aseismic design of shallow (rocking) foundations · aseismic design of shallow (rocking)...

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Aseismic Design of Shallow (rocking) Foundations

November 28 2012

Michael Pender

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MJP starting point 1

Structure and foundation form a single entity

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Foundation behaviour is nonlinear

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Elastic soil-structure interaction doesn’t work hence the terminology SFSI (soil-foundation-

structure-interaction)

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Elastic SSI diagram

uhhe

heus

Me

u = us + uh + he

Ks

KhK

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Elastic SSI for a water tower

0 1 20

5

10

15

Frequency ratio

Res

pons

e ra

tio

Fixed base

Elastic soil

su 50 kPa Vs 118 m/s M 50 tonnes h 20 m D 9 m (LRFD)

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Priestley et al 2007: Displacement-based seismic design of structures

use of replacement structure Paper by Trevor Kelly in Bull. NZSEE 2009

many buildings not heavy enough to prevent rocking need better understanding of soil response

Paper by Priestley, Evison & Carr Bull. NZSEE 1978 related NZS4203 (1976) based on Housner BSSA 1963 (a famous paper)

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Nonlinear SFSI

Need a “design” method for modelling foundation moment-rotation curves hands-on approach – quick check on software output or a peer-review tool

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Shibata and Sozen - 1976

Mom

ent

Rotation

M - for substitute(ductile) structure

M - cracked section

M - uncracked section

For a structural component – beam or column

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Priestley replacement structure

Set of equations for elastic pile head stiffness of long piles Extension to include nonlinear behaviour Provides a “spreadsheetable” design environment (or design checking) Could be applied to the Substitute Structure idea of Sozen (1976) and Priestley et al (2007)

Displacement

Shea

rfor

ceSDOF simulationFoundation: shallow or pile

F

he ks

me

Ke

Horizontal & rotationalstiffness

ks

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Nonlinear foundation moment-rotation relation neglect horizontal deformation at foundation level

linear structural behaviour

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Nonlinear foundation response

Experimental data – Tom Algie’s PhD thesis

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Shallow foundation pull-back

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Shallow foundation pull-back

0 5 10 15 20 25 300

20

40

60

80

100

Rotation (millirads)

Mom

ent (

kNm

)

Snap 1Snap 2Snap 3Snap 4Snap 5Snap 6Snap 7Snap 8Snap 9

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Shallow foundation snap-back

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Normalised Rotation - θ0/α

Hal

f Per

iod

(sec

s)

Housner's equationTest 6Test 7Test 9

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Shallow foundation snap-back

10-1

100

101

102

0

10

20

30

40

50

60

Half Amplitude Rotation (millirads)

Dam

ping

Rat

io (%

)

Test 5 eastTest 6 eastTest 6 westTest 7 eastTest 7 westTest 9 eastTest 9 west

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Tom’s Abaqus modelling

0 5 10 15 20 25 300

20

40

60

80

100


Mom

ent

(kN

m)

ExperimentsAbaqus

(Hence not dependent on spring bed modelling.)

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Tom Algie’s finite element work

0 2 4 6 8 100

20

40

60

80

100

120

140


Mom

ent (

kNm

)

Gezatas formulaAbaqusOpenSEES - constant elasticRuaumoko - constant elasticOpenSees - FEMA elastic

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Hyperbolic M-θ curve fit

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

1.2

Normalised foundation rotation

Norm

alise

dm

omen

tcap

acity Normalised moment capacity at applied vertical load

Best fit curve through measured moment-rotation data

Measured moment-rotation data

a

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Hyperbolic curve as a secant modulus

0 0.05 0.1 0.15 0.2 0.25 0.30

0.2

0.4

0.6

0.8

1

1.2

Normalised foundation rotation

Norm

ailse

dse

cant

rota

tiona

lstif

fnes

s

Foundation rotational stiffness based on Gmaxb

Rotation

Mom

ent

1

K _secant

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Secant modulus on a log rotation scale

10-5 10-4 0.001 0.01 0.1 10

0.2

0.4

0.6

0.8

1

1.2

Normalised foundation rotation (log 10 scale)

Norm

alise

dse

cant

rota

tiona

lstif

fnes

s

Foundation rotational stiffness based on Gmax

Measured data

c

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What about damping?

Important for forced-based and displacement-based design hysteretic damping rather than radiation

not frequency dependent

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Nonlinear finite element damping using PLAXIS 3D

4− 10 3−× 0 4 10 3−×

1− 104×

5− 103×

5 103×

1 104×

Rotation (radians)

Foun

datio

n m

omen

t (kN

m)

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Shallow foundation example

0 0.02 0.04 0.06 0.08 0.10

5 104×

1 105×

1.5 105×

2 105×

Rotation (radians)

Mom

ent (

kNm

)

Hyperbolic moment- rotation curve

stiffness for second iteration

elastic stiffness for first iteration

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Shallow foundation iteration

0 2 4 6 80

1 105×

2 105×

3 105×

Iteration

Foun

datio

n m

omen

t (kN

m)

Mult

FMult ΦMult

Mult

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Pile foundation nonlinear

0 20 40 60 800

50

100

150

Pile head horizontal displacement (mm)

Pile

head

horiz

onta

lshe

ar(k

N)

OpenSeesPL

Davies & Budhu

Field load-unload curve

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Conclusions

An approach to incorporating nonlinear foundation moment-rotation curves into modelling the rocking of shallow foundations reduced foundation actions when compared with classical SSI

nonlinearity at the “middle” of the moment-rotation curve important

based on field test data and 3D nonlinear finite element modelling with foundation loss of contact

not dependent on spring-bed modelling relatively simple hands-on calculation as a design aid or peer review tool.

aseismic design of shallow (rocking) foundations · aseismic design of shallow (rocking)...

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