IMPACT OF FOUNDATION MODELING ON THE ACCURACY OF RESPONSE HISTORY ANALYSIS OF A TALL BUILDING Part II - Implementation F. Naeim, S. Tileylioglu, A. Alimoradi and J. P. Stewart

Choice of Software (nonlinear capable) Commonly used for seismic analysis and design –ETABS –SAP2000 –Perfrom-3D Public-domain (not user friendly) –OpenSees General F.E. (if you are suicidal!) –Adina –Abaqus –Ansys –and more

MA Model Spring ends constrained to the ground motion history Foundation walls modeled with the actual stiffness and strength

Rigid pedestal, free at the bottom and connected to a rigid plate at the top. Vertical and horizontal displacements induced at the bottom. Vertical nonlinear springs and dashpots connecting the top of rigid plate to the bottom of mat foundation. Horizontal nonlinear springs and dashpots connected to the basement wall. Horizontal ground displacements are induced at the free end of each spring and dashpot. Note that the same configuration exists at the other end.

Vertical Soil Springs Pedestals Lateral Soil Springs

Footing for the gravity system Lateral Soil Springs

Nonlinear ETABS Model (MA) Vertical masses included > Eigenvalue analysis does not work 50 Ritz vectors are utilized. –The first 12 mode shapes used as Ritz vectors –Subbasement deformations used as Ritz vectors The gravity load was imposed as a ramp function followed by imposed horizontal and vertical ground displacements Damping: 1% critical, except for modes 1 and 4 (1.8%).

Comparison with system identification results Direction Identified Periods (sec.) MA Model Periods (sec.) Mode 1Mode 2Mode 1Mode 2 E-W N-S Torsional

Period Comparisons Model Reported vibration periods for first five Ritz vectors (sec.) MA* A B C A B C D

Recorded Mathematical Model

Recorded Mathematical Model

Recorded Mathematical Model (Baseline Corrected)

Recorded Mathematical Model (Baseline Corrected)

Recorded Mathematical Model

Recorded Mathematical Model

Recorded Mathematical Model

Recorded Mathematical Model

Recorded Mathematical Model

Recorded Mathematical Model

Recorded Mathematical Model

Recorded Mathematical Model

Recorded Mathematical Model

Recorded Mathematical Model

Recorded Mathematical Model

Recorded Mathematical Model

Recorded Mathematical Model

Recorded Mathematical Model

Recorded Mathematical Model

Recorded Mathematical Model

Recorded Mathematical Model

Approximation #3b: Rigid soil beneath base slab and basement wall springs (tension allowed) with fixed ends INPUT MOTIONS: Free-Field Accelerations applied at the base

Ritz Period Comparison Mode No.MA Model (sec) App. 3B (sec)

MA 3B NOTE: 3B model reports relative displacements. MA results are absolute displacements.

MA 3B NOTE: 3B model reports relative displacements. MA results are absolute displacements.

MA 3B

MA 3B

Approximation #3c: Rigid soil beneath base slab and no interaction of soil with basement walls INPUT MOTIONS: Same as #3d, u g (z=0)

Ritz Period Comparison Mode No.MA Model (sec) App. 3C (sec)

MA 3C

MA 3C

MA 3C

MA 3C

MA 3C

MA 3C

Approximation #3d: Embedded portion of structure neglected and fixed base assumed at ground level INPUT MOTIONS: Free-field ground surface, u g (z=0);  f =0

Ritz Period Comparison Mode No.MA Model (sec) App. 3D (sec)

MA 3D

MA 3D

MA 3D

MA 3D

Preliminary Findings Effects on modal properties are small Significant effect on drift distribution over height of structure Two models do a poor job: – 3B model: u g applied at base and fixed-end horizontal springs –3D model: Fixed base at ground level Not so bad (for this building): fixed base at base level of structure

Approximation 3a Spring ends constrained to the ground motion history Foundation walls modeled with the actual stiffness and strength Tension allowed at soil- foundation interface

Ritz Period Comparison Mode No.MA Model (sec) App. 3A (sec)

MA 3A

MA 3A

MA 3A

MA 3A

Approximation #1: Rigid Foundation Structural Elements INPUT MOTIONS same as MA

Ritz Period Comparison Mode No.MA Model (sec) App. 1 (sec)

MA 1

MA 1

MA 1

MA 1

Approximation #2a: No kinematic base rocking INPUT MOTIONS: same as MA except no vertical motion

Ritz Period Comparison Mode No.MA Model (sec) App. 2A (sec)

Approximation #2b: No kinematic loading from relative soil displacements adjacent to basement walls INPUT MOTIONS: MA with modification All horizontal spring Motions set equal to the ones at the base Foundation walls modeled with the actual stiffness and strength

Ritz Period Comparison Mode No.MA Model (sec) App. 2B (sec)

Approximation #2c No kinematic interaction effects on the base motion INPUT MOTIONS: Free-field horizontal motions. Taken as u g (z=0) at all levels. No vertical input.

Ritz Period Comparison Mode No.MA Model (sec) App. 2C (sec)

Conclusions Soil-structure interaction can affect the response of buildings with subterranean levels While procedures are available to account for these effects, they are seldom utilized in engineering practice With reasonable tuning of superstructure damping, the MA model accurately reproduces the observed response to the 1994 Northridge earthquake. There are hurdles to the implementation of SSI in building design. –Multiple support excitations –Lack of direct integration (ETABS) –Acceleration spikes (ETABS) We anticipate these hurdles to go away real soon

Conclusions (continued) Factors found to generally have a modest effect on building response above ground level: –compliance of structural foundation elements –kinematic interaction effects (on translation or rocking) –depth-variable ground motions applied to the ends of horizontal soil springs/dashpots. However, these factors did generally affect below-ground response as measured by interstory drift

Conclusions (continued) Properly accounting for foundation/soil deformations does not significantly affect vibration periods for this tall building (which is expected), It does impact significantly the distribution of inter-story drifts over the height of the structure. To our knowledge, the latter observation is new to this study.

Conclusions (continued) Two approximations commonly used in practice are shown to provide poor results: 1.fixing the structure at ground line with input consisting of free-field translation and 2.fixing the structure at the base level, applying free-field motions as input at the base level, and using horizontal foundation springs along basement walls with their end condition fixed to the free-field ground motion.

Thank you!