ALERT2013 Martinelli Tamagnini

Modeling SSI on piled foundations:

the effects of kinematic interaction

Mario Martinelli

Claudio Tamagnini

Introduction

2M. Martinelli and C. Tamagnini ALERT 2013

EMBEDDED PILES under seismic loadings

1. The transit of seismic waves through the soil

during earthquakes may cause significant

strains. If embedded piles are present,

curvature will be imposed to the piles by soil

movement, which will generate bending

moments along the entire pile length

2. Due to the stiffness mismatch between the

foundation and the surrounding soil, the pile

is unable to comply with the free-field soil

deformation pattern. Therefore, the

Foundation Input Motion (FIM) is in

general different from the free-field motion.

Introduction

3

PILE DAMAGES

Pile extraction

from the soil

Pile damages

Niigata Earthquake, 1964 (M = 7.5)

M. Martinelli and C. Tamagnini ALERT 2013

Introduction

4

PILE DAMAGES

Friuli Earthquake, 1976 (M = 6.5)

Bridge on Ledra river: failure at the pile head

Udine-Carnia-Tarvisio highway


Introduction

5

PILE DAMAGES

Loma Prieta Earthquake, 1989 (M = 6.9)

Watsonville viaduct (Seed et al., 1990)

Pile collapse

Soil-pile detachment

Collapse of inclined piles (SEAOC,1991)


Introduction

6

PILE DAMAGESCosta-Rica Earthquake, 1991 (M = 7.7)

Collapse of Rio Viscaya bridge

(Priestly et al., 1991)

Collapse of Rio Banano bridge

(Priestly et al., 1991)


PILE DAMAGES

7

Introduction

Observations (field, laboratory, and computer simulations) showed that kinematic pile

bending may be severe in the case of piled foundations constructed in weak soil

conditions (mostly near interfaces separating soil layers of sharply different stiffness)

and on the pile head in presence of a stiff restraining cap

Recently technical regulations (in particular Eurocode 8) prescribes to compute

bending moments due to kinematic interaction when all of the following conditions

occur simultaneously:

the ground profile is of type D, S1 or S2, and contains consecutive layers of sharply

differing stiffness;

the zone is of moderate or high seismicity;

the structure is of importance class III or IV.


KINEMATIC INTERACTION ANALYSIS

8

Introduction

The approaches suggested in the technical literature for the kinematic interaction effects

are summarized in three different categories:

1. Approaches based on the results of freefield, 1d wave propagation analyses (pile

follows exactly the soil displacements without considering SSI). (Margason, 1975;

Margason et Holloway, 1977; NEHRP recommendations, 1997)

It assumes (1/)= (1/)2/)/1( sffff VaR =



9

Introduction





Margason et Holloway, 1977; NEHRP recommendations, 1997)

It assumes (1/)= (1/)

Drawbacks:

No frequency content, pile-soil relative stiffness and damping parameters are taken

into account ;

since aff increases as approaching the ground level, , = (true onlyfor no-rotation head piles but wrong for free-rotation head piles);

This Approach not valid for layered soil (soil curvature at interface separating soil layers

of different stiffness tends to infinity) and applying this formula slightly above or below

the interface may underestimate the pile curvature. (Nikolaou et al., 2001)

2/)/1( sffff VaR =



10

Introduction





Margason et Holloway, 1977; NEHRP recommendations, 1997);

2. Approaches based on simplified numerical methods which consider the pile as a beam

on a dynamic Winkler foundation (BDWF), characterized by a given distribution of

stiffness and damping coefficients with depth. These approaches allow to account for

soilpile interaction, stiffness discontinuities along the pile axis (i.e., layered soils), and

different boundary conditions at the pile ends [Mylonalis, 2001; Nikolaou et al. 2001];



11

Introduction





Margason et Holloway, 1977; NEHRP recommendations, 1997);

2. Approaches based on simplified numerical methods which consider the pile as a beam

on a dynamic Winkler foundation (BDWF), characterized by a given distribution of

stiffness and damping coefficients with depth. These approaches allow to account for

soilpile interaction, stiffness discontinuities along the pile axis (i.e., layered soils), and

different boundary conditions at the pile ends [Mylonalis, 2001; Nikolaou et al. 2001];

3. Approaches based on continuous medium: use the finite element (FE) or boundary

element (BE) approximations to integrate the dynamic equations of motion [Cairo and

Dente, 2007; Dezi et al., 2009; Maiorano et al., 2009; Di Laora, 2009; Martinelli, 2012].



