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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 19:34:17 +0000Modal Identification Method for Structures Subjected to
Unmeasured Random Excitations
https://resolver.caltech.edu/CaltechAUTHORS:20130507-091005468
Authors: Conte, Joel P.; Krishnan, Swaminathan
Year: 1995
This paper describes a system identification technique useful in the practical case of structures
subjected to unmeasured, stationary (ambient) excitations typically encountered in wind,
ocean, and earthquake engineering. The method uses only the structural response records available
and assumes a parametric form for the second-order statistics of the loading process. Both
loading and structural modal parameters are extracted from the second-order statistics of the
structural response, which are estimated from the response records (e.g., accelerograms). The
proposed method was validated using extensive simulation tests, an example of which is presented
here.https://authors.library.caltech.edu/records/njj5t-63529Three-Dimensional Nonlinear Analysis of Tall Irregular Steel Buildings Subject to Strong Ground Motion
https://resolver.caltech.edu/CaltechEERL:EERL-2003-01
Authors: Krishnan, Swaminathan
Year: 2003
Strong ground motion from a nearby fault has frequency content in the same range as the natural frequencies of tall buildings. This may have serious repercussions and is the topic of this dissertation.
Buildings are designed per building code standards. But, are the code provisions adequate? Strong motion from large earthquakes has been recorded only in recent times in the near-source region. Have the current codes used this information to update tall structure design guidelines? Considerable damage has been observed in tall buildings from the Northridge, Kobe, Turkey, and Taiwan earthquakes. How will tall buildings designed per the latest code regulations perform if they were to be shaken by any of these earthquakes? This thesis attempts to answer these questions.
Tall buildings by their nature are computationally intensive to analyze. They consist of thousands of degrees of freedom and when subjected to strong ground motion from a nearby source, exhibit inelastic response. Modeling this inelastic response requires an iterative approach that is computationally expensive. Furthermore, a large class of buildings, classified as irregular, exhibits complex behavior that can be studied only when the structures are modeled in their entirety. To this end, a three-dimensional analysis program, FRAME3D, has been developed incorporating two special beam-column elements -- the plastic hinge element and the elastofiber element that can model beams and columns in buildings accurately and efficiently, a beam-column joint element that can model inelastic joint deformation, and 4-noded elastic plane-stress elements to model floor slabs acting as diaphragms forcing the lateral force resisting frames in a building to act as one unit. The program is capable of performing time-history analyses of buildings in their entirety.
Six 19-story irregular steel moment frame buildings (with buildings 2A and 3A being variants of buildings 2 and 3, respectively) have been designed per the latest code (Uniform Building Code, 1997). Two of these buildings have reentrant corners and the other two have torsional irregularity. Their strength and ductility are assessed by performing pushover analyses on them. To assess their performance under strong shaking, FRAME3D models of these buildings are subjected to near-source strong motion records from the Iran earthquake (M[subscript w] = 7.3, Tabas Station) of 1978, the Northridge earthquake (M[subscript w] = 6.7, Sylmar Station) of 1994 and the Kobe earthquake (M[subscript w] = 6.9, Takatori
Station) of 1995. None of the buildings collapsed under these strong events in the computer analyses. However, when compared against the acceptable limits for various performance levels in FEMA 356 document, the damage in terms of plastic deformation at the ends of beams and columns and at joints would render the buildings inadequate in terms of life safety in quite a few cases and would even indicate possible collapse in a couple of cases. Thus, in these terms, the code falls short of achieving its life safety objective, and the near-source factors introduced in the code in 1997 in recognition of the special features of near-source ground motion seem to be inadequate.
The ductility demand, in terms of plastic rotation at the ends of beams and columns and in joints, on these buildings during this class of earthquakes is up to 6% of a radian, which is far greater than a typical limiting plastic rotation of 3% associated with fracture and consequent failure of large wide-flanged steel sections during experiments. Thus, if strength degradation due to fractures, local buckling, etc., were to be included in the analysis, then the results would likely to be worse, as far as the ability of these buildings to withstand these earthquakes without collapse is concerned.
Due to damage localization, the peak drifts observed in the structure far exceeded the inelastic drift limit in the code of 0.02 (in some cases up to 3 times). This points to serious non-structural damage to facades, interior dry wall, etc. Furthermore, large roof permanent offsets after the events indicate significant post-earthquake repair requiring considerable disruption and building closure.
Column yielding was minimal thus validating the strong-column weak-beam criterion in the code. Redundancy factors used to assess the redundancy in the system need to take into account the case of torsionally sensitive structures where frames in both principal directions are simultaneously activated. Stress concentration was not observed at the reentrant corners in L-shaped buildings.
Finally, the data catalogued in this work could be useful for future code development and tall structure design guidelines.https://authors.library.caltech.edu/records/rz73s-dxb56FRAME3D - A Program for Three-Dimensional Nonlinear Time- History Analysis of Steel Buildings: User Guide
https://resolver.caltech.edu/CaltechEERL:EERL-2003-03
Authors: Krishnan, Swaminathan
Year: 2004
FRAME3D is a program for the three-dimensional nonlinear analysis of steel buildings. It aims to overcome the computational challenges posed by full 3D analysis of buildings subject to earthquake ground motion. The element library consists of a plastic hinge beam element, an elastofiber beam element, a panel zone element, a 4-noded diaphragm element to model floor slabs, and an elastic translational/rotational spring element to model foundations and supports. The program utilizes a Netwon-Raphson iteration strategy applied to an implicit Newmark time-integration scheme to solve the nonlinear equations of motion at each time-step. Geometric nonlinearity and shear deformation are included in the formulation. This document serves as a User Guide to the program. All the input and output variables encountered by the user are described here along with brief descriptions of the various types of elements. In addition, 2 examples illustrating the capabilities and usage of the program are presented. Finally a glossary of all the variables is alphabetically listed at the end of the document for the user's convenience.https://authors.library.caltech.edu/records/jng5h-hfd57Performance of 18-Story Steel Momentframe Buildings during a large San Andreas Earthquake - A Southern California-Wide End-to-End Simulation
https://resolver.caltech.edu/CaltechEERL:EERL-2005-01.1010
Authors: Krishnan, Swaminathan; Ji, Chen; Komatitsch, Dimitri; Tromp, Jeroen
Year: 2005
The mitigation of seismic risk in urban areas in the United States and abroad is of major concern for all governments.
Unfortunately no comprehensive studies have attempted to address this issue in a rigorous, quantitative manner. This
study tackles this problem head-on for one typical class of tall buildings in southern California. The approach adopted
here can be used as a template to study earthquake risk in other seismically sensitive regions of the world, such as
Taiwan, Japan, Indonesia, China, South American countries (Chile, Bolivia, etc.), and the west coast of the United
States (in particular, Seattle).
In 1857 a large earthquake of magnitude 7.9 [1] occurred on the San Andreas fault with rupture initiating at
Parkeld in Central California and propagating in a southeasterly direction over a distance of more than 360 km.
Such a unilateral rupture produces signicant directivity toward the San Fernando and Los Angeles basins. Indeed,
newspaper reports (Los Angeles Star [2, 3]) of sloshing observed in the Los Angeles river point to long-duration (1-2
min) and long-period (2-8 s) shaking, which could have a severe impact on present-day tall buildings, especially in
the mid-height range. To assess the risk posing tall steel moment-frame buildings from an 1857-like earthquake on the
San Andreas fault, a nite source model of the magnitude 7.9 November 3, 2002 Denali fault earthquake is mapped
on to the San Andreas fault with rupture initiating at Parkeld in Central California and propagating a distance of
about 290 km in a south-easterly direction. As the rupture proceeds down south from Parkeld and hits the big bend
on the San Andreas fault, it sheds off a signicant amount of energy into the San Fernando valley, generating large
amplitude ground motion there. A good portion of this energy spills over into the Los Angeles basin with many cities
along the coast such as Santa Monica and Seal Beach and more inland areas going east from Seal beach towards
Anaheim experiencing long-duration shaking. In addition, the tail-end of the rupture sheds energy from SH/Love
waves into the Baldwin Park-La Puente region, which is bounded by a line of mountains that creates a mini-basin,
further amplifying the ground motion. The peak velocity is of the order of 1 m.s in the Los Angeles basin, including
downtown Los Angeles, and 2 m.s in the San Fernando valley. Signicant displacements occur in the basins but not
in the mountains. The peak displacements are in the neighborhood of 1 m in the Los Angeles basin and 2 m in the San
Fernando valley. The ground motion simulation is performed using the spectral element method based seismic wave
propagation program, SPECFEM3D.
To study the effects of the ground motion simulated at 636 sites (spread across southern California, spaced at
about 3.5 km each way), computer models of an existing 18-story steel moment-frame building and a redesigned
building with the same conguration (redesigned to current standards using the 1997 Uniform Building Code) are
analyzed using the nonlinear structural analysis program, FRAME3D. For these analyses, the building Y direction is
aligned with the geographical north direction. As expected, the existing building model fares much worse than the
redesigned building model. Fracture occurs in at least 25% of the connections in this building when located in the
San Fernando valley. About 10% of connections fracture in the building when located in downtown Los Angeles and
the mid-Wilshire district (Beverly Hills), while the numbers are about 20% when it is located in Santa Monica, west
Los Angeles, Inglewood , Alhambra, Baldwin Park, La Puente, Downey, Norwalk, Brea, Fullerton, Anaheim and Seal
Beach. The peak interstory drifts in the middle-third and bottom-third of the existing building are far greater than the
top-third pointing to damage being localized to the lower oors. The localization of damage in the lower oors rather
than the upper oors could potentially be worse because of the risk of more oors pancaking on top of each other if a
single story gives way. Consistent with the extent of fracture observed, the peak drifts in the existing building exceed
0.10 when located in the San Fernando valley, Baldwin Park and neighboring cities, Santa Monica, west Los Angeles
and neighboring cities, Norwalk and neighboring cities, and Seal Beach and neighboring cities, which is well into the postulated collapse regime. When located in downtown Los Angeles and the mid-Wilshire district, the building would
barely satisfy the collapse prevention criteria set by FEMA [4] with peak drifts of about 0.05.
