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a numerical investigation on bearing capacity of multi edge foundations using FLAC 3D software.
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Numerical Analysis of Load-Settlement Behavior of Multi Edge
foundations
K.N.T. University of TechnologyFaculty of Civil Engineering
Supervisor:Dr. Mahmoud Ghazavi
By:
Soroush Mokhtari
March 2007
Introduction
Improving Bearing capacity
Improving soil bearing capacity
Improving geometry of foundation
Geosynthetics
Soil Reinforcment
....
Skirted foundations
Shell foundations
Multi edge foundations
...
1st Season :
Usage of experimental result
in Numerical methods
Controlling the Numerical model
What are the effective parameters ?
Pervious Studies
2nd Season:
Ghazavi & Hadiani
(2004)
)(3926.3
3926.3
0114.0
0269.1
LLsquareuHshapeu q
LB
LB
q
)(7223.3
7223.3
0030.0
9905.0
LLsquareushapeu q
LB
LB
q
)(6716.2
6716.2
0241.0
0257.1
LLsquareuTshapeu q
LB
LB
q
Bearing capacity of cross shape foundations are more than square foundations when they have the same width
Bearing capacity of cross shape foundation is more than the others
The bearing capacity of these foundations can be estimated by the following equations.
qult
B
qult
B
X
qult
B
qult
B
X
qult
B
qult
B
X
qult
B
qult
B
X
Pervious Studies
2nd Season:
NDBNqq qult .).2(5.0.
..5.0.. NBNqq qqult
NBNqq qult ..5.0.
NBNqq qult ..5.0.
Stuart’s theory (1962):
Which parameters
can affect the results ?
Size of the model
Fragment of elements in Regions with High stress gradient
Propriety of neighbor elements
Magnitude of load increments
3ed season:
Modeling (FLAC 3D) & Controlling the model
Controlling Numerical
model
3ed season:
The effect of size and location of the supports
effectsSmall model Absorption of plastic deformation
Large model Waste of time and computer memory
There is an appropriate size which will neither affect the results nor
waste time
0
20
40
60
80
100
120
140
160
0 5 10 15 20)mm( نشست
) kpa
ر )شا
ف
Brick 30*30cm
Brick 60*60cm
Brick 120*120cm
Brick 150*150cm
Footing properties:
6 cm width Square
Soil properties:
E = 27 MPa
υ = .35
C ~ 0 kPa
Φ = 38.1 deg
3ed season:
Size and Propriety of elements
effectsLarge elements less accurate results
Very small elements waste of time and computer memory
0
20
40
60
80
100
120
140
0 2 4 6 8 10 12 14)mm( نشست
)kpa
ر )شا
ف
3*3 under footing
10*10 under footing
12*12 under footing
6*6 under footing
effectsLarge increments increase loading shocks
Very small increment waste of time
3ed season:
Magnitude of load increments
0
20
40
60
80
100
120
140
0 5 10 15)mm( نشست
) kpa(
ر شا
ف
5E-5 cm/cycle
1E-4 cm/cycle
5E-4 cm/cycle
2E-3 cm/cycle
Footing properties:
6 cm width square
Soil properties:
E = 27 MPa
υ = .35
C ~ 0 kPa
Φ = 38.1 deg
3ed season:
The effects of soil parameters
How can soil parameters affect the load-settlement behavior of the model
Controlling the model
Module of elasticity
Poassio’s ratio
Internal friction angle
cohesion
Dilatation angle
Elastic parameters
Strength parameters
Post failure behavior
Load-settlement behavior
Estimating unknown parameters
3ed season:
Effect of module of elasticity & poassio’s ratio
0
20
40
60
80
100
120
140
0 5 10 15)mm( نشست
)kPa (
ر شا
ف
E = 10 MPa
E = 50 MPa
E = 20 MPa
Footing properties:
6 cm width square
Soil properties:
C ~ 0 kPa
Φ = 38.1 deg
E = 10 MPa υ = .2
E= 20 MPa υ = .3
E= 50 MPa υ = .35
In sand E varies from 5 to 85 Mpa and υ form 0.3 to 0.4
3ed season:
Effect of dilatation angle
Potential function
Dilatation angle
Post failure behavior
0
20
40
60
80
100
120
140
160
180
0 2 4 6 8)mm( نشست
) kpa
ر )شا
ف
Dil = 1 deg
Dil = 4 deg
Dil = 3 deg
elastic
plastic
Footing properties:
6 cm width square
Soil properties:
E = 27 MPa
υ = .35
C ~ 0 kPa
Φ = 38.1 deg
Dilatation angle: the change in the orientation of grains on a shear plane
3ed season:
Numerical vs experimental results
0
20
40
60
80
100
120
140
160
180
0 2 4 6 8 10)mm( نشست
) kPa
ر )شا
ف
Square B = 12 cm, Dense sand
Ghazavi & Hadiani
0
20
40
60
80
100
120
140
0 5 10 15)mm( نشست
) kPa(
ر شا
ف
Square B=12 cm, loose sand
Ghazavi & Hadiani
Dense sand:
E : 65 < 70 < 98 MPa
Ψ : 5 < 12.6 Deg
Loose sand:
E : 35 < 36 < 59 MPa
Ψ : 4 < 7.6 Deg
Footing properties:
12 cm width square
Soil properties:
Ψ=?
