collapse evaluation of seismically isolated building impacting moat wall

Quake SummitJuly 2012

Tools for Isolation and Protective SystemsNEEStips

Collapse Evaluation of Seismically Isolated Building Impacting Moat Wall

Armin MasroorGraduate Research Assistant

Gilberto MosquedaAssociate Professor

Department of Civil, Structural and Environmental EngineeringUniversity at Buffalo



NEES TIPS: Tools for Isolation and Protective Systems Four year research and education effort aimed at increasing applications of seismic isolation in the United

States (NSF Grant No. CMMI-0724208, PI Keri Ryan)

Conduct a series of “limit state” tests that examine the ultimate behavior of isolated buildings under various failure modes. Such failure modes include:

Isolated building pounding against an

outer moat wall

Elastomeric bearings subjected to large

strain limits (beyond stability limits)



Prototype Building-Basic Design Information Code : IBC 2006, ASCE 7-05, and AISC Steel Manual Building Location: Los Angeles, CA Site Class: D (Vs=180 m/s to 360 m/s) Mapped spectral accelerations: Ss = 2.2 g, S1 = 0.74 g Lateral System R Drift Limit

Isolated Intermediate Moment Frame (IMRF) 1.67 1.5% Properties of isolation systems

Isolator Properties DBE MCEEffective Period (TD, TM) 2.77 s 3.07 s

Effective Damping (BD,BM) 24.2% 15.8%

Isolator Displacement (DD, DM) 12.7 in. 24.3 in.

Total isolator displacement (DTD, DTM)

15.3 in. 29.4 in.

3D View (Isolated IMRF)



• The test specimen represents a single bay of an internal moment frame in the prototype structure.

• The test setup consisted of :– Structural frame (¼ scale 3-story IMRF)

– Gravity frame (one by one bay frame with, pin-pin columns and braced out of plane)

– Isolators (single friction pendulum R=30 in. and displacement capacity of 7 in.).

– The effective period of the isolated model at MCE displacement is 1.5 sec.

– Concrete blocks (designed to simulate impact surfaces)

– Retaining walls (consist of concrete wall with soil back fill and rigid steel wall)

Test Setup



Moat wall setup• Different scaled concrete wall thicknesses of 2, 4, and 6 in were

tested to examine the effect of wall stiffness on the pounding behavior.

• A rigid steel wall was also used to cover a wider range of wall properties (With and without weld).



Overview of the tests conducted• System identification tests

– Snap back, Pull back, White noise, Sine sweep, Table impulse, Sinusoidal• Fixed base model

– Investigate the post-yield behavior of the fixed-base structure.• Isolated base model without impact

– Investigate properties of isolation device and isolated base structure under MCE motions.

• Isolated base model with impact – Investigate the effect of pounding on superstructure– Different wall stiffness– Variable gap distance– Different contact surface



Ground motion selection• Based on capacity limits of the shake table, five ground motions were selected from

the SAC and PEER database.• All the ground motions were scaled to MCE level based on target periods T=0-3 sec.

MCE scale factor

Scaled PGA (g)

Magnitude (M)

Duration (sec)

Peak base plate disp. (in)

Newhall Fire Station-comp. 2 1.46 0.86 6.69 40.0 4.24Takatori-comp. 2 0.89 0.55 6.90 40.9 2.83Sylmar Converter Station-comp. 1 1.11 0.68 6.69 40 4.88Erzincan-NS 1.76 0.91 6.69 21.3 6.62Erzincan-EW 1.76 0.87 6.69 21.3 3.36

DM/4 = 6 in



Fixed base structure

• Base shear versus maximum roof drift ratio:-It can be conclude that the base isolation model withstood the MCE level ground motion with only slight yielding

Base isolated structure without impact

• The maximum interstory drift ratio exceeding 5% drift occurs at the middle level.

• All levels start to show softening behavior due to yielding at 2% drift.



Base isolated structure with impact

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-50-40-30-20-10

01020304050

Displacement (in)

Vel

ocity

(in/

s)

• The second impact to the east wall occurred at a higher velocity due to the rebound from first impact.

• The sudden drop in base velocity at the instances of impact can be observed for both the 4 and 6 in. gaps.

• This increased acceleration could consist of the effect of both rigid body motion and also local waves in the steel plate where the accelerometers were installed.

0 1 2 3 4 5 6-7-5-3-11357

Time (s)

Acc

eler

atio

n (g

)

4 in gap6 in gapNo impact



Impact Force In a structural collision, contact between two objects consists first a local phase

followed by a second global (vibration) response phase. • Local behavior: The first phase of impact is indentation of two objects

at the point of the contact. The contact force generated in this phase is generally a function of the shape and material properties of colliding objects as well as impact velocity.

• Vibration aspect of impact: The contact force in this second phase can be affected by external seismic forces, and dynamic properties of the two objects including mass and stiffness.

