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### Bridge Scour Computations

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Lecture - 16: Bridge Scour-II

Welcome, all of you for this interesting class on Bridge Scour and the Jet Scours. In the last class, we discussed how to estimate the scour because of contractions and because of abutment positions. Today, we will further discuss abutment scours, then we will discuss the scour due to the pier. That is the bridge scour part we will complete it with examples. And with the standard guidelines what is available for scour estimations. As you know, we have been following basically the HEC-RAS 5.0. This is the HEC-RAS model. The reference manual is part of the US Corp of Engineers and also we are following part from the books of fluvial hydrodynamics, and also this part we are following this river mechanics of P. Y. Julian’s book. So, the basic idea is now to compute the scour depths in bridge locations. That is what today we will talk about bridge abutment scour. Yesterday in the last class, we discussed about that but further we will discuss how to estimate the bridge abutment scour. We will talk about computations of pier scours. We also will talk from computations of total scours which is there in HECRAS models or you can say it is there from HEC-18 models. So basic concept what we will follow it, HECRAS or HEC-18 manuals, that is what how to compute total scours. Then also we talk about scour counter measures, how to reduce the scour depth in a particular pier locations or abutment locations that what is scour counter measures, then you will have a simple example problems. That is what today lectures content. If you look at the scour part, it is having a computational, the sediment and the flow structures, maybe abutment, maybe you have bridge piers or you have any structures. That is the reasons it is having the 3 interactions are happening in both the way. All are linked to each others; the flow behaviors, sediment behaviors and the structural interferences. That is the complex process. Most of the times, we do physical models like the scale models what you have seen this.

The scale models what we conduct in the laboratory and followed by we do a dimensional
analysis and we develop empirical equations. That is what I have been presenting you empirical
relationship and that relationship when you implement in the field, we do the field measurements
as well engineering experience that if you do this type of design how much failures are
happening, what are the problems are encountered during implementations of the bridge.
Those experiences we consider it and along with the some field measurement, we develop a
design guidelines and many of the times nowadays also river mathematical models we use it and
maybe this is the one dimensional or 2 dimensional or the 3 dimensional models. We try to use it
again further refinement of this field measurement experiments and the empirical relations and
further we modify the design guidelines. That is the concept what we follow it and we will have
(Refer Slide Time: 04:41)Now if you look at this abutment locations, the abutment structures like these and if you have a
flow from these directions, very easily you can understand it. There will be a down flow and
there will be the vortex formations, primary vortex formation, which is the vortex formations
happens and that the vortex formations what we reference it as we call is the horseshoe vortex.
As we call it is a horseshoe vortex patterns.
Then you will have a secondary vortex and followed by we can have a weak vortex. This is the
hydrodynamic behavior. Because of that, the sediment is removed from this back, the scour hole
formations will be there and there will be extend of the material. So if you look at that the scour
at the bridge abutment, it depends upon the flow characteristics in terms of vortex formations,
downflow, wake vortex formations, bed sediment materials, what type of bed materials are there
and what is the shape, size of abutments.
That is the reasons we try to have with the equations which we try to develop it having a
functions of the abutment characteristics in terms of shape, size, length, flow characteristics.
That is what we can measure it like in upstream flow Froude numbers, the velocity and the
depth, also we try to know it the bed material characteristics in terms of D50, D90 or D95. So
this is quite complex flow, as this discussed is a 3 dimensional vortex around the structure.That is what it is complex but today we have a lot of literatures to do this type of work. It is not
that difficult now. I just tend to remind it, the 72 percent of abutment damage involved 383
bridge failures, okay most of the bridge failures because of abutment in not appropriate design of
abutment can have the failure consequently you can have the bridge failures.
(Refer Slide Time: 06:54)
This is the concept what we discussed in last class that how the vortex formations happen and
how it creates in a wake vortex, the horseshoe vortex and the secondary vortex. That is the
processes, which happens in it.
