A Deterministic Bank-Stability
and Toe-Erosion Model
(BSTEM Version 5.4)
Andrew Simon, Robert Thomas, Andrea
Curini and Natasha Bankhead
USDA-ARS National Sedimentation Laboratory,
Oxford, MS
andrew.simon@ars.usda.gov
National Sedimentation Laboratory
What a Model Needs to Incorporate
If we want to model and control bank erosion we
need to quantify and simulate the underlying
processes. These are:
•
•
•
Bank shear strength (resistance to bank failure:
geotechnical processes)
Bank-toe erodibility (resistance to toe erosion and
steepening: hydraulic processes)
The effects of stabilization measures on these
processes (roughness, root reinforcement,
transpiration)
National Sedimentation Laboratory
Bank Stability – The Factor of Safety
Factor of Safety (Fs) =
Resisting Forces
Driving Forces
If Fs is greater than 1, bank is stable. If Fs is less than 1, bank
will fail. (We usually add a safety margin: Fs >1.3 is stable.)
Resisting Forces
soil strength
vegetation
reinforcement
Driving Forces
bank angle
weight of bank
water in bank
Factor of Safety Equation
for Planar Failures
Fs =
S c’iLi + (Si tanfib) + [Wi cosb – Ui + Pi cos (a-b)] tanfi’
S Wi sinb – Pi sin (a-b)
c’ = effective cohesion;
L = length of failure plane;
S = force produced by matric suction on the unsaturated part of the failure surface;
fb = rate of increasing shear strength with increasing matric suction;
W = weight of failure block;
b= failure-plane angle;
U = hydrostatic-uplift force due to positive pore-water pressures on the saturated part of
the failure plane;
P = hydrostatic-confining force provided by the water in the channel; and
f’ = angle of internal friction (rate of increasing shear strength with increasing normal
force).
Simon et al., 2000
Bank-Failure Modes
•
•
Planar Failures, with and without tension
cracks
Cantilever Failures following Undercutting
Model Selects Failure Model based on
minimum Factor of Safety
Root-Strength Can be Incorporated
TENSILE STRENGTH, IN MEGAPASCALS
80
River Birch
Eastern Sycamore
Sweetgum
Black Willow
Gamma grass
Switch grass
Cottonwood
Pine
Oregon Ash
Douglas Spirea
Himalayan Blackberry
60
40
20
0
0
2
4
6
8
10
12
14
16
18
ROOT DIAMETER, IN MILLIMETERS
Cohesion due to roots is a function of the tensile strength
of the roots and their distribution (root-area ratio)
Bank-Stability Model
Version 5.4
shear surface
Tensiometers
(pore pressure)
1.6
1.5
85
Factor of safety
Effect of confining pressure
B
84
1.4
83
Bank failures
1.3
1.2
82
1.1
1.0
0.9
12/29/97
81
Stage
01/05/98
01/12/98
01/19/98
01/26/98
80
02/02/98
RIVER STAGE, IN METERS ABOVE
SEA LEVEL
Confining
pressure
WATER LEVEL, M
•
•
•
•
2-D wedge- and cantilever-failures
Tension cracks
Search routine for failures
Hydraulic toe erosion
Increased shear in meanders
Accounts for grain roughness
Complex bank geometries
Positive and negative pore-water
pressures
Confining pressure from flow
Layers of different strength
Vegetation effects: RipRoot
Inputs: gs, c’, f’, fb , h, uw,
k, tc
FACTOR OF SAFETY
•
•
•
•
•
•
•
•
Input Geometry Sheet
Input bank geometry and flow conditions
Definition of points used in bank
profile
A
B
Work through all 4 sections then hit the "Run Bank Geometry Macro" button.
1) Select EITHER Option A or Option B for Bank Profile and enter the data in the relevant box- cells in the
alternative option are ignored in the simulation and may be left blank if desired.
2) Enter bank material layer thicknesses (if bank is all one material it helps to divide it into several layers).
3) If bank is submerged then select the appropriate channel flow elevation to include confining pressure
and calculate erosion amount; otherwise set to an elevation below the bank toe.
To ensure bank profile is correct you can view it by clicking the View Bank Geometry button.
Option B - Enter a bank height and angle,
the model will generate a bank profile
Option A
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Station
(m)
Option B
Elevation
(m)
0.00
5.00
5.03
5.05
5.08
5.11
5.13
5.16
5.19
5.21
5.24
5.21
5.08
4.92
4.94
5.28
5.30
5.51
5.69
5.87
5.92
6.15
7.16
5.00
5.00
4.69
4.39
4.08
3.78
3.47
3.17
2.86
2.56
2.25
1.94
1.62
1.30
1.00
0.72
0.37
0.19
0.10
0.01
0.00
0.00
0.00
Top of
toe?
