ENV-2E1Y
Fluvial Geomorphology
2004 - 2005
Slopes and related topics
Section 6 Stability of River Banks
Slope Stability and Related Topics
6. Stability of River Banks
6.1 Introduction
The methods to analyse the stability of slopes have been
covered in section 5, and while the methods described
may be relevant to studies of the behaviour of river
banks in some situations, in most cases, the methods are
inappropriate even though river bank failures are in
effect small scale slope failures. The reason for this is
that the mechanism of failure is often very different and
these differences arises from the relative contribution of
cohesion to the stability of slopes.
In the late 1970's several other mechanisms of failure
were identified by Colin Thorne working under the
direction of Drs R.D Hey and N.K. Tovey and followed
extensive on site examination of failures by the group.
Fig. 6.1 Failure of a river bank as a typical slope failure.
The height of the slope relative to the depth of
tension cracks is large.
It is thus necessary to categorise river banks into three
groups based on the types of failure mechanism that will
occur.
Failures by this means can occur on quite shallow slopes
(e.g. 5o) particularly in quick clays (e.g. Scandinavia and
southern Canada). In very cohesive soils, the angle of
friction may be quite low (~ 5o) resulting in deep seated
failures which often have the toe partly in the river. In
periods of heavy rain, pore water pressures can develop
behind the clay skin to such an extent that the clay layer
is lifted off from the parent block leaving a freshly
fractures micro-surface free for attack by the river again.
On non-vertical banks, rain-drops impinging on the
surface of the clay can also break up this surface layer,
sometimes giving a prismatic appearance.
An eroding river will often produce a steep near vertical
bank up to a few metres in height. Shear stresses on the
outer bend of the water may be sufficient to remove
material directly if there is a high silt, sand or gravel
content. In highly cohesive banks, the clay present tends
to be smoothed by the action of the flowing water which
in turn will tend to seal the bank from further erosion
directly from the water. Surface layers of the clay with
highly orientated clay layers can form and these can
become significantly more impermeable to water.
Cohesive river banks can be stable in the short term from
cohesion present and negative pore water pressures.
6.2.2 River banks of moderate height ( typically 2 5m)
6.2 Type of failure in river banks.
These banks are assumed to be composed of overconsolidated sediments. The over-consolidation in many
cases will arise solely from desiccation. In these river
banks the depth of tension cracks (at about 2m) become
significant and the mechanism of failure tends to become
more slab like even in near vertical river banks. Tension
cracks develop in dry weather a ped boundaries (those
doing Soil Science will know what a ped is!), and these
tend to be spaced at about 0.3 m intervals in the typical
river deposits found in many UK river valleys.
6.2.1 River banks (slopes) higher than approximately
5m
River banks which are relatively high (> 5m) have
potential failure mechanisms similar to those discussed in
section 5. Even when cohesion is present the maximum
depth of tension cracks rarely exceeds 2m (for a cohesion
of 40 kPa - see equation 5.6). Typical failures will be
arcs of circles and failure will occur via a rotational slip
into the river. Such river banks are frequently in material
with moderate cohesion and are dominated in terms of
time of failure by antecedent rainfall. River erosion at
the base can cause over-steepening, but this in itself
rarely triggers a failure.
Failure zones (usually nearly straight - but sometimes
slightly curved) may form. These failure surfaces are
often at nearly 450 to the horizontal, and the base may be
above the base of the cut river channel.
Fig. 6.1 shows an example of such a failure.
Failure is this mode is particularly likely during a period
of heavy rain immediately following a dry spell. At the
onset of rain, the cracks are open (sometimes hey can
75
N.K. Tovey
ENV-2E!Y Fluvial Geomorphology: 2002 - 2003
be as wide as 10 - 20 cm or more) and rapidly fill with
water. The hydrostatic pressure from the water will
rapidly decrease the stability of the slab even before the
river level rises in response to the storm. At this stage
the pore water pressure on the actual failure surface may
still be negative, but it is the sudden increase in the
additional lateral force which may cause failure.