(Refer Slide Time: 07:17)And now if you look at in the last class, we call it HIRE equation which is developed from the
end of the scour, as similar to the abutments. So if you have the spur data is collected from the
Mississippi rivers and that Mississippi rivers data when they do a non-dimensional analysis and
try to find the scour depth is as functions of upstream flow depth, that is what is the option and
this is the correction factor because of the abutment shape.
This is the correction factor related to angle and this is the upstream flow Froude number. See if
you look at that, it depends upon the upstream flow depth, upstream flow Froude numbers which
is indirectly representing us the strength of the vortex for flow what it happens it and the shape
and the K2 is talking about the what type of abutment shape and the angle of attack. That is the
thing what we will discuss it.
Now if you look at that if I have the river you can construct a vertical wall abutment. So, you can
have the flow and you can have a vertical abutment like this as vertical structures, vertical wall
structures. In that case the coefficient is equal to 1, but some of the cases that is what is the
vertical wall, but some other cases what if you look at the conditions that we do not design like a
vertical wall unless this is smaller bridge, generally have to construct the width having the side
flank.
So we always design the spill through the abutment conditions or the abutment with wing walls.
So when you constructed that, as you can understand it the flow stream lines, the vortex strength
will be much lesser than the vertical walls. That is the reason the scour depth will be the lesser;
that means if you look at the abutment shape, if it is a vertical wall and the spill through
abutment, they are almost 45% reductions in the scour depth.
This is the multiplications constant. That is what is the multiples constant 0.55 to the K1 is it. So,
most of the times unless otherwise we have a small river we have a vertical wall abutment or
most of the times we create embankment which will be spilled through abutment. That is the
reasons there is a reduction of the scour depth. That is the advantage what we get it when you
design a spill through abutment.
(Refer Slide Time: 10:25)Now if you talk about the angles, so if you look it, this is a flow passing through like this and this
is the abutment is making the angle theta. As when the theta becomes 90 degree, it is just
perpendicular to the flow, when theta equal to 90 degree, so angle of attack will be abutments or
perpendicular to the flow. So that the; conditions we generally accept it, but we do not know the
flow behaviors.
Most of the times we cannot have the perpendicular, but as a designer we try to make it as close
to the perpendiculars. If you have 90 degree, then your K2 value comes to close to the 1. That
means this equation is normalized to the conditions when you have a perpendicular to the angle
of attack is equal to 90 degree and flow is perpendicular to these conditions, but if you have a
theta equal to beyond to 90 degree, that is the conditions you will have more the scour.
The less 90 degree you will have the less scour. That is what you can look it. Just try to
understand that as we are changing the angle of attack and how the scour is having a
multiplications factor, which is plotted here. So, beyond 90 degree, this factor is more than one
values other than it is a less than one value. That is always the reductions of the scour depth.
That is what it happens. So you can see it, how to compute the K2 value.
When theta is greater than 90, you can apply these equations and you can get the K2 value or
from the graph you can get the K2 value. So we know this K1, you know this K2 and y1, Fr1, Ican easily compute it, what will be the scour depth, but try to understand it these are data driven
methods. Considering the Mississippi river data, they establish a non-dimensional number
relationship and that non-dimensional relationship having a functions with upstream flow depth,
upstream flow Froude numbers and the K1 K2, which depends upon angle of attack and the
shape of abutment. You try to understand these empirical equations, which is very interesting to
know it, how those scour phase happens it.
(Refer Slide Time: 13:06)
Now if you look at the live bed scour measurements, that means the river at the live condition the
sediments transports are happening it, in that case the 170 live bed scour measurements is done
in the laboratory flumes, which with regressions analysis, analyzed it and established the
relationship between the scour depth, upstream flow depth and ya and K1 K2. So for the live bed
scour measurement, which is obtained from the laboratory from analysis followed by the
regressions analysis, it establish the scour depth is a relationship with K1 K2.