5.0
a) Input bank height (m)
85.0
b) Input bank angle (o)
1.0
c) Input bank toe length (m)
25.0
shear surface
emergence
Q
shear
surface
angle
R-U
V
Station (m)
Bank
material
d) Input bank toe angle (o)
Layer 1
Input shear surface angle
Layer 2
Bank layer thickness (m)
Elevation of
layer base (m)
Top Layer
Layer 1
1.00
4.00
Layer 2
1.00
3.00
Layer 3
1.00
2.00
Layer 4
1.00
Layer 5
1.00
Shear emergence elev
1.00
0.00
Bottom
Layer
a
Parallel layers, starting from point B
Point
C-P
Elevation (m)
Option A - Draw a detailed bank
profile using the boxes below
A - bank top: place beyond start
of shear surface
B - bank edge
C-P - breaks of slope on bank
(if no breaks of slope place
as intermediary points)
Q - top of bank toe
R-U - breaks of slope on bank toe
(if no breaks of slope then
W
insert as intermediary
points)
V - base of bank toe
W - end point (typically mid point
of channel)
Layer 3
Notes:
Bank profile may overhang.
If the bank profile is fully populated,
the shear surface emergence point
should be anywhere between points
B and Q.
The shear surface emergence point
must not be on a horizontal section the elevation of this point must be
unique or an error message will
display.
Layer 4
c Toe
material
Layer 5
b
d
Bed material
Shear surface angle
Channel and flow parameters
100
0.0035
Input reach length (m)
Input reach slope (m/m)
2.00
Input elevation of flow (m)
12
Input duration of flow (hrs)
View Bank
Geometry
Run Bank
Geometry Macro
National Sedimentation Laboratory
View Geometry and Select Top of Bank Toe
Input bank geometry and flow conditions
Definition of points used in bank
profile
A
B
Work through all 4 sections then hit the "Run Bank Geometry Macro" button.
1) Select EITHER Option A or Option B for Bank Profile and enter the data in the relevant box- cells in the
alternative option are ignored in the simulation and may be left blank if desired.
2) Enter bank material layer thicknesses (if bank is all one material it helps to divide it into several layers).
3) If bank is submerged then select the appropriate channel flow elevation to include confining pressure
and calculate erosion amount; otherwise set to an elevation below the bank toe.
To ensure bank profile is correct you can view it by clicking the View Bank Geometry button.
Option A
Station
(m)
Elevation
(m)
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
0.00
8.14
8.26
8.37
8.49
8.60
8.72
8.83
8.95
9.06
9.18
9.29
9.41
9.52
9.64
9.75
9.87
10.06
10.25
10.45
10.64
10.83
11.83
5.00
5.00
4.68
4.37
4.05
3.74
3.42
3.10
2.79
2.47
2.16
1.84
1.52
1.21
0.89
0.57
0.26
0.21
0.16
0.10
0.05
0.00
0.00
Option B
Top
of
toe?
5.0
a) Input bank height (m)
70.0
b) Input bank angle (o)
1.0
c) Input bank toe length (m)
15.0
shear surface
emergence
Q
shear
surface
angle
R-U
V
Station (m)
Bank
material
o
d) Input bank toe angle ( )
Notes:
Bank profile may overhang.
If the bank profile is fully populated,
the shear surface emergence point
should be anywhere between points
B and Q.
The shear surface emergence point
must not be on a horizontal section a the elevation of this point must be
unique or an error message will
display.
85
Layer 1
50.0
Input shear surface angle
84
Layer 2
Bank layer thickness (m)
Elevation of
layer base (m)
Top Layer
Layer 1
1.00
4.00
Layer 2
1.00
3.00
Layer 3
1.00
2.00
Layer 4
1.00
1.00
Layer 5
1.00
0.00
Shear emergence elev
Bottom
Layer
Parallel layers, starting from point B
Point
Elevation (m)
Option B - Enter a bank height and angle,
the model will generate a bank profile
C-P
ELEVATION (M)
Option A - Draw a detailed bank
profile using the boxes below
A - bank top: place beyond start
of shear surface
B - bank edge
C-P - breaks of slope on bank
(if no breaks of slope place
as intermediary points)
Q - top of bank toe
R-U - breaks of slope on bank toe
(if no breaks of slope then
W
insert as intermediary
points)
V - base of bank toe
W - end point (typically mid point
of channel)
83
82
81
Layer 3
Layer 4
c Toe
80
material
Layer 5
b
79
-2
d
0
Bed material
2
4
6
8
STATION (M)
Shear surface angle
Channel parameters
Input reach length (m)
Input reach slope (m/m)
Input concentration (kg/kg)
Input elevation of flow (m)
View Bank
Geometry
Run Bank
Geometry Macro
Input duration of flow (hrs)
National Sedimentation Laboratory
Enter Bank-Layer Thickness
Input bank geometry and flow conditions
Definition of points used in bank
profile
A
B
Work through all 4 sections then hit the "Run Bank Geometry Macro" button.
