1
00:00:11,769 --> 00:00:17,000
Ok so let’s recap of the idea behind the
bearing capacity I think I mentioned the other
2
00:00:17,000 --> 00:00:21,590
day with lower bound and upper bound equilibrium
versus mechanism
3
00:00:21,590 --> 00:00:27,730
So the equilibrium is just equilibrium of
forces which we saw one case the mechanism
4
00:00:27,730 --> 00:00:33,140
is basically a rotation or displacement case
where u know the equilibrium you know the
5
00:00:33,140 --> 00:00:36,500
condition of ultimate strength is achieved
after failure
6
00:00:36,500 --> 00:00:42,230
So if you look at the case that we are going
to look at is the second case First case we
7
00:00:42,230 --> 00:00:49,530
have already seen this we just equated the
horizontal pressures and active pressure versus
8
00:00:49,530 --> 00:00:55,040
the overburden pressure on the right hand
side and then trying to equate and we derived
9
00:00:55,040 --> 00:01:00,610
a simple formulaWhich is giving the relationship
between undrain shear strength of soil with
10
00:01:00,610 --> 00:01:07,189
respect to the load at which the soil will
fail because of the equilibrium case
11
00:01:07,189 --> 00:01:13,820
And we have us reduced case where if the foundation
is at the surface level just like of our off
12
00:01:13,820 --> 00:01:19,530
floor mud matts you where we just placed it
on top we have reduced the equation to quite
13
00:01:19,530 --> 00:01:25,490
a simple four times the undrain shear strength
now this 4 is a numerical coefficient depending
14
00:01:25,490 --> 00:01:31,439
on the failure mode we apply it maybe different
it maybe 5 it maybe 6 now this is for the
15
00:01:31,439 --> 00:01:39,479
simple case where 5 is equal to 0 that means
is purely clay type of soil now let’s go
16
00:01:39,479 --> 00:01:42,209
back to one more simplified case
17
00:01:42,209 --> 00:01:47,439
Where the failure is not by means of equilibrium
it is going to be a mechanism that is means
18
00:01:47,439 --> 00:01:52,909
is a rotational failure so you can here from
this picture easily that the pressure applied
19
00:01:52,909 --> 00:01:57,479
on the bottom of the foundation excavated
foundation to a depth of D and it is trying
20
00:01:57,479 --> 00:02:03,060
to fail by means of a failure along the lines
of circular shape
21
00:02:03,060 --> 00:02:08,369
What I have just noted down there So the mechanism
is about the point of rotation is this and
22
00:02:08,369 --> 00:02:13,790
the resistance is going to come from the shear
strength of the profile of their So if you
23
00:02:13,790 --> 00:02:18,360
equate the moment at that particular point
and you can find out the equation that’s
24
00:02:18,360 --> 00:02:25,420
what is trying to do we do here and the overburden
pressure is same Q knot is the depth times
25
00:02:25,420 --> 00:02:30,860
the and you know the density of soil in this
case will take gamma dash because we will
26
00:02:30,860 --> 00:02:34,810
be having the submerged condition
27
00:02:34,810 --> 00:02:41,390
So you see here we just write the equilibrium
equation for the moment you will get Q U is
28
00:02:41,390 --> 00:02:47,000
equal to 2 phi C U which is basically the
arc length multiplied by the undrain shear
29
00:02:47,000 --> 00:02:53,450
strength which is going to create the resistance
against the rotation plus your Q knot which
30
00:02:53,450 --> 00:02:57,250
is nothing but the overburden pressure
31
00:02:57,250 --> 00:03:01,980
So the resistance is coming from the friction
path as well as from the overburden path which
32
00:03:01,980 --> 00:03:06,671
is just imagine if this whole thing is under
surface then you will not have the Q knot
33
00:03:06,671 --> 00:03:10,520
there because there is no overburden and the
acting movement is basically the movement
34
00:03:10,520 --> 00:03:16,040
due to the pressure multiplied by half the
distance just taking the U D L to the point
35
00:03:16,040 --> 00:03:21,630
of center from this point of rotation that
is what we have done here
36
00:03:21,630 --> 00:03:28,530
You know the active path and the resisting
path resisting path is the shear friction
37
00:03:28,530 --> 00:03:34,030
or the shear strength and basically the overburden
time and this is the acting moment due to
38
00:03:34,030 --> 00:03:39,340
applied load which is Q times B times half
the you know basically this is acting at this
39
00:03:39,340 --> 00:03:45,280
point at the middle point and nekated by or
opposed by the friction plus
40
00:03:45,280 --> 00:03:53,480
So it is a simple mechanism by which we are
trying to equate the again this type of soil
41
00:03:53,480 --> 00:03:59,970
is basically purely clay type of soil phi
is not there Based on this we got a you know
42
00:03:59,970 --> 00:04:05,950
basically if you take Q not equals to 0 bring
the foundation to the surface you get 6 point
43
00:04:05,950 --> 00:04:12,200
2 eight times C U Now the previous one we
saw four times U this one we are seeing so
44
00:04:12,200 --> 00:04:17,329
this is that is the lower bound is the upper
bound solution So we can see soil can fail
45
00:04:17,329 --> 00:04:22,490
either way but what we don’t know is which
one to select And basically that’s one of
46
00:04:22,490 --> 00:04:27,330
the idea that the solution is bound by this
much from 4 to 6 it can wary and it can be
47
00:04:27,330 --> 00:04:33,499
anywhere depending on the nature of soil even
if it is pure clay
48
00:04:33,499 --> 00:04:40,020
Now what we are going to just see the next
one is a generic soil where you will have
49
00:04:40,020 --> 00:04:45,939
shear strength as well as the angle of internal
friction which is a generalized soil we called
50
00:04:45,939 --> 00:04:51,580
it C phi soil which in many cases you will
find in real nature in when you are designing
51
00:04:51,580 --> 00:04:56,449
foundation you are not going to get a pure
sand because it is not under your control
52
00:04:56,449 --> 00:05:01,999
so if you see this picture slightly complicated
of course this picture goes back to us as
53
00:05:01,999 --> 00:05:07,789
