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TopicDYNAMIC HORIZONTAL AND VERTICAL
STIFFNESSES OF CAISSON FOUNDATIONS IN HOMOGENOUS SOIL
ADVISOR: Prof. Dr. Shahid AhmadCommittee Member: Prof. Dr. Sabanayagam Thevanayagam
Objective
To determine the horizontal and vertical stiffness and damping coefficients for caissons.
INTRODUCTION
Definition: Caissons, Pier or drilled shafts;• Massive Cylindrical Embedded Found, Precast or cast in place concrete with steel reinforcement and steel jacket or casing.• Diameter Range: 2-12 feet.• Depth to Dia ratio: 0.5-4Uses: 1. Bridge foundation elements2. Foundation components of transmission
towers3. Foundations at marine sites
Caisson
Schematic Diagram of circular Caisson.
D
B
LITERATURE REVIEW
• G. Gazetas (2005) Lateral Response of
Caissons of D/B=1-3 by Winkler model
• Varun et al. (2009) Lateral Response of
Caissons, D/B=1-6.
• Carolin Birk and Behnke (2010) dynamic
response of foundations by scaled boundary
finite element method.
• S. Ahmad, A.S.M. Israil and K. Chen (1988) Dynamic stiffness of rigid square and
rectangular foundations by DBEM and IBEM.
•S. Ahmad, A.K. Rupani (1999) Horizontal
impedance of square foundation in layered soil
• P. K. Pradhan et al (2004) presented vertical
dynamic response of foundation using Cone Model
• Iftekhar Anam and Jose M. Roesset (2004)
Dynamic stiffness’s of surface foundations
• Y. Q. Cai et al (2009) Vertical dynamic response of a
rigid foundation embedded in poroelastic soil layer.
• Artur Pais and Kausel (1988) Approximate
formulas for dynamic stiffness’s of rigid
foundations.
• H. L. Wong and J. E. Luco (1985) Tables of
impedance functions for square foundations on
layered media.
• S. Ahmad and A. Bharadwaj (1991) presented
horizontal impedance of embedded strip
foundations
CONVERGENCE STUDY OF BOUNDARY ELEMENT DISCRETIZATION AND COMPARISON WITH PUBLISHED
RESULTS
• Poisson’s ration= 0.35
• Shear Wave Velocity, Vs=1
• Radius of Caisson, B=1
• Normalized Elastic Modulus ES=2.7
.
Typical discretization pattern for embedded foundation over half-space
.
Surface Foundation Boundary Element Discretization (soil-foundation interface)
0.00 0.50 1.00 1.50 2.00 2.500.00
0.20
0.40
0.60
0.80
1.00
1.20
Vertical stiffness co-efficient
3 Elements2 Elements4 Elements
a0
kv
0.00 0.50 1.00 1.50 2.00 2.500.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
2.00
Vertical Dashpot co-efficient
2 Elements3 Elements4 Elements
a0
Cv
.
Convergence study on free surface discretization for surface foundation
0.00 0.50 1.00 1.50 2.00 2.500.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
Vertical Stiffness Co-efficient
3 B 7 B12 B Y. Q. Cai, Hong (2009)
a0
kv
0.00 0.50 1.00 1.50 2.00 2.500.00
0.50
1.00
1.50
2.00
2.50
Vertical Dashpot co-efficient
3 B 7 B12 B Y. Q. Cai, Hong (2009)
a0
Cv
.
Convergence study on free surface discretization for caisson, D/B=6
0.00 0.20 0.40 0.60 0.80 1.00 1.200.00
0.20
0.40
0.60
0.80
1.00
1.20
Horizontal stiffness co-efficient
17 B 25 B Varun et al.(2009)
a0
kx
0.00 0.20 0.40 0.60 0.80 1.00 1.200.00
0.50
1.00
1.50
2.00
2.50
3.00
Horizontal dashpot co-efficient
17 B 25 B Varun et al.(2009)
a0
CX/E
S
RESULTS, COMPARISON AND DISCUSSIONS
Horizontal Static Stiffness of caissons.
