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

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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.

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Thanks for your attention..

Indian Institute of Technology Kanpur