The performance of the newly designed 18-story steel building is signicantly better than the existing building for
the entire region. However, the new building still has signicant drifts indicative of serious damage when located in
the San Fernando valley or the Baldwin Park area. When located in coastal cities (such as Santa Monica, Seal Beach
etc.), the Wilshire-corridor (west Los Angeles, Beverly Hills, etc.), the mid-city region (Downey, Norwalk, etc.) or
the booming Orange County cities of Anaheim and Santa Ana, it has peak drifts of about 0.05, once again barely
satisfying the FEMA collapse prevention criteria [5]. In downtown Los Angeles it does not undergo much damage in
this scenario. Thus, even though this building has been designed according to the latest code, it suffers damage that
would necessitate closure for some time following the earthquake in most areas, but this should be expected since this
is a large earthquake and building codes are written to limit the loss of life and ensure "collapse prevention" for such
large earthquakes, but not necessarily limit damage. Unfortunately, widespread closures such as this could cripple the
regional economy in the event of such an earthquake.
A second scenario considered in the study involves the same Denali earthquake source mapped to the San Andreas
fault but with rupture initiating in the south and propagating to the north (with the largest amount of slip occurring to
the north in Central California) instead of the other way around. The results of such a scenario indicate that ground
shaking would be far less severe demonstrating the effects of directivity and slip distribution in dictating the level of
ground shaking and the associated damage in buildings. The peak drifts in existing and redesigned building models
are in the range of 0.02-0.04 indicating that there is no signicant danger of collapse. However, damage would still
be signicant enough to warrant building closures and compromise life safety in some instances.
The ground motion simulation and the structural damage modeling procedures are validated using data from the
January 17, 1994, Northridge earthquake while the band-limited nature of the ground motion simulation (limited to
a shortest period of 2 s by the current state of knowledge of the 3-D Earth structure) is shown to have no signicant
effect on the response of the two tall buildings considered here with the use of observed records from the 1999 Chi
Chi earthquake in Taiwan and the 2001 Tokachi-Oki earthquake in Japan.https://authors.library.caltech.edu/records/4qemw-m0q51Modeling Steel Frame Buildings in Three Dimensions. I: Panel Zone and Plastic Hinge Beam Elements
https://resolver.caltech.edu/CaltechAUTHORS:20130311-091205741
Authors: Krishnan, Swaminathan; Hall, John F.
Year: 2006
DOI: 10.1061/(ASCE)0733-9399(2006)132:4(345)
A procedure for efficient three-dimensional nonlinear time-history analysis of steel framed buildings is derived. It incorporates two types of nonlinear beam elements—the plastic hinge type and the elastofiber type—and nonlinear panel zone elements to model yielding and strain-hardening in moment-frames. Floors and roofs of buildings are modeled using 4-node elastic diaphragm elements. The procedure utilizes an iteration strategy applied to an implicit time-integration scheme to solve the nonlinear equations of motion at each time step. Geometric nonlinearity is included. An overview of the procedure and the theories for the panel zone and the plastic hinge elements are presented in this paper. The theory for the elastofiber element along with illustrative examples are presented in a companion paper. The plastic hinge beam element consists of two nodes at which biaxial flexural yielding is permitted, leading to the formation of plastic hinges. Elastic rotational springs are connected across the plastic hinge locations to model strain-hardening. Axial yielding is also permitted. The panel zone element consists of two orthogonal panels forming a cruciform section. Each panel may yield and strain-harden in shear.https://authors.library.caltech.edu/records/yh1at-tfx37Modeling Steel Frame Buildings in Three Dimensions. I: Panel Zone and Plastic Hinge Beam Elements
https://resolver.caltech.edu/CaltechAUTHORS:20130311-091205741
Authors: Krishnan, Swaminathan; Hall, John F.
Year: 2006
DOI: 10.1061/(ASCE)0733-9399(2006)132:4(345)
A procedure for efficient three-dimensional nonlinear time-history analysis of steel framed buildings is derived. It incorporates two types of nonlinear beam elements—the plastic hinge type and the elastofiber type—and nonlinear panel zone elements to model yielding and strain-hardening in moment-frames. Floors and roofs of buildings are modeled using 4-node elastic diaphragm elements. The procedure utilizes an iteration strategy applied to an implicit time-integration scheme to solve the nonlinear equations of motion at each time step. Geometric nonlinearity is included. An overview of the procedure and the theories for the panel zone and the plastic hinge elements are presented in this paper. The theory for the elastofiber element along with illustrative examples are presented in a companion paper. The plastic hinge beam element consists of two nodes at which biaxial flexural yielding is permitted, leading to the formation of plastic hinges. Elastic rotational springs are connected across the plastic hinge locations to model strain-hardening. Axial yielding is also permitted. The panel zone element consists of two orthogonal panels forming a cruciform section. Each panel may yield and strain-harden in shear.https://authors.library.caltech.edu/records/0z74g-f6c59Case Studies of Damage to Tall Steel Moment-Frame Buildings in Southern California during Large San Andreas Earthquakes
https://resolver.caltech.edu/CaltechAUTHORS:20130305-081257267
Authors: Krishnan, Swaminathan; Ji, Chen; Komatitsch, Dimitri; Tromp, Jeroen
Year: 2006
DOI: 10.1785/0120050145
On 9 January 1857, a large earthquake of magnitude 7.9 occurred on the San Andreas fault, with rupture initiating at Parkfield in central California and propagating in a southeasterly direction over a distance of more than 360 km. Such a unilateral rupture produces significant directivity toward the San Fernando and Los Angeles basins. Indeed, newspaper reports of sloshing observed in the Los Angeles river point to long-duration (1–2 min) and long-period (2–8 sec) shaking. If such an earthquake were to happen today, it could impose significant seismic demand on present-day tall buildings. Using state-of-the-art computational tools in seismology and structural engineering, validated using data from the 17 January 1994, magnitude 6.7 Northridge earthquake, we determine the damage to an existing and a new 18- story steel moment-frame building in southern California due to ground motion from two hypothetical magnitude 7.9 earthquakes on the San Andreas fault. Our study indicates that serious damage occurs in these buildings at many locations in the region in one of the two scenarios. For a north-to-south rupture scenario, the peak velocity is of the order of 1 m•sec^(−1) in the Los Angeles basin, including downtown Los Angeles, and 2 m•sec^(−1) in the San Fernando valley, while the peak displacements are of the order of 1 m and 2 m in the Los Angeles basin and San Fernando valley, respectively. For a south-to-north rupture scenario the peak velocities and displacements are reduced by a factor of roughly 2.https://authors.library.caltech.edu/records/7vf1x-b6q68Analysis of Simultaneous Operational Failure of Critical Facilities due to Earthquake, for a California Utlity
https://resolver.caltech.edu/CaltechEERL:EERL-2006-01
Authors: Porter, Keith A.; Krishnan, Swaminathan; Xu, Xin
Year: 2006
This study presents an estimate of the probability that a single earthquake could cause
simultaneous operational failure of geographically disperse data centers operated by a
California utility. Three facilities are considered: a grid control facility (denoted herein by
GCF), a data processing facility (DPF), and a backup data facility (BDF) that can perform
the functions of either GCF or DPF, should either be rendered inoperative. This study
estimates two probabilities: (1) that within the next 5 years a single earthquake could render
both the grid control and backup facilities inoperative; and (2) that within the next 5 years a
single earthquake could render both the data processing and backup facilities inoperative.
The work was performed by researchers at the California Institute of Technology in
Pasadena, CA, in collaboration with researchers at the United States Geological Survey in
Pasadena, CA and Golden, CO. Caltech designed and directed the research, examined the
seismic vulnerability of the three sites, and quantified the two probabilities desired. The
USGS performed the hazard analysis.https://authors.library.caltech.edu/records/4s9bq-ycg68Performance of Two 18-Story Steel Moment-Frame Buildings in Southern California During Two Large Simulated San Andreas Earthquakes
https://resolver.caltech.edu/CaltechAUTHORS:KRIes06
Authors: Krishnan, Swaminathan; Komatitsch, Dimitri; Tromp, Jeroen
Year: 2006
DOI: 10.1193/1.2360698
Using state-of-the-art computational tools in seismology and structural engineering, validated using data from the Mw=6.7 January 1994 Northridge earthquake, we determine the damage to two 18-story steel moment-frame buildings, one existing and one new, located in southern California due to ground motions from two hypothetical magnitude 7.9 earthquakes on the San Andreas Fault. The new building has the same configuration as the existing building but has been redesigned to current building code standards. Two cases are considered: rupture initiating at Parkfield and propagating from north to south, and rupture propagating from south to north and terminating at Parkfield. Severe damage occurs in these buildings at many locations in the region in the north-to-south rupture scenario. Peak velocities of 1 m.s−1 and 2 m.s−1 occur in the Los Angeles Basin and San Fernando Valley, respectively, while the corresponding peak displacements are about 1 m and 2 m, respectively. Peak interstory drifts in the two buildings exceed 0.10 and 0.06 in many areas of the San Fernando Valley and the Los Angeles Basin, respectively. The redesigned building performs significantly better than the existing building; however, its improved design based on the 1997 Uniform Building Code is still not adequate to prevent serious damage. The results from the south-to-north scenario are not as alarming, although damage is serious enough to cause significant business interruption and compromise life safety.https://authors.library.caltech.edu/records/mv9s9-0p816Case studies of damage to 19-storey irregular steel moment-frame buildings under near-source ground motion
https://resolver.caltech.edu/CaltechAUTHORS:20130305-075249536
Authors: Krishnan, Swaminathan
Year: 2007
DOI: 10.1002/eqe.657
This paper describes the three-dimensional nonlinear analysis of six 19-storey steel moment-frame buildings, designed per the 1997 Uniform Building Code, under strong ground motion records from near-source earthquakes with magnitudes in the range of 6.7–7.3. Three of these buildings possess a reentrant corner irregularity, while the remaining three possess a torsional plan irregularity. The records create drift demands of the order of 0.05 and plastic rotation demands of the order of 4–5% of a radian in the buildings with reentrant corners. These values point to performance at or near 'Collapse Prevention'. Twisting in the torsionally sensitive buildings causes the plastic rotations on the moment frame on one face of the building (4–5% of a radian) to be as high as twice of that on the opposite face (2–3% of a radian). The asymmetric yield pattern implies a lower redundancy in the lateral force-resisting system as the failure of the heavily loaded frame could result in a total loss of resistance to torsion.https://authors.library.caltech.edu/records/17mtr-4f432Modeling steel moment frame and braced frame buildings in three dimensions using FRAME3D
https://resolver.caltech.edu/CaltechAUTHORS:20130306-075744206
Authors: Krishnan, S.
