
Design a channel to carry a peak flow of 50 cfs. The constructed channel must have side slopes of 3H:1V and will be lined with Bermuda grass. The land has an average slope of 0.003 ft/ft and can only be excavated to a depth of 1.5 ft.

The recommended permissible velocity from the U.S. Army Corps of Engineers for Bermuda grass is 1.8 m/s. Using the conversion factor for m/s to ft/s, this permissible velocity is 5.91 ft/s.

The Manning's n coefficient for vegetated lining is 0.030.

Using the mathematical definition of volumetric flow rate, the area is determined to be:

$$A = \frac{Q}{v} = \frac{50 ft^3/s}{5.91 ft/s} = 8.46 ft^2 $$

Substituting values for v, n, and S0 into Manning's equation and solving for R, we get R = 3.20 ft. Then using area to solve for wetted perimeter, we get:

$$ P = \frac{A}{R} = \frac{8.46}{3.20} = 2.64 ft $$

The equations for area and wetted perimeter of a trapezoid and the maximum possible depth of 1.5 ft are then used to find the channel bottom width:


 * Equation for Area: $$ A = by + my^2 $$

where b is the channel bottom width, m is the horizontal side slope and y is the flow depth.


 * $$ 8.47 = b*1.5 + 3*(1.5)^2 $$
 * $$b = 1.14 ft $$

Therefore, if the channel is built to have a depth of 1.5 ft, the minimum channel bottom width needed to prevent channel erosion is 1.14 ft.

Outline Page for CEE 5384 Wikipedia Assignment
Currently, wikipedia pages exist with a brief, general definition of erosion in stream channels (see Links to Other Wiki Pages below, but there is no quantitative support or examples for such definitions. My assignment will create a page titled 'Bank Erosion' that defines streambank erosion more explicitly and provides supporting equations and examples. One of the main concepts involved in streambank erosion is the idea of permissible velocity, which will also be defined and supported with equations/examples on the Bank Erosion page that will be created.

PROBLEM: A page titled bank erosion already exists. Should I call mine channel erosion? Or can I completely re-do the existing bank erosion page?

Project Outline:
 * introduce bank (or channel) erosion
 * definition: "removal of sediment by concentrated flow" from a stream bank (Ward, Environmental Hydrology, pg 309)
 * erosion leads to sediment transport through streams & rivers
 * reference 1) permissible velocity, 2) shear stress as two methods to quantitatively estimate if a streambank will erode
 * introduce permissible velocity (definition)
 * table of common permissible velocities for stream channels (Chaudry, Open Channel FLow, pg 287 Table 9-3 - comes from US Army Corps of Engineers)
 * reference Manning formula to determine velocity
 * reference variables in this equation
 * hydraulic radius
 * wetted perimeter
 * present and walk through an example
 * introduce shear stress
 * shear stress varies over cross-section
 * image from Chow's book?
 * approximation for trapezoidal channel (Chaudry, Open Channel Flow, pg 289):
 * tau (@ bottom) = gamma*y*So
 * tau (@ sides) = 0.76*gamma*y*So
 * gamma = specific weight of fluid (water in streamflow)
 * y = depth
 * So = channel slope
 * describe shear stress as it relates to bank erosion
 * critical stress marks the point where erosion will occur
 * critical shear on sediment transport page uses particle Reynolds number to calculate initiation of motion
 * Is this method worth understanding or should I merely reference it?
 * permissible shear can be determined based on particle diameter/size or bulk density
 * Chaudry, Open Channel Flow (pg 293)
 * describe how it relates to permissible velocity (?)

Possible topics to expand upon and include sections at end:
 * discuss how natural bank erosion is normal and natural
 * this is how rivers meander and change course
 * discuss implications of human-accelerated erosion rates
 * "accelerated erosion: erosion much more rapid than normal, natural, or geological erosion, primarily as a result of the influence of the activities of humans" (Ward, Environmental Hydrology, App. B: Glossary)
 * stream restoration efforts to stabilize banks
 * erosion control efforts

Possible Resources To Be Used

 * M. H. Chaudhry, Open-Channel Flow. New York: Springer, 2008.
 * Chapter 4: Uniform Flow
 * Chapter 9: Channel Design
 * Ward, A.D. and S.W. Trimble. 2004. Environmental Hydrology, 2nd Edition. CRC Press: Boca Raton, FL. Pp. 475.
 * Moglen, G.E. (2011) Lecture notes from CEE 4324/5984: Open Channel Flow, Virginia Tech.
 * Wynn-Thompson, T.M. (2012) Lecture notes from BSE 3324: Small Watershed Hydrology, Virginia Tech.
 * In addition, several PDF documents that were used in lectures (will be linked later on - I have saved on my computer)
 * Krometis, L.H. (2013) Lecture notes from BSE 3334: NPS Assessment & Control, Virginia Tech.
 * Manning n Table []

Links to Other Wikipedia Pages
This is a list of other wikipedia pages that relate to my topic, including both pages that I will reference in my page, and pages that can reference my page:
 * Erosion - Rivers & Streams
 * Open Channel Flow
 * stream, river
 * Hydraulic Action
 * Manning formula