Hello, everybody.
Happy new year, and welcome back from the shutdown.
So this is our first seminar of the year here.
And we’ll be back to having seminars regularly
every Wednesday, barring another shutdown.
And next week, we’ll be having Anne Hulsey from Stanford come to talk
to us about tall buildings and cordoned- off areas following earthquakes.
And now I will hand things over to Tom Hanks to introduce today’s speaker.
Here you go, Tom.
- Hi, Jack. [laughs] Good to see you again.
Excuse me. I’m still getting over a cold.
Let’s see. I’ve known Jack for, well, probably too long. [laughs]
2001 or something.
I met him as a graduate – when he was a graduate student up at Stanford.
He and Dave Shelly got undergraduate degrees at Whitman College in
mathematics and physics together. And so we’ve – that’s been a great
connection for us with both of them. Then he went to Stanford and
got a master’s degree in structural engineering and statistics.
And then a Ph.D. with Allin Cornell. And I think that’s where I first met you.
And then went to ETH and was there for a year and then came back to Stanford
and has been on the faculty there since. And I guess you’re
a full professor by now. - Not quite.
- Not quite. Okay, well, you have something to
look forward to other than, of course, giving us another talk here.
I got to know Jack through the Extreme Ground Motion project
at Yucca Mountain. And – oh, let’s see. Let me say –
he’s won all kinds of engineering awards that I’m not going to tell you too much
because, more importantly, at least to us, I think,
are his connections to the Earth sciences.
He’s been an editor for the Bulletin of the Seismological Society of America,
and he sits on the planning committee of SCEC.
And I got to know him really well through the Extreme Ground Motion
project at Yucca Mountain. And, among other things,
Jack made a lot of probabilistic sense out of fragile geologic structures.
And I was thinking the other night – or, last night, when this – have you
ever thought about thinking about fragile engineering structures in the
same context? You know, in terms of a population of such things?
And I think the answer is probably no, but – and that’s good because he’s
going to talk about use of ground motion simulations in engineering practice.
Okay, thanks for being here, Jack, right.
Shall I give this to you?
- Good morning. Is it – can you hear that? Okay, good.
Well, thanks. Thank you, Tom. And thanks to all of you for the
invitation to come back and speak. I’m very pleased to be here,
and I’m pleased that you’re back open for business,
and we can kind of continue our engagement,
and you can continue your important work that you’re doing here.
I brought a few slides this morning. I think the initial conversations
were around kind of ground motion simulations and tall buildings
and some various things that you were interested in.
And I guess with the kind of – my understanding of some interest here,
I brought a few slides to kind of just give you some general background
about how structural engineers think about ground motions and how ground
motion simulations that geophysicists are producing might be used, or will
be used, by the engineering practice. And then a little bit of kind of research
that we’ve done in that area to think about how we might ask questions
and answer questions that we have from the engineering community
about some of the work that’s going on in the Earth sciences.
So I’ll thank – so Ganyu Teng and Lynne Burks are Ph.D. students
and former – Lynne is a former Ph.D. student at Stanford.
He’s done a lot of the work that I’ll show here.
And a couple collaborators, and then Rob Graves, Kim Olsen,
Scott Callaghan were really instrumental in kind of providing a lot of the
data we’re looking at here. And SCEC has been a financial
supporter of this, so definitely appreciate the collegiality and the
support from the Earth sciences community as we kind of wander
around asking questions as engineers in this – in this domain.
Okay, so to get into things, to think about how we use ground
motions in earthquake engineering. So I think the – you know, the easiest
conceptual thing to think about, and kind of cartoon version, is to say, you know,
we could think about, you know, earthquake source models and do,
you know, rupture simulation, wave propagation, produce time series,
and put those into buildings and kind of see what happens to the buildings.
And that gets kind of colloquially called rupture-to-rafters simulations
over – kind of the entire thing is this one pipeline of numerical,
you know, calculations and simulations and things like that.
And that’s certainly interesting and has been impactful in some of these
big projects like the ShakeOut scenario or the HayWired scenario, in terms of
kind of understanding what the – what a particular earthquake scenario
might produce in terms of damage. But it – and so I don’t mean to be critical
of any of those efforts, but only to point out, that’s in contrast to the
way that most engineers really interface with this type of data in
their day-to-day work and in the practice of designing buildings or
analyzing individual buildings. And we take kind of a more circuitous route.
And I’ll – to the extent that this is not familiar to you, hopefully this is
something educational and – that I can both tell you a little bit about the process
and kind of how this all came about.
So really, as I think about it, we’ve got kind of a first stage
of analysis, which is – which is hazard analysis.
And that – the Survey is very familiar with as kind of the holder of the
national seismic hazard assessments and a lot of research and other projects
going on in that area. But we really go from kind of
the earthquake ruptures and wave propagation and we do this probabilistic
assessment of all possible ruptures and all possible, you know,
permutations of ground motions that could result from these ruptures.
And there’s that whole process that goes on.
But the outcome of that, from an engineering perspective,
is a design response spectrum. And so this is loosely based on
ground motion amplitudes in terms of spectral accelerations.
And it’s loosely based on – well, it is based on spectral accelerations.
It’s loosely based on amplitudes that are exceeded with something like a,
you know, target return period, although there’s modifiers for caps
and risk adjustments and things like that.
But it’s ultimately driven by kind of the frequency of simulations or calculations
that predict a ground motion amplitude of some sort.
And ground motion simulations play an important role here, increasingly.
So, you know, traditionally the ground motion amplitude predictions
have been based on kind of empirical models.
But increasingly, we’re thinking about ways to use simulations there that,
in Los Angeles, there’s activity going on around SCEC.
In Seattle, Art Frankel has been, you know, pushing at these
directions for a long time. I know there’s work in Memphis,
and the Survey’s got their involvement in kind of all of those efforts.
So certainly that target response spectrum could be computed
with consideration of ground motion simulations and the particular insights
they might provide about the amplitude of shaking that any
particular site could see. And that’s important.
That is kind of almost entirely an Earth science problem, and I’m interested in it,
but that’s not kind of what I’ll focus on today.
What I thought would be interesting to talk about with you today is
really kind of a second step. And this is where the engineers –
practicing engineers typically come into the picture.
And so an engineer will come along, and whether they’re using the
USGS hazard maps, or they’re using some site-specific study
that’s been performed, they’ll start with that target response spectrum.
And the engineer is not doing any sort of calculations themselves to get that.
That’s coming from some sort of external group.
And then they are going to do some analysis to assess the
performance of their structure under ground shaking with that intensity.
And I should say – so the focus of my talk will be about, you know,
how might simulated ground motions play a role here?
Because that’s another stage in which we will use ground motions.
We typically use many fewer ground motions.
So on the order of a dozen or so ground motions rather than, you know,
thousands or hundreds of thousands that might be done
in the hazard analysis stage.
And actually, typically, we don’t use any ground motions at all.
So I should note, and maybe some of you have heard this before,
but 99% of structures are designed or analyzed using some sort of a
static loading that’s deemed equivalent to the dynamic loading that would be
associated with that response spectrum. So most of the time, we’re not building
dynamic models or analyzing dynamic models of the way
that structures perform. It’s just a – it’s a complicated and
labor-intensive effort, and it’s deemed kind of not necessary
for your Home Depots or for your residential houses
or your three-story office buildings and things like that.
For special structures – so high-rise buildings or base-isolated buildings
or hospitals – you know, certain classes of structures that are special or have
something unusual in their structural performance, or there’s something about
the system that’s really – you need to understand the dynamic behavior,
then we go to this domain. And those are the – you know,
those are typically – you know, typically good engineers that have a,
you know, understanding of advanced analysis techniques.
There’s more resources available for the analysis.
And that’s a place where simulated ground motions could play
an important role, and that’s really kind of the piece where myself, as a
trained structural engineer, I’m kind of interested in interfacing to.
So hopefully – with that background, hopefully that’s, you know,
educational or interesting to some of you.
And I want – let’s dig into that a little more.
So today, I’ll think about this kind of right-hand side of the picture.
This passage from the target response spectrum
on to assessing structural response.
And I should say, kind of traditionally, this has been done using
recorded ground motions. So we’ll take recordings from some
sort of earthquake deemed comparable to the one that we’re thinking about
that might affect our structure.
Maybe we’ll do some processing of that ground motion and proceed.
And so I’ll be interested in saying, well, you know, if we did this with recordings
or if we did this with simulations, you know, what would be the
differences and what would be the pros and cons?
I want to talk about that a little bit through a few examples today.
And I’ll tell you a little bit about the specific requirements
that go into that as well. So here is some more background
that, again, might be interesting or educational for some of you.
