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Shallow Foundations for low-cost houses: some aspects of seismic soil-structure interaction
Prishati Raychowdhury, PhDIndian Institute of Technology Kanpur
June, 2016IIT Guwahati
1
Seismic Damage of Buildings
Structural Issues Geotechnical Issues
1999 Turkey Earthquake(Courtsey: USGS) 2
Seismic SSI for Shallow Foundations
• Shallow foundations are commonly used for low to medium-rise buildings
• Shallow foundation: depth ≤ width of foundation• Seismic SSI is the response dictated by interactions
between:– Structure– Foundation– Underlying soil/rock
• Two main aspects of seismic SSI:– Kinematic interaction– Inertial interaction
3
Kinematic Interaction
ROCKING
SWAYFREE FIELD MOTION
SETTLEMENT
Effect of the presence of structure on the characteristics of ground motions, i.e. Free-field motion vs. Foundation input motion
4
Kinematic Interaction
• Base Slab Averaging • Embedment Effect
5
Inertial Interaction
• Inertia from vibration of structure and foundation• Foundation deformations
– Alters the system flexibility and mode shapes– Introduces foundation damping
Foundation Deformations Modes Hysteretic Damping Radiation Damping 6
How to estimate the influence of SSI on structures?
7
Modeling of SSI
Numerical Modeling
Continuum Finite element approach
Macro-element formulation
Winkler-based approach
Experimental Modeling
Reduced Scaled modeling
Full scale Modeling
Shake Table experiments
Centrifuge experiments
Mass shaker experiments
8
• Considers foundation and surrounding soil as a single macro-element
• Constitutive model that relates the forces and displacements
Macro-Element Model
Gajan (2005), Gajan et al. (2008) 9
Winkler-based Model• Beam on Nonlinear Winkler Foundation (BNWF) approach
-600
0
600
Mom
ent (
KN
m)
-150
0
150
She
ar (K
N)
0 1000 2000 3000Time (s)
-160
-80
0
Set
tlem
ent (
mm
)UCD centrifuge test (Gajan, 2006)BNWF Simulation
0 1000 2000 3000Time (s)
-20
0
20
40
Slid
ing
(mm
)
(a) (b)
(c) (d)
Raychowdhury and Hutchinson (2009): Earthquake Engineering and Structural Dynamics
Raychowdhury and Hutchinson (2010)ASCE Journal of Geotechnical and Geoenvironmental Engineering
Raychowdhury and Hutchinson (2011)International Journal for Numerical and Analytical Methods in Geomechanics 10
Inertial Interaction: Effect on System Response
• Period lengthening and modified damping:
– Period lengthening
– Modified damping
= Flexible base properties (i.e. considering SSI); T, β = Fixed-base properties (i.e. not considering SSI)
FEMA 450 & NEHRP (2003)
11
Inertial Interaction: Effect on System Response
Stewart et al., 2003 12
Influence of Inertial SSI on Buildings: An Experimental Study
13
Parameters considered: base condition, relative density of sand, depth of embedment, vertical factor of safety, and type of structure
14
Expe
rimen
tal P
lan
Exp No. ModelLoad case
(LC)Load on
footing (N)Base condition D/B