early as 1950’s where Terzaghi first initially
assumed certain configuration like what I
54
00:05:07,789 --> 00:05:12,800
am deriving but later it become quite complex
because this is not going to be a so nice
55
00:05:12,800 --> 00:05:17,669
straight line you know several researches
have come up with different profile and different
56
00:05:17,669 --> 00:05:21,189
bearing capacity coefficients and that’s
the history
57
00:05:21,189 --> 00:05:25,740
But the starting point is something like this
where integration can be done very easily
58
00:05:25,740 --> 00:05:30,900
So what he has assumed is basically a triangle
just below the foundation path which going
59
00:05:30,900 --> 00:05:35,120
to become part of foundation itself that’s
the idea behind that So you see the triangle
60
00:05:35,120 --> 00:05:41,449
drawn in light light green color down there
is just half of it I have drawn just for clarity
61
00:05:41,449 --> 00:05:47,510
Actually the other side also will be filled
with the similar So this soil below the foundation
62
00:05:47,510 --> 00:05:52,499
with certain height which you could calculate
and the width is same as the foundation this
63
00:05:52,499 --> 00:05:55,889
soil becomes the part of the foundation load
itself
64
00:05:55,889 --> 00:06:00,360
So it is just going to go down together so
that is the first assumption and instead of
65
00:06:00,360 --> 00:06:05,599
failure at the interface see if you go back
to the first one we were looking at failure
66
00:06:05,599 --> 00:06:12,580
along the vertical line the line just coming
down form the excavated surface So that is
67
00:06:12,580 --> 00:06:17,000
the place where we are equating the left pressure
is equal to right pressure so that is the
68
00:06:17,000 --> 00:06:22,050
equilibrium line we were looking at instead
what Terzaghi was looking at is basically
69
00:06:22,050 --> 00:06:27,610
a incline d surface joining A and B which
is something slightly different from what
70
00:06:27,610 --> 00:06:28,650
was our assumption
71
00:06:28,650 --> 00:06:35,539
It all depends on imagine if all this is water
the vertical line assumption is correct if
72
00:06:35,539 --> 00:06:40,430
it is a very soft clay it is going to go down
like this but if it is a C5 soil with good
73
00:06:40,430 --> 00:06:44,339
amount of sand and clay probably the assumption
made by Terzaghi is very correct because it
74
00:06:44,339 --> 00:06:49,520
is going to take a inclines failure surface
and that’s why this is actually a reasonable
75
00:06:49,520 --> 00:06:55,520
assumption So the failure line is assumed
from A to B Now we need to find the equilibrium
76
00:06:55,520 --> 00:07:01,770
of vertical forces which will make them stable
The vertical force equilibrium is applied
77
00:07:01,770 --> 00:07:07,219
force is this P you can calculate the unit
pressure P by width
78
00:07:07,219 --> 00:07:11,759
Because what we are looking at is an infinite
or a very long footing So we are not looking
79
00:07:11,759 --> 00:07:16,880
at three dimensional effect it just the two
dimensional effect and the load applied plus
80
00:07:16,880 --> 00:07:22,169
the weight of the soil itself which is going
to become part of the wedge the green wedge
81
00:07:22,169 --> 00:07:26,689
which you can find out the vertical component
both them as vertical what we need to find
82
00:07:26,689 --> 00:07:30,749
out is the resisting component coming from
the soil surrounding the foundation
83
00:07:30,749 --> 00:07:36,150
So which we can find out from a horizontal
earth pressure which we have learned about
84
00:07:36,150 --> 00:07:41,749
lateral earth pressure you know active and
passive so we need to find out what is P from
85
00:07:41,749 --> 00:07:46,960
which we can find out a component which is
resisting this movement of the foundation
86
00:07:46,960 --> 00:07:52,479
plus the wedge which is going to go down In
order to do that several things needs to be
87
00:07:52,479 --> 00:07:56,139
taken care for example when the foundation
load is applied this way this is going to
88
00:07:56,139 --> 00:08:02,300
be a the surface is going to active pressure
wedge whereas with is pressure this side this
89
00:08:02,300 --> 00:08:06,210
angle this soil is going to go passive because
it is going to be pushed away
90
00:08:06,210 --> 00:08:12,340
And basically from the previous cases the
passive angle of failure is 45 minus phi by
91
00:08:12,340 --> 00:08:19,740
2 and active failure is 45 plus phi by 2 So
that is what I have just summarized the parameters
92
00:08:19,740 --> 00:08:26,849
what we have learned over last few classes
so that you will just take it and substitute
93
00:08:26,849 --> 00:08:32,409
so from this picture if you tale a elemental
soil we could actually equate the vertical
94
00:08:32,409 --> 00:08:37,469
pressure which is nothing but your overburden
pressure gamma times whatever the depth and
95
00:08:37,469 --> 00:08:47,310
if you are able to find out the horizontal
pressure which is 1 sigma 1 of the element
96
00:08:47,310 --> 00:08:52,940
2 based on the lateral earth pressure theory
for passive pressure basically we will use
97
00:08:52,940 --> 00:08:58,520
our previous equations that we had
98
00:08:58,520 --> 00:09:04,649
You simply substitute sigma 1 will be equal
to sigma 3 into K P plus two times C because
99
00:09:04,649 --> 00:09:10,460
this not pure sandy or clayey soil so you
will have a both components so you can substitute
100
00:09:10,460 --> 00:09:15,210
and arrived at this This equation we have
derived earlier and then integrate with this
101
00:09:15,210 --> 00:09:20,490
for full depth of from here to here because
that is what is happening here This is a dot
102
00:09:20,490 --> 00:09:24,910
place what you are going to do is integrate
that and that what we have done ultimately
103
00:09:24,910 --> 00:09:31,520
you will get the total passive pressure from
the triangular wedge on the right hand side
104
00:09:31,520 --> 00:09:36,210
based on the equation for what we derived
from sigma 3 to sigma 1
105
00:09:36,210 --> 00:09:42,620
