Pushover analysis with ZSOIL - Zace Services Ltd, … · Pushover analysis with ZSOIL Stéphane Commend, GeoMod SA 08.2014, Lausanne (Switzerland) Why pushover? Brief recall of pushover

Pushover analysis with ZSOIL

Stéphane Commend

GeoMod Ing. SA, Lausanne

[email protected]

mailto:[email protected]


Stéphane Commend, GeoMod SA

08.2014, Lausanne (Switzerland)

Why pushover?

Brief recall of pushover theory

Application: 2-storey RC frame

Nonlinear time history analysis (reference solution)

Nonlinear pushover analysis

Taking soil into account

Example: D0211 building

Contents




Why pushover?







Contents




Motivation: why pushover?

Seismic analysis To design (new structures) or assess (existing structures): - Linear simplified static analysis (replacement forces) - Linear modal analysis - 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 - Until now, applies mainly to buildings and bridges (structural only) Future: include soil (=> tunnels, retaining walls, ... ?)

- Consists in applying a lateral load distribution, increase it (see theory recall)

- 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)




Why pushover?







Contents




Theory

Nonlinear pushover analysis in ZSOIL -Based on N2 method developed by Fajfar et al.

- 2D or 3D are possible (2D only if building is « regular »)

- 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 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




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

How to build SDOF model?

a. Assume F = displacement shape, for instance: F = f1 (first mode) F = 1 (1 in direction of earthquake, 0 else) F linear b. N2 method first assumption: load distribution F = p[M]F or Fi = pmiFi

c. Equivalent mass of SDOF system: m* = S(miFi) Fn = 1 (n = roof level)

Magnitude of lateral loads

Diagonal mass matrix




Theory

d. Write equation of motion for MDOF system (no damping assumed, influence will be adressed in design spectrum) e. Statics imply internal R and external forces F are equal f. N2 method second assumption: displacement shape is constant

Diagonal mass matrix

Relative displacement

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

Top floor displacement = f(t)




Theory

g. Multiply eq. of motion by FT and by leads to (using e. and f.): And the equation of motion for the equivalent SDOF system writes:

m* m* 1/G 1/G pm* = Vb

Modal participation factor Base shear of MDOF model

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




Why pushover?







Contents




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




Application: Model

Distributed masses

Dead and live loads

3.3 kN/m2 x 5 m = 16.5 kN/m

Nodal loads

Dead and live loads

16.5 kN/m x 5 m / 2 = 41.25 kN

Fixed BCs: ux = uy = 0, rz = 0

Columns: material 1

Nonlinear beam

Flexibility based

Floors: material 2 and 3

NL beam, flex. based

Pushover control node




Application: Seismic demand

COMPATIBLE P

USH

OV

ER

TIM

E H

ISTO

RY

Accelerogram generated Synthetically (Sabetta)




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




Application: Pushover analysis

ALSO TRIED









0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.05 0.1 0.15 0.2

V*/

(gM

*) [

-]

d* [m]

Single DOF Capacity Curve & Demand Spectrum (A-D)

a*/g(PSH 1/Default)

a*_b/g(PSH 1/Default)

Sa/g(PSH 1/Default)

Sae/g(EC8 default)





Pushover analysis report

Item Unit PSH 1/Default

MDOF Free vibr. period........T [s] 0.446894

SDOF Free vibr. period.......T* [s] 0.785174937

SDOF equivalent mass.........M* [kg] 12369

Mass participation factor Gamma - 1.20402

Bilinear yield force value..Fy* [kN] 49.04143356

Bilinear displ. at yield....Dy* [m] 0.061915828

Target displacement.........Dm* [m] 0.166110198

SDOF displacement demand....Dt* [m] 0.050560935

Energy......................Em* [kN*m] 6.628061725

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

Demand ductility factor......mi - 3.285346622

Capacity ductility factor...miC - 2.682838978

MDOF displacement demand.....Dt [m] 0.060876377








Why pushover?