E-1 LC1_3S 101.28 Fixed base -E-2 LC2_3S 185.89 Fixed base -E-3 LC3_3S 248.12 Fixed base -E-4 LC4_3S 297.48 Fixed base -E-5 LC1_3S 101.28 Dense sand (Rd = 80%) 0.5E-6 LC2_3S 185.89 Dense sand (Rd = 80%) 0.5E-7 LC3_3S 248.12 Dense sand (Rd = 80%) 0.5E-8 LC4_3S 297.48 Dense sand (Rd = 80%) 0.5E-9 LC1_3S 101.28 Dense sand (Rd = 80%) 0E-10 LC2_3S 185.89 Dense sand (Rd = 80%) 0E-11 LC3_3S 248.12 Dense sand (Rd = 80%) 0E-12 LC4_3S 297.48 Dense sand (Rd = 80%) 0E-13 LC1_3S 101.28 Loose sand (Rd = 40%) 0.5E-14 LC2_3S 185.89 Loose sand (Rd = 40%) 0.5E-15 LC3_3S 248.12 Loose sand (Rd = 40%) 0.5E-16 LC4_3S 297.48 Loose sand (Rd = 40%) 0.5E-17 LC1_3S 101.28 Loose sand (Rd = 40%) 0E-18 LC2_3S 185.89 Loose sand (Rd = 40%) 0E-19 LC3_3S 248.12 Loose sand (Rd = 40%) 0E-20 LC4_3S 297.48 Loose sand (Rd = 40%) 0E-21 LC1_6S 207.09 Fixed base -E-22 LC2_6S 245.71 Fixed base -E-23 LC3_6S 295.07 Fixed base -E-24 LC4_6S 333.70 Fixed base -E-25 LC1_6S 207.09 Dense sand (Rd = 80%) 0.5E-26 LC2_6S 245.71 Dense sand (Rd = 80%) 0.5E-27 LC3_6S 295.07 Dense sand (Rd = 80%) 0.5E-28 LC4_6S 333.70 Dense sand (Rd = 80%) 0.5E-29 LC1_6S 207.09 Dense sand (Rd = 80%) 0E-30 LC2_6S 245.71 Dense sand (Rd = 80%) 0E-31 LC3_6S 295.07 Dense sand (Rd = 80%) 0E-32 LC4_6S 333.70 Dense sand (Rd = 80%) 0E-33 LC1_6S 207.09 Loose sand (Rd = 40%) 0.5E-34 LC2_6S 245.71 Loose sand (Rd = 40%) 0.5E-35 LC3_6S 295.07 Loose sand (Rd = 40%) 0.5E-36 LC4_6S 333.70 Loose sand (Rd = 40%) 0.5E-37 LC1_6S 207.09 Loose sand (Rd = 40%) 0E-38 LC2_6S 245.71 Loose sand (Rd = 40%) 0E-39 LC3_6S 295.07 Loose sand (Rd = 40%) 0E-40 LC4_6S 333.70 Loose sand (Rd = 40%) 0
3 st
orey
mod
el6
stor
ey m
odel
15
0 10 20 30 40 50 60Frequency (Hz)
0
400
800
1200
FRF
mag
nitu
de
Floor 1Floor 2Floor 3
0 10 20 30 40 50Frequency (Hz)
0
50
100
150
200
250
FRF
mag
nitu
de
Floor 1Floor 2Floor 3Floor 4Floor 5Floor 6
3-story building
6-story building
Frequency Response Function
16
80 160 240 320Vertical load on footing (N)
0.15
0.2
0.25
0.3
Perio
d (s
)
(b) Second Mode (a) Fundamental Mode
80 160 240 320Vertical load on footing (N)
0.04
0.05
0.06
0.07
0.08
D/B = 0Df/B = 0.5Df/B = 0Df/B = 0.5Fixed base
} Loose sand
} Dense sand
200 240 280 320 360Vertical load on footing (N)
0.3
0.35
0.4
0.45
Perio
d (s
)
(b) Second Mode (a) Fundamental Mode
200 240 280 320 360Vertical load on footing (N)
0.09
0.1
0.11
0.12
0.13
0.14D/B = 0Df/B = 0.5Df/B = 0Df/B = 0.5Fixed base
} Loose sand
} Dense sand
3-story building
6-story building
17
Base flexibility effect: on Period
0.24
0.32
0.40
0.48
Per
iod
(s)
base1 base2 base3 base4 base5
Base condition
3-storey (load case: LC4_3S)6-storey (load case: LC4_6S)
Fixedbase
Dense (D/B=0.5)
Dense (D/B=0)
Loose (D/B=0.5)
Loose (D/B=0)
18
Period Elongation
1.00
1.05
1.10
1.15
1.20
Perio
d el
onga
tion
ratio
base1 base2 base3 base4 base5
Base condition
3-storey (load case: LC4_3S)6-storey (load case: LC4_6S)
Fixedbase
Dense (D/B=0.5)
Dense (D/B=0)
Loose (D/B=0.5)
Loose (D/B=0)
19
Estimation of Damping
2 4 6 8 10Frequency (Hz)
0
200
400
600
800
FRF
mag
nitu
de
f2f1
Hmax
fn
2/maxH
Estimation of damping using half-power band width method
So
Deq E
Eπ
ζ41
=
Equivalent viscous damping method20
0
2
4
6
Dam
ping
ratio
(%)