1) Select EITHER Option A or Option B for Bank Profile and enter the data in the relevant box- cells in the
alternative option are ignored in the simulation and may be left blank if desired.
2) Enter bank material layer thicknesses (if bank is all one material it helps to divide it into several layers).
3) If bank is submerged then select the appropriate channel flow elevation to include confining pressure
and calculate erosion amount; otherwise set to an elevation below the bank toe.
To ensure bank profile is correct you can view it by clicking the View Bank Geometry button.
Option B - Enter a bank height and angle,
the model will generate a bank profile
Option A
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Station
(m)
Option B
Elevation
(m)
0.00
5.00
5.03
5.05
5.08
5.11
5.13
5.16
5.19
5.21
5.24
5.21
5.08
4.92
4.94
5.28
5.30
5.51
5.69
5.87
5.92
6.15
7.16
5.00
5.00
4.69
4.39
4.08
3.78
3.47
3.17
2.86
2.56
2.25
1.94
1.62
1.30
1.00
0.72
0.37
0.19
0.10
0.01
0.00
0.00
0.00
Top of
toe?
5.0
a) Input bank height (m)
85.0
b) Input bank angle (o)
1.0
c) Input bank toe length (m)
25.0
shear surface
emergence
Q
shear
surface
angle
R-U
V
Station (m)
Bank
material
d) Input bank toe angle (o)
Layer 1
Input shear surface angle
Layer 2
Bank layer thickness (m)
Elevation of
layer base (m)
Top Layer
Layer 1
1.00
4.00
Layer 2
1.00
3.00
Layer 3
1.00
2.00
Layer 4
1.00
Layer 5
1.00
Shear emergence elev
1.00
0.00
Bottom
Layer
a
Parallel layers, starting from point B
Point
C-P
Elevation (m)
Option A - Draw a detailed bank
profile using the boxes below
A - bank top: place beyond start
of shear surface
B - bank edge
C-P - breaks of slope on bank
(if no breaks of slope place
as intermediary points)
Q - top of bank toe
R-U - breaks of slope on bank toe
(if no breaks of slope then
W
insert as intermediary
points)
V - base of bank toe
W - end point (typically mid point
of channel)
Layer 3
Notes:
Bank profile may overhang.
If the bank profile is fully populated,
the shear surface emergence point
should be anywhere between points
B and Q.
The shear surface emergence point
must not be on a horizontal section the elevation of this point must be
unique or an error message will
display.
Layer 4
c Toe
material
Layer 5
b
d
Bed material
Shear surface angle
Channel and flow parameters
100
0.0035
Input reach length (m)
Input reach slope (m/m)
2.00
Input elevation of flow (m)
12
Input duration of flow (hrs)
View Bank
Geometry
Run Bank
Geometry Macro
National Sedimentation Laboratory
Channel and Flow Parameters
(for Toe- and Total Erosion Calculations)
Input bank geometry and flow conditions
Definition of points used in bank
profile
A
B
Work through all 4 sections then hit the "Run Bank Geometry Macro" button.
1) Select EITHER Option A or Option B for Bank Profile and enter the data in the relevant box- cells in the
alternative option are ignored in the simulation and may be left blank if desired.
2) Enter bank material layer thicknesses (if bank is all one material it helps to divide it into several layers).
3) If bank is submerged then select the appropriate channel flow elevation to include confining pressure
and calculate erosion amount; otherwise set to an elevation below the bank toe.
To ensure bank profile is correct you can view it by clicking the View Bank Geometry button.
Option B - Enter a bank height and angle,
the model will generate a bank profile
Option A
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Station
(m)
Option B
Elevation
(m)
0.00
5.00
5.03
5.05
5.08
5.11
5.13
5.16
5.19
5.21
5.24
5.21
5.08
4.92
4.94
5.28
5.30
5.51
5.69
5.87
5.92
6.15
7.16
5.00
5.00
4.69
4.39
4.08
3.78
3.47
3.17
2.86
2.56
2.25
1.94
1.62
1.30
1.00
0.72
0.37
0.19
0.10
0.01
0.00
0.00
0.00
Top of
toe?