Contents




Motivation: why take soil into account?

qdB

B

A

MA = q(L2/3)

11qL4

120EIdB =

L

Mstruct

Msol

M

d,q

Mpstruct

Mpsol2

Mpsol1




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

Taking soil into account in calculation

=> “Rocking” allowed

=> Less damage in structure

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




Taking soil into account: soil hypotheses

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

b = 1.4 m

h = 0.5 m

Interface elements




Taking soil into account: pushover analysis

0

10

20

30

40

50

60

70

0 0.05 0.1 0.15 0.2 0.25

V [

kN]

d [m]

Multi DOF Capacity Curve

Structure only






0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.05 0.1 0.15 0.2 0.25

V*/

(gM

*) [

-]

d* [m]


a*/g(PSH 1/Default)


Sa/g(PSH 1/Default)

Sae/g(EC8 default)









SDOF equivalent mass.........M* [kg] 14015.6






Energy......................Em* [kN*m] 1.098105061

Reduction factor.............qu - 1.256356429











Comparison




Parametric study

Time history analysis Pushover analysis

|dtop| max drift floor1 max |M| max dt drift floor1 (dt) |M| max (dt)

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

structural only 4.0 2.0 113 6.1 2.9 101

with soil, E 8.0 3.6 66 7.6 4.0 64

with soil, E = E/4 10.4 5.4 54

with soil, stiff foundation 7.5 3.8 95




Why pushover?







Contents




D0211 buidling




D0211 buidling




D0211 buidling




D0211 buidling

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Sae

[-]

T [sec]

[EC8 default] Elastic Response Spectrum (A-T)

Sae/g

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Sae

[-]

d [m]

[EC8 default] Elastic Response Spectrum (A-D)

Sae/g




Distributed weight

53 kN/m or

30 kN/m (roof)

Corresponding nodal load

at each column top

Col. B Col. B Col. B Col. A

Col. A

Col. A

Col. A

Col. A

Col. A




D0211 buidling

0

100

200

300

400

500

600

700

800

900

1000

0 0.05 0.1 0.15 0.2 0.25

V [

kN]

d [m]


Vb (PSH 1/Default)




D0211 buidling




D0211 buidling











Energy......................Em* [kN*m] 27.813644








D0211 buidling




D0211 buidling

Footing bearing capacity Say b = 2 m, t = 0.5 m sfail = 5 kPa x 46 + 10 kPa x 33 + 20 kPa x 40 = 1360 kPa

Most loaded column: 1340 kN (service) x 1.5 => Nd = 2000 kN

sd = 2000 kN / 2 m / 1 m’ = 1000 kPa OK !

Soil type C (HSS model) E50 = 80 MPa, Eur = 320 MPa, E0 = 800 MPa sh,ref = 100 kPa g= 20 kN/m3, c = 5 kPa, f = 35 , y = 12




D0211 buidling




D0211 buidling

0

100

200

300

400

500

600

700

800

900

0 0.05 0.1 0.15 0.2 0.25

V [

kN]

d [m]


Vb (PSH 1/Default)




D0211 buidling

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

V*/

(gM

*) [

-]

d* [m]


a*/g(PSH 1/Default)


Sa/g(PSH 1/Default)

Sae/g(EC8 default)




D0211 building











Energy......................Em* [kN*m] 35.76587353








D0211 buidling




D0211 building




D0211 buidling

2D Stahlbetonrahmen [1]

2D fünfstöckiges Gebäude

aus Stahlbeton, Rahmen B [5]

dt |M| max (dt) dt |M| max (dt)

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

Nur Struktur 6.1 101 8.8 483

Mit Boden, Flachgründung “gross”

7.5 95 11.2 482

Mit Boden, Flachgründung “klein”

7.6 64 12.2 340

Documents

Pushover analysis with ZSOIL - Zace Services Ltd, … · Pushover analysis with ZSOIL Stéphane Commend, GeoMod SA 08.2014, Lausanne (Switzerland) Why pushover? Brief recall of pushover