Matias Mario Mendez Larrain
CE 598- River Restoration

Stability and Erosion components in River Bank Stability Analysis

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Abstract
Stability and erosion componenets in river bank stability analysis plays a important
role in the behavior of a river.Many problems downstream are related to a bad manage
of the bank slopes upstream. This term paper is related to identify and analyse the
conditions of a bank slope. Also, the term paper will be related on how erosion contributes
to create the insatability of a bank slope.
The paper correlated the percent decrease in factor of safety to intensity of river
flow and duration. The methods to quantify flow induced erosion were assessed
based on observed erosion and the second on theoretically calculated erosion.
Focused on theorical calcualtions the paper involved the use of theoretical equations to
quantify erosion given the river elevation of a specific flow year.



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Introduction

Environmental river bank failure and erosion has been a focus of recent concern for many major rivers of the world. River bank erosion is important geomorphologically in effecting changes in the rivers channel course and in development of the flood plain. River bank erosion is also important economically due to the loss of the farm lands and the undermining of structures adjacent to the river channel (El-Sersawy, 1995). It was deduced that a river bank erosion is a complex phenomenon (Pilarezyk, 1990), which includes interaction between river hydraulic environment, geotechnical environment and a structure.
Most routine analyses of slope stability concentrate on defining the conditions under which failure will occur. The factor of safety is the factor by which strength may be reduced to bring the slope to limiting equilibrium. The results of stability analyses should be viewed as a means for comparing the overall factors of safety obtained form specific designs with those previously determined for the existing banks – characteristics. Analysis of stability of alluvial stream banks (Springer, 1985) indicated the following:
a) the formation of tension cracks, and the filling of these tension cracks with water,
b) the values of the effective angle of internal friction, and the values of unit weight of the soils composing these banks,
c) the height of capillary rise, and the flood hydrograph, and
d) the time rate of tension crack formation.
The following processes can be identified as being of particular importance for a river bank erosion and failure (Simons, 1981):
a) Shear erosion of the bank material by water flow in the river,
b) Surface erosion of the bank slopes above the water level by rainfall and surface runoff, and
c) Seepage erosion of the bank soil by groundwater flow and seepage force.


Slope Stability Definition and Determination Guideline

Long term stable slope line consists about the Stability Component and the Erosion Component

STABILITY COMPONENT

The setback gradient line measured from the toe of the slope, or channel assuming the
location of the toe remains fixed with time. (See Figures 1 and 2).
The factors of consideration are:
- Soil Strength
- Groudnwater Conditions
- Slope Geometry
- Condition of Vegetation
- Changing Load Conditions
- Weathering of Slope Face
- Increases in Surface Runoff over Slope

The method of stablishing this component differs. The methodolgy follows a condtion explained below.
A minimum factor of safety is given, FS=1.5

EROSION COMPONENT

The regression of the slope toe/channel bank due to erosion over the design life of the structure at the
crest of the slope and is measured as a horizontal distance. (See Figure 4a).
The factors of consideration are:
- Proximity of the slope toe to the watercourse
- Average and peak flow rates and velocities of the watercourse
- Susceptibility of the soils to erosion
- Type and extent of vegetation
- Sediment load carried by the watercourse
- Fluvial geomorphological processes affecting the reach within which the site is located
- Increases in surface runoff over slope
- Weathering of slope face

The method of calculation is explained in the following figures. The distance from the toe of the valley wall to the
watercourse channel bank as well as the design erosion allowance must be determined.
The erosion is measured horizontally from the top of the channel bank or the location of the
bankfull flow, whichever is lower in elevation (See Figure 4b).


DEVELOPMENT SETBACK COMPONENT

A minimum allowance from the identified slope hazard area to take into account external conditions
which could have an adverse effect on the existing natural conditions of the slope. This setback distance maybe
superseded by more stringent municipal or provincial requirements.
The factors of consideration are:
- Provide an acces point along the crest of the slope
- Keep heavy equipment away from the slope
- Allow for the redirection of surface flows away form the slope hazard area
- Allow for the placement of sediment control measures and limit of working easement if necessary
- Provide tableland area for potential [[#|future]] revegetation and/or reforestation
The method of calculation consists in measuring the horizontal distance from the approved top of bank or from the combined distance derived
from the Stability and Erosion Components whichever is the greater.