5.0
a) Input bank height (m)
85.0
b) Input bank angle (o)
1.0
c) Input bank toe length (m)
25.0
shear surface
emergence
Q
shear
surface
angle
R-U
V
Station (m)
Bank
material
d) Input bank toe angle (o)
Layer 1
Input shear surface angle
Layer 2
Bank layer thickness (m)
Elevation of
layer base (m)
Top Layer
Layer 1
1.00
4.00
Layer 2
1.00
3.00
Layer 3
1.00
2.00
Layer 4
1.00
Layer 5
1.00
Shear emergence elev
1.00
0.00
Bottom
Layer
a
Parallel layers, starting from point B
Point
C-P
Elevation (m)
Option A - Draw a detailed bank
profile using the boxes below
A - bank top: place beyond start
of shear surface
B - bank edge
C-P - breaks of slope on bank
(if no breaks of slope place
as intermediary points)
Q - top of bank toe
R-U - breaks of slope on bank toe
(if no breaks of slope then
W
insert as intermediary
points)
V - base of bank toe
W - end point (typically mid point
of channel)
Layer 3
Notes:
Bank profile may overhang.
If the bank profile is fully populated,
the shear surface emergence point
should be anywhere between points
B and Q.
The shear surface emergence point
must not be on a horizontal section the elevation of this point must be
unique or an error message will
display.
Layer 4
c Toe
material
Layer 5
b
d
Bed material
Shear surface angle
Channel and flow parameters
100
0.0035
Input reach length (m)
Input reach slope (m/m)
2.00
Input elevation of flow (m)
12
Input duration of flow (hrs)
View Bank
Geometry
Run Bank
Geometry Macro
National Sedimentation Laboratory
Run Bank Geometry Macro
Input bank geometry and flow conditions
Definition of points used in bank
profile
A
B
Work through all 4 sections then hit the "Run Bank Geometry Macro" button.
1) Select EITHER Option A or Option B for Bank Profile and enter the data in the relevant box- cells in the
alternative option are ignored in the simulation and may be left blank if desired.
2) Enter bank material layer thicknesses (if bank is all one material it helps to divide it into several layers).
3) If bank is submerged then select the appropriate channel flow elevation to include confining pressure
and calculate erosion amount; otherwise set to an elevation below the bank toe.
To ensure bank profile is correct you can view it by clicking the View Bank Geometry button.
Option B - Enter a bank height and angle,
the model will generate a bank profile
Option A
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Station
(m)
Option B
Elevation
(m)
0.00
5.00
5.03
5.05
5.08
5.11
5.13
5.16
5.19
5.21
5.24
5.21
5.08
4.92
4.94
5.28
5.30
5.51
5.69
5.87
5.92
6.15
7.16
5.00
5.00
4.69
4.39
4.08
3.78
3.47
3.17
2.86
2.56
2.25
1.94
1.62
1.30
1.00
0.72
0.37
0.19
0.10
0.01
0.00
0.00
0.00
Top of
toe?
5.0
a) Input bank height (m)
85.0
b) Input bank angle (o)
1.0
c) Input bank toe length (m)
25.0
shear surface
emergence
Q
shear
surface
angle
R-U
V
Station (m)
Bank
material
d) Input bank toe angle (o)
Layer 1
Input shear surface angle
Layer 2
Bank layer thickness (m)
Elevation of
layer base (m)
Top Layer
Layer 1
1.00
4.00
Layer 2
1.00
3.00
Layer 3
1.00
2.00
Layer 4
1.00
Layer 5
1.00
Shear emergence elev
1.00
0.00
Bottom
Layer
a
Parallel layers, starting from point B
Point
C-P
Elevation (m)
Option A - Draw a detailed bank
profile using the boxes below
A - bank top: place beyond start
of shear surface
B - bank edge
C-P - breaks of slope on bank
(if no breaks of slope place
as intermediary points)
Q - top of bank toe
R-U - breaks of slope on bank toe
(if no breaks of slope then
W
insert as intermediary
points)
V - base of bank toe
W - end point (typically mid point
of channel)
Layer 3
Notes:
Bank profile may overhang.
If the bank profile is fully populated,
the shear surface emergence point
should be anywhere between points
B and Q.
The shear surface emergence point
must not be on a horizontal section the elevation of this point must be
unique or an error message will
display.
Layer 4
c Toe
material
Layer 5
b
d
Bed material
Shear surface angle
Channel and flow parameters
100
0.0035
Input reach length (m)
Input reach slope (m/m)
2.00
Input elevation of flow (m)
12
Input duration of flow (hrs)
View Bank
Geometry
Run Bank
Geometry Macro
National Sedimentation Laboratory
On Bank-Model Output Page
(if you want to check layering)
Bank model output
Verify the bank material and bank and bank-toe protection information entered in the "Bank Material" and "Bank Vegetation and Protection"
worksheets. Once you are satisfied that you have completed all necessary inputs, hit the "Run Bank Stability Model" button (Center of this
page).