Which we have just got the approximate equation
there once we know the PP then it is a matter
106
00:09:42,620 --> 00:09:48,770
of geometric calculation to find out the vertical
force So in this interface between A and B
107
00:09:48,770 --> 00:09:54,210
we have got two components one is the resistance
coming from the earth pressure the second
108
00:09:54,210 --> 00:09:58,680
one is coming from the pure friction along
the surface very similar to what you just
109
00:09:58,680 --> 00:09:59,680
now did
110
00:09:59,680 --> 00:10:05,290
In here we have got a frictional the soil
is trying to rotate this way but the frictional
111
00:10:05,290 --> 00:10:09,350
resistance along the surface is trying to
resist it Exactly same way if you go back
112
00:10:09,350 --> 00:10:14,490
to this picture we have got a frictional interface
between A and B and is trying to push the
113
00:10:14,490 --> 00:10:19,340
soil up because its unable to break the shear
strength of the soil so basically two component
114
00:10:19,340 --> 00:10:26,141
of resisting two component of acting basically
the P plus W is acting downwards and a friction
115
00:10:26,141 --> 00:10:33,830
plus the vertical component of the the earth
pressure is going to be acting opposing resisting
116
00:10:33,830 --> 00:10:38,370
the failure So what we need is just computation
of that components and which we have already
117
00:10:38,370 --> 00:10:43,540
got PP from geometry which I have drawn at
this interface
118
00:10:43,540 --> 00:10:50,750
You could easily derive just a geometric arrangements
Finally you will you will come with a equation
119
00:10:50,750 --> 00:10:57,920
relationship between PP and PP vertical which
is just I have summarized in this at the last
120
00:10:57,920 --> 00:11:03,830
term here the relationship between PP V and
PP is basically cos phi and that is what I
121
00:11:03,830 --> 00:11:08,490
am just giving you you can go through simple
geometric calculation of shifting from one
122
00:11:08,490 --> 00:11:17,040
to other and basically here the beta and phi
is used because you see here this is beta
123
00:11:17,040 --> 00:11:23,680
and this is alpha and you got to draw both
the triangles super impose 90 degree shift
124
00:11:23,680 --> 00:11:28,650
So that’s the idea behind So basically this
is the diagram that we will derive relationship
125
00:11:28,650 --> 00:11:35,360
between PP and PP V Once you have this relationship
then you can simply substitute
126
00:11:35,360 --> 00:11:41,750
This is the applied pressure from the foundation
load which is just load divided by the B by
127
00:11:41,750 --> 00:11:49,370
2 I have taken half because of cemetery purpose
you can take this half you can just leave
128
00:11:49,370 --> 00:11:54,200
it the other side or else you have to multiply
by 2 so am just taking applied load at failure
129
00:11:54,200 --> 00:11:57,300
state it is become Q becomes Q U so that’s
the idea
130
00:11:57,300 --> 00:12:04,280
And the W will be calculated by the height
of you know the triangle and width half and
131
00:12:04,280 --> 00:12:09,970
gamma is the density so that is the acting
and the resisting is the friction the length
132
00:12:09,970 --> 00:12:15,300
is calculated in that particular inclined
length from A to B has to be calculated multiplied
133
00:12:15,300 --> 00:12:23,590
by the shear strength and basically the passive
resistance the relationship coming from PP
134
00:12:23,590 --> 00:12:29,110
and once you have this equation you simplify
this in terms of KP you go back to geometric
135
00:12:29,110 --> 00:12:35,180
identities substitute expand this sin 90 minus
alpha and all that re substitution
136
00:12:35,180 --> 00:12:41,760
You will get something like this so first
stamp is combining CU with all this replacement
137
00:12:41,760 --> 00:12:48,820
you will get certain things inside which is
basically a substitution you get KP and the
138
00:12:48,820 --> 00:12:55,140
second term is Q knot which is your your overburden
pressure effect and the third term is the
139
00:12:55,140 --> 00:13:00,200
self-height of wedge itself so the from here
you have to do a lot of substitution to get
140
00:13:00,200 --> 00:13:05,690
replacement like this so what we have is one
is the pressure applied pressure weight the
141
00:13:05,690 --> 00:13:10,310
friction between the right side and left side
or inclined failure surface and the last one
142
00:13:10,310 --> 00:13:13,741
is the passive resistance coming from the
overburden effect
143
00:13:13,741 --> 00:13:21,590
Now you see here Terzaghi has simplified this
equation in terms of CU multiplied by a term
144
00:13:21,590 --> 00:13:30,510
just denoted by NC which is basically a bearing
capacity factor and NQ and N gamma so what
145
00:13:30,510 --> 00:13:35,870
he that what he was doing is just removing
this complex equations and noting down by
146
00:13:35,870 --> 00:13:42,410
such simple you know notations so that you
can later calculate each one of them
147
00:13:42,410 --> 00:13:48,690
See NC NQ and N gamma are called bearing capacity
factors for different purposes So could actually
148
00:13:48,690 --> 00:13:53,780
plot this equations in terms of chart for
different characteristic of soil you can go
149
00:13:53,780 --> 00:13:57,350
and pickup and that is what you will see from
some of the graphs
150
00:13:57,350 --> 00:14:02,030
Something like this so what I have done is
just plotted in excel So given angle of internal
151
00:14:02,030 --> 00:14:08,640
friction for any sandy type of material you
can see her is taking this kind of variations
152
00:14:08,640 --> 00:14:14,350
So you can calculate and then substitute so
the idea behind this original equation is
153
00:14:14,350 --> 00:14:17,780
basically the passive earth pressure coefficient
is known then you can straight away calculate
154
00:14:17,780 --> 00:14:25,880
everyone of them and for that if it is pure
sandy soil the sea component will go away
155
00:14:25,880 --> 00:14:30,940
then it becomes even simpler So that’s the
