pushover analysis with zsoil · pushover analysis with zsoil taking soil into account stéphane...

Pushover analysis with ZSOIL taking soil into account

Stéphane Commend

GeoMod Ing. SA, Lausanne

[email protected]

mailto:[email protected]


Stéphane Commend, GeoMod SA

08.2013, Lausanne (Switzerland)

Motivation

Why pushover?

Why take soil into account?

Brief recall of pushover theory

Application: 2-storey RC frame

Structural-only analysis

Nonlinear time history analysis (reference solution)

Nonlinear pushover analysis

Taking soil into account

Nonlinear time history analysis with DRM (reference solution)


Comparison of solutions

Conclusions and perspectives

Contents




Motivation: why pushover?

To design (new structures) or assess (existing structures) wrt seismic loading: - Replacement forces (linear) - Modal analysis (linear) - Nonlinear pushover analysis - Nonlinear time-history analysis -Nonlinear pushover analysis represents a good compromise between

- replacement forces, where nonlinearity is taken into account by a single behavior coefficient q (too simple) - nonlinear time-history, very time consuming




Motivation: why pushover?

Nonlinear pushover analysis (in ZSOIL, N2 approach [Fajfar]) - Until now structural only => applies mainly to buildings and bridges - Future: include soil => tunnels, retaining walls, ... ? - Returns a target displacement = maximal displacement during a certain earthquake, used in displacement-based seismic assessment (in Switzerland, since 2004, documented in CT SIA 2018) aeff = wRd /wd (SIA CT 2018)

aeff compliance factor

wRd allowable displacement (capacity of deformation) wd deformation during earthquake

aeff < amin intervention necessary

amin ≤ aeff ≤ aadm intervention if proportionate

aadm ≤ aeff no intervention

amin, aadm= f(structure type, lifetime)




Motivation

Why pushover?












Contents




Motivation: why take soil into account?

Seismic action => inertia forces




Motivation: why take soil into account [Gazetas et al]?

Taking soil into account in calculation (in Case 2)

=> “Rocking” allowed

=> Less damage in structure

=> Design with soil is more favorable than with structure only




Motivation

Why pushover?












Contents




Theory

STEP 1: Define Seismic demand, elastic acceleration spectrum Sae

Elastic ADRS demand spectrum

f(structure type, soil conditions, zone)

Sae Sae

Sde

Sde Sae




Theory

STEP 2: Build structural model and apply gravity loads

Vertical and horizontal members have to be modelled with nonlinear model (typically: reinforced concrete with fc and ft in concrete and steel)




Theory

STEP 3: Choose and apply lateral load distribution and increase

F

F represents the inertial forces which would be experienced by the structure during the earthquake

- Load pattern is applied in one direction at a time, meaning several calculations have to be conducted to fully assess the structure:

- in x and z direction, in plus and minus directions - with different load patterns (uniform, linear or modal)




Theory

STEP 4: Plot capacity curve

d F

Vb

Base shear, Vb

Top displacement, d

Capacity curve




Theory

STEP 5: build equivalent single degree of freedom (SDOF) model

d F

Vb

m*

d* = d / Γ

F*

Equivalent SDOF




Theory

Equation of motion for MDOF system (no damping assumed, influence will be adressed in design spectrum) N2 assumptions + some math. => Equation of motion for the equivalent SDOF system

𝑴 𝒖 + 𝑹 = 𝑴 𝟏 𝑎

Diagonal mass matrix

Relative displacement

Internal forces = f(u) Ground acceleration = f(t)

𝑚∗𝑑∗ + 𝐹∗= 𝑚∗a

d* = Dt / G = displacement of SDOF system

F* = Vb / G = force of SDOF system




Theory

Base shear, Vb

Top displacement, d

Capacity curve

F*

d*

SDOF Capacity curve (bi-lin.)

F*

m*

d*

Capacity spectrum

dm* dy*

dy*

Sa =

dy* = 2 (dm* - Em*/Fy*)

T* = 2p SQRT(m* dy* / Fy*)

dm*: assumed target displacement => Iterative procedure !!

Fy*

Fy*

m*

From Capacity curve to Capacity spectrum

Em*

Acceleration spectrum

Elastic period of idealized bilinear SDOF system

Assumption: post-yield stiffness = 0




Theory

d*

ADRS demand spectrum

f(structure type, soil conditions, zone)

capacity spectrum

F*

m*

TC

T*

dt*

dt = Γ dt*

Target displacement

Modal participation factor

STEP 6: compare demand and capacity spectra (*) and retrieve dt

(*) not straightforward, because capacity spectrum is nonlinear




Motivation

Why pushover?












Contents




Application: 2-storey RC frame [Gelagoti et al, 2012]




Application: Model

Pushover control node

Dead and live loads: 3.3 kN/m2




Application: Material definition for RC members




Application: Seismic demand

COMPATIBLE P

USH

OV

ER

TIM

E H

ISTO

RY

Accelerogram generated Synthetically (Sabetta)




Motivation

Why pushover?












Contents




Application: Time history analysis (reference solution)




Application: TH – displacement time history

ux max = 4 cm




Application: TH – bending moment envelope during TH

M max = +106 / -103 kNm




Motivation

Why pushover?