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Erosion
Erosion is the process by which soil particles are removed from the bed and banks of the channel and entrained into the flow of the river (Richards 1982). Erosion depends on a number of factors that include the intensity of flow (river elevation), soil characteristics of the bed and banks, geometry of the channel, ice effects and characteristics of the fluid. Quantifying the amount of soil eroded from the bed and banks of the channel under a given river flow is of interest. To calculate this value three variables are required:
  • Fluid Shear Stress
  • Critical Shear Stress
  • Erosion Rate

FLUID SHEAR STRESS

Fluid shear stress is defined as the force per unit area in the direction of flow (Chang 1988). The shear stress distribution in a steady and uniform two-dimensional flow in a channel can be explained by figure 5. The figure shows all of the forces acting on a unit volume of water described by ABCD within the channel. The x-axis is in the direction of flow along the slope of the channel defined by S with the z-axis perpendicular to the flow (Chang 1988). The forces and stresses acting on the unit volume include the hydrostatic forces on AB and
CD, shear stress τacting on BC and the x-component of the fluid weight Wx in the unit volume. All forces act in the x-direction.
If the flow is uniform the hydrostatic forces are equal and opposite and hence the remaining force Wx (= WS) must be counterbalanced by the shear force.

WS =τ Pdx
γ∀S =τPdx
γAdxS =τPdx
R = A/P
where,
τ= fluid shear stress
P = wetted perimeter
A = Area
∀= Volume
Isolating the above equations for τ produces the following equation.This equation is the average shear stress exerted on the bed of the channel. R is defined as the hydraulic radius of the channel and γ is the unit weight of the soil.
τ=γRS

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Figure 5. Schematic of forces actingon a unit volume of flow

The graphical distribution is shown in Figure 6(a) where shear stresses are a maximum along the bed and a minimum at the top of the bank. For this particular cross-secti on of side slope 2:1, the maximum shear on the bed is 1.37γRS and on the bank is 1.08γRS approximately one third from the bed. The coefficients of maximum γRS were adjusted for the bed and bank as a function of the ratio of channel width (b) to water depth (D). Values for the coefficient of maximum shear stress werealso provided for channels of different side slopes. The graphs in Figures 6(b) and 6(c) show for a channel of side
slope 2:1, as the b/d decreases the coefficient for γRS approaches 1.0. However, as b/d increases the coefficient can be as high as 1.4

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Figure 6. Distributions of boundary shear stress

CRITICAL SHEAR STRESS


Represents the minimum shear stress required in order for erosion to takeplace.The resisting forces of the particle depend on the characteristics of the soil. Non-cohesive soils such as sands and gravels resist erosion by gravitational forces through their submerged weight (Richards 1982). The Shields curve shown in Figure 7 is commonly used to determine the critical shear of non-cohesive soils, based on the diameter of the particle. The curve is based on a series of flume experiments of water flowing over flat sand beds and offers a range of critical shear stresses forparticles of 0.1 mm to 10,000 mm in diameter with shear stresses ranging from 0.1 Pa to 10 Pa.
The reasoning for the method was that particles on a stream bed are subjected to a tractive force acting in the direction of flow whereas particles on a side slope are additionally subjected to a gravitational force parallel to the slope which causes the particles to roll down into the channel. Many other methods have been developed by other researchers to estimate the critical stress. Those methods at some point consider more inputs in the behavior.

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Figure 7. Diagram for determining the critical shear stress of cohesive soils

EROSION RATE

The final quantity required to quantify erosion is the erosion rate. Represents the amount of soil eroded in a unit of time (e.g. mm/hr). Erosion Rate is multiplied by the amount of time over which the fluid shear stress is above the critical shear stress to determine the quantity of erosion in a time increment sum up the quantity as a function of position and time and we can determine the change in riverbank profile. Erosion rates for cohesive soils can be calculated using an excess shear stress approach proposed by Partheniades (1965) given by the following equation.

ε = k (τo−τc)^a
where
k = erodibility coefficient
τo-τc = Excess shear stress
a = an exponent often assumed equal to 1.0
The value of k is determined experimentally. According to experiments completed on almost 200 soil samples at stream sites from Nebraska, Iowa and Mississippi k was estimated as a function of τc given by:
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The Briaud et al. (2001) method for erosion rate is based on a equation where h is the height of sample eroded which is a standard 1 mm for all tests and t is the amount of time required to erode the sample to be flush with the bottom of the pipe.
Z=H/T
The final output is a curve which shows the shear stress on the x-axis and the erosion rate on the y-axis. The point on the curve where the erosion rate first increases from the zero point corresponds to the critical shear stress. Briaud et al. (2001) states the erosion rate will vary from 0.3 to 30 mm/hr and the
erosion rate of fine grained soil is thousands of times slower than the erosion rate of coarse-grained soils. See Figure 8 as an example.
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Figure 8. EFA test

OBSERVED EROSION

Researchers have stated that erosion is a contributor to riverbank instability. As river flows increase, greater erosion occurs, which causes greater instability. However, none of the research has quantified the decrease in factor of safety due to erosion from annual river flow. The goal is to quantify erosion from yearly flow events and relate the intensity and duration of the flow events to the percent decrease in factor of safety. The procedureinvolves the following steps:
- Obtain consecutive yearly riverbank cross-sections at a specific location along the river.
- Align the cross-sections in reference to a common datum
- Measure the horizontal distance at the toe of the bank between consecutive annual cross-sections. This quantity represents the yearly erosion due to that years flow event.
- Model the riverbank cross-sections from consecutive years using a numerical slope stability model to quantify the factor of safety for each cross-section. The percent decrease in slope stability is calculated based on the difference between the factors of safety.