Section 6
Though the failure mechanism is very different from
those discussed in section 5, the method of analysis is
exactly the same. In effect the slab is equivalent to a
single slice in the general method of analysis discussed in
section 5.8.
6.2.3 River banks with heights less than 2m and also
composite river banks less than 5m high.
A typical slab like failure in a bank of moderate height is
shown in Fig. 6.2.
There are two categories of river bank here:1) Those in recently deposited sediments which are
normally or lightly over-consolidated such as the
banks for rivers in recent marine deposits in
estuaries etc.
2) Those which are composite in nature usually
consisting of a sandy gravel overlain by a cohesive
upper bank. The gravel/sand granular layer may
also have some cohesion, but this is must less than
that of the upper bank.
The granular layer may be imbricated with plate
shaped gravel-sized particles laid with their long
axis nearly horizontal. These structures arise from
flood conditions in the river where the gravel is laid
down as point bars. Subsequent vegetation growth
will trap finer clays and build up the cohesive upper
bank.
Fig. 6.2 Failure of river banks which are of moderate
height.
Such sections become exposed again as the river
meanders across the valley floor. When a river
erodes at the extreme side of the valley floor, the
outer bend cannot be of composite nature and the
bank and valley slope will usually be much higher
than on the other side. For these latter banks, the
methods of analysis discussed in section 6.2.1 and
6.2.2 are relevant.
The depth of tension cracks is comparable to the bank
height. Failure is usually on a near planar surface.
Water infiltrating the crack immediately after a dry
period can cause a critical time for failure. Failure is
unlikely at bankful discharge, but may fail (if is has not
previously) after the stage falls. However, if the crack
closes following swelling this will tend to increase
stability.
6.2.4 River banks (< 2m) in recent deposits
If the slab survives the initial water ingress, the rise the
in river stage will saturate the block and provide
buoyancy to the block and also counter-balance the
lateral forces of the water in the crack . Failure during
this time is unlikely.
The material forming these banks is normally
consolidated or lightly over-consolidated at best and the
stress point will lie to the right of the critical state line in
the e - log  plot. The material will be at high at a
voids ratio often at or above the liquid limit (i.e. the
Liquidity Index will be near 1.0). The shear stresses
developed in flowing water will often be sufficient to
entrain parts of the clay causing a steepening of channel.
This will in turn will impose relatively rapid increases in
the mobilising shear forces on potential failure zones
results in deformation with the build up of excess pore
water pressure and thus rapid failure.
The clay around the crack will begin to swell and fill the
crack and the effects of the lateral water pressure will
diminish. However, if the stage level falls before the
crack seals, a second more critical phase regarding
stability will occur. Positive water pressure will now
exist on the potential failure surface and also as the
buoyancy effect is removed, the full saturated bulk unit
weight of the block comes into play. Previously
immediately after the start of the rainstorm, a partially
dry unit weight would have been the relevant weight. If
the crack seals, then the effective failure surface
increases and failure is not as likely to occur.
Frequently failure occurs in banks of low height for this
reason. Traditional methods of analysis are relevant for
analysis, but as the geometry of the slope is changing
rapidly (e.g. each tidal cycle in estuaries), it is difficult to
precisely define the critical slope shape before failure.
76
N.K. Tovey
ENV-2E!Y Fluvial Geomorphology: 2002 - 2003
Section 6
6.3 Composite river banks
on the outside of the upper blank protecting it from
further erosion.
6.3.1 General description of banks and erosion of lower
bank
6.3.2. Failure of the Cohesive Upper Bank
With continued erosion a cantilever overhang will
develop and the stability of this part of the bank will be
dependant on the density of the root matting of the
vegetation and also the cohesive and in particular the
tensile strength within the bank material.