first equation derived by Terzaghi as a basic
156
00:14:30,940 --> 00:14:38,920
form of bearing capacity of a spread footing
in two dimension that means the third or the
157
00:14:38,920 --> 00:14:42,510
length is very long that the effect is negligible
158
00:14:42,510 --> 00:14:52,410
So that is the idea behind this so what we
have now got slightly complex shape of the
159
00:14:52,410 --> 00:14:58,280
triangle or the wedge which is resisting and
this work was done by several people you know
160
00:14:58,280 --> 00:15:03,480
you started with Mayor Horf bridge and then
several other researches they found based
161
00:15:03,480 --> 00:15:11,810
on testing you know the shape is slightly
complex and have lot of mathematical expressions
162
00:15:11,810 --> 00:15:18,400
ultimately instead of looking at this you
could actually get some of them proposed numerical
163
00:15:18,400 --> 00:15:25,620
coefficients of varying nature base and testing
then comparison and you know if you look at
164
00:15:25,620 --> 00:15:29,560
several course you go to other Indian course
of British course you will find these equations
165
00:15:29,560 --> 00:15:33,000
are plotted against either a SPT values
166
00:15:33,000 --> 00:15:36,670
Sometime you have relationship directly with
this SPT values or with angle of internal
167
00:15:36,670 --> 00:15:43,540
friction which is your phi angle or with shear
strength so you can find many ways of finding
168
00:15:43,540 --> 00:15:52,370
this coefficients which can be used with this
bearing capacity equation basically Now in
169
00:15:52,370 --> 00:15:56,690
fact final form of equation for NQ is given
like this
170
00:15:56,690 --> 00:16:04,430
If you back and compare this NQ in here you
simplified this equation in in terms of something
171
00:16:04,430 --> 00:16:11,500
like this and NC something like this and N
gamma so is all final form of equations but
172
00:16:11,500 --> 00:16:17,350
if look at later part of the you know like
70’s and 80’s even this equations got
173
00:16:17,350 --> 00:16:21,070
modified slight difference but the numbers
are not very big difference
174
00:16:21,070 --> 00:16:26,280
Still may times we continue use the work done
by Terzaghi for simple spread footing foundations
175
00:16:26,280 --> 00:16:33,010
even So for all practical purposes we will
use this equations to calculate if it is you
176
00:16:33,010 --> 00:16:40,380
know sandy type of soil or C phi type of soil
where NC is related is with NQ and you can
177
00:16:40,380 --> 00:16:42,910
find out NC from there
178
00:16:42,910 --> 00:16:49,820
That is the chart which I was just discussing
about we could use it without ant problem
179
00:16:49,820 --> 00:16:58,360
So you have to little bit careful h use of
this chart here only angle of internal friction
180
00:16:58,360 --> 00:17:03,110
is given but though you can even get the NC
values if you look at the NC is red color
181
00:17:03,110 --> 00:17:10,890
2345 I think it is about 5.14 if you calculate
using this equation you will get 5.14So remember
182
00:17:10,890 --> 00:17:19,010
we derived two cases for a clay type of soil
we got four for lower bound 628 for upper
183
00:17:19,010 --> 00:17:23,320
bound so this 5.14 is somewhere in between
So that’s the idea behind
184
00:17:23,320 --> 00:17:30,880
Now the general form of bearing capacity equation
so we have we have been looking at vertical
185
00:17:30,880 --> 00:17:35,870
loading pure vertical loading which is and
a rectangular footing
186
00:17:35,870 --> 00:17:42,120
Instead we could generalize a bearing capacity
evaluation in terms of load directions slightly
187
00:17:42,120 --> 00:17:48,470
inclined or maybe sometimes you get horizontal
loads and then you will have non-rectangular
188
00:17:48,470 --> 00:17:57,670
shapes so we have a effect of shape coming
into picture and depth It could be at the
189
00:17:57,670 --> 00:18:02,990
surface it could be going to down load inclination
factors which is just I was mentioning about
190
00:18:02,990 --> 00:18:08,980
and basically these three will be very common
in ant type of foundation except maybe you
191
00:18:08,980 --> 00:18:13,290
know primarily gravity type of loading from
buildings
192
00:18:13,290 --> 00:18:17,430
You may have a very little wind effect but
for optional structures you know even if it
193
00:18:17,430 --> 00:18:21,930
is temporary you will see that a lot of wave
and current loads will be coming so you have
194
00:18:21,930 --> 00:18:27,840
to take into account So this you can easily
understand the first one very-very simple
195
00:18:27,840 --> 00:18:35,490
for example you take a circular shape of foundation
when you apply loading to a circular shape
196
00:18:35,490 --> 00:18:40,760
foundation the foundation tries to settle
down because of applied pressure so the settle
197
00:18:40,760 --> 00:18:46,150
down means the soil around the circular footing
is trying to squeeze out isn’t it
198
00:18:46,150 --> 00:18:51,450
Very simple idea because you are pressing
down what will happen The squeezing out effect
199
00:18:51,450 --> 00:18:57,800
is going to be uniform throughout the periphery
of the circle instead of that if you actually
200
00:18:57,800 --> 00:19:02,940
take a rectangular shape for example just
like a rectangular shape the squeezing out
201
00:19:02,940 --> 00:19:08,370
effect will be more on the width side rather
than length side because the length is more
202
00:19:08,370 --> 00:19:13,840
Very similar to our you know the slab design
I think if you have learned about RC slap
203
00:19:13,840 --> 00:19:14,840
design
204
00:19:14,840 --> 00:19:20,970
Two way action versus one way action for circular
it is multiple directions you know everywhere
205
00:19:20,970 --> 00:19:25,960
you have a similar effect so that mean which
is better Which is better is circulars definitely
206
00:19:25,960 --> 00:19:31,370
going to be better because the effect of overburden
all around is going to be effective you know
207
00:19:31,370 --> 00:19:38,440
So circular shape is always better but construction