Year: 2008
A procedure for the efficient three-dimensional nonlinear time-history analysis of steel framed buildings is
derived. It incorporates three types of nonlinear beam elements - the plastic hinge type, the elastofiber type,
and the 5-segment modified elastofiber type – and nonlinear panel zone elements to model yielding and
strain-hardening in moment frames, and buckling in braced frames. Floors and roofs of buildings are modeled
using 4-node elastic diaphragm elements. The procedure utilizes an iteration strategy applied to an implicit
time-integration scheme to solve the nonlinear equations of motion at each time-step. Geometric nonlinearity
is included. The plastic hinge beam element consists of two nodes at which biaxial flexural yielding is
permitted, leading to the formation of plastic hinges. Elastic rotational springs are connected across the plastic
hinge locations to model strain-hardening. Axial yielding is also permitted. A normalized PMM interaction
surface is calculated for one of the model sections, and used to characterize the axial force-biaxial moment
interaction for all model sections. The panel zone element consists of two orthogonal panels forming a
cruciform section. Each panel may yield and strain-harden in shear. The elastofiber beam element is divided
into three segments - two end nonlinear segments and an interior elastic segment. The cross-sections of the
end segments are subdivided into fibers. Associated with each fiber is a nonlinear hysteretic stress-strain law
for axial stress and strain. This accounts for coupling of nonlinear material behavior between bending about
the major and minor axes of the cross-section and axial deformation. While beams and columns in
moment-frames can be modeled using the elastofiber beam element, braces and columns susceptible to buckling
may be modeled using a modified elastofiber beam element with the elastic segment in the standard elastofiber
beam element subdivided into two elastic segments and a central nonlinear segment. First mode buckling in
the element is simulated through yielding of the central nonlinear segment. All these elements are integrated
into a building analysis program, FRAME3D. The various elements and the program are validated against
analytical solutions of simple problems, as well as scaled and full-scale tests of beam-column assemblies and
4-6 story structures.https://authors.library.caltech.edu/records/rp8h3-bab12SHAKEOUT 2008: Tall Steel Moment Frame Building Response
https://resolver.caltech.edu/CaltechAUTHORS:20130305-134018243
Authors: Krishnan, Swaminathan; Muto, Matthew M.
Year: 2008
In 2008, there was a significant campaign undertaken in southern California to
increase public awareness and readiness for the next large earthquake along the
San Andreas fault that culminated in a large-scale earthquake response exercise.
The USGS ShakeOut scenario was a key element to understanding the likely
effects of such an event. In support of this effort, a study was conducted to assess
the response of tall steel structures to a M7.8 scenario earthquake on the southern
San Andreas Fault. Presented here are results for two structures. The first is a
model of an 18-story steel moment frame building that experienced significant
damage (fracture of moment-frame connections) during the 1994 Northridge
earthquake. The second model is of a very similar building, but with a structural
system redesigned according to a more modern code (UBC 97). Structural
responses are generated using three-dimensional, non-linear, deteriorating finite
element models, which are subjected to ground motions generated by the scenario
earthquake at 784 points spaced at approximately 4 km throughout the San
Fernando Valley, the San Gabriel Valley and the Los Angeles Basin. The
kinematic source model includes large-scale features of the slip distribution,
determined through community participation in two workshops and short lengthscale
random variations. The rupture initiates at Bombay Beach and ruptures to
the northwest before ending at Lake Hughes, with a total length of just over 300
km and a peak slip of 12 m at depth. The resulting seismic waves are propagated
using the SCEC community velocity model for southern California, resulting in
ground velocities as large as 2 m/s and ground displacements as large as 1.5 m in
the region considered in this study. The ground motions at the sites selected for
this study are low-passed filtered with a corner period at 2 seconds. Results
indicate a high probability of collapse or damage for the pre-1994 building in
areas of southern California where many high-rise buildings are located.
Performance of the redesigned buildings is substantially improved, but responses
in urban areas are still large enough to indicate a high-probability of damage. The
simulation results are also used to correlate the probability of building collapse
with damage to the structural system.https://authors.library.caltech.edu/records/abf7r-k8h97Seismic Loss Estimation Based on End-to-end Simulation
https://resolver.caltech.edu/CaltechAUTHORS:20120831-141621989
Authors: Muto, M.; Krishnan, S.; Beck, J. L.; Mitrani-Reiser, J.
Year: 2008
Recently, there has been increasing interest in simulating all aspects of the seismic risk problem,
from the source mechanism to the propagation of seismic waves to nonlinear time-history analysis of
structural response and finally to building damage and repair costs. This study presents a framework for performing
truly "end-to-end" simulation. A recent region-wide study of tall steel-frame building response to a
M_w 7.9 scenario earthquake on the southern portion of the San Andreas Fault is extended to consider economic
losses. In that study a source mechanism model and a velocity model, in conjunction with a finite-element
model of Southern California, were used to calculate ground motions at 636 sites throughout the San Fernando
and Los Angeles basins. At each site, time history analyses of a nonlinear deteriorating structural model
of an 18-story steel moment-resisting frame building were performed, using both a pre-Northridge earthquake
design (with welds at the moment-resisting connections that are susceptible to fracture) and a modern code
(UBC 1997) design. This work uses the simulation results to estimate losses by applying the MDLA (Matlab
Damage and Loss Analysis) toolbox, developed to implement the PEER loss-estimation methodology. The
toolbox includes damage prediction and repair cost estimation for structural and non-structural components
and allows for the computation of the mean and variance of building repair costs conditional on engineering
demand parameters (i.e. inter-story drift ratios and peak floor accelerations). Here, it is modified to treat
steel-frame high-rises, including aspects such as mechanical, electrical and plumbing systems, traction elevators,
and the possibility of irreparable structural damage. Contour plots of conditional mean losses are generated
for the San Fernando and the Los Angeles basins for the pre-Northridge and modern code designed
buildings, allowing for comparison of the economic effects of the updated code for the scenario event. In
principle, by simulating multiple seismic events, consistent with the probabilistic seismic hazard for a building
site, the same basic approach could be used to quantify the uncertain losses from future earthquakes.https://authors.library.caltech.edu/records/34e0p-2fj31Preparing for the Big One
https://resolver.caltech.edu/CaltechAUTHORS:20130305-104209854
Authors: Krishnan, Swaminathan
Year: 2009
Approximately 2.75 million deaths have occurred in 3000 earthquakes in the last 105 years between 1900 and 2004 (Figure 1A). About one-half of these occurred in the seven deadliest events, i.e., a few events dominate historical death count. These events did not necessarily have large magnitudes, but occurred close to heavily populated regions. If these not-so-large earthquakes could cause such destruction, one can only imagine what would happen if an extreme event were to occur. An extreme event can be defined as one of large magnitude occurring in the proximity of a densely populated region. Extreme events are rare because large magnitude events are rare. Shown in Figure 1B is the Gutenberg-Richter relation for all earthquakes that have occurred between 1904 and 2000 (Kanamori and Brodsky 2001). In these 96 years, fewer than one magnitude 8.0 earthquake has occurred on average each year. Traditionally, civil engineers have adopted an observe, learn, and improve approach for earthquake damage mitigation. Unfortunately, with extreme events being rare, the learning process is slow and, as a result, corrective measures are ineffective. In fact, we have not seen the effects of a large magnitude earthquake occurring close to heavily populated urban regions such as Los Angeles, Seattle, Istanbul, Jakarta, Tokyo, Taipei, Kaosiung, Delhi, Mumbai, Calcutta, Beijing, etc. in recent years. The recent magnitude 6.7, January 17, 1994, Northridge earthquake, the magnitude 6.9, January 17, 1995, Kobe earthquake, the magnitude 7.4, August 17, 1999, Kocaeli earthquake, and the magnitude 7.7, September 21, 1999, ChiChi earthquake have provided us with glimpses of what we can expect from a major earthquake. But the data from magnitude 8 earthquakes in urban settings is quite limited. Although the magnitude 8.0, September 19, 1985, Michoacan earthquake killed 10000 people and caused significant damage in Mexico City, it was centered more than 360 km away from Mexico City. Both the magnitude 9.5, May 22, 1960, Chile and the magnitude 9.2, March 28, 1964, Prince William Sound, Alaska earthquakes occurred close to sparsely populated regions. The magnitude 7.8, July 28, 1976, Great Tangshan earthquake, the magnitude 8.3, September 1, 1923, Great Kanto earthquake, and the magnitude 7.7, April 18, 1906, San Francisco earthquake provide the best clue to what could be expected from a large earthquake close to an urban center. The fires following the 1923 and 1906 earthquakes destroyed the cities of Tokyo and San Francisco, respectively, although quite a bit of damage can be attributed to ground shaking as well. Ninety percent of the buildings in the city of Tangshan were flattened in the 1976 earthquake. Unfortunately, recorded data from these earthquakes is minimal. As a result, if we are to prepare for an extreme earthquake striking one of our major metropolitan centers, we cannot rely solely on the traditional approach of learning from observations.https://authors.library.caltech.edu/records/hdsaz-a0z79On the Modeling of Elastic and Inelastic, Critical- and Post-Buckling Behavior of Slender Columns and Bracing Members
https://resolver.caltech.edu/CaltechEERL:EERL-2009-03
Authors: Krishnan, Swaminathan
Year: 2009
Analyzing tall braced frame buildings with thousands of degrees of freedom in three dimensions subject to
strong earthquake ground motion requires an efficient brace element that can capture the overall features of
its elastic and inelastic response under axial cyclic loading without unduly heavy discretization. This report
details the theory of a modified elastofiber (MEF) element developed to model braces and buckling-sensitive
slender columns in such structures. The MEF element consists of three fiber segments, two at the member
ends and one at mid-span, with two elastic segments sandwiched in between. The segments are demarcated
by two exterior nodes and four interior nodes. The fiber segments are divided into 20 fibers in the crosssection
that run the length of the segment. The fibers exhibit nonlinear axial stress-strain behavior akin to
that observed in a standard tension test in the laboratory, with a linear elastic portion, a yield plateau, and a
strain hardening portion consisting of a segment of an ellipse. All the control points on the stress-strain law
are user-defined. The elastic buckling of a member is tracked by updating both exterior and interior nodal
coordinates at each iteration of a time step, and checking force equilibrium in the updated configuration.