These river banks will normally be less than 2m in height
(occasionally up to 5m) with a lower imbricated gravel
layer and a cohesive layer above covered with
vegetation. The stability of these banks cannot be
analysed by even a modification of the traditional
methods of analysis as the modes of failure are very
different.
Eventually, the upper bank will fail as a single unit, but
the mode of failure depends SOLELY on the geometry of
the system. Whether or not it actually fails does depends
on the material properties, but the actual mode depends
on the overhang to depth ratio. It can be further shown,
that in most situations, failure will occur when the
overhang reaches 0.3 m in width.
The underlying gravel tends to be more easily eroded
than the cohesive upper bank, although in some special
conditions the reverse is true.
The failure of these cantilevers occurs as a solid block.
Usually they are between 0.5 and 1.0 m in length.
6.3.3. Development of Desiccation Cracks from base of
cantilever block
Fig. 6.3
Once an overhang develops and the stage level falls, the
cantilevered block will dry, and as it does so its unit
weight will decrease, and in many situation, this will
increase the stability of the block.
However, it is
commonly observed that a desiccation crack appear to
develop upwards from the base of the overhang (see Fig.
6.3). The exactly position of the crack is governed partly
by stress release and also the presence of ped boundaries.
Once the crack begins to form, it readily widens as any
loose material will fall from it (unlike the cracks which
develop at the top of a slope where the debris will tend to
fill the crack once they exceed the critical depth). This
crack will propagate upwards and is usually arrested by
the root matting which will act as reinforcement and
prevent further propagation.
Development of desiccation crack in a
composite river bank. In many areas the
depth of the vegetation and root matting is
around 30 cm. The lower non-cohesive
bank is more readily eroded creating a
cantilever overhang.
The lower bank is frequently attached by the shear
stresses in the water as the river stage rises and entrains
the smaller sand and gravel particles from this layer. At
low flows, there will be little entrainment, but aeolian
action arising from the desiccation of the surface crust of
the vertical lower bank will cause the finer particles to
loose their adhesion to the bank (removal of the negative
pore water pressure), and will fall away onto the debris
slope beneath).
6.3.4 Development of normal tension cracks at top of
cantilever block
In normal slopes, tension cracks will develop at the
surface of a slope. In the failure of cantilever blocks,
these only occur shortly before failure, and it is rare to
see evidence of such cracks except immediately prior to
failue. The reason for the later development in this case
is that the root matting offers a resistance to crack
development which is significant proportion of the forces
involved.
At high flows, direct action arising from the shear
stresses set up in the water will cause the finer granular
particles to be remove from within the voids in the
imbricated gravel, and this in turn will expose the platy
gravel particles to drag forces which may or may not be
sufficient to remove them from the bank. If removal
takes place, the fresh bank may be attacked and the
upper cohesive bank may be undercut causing a
cantilever overhang. If the discharge is at bank full, then
significant shear stress may develop and erosion of the
low bank may be pronounced. Erosion of the upper
bank, even though it is now covered by water, tends to be
much less because of the smearing of the clay particles
6.3.5 Modes of Failure of Cantilever Blocks
As indicated above, the modes of failure of the upper
bank are dependant on geometry, but 3 basic modes of
failure have been noted:77
N.K. Tovey



ENV-2E!Y Fluvial Geomorphology: 2002 - 2003
directly in the river) immediately adjacent to the
bank and with the grass root matting intact and
pointing upwards. The grass surface will be nearly
horizontal or tilting backwards slightly.
shear type failure
beam type failure
tensile failure
Direct observation of the failed blocks allows the actual
mode of failure to be determined. Thus:a)
Section 6
Occasionally a hybrid failure (~ 5% of failures) between
beam and tensile failures is noted. Of the three failures,
shear type failures are not common.
