Transcript Engineering Mechanics

Advance Design of RC Structure
Lecture 9
Design of Raft Foundation
Lecture 9
Advance Design of RC Structure
1
Raft Foundations

2
Raft foundations
 A raft is essentially a very large spread footing that usually encompasses
the entire footprint of the structure. They are also known as mat
foundation.

Foundation engineers often consider mats when
 The structure loads are so high or the soil conditions so poor that the
spread footings would be exceptionally large. If spread footings would
cover more than about one third of the building area, a mat will be more
economical.
 The soil is very erratic & prone to excessive differential settlements. The
continuity & rigidity of the mat foundation helps in reducing differential
settlement of individual columns relative to each other.
 Lateral loads are not uniformly distributed through the structure & thus
may cause differential horizontal movements in spread footing. The
continuity & rigidity of the mat will resist such movements.
 The uplift loads are larger than spread footing can accommodate.
Lecture 9
Advance Design of RC Structure
Raft Foundations
 The bottom of the structure is located below the groundwater table, so
waterproofing is an important concern. The weight of the mat also helps
resist hydrostatic uplift forces from the groundwater.

Types of raft foundation
 Cellular raft foundation
 Used on site where, poor ground must
resist high bending moments
 Crust raft foundation or blanket mat
 Slab with thickening under the columns
& walls
 Plane raft foundation
 Piled rafts
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Advance Design of RC Structure
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Raft Foundations

Methods of designing raft foundation
 The conventional rigid method
 This method is easy to apply & the computations can be carried out
using hand calculations.
 The application of this is limited to rafts with relative regular
arrangement of columns.
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Advance Design of RC Structure
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Raft Foundations
 The finite element method
 This method can be used for the analysis of raft regardless of the
column arrangements, loading conditions, & existence of cores &
shear walls.
 Commercially available computer programs like SAP2000 & SAFE
can be used.
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Advance Design of RC Structure
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Geotechnical Design

Bearing capacity
 The allowable bearing capacity of a raft footing is given by
2
q all
N 
1   0.33D f  s 

1


 1 


0.08  3.28B  
B  25.4 
For B < 1.2m
q all 
N  s 


0.08  25.4 
Where
qall is allowable bearing capacity in kilopascals
N is standard penetration test (SPT) blow count
B is the width of the footing
s is the settlement in millimeters
Df is the depth of the footing in meters
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Advance Design of RC Structure
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Geotechnical Design
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Settlement of raft foundation
 The settlement of raft footing can be estimated in a manner similar to
that of spread footings.
 Immediate Settlement; based on the theory of elasticity can be used to
estimate the corner settlement of a rectangular footing with dimensions
of L' and B',
1 v s 2 
1  2v s 
s i  qB '
I

I 2 I F
 1
Es 
1 v s

Where
q is the contact stress
B’ is the least dimension of the footing
vs is the Poisson ratio of the soil
Es is the elastic modulus of the soil
I1 , I2 & IF are obtained from, the table & the figure attached, in terms
of the rations N = H/B’ (H = layer thickness), M = L’/B’ & D/B
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Advance Design of RC Structure
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Structural Design of Raft Foundation 8

Conventional rigid method
Step 1: Check soil pressure
The resultant of columns working loads
equals:
Ptotal  P1  P2  P3  ...   Pi
The soil pressure at any point can be
obtained;
q
M
Ptotal M x

y  y x  q allowable
A
Ix
Iy
Where;
A = area of the raft (BL)
Ix = moment of inertia of the raft about
x-axis = BL3/12
Iy = moment of inertia of the raft about
y-axis = LB3/12
Lecture 9
Advance Design of RC Structure
Structural Design of Raft Foundation 9
Mx = moment of applied loads about the x-axis = Ptotal  ex + Mx
My = moment of applied loads about the x-axis = Ptotal  ey + My
The ex & ey are the eccentricities of the resultant from the C.G. of the raft.
The coordinate of the eccentricities are given by:
X '
P1x 1  P2 x 2  P3x 3  ...
Ptotal
e x  X '
Y '
B
2
P1 y 1  P2 y 2  P3 y 3  ...
Ptotal
e y Y '
L
2
Compare the maximum soil pressures with net allowable soil pressure
q max  q n ,all
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Advance Design of RC Structure
Structural Design of Raft Foundation 10
Step 2: Draw the shear force & bending moment diagrams
Divide the raft into several strips in the X-direction (B1, B2, B3)
& in the Y-direction (B4, B5, B6, B7)
The soil pressure at the center-line of the strip is
assumed constant along the width of the strip.
P
M
L
All the loads has
q (u ) B  (u )total  (u ) x
A
I x 2 to be factored
P
M
L
q (u ) E  (u )total  (u ) x
A
Ix 2
The average pressure equals:
q (u )avg 
q (u ) B  q (u ) E This value shall be used in
the analysis of the strip
2
The total soil reaction (RB-E) for the strip B-E is equal to:
R B E  q (u )avg  B 2  L
The total soil reaction (RB-E) for the strip B-E is equal to:
PB E  P(u )5  P(u )6  P(u )7  P(u )8
Lecture 9
Advance Design of RC Structure
Structural Design of Raft Foundation 11
The achieve equilibrium, columns loads & soil reaction must be
modified such that the sum of the forces is equal to zero
R
 PB E
P(u )avg  B E
2
The modified soil pressure equals:
P
q mod  (u )avg
L
The modified columns loads are obtained by multiplying each of the
applied loads by the factor  given by;
P
  (u )avg
PB  E
The shear & bending moment can be
computed using regular structure analysis
The same process should be carried out
for all the strips in the raft foundation
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Advance Design of RC Structure
Structural Design of Raft Foundation 12
Step 3: Design for flexure
The maximum positive & negative moments can be obtained.
The negative moments need top reinforcement & positive
moment needs bottom reinforcement.
Lecture 9
Advance Design of RC Structure
Discussions
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Any Question?

Notes
Lecture 9
Advance Design of RC Structure
I1 and I2 for Settlement Equation
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Advance Design of RC Structure
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I1 and I2 for Settlement Equation
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Advance Design of RC Structure
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IF For Settlement Equation
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Advance Design of RC Structure
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