Inelastic post-buckling response is captured by fiber yielding in the nonlinear segments. A user-defined
probability distribution for the fracture strain of a fiber in a nonlinear segment enables the modeling of
premature fracture, observed routinely in cyclic tests of braces. If the probabilistically determined fracture
strain of a fiber exceeds the rupture strain, then the fiber will rupture rather than fracturing. While a fractured
fiber can take compression, it is assumed that a ruptured fiber cannot. Handling geometric and material nonlinearity
in such a manner allows the accurate simulation of member-end yielding, mid-span elastic buckling
and inelastic post-buckling behavior, with fracture or rupture of fibers leading to complete severing of the
brace. The element is integrated into the nonlinear analysis framework for the 3-D analysis of steel buildings,
FRAME3D. A series of simple example problems with analytical solutions, in conjunction with data
from a variety of cyclic load tests, is used to calibrate and validate the element. Using a fiber segment length
of 2% of the element length ensures that the elastic critical buckling load predicted by the MEF element is
within 5% of the Euler buckling load for box and I-sections with a wide range of slenderness ratios (L/r =
40, 80, 120, 160, and 200) and support conditions (pinned-pinned, pinned-fixed, and fixed-fixed). Elastic
post-buckling of the Koiter-Roorda L-frame (tubes and I-sections) with various member slenderness ratios
(L/r = 40, 80, 120, 160, and 200) is simulated and shown to compare well against second-order analytical
approximations to the solution. The inelastic behavior of struts under cyclic loading observed in the Black
et al. and the Fell et al. experiments is numerically simulated using MEF elements. Certain parameters of
the model (e.g., fracture strain, initial imperfection, support conditions, etc.) that are not controllable and/or
unmeasured during the tests are tuned to realize the best possible fit between the numerical results and the
experimental data. A similar comparison is made between numerical results using the MEF element and the
experimental data by Tremblay et al. collected from cyclic testing of single-bay braced frames. Finally, a
FRAME3D model of a full-scale 6-story braced frame structure that was pseudodynamically tested by the
Building Research Institute of Japan subjected to the 1978 Miyagi-Ken-Oki earthquake record, is analyzed
iv
and shown to closely mimic the experimentally observed behavior. To summarize, the MEF element is able
to incorporate all the characteristic features of slender columns and braces that significantly affect their elastic
and inelastic, critical and post-buckling behavior, and is remarkably effective in capturing the essence of
said behavior, even with the vast uncertainty associated with the buckling phenomenon.
To aid in the evaluation of the collapse-prediction capability of competing methodologies, a benchmark
problem of a water-tank subjected to the Takatori near-source record from the 1995 Kobe earthquake, scaled
down by a factor of 0.32, is proposed. The water-tank is so configured as to have a unique collapse mechanism
(under all forms of ground motion), of overturning due to P - instability resulting from column and
brace buckling at the base. A FRAME3D model of the tank reveals severe buckling in the bottom megacolumns
on the west face of the tower, followed almost instantaneously by compression brace buckling on
the north and south faces, when the structure is hit by the Takatori near-source pulse, resulting a tilt in the
structure. Subsequent shaking induces P - instability resulting in complete collapse of the tank.https://authors.library.caltech.edu/records/4yssk-sd448FRAME3D V2.0 - A Program for the Three-Dimensional
Nonlinear Time-History Analysis of
Steel Structures: User Guide
https://resolver.caltech.edu/CaltechEERL:EERL-2009-04
Authors: Krishnan, Swaminathan
Year: 2009
This is Version 2.0 of the user guide and should be used along with Version 2.0 of the program. Updates
include: 1. Realistic PMM interaction surfaces for plastic hinge elements (output file PMM). 2. 5-Segment
modified elastofiber element for brace and slender column modeling. 3. Eigen value problem solver using
subspace iteration (output files MODES and EIGEN). 4. Output the sum of forces of groups of elements
(output file ELMGRPRES). Additional input is required as a result of these additions to the program. However,
the example input files shown in chapter 6 correspond to the input format from Version 1.0 and do not
reflect the changes in the input file from Version 1.0 to Version 2.0.
Updates in Version 1.1 include: 1. Output files FRAC, FRACSUM, and FRACTOT, summarizing the
fractures in the elastofiber beam elements; 2. Output file RUP listing the fibers that have ruptured during
the course of the analysis; 3. Output file FAIL listing the elastofiber elements that have a complete segment
failure; 4. Output files FEMA356 and PERF summarizing the performance of the beams, columns, and
panel zones, relative to the Federal Emergency Management Agency document FEMA356 (FEMA 2000)
acceptance criteria; 5. Output files XDRFT, YDRFT, AVGPKDRFT, and PKDRFT listing the average and
peak interstory drifts in the building. Additional input is required for this output processing. In addition,
some typographical errors in the version 1.0 of the user guide were also corrected, the most notable of these
being sections 4.1.8 and 4.1.9 dealing with elastofiber element fiber fracture.
FRAME3D is a program for the three-dimensional nonlinear analysis of steel buildings. It aims to
overcome the computational challenges posed by full 3D analysis of steel buildings subject to earthquake
ground motion through efficient finite elements that are designed to capture the essence of material behavior
and geometry evolution. The element library consists of a plastic hinge beam element, an elastofiber beam
element, a 5-segment modified elastofiber element, a panel zone element, a 4-noded diaphragm element to
model floor slabs, and an elastic translational/rotational spring element to model foundations and compliant
supports. The program utilizes a Newton-Raphson iteration strategy applied to an implicit Newmark timeintegration
scheme to solve the nonlinear equations of motion at each time-step. Geometric nonlinearity and
shear deformation are included in the formulation. This document serves as a User Guide to the program.
All the input and output variables encountered by the user are described here along with brief descriptions of
the various types of elements. In addition, 2 examples illustrating the capabilities and usage of the program
are presented. Finally a glossary of all the variables is alphabetically listed at the end of the document.https://authors.library.caltech.edu/records/3gvm3-7w866Modified Elastofiber Element for Steel Slender Column and Brace Modeling
https://resolver.caltech.edu/CaltechAUTHORS:20101108-142429209
Authors: Krishnan, Swaminathan
Year: 2010
DOI: 10.1061/(ASCE)ST.1943-541X.0000238
An efficient beam element, the modified elastofiber (MEF) element, has been developed to capture the overall features of the elastic and inelastic responses of slender columns and braces under axial cyclic loading without unduly heavy discretization. It consists of three fiber segments, two at the member ends and one at midspan, with two elastic segments sandwiched in between. The segments are demarcated by two exterior nodes and four interior nodes. The fiber segments are divided into 20 fibers in the cross section that run the length of the segment. The fibers exhibit nonlinear axial stress-strain behavior akin to that observed in a standard tension test of a rod in the laboratory, with a linear elastic portion, a yield plateau, and a strain-hardening portion consisting of a segment of an ellipse. All the control points on the stress-strain law are user defined. The elastic buckling of a member is tracked by updating both exterior and interior nodal coordinates at each iteration of a time step and checking force equilibrium in the updated configuration. Inelastic postbuckling response is captured by fiber yielding, fracturing, and/or rupturing in the nonlinear segments. The key features of the element include the ability to model each member using a single element, easy incorporation of geometric imperfection, partial fixity support conditions, member susceptibility to fracture defined in a probabilistic manner, and fiber rupture leading to complete severing of the member. The element is calibrated to accurately predict the Euler critical buckling load of box and I sections with a wide range of slenderness ratios (L/r=40, 80, 120, 160, and 200) and support conditions (pinned-pinned, pinned-fixed, and fixed-fixed). Elastic postbuckling of the Koiter-Roorda L frame (tubes and I sections) with various member slenderness ratios (L/r=40, 80, 120, 160, and 200) is simulated and shown to compare well against second-order analytical approximations to the solution even when using a single-MEF element to model each leg of the frame. The inelastic behavior of struts under cyclic loading observed in the experiments of Black et al., Fell et al., and Tremblay et al. is accurately captured by single-MEF-element models. A FRAME3D model (using MEF elements for braces) of a full-scale six-story braced frame structure that was pseudodynamically tested at the Building Research Institute of Japan subjected to the 1978 Miyagi-Ken-Oki earthquake record is analyzed and shown to closely mimic the experimentally observed behavior.https://authors.library.caltech.edu/records/s7410-6pt81Modified Elastofiber Element for Steel Slender Column and Brace Modeling
https://resolver.caltech.edu/CaltechAUTHORS:20101108-142429209
Authors: Krishnan, Swaminathan
Year: 2010
DOI: 10.1061/(ASCE)ST.1943-541X.0000238
An efficient beam element, the modified elastofiber (MEF) element, has been developed to capture the overall features of the elastic and inelastic responses of slender columns and braces under axial cyclic loading without unduly heavy discretization. It consists of three fiber segments, two at the member ends and one at midspan, with two elastic segments sandwiched in between. The segments are demarcated by two exterior nodes and four interior nodes. The fiber segments are divided into 20 fibers in the cross section that run the length of the segment. The fibers exhibit nonlinear axial stress-strain behavior akin to that observed in a standard tension test of a rod in the laboratory, with a linear elastic portion, a yield plateau, and a strain-hardening portion consisting of a segment of an ellipse. All the control points on the stress-strain law are user defined. The elastic buckling of a member is tracked by updating both exterior and interior nodal coordinates at each iteration of a time step and checking force equilibrium in the updated configuration. Inelastic postbuckling response is captured by fiber yielding, fracturing, and/or rupturing in the nonlinear segments. The key features of the element include the ability to model each member using a single element, easy incorporation of geometric imperfection, partial fixity support conditions, member susceptibility to fracture defined in a probabilistic manner, and fiber rupture leading to complete severing of the member. The element is calibrated to accurately predict the Euler critical buckling load of box and I sections with a wide range of slenderness ratios (L/r=40, 80, 120, 160, and 200) and support conditions (pinned-pinned, pinned-fixed, and fixed-fixed). Elastic postbuckling of the Koiter-Roorda L frame (tubes and I sections) with various member slenderness ratios (L/r=40, 80, 120, 160, and 200) is simulated and shown to compare well against second-order analytical approximations to the solution even when using a single-MEF element to model each leg of the frame. The inelastic behavior of struts under cyclic loading observed in the experiments of Black et al., Fell et al., and Tremblay et al. is accurately captured by single-MEF-element models. A FRAME3D model (using MEF elements for braces) of a full-scale six-story braced frame structure that was pseudodynamically tested at the Building Research Institute of Japan subjected to the 1978 Miyagi-Ken-Oki earthquake record is analyzed and shown to closely mimic the experimentally observed behavior.https://authors.library.caltech.edu/records/2yfwv-bqm08Case study of the collapse of a water tank
