Collapse Evaluation of Seismically Isolated Building Impacting Moat Wall

1. Collapse Evaluation of Seismically Isolated Building Impacting Moat Wall Armin Masroor Graduate Research Assistant Gilberto Mosqueda Associate Professor Department of Civil, Structural and Environmental Engineering University at Buffalo

2. Conduct a series of “limit state” tests that examine the ultimate behavior of isolated buildings under various failure modes. Such failure modes include: NEES TIPS: Tools for Isolation and Protective SystemsFour year research and education effort aimed at increasing applications of seismic isolation in the United States (NSF Grant No. CMMI-0724208, PI Keri Ryan) • Isolated building pounding against an outer moat wall • Elastomeric bearings subjected to large strain limits (beyond stability limits)

3. 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 3D View (Isolated IMRF)

4. Test Setup • 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)

5. 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).

6. 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

7. 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. DM/4 = 6 in

8. Fixed base structure • 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 without impact • 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

9. Base isolated structure with impact • 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.

10. 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.

11. 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.

12. 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

13. 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. • Coefficient of restitution

14. 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.

15. 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

16. 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. Boundary conditions:

17. Simplified Moat wall Model • 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

18. Simplified Moat wall Model • Substituting obtained from the frequency equation in equation of motion leads to modal frequencies and shape functions: • Using Modal orthogonality: Modal frequency Shape function generalized forced vibration equation

19. 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. • 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.

20. Experimental Verification • The concentrate hinge stiffness, was assumed equal to the post concrete crack stiffness. • Winkler spring was assumed to model soil backfill.

21. Impact Force

22. Superstructure Response

23. 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 and Conventional Steel Moment-Resisting Frame Buildings”, Journal of Structural Engineering, Vol. 137, No. 10.

24. 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.

25. 3-Dimensional Moat Wall Model • Moat wall columns are connected to each other using shear spring representing continues wall behavior.

26. 3-Dimensional Moat Wall Model • Moat wall columns are connected to each other using shear spring representing continues wall behavior. • Shear springs are calibrated using Finite Element study of concrete moat walls in Abaqus.

27. 3-Dimensional Moat Wall Model • Moat wall columns are connected to each other using shear spring representing continues wall behavior. • Shear springs are calibrated using Finite Element study of concrete moat walls in Abaqus.

28. 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.

29. IDA Curves • IDA conducted for different moat wall gap sizes and fragility curves plotted based on 5% interstory drift ratio limit. Base Isolated Model without Moat wall Base Isolated Model with Moat Wall at 20” gap

30. 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.

31. 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.

32. Thank you!