There’s a few different documents that might guide an engineer in
doing these types of assessments. In most cases, it would be
this ASCE 7 standard. So this is a technical standard
that’s produced by the – a few different agencies,
but the American Society of Civil Engineers and Structural
Engineering Institute publish this. And then a lot of building codes will
then, by reference, adopt this and say, the loadings on your buildings will
have to conform to this standard. And then that building code is going to
drive the acceptance of a particular building design
in a particular jurisdiction. So through kind of, you know,
a few different stages, this is the document that ultimately is
specifying what has to happen. And it’ll say, you know,
under what circumstances you actually have to do dynamic analysis.
And if you do choose to do dynamic analysis, it’s Chapter 16 of this thing,
for those that are interested. And there’s, you know, a dozen pages
or so kind of talking through what the requirements are.
And I just wanted to grab a few that might be interesting.
So it’s going to reference off to the hazard assessment and
reference off to the target spectrum. That’s described elsewhere.
And so we have this language. You’ve probably read it
a couple minutes ago. So we’re going to have to select
ground motions from events with the same tectonic regime,
having generally consistent magnitude and fault distances and those controlling
the target spectrum and have similar spectral shape to that target spectrum.
So that’s that kind of spectrum that I drew on the previous page.
So the engineer will go determine that spectrum from some source
and then use something like de-aggregation to figure out
magnitudes and distances that are interesting.
And then you can kind of identify tectonic regime pretty quickly.
So we would – you know, sitting here, if we were going to put a new building in
this neighborhood, we’d go get our target spectrum, which would be pretty high.
We’d see that the hazard is controlled by probably magnitude 8 San Andreas
events at 15 kilometers away, or whatever it is, to here.
And then we’ll go try to, you know, find some ground motions to conform to that.
In terms of finding them, we – let’s see. Somewhere in here, we should
have some sort of recordings. Oh, yeah. So there’s an implicit
preference for recorded ground motions.
And that’s just kind of reflecting historical practice rather than some sort
of conscious decision, I think, talking to the code writers that are in this.
So we’re going to go look for recordings.
And then it says, when they’re not available,
you can use – supplement those with simulated ground motions.
And this is, I think, historically – some of this language, I think,
dates back 20 or 30 years to where the balance between –
well, there are many fewer recordings and then also many fewer
simulations and much less-refined simulation technology.
And I think this is largely applied in the eastern U.S., where there are
just more recordings in stable continental regions appropriate for New Madrid-type
events or something like that. And so they put in this thing.
So, both in the – in the – in these words, as well as in professional practice,
there is this preference toward recorded ground motions if present.
And just one note that, you know, buildings are three-dimensional, and so
we need – at a minimum, we need two horizontal components of ground motion.
And you do some evaluations to decide if vertical shaking is going to
be important for your building or not. In a lot of cases, it’s not really a big
driver of demands in the structure. But, if you need a – if you think vertical
shaking is important, then you have to go get the vertical component as well.
So we need at least two component, maybe three component ground motions.
So that’s just something that influences the suitability of
some ground motion simulation algorithms.
So that’s increasingly not an issue for simulators.
Okay, so this document gets updated every five years or so –
the latest round coming out in 2016.
And so, in 2013 or ’14, when this was kind of undergoing revision,
we did a few studies to kind of look at updates to the language
and what impact it would have. And one is, we wanted to put a little
more language in the commentary especially, but just do some experiments
about kind of how simulations might work in these situations.
And so, for a few slides here, I’ll show you one example of a study
that kind of went along with that code update that Lynne Burks, the student
at Stanford, and a practicing engineer and myself did a few years ago.
So this practicing engineer, Reid Zimmerman, was one of the
people who was tasked with saying, you know, as we update this code
language, we want to make sure that we don’t accidentally kind of trigger
some very – you know, relaxation of our rules or a big increase
in the rules that was unintentional. And so we take a series of buildings
that satisfied the previous code and kind of re-analyze them under the new
building code just to try to understand, are we – do we think we’re doing
a better job in terms of the requirements, or did we miss something?
And so this was a building that he had recently designed and worked with.
So it’s kind of a mid-rise building. It’s the type of building you wouldn’t
probably typically analyze dynamically, but he had a dynamic model that he had
built for other reasons consisting of kind of – so the top figure is a –
kind of a picture of just the lateral force-resisting system,
which is the important part of the building for earthquakes.
And then the bottom picture is a plan view showing kind of the
lines of the particular framing that would be resisting earthquake forces.
So it’s kind of moment frames, braced frames – the typically structural
systems we see kind of all over here for office buildings, residential buildings,
and things. This is actually a dormitory on the Berkeley campus.
So I think you all probably know the Bay Area picture pretty well.
The building is kind of up in the upper left.
And it’s about a kilometer away from the Hayward Fault,
just right at the south end of the Berkeley campus.
So in red, which may not be real clear there, but you – but you can
see the Berkeley stadium with the Hayward Fault, you know,
passing right through the middle of there.
And we’re just a kilometer off to this building location.
So this is an interesting, you know, example in that the – so Berkeley had
kind of – when they built this dorm, had done some extra analysis
the first time through. And this is a case where you might say,
well, simulations would be great because I don’t have that many
observations of these very near-fault ground motions strong intensities,
but I can simulate some.
And, you know, that would be convenient instead of having to
scrape around in my recordings to try to find something this close to a fault.
So what we did is we went through two parallel selection exercises.
So, on the left, we used recordings from the PEER ground motion database.
So this is a database, at the time, was a 3,000-or-so kind of
strong ground motion recordings. Now somewhere between 8,000
and 20,000, depending on kind of what you count as relevant for engineers.
And that would be the traditional practice even today is you’d go to
a database like this, and you’d go filter it and look for kind of
matching magnitudes, distances. At the time, this was all shallow
crustal earthquakes, so the tectonic regime matched naturally.
And now they’ve got permutations in the database
for other types of tectonic regimes.
And then we also used the SCEC broadband platform.
So this is the software platform that implements a few different
ground motion simulation algorithms and in a way that is kind of intended to
facilitate other types of studies where you don’t have to kind of
go to the scientist themself and have them produce ground motions.
And so we thought that was kind of well-suited that there’s some potential
that, you know, engineering practice could adopt a tool like that or engage
with people who are able to use tools like that to produce ground motions.
So this particular study will use – there’s kind of multiple algorithms built into it,
but we used – most of the pieces of it were from Graves and Pitarka with
one component from San Diego State from Kim Olsen.
And this is a – I should note this is a – it’s called kind of hybrid broadband
ground motion simulations, for those of you in the – in the business.
So there’s a – there’s kind of the low frequencies are produced
using a deterministic kind of a rupture realization and wave propagation.
But we also need high-frequency ground motions for these engineering analyses.
We need kind of a full broadband set of energy input to the structure.
And so that’s produced using a separate algorithm,
which is the stochastic algorithm, and so those are stitched together.
And so this is just referencing the particular algorithms,
but the general workflow could work with other types of algorithms.
Okay, so then a little hesitant to sometimes put up tables in PowerPoints,
but to give you a sense of what would happen.
So the current – the building code we were looking at – ASCE 7-16 –
requires 11 ground motions as inputs to these analyses.
So we’ve got kind of 11 rows in the table.
On the left is what we would typically come up with with current practice.
So these are recordings from kind of our favorite earthquakes – Imperial Valley,
Loma Prieta, Northridge. We’ll go to, you know, other places
in the world, like Chi-Chi, maybe to get a larger magnitude event, or a few.
And then we’re looking for, you know, similar magnitudes.
So we’ve got kind of 6-1/2, 6.7, 7.6 – and I should, sorry, back up that –
so, given the location of that site, we’re looking for magnitude 7
Hayward-type ruptures. So I’d like a magnitude 7 strike-slip,
you know, rupture, and I’d like to have a recording a kilometer away from it.
You know, these recordings on the left are close – you know,
between 1 and 12 kilometers – but they’re not exactly 1.
The site conditions are going to vary a little bit just based on
where the instruments are. And then, because this design spectrum
is very large – like, we’re designing for very rare ground motions.
I may have alluded to it loosely. Again, it’s a little more
complicated than this. We can think about ground motions
that occur – or, ground motions that are exceeded once every
2,500 years in terms of those amplitudes. And if the Hayward rupture is something
that’s happening every 200 or 300 years, our design amplitudes are going to be
much bigger than an average ground motion from a Hayward-type rupture.
We’re thinking about, like, a Hayward rupture, but, you know,
a factor of 2 or 3 larger in amplitude, given the variability from rupture to
rupture we might see. So very large amplitudes we’re designing for.
And so that final column of the recordings shows scale factors.