https://resolver.caltech.edu/CaltechEERL:EERL-2010-01
Authors: Krishnan, Swaminathan
Year: 2010
A 48.76m high water tank with the supporting steel lattice comprising 5 segments with uniform member configuration is conceived. Its collapse behavior is investigated through a suite of ground motion analyses. First, the tank is analyzed under 13 three-component ground motion records from the Chi-Chi and Hokkaido earthquakes. It is shown that the tank always collapses in the same manner as a result of overturning due to P-Delta instability resulting from column and brace buckling at the base. This is the consequence of the uniform member sizing in each of the five segments of the supporting lattice. Incremental dynamic
analyses are performed using the Takatori near-source record from the 1995 Kobe earthquake. It is shown
that the structure collapses at a ground motion scaling factor of 0.32. The FRAME3D model of the tank
reveals severe buckling in the bottom mega-columns on the west face of the tower, followed almost instantaneously
by compression brace buckling on the north and south faces, when the structure is hit by the Takatori near-source pulse, resulting a tilt in the structure. Subsequent shaking induces P-Delta instability resulting in complete collapse of the tank. To aid in the evaluation of the collapse-prediction capability of competing methodologies, detailed results (time-history plots as well as ordinates of crests and troughs in these histories) are provided for the analysis at 0.32 scaling.https://authors.library.caltech.edu/records/rt8zd-92j05Mechanism of Collapse, Sensitivity to Ground Motion Features, and Rapid Estimation of the Response of Tall Steel Moment Frame Buildings to Earthquake Excitation
https://resolver.caltech.edu/CaltechEERL:EERL-2011-02
Authors: Krishnan, Swaminathan; Muto, Matthew
Year: 2011
This study explores the behavior of two tall steel moment frame buildings and their variants under strong
earthquake ground shaking through parametric analysis using idealized ground motion waveforms. Both
fracture-susceptible as well as perfect-connection conditions are investigated. Ground motion velocity waveforms are parameterized using triangular (sawtooth-like) wave-trains with a characteristic period (T), amplitude(peak ground velocity, PGV ), and duration (number of cycles, N). This idealized representation
has the desirable feature that the response of the target buildings under the idealized waveforms closely
mimics their response under the emulated true ground motion waveforms. A suite of nonlinear analyses are
performed on four tall building models subjected to these idealized wave-trains, with T varying from 0.5s
to 6.0s, PGV varying from 0.125 m/s to 2.5 m/s, and N taking the values of 1 to 5, and 10. This range
of parameters should be adequate to characterize the ground motions that can be expected to occur during
earthquakes in the 6-8 magnitude range at some distance (say, > 2km) away from the fault. Databases of
peak transient and residual interstory drift ratio (IDR), and permanent roof drift are created for each model.
The sensitivity of structural response to T, PGV , and N is studied. Severe dynamic response is induced
only in the long-period, large-amplitude excitation regime. Through a simple examination of the energy
balance during earthquake shaking, it can be shown that the input excitation energy is small for excitation
with periods shorter than the structural period, whereas it is proportional to the square of the ground velocity
if the excitation periods are much longer than the structural periods. Thus, collapse-level response
can be induced only by long-period, moderate to large PGV ground excitation. The collapse initiation
regime expands to lower ground motion periods and amplitudes with increasing number of ground motion
cycles. It should be noted that the energy balance analysis is not appropriate for excitation velocities that are
extreme where conservation of momentum may be more applicable. However, peak ground velocity from
earthquakes seldom exceeds 2.5m/s and energy balance would generally be applicable.
The close examination of one instance of collapse shows damage (yielding and/or fracture) localizing
in a few stories in the form of a "quasi-shear" band (QSB) comprising of plastic hinges at the top of all
columns in the uppermost story of the band, at the bottom of all columns in the lowermost story of the
band, and at both ends of all beams in the intermediate stories. Such a pattern of hinging results in shear-like
deformation in these stories, resembling plastic shear bands in ductile solids. Most of the lateral deformation
due to seismic shaking is concentrated in this band. When the overturning 1st-order and 2nd-order (P -
) moments from the inertia of the overriding block of stories exceed the moment-carrying capacity of
the quasi-shear band, it loses stability and collapses. This initiates gravity-driven progressive collapse of
the overriding block of stories. Thus, the collapse mechanism initiates as a sidesway mechanism that is
taken over by gravity once the quasi-shear band is destabilized. There are Ns(Ns+1)
2 possible quasi-shear
bands (and an equal number of sidesway collapse mechanisms) in either principal direction of an Ns-story
moment frame building. More than one quasi-shear bands could occur during the entire duration of strong
earthquake shaking. The band exhibiting the greatest distress (termed the "primary" quasi-shear band)
iv ultimately evolves into a sidesway collapse mechanism.
The formation of the quasi-shear band under single-cycle excitations is explained through the classical
uniform shear-beam analogy to moment frame buildings. Under low-intensity motions (PGV < 0.25m/s)with periods in the 0.5s-6s range excitation energy is low. As a result, structural response is predominantly elastic and is analogous to that of a uniform elastic shear-beam through which a shear wave propagates. For moderate-intensity excitations (0.25m/s PGV < 1.5m/s), the reverse phase of the incident pulse constructively interferes with the reflected forward phase causing yielding in the region of positive interference,very similar to what would occur in a uniform inelastic shear-beam. The primary quasi-shear band migrates down the building with increasing pulse period. However, this migration slows down with increasing period
and gets arrested nominally between floors 3 and 9 for the existing building, and between floors 3 and 8
for the redesigned building, whereas the peak strain in the corresponding inelastic uniform shear-beam continues
to migrate to the very bottom. This is a direct result of the non-uniformity of the buildings. Going from the top of the building to the bottom, there is a gradual increase in the strength and stiffness of the structure. The increased strength at the bottom does not allow yielding to permeate into those stories. Now,excitation energy imparted to the structure can be large enough only under long-period ground motion in the context of the target buildings. Therefore, collapse-level response must be accompanied by the formation of the primary quasi-shear band in the vicinity of the stories where the downward migration of the QSB (with
increasing T) is arrested.
For high-intensity excitations (PGV > 1.5m/s) that are sufficiently long-period, the pulse may yield
the structure on its way up the building. The strength of the building drops as the pulse travels up the
building. However, inertial forces drop as well, as a result of fewer stories above contributing to the mass.
The narrow band of stories with an optimal combination of low-enough strength and high-enough inertial
force demand is where peak yielding occurs. This region is identical to the region where the downward
migration of the primary quasi-shear band is arrested under moderate-intensity, long-period excitation. This
is because the governing factor dictating the location of the band in both cases is strength non-uniformity. As
the wave travels up the building, it is reflected off the roof with a change in sign. Because the period of the
incident wave is sufficiently long (a necessary condition for large input excitation energy), the reverse phase
of the incident pulse constructively interferes with the reflected forward phase causing greatest yielding
in the same region as the pre-reflection yielding. To summarize, under both moderate-intensity and highintensity
ground motions, input excitation energy large enough to collapse the building requires long-period
excitation. Such long-period excitation always causes the formation of the primary quasi-shear band in an
optimal set of stories governed by the mass and strength distribution of the building over its height, which are
characteristics solely of the structure and not the ground motion. When T and PGV are large enough, it is
this band that evolves into a collapse mechanism. This points to the existence of a "characteristic" collapse
mechanism or only a few preferred collapse mechanisms (out of the Ns(Ns+1)2 possible mechanisms) in
either principal direction of the building. If multiple preferred collapse mechanisms exist, they would be
clustered together with significant story-overlap amongst them.
The simulations of the four models under idealized ground motion waveforms where collapse occurs do
not show the formation of a single (unique) collapse mechanism. However, in each model only one to five
v collapse mechanisms occur out of a possible 153 mechanisms in each principal direction of the building.
Furthermore, if two or more preferred mechanisms do exist, they have significant story-overlap, typically
separated by just one story. For example, the strongly preferred collapse mechanisms in the existing building
model (perfect connections) under X direction excitation occur between floors 3 and 9, and floors 4 and 9,
while the weakly preferred mechanisms occur between floors 3 and 8, and floors 4 and 8 (four preferred
mechanisms out of 153 possible mechanisms, all clustered together within a narrow story zone; two of these
mechanisms are in fact a subset of the other two mechanisms).
The characteristic and/or preferred collapse mechanisms can be identified by applying the Principle
of Virtual Work to all possible quasi-shear bands in a building. Based on plastic analysis principles, the
band that is destabilized by the smallest acceleration of the over-riding block of stories is the characteristic
collapse mechanism. If one or more bands exist that have destabilizing accelerations close to that of the
characteristic collapse band, say within 5%, then these bands may evolve into collapse mechanisms as well.