wise not preferred because it’s quite difficult
208
00:19:38,440 --> 00:19:43,780
That’s why most of the time this spread
footings will be either rectangle or a combined
209
00:19:43,780 --> 00:19:46,290
rectangle something like this
210
00:19:46,290 --> 00:19:52,030
So shape factor is very simple depending on
the type and the shape of the foundation you
211
00:19:52,030 --> 00:19:58,890
will be able to get the factor its greater
than one or not basically circular shape to
212
00:19:58,890 --> 00:20:05,520
rectangular rectangular to strip some very
rare cases we have triangular foundation but
213
00:20:05,520 --> 00:20:10,570
what normally we do is we convert the triangular
foundation into an equivalent circular shape
214
00:20:10,570 --> 00:20:16,120
because it is very hard to find out the shape
factor and then find out the capacity in off
215
00:20:16,120 --> 00:20:22,710
shore applications we have many-many cases
circular non circular shapes like triangular
216
00:20:22,710 --> 00:20:26,640
and rectangular circular very-very few cases
we have used
217
00:20:26,640 --> 00:20:31,290
So you will have definitely the effect of
shape from the bearing capacity calculated
218
00:20:31,290 --> 00:20:40,030
based on a simple simple you know long rectangle
I would say strip footing to a various shapes
219
00:20:40,030 --> 00:20:44,880
needs to be taken into account by means of
these factors Depth factors is very straight
220
00:20:44,880 --> 00:20:50,929
forward because the more that you go you get
a better soil and you get more overburden
221
00:20:50,929 --> 00:20:58,130
pressure Load inclination factor basically
is very important because the more- more horizontal
222
00:20:58,130 --> 00:21:01,550
load the frictional effect will come into
picture
223
00:21:01,550 --> 00:21:06,910
And failure will be earlier than actual vertical
load so that is one of the important thing
224
00:21:06,910 --> 00:21:13,640
we need to remember So all these things can
be found from textbooks I will cover only
225
00:21:13,640 --> 00:21:19,670
what is relevant for the cases that we are
looking at
226
00:21:19,670 --> 00:21:27,390
Some somebody of you know the three cases
rectangular shape from strip footing to a
227
00:21:27,390 --> 00:21:33,860
square shape to a circular shape So basically
you can see here circular shape is just substitution
228
00:21:33,860 --> 00:21:41,860
of B and L equal to same So will get 1.2 times
both are same you know breath for circular
229
00:21:41,860 --> 00:21:46,610
shape is similar and for square shape basically
1.2
230
00:21:46,610 --> 00:21:52,900
All other factors not getting so much affected
basically the last one is the effect of the
231
00:21:52,900 --> 00:22:00,000
shape itself So can substitute from rectangular
shape to square square to circle So you have
232
00:22:00,000 --> 00:22:06,220
to remember this formulas what are the coefficients
from this to this only shear factor is applied
233
00:22:06,220 --> 00:22:10,809
here off course inclination factor we have
to calculate and multiply for each component
234
00:22:10,809 --> 00:22:14,460
separately
235
00:22:14,460 --> 00:22:20,450
I think that that is the derivation that is
looking at various factors shear factors that
236
00:22:20,450 --> 00:22:28,000
depth factors You can use this formulas for
phi is equal to zero type like clay type of
237
00:22:28,000 --> 00:22:29,000
soil
238
00:22:29,000 --> 00:22:35,550
Now when you have SPT values are given directly
calculation of bearing capacity I have just
239
00:22:35,550 --> 00:22:40,730
referred to several textbooks you could not
find actually this is one of the application
240
00:22:40,730 --> 00:22:46,850
where you will be very useful instead of converting
from SPT values to say angle of internal friction
241
00:22:46,850 --> 00:22:53,740
or CU basically in this particular reference
they have given a I think I have forgotten
242
00:22:53,740 --> 00:22:59,790
to put the in fact its given in Bowl’s book
but work is done by somebody else
243
00:22:59,790 --> 00:23:06,060
You know basically numerical relationship
is given directly can be used One of the advantage
244
00:23:06,060 --> 00:23:10,810
of this particular method is he has tried
to relate the foundation capacity with respect
245
00:23:10,810 --> 00:23:18,160
to a given settlement If you look at this
equations what we have derived so far
246
00:23:18,160 --> 00:23:22,990
if you look at the whole equation it does
not tell at this time of failure or at this
247
00:23:22,990 --> 00:23:28,170
type of equilibrium what could be the potential
settlement of the soil so that means the bearing
248
00:23:28,170 --> 00:23:33,340
capacity is delinked from the settlement what
is going to happen
249
00:23:33,340 --> 00:23:39,450
So that is why later using the same load you
calculate the settlement of the foundation
250
00:23:39,450 --> 00:23:44,720
and try to see what can be achieved or what
you can actually allow a settlement then you
251
00:23:44,720 --> 00:23:49,981
have to come and correct the bearing capacity
according So that means you got to do some
252
00:23:49,981 --> 00:23:57,110
extra work whereas in this particular case
he has given relationship which actually given
253
00:23:57,110 --> 00:24:03,740
for 25mm the settlement basically normalized
with respect to 25mm only thing is this is
254
00:24:03,740 --> 00:24:09,059
numerical formula sometime you have to be
little bit careful not very straight forward
255
00:24:09,059 --> 00:24:14,500
Depending on the situation you have to correct
it so basic idea is this is one formula where
256
00:24:14,500 --> 00:24:24,060
you will find use of N60 So from SPT you calculate
the N60 and then apply that Typically we need
257
00:24:24,060 --> 00:24:32,110
to just remember some you know basically the
bearing capacity what could be the range So
258
00:24:32,110 --> 00:24:42,740
if you look at very soft material at the bottom
is about 75 know basically soft and silt clay
259
00:24:42,740 --> 00:24:48,460
less than 75 kilo newton per square meters