Already we have discussed what is the K1 and K2 and it is L’, y1 and the flow Froude numbers.
So the corresponding factor of angle of attack, already we discussed about that. The length of
abutment this L’ stands for, which is projected normal to the flow. It can have a unit of feet or
the meter. Average ya is average the flow depth on the flood plain at the approaching section.Froude numbers flood plain at the approach structure, so that is what is you can look it the flow
velocities and all. So, if you look at the strength of these equations, again it is a laboratory flume
experimental data established by dimensional analysis, but it is not a non-dimensional equation,
but its looks like non-dimensional form also. It can be done it. So it looks like a non-dimensional
form of regressions and that is what we give it.
(Refer Slide Time: 15:06)
And this is what like how to compute the average and the flow approach and there are the
notations is that what we should do it, when you have to use for the design purpose, which is
there in HECRAS manual 5. So that is what we will give it that it calculate the abutment scours
with including ya. That is what HECRAS manual says that when you interpreted the scour depth
using the HECRAS models, you can know it what does it compute?
(Refer Slide Time: 15:59)That is what is representing here and let me come into the next part very interesting to look at
what the flow behaviors at bridge piers. So if you look at that part, it is quite interesting now.
That is nowadays is possible to do with a very, very precise experiments in the fluid mechanics.
Try to know this flow structures what it happens, when you have a bridge pier. That is what if
you have a bridge pier and if you look at that downward flow things are happening, creating the
vortex patterns.
See you can know it how this the scouring patterns and all the things very interesting experiment
nowadays can be done at very advanced level of fluid mechanics experiment. To know it very,
very microscopic scale, how this turbulence happening it, how the vortex formations are
happening as a horseshoe vortex as the wake part is permitted. That is what, today it is possible
to do this type of high end experiment to know the velocity, vertical velocity jet.
That is what is happening it here and the formations of horseshoe vortex. That is the recent
publications what you are showing it. So if you look at that, again I talk about the horseshoe
vortex and it is a three dimensional flow separations happen and forming a vortex flow there will
be a periodical vortex shedding happens. It is vortex shedding also process happenings. So flow
separations, vortex flow as well as the periodically vortex shedding downstream happens.So that is the reasons it is very complex. Now as we discussed in flow through the abutment, the
same conditions happens in when you have a flow and try to look at the hydrodynamic
behaviors, which indicates for us 3 dimensional flow separations, vortex flow and also the
periodically vortex downstream. That is what it happens it. It is very complex process and as I
said it nowadays we can do quantification. It is not a big issue.
(Refer Slide Time: 18:20)
When you have this bow wave formations happens at the free surface adjacent to the pier surface
is rotating in a directions opposite that to horseshoe vortex. It is pertinent in a relatively shallow
flow reduce the downward velocity. So you can have a bow wave. Similar way, you will have a
stagnation pressure that is what will happen flow separate the site of the pier and the wake what
is formations happen is cast off the vortices at the interface of the main flow.
Because of that, digging process start, the removal of the bed material started and it continues till
a quasi-equilibrium state it happens. The strength of the vortex is or the bed shear states acting
after the scour, it will not have that much of strength to take out the bed materials and that is the
position we will have the quasi bed equilibrium state. That means during this state, the dynamic
angle of repose we call about dynamic angle of repose, which is almost 10 to 20% higher than
the angle of repose.So that means, when you have this horseshoe vortex formations and all the things, it creates a
dynamic angle of repose, which is 10 to 20% higher than the angle of repose. You try to
understand it that when there is a formations of vortex and that what is the supplement the
additional forces, so that the dynamic angle of repose is 10 to 20% higher than the angle of
repose of the sediment in still water.
Downstream, there will be dune formations will appear, which is your depositions of a sediment
material and side scouring whatever the sedimentary material is covered at the local of the bridge
pier, that is what will be deposited as a dune formations and side scoring some performances and
that what in very interesting figures what we will show to you.