In shear failures, the block will slide bodily
downwards and come to rest on the lower bank (or
Fig. 6.4 Modes of failure in composite river banks. A). Shear type failure; B) Tensile failure; C). Beam type
rotational failure.
b)
c)
In tensile failures, the lower part of the cantilever
block becomes so heavy that it exceed the tensile
strength of the soil and the lower part drops bodily
to the lower bank (or river). The final position of
the block is identical to that in shear failures except
that the upper surface (including the vegetated mat)
remain in place at the top of the bank. The failed
block has no vegetation on it.
Not infrequently the base of the root matting is the
plane of weakness along which failure occurs, but
this is not always the case.
lower bank on the debris slope. On the other hand at the
outside of rapidly eroding bends, they may fall into the
river and affect the flow of water in the vicinity. During
failure, the blocks usually fail as one complete block,
occasionally splitting into 2 or 3, but largely the blocks
remain intact.
If the blocks are submerged, then the surface of the
cohesive material will become smeared and this will tend
to protect the block from further erosion of the river.
Sometimes the blocks fall into the water close to the
bank, and will thus protect the lower bank from
subsequent erosion.
In beam failures, the block rotates during failure
and ends up on the lower bank or in the river with
the vegetated mat still in place but lying in a
vertical plane and pointing towards the river.
Some cases have been noted where such failed blocks
have deflected the main filament of the water flow away
from the eroding section, and what was previously an
actively eroding section now stabilises and vegetation
takes hold on the lower bank entrapping any cohesive
material which may pass in the relatively stagnant water
during higher stage flows.
6.3.6. Post failure of the composite river bank
After failure, the final resting position of the failed block
is important to the subsequent sequence of erosion effect
by the river. Blocks may remain relatively dry on the
78
N.K. Tovey
ENV-2E!Y Fluvial Geomorphology: 2002 - 2003
The weight of the block reduced while submerged ( unit
weight is acting), and it is possible for the whole block to
be moved bodily by the current although more usually
this is by a rolling motion. However, this rarely occurs
unless the block falls so that it is at an angle to the river
and a small movement in such a direction tends to move
into the broadside on position. In some cases, several
failed blocks have been noted which have moved by
rotation and then interfered with each other such that a
small dam has been created across part of the river. This
clearly will greatly affect the river flow during periods of
low flow, and to a lesser extent high flow.
Section 6
6.4 Mechanisms of failure of composite
river banks
6.4.1 Stability Charts
The modes of failure and the forces involved are shown
in Fig. 6.5
If blocks do start rolling in subsequent high stage flows,
then they may break and abrade, and as they do so they
are more readily entrained. Failed blocks have been seen
to remain in their initial failed position (or close by) for
several months or even years, and can thus significantly
affect the next stage of erosion of the lower bank.
6.3.6 Behaviour of in composite river banks as the
river stage level changes.
At low river stages, the cantilever overhangs will
normally desiccate and as they do so the unit weight will
fall which will mean that the weight potentially causing
failure will reduce and the block will become more
stable. Further since erosion of the non-cohesive lower
bank only takes place during high stages, there will be
minimal increase in the overhang, apart from a small
amount of sub-aerial weathering.
Fig. 6.5
Forces associated with different modes of
failure
It is necessary to specify the geometry of the cantilever
block as shown in Fig. 6.6.
However, a lower desiccation crack will begin to form,
and this is assumed to follow a former ped boundary.
The crack propagates upwards, and unlike tension cracks
at the top of normal failures, and material falling from
the sides of the crack will be lost for ever.
The proportion of the block attached will reduce, and this
will thus reduce its resistance to failure.
Immediately after the river stage rises, the block
saturates which means that the unit weight increases, and
potentially the stability decreases. However, there is
also the bouyancy of the river water itself, and thus the
submerged unit weight is thus appropriate, and this will
be much less than either the cry or the saturated bulk unit
weights, and thus the block will become more stable.
Fig. 6.6 Geometry of cantilever block and two geometric
non-dimensional groups.