So if you convert into ton seven seven and
260
00:24:48,460 --> 00:24:51,299
a half ton per square meters which is reasonably
a good load
261
00:24:51,299 --> 00:24:58,020
But if you go to a very soft clay you will
find even less than that like 51015 such type
262
00:24:58,020 --> 00:25:03,960
of soil even if you apply a slight pressure
will be settling down So the bearing capacity
263
00:25:03,960 --> 00:25:08,050
magnitude we need to remember is just keep
in mind that when you are doing computation
264
00:25:08,050 --> 00:25:14,390
this is not come up with some large numbers
So if you go back all the way to a very large
265
00:25:14,390 --> 00:25:21,980
number like 600 kilonewton per square meter
So what is means is nearly 60 ton per square
266
00:25:21,980 --> 00:25:24,460
meter for a dense gravel or dense sand
267
00:25:24,460 --> 00:25:30,920
So that means you can play 60 ton load within
one square meter of so you can imagine to
268
00:25:30,920 --> 00:25:36,120
get the 60 ton load how much of how many concrete
blocks you have to stack up several probably
269
00:25:36,120 --> 00:25:43,410
more than 1015 So that is the idea behind
you can understand the capacities of good
270
00:25:43,410 --> 00:25:50,210
sand is so much compare to soft clay so in
between you will have several cases where
271
00:25:50,210 --> 00:25:55,760
you can keep the numbers as a reference values
but not exactly you’re not you’re not
272
00:25:55,760 --> 00:25:57,190
suppose to use this numbers
273
00:25:57,190 --> 00:26:04,000
Because even after defining medium dense sand
you will have a very large you know the range
274
00:26:04,000 --> 00:26:09,929
of values so have to be little bit careful
but just for information I have taken from
275
00:26:09,929 --> 00:26:15,670
the BS codes quite reasonable when you will
calculate you will get somewhere around here
276
00:26:15,670 --> 00:26:20,640
These are bearing capacity fact is given by
API slightly different from what Terzaghi
277
00:26:20,640 --> 00:26:26,260
has given this is bases on works by I think
mayor Horf and when we are designing mudmatts
278
00:26:26,260 --> 00:26:28,060
for offshore foundation we should use this
279
00:26:28,060 --> 00:26:35,480
That is why I have reproduced that from the
for easy and convenience they also have given
280
00:26:35,480 --> 00:26:40,679
numbers so that you don’t need to read for
given soil friction angle you can straight
281
00:26:40,679 --> 00:26:45,470
away read it But if you’re not comfortable
you can use this numbers This are given for
282
00:26:45,470 --> 00:26:50,420
every five degrees them you can just interpolate
in between them So for examination point I
283
00:26:50,420 --> 00:26:56,429
will give you this table so that you can just
interpolate wherever you require
284
00:26:56,429 --> 00:27:06,480
So this the second thing is instead of applying
basically the inclination factor API recommends
285
00:27:06,480 --> 00:27:12,370
use the method of effective bearing area For
example if you have only a vertical load what
286
00:27:12,370 --> 00:27:20,760
will happen The whole contact surface between
the foundation and soil will be positive compression
287
00:27:20,760 --> 00:27:26,710
pressure isn’t it Pure vertical load But
if the vertical load is shifted by say few
288
00:27:26,710 --> 00:27:33,940
meters to one side what will happen there
will be a there will be a non-uniform pressure
289
00:27:33,940 --> 00:27:36,940
on one side is higher one side is lower
290
00:27:36,940 --> 00:27:42,799
So what you will you happen whenever the pressure
on one side becomes negative that means the
291
00:27:42,799 --> 00:27:48,419
extensity is on too much so what will happen
is the foundation is trying to tilt But since
292
00:27:48,419 --> 00:27:53,980
there is no you know basically tensile stress
can be taken by soil what will happen the
293
00:27:53,980 --> 00:28:00,110
foundation will start lifting off and that
area will not have a contact surface Now what
294
00:28:00,110 --> 00:28:04,890
will happen when the when this is trying to
happen when the foundation load is very far
295
00:28:04,890 --> 00:28:08,220
and foundation is trying to readjust itself
296
00:28:08,220 --> 00:28:14,110
It is basically the contact pressure will
start increasing in the area where the contact
297
00:28:14,110 --> 00:28:18,720
pressure is contact surface is there So that
means this load is same only the location
298
00:28:18,720 --> 00:28:23,750
of load is shifting and it is a continuous
equilibrium it will achieve its equilibrium
299
00:28:23,750 --> 00:28:28,180
as long is able to take it if it is not able
to take it what will happen The whole structure
300
00:28:28,180 --> 00:28:29,640
is going to overturn
301
00:28:29,640 --> 00:28:35,710
And that is not very easy defined Even today
they have no solution for this so that is
302
00:28:35,710 --> 00:28:41,850
why API recommends an approximate method simple
approximation you could use it because to
303
00:28:41,850 --> 00:28:47,480
find out that the contact surface after achieve
equilibrium is very difficult because the
304
00:28:47,480 --> 00:28:53,350
soil settlement also happens you know simultaneous
with the rotational behavior of the foundation
305
00:28:53,350 --> 00:28:58,150
So as the soil settles as the foundation goes
down the soil gets better
306
00:28:58,150 --> 00:29:03,000
Bearing capacity is increasing which we cannot
model it unless you can carry out a finite
307
00:29:03,000 --> 00:29:08,380
element analysis or a complex or carry out
an experiment you are not able to find out
308
00:29:08,380 --> 00:29:14,169
what settlement or what contact surface area
because is a iterative process So at the equilibrium
309
00:29:14,169 --> 00:29:19,290
there will be a reduced surface area and there
will be some settlement and basically the
310
00:29:19,290 --> 00:29:25,549
foundation will will be stable if is able
to achieve the required overturning moment
311
00:29:25,549 --> 00:29:28,330
from the the resisting pressure
312
00:29:28,330 --> 00:29:32,840
