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Transcript of NON LINEAR SOIL STRUCTURE INTERACTION IMPACT … 3... · NON LINEAR SOIL STRUCTURE INTERACTION :...
NON LINEAR SOIL STRUCTURE INTERACTION : IMPACT ON THE
SEISMIC RESPONSE OF STRUTURES
Alain PECKER
1OECD/NEA IAGE/ IAEA ISCC Workshop, on SSI Ottawa , 6‐8 October , 2010
OUTLINE OF PRESENTATION
• Review of existing foundation design practiceRequired changes in design philosophy
• Examined foundation behavior during cyclic loadingModeling aspects through dynamic macroelement
• Assess the impact of foundation non linearities and variability of seismic motion on structural behavior
• Draw some preliminary conclusions2
FOUNDATION DESIGN PHILOSOPHY
• Foundations are designed to remain elasticduring earthquakes
foundation cannot be easily inspected and repaired after an earthquake
• Ductility demand restricted to superstructure
• Alternative approachAccept permanent (limited and controlled) displacements at foundationPerformance based design ⇔ displacement based design
3
MOTIVATION FOR DISPLACEMENTS EVALUATION
• Soil structure interaction plays a dominant role in seismic response of the structure
Beneficial or detrimental ?? Controversial but all linear elastic studies
• Permanent foundation displacements affect the performance of the structure
4
WHY CONSIDERINGFOUNDATION NONLINEARITY / INELASTICITY ?
• Recent records revealed very strong seismic shaking
1994 Northridge : 0.98 g , 1.40 m/s1995 Kobe : 0.85 g , 1.50 m/s
and SA values reaching 2 g
• Retrofitting of existing/damaged structures impossible to accomplish elastically
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MOSS LANDING (Loma Prieta, 1989)
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MEXICO(Michoacan, 1985)
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IMPLICATIONS OF NON LINEARITIES GEOTECHNICAL EARTHQUAKE ENGINEERING
• Sliding of foundation
• Foundation uplift
• Partial loss of bearing capacity
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θc
CENTRIFUGE TESTS(Gajan et al., 2005)
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DIFFICULTIES OF NON LINEAR DYNAMIC ANALYSES
• Analyses are time consuming & expensive to runEspecially if soil is modeled (3D continuum)
• Results are very sensitive to small changes in input data
Input motionStructural characteristicsSoil characteristics
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N
MV
NEAR FIELD
FAR FIELD
K C
Nonlinearities :
• Geometrical (interface behavior) Uplift model
• Material (elasto‐plastic soil behavior) Plasticity model
Wave propagation :
• Dissipation of radiation energy
•Dynamic elasticimpedances
DYNAMIC MACRO ELEMENT
Mθ
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GENERALIZED FORCES AND DISPLACEMENTSRigid circular footing under planar loading
Q q?←⎯→
max
1N
V
M
Q DNQ Q DV
DNQ M
⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥= =⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦
1N z
V x
M y
q uq q u
Dq Dθ
⎡ ⎤⎡ ⎤⎢ ⎥⎢ ⎥= = ⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦
xu
zu
yθN
MV
el up plq q q q= + +
MECHANISM DISSIPATION REVERSIBILITY NON‐LINEARITY MACROELEMENT
Elasticity No Reversible No Elasticity
Uplift Non –dissipative Reversible Geometric Non‐linear
elastic model
Soil Yielding Dissipative Irreversible Material
Associated Plasticity model
MODEL COMPONENTS
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Possible load states are limited by ultimate bearingCapacity of foundation
Phenomenologicalnon‐linear elastic model
Elastic soil
NQ
MQ
Nq
Mq
MQ
Mq
0MQ
0Mq
MQ
Nq
( )Q qqK=
1. Matrix depends explicitly on
UPLIFT ON AN ELASTIC SOIL
K q2. No influence of on uplift VQ
[Crémer et al (2001)][Wolf (1985)]
Ellipsoidal bounding surface
NQ
,M VQ Q
Hypoplastic bounding surface plasticity1. Cyclic loading2. Continuous variation of plastic modulus3. Numerical implementation
DQP
FOOTING BONDED ON A COHESIVE SOILNo uplift allowed
Associative flow rule
soilSoil: UndrainedConditions
Interface:Uplift
Uplift
Associated Plasticity
DEFINITION OF ULTIMATE LOADS
u
σ
σ
τ
τ
Zero dissipation
SURFACE OF ULTIMATE LOADS(Chatzigogos et al, 2007)
NQVQ
MQ0
1
Total footing detachment
Ellipsoidal Bounding Surface
Uplift Initiation
UPLIFT – PLASTICITY COUPLINGVQ
NQ
Toppling limit
NQ
MQ
Elastoplastic response
Elastoplastic response with uplift
Ultimate surface
[Chatzigogos et al, 2010]
Total footing detachment
SWIPE TESTSImposed Horizontal Displacement
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DIFFICULTIES OF NON LINEAR DYNAMIC ANALYSES
• Analyses are time consuming & expensive to runEspecially if soil is modeled (3D continuum)
• Results are very sensitive to small changes in input data
Input motionStructural characteristicsSoil characteristics
21
INCREMENTAL DYNAMIC ANALYSIS(Cornell, 2002)
• Series of nonlinear time histories analysesSame time history scaled to increasing amplitudesTrack of characteristic quantities of the response
• IDA curve is a plot of selected IM vs selected DM
• IDA curve set : collection of IDA curvesSeveral time histories representing one EQ scenario for one selected IM and DM
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EXAMPLES OF IDA CURVES
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IDA curve
IDA curves set
INCREMENTAL DYNAMIC ANALYSES
• Series of non linear time history analyses30 records representing an earthquake scenario M=6.5‐6.9 d=20‐30kmTime histories scaled up according to Intensity Measures (IM)
• pga , SA(TS) , SA(TSSI) , CAV
• Damage measures (DM) calculatedFoundation settlements (residual or maximum)Foundation rotations (residual or maximum)Deck drift (residual or maximum)Structural ductility demand ……
24
EXAMPLE : BRIDGE PIER
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EXAMPLE OF SYSTEM RESPONSE
26
Single analysisIDA curves μ = f(CAV)
STRUCTURAL DUCTILITY DEMAND μ = f(CAV)
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Fixed base Linear SSI
Non linear SSI
μ
CAV
FOUNDATION SETTLEMENTS
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Non linear SSI
Price to pay for change in ductility demandNo sign of distress even for increasing motion
RESULTS OF NUMERICAL ANALYSES
• Consideration of non linear soil structure interaction beneficial
drastically reduces the ductility demand in the structure
• Counterbalanced bylarger displacements and rotations at the foundation
May become unacceptable
• Variability in the response becomes large as more demand is placed on the foundation
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REMAINING ISSUES• Increased variability
care must be exercised before accepting to transfer the ductility demand from the structure to the foundationthorough investigation of the variability of the response
• Requires careful definition of acceptable criteriafor the foundation performance
• IDA may represent a convenient tool for analysis30
CONCLUSION
• It is time to move from the concept ofductility demand restricted to the superstructureelastic behavior of foundations
• Tocontrolled share of ductility demand between the superstructure and the foundation
31