12

Introduction

At the interface between two layers The approaches ( 2, 3) have been used to derive a

number of practical design methods

All these methods:

are based, in most cases, on relatively simple linear or nonlinear elastic soil models;

completely neglect the possible effects of the solid skeletonpore water interaction in

saturated soils.

The objectives of this work:

1. influence that the use of advanced constitutive models on SSI and in particular the

impact of the development and dissipation of during the earthquake event on

soil deformations and pile loads;

2. to use the results of advanced numerical simulations as benchmarks to evaluate

the predictive capabilities of the simplified analysis methods


Review of some simplified design methods

The problem examined: single pile on a twolayer soil

- Problem geometry and seismic input

- Constitutive model adopted and soil properties

- Finite element model and analysis program

- Selected results

Performance of simplified methods

Concluding remarks

Summary

13M. Martinelli and C. Tamagnini ALERT 2013

Summary

14






- Selected results


Concluding remarks


Review of Simplified Design Methods

15

This model is based on the following assumptions:

1. the soil in each layer is homogeneous, isotropic and linear elastic;

2. both layers are thick enough so that boundary effects do not influence the response at

the interface between the two soils;

3. the pile is linear elastic and its axis is vertical;

4. perfect adhesion is assumed at the pilesoil interface;

5. the soil is subjected to a uniform static shear stress, , which generates a constant

shear strain within each layer;

6. the displacements are small.

Dobry & ORourke (1983)

)/( 12 GGFF =


FGIEM pp 14/1

14/3

max )(86.1 =


16

This model is based on the following assumptions:

1. the soil in each layer is homogeneous, isotropic and linear elastic;

2. both layers are thick enough so that boundary effects do not influence the response at

the interface between the two soils;

3. the pile is linear elastic and its axis is vertical;

4. perfect adhesion is assumed at the pilesoil interface;

5. the soil is subjected to a uniform static shear stress, , which generates a constant

shear strain within each layer;

6. the displacements are small.

Dobry & ORourke (1983)

FGIEM pp 14/1

14/3

max )(86.1 =)/( 12 GGFF =

No dynamic effect!



17

Mylonakis (2001)

the seismic excitation imposed at the base of the soil

prole is an harmonic displacement with frequency ;

both radiation and material damping are taken into

account by considering a viscoelastic Winkler model for

the soil reaction to the horizontal pile displacements;

The two layers in the soil prole are of nite thickness.

Improvements with respect to Dobry and ORourke (1983):

2max dJE

M

ppp =maximum pile bending strain

as the representative quantity



18

Mylonakis (2001)

the seismic excitation imposed at the base of the soil

prole is an harmonic displacement with frequency ;

both radiation and material damping are taken into

account by considering a viscoelastic Winkler model for

the soil reaction to the horizontal pile displacements;

The two layers in the soil prole are of nite thickness.

Improvements with respect to Dobry and ORourke (1983):

1. closed-form solution of the bending moment at the interface in harmonic

STEADY-STATE conditions

= (

)/

( ) ( )

1113124/1

121

14

01

ccEk

+ccdh

c= p

p?

2max dJE

M

ppp =maximum pile bending strain

as the representative quantity

strain transmissibility

2. TRANSIENT:

dh

,

GG

,

EE

,1

1

2

1

p

01dyn1

pp

=

??5.10.1 =



19

Nikolaou et al. (2001)

AM c =)(max0.5

1

2

0.65

1

0.33

=

VV

EE

dLdA p

042.0= 11Hasc =



Vertically

propagated shear

waves sa Acceleration at ground level



20


AM c =)(max0.5

1

2

0.65

1

0.33

=

VV

EE

dLdA p

042.0= 11Hasc =



Vertically

propagated shear




21


AM c =)(max0.5

1

2

0.65

1

0.33

=

VV

EE

dLdA p

042.0= 11Hasc =



2. TRANSIENT loading

),()(/)( maxmax resonanceNfMtM c==

Vertically

propagated shear




22

Maiorano et al. (2009) and Sica et al. (2011)