(Refer Slide Time: 20:38)
Later on we will show you to that and if you look at that.
(Refer Slide Time: 20:43)The basic concept if you look it, if this experiment setups which is the part of IIT Guwahati
experiment setup, if you look at the snap shot of bridge pier just instead. This is what the bridge
pier is and if you look at the scour depth, you can see these scour depth formations and also you
can see the deposition formations, formations of dune. Also we can see that from the
downstream and the upstream view, we can see that the flume you can see this experiment before
scour formations and after scour formations.
If you can look it, the scour formations, how it happened, if this is considered a circular bridge
pier and try to do it and look at the scour hole and the depositions pattern. More interestingly you
just look it, 3 dimensional plot.
(Refer Slide Time: 21:38)The scour depth, you can see it the scour depth formations and the depositions. It is a contour
lines. It is a clear cut indicating that the negative is indicating the scour depth formations and
positive is indicating is a depositions and if you take a profiles, so it will have a profile like this.
It is very interesting; a profile like this. There are the conditions of seepage and no seepage. We
are not discussing that, but mostly it will have a scour depth and followed by the depositions.
That is what is showing it, the scour depth and the depositions because of bridge piers, which we
conducted the experiment as a part of the PhD thesis and we can try to know it, how does the
scour depth is happening, how the deposition is happening it.
(Refer Slide Time: 22:31)Now the same experiment, if you look at more details with two piers, P1 and P2. So many of the
times you have the highway constructions which is much more two lane roads or the more than
two lane roads. So we cannot have a one pier. You can have a consecutively two piers. So if you
have a consecutively two piers, because two piers will have the distance apart from that. How do
they affect it and if you look at this two pier conditions and the scour hole, the first one is
generated, second two are also nearby.
If you look at the scour part and also the depositions because of these two conjugative piers are
there and how it is affecting both the upstream and the downstream looks. So what I need to tell
it that many things we can study if you have the laboratory setups, conduct a simple scour
experiment with the bridge piers and you can try to know it how the scour depth formations
happens because of one pier or the multiple piers. That is what we can do it.
It is not that difficult task. We can always do it and know it the scour hole formations and all. So
basically what I want to try to do it that when you talk about the affecting depth of the local
scour at the bridge piers.
(Refer Slide Time: 24:00)
It depends upon the velocity, flow depth which indirectly represents of the horseshoe vortex,
strength and wake vortex strength. So indirectly from the flow Froude numbers, the velocity
depth, this is the information about the width and the sides and these are all depends upon theshape of bridge piers, bed configurations, whether the dune or this and nowadays also we talk
about that because of presence of debris. This is what partly the research is going on.
So if you look at that, these are the controlling factors of those locals scours. Flow
characteristics, the bridge pier characteristics and the bed material characteristics, that is what are
bed configurations is. What types of beds are there?
(Refer Slide Time: 24:58)
So if you look it that way and that is what is the equations developed by Colorado State
University equations, which is Richardson 1990, which developed the maximum scour depth for
both live bed, clear water pier scour. This is all experimental. Now if you look at these
interesting scour depth equations, maximum scour depth equations which is functions of 2. K1
K2 K3 K4 a to the power 0.65 upstream flow depth, upstream flow Froude number.
Now we can locate this non-dimensional form of equations are giving a correction factors,
because of like K1 start for pier nose shape, K2 stands for angle of attack. These are correction
factors. It can have 1 or more than 1 or less than 1. That is what we do it. If you consider the pier
nose shape, it can be more than one or less than one value. Similarly, correction factor for bed
conditions, correction factor for armoring of bed materials, we will discuss more.So how much of scour reductions are happening in it, because of the bed material as you know
that it is always a mixed bed materials. It will have a different size of bed material mixture will
be there. There will be formations of armoring. Because of that, the scour reduction is what had
happened and then you have to have a bridge pier width, what we have.