E = ?
υ = ?
C ~ 0 kPa
Φ = 38.1 deg loose sand
Φ = 42.1 deg dense sand
3ed season:
Numerical vs experimental results
0
20
40
60
80
100
120
140
160
180
0 5 10 15)mm( نشست
)kPa (
ر شا
ف
B=6 , Dense
Ghazavi & Hadiani
0
20
40
60
80
100
120
140
0 1 2 3 4 5 6)mm( نشست
)KPa (
ر شا
فB=3 cm, Dense soil
Ghazavi & hadiani
0
20
40
60
80
100
120
140
160
0 5 10 15)mm( نشست
) Kpa
ر )شا
ف
B=6 cm, Soft sand
Ghazavi & Hadiani
0
20
40
60
80
100
120
140
160
180
0 2 4 6 8 10)mm( نشست
)kP
aر )
شاف
B=4 cm, Dense soil
Ghazavi & Hadiani
Footing properties:
Cross shape footing with different sizes
Soil properties:
Same as the parameters for square foundations
0
20
40
60
80
100
120
140
0 5 10 15)mm( نشست
) kpa(ر شا
ف
B=6 cm, loose sand
Ghazavi & Hadiani
0
20
40
60
80
100
120
140
160
180
0 2 4 6 8 10)mm( نشست
)Kpa
ر )شا
ف
B=6 cm, Dense sand
Ghazavi & Hadiani
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10)mm( نشست
( kPa
) شار
ف
H-shape, B = 4cm
Ghazavi & Hadiani, Dense sand
0
20
40
60
80
100
120
0 5 10 15)mm( نشست
)kP
aر )
شاف
H-soft, b=4cm
Ghzavi & Hadian,loose sandi
3ed season:
Numerical vs experimental results:
Footing properties:
H shape foundations with different sizes
Soil properties:
Same as the parameters for square foundations
4th season: analysis of the results
Introduction
Orientation of displacement vectors are different in each zone
Interfering foundations:
1 -interference increase in bearing capacity
2 -bearing capacity of too far or too near footings will increase less.
Who to separate different shear areas under the footing?
No interference between shear zones
Interference is more
efficient
Blo
ckin
g is
hap
pene
d
4th season:
Cross shape foundations
0
100
200
300
400
500
600
700
0 10 20 30 40 50)mm( نشست
) kPa( رشا
ف
+shape, B=49cm, L=124cm
Square, B=99cm, loose sand
0
100
200
300
400
500
600
700
800
900
0 10 20 30 40 50
)mm( نشست
)kPa ( ارشف
+shape, B=49cm, L=124cm
Square, B=99cm, Densesand
0
200
400
600
800
1000
1200
0 10 20 30 40 50)mm( نشست
) kPa(ر شا
ف+shape, B=28cm , L=188cm
Square, B=99cm, Dense sand
0
100200
300
400500
600
700
800
900
1000
0 10 20 30 40 50
)mm( نشست
) kPa( رشا
ف
+shape, B=28cm, L=188cm
Square, B=99cm, Loosesand
Soil properties:Dense sand
Ψ=5
E = 70 MPa
υ = .35
C ~ 0 kP
Φ = 42.1 deg
Loose sand
Ψ=4
E = 36 MPa
υ = .3
C ~ 0 kP
Φ = 38.1 deg
Decrease in ratio of B/L difference in bearing capacities
0
100
200
300
400
500
600
700
0 10 20 30 40 50)mm( نشست
) kPa( رشا
ف
+shape, B=49cm, L=124cm
Square, B=99cm, loose sand
NDBNqq qult .).2(5.0.