We try to limit them, but, you know, some of these are
doubled or tripled in amplitude relative to what was recorded as a way to
bump up the ground motion amplitudes up to that design spectrum.
And so, you know, this business of trying to kind of mix – you know,
make these recordings work for the case we’re thinking about is not anything
that’s – you know, we’re excited about, but that’s kind of the best we can do
in terms of getting realistic dynamic loading for the structure at present.
So then, over on the right, the story is a lot cleaner conceptually, right?
I can just set up the broadband platform to generate ruptures of magnitude 7
vertical strike-slip earthquakes, and I can put receivers a kilometer away
from the simulation, and then we generate it on the order of, I think,
150 simulations, or 200 simulations, under those conditions.
And then the – you know, out of that, there was enough that we’re close to
the design spectrum that we could take – we don’t have to scale them.
We can just generate more simulations until we get suitable ones.
So there’s no need to kind of post-process.
We can specify the site conditions, and so on.
And so something that’s kind of a much cleaner conceptual fit
with what you’re trying to achieve, and that would be the – I think,
where engineers would find a lot of value out of these simulations,
particularly if – you know, if we could, you know, continue adding features
about the particular region or the particular fault or the
particular site that would, you know, produce realistic waveforms
for what would anticipate in the future.
Okay, so here’s a plot of – so these are response spectra.
Let me point out a few things. So on the left is the set of recordings.
On the right is the set of simulations.
So – and so I should say, so on the horizontal axis, this is the period,
or the reciprocal of the frequency.
And on the vertical axis is the spectral acceleration.
And this is – since we’re going to talk about response spectra
for a few slides here, just to make sure everybody’s on the same page.
So this is – we’re measuring kind of the amplitude of an elastic oscillator
that has the specified period and has some – it’s kind of lightly damped.
So it’s – in some senses, it’s analogous to, like, a smoothed Fourier amplitude.
But it – but it’s not. It’s a – it’s a response of an oscillator.
And so a couple things to point out here. So the dashed black line is –
at the very bottom of all these plots – is what we would anticipate is the
median shaking from a Hayward-like scenario at 1 kilometer away.
And then the solid black line is our design spectrum.
So this is what I was pointing out that this kind of factor of
almost 2 bigger amplitude than the median response spectrum.
So we’re designing for these very large ground motions
that we expect to occur, but to occur very rarely.
And that, you know, is the right thing to do but creates problems in terms of
finding ground motions that are going to match that naturally.
So then the light lines in both figures are the response spectra
of individual ground motions. And then the heavy blue line is the
mean of those ground motions, and that mean needs to be kind of
equal to or above the design spectrum over the range of periods that’s
kind of deemed important for the response of the building.
And there’s various ways to determine that.
So the point here was just to – we don’t need to worry too much about the
subtleties of the shapes, but just to note that the recordings and the simulations
have basically comparable amplitudes as measured via response spectra.
Here are some time histories. Sometimes I’ll have people guess
kind of which ones are the recordings or the simulations, but they’re actually
in kind of the same order as the previous slide.
So on the left is the velocity time histories of some of the recordings.
On the right, comparable for the simulations.
And so, you know, those look like real ground motions.
They have the complexities of real ground motions.
These aren’t some sort of kind of idealized white noise-type times series,
but they’ve got, you know, kind of all the complexities
that the simulators think are appropriate in here.
So in terms of amplitudes, everything looks comparable from that response
spectra in terms of time series. Certainly, those would be something
that anybody would be comfortable with from an engineering perspective.
And then we go put these into the dynamic model.
And so here’s a couple videos of – since the model is dynamic,
you can actually kind of measure what’s going on over time.
And the engineer will then monitor kind of displacements of particular
points in the building, measure the forces that individual components
in the building are having to carry, and then we’ll check those against
kind of allowable displacements and forces and accelerations.
So just to make tangible that there is kind of this
full dynamic analysis going on in the design office.
So what we did – or, what Reid did, our collaborator – he ran the full,
you know, set of dynamic analysis for each of the 11 recordings,
for each of the 11 simulations, and then we’re typically interested
in kind of peak displacements and peak forces up, you know, that are resulting
from these. And then we’ll continue on to do the checking with those.
Okay, so this is the type of things that we’ll look at out the
back of those analyses. So these are plots of story drift ratio
in the building, and this is in the fault normal direction that the building was
roughly oriented kind of perpendicular and parallel to the fault.
So in the fault normal direction. We’ve got plots of this story drift ratio,
which is, at each story, the peak displacement of the top of the story
relative to the bottom of the story divided by the story height.
So it’s kind of like a rotation in radians.
The biggest rotation we got kind of at that story.
And things like, you know, 4% or so is – we can manage
to design these types of frames to resist that type of deformation.
And, you know, 1 or 2 or 3% is – we’re going to see damage to drywall
and things like that, but the building will be safe for the occupants.
And so that’s the type of thing we’re checking.
The plots of the height of the building will look like this, in that, from the
zero to 1, there was a concrete wall basement that’s very stiff and rigid,
and the displacements aren’t a problem down there.
And in the upper stories, we get these drifts.
And so the light gray lines are the profiles from each
individual dynamic analysis. And then the red line is the average
of those kind of story by story, so the average in the horizontal direction.
And it’s the average of the 11 that we’re checking against with the
motivation being that we understand there will be variability from simulation
to simulation, but with only 11 ground motions, which is
kind of practically what’s doable in a design office.
We’re not actually going to capture the full variability in the – in the – I’m going
to say kind of the extreme large demand. So there’s kind of other factors built
into the codes to account for that. And the engineer’s job is just to
figure out, kind of on average, what would those deformations be.
So we got a set of results from the recordings and the simulations.
Hard to see anything dramatic there, so we can stack those on top of each
other to do some more assessment. So on the left is that same data from the
previous slide but just the mean values. And in blue are the recordings.
And in red are the simulations.
So we got 10% bigger demands out of the simulations.
And on the right is the same thing but in the fault parallel direction.
And the reverse happened there where the simulations produced less demands.
So a couple comments here is that, because the structural systems were
different in the two directions, that’s the primary reason why the story
drift ratios on the right are smaller. So it’s a stiffer structural system in that
fault parallel direction, and the system can just
resist deformations quite a bit more.
So the structural system plays a – you know, a much bigger role
in the amount of deformations that are getting produced than the input source.
And then, in terms of these differences on the order of 10% or so,
kind of digging into it, it turns out it was just that the simulations were
more strongly polarized with larger amplitudes in the fault normal direction.
With the recordings, we had maintained normal fault parallel orientations of the
recordings and kind of applied those appropriately to the building.
But I think, because of the variety of earthquakes,
we didn’t have all strike-slip earthquakes.
We didn’t have all of them very close into the fault.
We were probably unlikely to be capturing the near-fault polarization
of the ground shaking, whereas the simulations can handle that
quite naturally because we can get exactly the conditions we want.
So I think this is a case where everybody found things pretty satisfying.
So, to a first order, 10% is not something that we’re going to lose sleep over
from an engineering design perspective. I had an engineering professor
a long time ago say, you know, we’re not designing Steinways
with these things. Like, there’s a lot of uncertainty in the analysis.
There’s a lot of uncertainty in the loading.
If we’re getting ourselves down to the last 10% whether things are
going to work or not, you know, we’re overthinking it a little bit.
So we wouldn’t – we wouldn’t, you know, dramatically change
the design based on these numbers. So, in a sense, we’re getting kind of
stable, you know, believable numbers out of both sources of ground motions.
And, to the extent that the simulations are different, they’re different for
a reason that we could physically, you know, anticipate to be real.
We’re not – it’s not some artifact of the simulation, necessarily.
And so we are getting some sort of insight
that maybe we’re not getting from traditional methods.
So I think everybody felt that was a success in that regard.
I’m going to show you a couple more types of these figures.
So these are plots of the story shear. So this is, story by story, if you took
a cut through all of the columns, and you looked at how much force
was getting transferred in the lateral direction by all of those columns –
and, I should say, the braces and things at that story, you know, how much –
how much lateral force is having to be carried through the building.
So that increases as you go down the building because each lower story has
to carry the entire building above it as it’s getting shaken laterally.
Those results were almost identical. And that’s largely because of the
way the structure is designed. So it’s designed to, you know,
carry loads up to a certain point, and then yield and kind of distribute
those loads in a predictable manner. And so, even with some variability
in the loading conditions, the forces are going to be pretty well understood.
And so – yeah, so I guess to kind of finish discussion of that example, we –
yeah, we felt that things were – looked reasonable and that nobody
had any concerns about using that particular set
of simulations to think about analyzing a building.
Okay, so let me look at a kind of related study, but somewhat distinct.
So this idea of the – of the horizontal polarization
of the ground motions was interesting to us.