6.00
0
5.00
0
ELEVATION (M)
0
base of layer 2
kPa
Layer 1
Pore Pressure From
Water Table
-24.52
Layer 2
-14.71
basewater
of layer
4
surface
Layer 3
-4.90
table 5
basewater
of layer
Layer 4
4.90
failure plane
Layer 5
14.71
3.00
basebase
of layer
of layer13
2.00
of layer24
basebase
of layer
base of layer 5
0.00
0.00
base of layer 3
2.00
4.00
6.00
8.00
10.00
12.00
STATION (M)
14.00
water surface
2.00
4.00
Own Pore
Pressures
failure plane
-1.00
0
0
bank profile
1.00
0
Input own pore pressures (kPa)
base of layer 1
4.00
0
0
0.00
bank profile
Water table depth (m) below bank top
3.00
Use water table
6.00
8.00
10.00
12.00
14.00
water table
Select and Input Bank Materials
Select material types (or select "own data" and add values below)
Layer 1
Bank Material
Layer 3
Layer 2
Own data
Own data
Own data
Bank Toe Material
Layer 4
Layer 5
Own data
Own data
Own data
Select material types (or select "own data" and add values below)
Layer 1
Bank Material
Layer 3
Layer 2
Moderate soft clay
Moderate soft clay
Moderate silt
Bank Toe Material
Layer 4
Hydraulic resistance
Layer 5
Erodible silt
Own data
Moderate silt
Bank and bank-toe material data tables.
These are the default parameters used in the model. Changing the values or descriptions will change the
values used when selecting soil types from the list boxes above. Add your own data using the white boxes.
Material Descriptors
Bank material
type
1
2
3
4a and 4b
5a and 5b
6a, 6b and 6c
7a, 7b and 7c
8a, 8b and 8c
Description
Friction angle
f ' (degrees)
Cohesion c'
(kPa)
0.512
0.128
0.0113
42.0
42.0
36.0
0.0
0.0
0.0
Bank Model Input Data
Saturated unit
weight
fb
(kN/m 3 )
20.0
20.0
20.0
0.00035
0.00035
36.0
27.0
0.0
0.0
-
30.0
25.0
20.0
3.0
10.0
15.0
Mean grain
size, D 50 (m)
Boulders
Cobbles
Gravel
Angular sand
Rounded sand
Silt
Soft clay
Stiff clay
Groundwater Model Input Data
15.0
15.0
15.0
Chemical
concentration
(kg/kg)
-
Hydraulic
Conductivity
k sat (m/s)
1.745E-03
1.745E-03
3.160E-03
18.0
18.0
15.0
15.0
-
18.0
18.0
18.0
15.0
15.0
15.0
-
(degrees)
Own data layer 1
Own data layer 2
9
Own data layer 3
Own data layer 4
Own data layer 5
Own data Bank Toe
Need to know the critical shear stress (tc) ?
Need to know the erodibility coefficient (k ) ?
Input non-cohesive particle diameter (mm)
Input critical shear stress tc (Pa)
Critical Shear Stress tc (Pa)
Erodibility Coefficient (cm3/Ns)
Geotechnical
resistance
Toe Model Input Data
Bulk Modulus
(Pa)
Porosity
Residual
water content
6.556E+08
6.556E+08
1.354E+08
0.280
0.280
0.320
0.090
0.090
0.070
van
Genuchten a
(1/m )
3.5237
3.5237
3.5237
7.439E-05
1.130E-06
1.354E+07
6.056E+07
0.375
0.380
0.053
0.033
3.5237
4.0563
3.1769
2.3286
Coarse (0.71 mm) or
Fine (0.18 mm)
5.064E-06
9.473E-07
1.708E-06
1.049E+07
1.354E+06
5.417E+06
0.489
0.442
0.459
0.050
0.079
0.098
0.6577
1.5812
1.4962
1.6788
1.4158
1.2531
Erodible (0.100 Pa),
Moderate (5.00 Pa), or
Resistant (50.0 Pa)
COMING
SOON!
van
Genuchten n
tc (Pa)
k
(cm3/Ns)
2.3286
2.3286
2.3286
498
124
11.0
0.004
0.009
0.030
Bank Material Sheet: Geotechnical Data
Select material types (or select "own data" and add values below)
Layer 1
Bank Material
Layer 3
Layer 2
Moderate silt
Moderate silt
Moderate silt
Bank Toe Material
Layer 4
Moderate silt
Layer 5
Own data
Moderate silt
Bank and bank-toe material data tables.
These are the default parameters used in the model. Changing the values or descriptions will change the
values used when selecting soil types from the list boxes above. Add your own data using the white boxes.