E-1 E-2 E-3 E-4 E-5 E-6 E-7 E-8 E-9 E-10E-11
E-12E-13
E-14E-15
E-16E-17
E-18E-19
E-20
Experiment number
0
2
4
6
Dam
ping
ratio
(%)
E-21E-22
E-23E-24
E-25E-26
E-27E-28
E-29E-30
E-31E-32
E-33E-34
E-35E-36
E-37E-38
E-39E-40
Experiment number
3-story building
6-story building
21
Base flexibility effect: on Damping
1
2
3
4
5
6
Aver
age
dam
ping
ratio
(%)
base1 base2 base3 base4 base5
Base condition
3-storey6-storey
Fixedbase
Dense (D/B=0.5)
Dense (D/B=0)
Loose (D/B=0.5)
Loose (D/B=0)
22
Base flexibility effect: on Damping Amplification
1
1.5
2
2.5
3
3.5
Aver
age
dam
ping
am
plifi
catio
n (ζ
flex/ζ f
ixed
)
base1 base2 base3 base4 base5
Base condition
3-storey6-storey
Fixedbase
Dense (D/B=0.5)
Dense (D/B=0)
Loose (D/B=0.5)
Loose (D/B=0)
23
1 1.1 1.2 1.3
Period elongation ratio
3.0
4.0
5.0
6.0D
ampi
ng ra
tio (%
)3-storey6-storey
y = 5.29*x - 2.50 R2 = 0.8119
y = 29.13*x - 27.82 R2 = 0.7833
Relation between period elongation and damping ratio
24
Analysis vs. Experiment
25
Analysis vs. Experiment: Period Elongation
0
0.5
1
1.5
2
Perio
d el
onga
tion
ratio
ExperimentOpenSees AnalysisFEMA-356
E-1 E-2 E-3 E-4 E-5 E-6 E-7 E-8 E-9 E-10E-11
E-12E-13
E-14E-15
E-16E-17
E-18E-19
E-20
Experiment No.
Loose sandDense sandFixed
0
0.5
1
1.5
2
Perio
d el
onga
tion
ratio
ExperimentOpenSees AnalysisFEMA-356
E-21E-22
E-23E-24
E-25E-26
E-27E-28
E-29E-30
E-31E-32
E-33E-34
E-35E-36
E-37E-38
E-39E-40
Experiment No.
Loose sandDense sandFixed
(a) 3-storey building
(b) 6-storey building
26
Analysis vs. Experiment: Damping amplification
0 2 4 6 8
ζflex/ζfixed (Experiment)
0
2
4
6
8 ζ
fl ex/ζ
fixed
(FE
MA)
3-storey 6-storey
1:1 line
27
Conclusions
• Period and damping amplifications are more prominent in case of the 3-storey building than the 6-storey building, indicating more sensitiveness of short to medium buildings to SSI effects over taller ones
• Damping also shows dependence on the supporting soil density and depth of embedment of foundation
• Damping ratio of the structure-foundation systems is observed to be approximately linearly correlated with the period elongation ratio
• OpenSees simulation shows good comparison with the experiment, while FEMA methods largely over-estimate the fundamental period and damping, particularly for the 6-storey building
28
Overcoming the limitations
29
Laminar soil box for shake-table tests Minimizes boundary effect and wave reflections Pioneering Facility in India: to the best of my knowledge, this is the first facility in India involving laminar box for seismic SSI study
Sponsored by DST (under Fast Track Scheme for Young Scientists)
Acknowledgement
• The research is funded by Department of Science and Technology (DST), India, under the Fast Track Grant for Young Scientists. The financial support is greatly appreciated.
Vivek, B. and Raychowdhury, P. (2016): International Journal of Geomechanics (ASCE)
Vivek, B. and Raychowdhury, P. (2015): 6th Inational Conference on Earthquake Geotechnical Engineering, 1-4 November 2015, Christchurch, New Zealand.
30
Thanks for your attention..
Indian Institute of Technology Kanpur