And because the buildings are 3D, and because the – so the direction
of the large-amplitude shaking is important to us as we think about
the behavior of these buildings, we were interested in polarization.
And we had seen some hints that there might – things might not
always be as smooth as they were in the previous study.
So, in this case, we used the broadband platform again.
Same software platform, but we looked at a few different algorithms.
And, in this case, we looked at historical ground motions.
So, you know, there’s various ways to do comparisons.
So, in the previous case, we looked at kind of
recordings selected using a building code procedure versus simulations.
In this case, we’re going to look at recordings from a specific event –
the Loma Prieta earthquake – versus simulations of that same event.
So these are kind of recording stations that recorded the
Loma Prieta earthquake. And so we’ve got – and then I guess
we looked at the kind of nearby stations.
So all the stations within 20 kilometers of that rupture projection.
And so we’ve got response spectra over on the right from those.
And then we took a comparable set of simulations from this broadband
platform, and there was a big validation exercise going on at the time,
where the simulators were participating, and a third-party group was kind of
vetting the results and things. We used the same data.
And we looked at three different algorithms.
So this EXSIM that Gail Atkinson and Dave Boore have been involved in.
This – GP is the Graves Pitarka algorithm – the same one
from the previous slides. And then CSM is a composite source model,
and John Anderson at Nevada-Reno – or, I guess the U.S. Geological Survey
now, is – was involved with kind of coding up that algorithm.
And so over on the right is an example of some of the response spectra at those
same sites from the Graves and Pitarka algorithm.
And so some others were looking at the absolute amplitudes of these things,
but we were interested in the polarization in particular.
And so, just to think about the way we polarize – or, we measure polarization,
so this is actually – Dave Boore came up with these metrics.
I understand he’s laid up at the moment,
but I was thinking about him as I was putting together these slides.
Sorry, I should – I should back up for a second.
So, as we think about the kind of – the loading over multiple directions
in this building, the – what I’ve got here is plotted on the horizontal axis here
displacement traces from the Imperial Valley El Centro Differential Array
recording, just as an example. And then we’ve got an elastic
oscillator sitting on top of it. And this oscillator’s got the same period
in kind of any axis, and so we can – we can let these oscillators move.
So on the left is a 1-1/2-second oscillator.
And on the right is a 3-second oscillator.
And so let me let that roll. So on the – up in space is the
differential displacement of the – of the oscillator relative to the ground.
And those displacements are what we ultimately turn into the response spectra.
But, as we look in different orientations,
the peak displacement is going to be different. And so here we can
kind of rotate it up and just look at the differential displacements.
So the thing I like to use these things to point out is that, you know, we think about
this loading in multiple directions and, you know, if you’re designing a flagpole,
kind of the maximum displacement in any direction would be
what you would be worried about. But in real buildings, we typically
have kind of two planes where we have frames.
And it’s going to be those frames worked individually
to resist forces that’s important. And so the – kind of the orientation
of large demands versus those frames is important to us.
So this is the ground motion that’s relatively polarized.
There’s particular orientations where the displacements
are much bigger than others.
But even for a particular ground motion, you know,
polarization is frequency-dependent. So here you can see the 1-1/2-second
oscillator peak displacements were almost orthogonal
to the 3-second oscillator peak displacements,
even though the input was identical in both cases.
So, you know, from a – I guess for you all to think about the –
kind of the insights that we can get about potential polarization of shaking
and the inputs to simulations that are influencing these polarization
are important to us. And then, from the engineer’s
perspective, there’s – I think there’s sometimes a rush to think about, like,
well, what’s the strong direction of the shaking?
And there is no strong direction of shaking.
It depends on kind of what the dynamic properties of your – of your system are.
And we just need kind of realistic representations
of the complexities that the real world is going to throw at us.
Okay, so with that is kind of a little bit of motivation.
And we think about measuring this polarization.
And so – let me think.
Let me remind myself kind of how far we go.
So we’ve got kind of examples of these traces.
So these are – these are traces from 0.2-second oscillators.
And so I’ve got, on the left, a recording from Loma Prieta.
On the right, a Graves Pitarka simulation.
And on the – in the middle, Graves Pitarka.
On the full – on the far right, this composite source method simulation.
And these are kind of the medium – or, the median polarized out of the suite.
So there’s kind of half of them that are more polarized than this
and half that are less. And so – yeah, so Dave Boore
was the one who kind of came up with our current parameterization of this,
which is to say, if I’m thinking about how strong a multi-component ground
motion is, I could look at the peak displacement demand
over all possible orientations. And that’s what we now
call the RotD100 metric. So the kind of 100th percentile
displacement demand over all rotation angles.
Or we could think about the median over the rotation angles,
which we call the RotD50 for a 50th percentile amplitude.
And so the – in a figure like on the left, the difference between those two
would be relatively small. So the median amplitude would be,
you know, similar to the 100th percentile amplitude.
On a trace like on the far right, the ratio would be bigger.
And the ratio can get as big as square root of 2, or 1.41, just from
kind of geometry of these rotations. And the ratio can get as small as 1.
If you had the same shaking amplitude in all directions,
the median would be identical to the – to the maximum.
And so that’s an easy way to kind of look at this polarization.
And then the – we see a typical pattern that, at longer periods,
we see more strong polarization in the ground motions.
And some of that’s just duration-dependent.
I think you have less time to get through a lot of cycles of an oscillator when the –
when the period of the oscillator is longer compared to the
duration of shaking. And then some of that has –
I think is kind of real polarization as well, that there’s just more
kind of directional scattering maybe at lower frequencies.
Okay, so here’s these ratios I was talking about.
So the horizontal axis I’ve got periods plotted, and then on
the vertical axis is this ratio. So we can look at the RotD100
divided by RotD50, and the scale is going to go from – the smallest it can
be is 1 at the bottom of the plot, up to square root of 2 at the top of the plot.
And you can compute these things for empirical ground motions,
and they’re really stable – large magnitudes and small magnitudes
and distant recordings or close recordings or soft soils or hard soils.
The ratios really seem quite stable on average.
So here’s a couple empirical models that have been developed over the years.
And so you see kind of 1.2 at short periods up to 1.25 or 1.3
maybe at long periods. That’s really a pretty reliable kind of
median estimate, and that’s not to say there aren’t circumstances
where things could change, such as, you know, near-fault directivity
or something like that. But, on average, that’s kind of what we expect.
There in black is the set of recordings from Loma Prieta.
So there’s 20 recordings, and you can see it’s – you know,
it’s bouncing around a little bit because there is some small-sample variability,
but it’s in the neighborhood of those models, and that’s kind of a benchmark
of, you know, what a stable answer might be.
And then here’s a couple set of simulations.
So in blue is this Graves and Pitarka simulations, and they’re, you know,
a little more variable around that target ratio.
This is, you know, a couple iterations ago. I think probably the later iterations
of the algorithm are even a little more stable in terms of this.
And then up at the very top is this composite source method.
And in talking to John Anderson, he said that there’s kind of a radiation
term associated with this as he steps along the fault, and that was not kind of
randomized reflecting kind of geometrical complexities and things
and that he thought, if it was randomized, that that would
really break up that polarization. So that was a case where we saw
something in the ground motions that doesn’t show up in kind of traditional
response spectra metrics. But this directional polarization
is important for buildings, and it is something that’s not physical,
but it’s something that could be easily kind of addressed and, you know,
rolled into future iterations of these simulation algorithms.
So I think that’s also the role that we hope to play as engineers is
kind of pointing out some of these features that we’d like further refined.
And without us pulling it out, if – you know, there’s no need
to be thinking about things like this.
- [inaudible] - Sure.
- [inaudible]
- TS? - [inaudible]
- Ah, yeah, okay. Thank you. - Oscillator period.
- Got it. Got it. Yeah, so – thank you. So the question was about what
the period on the horizontal axis is. So the period stays the same
in all horizontal directions. So I would take a 1-1/2-second
oscillator, say from the previous slide, and I would look at a 1-1/2-second
oscillator at all possible orientations.
And then I would take the maximum and the median of those. So, yeah.
- Thank you. - Yep.
Okay. So then, to pick a kind of a final example, and I’ll go through
this one a little more quickly. We’re not quite done with it, but just
to show kind of where we’re going. So now here we’ve moved on
to southern California, and we’re using the CyberShake simulation.
So this is another simulation infrastructure that’s run by Southern
California Earthquake Center. And I think this is a case that’s
getting a lot of attention on the hazard analysis side.
So Los Angeles is thinking about using these simulations
to update their hazard analysis.
And we were interested in the – in the engineering side – the dynamic analysis.
This one’s also interesting relative to the broadband platform because
there’s a full 3D velocity model that’s used for the wave propagation.