0 0.1 0.2 0.3 0.4-55

15253545556575

Time (s)

Con

tact

For

ce (k

ips)

15 cm thick concrete wallSteel wall w/o weldSteel wall with weld

-1 0 1 2 3-55

15253545556575

Displacement (in)

Con

tact

For

ce (k

ips)



Effects of wall stiffness and gap distance• Minimum and maximum acceleration and

interstory drift ratio are plotted in separate figures to investigate effect of each impact.

• By increasing the moat wall stiffness, both acceleration and drift increased at all stories of the model, although effect of the moat wall stiffness is more apparent on lower floor accelerations and upper floor drifts.

• The effect of impact on interstory drift is apparent after the first impact to west wall, which yields the superstructure in the negative direction, while maximum positive drifts are influenced by both west and east wall impacts.

• Exceeding the response in the negative direction as observed for the 4 and 6 in concrete walls, the stiffer moat wall yielded the superstructure after the first impact and affects the drifts after second impact.



Numerical Simulation

• A numerical model of the experimental setup was developed in OpenSees.

• Elastic beam-column elements and zero length nonlinear rotation spring elements(Modified Ibarra Krawinkler model, 2009)

• Panel zones modeled using Gupta and Krawinkler model (1999).

• P-Delta effects were simulated by a leaning column.

Figure from OpenSees wiki



Classical theory of impact• The classical theory of impact, called stereomechanics, is based preliminary on

the impulse-momentum law for rigid bodies.

• It is evident that this theory does not account for • impact duration • transient forces• local deformations at the contact point

• Assumes that a negligible fraction of the initial kinetic energy of the system is transferred into local vibrations of colliding bodies.

2 1 21 1

1 2

( )(1 ) i it i

m v vv v em m

1 1 22 2

1 2

( )(1 ) i it i

m v vv v em m

Coefficient of restitution



Local Deformation Phase Produced by Impact

• In this case, the two bodies will undergo a relative indentation in the vicinity of the impact point. The energy required to produce this local deformation may be an appreciable fraction of the initial kinetic energy.

• Most research related to structural impact has proposed force-displacement models to capture this phenomenon such as a linear spring, Kelvin, Hertz, and Hertz model with nonlinear dampers.

00

Penetration

Con

tact

For

ce Hertz Damped

Model

Hertz Model



Vibration Aspect of Impact

• The disturbance generated at the contact point propagates into the interior of the bodies with a finite velocity and its reflection from the boundaries produces oscillations or vibrations in the solids.

• Considerable amount of energy is transformed into vibrations in the collision of bodies with low natural frequencies.

Using several beam elements having plastic hinges at both ends for wall, and in-plane elements for soil backfill



Simplified Moat wall Model

• A continuous cantilever beam supported by an elastic foundation and external distributed damping was assumed.

• A rotational spring was assumed at the base of the beam to capture the post-elastic behavior due to the formation of a plastic hinge.

2 2 2

2 2 2 ( , )v v vEI x C Kv m x F x tx x t t

2

0 20 0

2 3

2 3

0;

0; 0

xx x

x L x L

v vv EI Kx x

v vx x

Boundary conditions:




• Solving homogeneous equation ( ) using separation of variable:

• Yields to two ODEs:

• Solving the 2nd equation with boundary condition leads to characteristic equation of:

• In which

( , ) 0F x t

, .v x t X x Y t

44

4 0X Xx

2

42 0A Y C Y K Y

EI t EI t EI

sinh .cos sin .cosh 1 cos .cosh 0L L L L L K L L

K LK

EI




• Substituting obtained from the frequency equation in equation of motion leads to modal frequencies and shape functions:

• Using Modal orthogonality:

i

4i i

K EIA A

1

2sin( ) sinh( ) cos( )cosh( ) sinh( )

cos( ) cosh( )

2sinh( ) sin( ) cosh( )cos( ) sin( )

cos( ) cosh( )

ii i i

i i ii i i

ii i i

i ii i

LL L LK

X x A x xL L

LL L LKx x

L L

2 4

2 2 22 40 0 0 0

. ( )L L L Ln n n

n n n n n

Y t Y t XA X dx C X dx EI X dx K X dx Y t F tt t x

Modal frequency

Shape function

generalized forced vibration equation



Simplified Moat wall Model• Simulation of impact forces in structural analysis should consider the two phases

of impact to capture both the effects of local deformation at the impact point and the vibration aspect of the colliding objects.

• Hertz damped model captures forces during the first phase of impact.

i

• The force obtained in the first phase can be implemented in Single degree of freedom (generalized forced vibration equation) to find lateral displacement of the wall and also resisting force imposed on the striker body.



Experimental Verification

Wall typeWall thickness (in) Local parameters Vibration parameters

Front wall Back wall e

Concrete 2 4 4400 0.7 0.23 0.08 0.9 180

4 2 4400 0.7 0.10 0.15 1.2 160

6 4 4400 0.7 0.02 0.28 2.0 200

Steel 5 NA 8200 0.7 - 0.40 100.0 40

3 2( )hK kips in K M kips K kips in %

• The concentrate hinge stiffness, was assumed equal to the post concrete crack stiffness.

• Winkler spring was assumed to model soil backfill.