Otherwise the foundation will or the whole
system will just rotate and fail by overturning
313
00:29:32,840 --> 00:29:37,660
So this you see from this picture there is
a length and width of the foundation and the
314
00:29:37,660 --> 00:29:42,980
load is applied off course load is applied
eccentrically or load is applied with some
315
00:29:42,980 --> 00:29:46,790
movement which both the cases are same So
you can see here in this case the extensity
316
00:29:46,790 --> 00:29:51,980
is that applies movement divided by the normal
load or the other way around
317
00:29:51,980 --> 00:29:57,809
If you have just load applied at eccentrically
at the point here then the moment is basically
318
00:29:57,809 --> 00:30:01,430
the load times the distance which will give
you the movement So because of that the contact
319
00:30:01,430 --> 00:30:10,340
surface is only shown in that you know the
hatch color area and that is the area effective
320
00:30:10,340 --> 00:30:15,690
so after this what you will do is the vertical
load divided by the effective area That means
321
00:30:15,690 --> 00:30:20,610
the increased bearing pressure But what difference
we are making For example this you are going
322
00:30:20,610 --> 00:30:27,070
to do total load divided by that reduced the
area but uniform pressure
323
00:30:27,070 --> 00:30:31,630
But if you actually draw a pressure diagram
basically if you just look at the base of
324
00:30:31,630 --> 00:30:43,290
the foundation originally so that is the area
where negative pressure because this is your
325
00:30:43,290 --> 00:30:55,940
foundation and probably that is your Q applied
with movement something like this increased
326
00:30:55,940 --> 00:31:09,309
pressure negative pressure but now this maybe
say f2 max this is F1 max this is negative
327
00:31:09,309 --> 00:31:16,360
now reduced the area probably you will be
taking something like this or you adjust it
328
00:31:16,360 --> 00:31:18,150
that is the width finally available
329
00:31:18,150 --> 00:31:32,340
What you are trying to do is or I can draw
it something like this Now what we are ignoring
330
00:31:32,340 --> 00:31:39,970
is this slightly increased pressure because
we are going to take a this is the average
331
00:31:39,970 --> 00:31:47,630
not the peak pressure because we are to find
out this by Q divided by A dash A dash is
332
00:31:47,630 --> 00:31:56,110
nothing but the effective area after re-distribution
which may actually not hundred percent correct
333
00:31:56,110 --> 00:32:01,820
but that is going to be a quite small difference
so we are just going to use that method
334
00:32:01,820 --> 00:32:09,830
Otherwise finding out the actual re-distribution
pressure is going to be quite troublesome
335
00:32:09,830 --> 00:32:16,260
The reason why we need to do this in comparison
to building design building design we don’t
336
00:32:16,260 --> 00:32:22,080
encounter this problem because the horizontal
loads are very-very small compared to the
337
00:32:22,080 --> 00:32:28,080
vertical loads The vertical loads are predominant
the magnitude is so huge that even horizontal
338
00:32:28,080 --> 00:32:31,289
loads are there its negligible effect will
be under foundation
339
00:32:31,289 --> 00:32:35,539
Whereas in offshore structures especially
in the temporary phase when the jacket is
340
00:32:35,539 --> 00:32:42,460
placed is very light structure and the horizontal
loads are predominant because the design why
341
00:32:42,460 --> 00:32:48,370
we make it light because we make it buoyant
remember all the jacket members are made buoyant
342
00:32:48,370 --> 00:32:53,960
so that when you place the jacket on water
it should float number one and we make it
343
00:32:53,960 --> 00:32:57,070
vertical by just little bit of water and we
place it
344
00:32:57,070 --> 00:33:00,020
So at that time the jacket is not going to
be very heavy it is going to be very light
345
00:33:00,020 --> 00:33:06,299
structure now vertical load is small horizontal
load is going to be subsequently larger and
346
00:33:06,299 --> 00:33:11,360
that is where we encounter this problem compared
to on shore structures we have a serious problem
347
00:33:11,360 --> 00:33:16,500
to resolve that’s why we have to learn little
bit more about eccentrically loaded foundation
348
00:33:16,500 --> 00:33:21,240
but we cannot apply the conventional method
of foundation design thats why API has given
349
00:33:21,240 --> 00:33:28,740
this method and it has suggested that this
error in taking average pressure is not going
350
00:33:28,740 --> 00:33:30,590
to be that too much
351
00:33:30,590 --> 00:33:37,020
But some of the times the method proposed
by API has also has been challenged because
352
00:33:37,020 --> 00:33:42,010
the difference between the average pressure
and the peak pressure what we have here is
353
00:33:42,010 --> 00:33:49,930
more than 10 to 15% There are several other
methods proposed by different course Which
354
00:33:49,930 --> 00:33:55,160
we may discuss in the later part of the tutorial
time
355
00:33:55,160 --> 00:34:00,160
Basically this is the chart given by API for
one side or two side eccentricities So you
356
00:34:00,160 --> 00:34:06,169
could read the factors varying from zero to
one depending on the eccentricities factors
357
00:34:06,169 --> 00:34:16,309
So basically the eccentricity is E2 or E1
E1 is so for circular one is basically in
358
00:34:16,309 --> 00:34:21,420
this because in any direction eccentricity
is going to be same so you read that or if
359
00:34:21,420 --> 00:34:31,000
it is a single side even you read this or
double one you read this and basically the
360
00:34:31,000 --> 00:34:36,940
reduction in area is given as A dash by A
A is your original area A dash is the reduced
361
00:34:36,940 --> 00:34:38,020
area
362
00:34:38,020 --> 00:34:43,850
And basic idea is if E2 is zero you will see
that full area you will be getting so either
363
00:34:43,850 --> 00:34:49,460
you go by this line or go by this line depending
on whether E1 and E2 are present So you can
364