And so things like sedimentary basins and other kind of geometric complexities
that we think are important down there, those are very hard features to represent
in recorded ground motions when we’re taking recorded ground
motions from all over the world. So if we could get simulations that
are reflecting those complexities, and we felt comfortable using them,
I think that would be a great opportunity for engineers designing, say,
the tall buildings in that area.
So we thought about a site in L.A. downtown – that’s that LADT site.
And so that’s kind of partially in this basin – the L.A. Basin.
And it’s a place where we’re designing tall buildings and
building tall buildings that are using dynamic analysis, and there are
sophisticated engineers who would be open to these types of things.
So we wanted to show them kind of what these ground motions
would look like. So I’ll go through a little more quickly.
So the dashed black line here is that target spectrum
from ASCE 7-16 – the same one we talked about before.
And then what we did is, we went through the CyberShake database
and went and selected ground motions, and so here those simulations
were already available. And we just went to the LADT site
and said, what are the ground motions most closely matching that
target spectrum? And so those are shown in green here.
There were 400,000 ground motions to choose from, so it was pretty easy
to find a few that were closely matching that target spectrum.
And kind of the same game. So in the top row is this
L.A. downtown site. On the left are the simulations,
and on the right are the – we did a comparable set of selections from
recordings, again, to do the comparison. And we did the whole exercise at a
second site in Pasadena outside of the basin, and that’s in the bottom row.
So I’ll kind of flash at you a couple of the same types of things.
So on the – on the left here, I’ll show you – so the tectonics are a little more
complicated in southern California than they were at that Berkeley site.
So de-aggregation now shows contributions to shaking from
a lot of different sources. So the far left column –
and so the top row is L.A. downtown. The bottom row is Pasadena.
In the top, we’ve got a de-aggregation at a 1-second period.
So we see lots of contributions from kind of zero to 20 kilometers on the far right.
And kind of magnitudes 6 to 7-1/2, something like that.
Puente Hills is a big contributor and kind of other [inaudible].
If we go to the middle column, in that top row, now we can see –
I don’t know if this – does this mouse show?
We get this contribution from the San Andreas Fault that pops up.
So magnitude 8s out at 50 kilometers. So one thing that I always try to kind of
communicate to engineers, if we go back to that language in the building code
about, we need time series that match the magnitudes and the distances of the –
of the faults, you know, causing the ground motions, if you look across
a wide range of periods, there is no unique set of faults kind of
causing the ground shaking at all periods.
Yet, we need time series that kind of represent kind of all periods.
So we’re always in a little bit of a conundrum there.
But – so but anyways, with these de-aggregations as motivation,
we went and selected ground motions. So with the NGA-West recordings –
so these are the empirical recordings – we manually tried to fit those –
you know, tried to match those distributions.
Although it’s pretty hard to find kind of large-magnitude recordings that have
kind of the right response spectra. So we didn’t do well there.
With CyberShake, we didn’t have to try – we didn’t constrain
the faults or the magnitudes and distances very much.
We primarily were just searching off the response spectrum.
And we could do a better job of kind of getting a few San Andreas ruptures
and things into the record set without messing around too much.
So we get kind of 11 ground motions and 11 ground motions again.
These are some of the CyberShake ground motions.
Just a flash that – say, on the left, there’s a couple Puente Hills
simulations that are kind of 10 or 15 seconds of shaking –
kind of very intense shaking, you know, close by to the site.
And then, on the right, you know, those fonts are maybe a little small,
but the time scales changed.
So these are much longer kind of time windows on the right.
These are some kind of big – there’s a Newport/Inglewood magnitude 7-1/2
and a San Andreas in the lower right kind of shaking for a minute or two.
You can maybe see some kind of basin resonance in that upper-right one,
and you can see some kind of static offset in the lower-right one.
So we see kind of the complexities that we would anticipate from some of these
rupture scenarios, which would be interesting for engineers to probe.
We’d like to see kind of this kind of dynamic feature diversity.
Because we’re trying to probe these buildings and see, you know,
under different types of circumstances, how is it going perform.
We checked this polarization. So as long as we defined that plot
before, I’ll show you another one. So this is that
RotD100-over-RotD50 plot. And the red line is showing an
empirical model. And the green and blue are showing their record set.
So everything looks good in terms of the polarization.
Kind of no concerns about that.
One thing that we did pause on, and we’re kind of continuing to talk to
Rob Graves about, is we did see some circumstances where we
saw strong polarization. Try to do this a little quickly.
So we – there were a few ground motions that came in
kind of unusually polarized. And so we kind of tried to probe
a little bit, what are the circumstances. So there are some situations – let me try
to not spend too long on these figures, but – so this is – we tried to pick some
different types of scenarios where we were – trying to get the mouse up
on the screen – where we were looking at this polarization.
So the maps show kind of a rupture and an epicenter and a station
where we took a recording from. And then these traces show velocity
versus velocity in the north-south-east-west directions.
So we can kind of get a sense of how strong
the shaking is in different orientations.
And then we’ve got a similar map – and we tried to look at a –
kind of a backwards directivity and a forwards directivity type of case.
So these are magnitude 7-1/2 or so ruptures on the San Andreas Fault.
The station is about 50 kilometers away.
And over all the different ruptures, there’s about 100 realizations, I think,
of this rupture with different epicenters, different slip distributions.
And over here is the – in kind of a dashed line,
is this referenced empirical model. Oop – went too far.
This reference empirical model for this polarization –
the RotD100 over RotD50.
And then the solid line is the – is the median of the – all the simulations.
And so we – usually we see things that look kind of
like the right, which is what we would expect to see.
So here’s a second case. I’m bouncing around.
So we moved in a little closer. This is 30 kilometers away from the rupture.
Same types of patterns. We see kind of good agreement.
Or now I’m lost of which one I was looking at.
So Case 1, Case 2 – these are 50 kilometers, 30 kilometers away.
Oh, man. I think this mouse is running backwards to what I expect.
Okay, so those look fine. But then there are some cases –
so this is a case kind of off the end of the fault where you might expect
a little more directivity, but it’s 50 kilometers away,
which is a pretty long distance for kind of coherent polarization
of the ground motions as we see it in empirical ground motions.
And, in this case, almost every ground motion was somewhat polarized in
the fault normal direction, roughly. And we get these plots where we
switch to kind of very strong polarization at long periods
in basically 100% of the ruptures. And so, to me, there’s some mix of
either kind of stronger – some sort of kind of radiation pattern or directivity
or something that’s really strongly polarizing these in a way that we
don’t have observed in our recorded ground motions.
Or there’s maybe something in the – you know, in the rupture generation or
some piece of the simulation algorithm. And so this is where – again, I’ll say
Rob Graves has been tremendously helpful in kind of explaining lots of
things through here, and we’re kind of continuing to talk with him about kind of
how pervasive this type of situation is, and is it real, or is it –
you know, is it an artifact of something in the simulation.
So, to me, I find those conversations really productive in trying to
move forward these things to engineering practice.
So these ground motions are all selected. They’re currently getting run
through a couple of building models. Again, working with practicing
structural engineers. So they’re kind of 3D dynamic building models.
The left building – this is a 40-story building.
Kind of one of these condo buildings that are going up in San Francisco
and Los Angeles that an engineering firm is analyzing for us.
That’s a real building that’s being built.
On the right is a building from Christchurch.
We found a – kind of an engaged structural engineer in Christchurch,
New Zealand, that was interested in kind of probing these things
and is running it through a model that they had available as well.
And so we’re kind of collecting those results and processing, interpreting,
to try to see, you know, what are we seeing as differences
between the recordings and simulations.
I think I’m going to go by this one.
I think this one will be kind of more interesting.
So, as we think through these exercises, and we’re trying to do these
comparisons, you know, on one hand, it’s a – it’s a relatively standard set
of analyses that we’re doing. The ground motion selection,
the structural analysis, is not groundbreaking
in any sort of academic sense. But what we really need to do is
kind of set the stage thinking about how these things hit the ground
in the real world. And so the things I think about is –
you know, as I’ve kind of worked with engineers who are designing buildings
or worked on some of these projects, you know, typically, there’s a –
there’s a very tight timeline and not a lot of slop in the budget.
I’m thinking about, you know, kind of commercial building projects.
You know, things get a little different if it’s a – kind of some sort of
unusual defense facility or a nuclear power plant or something like that.
But if it’s a – if it’s a condo building or something, there’s a developer
who wants that thing open as soon as possible.
And they don’t want to wait around for extra weeks or months for
kind of curiosity-driven kind of analysis of the building.
And the – you know, the engineers who are doing these are bidding
competitively on these projects, so they don’t put in, kind of, you know,
lots and lots of extra time to be kind of curiosity-driven analysis.