AtM c=)(max

007.0=

Straight to Transient Loading

11Gc =

053.0=FEM (VERSAT-P3D) - Maiorano et al. (2009)

BDWM - Sica et al. (2011)

0.5

1

2

0.65

1

0.33

=

VV

EE

dLdA p

From Nikolaou et al. (2001) expression

1 Is from 1D site response



23


AtM c=)(max

007.0=


11Gc =



0.5

1

2

0.65

1

0.33

=

VV

EE

dLdA p





24


AtM c=)(max

007.0=


11Gc =



0.5

1

2

0.65

1

0.33

=

VV

EE

dLdA p


( )

0,50,25

111 1

2

1c

EE

+

dh=

pp? 10,93 =

a new semi-analytical relation calibrated on FEM parametric study results

Di Laora et al. (2012)



Summary

25





- Selected results


Concluding remarks




26

Based on EN 19981 (EC8) soil prole classication: class D.

Geometry

Pile length (in each layer) is larger than active length Long pile

Pile Youngs modulus Ep = 24 GPa

Pile head free to rotate



27

ACC4 ACC9

A number of recordings of real accelerograms considered and scaled in order to obtain a

series of (on average) spectrumcompatible accelerograms with the response spectrum (EC8)

for soil type A.

Seismic input


Critical state Framework (State Parameter: )


28

The Constitutive model: Dafalias & Manzari (2004)

YS - a cone with vertex in the origin of the stress space

Inside YS: hypo-elastic behavior ),,,( 0GeDD elel =

csee =

The movement of YS constrained by

Bounding Surface (BS) function of .

4 Surfaces: YS, BS, CSS and DS

Projection rule -->b

Hardening evolution law=f

],2,1,)([ inb ccf =&0)(


29

The constitutive model

Other two surfaces:

DS : Dilatancy = 0

CS : Critical state condition

The shape of each surface is f() : Van Eekelen (1980)

0


30

Two surfaces:

DS : Dilatancy = 0

CS : Critical state condition

( ) n=d dd :

The plastic flow direction R deviatoric part dR normal to the CSS at

c

Isotropic part D function of

and z

fabric-dilatancy tensor evolutionz&on the dilatancy coefficient D represents an important feature of this

constitutive model that can capture

the undrained response of sand

material under cyclic loading




31

q

p

M

e p0 > 0

0 = e ecs > 0

Loose Sand

Md,0

Mb,0

Md and Mb are defined as a

function of the updated .

In the figures they are

plotted as function of the

initial 0.




32

q

p

M

e p

TXCIU test

Monotonic loading

Mb,0

Md and Mb = f()

0 > 0

Loose Sand

Md,0The constitutive model



33

q

p

M

e p

0 = e ecs < 0

Md,0

Md and Mb = f()

0 < 0

Dense Sand

Mb,0




34

q

p

M

e p

Md,0

Mb,0TXCIU test

Monotonic loading

0 < 0

Dense Sand

Md and Mb = f()




35

Undrained Simple shear test

Cyclic loading

e p

B

A

Dense Sand

0A < 0

B < 0

(Dense)

(Medium- Dense)




36


Cyclic loading

Dense Sand

0A < 0

B < 0

Dense

State A




37


Cyclic loading

Dense Sand

0A < 0

B < 0

Dense Medium Dense

State A State B




38



p (kPa)

a(%)

q

(

k

P

a

)

q

(

k

P

a

)

q

(

k

P

a

)

q

(

k

P

a

)

p (kPa)

a(%) Dafalias & Manzari (2004)


39

Soil properties

Soil1

K = 1.0e-2 m/sSoil2

K = variable

initial stress state centered

with respect to the YS

0=zInitial Fabric

(State parameter)

(modif. Toyoura Sand)

(Nevada Sand)



40

FE model and analysis program

Soil: 264 8noded isoparametric hexahedral elements (u-p formulation)

Pile: Twonoded, linear elastic beam

Soil1

Soil2Additional beams for soil-pile

connection (No interface element)



41



Soil1

Soil2




42



Periodic boundary conditions

Impervious (no flow)

Soil1

Soil2




43


Soil1

Soil2



44


0 : Drained Conditions

Soil1

Soil2



45


Soil1 Undrained Conditions

Soil1

Soil2



46


Consolidation

Soil1

Soil2


Summary

47





- Selected results


Concluding remarks




48

Selected Results: The hydraulic conditions

ACC4

(Analysis: r1, r2 and r3)

Effect of the Hydraulic

conditions



49

ACC4


conditions


Reference analysis




50

ACC4


conditions


Reference analysis




51

ACC4


conditions


Mmax increases as the

permeability of Soil1

decreases ( increases)




52

The time at which Mmax is

attained is significantly

different!