As with much of the rest of this course it is convenient to
unify all analyses into a single chart and for this we need
to identify three non-dimensional groups.
The first two are purely geometric and relate to the
breadth to height ratio (B) and the proportion of the
block that is unaffected by the desiccation crack ( b)
If the stage falls immediately, before any further erosion
takes place, then this will be the most critical time with
regards for stability, as the bouyancy is lost and the full
unit weight acts.
Further the desiccation crack
developed during the previous low stage will have
reduced the stability and failure may occur.
b
H
H
and  
H
i.e.
B
At high stages, erosion is most prevalent, and further
undercutting takes place thereby decreasing the stability
of the block. The mode of failure is solely dependant on
the geometry of the block. Whether the block actually
fails depends on the material properties of the block.
79
N.K. Tovey
ENV-2E!Y Fluvial Geomorphology: 2002 - 2003
Section 6
The final non-dimensional parameter is A which relates
the tensile strength (t) of the soil to the unit weight and
the breadth b
A
i.e.
t
b
To evaluate the stability in a particular mode, the nondimensional parameters are first evaluated. For many
soils, the tensile strength is around 5 kPa, and since the
unit weight is between 15 and 20 kPa,, the factor A will
be between 0.25 and 0.33 time the breadth of the block.
As an approximation, and initial value of 0.3b may be
used for A.
We must now examine the stability of the block with
respect to all three modes of failure.
6.4.2. Shear failure
Fig. 6.8 Stability chart for tension failure
Assuming that there is no upper tension crack, there is
only one failure line associated with shear failure (Fig.
6.7), and the value on the Y - axis is read off
corresponding to the relevant value of b as defined by
the line. This value of Fss / A is noted, where Fss
refers to the factor of safety against shear failure. At this
stage we do not have to work out the specific value of the
factor of safety - merely the non-dimensional ratio.
6.4.4. Beam Failure
For this we use exactly the same procedure as for the
tension test except that this time we use Fig. 6.9 to
obtain. Fsb / A .
Fig
. 6.9 Stability chart for Beam Failures
Fig. 6.7 Stability chart for shear failure
6.4.5 Mode of Failure
6.4.3 Tension Failure
The charts 6.7 – 6.9 show the non dimensional Factor of
Safety for the three modes of failure. The failure mode
most likely to occur is the one which has the lowest
values of Factor of safety, i.e. the lowest value of Fs/A.
A composite Stability Chart incorporating the three
charts Figs 6.7 - 6.9 is shown as Fig. 6.10.
We use a similar procedure using a graph similar to Fig.
6.8, but this time we must select the line with
appropriate value of the non-dimensional parameter B.
(i.e. b / H). Once again we read off on the X - axis and
move vertically upwards until we meet the appropriate
curve. We then read off the Y - axis value corresponding
to this point. This will give use the value of Fst / A .
80
N.K. Tovey
ENV-2E!Y Fluvial Geomorphology: 2002 - 2003
Section 6
Fig. 6.10 Stability Chart for Analysis of Composite River Banks.
B=0.05
5.0
4.0
3.0
Fs /A
2.0
0.5 0.4 0.3 0.2 0.1
0.1
1) Evaluate , , and B, and also 1/A = b/t
[Note: t is often about 5 kPa and  ~ 15
so 1/A is approximately 3b].
m
kNm-3
,
2) Plot point 1/A as Y-value and  (or  - ) as X.
3) If point is below appropriate B line, block is stable.
Failure is most likely in mode for which B line is closest
to plotted point. Factor of safety is ratio of Y -values at
B line and plotted point.
0.2
Note:
a) Use only  for X - axis for tension
case
b) Use B' instead of B (if relevant) in
beam case.
c) Chart is drawn for r (i.e. t/c) =
0.1 which is close to average ratio.
For other values of r, multiply Y
value (in beam case only) by
1.1/(1+r).