Material Descriptors
Bank material
type
1
2
3
4a and 4b
5a and 5b
6a, 6b and 6c
7a, 7b and 7c
8a, 8b and 8c
Description
Mean grain
size, D 50 (m)
Boulders
Cobbles
Gravel
Angular sand
Rounded sand
Friction angle
f ' (degrees)
Bank Model Input Data
Saturated unit
Cohesion c'
weight
(kPa)
(kN/m 3 )
0.0
20.0
0.0
20.0
0.0
20.0
0.512
0.128
0.0113
42.0
42.0
36.0
0.00035
0.00035
36.0
27.0
0.0
0.0
-
25.0
30.0
10.0
5.0
10.0
15.0
Silt
Soft clay
Stiff clay
18.0
18.0
15.0
15.0
7.439E-05
1.130E-06
18.0
16.0
18.0
15.0
15.0
15.0
5.064E-06
9.473E-07
1.708E-06
f
(degrees)
Own data layer 1
Own data layer 2
9
C
J
5.0
5.0
5.0
Hydraulic
Conductivity
k sat (m/s)
1.745E-03
1.745E-03
3.160E-03
b
Own data layer 3
Own data layer 4
Own data layer 5
Own data Bank Toe
Need to know the critical shear stress (tc) ?
Need to know the erodibility coefficient (k ) ?
Input non-cohesive particle diameter (mm)
Input critical shear stress tc (Pa)
Critical Shear Stress tc (Pa)
Erodibility Coefficient (cm 3/Ns)
Bank Material Sheet: Hydraulic Data
Toe Model Input Data
tc (Pa)
k (cm3/Ns)
498
124
11.0
0.004
0.009
0.030
Coarse (0.71 mm) or
Fine (0.18 mm)
Erodible (0.100 Pa),
Moderate (5.00 Pa), or
Resistant (50.0 Pa)
Own data layer 1
Own data layer 2
Own data layer 3
Own data layer 4
Own data layer 5
Own data Bank Toe
Need to know the erodibility coefficient (k ) ?
Need to know the critical shear stress (tc) ?
Input non-cohesive particle diameter (mm)
20.000
Input critical shear stress tc (Pa)
5.000
Critical Shear Stress tc (Pa)
19.44
Erodibility Coefficient (cm3/Ns)
0.045
Toe Erosion
Select material types (or select "own data" and add values below)
Layer 1
Bank Material
Layer 3
Layer 2
Erodible silt
Erodible silt
Erodible silt
Bank Toe Material
Layer 4
Erodible silt
Layer 5
Erodible silt
Erodible silt
For the case: slope = 0.003, flow depth = 2 m; duration = 6 hrs.
Toe Model Output
Verify the bank material and bank and bank-toe protection information entered in the "Bank Material" and "Bank Vegetation and Protection"
worksheets. Once you are satisfied that you have completed all necessary inputs, hit the "Run Toe-Erosion Model" button (Center Right
of this page).
Bank Toe Material
Layer 1
Erodible cohesive
Layer 2
Erodible cohesive
Bank Material
Layer 3
Erodible cohesive
Layer 4
Erodible cohesive
Layer 5
Erodible cohesive
Erodible cohesive
0.10
0.10
0.10
0.10
0.10
0.10
0.316
0.316
0.316
0.316
0.316
0.316
6.00
5.00
Base of layer 1
ELEVATION (M)
4.00
Base of layer 2
Run Toe-Erosion
Model
Material
Critical shear stress
(Pa)
Erodibility Coefficient
(cm3/Ns)
Account for:
Stream Curvature
Effective stress
acting on each grain
Base of layer 3
3.00
Pa
Average applied boundary shear stress
Base of layer 4
Maximum Lateral Retreat
0.000
cm
Base of layer 5
Eroded Area - Bank
0.000
m2
Eroded Profile
Eroded Area - Bank Toe
0.000
m2
Eroded Area - Bed
0.000
m2
Eroded Area - Total
0.000
m2
2.00
1.00
0.00
-1.00
-1.00 0.00
Initial Profile
Water Surface
1.00
2.00
5.00
4.00
3.00
STATION (M)
6.00
7.00
8.00
9.00
Export New (Eroded) Profile into Model
Toe Erosion
Select material types (or select "own data" and add values below)
Layer 1
Bank Material
Layer 3
Layer 2
Erodible silt
Erodible silt
Erodible silt
Bank Toe Material
Layer 4
Erodible silt
Layer 5
Erodible silt
Erodible silt
For the case: slope = 0.003, flow depth = 2 m; duration = 6 hrs.