ACC4

Consolidation

Undrained

Drained


53

Even if both soil layers are

relatively dense, positive excess

pore water pressures are

generated in the upper layer due

to the high contractancy of

Nevada sand

u remains quite large

close to the bottom

drainage boundary (ow

downwards impervious

boundaries)

u decrease upwards;

Due to the high K of soil2,

the excess pore pressure in

this layer are constant.(Negative values of u are due to soil contraction)



Soil1

Soil2


54

u decrease upwards (boundary condition)



Soil1

Soil2


55

For Soil1: u (Consolidation) < u (Undrained)



Soil1

Soil2


56


For Soil2: u (Consolidation) > u (Undrained)



Soil1

Soil2


57


For Soil2: u (Consolidation) > u (Undrained)

Small water flow

(Soil1 -> Soil2)Large water flow

(Soil1 -> Soil2)



Soil1

Soil2


58



Soil1

Soil2


59



Soil1

Soil2


60



Soil1

Soil2


61


FF motion Pile head motion (Pile is flexible)


Soil1

Soil2


62



Big difference in the response spectrum

depending on the hydraulic conditions (soil

Stiffness changes)


Soil1

Soil2


63



Big difference in the response spectrum

depending on the hydraulic conditions (soil

Stiffness changes)

Differently from what is typically observed in

piles with xed rotation at the head

Sa,pile > Sa,ff (pile head free to rotate)


Soil1

Soil2


64

(Analysis: r2 and r5)

Selected Results: The Seismic input



65


ACC4 is characterized by the largest

peak in acceleration


Arias Intensity




66



peak in acceleration


Arias Intensity

Caution in using simplied models

to estimate Mmax which characterize

the seismic input in terms of peak

acceleration at ground surface only!



Summary

67





- Selected results


Concluding remarks




68

The simplified methods



69

The input data: 1D Linear Elastic site response analysis

The input data for each simplified method is obtained from a linear equivalent site

response analysis performed with the code EERA

The stiffness degradation and damping curves obtained by simulating a series of

cyclic simple shear tests (Drained and Undrained) with the Dafalias & Manzari

(2004) model.

1 modulus decay curve is considered for Drained conditions

2 different modulus decay curves are considered for Undrained conditions

(extremely high tendency of shear stiffness to increase for larger than 103)



70

1D site response results

EERAFEM



71


EERAFEM

The real material response is more dissipative than that provided by the

simple nonlinear model implemented in EERA.



72


In Soil1: the EERA simulations tend to underestimate signicantly the

In Soil2: EERA and FEM results appear in substantial agreement

It is also interesting to note that the EERA results appear quite sensitive to the adopted

shear modulus decay curve.


EERA

FEM

Results at

the end of

analysis


73

Simpl. Meth. Predictions FEM Results

Mmax is the maximum bending moment predicted by each simplied method

is the corresponding maximum bending moment obtained from the 3d

FE simulations with the Dafalias & Manzari model

FEMM max


Summary

74






- Selected results


Concluding remarks


Concluding Remarks

75

Conclusions

series of 3d, fully coupled dynamic consolidation analyses have been used to

investigate the kinematic interaction effects in the classical problem of a single end

bearing pile immersed in a twolayer soil profile with a significant stiffness

significant pore pressure buildup can occur under seismic conditions even in soils

with relatively high permeability and density.

The results of the numerical simulations clearly show that :

u build-up can have an important effect in determining the response of the soilpile

system

The results of the numerical simulations have also been used to assess the predictive

capabilities of a number of simplified methods for the evaluation of at the

stratigraphic contact between the two layers.

Di Laora et al. --> the best performance overall

the predictive capabilities of currently available design procedures

appears relatively satisfactory in drained conditions

some care must be taken in Undrained or partially Undrained conditions


Modeling SSI on piled foundations:

the effects of kinematic interaction

Mario Martinelli

Claudio Tamagnini

ALERT2013 Martinelli Tamagnini

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