This method identifies all the preferred collapse mechanisms in all four building models satisfactorily.
One application of the structural response database built for the sensitivity study is the rapid estimation
of structural response immediately following an earthquake if the ground motion records become available.
The best fit of the idealized wave-trains in the database to the ground motion record can be determined using
the least absolute deviation method. The corresponding key structural response metrics can be extracted
from the database using a simple table look-up approach. Such a method, when applied to a suite of nearsource
records, predicts peak transient IDR remarkably well. Gaussian mean estimation error on the peak
transient IDR is 0.0006, with a standard deviation of 0.0069. A minor modification to this approach is
needed when applying it to multi-cycle far-field records. This modified approach is used to estimate the
peak transient IDR response of the buildings under synthetic waveforms from a large hypothetical San
Andreas fault earthquake. The Gaussian mean error for this estimation is 0.0011, with a standard deviation
of 0.0209, slightly worse than for the near-source records, nevertheless within one "performance level"
- good enough for emergency response decision-making. The same approach can be used for ball-park
estimation of structural response under any given earthquake record, in lieu of comprehensive nonlinear
analysis.https://authors.library.caltech.edu/records/8spmb-x5x69Hope for the Best, Prepare for the Worst: Response of Tall Steel Buildings to the ShakeOut Scenario Earthquake
https://resolver.caltech.edu/CaltechAUTHORS:20110922-134535249
Authors: Muto, Matthew M.; Krishnan, Swaminathan
Year: 2011
DOI: 10.1193/1.3563621
This work represents an effort to develop one plausible realization of the effects of the scenario event on tall steel moment-frame buildings. We have used the simulated ground motions with three-dimensional nonlinear finite element models of three buildings in the 20-story class to simulate structural responses at 784 analysis sites spaced at approximately 4 km throughout the San Fernando Valley, the San Gabriel Valley, and the Los Angeles Basin. Based on the simulation results and available information on the number and distribution of steel buildings, the recommended damage scenario for the ShakeOut drill was 5% of the estimated 150 steel moment-frame structures in the 10–30 story range collapsing, 10% red-tagged, 15% with damage serious enough to cause loss of life, and 20% with visible damage requiring building closure.https://authors.library.caltech.edu/records/6yjbp-rgd42Rupture-to-Rafters Simulations: Unifying Science and Engineering for Earthquake Hazard Mitigation
https://resolver.caltech.edu/CaltechAUTHORS:20110712-113612355
Authors: Krishnan, Swaminathan; Muto, Matthew M.; Mourhatch, Ramses; Bjornsson, Arnan Bjorn; Siriki, Hemanth
Year: 2011
DOI: 10.1109/MCSE.2011.23
High-performance computing has brought about a renaissance in computational seismology and earthquake engineering. Researchers in both fields are using advanced numeric tools and high-fidelity numerical models synergistically to create rupture-to-rafters simulations. This end-to-end approach promises to significantly advance earthquake
damage prediction, preparation, mitigation, and disaster response.https://authors.library.caltech.edu/records/33pkz-gw934Mechanism of Collapse of Tall Steel Moment Frame
Buildings Under Earthquake Excitation
https://resolver.caltech.edu/CaltechAUTHORS:20130305-151321662
Authors: Krishnan, S.; Muto, M.
Year: 2012
We expound on the nature of collapse of one class of tall buildings (steel moment frame buildings) under
earthquake excitation. Using a parametric analysis of a couple of index buildings subjected to idealized ground
motion histories, we establish the ground motion features that cause collapse in these structures. Systematically
mapping damage localization patterns, we track the evolution of the collapse mechanism. We demonstrate the
existence of a select few preferred mechanisms of collapse in these buildings and describe the associated physics
using wave propagation through a shear beam. A simple theory based on work-energy principles can identify
these mechanisms.https://authors.library.caltech.edu/records/qch0g-bfj75High Frequency Ground Motion High-Simulation Using a Source- and Site-Specific Empirical
Green's Function Approach
https://resolver.caltech.edu/CaltechAUTHORS:20130306-081454955
Authors: Mourhatch, R.; Krishnan, S.
Year: 2012
A key limitation of seismic wave propagation simulations is that the seismic wave-speed structure of the earth is
not well resolved for propagating high-frequency waves. The high frequencies in the ground motion must be
simulated through other means. Toward this end, we adopt the classical empirical Green's function (EGF)
approach of summing recorded seismograms from past small earthquakes with suitable time-shifts to generate
seismograms for large events. Whereas, in the past, the magnitude of events used as EGFs were limited to within
1 or 2 units of the target event's magnitude, this source- and site-specific approach allows us to use vast number
of seismograms from very small earthquakes (magnitudes 2.5-3.5) as EGFs to produce the high-frequency
content of large earthquakes. We are expanding the envelope of the empirical Green's functions approach by
using large number of seismograms from small earthquakes as EGFs to produce high frequency content of large
earthquakes.https://authors.library.caltech.edu/records/rvxp4-02541A Retrofitting Framework for Pre-Northridge Steel
Moment-Frame Buildings
https://resolver.caltech.edu/CaltechAUTHORS:20130305-150650156
Authors: Bjornsson, A. B.; Krishnan, S.
Year: 2012
In this paper, we design and evaluate one retrofit scheme for a pre-Northridge 18-story steel moment-frame
building using nonlinear time-history analyses under 3-component synthetic ground motion waveforms at 784
sites in the greater Los Angeles region from the magnitude 7.8 ShakeOut scenario San Andreas earthquake. We
realize a reduction of ~23% in the collapse potential of the building. This case study is part of a broader study to
construct a rigorous retrofitting framework for this class of existing buildings.https://authors.library.caltech.edu/records/acxcq-94m90A Recursive Division Stochastic Strike-Slip Seismic
Source Algorithm Using Insights from Laboratory
Earthquakes
https://resolver.caltech.edu/CaltechAUTHORS:20130305-152759959
Authors: Siriki, H.; Rosakis, A. J.; Krishnan, S.; Bhat, H. S.; Lu, X.
Year: 2012
There are a sparse number of credible source models available from past earthquakes and a stochastic source
model generation algorithm thus becomes necessary for robust risk quantification using scenario earthquakes.
We present an algorithm that combines the physics of fault rupture as imaged in laboratory earthquakes with
stress estimates on the fault constrained by field observations to generate probability distributions of rise-time
and rupture-speed for strike-slip earthquakes. The algorithm is validated through a statistical comparison of peak
ground velocity at 636 sites in Southern California from synthetic ground motion histories simulated for 10
rupture scenarios using a stochastically generated source model against that generated using a kinematic source
model from a finite source inversion. This model, selected from a set of 5 stochastically generated source
models, produces ground shaking intensities in Southern California with a median that is closest to the median
intensity of shaking from all 5 source models (and 10 rupture scenarios per model).https://authors.library.caltech.edu/records/m8447-nyn623-D Dynamic Analysis of Precariously Balanced Rocks Under Earthquake Excitation
https://resolver.caltech.edu/CaltechAUTHORS:20130306-085227002
Authors: Veeraraghavan, S.; Krishnan, S.
Year: 2012
Hundreds of Precariously Balanced Rocks (PBRs) exist in California. Since these rocks have been precariously placed for thousands of years, they can help in constraining the range of PGV (peak ground velocity) and frequency content of the ground motions that could not have occurred at this location during the time that the rock has been precariously positioned. We are developing 3-D models (with accurate rock-pedestal contact interface) of some of the PBRs that have been imaged using Terrestrial Laser Scanning (TLS) techniques. We use Rigid body dynamics to solve for the dynamic response of the rock models subjected to idealized and earthquake ground motions intensities to arrive at probabilistic constraints on region-wide ground shaking intensity by combining the results of this study with cosmogenic dating of these rocks. Such analyses could help quantify seismic hazards and validate ground motion simulations.https://authors.library.caltech.edu/records/b14vs-jdr21Simulation of an 1857-like Mw 7.9 San Andreas Fault Earthquake and the Response of Tall Steel Moment Frame Buildings in Southern California – A Prototype Study
https://resolver.caltech.edu/CaltechAUTHORS:20120831-140957276
Authors: Krishnan, S.; Ji, C.; Komatitsch, D.; Tromp, J.; Muto, M.; Mitrani-Reiser, J.; Beck, J. L.
Year: 2012
In 1857, an earthquake of magnitude 7.9 occurred on the San Andreas fault, starting at Parkfield and rupturing
in a southeasterly direction for more than 360 km. Such a unilateral rupture produces significant directivity
toward the San Fernando and Los Angeles basins. The strong shaking in the basins due to this earthquake
would have had significant long-period content (2-8 s), and the objective of this study is to quantify the impact
of such an earthquake on two 18-story steel moment frame building models, hypothetically located at 636 sites
on a 3.5 km grid in southern California. End-to-end simulations include modeling the source and rupture of a
fault at one end, numerically propagating the seismic waves through the earth structure, simulating the damage
to engineered structures and estimating the economic impact at the other end using high-performance computing.
In this prototype study, we use an inferred finite source model of the magnitude 7.9, 2002 Denali fault
earthquake in Alaska, and map it onto the San Andreas fault with the rupture originating at Parkfield and
propagating southward over a distance of 290 km. Using the spectral element seismic wave propagation code,
SPECFEM3D, we simulate an 1857-like earthquake on the San Andreas fault and compute ground motions at
the 636 analysis sites. Using the nonlinear structural analysis program, FRAME3D, we subsequently analyze
3-D structural models of an existing tall steel building designed using the 1982 Uniform Building Code (UBC),
as well as one designed according to the 1997 UBC, subjected to the computed ground motion at each of these
sites. We summarize the performance of these structural models on contour maps of peak interstory drift.