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.00.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
Horizontal Static stiffness at different D/B
Present EPRI(1982)
D/B Ratio
kx(s
tatic
)
.
Vertical Static Stiffness of caissons
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.01.450
1.500
1.550
1.600
1.650
1.700
1.750
1.800
Vertical static Stiffness at different D/B
Kv Static
D/B Ratio
kv(S
tatic
)
.
Surface Foundation
0.00 0.50 1.00 1.50 2.00 2.500.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
Vertical Stiffness co-efficient
Present Y.Q.Cai, Hong (2009)
a0
kv
0.00 0.50 1.00 1.50 2.00 2.500.00
0.50
1.00
1.50
2.00
2.50
Vertical Damping Coefficient
Present Y.Q.Cai, Hong(2009)
a0
Cv
.
Embedded Foundation of D/B=1, Vertical stiffness
0.00 0.50 1.00 1.50 2.00 2.50
-1.50
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
Vertical Stiffness co-efficient
Present Birk & Behkne(2010)
a0
kv
0.00 0.50 1.00 1.50 2.00 2.500.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
Vertical Damping co-efficient
Present Birk & Biehkne(2010)
a0
Cv
.
Caissons vertical stiffness at different D/B ratio’s.
0.00 0.50 1.00 1.50 2.00 2.50
-35.00
-30.00
-25.00
-20.00
-15.00
-10.00
-5.00
0.00
5.00
Vertical Stiffness Co-efficient
D/B=2 D/B=3 D/B=4 D/B=6 D/B=8
a0
kv
0.00 0.50 1.00 1.50 2.00 2.500.00
1.00
2.00
3.00
4.00
5.00
6.00
Vertical Dashpot co-efficient
D/B=2 D/B=3 D/B=4 D/B=6 D/B=8
a0
Cv
.
Embedded Foundation, D/B=2.
0.00 0.50 1.00 1.50 2.00 2.500.00
0.20
0.40
0.60
0.80
1.00
1.20
Horizontal stiffness co-efficient
Present Varun et al.(2009)
a0
kx
0.00 0.50 1.00 1.50 2.00 2.500.000.200.400.600.801.001.201.401.601.802.00
Horizontal dashpot co-efficient
Present Varun et al.(2009)
a0
Cx/E
s
.
Caissons of D/B=4, Horizontal Stiffness.
0.00 0.50 1.00 1.50 2.00 2.500.00
0.20
0.40
0.60
0.80
1.00
1.20
Horizontal stiffness co-efficient
Present Varun et al.(2009)
a0
kx
0.00 0.50 1.00 1.50 2.00 2.500.00
0.50
1.00
1.50
2.00
2.50
3.00
Horizontal Damping co-efficient
Present Varun et al.(2009)
a0
Cx/E
s
.
Caissons of D/B=6, Horizontal Stiffness.
0.00 0.50 1.00 1.50 2.00 2.500.00
0.20
0.40
0.60
0.80
1.00
1.20
Horizontal stiffness co-efficient
Present Varun et al.(2009).
a0
kx
0.00 0.50 1.00 1.50 2.00 2.500.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
Horizontal Damping co-efficient
Present Varun et al.(2009.
a0
Cx/E
s
.
Caissons of D/B=8, Horizontal Stiffness.
0.00 0.50 1.00 1.50 2.00 2.500.00
0.20
0.40
0.60
0.80
1.00
1.20
Horizontal stiffness co-efficient
Present
a0
kx
0.00 0.50 1.00 1.50 2.00 2.500.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
5.00
Horizontal Damping co-efficient
Present
a0
Cx/E
s
ConclusionResults for vertical and horizontal stiffness and damping coefficients are available in layered and non-homogeneous media. The results were taken over homogeneous half-space and compared with available results.
Thanks
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