RIVERBANK CROSS-SECTIONS AND SITE LOCATION

Erosion due to a given flow event can be quantified by comparing the riverbank cross-sections between consecutive years. The horizontal difference between the two cross-sections represents the erosion from the given flow event or a major movement caused by erosion from a number of flow events. Since the majority of erosion is concentrated at the toe of the bank it is necessary to have riverbank cross-sections that are surveyed below the water line, to the bottom of the channel. Site selection is a step to analyze the different cross sections, the criteria is:
- Must have cross sections along the time and present days
- Each cross-section must have a common datum to reference when aligning the cross-sections
- Study site must be a location along the river prone to yearly erosion, preferably an outside bend or transition. Erosion can be observed along all stretches of the river but is expected to be more pronounced on the outside bends and transitions
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Figure 9. Erosion Stages

Slope Stability

Assessing the stability of a riverbank is traditionally based on a limit equilibrium method used to calculate the factor of safety of the slope. The factor of safety (FS) is the ratio of maximum available resisting moments (MR-MAX) to the disturbing moments (MD) developed by gravity and other disturbing forces (FS = MR-max/MD). A value of 1.0 or close to 1.0 represents a failed slope or a slope that is approaching failure.
The factor of safety is traditionally calculated using a limit equilibrium method which is based on assuming a failure surface through the slope and then formulating the equilibrium equations for the disturbing and resisting forces acting on that surface. The disturbing forces and moment are a result of the weight of the soil mass and piezometric conditions in the soil. Resisting forces and moments are due to the shearing forces mobilized along the failure surface. However, in using this method there are several problems with solving the forces and moments. These include:
- Difficulties determining the center and weight of the sliding mass
- Mobilized shear resistance varies along the slip surface
- Seepage forces vary within the soil mass and along the failure surface and are typically unknown

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Figure 10. Slope Stability Interaction

Conclusions

River bank stability is a topic that involves many inputs to analyse. The erosion component and the stability component are the ones who more impact have in this topic. Also, is a fact that links between flood events and increasing erosion happens and to improve the analysis it is important to find bettter methods to measure erosion rates of specific materials to begin to examine the various bank conditions and materials. Collecting data is also a matter in this field. Geotechnical, hydrological and topographic data, gives a better understanding of the behavior in the bank. Examine the internal stability of the bank and the geotechnichal failures is a important part to analyse since we want to ahve a complete idea of how the river bank stability will develop.
This study has been conducted that has quantitatively demonstrated potential impacts of flood events on erosion and, considerable challenges to physically measure erodibility of riverbank sediments still exist.


References

J. Soenksen, Mary J. Turner, Benjamin J. Dietsch, U.S. Geological Survey, and Andrew Simon, National Sedimentation Laboratory, U.S. Department of Agriculture (2003). Stream Bank Stability in Eastern Nebraska. Water-Resources Investigations Report 03–4265

Bonelli, Stephane (2013). Erosion in Geomechanics Applied to Dams and Levees.

Springer, J., Ullrich, F.M., and Hagerty, D.J., "Stream Bank Stability", J. Geotech. Dir., ASCE, 1985.

Simons, B.B. (1981), "Bank Erosion on Regulated Rivers", Gravel Bed Rivers, McGraw-Hill, New York.

United States Department of Agriculture, Agricultural Research Service. Bank Stability and toe erosion model

Chang, H, 1988. “Fluvial Processes in River Engineering”, John Wiley & Sons, Inc., New York.

Olsen, O. J., Florey, Q.L., 1952. "Sedimentation Studies in Open Channels Boundary Shear and Velocity Distribution by Membrane Analogy, Analytical and Finite-Difference Methods," U.S. Bureau of Reclamation, Laboratory Report N. SP-34, August 5.

L. Fernando, "The effect of flow induced erosion on riverbank stability along the red river in winnipeg", August 2007

Briaud, J.L., Ting, F.C.K., Chen, H.C., Cao, Y., Han, S.W., Kwak, K.W., 2001. “Erosion Function Apparatus for Scour Rate Predictions”. ASCE Journal of Geotechnical and Geoenvironmental Engineering, Vol. 127, No. 2, February.