Contents




Application: Pushover analysis

ALSO TRIED





5.4 cm





Pushover analysis report

Item Unit PSH 1/Default

MDOF Free vibr. period........T [s] 0.445066

SDOF Free vibr. period.......T* [s] 0.837848363

SDOF equivalent mass.........M* [kg] 12369.6

Mass participation factor Gamma - 1.20401

Bilinear yield force value..Fy* [kN] 48.9047294

Bilinear displ. at yield....Dy* [m] 0.07030178

Target displacement.........Dm* [m] 0.166111577

SDOF displacement demand....Dt* [m] 0.053940741

Energy......................Em* [kN*m] 6.404596979

Reduction factor.............qu - 1

Demand ductility factor......mi - 3.079519728

Capacity ductility factor...miC - 2.362836024

MDOF displacement demand.....Dt [m] 0.064945192 dt = 6.5 cm





M max = +94 kNm




Motivation

Why pushover?








Nonlinear TH analysis with DRM (reference solution)




Contents




Taking soil into account: soil hypotheses

Soil (HSS model)E50 = 80 MPa, Eur = 320 MPa, E0 = 800 MPash,ref = 100 kPag = 20 kN/m3, c = 0 kPa, f = 30°, y = 10°

b = 1.4 m

h = 0.5 m

Interface elements(optional)




Motivation

Why pushover?








Nonlinear TH analysis with DRM (reference solution)




Contents




Taking soil into account: Time history analysis with DRM

• DRM => two models: a reduced model and a background model • Seismic input on reduced model = free-field motion of background model





45 m

15 m

Seismic input: linear deconvolution ofFig. 12.3 accelerogram

Periodic BCs: ux left = ux right

Horizontal acceleration read at top of soil columnBackground model (elastic) and free-field motion

10% Rayleigh damping on 2 Hz and 6 Hz => a = 1.88 and b = 0.004




Interior domain (HSS model)

Boundary layer (elastic)

Exterior domain (elastic)

Viscous dampers


Reduced model





ux max = -8.0 cm





M max = +47 / -43 kNm




Motivation

Why pushover?












Contents




Taking soil into account: pushover analysis

Vb max << Vb max (struct. Only)

Structural only





Pushover analysis report

Item Unit PSH 1/Default

MDOF Free vibr. period........T [s] 0.529679

SDOF Free vibr. period.......T* [s] 1.1692452

SDOF equivalent mass.........M* [kg] 14036

Mass participation factor Gamma - 1.28476

Bilinear yield force value..Fy* [kN] 19.58028002

Bilinear displ. at yield....Dy* [m] 0.048308883

Target displacement.........Dm* [m] 0.075135711

SDOF displacement demand....Dt* [m] 0.075181918

Energy......................Em* [kN*m] 0.998227533

Reduction factor.............qu - 1.556275235

Demand ductility factor......mi - 1.556275235

Capacity ductility factor...miC - 1.555318745

MDOF displacement demand.....Dt [m] 0.096590721 dt = 9.7 cm > dt (struct. only) = 6.5 cm





M max = +31 / -37 kNm




Motivation

Why pushover?












Contents




Comparison

STR

UC

TUR

AL

ON

LY

TAK

ING

SO

IL IN

TO A

CC

OU

NT

PLAY MOVIES




Comparison: «case 2» vs. «case 1»

0.00E+00

2.00E+01

4.00E+01

6.00E+01

8.00E+01

1.00E+02

1.20E+02

0.00E+00 5.00E-02 1.00E-01 1.50E-01 2.00E-01 2.50E-01

be

nd

ing

mo

me

nt

in c

olu

mn

just

ab

ove

fo

un

da

tio

n [

kN

m]

Top floor displacement [m]

found 1.4 m (right) strip (BIG) found struct only

0

0.2

0.4

0.6

0.8

1

1.2

0.00E+00 5.00E-02 1.00E-01 1.50E-01 2.00E-01 2.50E-01

mea

n st

ress

leve

l und

er fo

unda

tion

[-]

Top floor displacement [m]

found 1.4 m (right) strip (BIG) found

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.00E+00 5.00E-02 1.00E-01 1.50E-01 2.00E-01 2.50E-01

abso

lute f

ound

ation

disp

lacem

ent [

m]

top floor displacement [m]

found 1.4 m (right) strip (BIG) found

found 1.4 m

Strip (BIG) found

M struct

M struct

disp

disp

M struct

disp

Mean SL

Mean SL

Mean Stress Level

d(target) = 9.7 cmd(target) = 8 cm




Comparison

Time history (with DRM) Pushover analysis Difference PO vs. TH

dtop min/max drift min/max M min/max dt drift(dt) |M| max (dt) on |d| max on |M| max

[cm] [cm] [kNm] [cm] [cm] [kNm] [%] [%]

structural only -2.3/+4.0 -1.1/+2.0 -103/+106 6.5 3.1 94 63 -11

with soil -8.0/+4.0 -4.8/+2.3 -43/+47 9.7 5.9 37 21 -21

with soil, BIG foundation -4.8/+8.0 -1.4/+3.3 -81/+99 8 4.1 95 0 -4




Motivation

Why pushover?












Contents




Taking soil into account (if in case 2 !) leads to:

d >>

design M(struct) << => gain !

Needs more benchmarking

Thank you Thomas for ideas


pushover analysis with zsoil · pushover analysis with zsoil taking soil into account stéphane...

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