0.25
H

b
0.15
 H 


 H 
m

H
b
B
H
0.3
  
B1  B 

   

A t
b
0.4
0.5
shear
tension
Fss  5  A
0.7
beam
Fst 
1.0
1.0
Fsb 
2.0
0.0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
2
t

r
AB
(1  )
A w
(1  r ) B1
- tensile strength
- unit weight
- ratio of tensile to
compressive
strength.
based on Thorne and
Tovey (1981)
 or (  )
81
N.K. Tovey
ENV-2E!Y Fluvial Geomorphology: 2002 - 2003
Section 6
6.5. Examples of the use of stability charts.
Now suppose the block becomes fully submerged at high
stage. From an initially partially saturated block with
unit weight 16 kN m-3 its saturated bulk unit weight will
increase to say 18 kN m-3 but from buoyancy, the
submerged unit weight will now be 8 kN m-3 and the
parameter A will change, i.e.:-
6.5.1. Example 1.
A cantilever overhang is 0.1 m wide and 0.4 m high.
The unit weight is 16 kN m-3 and the tensile strength of
the soil if 8 kPa. There is no desiccation crack. In which
mode of failure is the block most likely to fail, and what
is the factor of safety against failure in this mode.
A =
Since there in no crack  = 1 and B = 0.25. From
the stability chart with respect to shear, Fss/A = 5.0.
From the corresponding chart for beam failure, Fsb / A
= 3.64, while from the tensile failure case, Fst / A is
off the scale and obviously must be  as tensile failure
can only occur if there is a desiccation crack.
8 / ( 8 x 0.1) = 10
and the value of 1 / A will now be 0.1 so the state point
will move vertically downwards to correspond to this
new Y - value and in doing so become twice as stable.
After the stage falls, the full saturated bulk unit weight
will now become operative and the value of A will
decrease to:-
The lowest value of the factor of safety parameter comes
from the beam mode of failure and this is the most likely
mode in which the for the overhang to fail.
A = 8 / (18 x 0.1) = 4.44 and the
associated factor of safety will be 16.18 for the beam
failure, i.e. it will be slightly less stable than originally.
We now evaluate the parameter A
= 8 / ( 16 x 0.1) = 5 ,
and hence the factor of safety will be 3.64 x 5 = 18.2
and so even in the most critical mode of failure, the
overhang is very stable.
6.5.3 Example 3
If on the other hand further erosion of the bank occurred
during the period of high stage, no desiccation crack
would develop, but the ratio B would increase. Suppose
the overhang increases to 0.2 m, the ratio B will now be
0.5 and the intersection of the B = 0.5 curve ( for the
critical beam failure) with the  = 1 line gives a Y value of 1.82. With the increased overhang, the value
of A will fall to
An alternative approach using the composite graph (Fig.
6.10) is to plot the state point corresponding to a factor
of safety of just unity, and then to compare its position
with the relevant failure lines for the three modes of
failure.
In the example above, the state point will plot at an Xaxis value of 1.0 (corresponding to  = 1 and since we
initially consider Fs as unity we plot the value of 1 / A
as the Y - value = 1/5 = 0.2
A =
8 / ( 8 x 0.2) = 5
and the effective factor of safety would become:
1.82 * 5.0 = 9.1.
This point will be on the extreme right of the graph. We
now move up the  = 1 line to find where the
respective failure lines cross (i.e. B = 0.25), and this
corresponds to a value of 3.64 (as previously noted) for
the beam failure, and 5.0 for the shear failure. No
tensile failure is possible.
In this case, immediately after the river stage drops the
factor of safety would drop to 2.22* 1.82 = 4.04 (the
2.22 comes from the revised value of A arising from the
saturated unit weight). Once again we would see that the
beam failure mode is most critical.
As the block dried, the unit weight would decrease again
and the parameter A would increase so that the factor of
safety would once again increase (or alternatively, the
state point would move downwards towards the X - axis).