4th season:Cross shape foundations
Cross shape foundation with large ratio of B/L:
4th season:Cross shape foundations
0
200
400
600
800
1000
1200
0 10 20 30 40 50)mm( نشست
) kPa(ر شا
ف
+shape, B=28cm , L=188cm
Square, B=99cm, Dense sand
..5.0.. NBNqq qqult
Cross shape footing with proper ratio of B/L
Coefficients have their maximum value
4th season:
Cross shape foundations
Cross shape foundation with small ratio of B/L
00.2
0.40.6
0.81
1.21.4
1.61.8
2
0 0.1 0.2 0.3 0.4 0.5 0.6B/L
Dense sand
Loose sand
4th season:Optimum ratio of B/L
There is no interference between two parts of the
footing
Reduction of q/A due to blocking
effect
Maximum value of q/A
0
100
200
300
400
500
600
700
800
900
1000
0 5 10 15 20 25 30 35 40)mm( نشست
)kPaر )
شاف
Square, B=99cm, Dense sand
H-Shape, B=28cm, L=188cm
0
100
200
300
400
500
600
700
800
0 5 10 15 20 25 30 35 40)mm( نشست
)kPa (
ر شا
ف
Square, B=99cm, loose sand
H-Shape, B=28cm, L=188cm
0
100
200
300
400
500
600
700
0 5 10 15 20 25 30 35 40)mm( نشست
)kPaر )
شاف
Square, B=99cm, loose sand
H-Sahpe, B=49, L=124
0
100
200
300
400
500
600
700
800
0 5 10 15 20 25 30 35 40)mm( نشست
)kPa (
ر شا
ف
Square, B=99cm, Dense sand
H-Shape, B=49cm, L=124cm
4th season:
H shape foundations
Soil properties:Dense sand:
Ψ=5
E = 70 MPa
υ = .35
C ~ 0 kP
Φ = 42.1 deg
Loose sand:
Ψ=4
E = 36 MPa
υ = .3
C ~ 0 kP
Φ = 38.1 deg
Decrease in ratio of B/L difference in bearing capacities
0
100
200
300
400
500
600
700
0 5 10 15 20 25 30 35 40)mm( نشست
)kPaر )
شاف
Square, B=99cm, loose sand
H-Sahpe, B=49, L=124
4th season:H shape foundations
H shape foundations with large ratio of B/L
NDBNqq qult .).2(5.0.
4th season:H shape foundations
0
100
200
300
400
500
600
700
800
900
1000
0 5 10 15 20 25 30 35 40)mm( نشست
)kPaر )
شاف
Square, B=99cm, Dense sand
H-Shape, B=28cm, L=188cm
..5.0.. NBNqq qqult
H shape foundation with proper ratio of B/L
Coefficients have their maximum value
4th season
H shape foundation
H shape foundation with small ratio of B/L
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0 0.1 0.2 0.3 0.4 0.5 0.6B/L
Dense sand
Loose sand
4th seasonOptimum value of B/L
There is no interference between two parts of the
footing
Reduction of q/A due to blocking
effect
Maximum value of q/A
0
200
400
600
800
1000
1200
0 10 20 30 40 50)mm( نشست
)kPaر )
شاف
H-Shape, B=28cm, L=188cm
+Shape, B=28cm, L=188cm
0
100
200
300
400
500
600
700
800
900
1000
0 10 20 30 40 50)mm( نشست
)kPaر )
شاف
H-Shape, B=28cm, L=188cm
+Shape, B=28, L=188
4th season
H shape Vs cross shape foundations
4th season
Uplift of soil around the multi edge foundations
No uplift due to blocking effect
qult
B
qult
B
X
Results
Maximum bearing capacity of multi edge foundations are more than bearing capacity of square foundations when they have the same area
Interference of shear zones under multi edge foundations have a significant effect on their bearing capacity
Ratio of dimensions of a multi edge foundation has a remarkable effect on its bearing capacity
In H shape foundations, the displacement of shear zones is not symmetric due to unequal width of interfering parts
In multi edge foundations there is no uplift of soil in the concave corners of the foundation