And, you know, especially on these developer projects,
that’s a lot of the stuff that goes up in downtowns.
These real estate developers really think about the earthquake
engineering as a commodity. Hopefully that’s changing as, you know,
we get this kind of nice run of public awareness of earthquake risks.
But I think generally, they say, you know, I want this building,
and what’s going to sell it is the beautiful floors and the beautiful views.
And whatever engineer can do this job for me on time and at a reasonable
budget, like, that’s who I’m hiring. I’m not hiring somebody because
they’re doing, you know, cutting-edge engineering,
you know, thinking. That’s – you know, each project
is different, but I would say that’s a pretty common situation.
And the other thing is, these unusual buildings, almost always,
when you have a dynamic analysis in the – somewhere in the loop
in the analysis, there’s a – there’s a lot more complexity that goes into that
structural analysis, and there’s a lot of decisions that the engineer has to make.
And those decisions can influence the – you know, the answers that
you’re getting out of your analysis, for good or for bad.
And so almost always, there’s a peer review team involved that’s kind of
watching over the shoulder and saying, did you think about this, you know,
what’s the basis for your assumption here?
Did you, you know, consider that this could go wrong?
And the idea is to kind of build in some robustness into the system that an
engineer doesn’t accidentally make an assumption that leads them to believe a
design is satisfactory when there was some overlooked flaw in their design.
But – so the good thing is that I think it builds some good robustness
into the system. The bad thing is it disincentivizes innovation, right?
So if I – if I’m the design engineer, and I walk in, and I say, I’ve got these
CyberShake ground motions, and I’m going to use these instead of recordings,
my peer reviewer may or may not be comfortable with that if they
haven’t seen some evidence that this is a reasonable way to proceed.
And so, you know, having, you know, literature available, having kind of prior
experience with these things is really important so that the overall team is
all comfortable with the path forward, that nobody wants to take a chance on –
you know, on some step in the analysis that, you know, drives the design of
a building that is hopefully going to be there for a hundred years and going to –
you know, influences the safety of the public.
And then the final one is that, you know, it’s pretty easy to
go get recorded ground motions. There’s these PEER websites.
There’s other software platforms. I could go get recorded ground motions
myself in, you know, five or 10 minutes, and I can go off and do my analysis.
And all the consultants that work in this space are comfortable with that.
If I want to use simulated ground motions, the story’s
a little more complicated, right? So 10 years ago, I had to, you know,
know the simulator and have some sort of plan.
You know, with some exceptions. Brad Aagaard had simulations up on his
website for many, many years, I know. You know, not everybody’s kind of
got those things out in public. Even if they are, you know, there’s still
questions about kind of the assumptions, and the engineer should have some
awareness of what’s going on. You know, some of these public
platforms for simulating ground motions have gotten better, but you still need,
you know, some understanding of how to get into those systems, and,
you know, it’s SQL queries to get at CyberShake ground motions and things.
And, again, given the tight budgets, tight timelines, to kind of stop and
do something out of the ordinary is just a friction in the system that’s not –
you know, not helpful in terms of getting to kind of a project delivery.
And so I raise these just to say, you know, none of these are
kind of irrational things. But they are real frictions that kind of
limit, you know, our ability to kind of innovate even if we have kind of pretty
good confidence that there are good ways to proceed.
And so, you know, if I kind of reflect on this, and I was putting these together last
night, I think, you know, a lot of these engineers, and the engineers that are –
that are running those structural models,
they’re all doing it on their own time, just volunteers.
They’re curious. They want to do a good job. They want to build good buildings.
And I think many of them say, well, you know, if you can tell me about,
you know, simulated ground motions and something new –
something that would make my design better, I’m all for it.
But, you know, looking at those above incentives, like, none of them incentivize
kind of, you know, trying to change the scheme there.
And so you really want to come in with a pretty good understanding of,
like, if I – if I make this change, and I don’t use my traditional method –
I use something new – I use simulations, what is the implications for the
performance of my building? What is the benefit for the project?
Because it’s going to be a risk.
It’s going to involve some kind of cost and time, potentially.
And so I think, you know, the more we can kind of put literature out there
showing that results are as expected or giving guidance on what features to be
thinking about when heading down this path, you know, the easier using
these simulations is going to be. And the other thing, kind of to that
last bullet point is, the easier it is to get a hold of appropriate simulations,
you know, the more likely they are to be used.
And that’s not science. It’s – you know, unfortunately it’s –
but it’s hard. It still takes time and resources
to kind of produce those portals or availability of data and things.
And so, you know, there are people at – you know, various people involved with
these simulations thinking about that. And I think that’ll be, like, another step
in this process of making these more mainstreamed.
Okay, so kind of wrap things up.
I’d say, you know, there’s a number of ways in which we could think about
using ground motion simulations or validating ground motion simulations.
Hopefully this was, you know, a little bit of a new way of thinking
for some of you, that really, it’s – you know, from the design spectrum
to the dynamic structural analysis, it’s kind of a distinct, you know, step or
distinct type of analyses relative to using these simulations for hazard analysis.
And actually, you know, the amplitude of these ground motions is not a –
kind of a first-order concern in the – in the talk today.
Like, the amplitude of the ground motions was specified before
I started any of these calculations. So if your simulations are a little low
in amplitude, I’m just going to produce more simulations until
I get some that are big enough, right?
So there’s a different set of questions involved with this step of the process.
And so we’re conditioned on that design shaking amplitude
and thought about kind of dynamic analysis and structures.
I would say, you know, big picture, the simulations we were looking at
were generally suitable for these types of purposes.
I think you’d get good designs, good assessments out of these.
And I think, in particular, if we think about situations like near-fault sites or
sites close to very large-magnitude – or, you know, faults that could produce
very large-magnitude earthquakes or sites in basins or some sort of unusual,
you know, geometric or geologic condition, you know, we could really
move beyond this traditional thinking of saying, well, I got to get a recording
from somewhere else, and if that doesn’t reflect all the, you know,
unique circumstances of my site, you know, that’s just what I got to do.
I think we could get around that, which would be really exciting and beneficial.
And so, you know, this work has all been kind of
in pretty close discussion with practicing engineers.
And I think we’re – kind of the next steps is to the continue kind of showing
these results to engineers, getting their questions, showing these results to the
people who do peer reviews and say, you know, if somebody brought these
to a project, what questions or concerns would you have
so that we can have them kind of addressed ahead of time and not kind of
get stuck in weeks and weeks of meetings to try to resolve them.
And then also think about, can we – can we produce some kind of standard
sets of simulations that might be available to be kind of more –
grabbed more quickly?
And all of that is certainly going on with the ground motion simulators.
And for me, personally, that’s happening a lot through SCEC.
And there’s other people around the world doing kind of similar things.
So those are a few thoughts of kind of where I think the state of engineering
practice is with use of these. I think the future is bright.
And hopefully these are kind of some food for thought about ways we might
be able to make progress in kind of mainstreaming these tools more
broadly in the engineering community. So thanks for your attention this
morning, and I’m happy to take questions for a while.
[Applause]
- [inaudible] your three-dimensional building model.
- Yeah.
- Maybe it’s a typo. You have two designations – BRBF.
- Yep. - And then BRRF.
Is that a typo, or … - It could have been. I don’t remember.
- Because what is BRRF? - Let’s make sure I got the
right slide first, and then let’s … - Yeah.
- We’ve got a buckling restrained brace frame.
Yeah. I think that’s a BRBF, that should be the acronym.
- Okay. - So that’s – these are these diagonal-
braced frames that have the kind of concrete
encasement around a steel brace so that they can kind of yield in compression
and tension. You see them kind of on lots of the projects around here.
So, yeah, it’s buckling restrain brace frames is all of the red portions.
And then the moment-resisting frames are these – the portals
without the diagonal brace in them.
[Silence]
- Thanks, Jack. That was a really great talk, and I learned a lot, for sure.
So I have a question about the scaling. And I know you’re not really
talking about that, but I think you do other work on scaling?
- Yeah. - Could you maybe go to
the table that I liked. [chuckles] So I guess maybe can you add some
insight – this, and then – and then – I guess my question is that,
in the simulations, you don’t have to scale because you’re specifying
the exact magnitude and distance and target that you want.
But on the recordings, you have to scale them.
And, as you said, you try not to scale them too much, which is great.
But aren’t you inherently then changing the frequency
content when you’re scaling them? And then, if you go to the next slide,
is that resulting in – oh, maybe it’s not as obvious.
But it seems like you get more – a wider range of periods on the recordings
than you do on the simulations. So is that …
- Yeah. - … better? Does that imply the
simulations are better in that sense? Or are you missing some …
- Yeah, that’s … - … variability? Or, inherently in the
recordings, you’re changing the stress drop of the events, right?