6.00
5.00
Base of layer 1
ELEVATION (M)
4.00
Base of layer 2
Stream Curvature
Effective stress
acting on each grain
Base of layer 3
3.00
Average applied boundary shear stress
33.650
Pa
Maximum Lateral Retreat
42.481
cm
Base of layer 5
Eroded Area - Bank
0.228
m2
Eroded Profile
Eroded Area - Bank Toe
0.519
m2
Eroded Area - Bed
0.000
m2
Eroded Area - Total
0.747
m2
Base of layer 4
2.00
1.00
0.00
-1.00
-1.00 0.00
Run Toe-Erosion
Model
Account for:
Initial Profile
Water Surface
1.00
2.00
3.00
4.00
5.00
STATION (M)
6.00
7.00
8.00
9.00
Export New (Eroded) Profile into Model
Click this button to export eroded profile to Option
A in Input Geometry worksheet
Profile Exported into Option A
Option A - Draw a detailed bank
profile using the boxes below
Option A
Point
Station
(m)
Elevation
(m)
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
0.00
10.08
10.16
10.23
10.30
10.38
10.45
10.53
10.60
10.68
10.75
10.82
10.89
10.92
10.91
10.90
10.97
11.45
11.80
12.15
12.26
12.72
13.76
5.00
5.00
4.72
4.45
4.17
3.89
3.62
3.34
3.06
2.78
2.51
2.23
1.95
1.66
1.36
1.06
0.62
0.44
0.25
0.06
0.00
0.00
0.00
Shear emergence elev
Shear surface angle
Top
of
toe?
Model redirects you back to the
“Input Geometry” sheet. You can
run another flow event or run the
Bank-Stability model.
To run Bank-Stability Model you
can select a shear-surface
emergence elevation and shearsurface angle or leave blank and
search routine will solve.
Results: Factor of Safety
Factor of Safety
Conditionally
stable
Failure width
Failure volume
Sediment loading
Constituent load
2.35
487
814176
814
Partly controlled by failure plane angle
Based on reach length
m
m3
kg
kg
Based on constituent concentration
Select material types, vegetation cover and water table depth below bank top
(or select "own data" and add values in 'Bank Model Data' worksheet)
Layer 1
Layer 2
Gravel
Angular sand
Rounded sand
Silt
Stiff clay
Layer 3
Gravel
Angular sand
Rounded sand
Silt
Stiff clay
Layer 4
Gravel
Angular sand
Rounded sand
Silt
Stiff clay
Gravel
Angular sand
Rounded sand
Silt
Stiff clay
Layer 5
Gravel
Angular sand
Rounded sand
Silt
Stiff clay
Bank top
vegetation cover (age)
None
Vegetation safety margin
50
Reach Length
(m)
100
Constituent
concentration (kg/kg)
0.001
Water table depth (m) below bank top
4.00
Use water table
6.00
Input own pore pressures (kPa)
5.00
bank profile
base of layer 1
4.00
ELEVATION (M)
1.09
base of layer 2
3.00
Own Pore
Pressures
kPa
Layer 1
Pore Pressure
From Water Table
-34.34
Layer 2
-24.53
Layer 3
-14.72
Layer 4
-4.91
Layer 5
4.91
base of layer 3
2.00
base of layer 4
failure plane
1.00
water surface
0.00
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
water table
-1.00
STATION (M)
57.5
Shear surface angle used
Export Coordinates back into model
Factor of Safety
1.09
Conditionally
stable
Failure width
Failure volume
Sediment loading
Constituent load
2.35
487
814176
814
m
3
m
kg
kg
Bank Model Output
Bank model output
Verify the bank material and bank and bank-toe protection information entered in the "Bank Material" and "Bank Vegetation and Protection"
worksheets. Once you are satisfied that you have completed all necessary inputs, hit the "Run Bank-Stability Model" button.
Layer 1
Soft Clay
Layer 2
Soft Clay
Bank Material Properties
Layer 3
Silt
Layer 4
Silt
Layer 5
Silt
Water table depth (m) below bank top
3.00
Use water table
6.00
5.00
Input own pore pressures (kPa)
bank profile
base of layer 2
kPa
Layer 1
Pore Pressure From
Water Table
-24.52
base of layer 3
Layer 2
-14.71
base of layer 4
Layer 3
-4.90
base of layer 5
Layer 4
4.90
failure plane
Layer 5
14.71
base of layer 1
4.00
ELEVATION (M)
Water-table
depth at 3.0 m
3.00
2.00
1.00
Own Pore
Pressures
water surface
-10.00
-5.00
0.00
0.00
5.00
10.00
15.00
water table
-1.00
Factor of Safety
0.87
0.81
STATION (M)
Unstable
Run Bank-Stability Model
Click “Run Bank-Stability Model”
Bank is
Unstable
Fs < 1.0
Bank Model Output: Specific Results
Failure dimensions
(loading)
Failure plane from
search routine
1.3
Shear emergence elevation
68.1
Shear surface angle used
Export New (Failed) Profile into Model
Failure width
Failure volume
Sediment loading
Constituent load
1.77
422
674210
0
m
m3
kg
kg
How can you make this bank more
stable or more unstable?