As we discussed that the Colorado State University equations establish the scour depth in terms
of flow upstream depth, flow Froude numbers, the width of the bridge pier plus there are four
correction factors. First correction factor for the pier nose, K2 correction factor for angle of
attack, K3 correction factor for bed conditions, K4 correction factor for the bed materials, that is
what is indicate for us that how we can compute it the scour depth for bridge parts, which is a
functions of flow depth, the bridge pier.
If you look at the scour depth equations is quite interesting equations as a non-dimensional
equations formations after conducting a series of experiment in live bed conditions, clear water
pier scour conditions and this equation if you look at that, it depends upon the flow
characteristics as upstream flow and flow Froude numbers followed by the pier characteristics
like the width of the piers, pier nose shape, angle of attack, layout of the piers and the riverbed
conditions, armoring of bed materials.
These are the correction factors. As I said it, the correction factor can be more than one or the
less than one or equal to one. So these are all K1, K2, K3, K4 are the correction factors and the
y1, Fr1 is the flow characteristics and the pier width conditions.
(Refer Slide Time: 28:42)Now if you look at that more details which if you look at that y is the flow depth directly
upstream of the piers and Fr1 is the flow Froude numbers upstream of the piers, but there is a
limit of the maximum scour depth. That is what we have to consider it. When the flow Froude
number less than equal to 0.8, it will be the scour depth will be 2.4 times of pier width. That
means if you consider the pier width is 0.5 meter, so pier width is 0.5 meters, then you will have
a 2.4 times of 0.5; that is maximum what will happen it as the maximum depth, when you have a
flow that is subcritical and less than 1.8, but if you look at this 3 times happening when the flow
is more than 8.
So that means if you flow Froude number is more than 0.8 that means coming closer to the flow
Froude super critical flow. In that case, you will have the 3 times of the scour depth. See ys will
be the 1.5 meters. So it is just an example what I am telling it. So you can see that what is the
bridge pier width, it is not in terms of 0.5 meters, some bigger reverse you can have a 10 meter
or 15 meters or more than that.
So if you look at that you can have a thumb rules to know it what could be the maximum scour
depth. That is what we try to look it and maximum scour depth is the relationship from the data
analysis they found it, it has a condition in terms of upstream flow Froude numbers is divided
into 2 zones. The first zone is a scour depth is 2.4 times of the pier width; more than 0.8, it will
have a 3 times of the pier width. That is the maximum scour depth what we get it.(Refer Slide Time: 30:55)
Now if you look at the corresponding factors, because of pier nose shape; so if you look at this
pier nose shape means, very small channel of the rivers we have the circular pier, but many of
the times you can have piers with nose shape, different nose shape. So you can have a square
nose, which will have more scouring, but if I have a round nose circular cylinders or group of
cylinders it is equal to one if you have a sharp nose of triangular, which is very difficult to
construct it.
In that case, you will have a less than 10% scour depth. So this is the correction factors as I said
it earlier is because of pier nose shape, what type of nose we have and what is the corresponding
factor for that. That is what you can look it and basic common sense of the fluid properties, the
streamlines behaviors we can understand it which will have a more, which one will you have a
lesser scour depth.
(Refer Slide Time: 32:15)The same way if I look at the K2, the L stands the length of piers along the flow lines, theta is
angle of attack and that is what is a sinϴ and cosϴ, L/a is bridge pier. Whenever L/a is a lesser
than 12, it is HECRAS models is L/a is a maximum and that the conditions it said it and if the K2
dominates it, K1 must be said to be 1 that the relationship between the K2 and K1 happens it
when you have the different L and y conditions.
(Refer Slide Time: 32:54)
Now if you look it, next part is bed conditions. Bed can have different conditions. For example,
it can have a clear water, that means bed is not like mobile conditions. You can have plane bed
or anti-dune formations, you have a dune formation. The bed can have a dune formation. Whenyou have the small dunes and all, so you have the correction factor 1.1 goes to the 1.3. So the
correction factors will go as 1.1 to 1.3 depending upon the river bed conditions.