We then perform an economic loss analysis for the two buildings at each site, using the Matlab Damage and
Loss Analysis (MDLA) toolbox developed to implement the PEER loss-estimation methodology. The toolbox
includes damage prediction and repair cost estimation for structural and non-structural components and allows
for the computation of the mean and variance of building repair costs conditional on engineering demand
parameters (i.e. inter-story drift ratios and peak floor accelerations). Here, we modify it to treat steel-frame
high-rises, including aspects such as mechanical, electrical and plumbing systems, traction elevators, and the
possibility of irreparable structural damage. We then generate contour plots of conditional mean losses for the
San Fernando and the Los Angeles basins for the pre-Northridge and modern code-designed buildings, allowing
for comparison of the economic effects of the updated code for the scenario event. In principle, by simulating
multiple seismic events, consistent with the probabilistic seismic hazard for a building site, the same basic
approach could be used to quantify the uncertain losses from future earthquakes.https://authors.library.caltech.edu/records/xbws2-2af15Mechanism of Collapse of Tall Steel Moment-Frame Buildings under Earthquake Excitation
https://resolver.caltech.edu/CaltechAUTHORS:20130125-100014925
Authors: Krishnan, Swaminathan; Muto, Matthew M.
Year: 2012
DOI: 10.1061/(ASCE)ST.1943-541X.0000573
The mechanism of collapse of tall steel moment-frame buildings is explored through three-dimensional nonlinear analyses of two 18-story steel moment-frame buildings under earthquake excitation. Both fracture-susceptible and perfect-connection conditions are investigated. Classical energy-balance analysis shows that only long-period excitation imparts energy to tall buildings large enough to cause collapse. Under such long-period motion, the shear-beam analogy alludes to the existence of a characteristic mechanism of collapse or a few preferred
mechanisms of collapse for these buildings. Numerical evidence from parametric analyses of the buildings under a suite of idealized sawtooth-like ground-motion time histories, with varying period (T), amplitude (peak ground velocity, PGV), and duration (number of cycles, N), is
presented to support this hypothesis. Damage localizes to form a quasi-shear band over a few stories. When the band is destabilized, sidesway collapse is initiated, and gravity takes over. Only one to five collapse mechanisms occur out of a possible 153 mechanisms in either principal
direction of the buildings considered. Where two or more preferred mechanisms do exist, they have significant story-overlap, typically separated by just 1 story. It is shown that a simple work-energy relation applied to all possible quasi-shear bands combined with plastic analysis principles
can systematically identify all the preferred collapse mechanisms.https://authors.library.caltech.edu/records/01j76-a2y52Mechanism of Collapse of Tall Steel Moment-Frame Buildings under Earthquake Excitation
https://resolver.caltech.edu/CaltechAUTHORS:20130125-100014925
Authors: Krishnan, Swaminathan; Muto, Matthew M.
Year: 2012
DOI: 10.1061/(ASCE)ST.1943-541X.0000573
The mechanism of collapse of tall steel moment-frame buildings is explored through three-dimensional nonlinear analyses of two 18-story steel moment-frame buildings under earthquake excitation. Both fracture-susceptible and perfect-connection conditions are investigated. Classical energy-balance analysis shows that only long-period excitation imparts energy to tall buildings large enough to cause collapse. Under such long-period motion, the shear-beam analogy alludes to the existence of a characteristic mechanism of collapse or a few preferred
mechanisms of collapse for these buildings. Numerical evidence from parametric analyses of the buildings under a suite of idealized sawtooth-like ground-motion time histories, with varying period (T), amplitude (peak ground velocity, PGV), and duration (number of cycles, N), is
presented to support this hypothesis. Damage localizes to form a quasi-shear band over a few stories. When the band is destabilized, sidesway collapse is initiated, and gravity takes over. Only one to five collapse mechanisms occur out of a possible 153 mechanisms in either principal
direction of the buildings considered. Where two or more preferred mechanisms do exist, they have significant story-overlap, typically separated by just 1 story. It is shown that a simple work-energy relation applied to all possible quasi-shear bands combined with plastic analysis principles
can systematically identify all the preferred collapse mechanisms.https://authors.library.caltech.edu/records/wwp3a-v7224Rapid Estimation of Damage to Tall Buildings Using Near Real‐Time Earthquake and Archived Structural Simulations
https://resolver.caltech.edu/CaltechAUTHORS:20130103-134600173
Authors: Krishnan, Swaminathan; Casarotti, Emanuele; Goltz, Jim; Ji, Chen; Komatitsch, Dimitri; Mourhatch, Ramses; Muto, Matthew M.; Shaw, John H.; Tape, Carl; Tromp, Jeroen
Year: 2012
DOI: 10.1785/0120110339
This article outlines a new approach to rapidly estimate the damage to tall buildings immediately following a large earthquake. The preevent groundwork involves the creation of a database of structural responses to a suite of idealized ground‐motion waveforms. The postevent action involves (1) rapid generation of an earthquake source model, (2) near real‐time simulation of the earthquake using a regional spectral‐element model of the earth and computing synthetic seismograms at tall building sites, and (3) estimation of tall building response (and damage) by determining the best‐fitting idealized waveforms to the synthetically generated ground motion at the site and directly extracting structural response metrics from the database. Here, ground‐velocity waveforms are parameterized using sawtoothlike wave trains with a characteristic period (T), amplitude (peak ground velocity, PGV), and duration (number of cycles, N). The proof‐of‐concept is established using the case study of one tall building model. Nonlinear analyses are performed on the model subjected to the idealized wave trains, with T varying from 0.5 s to 6.0 s, PGV varying from 0.125 m/s, and N varying from 1 to 5. Databases of peak transient and residual interstory drift ratios (IDR), and permanent roof drift are created. We demonstrate the effectiveness of the rapid response approach by applying it to synthetic waveforms from a simulated 1857‐like magnitude 7.9 San Andreas earthquake. The peak IDR, a key measure of structural performance, is predicted well enough for emergency response decision making.https://authors.library.caltech.edu/records/xk1ep-8jn36Sensitivity of the Earthquake Response of Tall Steel Moment Frame Buildings to Ground Motion Features
https://resolver.caltech.edu/CaltechAUTHORS:20130307-144505436
Authors: Krishnan, Swaminathan; Muto, Matthew
Year: 2013
DOI: 10.1080/13632469.2013.771587
The seismic response of two tall steel moment frame buildings and their variants is explored through parametric nonlinear analysis using idealized sawtooth-like ground velocity waveforms, with a characteristic period (T), amplitude (peak ground velocity, PGV), and duration (number of cycles, N). Collapse-level response is induced only by long-period, moderate to large PGV ground excitation. This agrees well with a simple energy balance analysis. The collapse initiation regime expands to lower ground motion periods and amplitudes with increasing number of ground motion cycles.https://authors.library.caltech.edu/records/fecv9-n0g97Response of tall steel buildings in southern California to the magnitude 7.8 shakeout scenario earthquake
https://resolver.caltech.edu/CaltechAUTHORS:20130306-130700318
Authors: Muto, M.; Krishnan, S.
Year: 2013
Currently, there is a significant campaign being undertaken in southern California to increase public awareness
and readiness for the next large earthquake along the San Andreas Fault, culminating in a large-scale
earthquake response exercise. The USGS ShakeOut scenario is a key element to understanding the likely
effects of such an event. A source model for a M7.8 scenario earthquake has been created (Hudnet et al.