The actual factors of safety can then readily be obtained
as indicated above by multiplying by the factor A.
The alternative approach has an advantage in that the
behaviour of the block through several cycles of
saturation/erosion/desiccation may be plotted on the
composite graph and the exact point at which failure
occurs, and also the mode of failure can be easily
determined. This aspect is explore further in later
examples.
If in this condition with the unit weight = 16 kN m-3 (i.e.
A = 2.5), a desiccation crack ( 0.1 m long) now
develops. The state point on the composite graph ( at coordinates x = 1.0, y = 0.4 (i.e. 1 / 2.5)) will now move
horizontally towards the left along the line y = 0.4 to the
X - axis value corresponding with  = 0.75 (i.e. the
non-dimensional parameter giving the length of the
crack).
At this point we check the failure curves to find the most
critical one. For shear, the Y value is 3.75, for beam
failures, the value is 1.02, while for a tensile failure the
In general terms, for stability of the cantilever, the state
point must always be below ALL of the failure lines, and
the closest failure line will dictate the mode of failure
that is most likely.
6.5.2. Example 2
82
N.K. Tovey
ENV-2E!Y Fluvial Geomorphology: 2002 - 2003
value is 2.0 All these value are above the state point and
so the overhang will still be stable, and the but the
lowest value is still the failure curve from the beam type
failures. The factor of safety is now 1.02 / 0.4 which is
approximately 2.5, so though stable is much more critical
than the original block.
Section 6
Using the stability chart in the manner shown enables us
to clearly see how and under what conditions a block
failure will occur.
Fig. 6.11 shows the trace of the state point as it passes
through the different stages represented by examples 1 to
3.
As the crack develops further, the state point will
continue to move to the left and will intersect the beam
failure line when  = 0.48 and this will be before a
tensile condition is reached. The factor of safety will
now be unity and failure will occur. the value of  =
0.48 corresponds to a crack length of 0.52 times the
block depth or 0.208 m.
Fig. 6.12 illustrates the regions most critical for each
type of failure for B = 0.3. Thus as the desiccation
crack propagates, so that  falls from a value of unity,
the most critical failure mode is first a beam type failure
to a value of =0.88, then a tensile failure to  = 0.41,
and finally beam failure becomes the most likely if the
crack propagates further.
While at all stages, the beam failure mode was most
critical this was only because of the initial geometry (i.e.
the block depth). If other block depths were present
(typically most seem to be between 0.6 and 0.9 m), then
at some states of development, one mode is most critical
while another becomes more critical at a later stage. In
some cases, a third mode of failure may become the
most critical.
Further Reading:Thorne and Tovey (1981) Stability of Composite River
Banks. Earth Surface
Process p469 - 484
Hey and Tovey (1989) Process and Bank Failure: In
Hemphill and Bramley: Protection of River and Canal
Banks p 7 - 39. Butterworths
space for further notes
83
.3
N.K. Tovey
ENV-2E!Y Fluvial Geomorphology: 2002 - 2003
0.4
Section 6
B=0.5 is relevant failure line
0.5
trace of state point
0.7
Failure occurs at X-value of 0.48
1.0
2.0
State Point in Example 1
0.4
0.5
0.6
0.7
0.8
Fig. 6.11 Stability Charts for Analysis of Composite River Banks – showing trace of State Point in Examples 1 – 3.
 or (  )
84
0.9
1
state point in Example 2
N.K. Tovey
ENV-2E!Y Fluvial Geomorphology: 2002 - 2003
Section 6
0.5 0.4 0.3 0.2 0.1
5.0
0.2
Tensile Failure most critical
4.0
Beam
Failure
most
critical
Beam Failure most critical
3.0
0.3
Fs/A
0.4
2.0
1.0
0.0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Fig. 6.12 Stability Chart showing critical regions for different modes of failure for B = 0.3
85
0.8
0.9
1