As you know it, the river can have the dunes formations, can have a smaller dunes and larger
dunes. If I have a larger dune height is more than 30 feet, then you will have a correction factor
is 1.3. If it is a 30 to 10 and that the conditions you have a correction to 1.1 to 1.2 and less than
10 to 2, you will have a 1.1. So if you look at that when you have the river bed, the river bed
dune formations as we discussed earlier it can make as a correction factors for river having more
morphologically active, where the larger dune formations happens it. The scour depth can
increase by 30%. That is the dune formations, the scour depth increase what we have to consider
it.
(Refer Slide Time: 34:32)
Now if you look it very interestingly if you look at another coefficients what is a K4 that because
of armoring of the scour depth, scour holes. That is what we consider when you have the most of
the rivers bed materials are not uniform. They are mixtures. There are the bigger size. There are
the smaller size. They are the medium size. That is the reasons we have a particle size
distribution curve.Because of that armoring processes happens it and we should try to look it because of the
armoring process you will have the reductions of the scour depth, that we will look it. Let me just
sketch it more details.
(Refer Slide Time: 36:18)
that you have a bridge pier and you have the flow and this is the bridge piers and initially when
you have a bed you can have a bed materials of bigger size and also the smaller size, could be
bigger size and could have the smaller size and if that is the conditions before scouring, before
local scour formations, you can have a bed materials with composition of bigger size, mixed size,
smaller size and medium size.
As you know that when you start the armoring process; starting off armoring process that means
the smaller particles will be washed out or moved from this bed. As you know it, the smaller
particles can easily be removed by the flow, because of higher bed space first, it will remove the
smaller particles. The bigger particles which are having the gravity force is more, that is what
will go over.
So what it actually happens is, as the flow process starts in a reverse, at first the finer materials
are washed out. The bigger materials remain on the bed. This is the process we call this
armoring. The same things also happen in case of scour formations. When you have the scourformations, if you look at, you will have a scour formation like this. This is the initial bed. So,
you can see that bigger mud particle, the armoring particles will be here.
Because of that, there will be reductions of the scouring depth as compared to the uniform size.
So we try to look the armoring things. These are also again it is experimental work. Try to look it
how to consider the particle size distributions curve and try to know it, how can the effect of
armoring we can consider during the scour formations. That is the idea. If you look at that, here
all as empirical equations but it is a non-dimensional form of empirical equations.
The K4 depends upon the VR is a normalized velocities in terms of upstream velocity Vi50,
Vc50, Vi90. You just look at the subscript. We will discuss more. The Vi50 and Vi95 have an
empirical relationship with D50 from the particle size distribution curve, D95 from the particle
size distribution curve, we can get it and they have the empirical equations like this. From this,
we can find a non-dimensional VR value and that what will be used here to compute the K4. So
now let us discuss what are they? If you look at these figures and try to understand it.
(Refer Slide Time: 38:39)
VR is a velocity ratio, as if you look at that. What is V1 is average velocity in the main channel
or the overbank area depending upon the piers where it is the upstream of these bridge locations.
That is what we can get it using the HECRAS models or you can do physical models. Vi90, 50 itis approach velocity required to initiate the scour at the grain size of D50. Again I want to repeat
it. Vi50 is approach velocity required to initiate the scour at the pier for grain size D50.
Same way I can define Vi95 is an approach velocity, which is required to initiate the scour at the
grain size of D95, so it consider the armoring process in terms of two representing grains, bed
material characteristics; one is D50 another is D95. For that respective what could be the
approach velocity to initiate the scour.
(Refer Slide Time: 40:02)
Same way, if you look at that Vc50 is a critical velocity from the sealed numbers or the
relationship here. We can find out for D50 materials, you can have this and they have a relations
with the D50 D90 upstream flow depth. So we can have a critical velocity, which is a function of
D50 and D95 and it has a coefficient. Now if you try to understand it this equation is developed