Impact Force

0 0.05 0.1 0.15 0.2-0.5

1.5

3.5

5.5

7.5

9.5

Time (sec)

Cont

act F

orce

(kip

s)

NumericalExperimental

-0.1 0.4 0.9 1.4-1

1

3

5

7

Displacement (in)

Con

tact

For

ce (k

ips)


-0.1 0.1 0.3 0.5 0.7 0.9 1-0.5

1.5

3.5

5.5

7.5

9.5

Displacement (in)

Con

tact

For

ce (k

ips)


0 0.05 0.1 0.15 0.2-1

1

3

5

7

Time (sec)

Con

tact

For

ce (k

ips)


-0.1 0.4 0.9 1.4 1.9 2.4 2.9-149

1419242934

Displacement (in)

Con

tact

For

ce (k

ips)


0 0.1 0.2 0.3 0.4-149

1419242934

Time (sec)

Con

tact

For

ce (k

ips)


0 0.15 0.30 0.45 0.600

10203040506070

Displacement (in)

Cont

act F

orce

(kip

s)


0 0.05 0.1 0.150

10203040506070

Time (sec)

Cont

act F

orce

(kip

s)




Superstructure Response

(a) First Story

(b) Second Story

(c) Third Story



3-Dimensional Prototype Model• Detailed three-dimensional (3D) numerical model

of base isolated IMRF building was developed in OpenSees (Sayani et al. 2011).

• Elastic beam-column elements and zero length nonlinear rotation spring elements(Modified Ibarra Krawinkler model, 2009) assigned to beam elements while fiber section used to define column elements.

• An elastic column element and an elastic-perfectly plastic spring were assembled in parallel to obtain the composite bilinear lateral force-deformation behavior shown here (Sayani et al. 2011).

Sayani P. J., Erduran E., Ryan K. L. (2011). “Comparative Response Assessment of Minimally Compliant Low-Rise Base-Isolated andConventional Steel Moment-Resisting Frame Buildings”, Journal of Structural Engineering, Vol. 137, No. 10.



3-Dimensional Moat Wall Model• Moat wall are modeled using a cantilever

column with concentrated plastic hinge.

• Soil backfill was modeled using log-spiral hyperbolic (LSH ) procedure (Shamsabadi et al. 2007)

• Local Impact was simulated using Hertz Damped model.



3-Dimensional Moat Wall Model• Moat wall columns are connected to each other using shear

spring representing continues wall behavior.




spring representing continues wall behavior.• Shear springs are calibrated using Finite Element study of

concrete moat walls in Abaqus.




spring representing continues wall behavior.• Shear springs are calibrated using Finite Element study of

concrete moat walls in Abaqus.

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6

Forc

e (ki

ps)

Displacement (in)

Single WallContinues Middle WallContinues Corner Wall



Collapse Evaluation using the Methodology of FEMA P695• Far filed ground motion set (22 ground

motion) in FEMA P695 was selected for collapse evaluation of isolated model pounding moat wall.

• Ground motions were scaled using PGV normalization method.

• IDA conducted for different moat wall gap sizes and fragility curves plotted based on 5% interstory drift ratio limit. 0 1 2 3 4

0

1

2

3

4

5

6

7

8

9

Period (sec)

Acc

eler

atio

n S

a (g

)

MedianMCE Spectrum



IDA Curves • IDA conducted for different moat wall gap sizes and fragility

curves plotted based on 5% interstory drift ratio limit.

0 2 4 6 8 100

0.5

1

1.5

2

2.5

Maximum Interstory Drift Ratio (%)

Inte

nsity

Sca

le F

acto

r

0 2 4 6 8 100

0.5

1

1.5

2

2.5

Maximum Interstory Drift Ratio (%)In

tens

ity S

cale

Fac

tor

Base Isolated Model without Moat wall

Base Isolated Model with Moat Wall at 20” gap



Fragility Curve• Fragility curves were plotted

using Adjusted Collapse Margin Ratio (ACMR) and total uncertainty of 0.4.

• Although the probability of collapse at MCE intensity is more than 10% for gap distance of 20”, it’s still less than 20% which is the limit for outliers. 0 1 2 3 4

00.10.20.30.40.50.60.70.80.9

1

Intensity Scale FactorP

roba

bilit

y of

Col

laps

e

No moat wall30" gap distance20" gap distance'



Conclusions• Shake table tests impacting a base isolated structure to the

moat wall were conducted as part o the NEES TIPS project.• Unique data set was generated including structural impact at

base level and propagation to superstructure.• A new impact element was proposed to simulate the effects of

two phases of impact. The required equations to calculate its parameters were derived for a generic moat wall considering nonlinearity in the moat wall and soil backfill.

• The response of full scale 3-story base isolated moment frame was investigated for various gap distances using the Methodology proposed in FEMA P695.

• The collapse margin ratio for the investigated moment frame is relatively insensitive to gap distance.



Thank you!

collapse evaluation of seismically isolated building impacting moat wall

Documents

isolated model

isolated base structure

isolated base model

isolated building pounding

concrete wall thicknesses

effect of wall stiffness

bay frame

wider range of wall