Experimenting with the following parameters provides an
understanding of controlling variables and
requirements for stability
•
•
•
•
•
Water surface elevation (Input Geometry sheet)
Shear angle (Input Geometry sheet)
Water-table height (Bank Model Output sheet)
Bank material types (Bank Material sheet)
Vegetation component (Vegetation and Protection sheet)
National Sedimentation Laboratory
Example With Undercut Toe
Under these conditions the bank is stable
•
Bank stability is reduced, but bank is still
stable.
National Sedimentation Laboratory
Bank is now unstable (Fs = 0.93) with
loss of confining pressure
National Sedimentation Laboratory
Factor of Safety without tension crack
•
In this case bank Fs without a
tension crack is 1.21
Factor of Safety with a tension crack
•
Bank Fs was 1.21
without a tension
crack but is 0.99
with a tension
crack
Root Reinforcement using RipRoot
Root Reinforcement using RipRoot
Simple Case: 1 species
1. Select “Meadow, Wet”
2. Enter age and percent
contribution to stand
3. Click when finished
RipRoot: Results
Evaluating the Role of Toe Protection
Toe Model Output
Verify the bank material and bank and bank-toe protection information entered in the "Bank Material" and "Bank Vegetation and Protection"
worksheets. Once you are satisfied that you have completed all necessary inputs, hit the "Run Toe-Erosion Model" button (Center Right
of this page).
Layer 1
Moderate cohesive
Layer 2
Moderate cohesive
Bank Material
Layer 3
Moderate cohesive
Layer 4
Moderate cohesive
Layer 5
Moderate cohesive
Bank Toe Material
Moderate cohesive
5.00
5.00
5.00
5.00
5.00
5.00
0.045
0.045
0.045
0.045
0.045
0.045
6.00
5.00
Base of layer 1
ELEVATION (M)
4.00
Base of layer 2
Critical shear stress
(Pa)
Erodibility Coefficient
(cm3/Ns)
Slope = 0.0035 m/m
Account for:
Depth = 2.5 m
Stream Curvature
Effective stress
acting on each grain
Base of layer 3
3.00
Base of layer 4
2.00
1.00
0.00
-1.00
-1.00 0.00
Run Toe-Erosion
Model
Material
Average applied boundary shear stress
51.060
Pa
Maximum Lateral Retreat
24.966
cm
Base of layer 5
Eroded Area - Bank
0.232
m
Eroded Profile
Eroded Area - Bank Toe
0.423
m2
Eroded Area - Bed
0.000
m2
Eroded Area - Total
0.655
m2
Initial Profile
Toe material: silt
2
Eroded: 0.66 m2
Water Surface
1.00
2.00
3.00
4.00
5.00
STATION (M)
6.00
7.00
8.00
Export New (Eroded) Profile into Model
9.00
Toe Model Output
Verify the bank material and bank and bank-toe protection information entered in the "Bank Material" and "Bank Vegetation and Protection"
worksheets. Once you are satisfied that you have completed all necessary inputs, hit the "Run Toe-Erosion Model" button (Center Right
of this page).
Layer 1
Moderate cohesive
Layer 2
Moderate cohesive
Bank Material
Layer 3
Moderate cohesive
Layer 4
Moderate cohesive
Layer 5
Moderate cohesive
Bank Toe Material
5.00
5.00
5.00
5.00
5.00
204.00
0.045
0.045
0.045
0.045
0.045
0.007
Rip Rap (D50 0.256 m) Material
6.00
5.00
Base of layer 1
ELEVATION (M)
4.00
Base of layer 2
Depth = 2.5 m
Account for:
Stream Curvature
Effective stress
acting on each grain
Base of layer 3
3.00
Base of layer 4
1.00
0.00
Average applied boundary shear stress
51.060
Pa
Maximum Lateral Retreat
24.159
cm
Base of layer 5
Eroded Area - Bank
0.232
m2
Eroded Profile
Eroded Area - Bank Toe
0.044
m2
Eroded Area - Bed
0.000
m2
Eroded Area - Total
0.276
m2
2.00
-1.00
-1.00 0.00
Run Toe-Erosion
Model
Slope = 0.0035 m/m
Critical shear stress
(Pa)
Erodibility Coefficient
(cm3/Ns)
Initial Profile
Water Surface
1.00
2.00
3.00
4.00
5.00
STATION (M)
6.00
7.00
8.00
9.00
Export New (Eroded) Profile into Model
Toe material: rip rap
Eroded: 0.28 m2
Summary
• The Bank-Stability and Toe-Erosion Model is a simple
spreadsheet tool that can be populated with field or default
values
• It can be used to test the effects of hydraulic scour, watertable height, vegetation, and stage on stability
• Used iteratively with a knowledge of the flow regime, it
can be used to predict widening rates.
• It can be used to test various mitigation strategies (rock,
vegetation, etc.) to control undercutting and mass failure.
• It also contains sound effects for bank collapse!