00:34:49,460 --> 00:34:55,800
read the chart and get the reduced area if
it is a square one is very easy if it is a
365
00:34:55,800 --> 00:35:00,099
rectangular one you have to proportionate
to the length and the width of the foundation
366
00:35:00,099 --> 00:35:02,599
According to the multiplication factor what
you are going to get
367
00:35:02,599 --> 00:35:08,720
So this chart is quite useful in terms of
trying to find out a simplified solution slightly
368
00:35:08,720 --> 00:35:15,080
approximative but still practically very easy
to do the problem basic idea is we will apply
369
00:35:15,080 --> 00:35:17,599
this method
370
00:35:17,599 --> 00:35:27,290
The next one is slightly a different problem
and also done by this researcher basically
371
00:35:27,290 --> 00:35:33,570
Davidson Booker several years back I think
1976 this this is predominantly interesting
372
00:35:33,570 --> 00:35:41,580
problem in off shore as I mentioned into the
first few classes these marine deposits for
373
00:35:41,580 --> 00:35:45,020
most of the you know the island has deposited
areas
374
00:35:45,020 --> 00:35:51,080
The younger clay keeps depositing sediment
particles and it just keep growing over the
375
00:35:51,080 --> 00:35:56,080
last hundred years or two hundred years you
will see that as the new layer get deposited
376
00:35:56,080 --> 00:36:01,540
the previous layer gets you know compressed
consolidated and the strength increased so
377
00:36:01,540 --> 00:36:06,270
when we do the bore hole we normally find
that first 30 to 40 meters of clay you see
378
00:36:06,270 --> 00:36:12,760
a very low shear strength at the top and then
the shear strength keeps increasing in a linear
379
00:36:12,760 --> 00:36:13,760
fashion
380
00:36:13,760 --> 00:36:18,740
Some places we have seen almost like 30 to
40 meters from 5kpi it goes to 40kpi something
381
00:36:18,740 --> 00:36:25,530
like this Now how do we use the knowledge
that we have developed on bearing capacity
382
00:36:25,530 --> 00:36:29,800
equations Because what we have derived three
three types of equations is just a uniform
383
00:36:29,800 --> 00:36:36,170
soil either a clay type of soil with a constant
shear strength to infinite or a very large
384
00:36:36,170 --> 00:36:41,390
depth or C phi soil with a characteristic
same whereas here we have a soil where strength
385
00:36:41,390 --> 00:36:47,062
is low at the top and strength keep on increasing
but then we could do one thing we can an average
386
00:36:47,062 --> 00:36:48,062
characteristic and do it
387
00:36:48,062 --> 00:36:55,130
But whether it is true or not it is not very
clear So he has done experiments on this type
388
00:36:55,130 --> 00:37:00,800
of soil and come up with a numerical coefficient
basically slightly improved Imagine if you
389
00:37:00,800 --> 00:37:04,970
take the lower shear strength for example
the top soil and just finish your foundation
390
00:37:04,970 --> 00:37:09,730
design you will get a bearing capacity of
some amount which is going to be very conservative
391
00:37:09,730 --> 00:37:13,020
because you are only considering the lower
strength
392
00:37:13,020 --> 00:37:18,040
Actually the strength increasing means is
going to boost the capacity by some amount
393
00:37:18,040 --> 00:37:23,030
and that’s what is going to be taken advantage
of that So he has proposed this method we
394
00:37:23,030 --> 00:37:27,340
called it Davidson Booker method is nothing
but we got back to the original bearing capacity
395
00:37:27,340 --> 00:37:34,260
equation multiplied by the effect due to increase
in shear strength by means of so called strength
396
00:37:34,260 --> 00:37:43,609
factor because of the variations and also
he added a component called the rate of increase
397
00:37:43,609 --> 00:37:44,680
of shear strength
398
00:37:44,680 --> 00:37:51,119
So if you draw a picture it will be something
like this you know basic profile that is your
399
00:37:51,119 --> 00:38:03,730
seabed so this is the shear strength at the
top and the shear strength at bottom So this
400
00:38:03,730 --> 00:38:14,760
is the slope is the rate of increase and that
is what the total height is H something like
401
00:38:14,760 --> 00:38:21,190
this so that’s the formula that you can
use that So C times NC is the same basic form
402
00:38:21,190 --> 00:38:25,619
of equation for a clay type of soil because
the reminder will go away and one plus SC
403
00:38:25,619 --> 00:38:27,380
is the shape coefficient
404
00:38:27,380 --> 00:38:33,150
Which I think we have derived for several
shape cases so one plus SC SC is calculated
405
00:38:33,150 --> 00:38:38,650
by the ratio N gamma by NC as per the Terzaghi
equation and B by L will come into picture
406
00:38:38,650 --> 00:38:43,460
for circular foundation it will become one
square foundation becomes one and N gamma
407
00:38:43,460 --> 00:38:52,460
by NC will become 1.2 when you go and calculate
and basic idea is the calculation of Fr is
408
00:38:52,460 --> 00:38:58,349
given by a chart I have tried to reproduce
because it was a 1976 paper basically to be
409
00:38:58,349 --> 00:39:05,150
used for calculations so just took the values
and re-plotted with respect to rate of increase
410
00:39:05,150 --> 00:39:08,349
and the fr value can be taken from this chart
411
00:39:08,349 --> 00:39:16,600
So for calculation purpose there is a equation
given by this particular paper I think that
412
00:39:16,600 --> 00:39:22,610
can also be used in one of the references
I the original paper was not giving but the
413
00:39:22,610 --> 00:39:26,750
later researches have came up with a equation
for this particular graph which I think for
414
00:39:26,750 --> 00:39:30,310
examination point of view I will try to give
that equation so that you can you don’t
415
00:39:30,310 --> 00:39:37,080
have to read the charts from here So this
method is very useful for many-many occasions
416
00:39:37,080 --> 00:39:42,020
where practical applications you will find
this type of strength increase in several
417
00:39:42,020 --> 00:39:42,480
sights