2007), and used in conjunction with a velocity model for southern California to generate simulated ground
motions for the event throughout the region (Graves et al. 2008). We were charged by the USGS to provide
one plausible realization of the effects of the scenario event on tall steel moment-frame buildings. We have
used the simulated ground motions with three-dimensional non-linear finite element models of three buildings
(in two orthogonal orientations and two different connection fragility conditions, for a total of twelve
cases) in the 20-story class to simulate structural responses at 784 analysis sites spaced at approximately
4 km throughout the San Fernando Valley, the San Gabriel Valley and the Los Angeles Basin. Based on
the simulation results and available information on the number and distribution of steel buildings, we have
recommended that the ShakeOut drill be planned with a damage scenario comprising of 5% of the estimated
150 steel moment frame structures in the 10-30 story range collapsing (8 collapses), 10% of the structures
red-tagged (16 red-tagged buildings), 15% of the structures with damage serious enough to cause loss of life
(24 buildings with fatalities), and 20% of the structures with visible damage requiring building closure (32
buildings with visible damage and possible injuries). This paper details the analytical study underlying these
recommendations.https://authors.library.caltech.edu/records/k2sgs-wrd98Impact of a Large San Andreas Fault Earthquake on Tall Buildings in Southern California
https://resolver.caltech.edu/CaltechAUTHORS:20130305-144306529
Authors: Krishnan, Swaminathan; Ji, Chen; Komatitsch, Dimitri; Tromp, Jeroen
Year: 2013
In 1857 a large earthquake of magnitude 7.9 (Sieh 1978b) occurred on the San Andreas fault with rupture initiating at Parkfield in Central California and propagating in a southeasterly direction over a distance of more than 360 km. Such a unilateral rupture produces significant directivity toward the San Fernando and Los Angeles basins. Indeed, newspaper reports (Agnew and Sieh 1978; Meltzner and Wald 1998) of sloshing observed in the Los Angeles river point to long-duration (1-2 min) and long-period (2-8 s) shaking, which could have a severe impact on present-day tall buildings, especially in the mid-height range. Using state-of-the-art computational tools in seismology and structural engineering, validated using data from the Northridge earthquake, we determine the damage in 18-story steel moment-frame buildings in southern California due to ground motion from a hypothetical magnitude 7.9 earthquake on the San Andreas fault. Our study indicates that serious damage occurs in these buildings at many locations in the region, leading to wide-spread building closures and seriously affecting the regional economy.https://authors.library.caltech.edu/records/90qs0-khc90Low-Complexity Candidate for Benchmarking Collapse Prediction of Steel Braced Structures
https://resolver.caltech.edu/CaltechAUTHORS:20141106-105505763
Authors: Bjornsson, Arnan B.; Krishnan, Swaminathan
Year: 2014
DOI: 10.1061/(ASCE)ST.1943-541X.0000938
To aid in the evaluation of the collapse-prediction capability of competing methodologies, a case study of a water tank subjected to the Takatori near-source record from the 1995 Kobe earthquake, scaled down by a factor of 0.32, is presented. The water tank, supported by a five-segment steel lattice tower, is so configured as to have a characteristic collapse mechanism that is triggered due to catastrophic column and brace buckling at the bottommost segment of the lattice under all forms of ground motion. A FRAME3D model of the tank reveals severe buckling in the bottom megacolumns and one of the two braces on the west face of the tower when the structure is impacted by the Takatori near-source pulse, resulting a tilt in the structure. This is followed by sequential compression buckling of braces on the south and north faces leading to P−Δ instability and complete collapse of the tank. In order to verify the predictions of the FRAME3D model, a comparable PERFORM-3D model of the tank, using fiber elements and constitutive material models that are suitably calibrated against experimental data, is developed. The response of this model to the scaled Takatori ground motion compares very well against that of the FRAME3D model; the smallest scaling factor needed to collapse the PERFORM-3D model is 0.323, whereas the corresponding factor needed to collapse the FRAME3D model is 0.315. The sequence of column- and brace-buckling failures and the collapse mechanisms are quite similar in the two models.https://authors.library.caltech.edu/records/pzwjp-8q133Low-Complexity Candidate for Benchmarking Collapse Prediction of Steel Braced Structures
https://resolver.caltech.edu/CaltechAUTHORS:20141106-105505763
Authors: Bjornsson, Arnan B.; Krishnan, Swaminathan
Year: 2014
DOI: 10.1061/(ASCE)ST.1943-541X.0000938
To aid in the evaluation of the collapse-prediction capability of competing methodologies, a case study of a water tank subjected to the Takatori near-source record from the 1995 Kobe earthquake, scaled down by a factor of 0.32, is presented. The water tank, supported by a five-segment steel lattice tower, is so configured as to have a characteristic collapse mechanism that is triggered due to catastrophic column and brace buckling at the bottommost segment of the lattice under all forms of ground motion. A FRAME3D model of the tank reveals severe buckling in the bottom megacolumns and one of the two braces on the west face of the tower when the structure is impacted by the Takatori near-source pulse, resulting a tilt in the structure. This is followed by sequential compression buckling of braces on the south and north faces leading to P−Δ instability and complete collapse of the tank. In order to verify the predictions of the FRAME3D model, a comparable PERFORM-3D model of the tank, using fiber elements and constitutive material models that are suitably calibrated against experimental data, is developed. The response of this model to the scaled Takatori ground motion compares very well against that of the FRAME3D model; the smallest scaling factor needed to collapse the PERFORM-3D model is 0.323, whereas the corresponding factor needed to collapse the FRAME3D model is 0.315. The sequence of column- and brace-buckling failures and the collapse mechanisms are quite similar in the two models.https://authors.library.caltech.edu/records/qfgsj-g0d75A Laboratory Earthquake‐Based Stochastic Seismic Source Generation Algorithm for Strike‐Slip Faults and its Application to the Southern San Andreas Fault
https://resolver.caltech.edu/CaltechAUTHORS:20150827-103413623
Authors: Siriki, Hemanth; Bhat, Harsha S.; Lu, Xiao; Krishnan, Swaminathan
Year: 2015
DOI: 10.1785/0120140110
There is a sparse number of credible source models available from large‐magnitude past earthquakes. A stochastic source‐model‐generation algorithm thus becomes necessary for robust risk quantification using scenario earthquakes. We present an algorithm that combines the physics of fault ruptures as imaged in laboratory earthquakes with stress estimates on the fault constrained by field observations to generate stochastic source models for large‐magnitude (M_w 6.0–8.0) strike‐slip earthquakes. The algorithm is validated through a statistical comparison of synthetic ground‐motion histories from a stochastically generated source model for a magnitude 7.90 earthquake and a kinematic finite‐source inversion of an equivalent magnitude past earthquake on a geometrically similar fault. The synthetic dataset comprises three‐component ground‐motion waveforms, computed at 636 sites in southern California, for 10 hypothetical rupture scenarios (five hypocenters, each with two rupture directions) on the southern San Andreas fault. A similar validation exercise is conducted for a magnitude 6.0 earthquake, the lower magnitude limit for the algorithm. Additionally, ground motions from the M_w 7.9 earthquake simulations are compared against predictions by the Campbell–Bozorgnia Next Generation Attenuation relation, as well as the ShakeOut scenario earthquake. The algorithm is then applied to generate 50 source models for a hypothetical magnitude 7.9 earthquake originating at Parkfield, California, with rupture propagating from north to south (toward Wrightwood), similar to the 1857 Fort Tejon earthquake. Using the spectral element method, three‐component ground‐motion waveforms are computed in the Los Angeles basin for each scenario earthquake and the sensitivity of ground‐shaking intensity to seismic source parameters (such as the percentage of asperity area relative to the fault area, rupture speed, and rise time) is studied.https://authors.library.caltech.edu/records/7cq3c-ff368Toppling Analysis of the Echo Cliffs Precariously Balanced Rock
https://resolver.caltech.edu/CaltechAUTHORS:20161213-141035303
Authors: Veeraraghavan, Swetha; Hudnut, Kenneth W.; Krishnan, Swaminathan
Year: 2017
DOI: 10.1785/0120160169
Toppling analysis of a precariously balanced rock (PBR) can provide insight into the nature of ground motion that has not occurred at that location in the past and, by extension, can constrain peak ground motions for use in engineering design. Earlier approaches have targeted 2D models of the rock or modeled the rock–pedestal contact using spring‐damper assemblies that require recalibration for each rock. Here, a method to model PBRs in 3D is presented through a case study of the Echo Cliffs PBR. The 3D model is created from a point cloud of the rock, the pedestal, and their interface, obtained using terrestrial laser scanning. The dynamic response of the model under earthquake excitation is simulated using a rigid‐body dynamics algorithm. The veracity of this approach is demonstrated through comparisons against data from shake‐table experiments. Fragility maps for toppling probability of the Echo Cliffs PBR as a function of various ground‐motion parameters, rock–pedestal interface friction coefficient, and excitation direction are presented. These fragility maps indicate that the toppling probability of this rock is low (less than 0.2) for peak ground acceleration (PGA) and peak ground velocity (PGV) lower than 3 m/s^2 and 0.75 m/s, respectively, suggesting that the ground‐motion intensities at this location from earthquakes on nearby faults have most probably not exceeded the above‐mentioned PGA and PGV during the age of the PBR. Additionally, the fragility maps generated from this methodology can also be directly coupled with existing probabilistic frameworks to obtain direct constraints on unexceeded ground motion at a PBR's location.https://authors.library.caltech.edu/records/na4ma-37d69Probabilistic Estimates of Ground Motion in the Los Angeles Basin from Scenario Earthquakes on the San Andreas Fault
https://resolver.caltech.edu/CaltechAUTHORS:20180427-151741871
Authors: Mourhatch, Ramses; Krishnan, Swaminathan
Year: 2018
DOI: 10.3390/geosciences8040126
Kinematic source inversions of past earthquakes in the magnitude range of 6–8 are used to simulate 60 scenario earthquakes on the San Andreas fault. The unilateral rupture scenario earthquakes are hypothetically located at 6 locations spread out uniformly along the southern section of the fault, each associated with two hypocenters and rupture directions. Probabilities of occurrence over the next 30 years are assigned to each of these earthquakes by mapping the probabilities of 10,445 plausible earthquakes postulated for this section of the fault by the Uniform California Earthquake Rupture Forecast. Three-component broadband ground motion histories are computed at 636 sites in the greater Los Angeles metropolitan area by superposing short-period (0.2–2.0 s) empirical Green's function synthetics on top of long-period (>2.0 s) spectral element synthetics. The earthquake probabilities and the computed ground motions are combined to develop probabilistic estimates of ground shaking in the region from San Andreas fault earthquakes over the next 30 years. The results could be useful in city planning, emergency management, and building code enhancement.https://authors.library.caltech.edu/records/yf7az-03g27Lower Bounds on Ground Motion at Point Reyes during the 1906 San Francisco Earthquake from Train Toppling Analysis
https://resolver.caltech.edu/CaltechAUTHORS:20190201-085310780
Authors: Veeraraghavan, Swetha; Heaton, Thomas H.; Krishnan, Swaminathan
Year: 2019
DOI: 10.1785/0220180327
Independent constraints on the ground motions experienced at Point Reyes station during the 1906 San Francisco earthquake are obtained by analyzing the dynamic response of a train that overturned during the earthquake. The train is modeled as a rigid rectangular block for this study. From this analysis, we conclude that the peak ground acceleration (PGA) and peak ground velocity (PGV) at Point Reyes station would have been at least 4 m/s^2 and 0.5 m/s, respectively. This lower bound is then used to perform simple checks on the synthetic ground‐motion simulations of the 1906 San Francisco earthquake. It is also shown that the hypocenter of the earthquake should be located to the south of Point Reyes station for the overturning of the train to match an eyewitness description of the event.https://authors.library.caltech.edu/records/v9k4v-p4a45Modeling the Rocking and Sliding of Free-Standing Objects Using Rigid Body Dynamics
https://resolver.caltech.edu/CaltechAUTHORS:20200514-144614293
Authors: Veeraraghavan, Swetha; Hall, John F.; Krishnan, Swaminathan
Year: 2020
DOI: 10.1061/(asce)em.1943-7889.0001739
A rigid body dynamics algorithm is presented in this paper to simulate the interaction between two rigid bodies, a free-standing rigid object, and a pedestal that has infinite mass, in the presence of static and kinetic friction forces. Earlier algorithms led to different solutions for the contact forces when parameters external to problem description, such as the ordering of contact points, are changed. This paper addresses the issue of selecting an appropriate solution for the contact forces and impulses from the infinite set of solutions by picking the solution that is closest to the previous state of the rigid body. The capability of this algorithm in simulating pure rocking, pure sliding, and coupled rocking-sliding response modes of a rectangular block is validated using analytical/semianalytical results. This validated algorithm is later used to identify the various response modes of a rectangular block, which is given an initial tilt and then released.https://authors.library.caltech.edu/records/0sb59-t4y92