Because you’re scaling the time series but not the frequency content?
- Right. Yeah.
- I don’t know if there was a question there. [laughs] My understanding.
- Yeah, no, no. I was going to say, that’s a great topic to probe a little bit –
this ground motion scaling. So it is pretty standard – I’m trying
to think if I’ve ever seen a project where it didn’t happen.
It’s pretty universal that we’re going to amplitude-scale these ground motions.
Because we’re looking at these high amplitudes where we just
don’t have a lot of recordings. And that’s one of these – so that,
I would say, is one of the big – one of the big question marks on
the use of recorded ground motions. It’s just been going on for 30 years.
And so we kind of quit asking the question as freshly as we ask the
questions about the new – the new alternative in town.
So I would say – so, when we do that, we basically take all the accelerations
and just multiply them by some constant. So this – in terms of these response
spectra, because it’s the response of a linear oscillator, if we – if we
double all the amplitudes, the response of the linear oscillator will just double.
So these response spectra will just move up and down vertically as we scale.
So there’s not any change in the –
like, the relative amplitudes with frequency or anything.
And so it’s convenient, actually, for finding ground motions
because I just have to go find a shape, and then I can pick the scale factor,
then kind of dial it in. It’s not physical.
And the – I think the – you know, it went out when the competitor was,
take a real recording and amplitude-scale it, or modulate white noise.
Because the real recording at least has some sort of non-stationarities
and some other complexities in it.
Although it’s no longer kind of the recording that came from an earthquake.
So, yeah, so that’s very much a flaw in the current scheme, or a limitation
of the – of the current practice. It’s just – it’s been done so many times
that there’s kind of more comfort with it. You know, and I – to a first order,
these response spectrum – and maybe I should have made that more explicit –
these response spectra are, like, the indicator of how the building
is going to perform. And so basically, when you see
these response spectra matching up strongly from left to right, you’ve got
a pretty strong sense that the building response is going to be the same.
So a building is more complex than a linear oscillator,
but these things are pretty predictive. And so, you know, some studies have
tried to use kind of unscaled ground motions versus ground motions scaled to
the comparable spectra and then look at the demands on the structure.
And, you know, in a lot of circumstances,
they’re pretty comparable. So I don’t – I don’t lose sleep over it,
but I think you’re very right to point this out as, that’s clearly
an inferiority of using recordings versus using simulations.
- So do you think there’s any advantage in that sense to the simulations, then?
- Yeah. Definitely. - And are you saying that
this is just one example? Is that something you’re
sort of advocating or seeing? - Yeah. So I think, you know,
in terms of this table, like, all – every one of these columns kind of
comes down on the side of the simulations, right?
I’ve got those – I’ve got the seismic, you know, event pinned down
exactly what I want. I’ve got my site pinned down exactly
what I want, especially if I’m doing kind of 3D, you know, crustal modeling.
And I’ve got the amplitudes kind of that are naturally resulting.
And so, yeah, conceptually, it’s far superior, right?
So I’m not – I’m not here to – yeah, I mean, I think it’s the future.
And I’m really just – I’m trying to think through, like, what are the steps we
need to – you know, to get through so that that future is realized?
- Keeping on the same theme, I think what Annemarie’s point –
when she was getting at the frequency is that the simulations for, like,
a magnitude 7 or, like, a real magnitude 7 may have different
frequency content than a magnitude 6.5 scaled up.
- Yeah. - So it’s not necessarily that the
scaling changes the frequency, but you actually have the wrong frequencies
when you’re scaling the recordings. - Sure.
- And so my question is, you showed the example for a five-story building.
And so it’s primarily going to be responding to higher frequencies.
Ground motions are a little more stable at, say, higher frequencies than they are
at sort of long periods, and especially when you’re scaling and you’re – if the
longer periods are more interesting, in the NGA-West2 database where
they filtered out a lot of long periods, we may see a bigger discrepancy.
And so I’m curious, are you aware of sort of systematic studies that have
looked at cases where you’re in in-close large-magnitude events where we think
PGV and PGD are going to have a greater importance,
and the scaling may be inaccurate showing that we may have issues
there when really – when we use that approach for design.
- Yeah. Let me think of – couple thoughts on that.
So, yeah, so I guess I see your point about the – when I’m taking some
of these events that are from kind of some different magnitudes, certainly it
relates to the frequency content. The site conditions, similarly.
And so there is – those things are playing a role in the –
in the frequency content present in the recordings.
I would say, in this particular step of the analysis, we mitigate that a lot because
we’ve specified a design spectrum. And so it may be that most
6-1/2-magnitude earthquakes have less, you know, low-frequency energy
than the one that I want, but because I’m specifying a design spectrum,
I’m only going to pick the 6-1/2-magnitude recordings
that had a lot of low-frequency energy consistent with what the
hazard analysis said. So it’s really the hazard analysis
that has to catch the appropriate kind of amplitudes.
And then here, we’re picking a kind of small subset of
recordings that match that. So I would say we’re somewhat robust
to that issue, but it is a – it is a real issue in this – again, in this manipulation here.
Yeah. So the one particular building I’ve got is not the – it’s not the
poster child for using simulations because it’s got a shorter period,
and that’s kind of where things are less interesting.
One of the buildings that’s currently getting analyzed is a 40-story building
with a 5-second period, and I think that’ll be more interesting in kind of
getting at some of those longer-period issues.
Yeah, there – I mean, there is some literature on kind of trying to look at
sensitivity of these record properties and what’s predictive of response.
And – but, you know, these giant data sets of simulations are going to let us
take a much more refined look at that, I think, than kind of the more limited
studies we’ve – to some degree, we’re limited when we use empirical
recordings to do this because we’ve got hundreds or thousands of permutations
we can try rather than, you know, many, many thousands.
- I have a more general question. You said that this kind of a dynamic
analysis is used for designing new buildings.
Is there any effort underway to look at the existing inventory of buildings
that weren’t designed with the sophistication now available to us
to see which ones are at risk?
- Yeah. Sure. So there’s – I think there’s two issues.
There’s kind of the – yeah, the sophistication of the building designs.
And then it’s – there’s a question of whether the building was designed
or analyzed using an explicit dynamic analysis
or some sort of an equivalent static analysis.
So the – I guess the broader question of kind of existing buildings
and their safety is a huge, you know, issue for us in the engineering
community and just as a society. And we have, you know, all sorts of
efforts going on in the research world and in the – you know, in practice to
upgrade older buildings and in the policy world, you know,
San Francisco and Los Angeles have been kind of leaders
in trying to mandate some of these upgrades.
In terms of the way that those buildings are assessed or the way that they are
designed, really the split is not so much on new and old as much as the
complexity of the response and whether we think kind of explicitly understanding
the dynamic behavior is important. So I might have a – you know,
a three-story concrete building, and it could be a brand-new building
that I think is going to perform excellently, or a 1960s building
that I think is really dangerous. It’s a – it’s a relatively simple problem
in terms of the way it’s going to respond dynamically.
And so generally, we think we can get a pretty good understanding of the
performance of that building, whether good or bad, by analyzing it statically.
And it’s just a much – it’s a much simpler problem to do a static analysis
and then to say, well, under this amount of static load,
I’m getting bad performance. So I can then infer that,
under strong earthquake shaking, I know I’m going to get bad performance.
So the two are related but somewhat independent questions.
And sometimes with these older buildings, it’s pretty clear-cut that the
performance is lacking in some way, and there’s maybe some particular detail,
like a beam-column connection that we know is lacking.
And building a sophisticated computer model isn’t going to
bring us more information. We know we need to improve it in some way.
And really, the question is about how to improve it rather than really getting a
detailed understanding of the dynamic behavior, if that makes sense.
- Yeah, Jack. For the 11 simulations, it was like you
got 11 earthquakes that are all the same. - Yep.
- And, of course, they aren’t. Or I hope they aren’t.
- No.
- And they aren’t, as showed by the response spectra.
Just what is the variability from one event to the other?
And is there any rupture propagation here if something starts off to the south?
- Yeah.
- These are kind of maybe 30-kilometer- long ruptures, just for example.
And it starts off to the south and ruptures toward you.
Your polarization is going to be one thing, but as it ruptures past you,
it will be very different. - Right.
- And, as it goes past you, it’ll be different yet again.
And then, as Annemarie was saying, the stress drop can vary.
- Yep.
- All kinds of things can vary, so yeah, what is the range of
variability in those models? - Yeah. So these are – yeah,
good question. I should anticipate that in this community.
So these are all kinematic rupture simulations, and the – I think the rupture
geometry was pinned down – kind of, if you pin the geometry
versus pinning the magnitude. I think the geometry was specified,
and there was 10 hypocenters placed, you know, a couple depths, and then a
long rupture in a few different places.
And then there’s a kinematic rupture generator, and I think we ran 10 ruptures
for each hypocenter location of just the slip distribution over time.
And so that’s – so it’s almost all rupture variability.
So there’s no path variability. It’s the same fault.
It’s the same site every time. And it’s just different realizations
of the – of the slip that are generating the variability in the ground motion and
the variability in the response spectra. - So that’s the closest distance because
then these different hypocenters could be – would be different
distances from the building. - Right. So some of them the hypocenter
is close to the site, and it’s mostly rupturing away, and some are bilateral.
Some are mostly rupturing south to north.
This is up pretty close to the north end of the fault, the site.
- Okay. And so, in the ...
What is the principle – is directivity an important source
in the variability that we’ll see on the next slide?
- Well, so the rupture – the variability is driving all of this.
Kind of how we – how much we want to attribute to directivity.
- Yeah.
- I would say – I mean, the interesting things is, because we’re – you know,
we’re specifying ground motion amplitudes that are bigger
than the median amplitude. And these simulations are
pretty well pinned that kind of median amplitudes look like
the medians we see in recordings.
But these high amplitudes are generally – kind of rupture towards
the site – kind of a classic forward-directivity-type situation.
Because the backwards directivity situation generally gives you
lower-amplitude shaking. And then we wouldn’t pick them, right?
So this is only a subset of all the simulations, and it’s basically the –
loosely speaking, it’s the 11 strongest simulations.
So – and that’s always a – you know, the question is not really explicit in our
hazard analysis or in our ground motion selection, but, you know, usually we’re
thinking about a magnitude and a distance, which is a pretty simple story.
But implicitly, I think there is an assumption in the forward directivity
when we’re saying we want a stronger- than-average ground motion amplitude.
Or whatever the rupture and wave propagation circumstances give us the
biggest amplitudes, more generally. - So one final question, then.
The short period – at short periods, the variability looks to be significantly less
for the simulations than the recordings. - Yeah.
- Do you have any thoughts on that? - I do. Yeah.
So this is the subtlety of this whole game that I didn’t bring up explicitly.
So when we – when we go find these time series, we have to – so there was
the language back on the – when I had the picture of the ASCE 7 book that said,
you have to find ground motions consistent with the response spectrum.
And it’s over a particular period range. So we do this – we establish ahead of
time what the period range that we think is important for the building.
So loosely speaking, we’ve got, like, kind of a first-mode period
of vibration. We double that.
And then we would go down to, like, a second- and a
third-mode period of vibration.
And say, over that whole range, I need to get a pretty good match.
And then outside of that range, I’m less concerned because
I don’t think that’s really indicating what’s going to happen to my building.
So when I work with recordings, that – as soon as I shut off that
kind of window, things can go a little bit more wild.
Because that’s where the record scaling, for instance, can be an issue.
If I’m not pinning the spectrum at these other frequencies, and if I’m bringing a
low-magnitude earthquake up to bigger amplitudes, those high frequencies
are coming up maybe too high. Whereas, in the simulations,
that’s less of an issue because I’m not doing the processing.
So it’s – that’s another thing that – and in these high-rise buildings,
these – you know, the short frequencies, you know, that might be a hertz still.
And that can be important. You know, the good news is,
our kind of – our scaling stuff that’s, you know, fingernails on a chalkboard
for many of you, I think, it only overloads the structures because
you get these big kind of high amplitudes over at the far left.
In the simulations. That’s a little bit less of a problem.
So it is an artifact of these complicated rules,
but I kind of dodged explaining all the details in them.
So good eyes to catch that.
- So I – you – I find it interesting that, on your drift plots, you have only 11 or
so records, and you choose the median, and it looks fine, and you move on.
- Yeah. - The building’s good.
But two or three of the records show the building is damaged.
- Yeah. Well, so yeah. That’s a – it’s an interesting thing,
and I sometimes talk with – so talk with engineers about this.
But certainly, in the code development – oh, I overshot, didn’t I?
In the code development world, we talk a lot about this stuff too.
So the idea – there we go.
So these figures were – we just kind of looked at the heavy red lines,
and we didn’t look at all those gray lines. But some of the gray lines can be,
you know, double the red line in terms of amplitudes.
So it’s not that we ignore those things. It’s that we don’t think we can measure
them from 11 dynamic analyses. So if you let me do 40 of these analyses,
or, you know, 50 or something, then I would start to feel more confident
about being able to estimate a probability distribution.
So what – but that is not – that’s kind of a deal-breaker from the people in these
design offices trying to get these designs to crank through.
So what we’ve done is we have – and building codes in general,
for other types of loads as well – live loads and wind loads and
everything, we do the same thing. That we really – we pin ourselves
off these nominal values. So I’ll say the average of my, you know,
drift ratios – or, story drift ratios has to be less than 4%.
And if that’s the case, and if I have some – as a code calibration exercise,
I’ve got an idea of how much variability I’m going to see in a typical building
of this type. There’s other factors in there that builds in – safety in.
So it’s not that if any one of these gets past 4%, the building is in –
you know, is not going to perform. It’s – I might think I’ve got a 6 or 7%
capacity, but I can – based on kind of uncertainty in what that capacity is, and
based on the variability from record to record in my responses, I can back off
that an average of 4% will get me kind of an acceptable kind of margin in here.
And there’s a whole bunch of factors like that.
There’s – some of you have probably heard about kind of R factors.
That’s kind of a big, famous one.
There’s factors around kind of the means versus the tails.
When we design – when we choose the return period of the ground motions
we’re designing for, there’s another factor, right?
And none of that is to say that the building is indestructible.
But we’re calibrating towards this kind of low probability that the
building could have a collapse. And all those decisions are somewhat
hidden from the designer so that the designer has got kind of a more limited
set of calculations they have to think about.
And then the code, hopefully, has built some robustness that,
if those limited checks are sufficient, then we’ve got confidence that the
real reliability of the system is okay. So that’s the philosophy behind that.
- Okay, we have maybe one last question from Mehmet, and then
we should probably wrap this up. - Okay.
Well, I hope this won’t take too long. But I was a little bit concerned about
the simulated – simulation table where you have Vs30, I guess,
because it’s not clear to see. You have all 500.
Now, how does that relate when you consider basin effects,
for example, as you mentioned in Los Angeles?
That we know from Tohoku, what happened in Osaka and Tokyo.
Then there’s Dubai – tall buildings, earthquakes from Iran.
And when you go to depths of 2,000, 3,000 meters, then obviously the Vs30
being to 500 meters per second doesn’t bode well at all.
I mean, we have evidence of this, and we have databases.
And writing – Brad can talk about this database and all this.
- Right. - Yeah, so in a sense, is there –
there’s no connection. I don’t see the connection.
Do you have some suggestion on this?
- Sure. Yeah. So for this particular site in Berkeley, they had geotechnical
investigations, and they had a site profile, and then this 500 …
- Oh, this is only for Berkeley.
- Yeah. This is for that Berkeley site. So basically, we specified the site
conditions, and then, in the broadband platform, you’ve got some kind of
limited ability to address that condition. So – but the basins – so more broadly,
thinking about the role of simulations, I think sites in basins is one place where,
again, simulations would – that’s the future.
Like, we just – we can’t make progress on that problem
with kind of traditional techniques. And so, to the extent that these
simulations can reflect basin effects, that’s going to be a great asset for us.
I will say, you know, kind of, as we think about this path forward, so the –
you know, the Los Angeles basin has been kind of a very, you know,
well-studied basin in the simulation world by some of the people
that I work with. You know, the amplitudes associated
with kind of waves, you know, getting channeled into that basin
and things have – they’re not, you know, necessarily fully stable across kind of
simulation algorithms or iterations of these things.
And then that Vs30, that near-surface site conditions, you know, when we
have very soft soils and we have nonlinear amplification, I think there’s
also still opportunities for the simulations to further improve
in some of those regards. So these are those complex situations
where we could really benefit from further insights.
But they’re also complex problems from the scientific perspective
to kind of get them right. And so I – yeah.
But even as we sit here today, there’s really big opportunities to get, you know,
more insights out of the data that’s existing today.
And I think that’ll only get better over time as you all continue your science.
Thanks. - All right. Well, great.
Thank you very much.
Please join me in giving our speaker another round of applause.
- Thank you.
[Applause]
- And if you’d like to join us for lunch, we’re going to leave pretty soon, so
please come on up, and we can continue this conversation over lunch. Thanks.
- Thank you.
- That was fantastic. - Thank you.