Limitations of vs30 etc.

Limitations of Vs30 for characterizing sites for
ground motion studies and guidance on the
conduct of nonlinear site response analyses
By Robert Pyke Ph.D., G.E.
Robert Pyke, Consulting Engineer, Walnut Creek, CA, USA
March 2020
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An explanation of the long title:
• This presentation combines several issues related to site effects on observed earthquake ground
motions at the ground surface
• It discusses how site effects are treated in building codes and explores possible improvements
• It also notes some issues with the new ASCE 7-16 requirements for Site Classes D and E
• While they are not always required and are sometime inappropriate, site response analyses
assuming vertically propagating shear waves can be helpful in understanding these issues
• But they can also give erroneous results if the engineer is not careful, so guidance is offered on
how to conduct modern nonlinear effective stress site response analyses
2Page 2 of 57

Outline
• Basic principles
• Complications
• Code issues
• Examples
• Comments on nonlinear effective stress site response analyses
3Page 3 of 57

Analytical framework
4
It is assumed that soil layering is horizontal and
that there is a semi-infinite half space below the analytical modelPage 4 of 57

Basic Principles
• For cases when it is reasonable to assume that the bulk of the incoming energy is in the form of
vertically propagating waves, which generally implies horizontal soil layer boundaries, the
amplitudes of motion at all frequencies will be increased
• For an elastic material, the increase can be computed as shown in Dobry, Borcherdt et al (2000) as
a function of the damping in the soil and the impedance ratio at the base, where the impedance is
given by the mass density times the shear wave velocity
• For nonlinear materials, e.g. soils with shear strains above 10-3 percent, strain dependent
hysteretic damping will increasingly wipe out the higher frequencies as the amplitude of the
incoming motion increases – see the next slide
5Page 5 of 57

6
As a result, short period motions are attenuated and longer period motions are amplified
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The significance of a clear impedance contrast
• The preceding mechanism, while generally true, applies most directly to sites that do not have a
clear impedance contrast ( 10 to 20 percent or more) between layers within the top several hundred
feet, say 100 m, of the ground surface.
• For sites that do have a clear impedance contrast between layers within the top several hundred
feet, there are additional considerations as waves reflected at the surface will be at least partially
reflected again at the impedance contrast. These are the sites for which site response analyses make
the most sense.
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Thus there are basically two kinds of sites:
• Those without a well-defined impedance contrast within the top several hundred feet, for which
site response analyses are not applicable and ground motion prediction equations (GMPEs) based
on something like the present building code site classes are the best way to obtain estimates of
ground motions at the ground surface
• And those with soft soils at shallower depths underlain by a strong impedance contrast, where site
response analyses can and likely should be conducted using input motions defined by response
spectra obtained from the building code or applicable GMPEs and deterministic or probabilistic
hazard analyses as input
8Page 8 of 57

Further complications:
Even if the assumption of vertically propagating shear waves being dominant is valid, the calculated
surface response will be a function of:
1. The depth to the first strong impedance contrast, if any
2. The “weighted average” shear wave velocity over that depth
3. The shear wave velocity of the half-space below the analytical profile
4. The presence of any horizontally continuous soft or liquefiable layers
5. The presence of any horizontally continuous stiffer layer can also impact the results by
increasing the cyclic shear strains in adjacent layers. This can have the surprising effect of
increasing the damping in those layers and lengthening the period of the site
Note that thin layers are generally a problem and may in fact just be lenses
If that is the case, they should be excluded from a 1D analysis
9Page 9 of 57

Thus there is variability in site response!
• Ground motion prediction equations that emphasize a single simplified parameter,
such as Vs30, have large standard deviations
• Site-specific site response analyses can be sensitive to input assumptions and
require some thought – they cannot be automated
10Page 10 of 57

History of code provisions
• Following earlier analytical studies of site response effects by Martin Duke at UCLA, Harry Seed and
Ed Idriss at UC Berkeley; and Bill Joyner, Roger Borcherdt and others at the USGS; and others; Seed,
Ugas and Lysmer (1976) developed an empirically based set of spectra for different soil conditions
that were scaled to the PGA.
• These standard shapes provided the basis for the recommendations contained in the ATC-3 report
• The Seed, Ugas and Lysmer and ATC-3 spectral shapes are shown on the next two slides
11Page 11 of 57

12
Seed, Ugas and Lysmer (1976)
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13
ATC-3 Spectra, which were based on Seed, Ugas and Lysmer
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Establishment of current site classes:
• Building on work done by the USGS, the current site classes, A through E plus F, were conceived in a
workshop held at USC in November 1992. The site class is determined by the value of Vs30, the weighted
average shear wave velocity over a depth of 30 m or 100 feet
• The boundaries between site classes A and E are shown on a subsequent slide. Site Class F, requires site-
specific site response analyses for sites with liquefiable layers or more than a specified thickness of peat,
high plasticity clay or soft to medium stiff clays
• The spectra are no longer scaled to pga, but set by factors Fa and Fv which multiply the spectral
amplitudes at 0.2 and 1.0 second periods for a reference Vs30 of 360 m/sec (the boundary between Class
B and Class C)
• The values Fa and Fv vary with the amplitude of the reference motions and the specified values have
varied over time. The current values are found in ASCE 7-16 and are discussed and illustrated in the next
two slides
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ASCE 7-16
• Provides the basis for 2019 building codes
• Shown on a semi-log plot on the next slide in order to go out to 10 seconds
• The spectra that are shown are for the minimum deterministic values of Ss = 1.5 g and S1 = 0.6 g
• The spectra for Site Classes D and E are not for direct use but the spectra obtained from site-
specific hazard / site response studies cannot be less than 80 percent of the spectra constructed
using the code specified parameters
• Relative to previous versions the “roof” on the Site Class C spectrum has been raised as a result of
increasing Fa to 1.2 from 1.0, and the spectra for Site Classes D and E have been “widened” in order
to increase the values at longer periods
15Page 15 of 57

16
ASCE 7-16 Spectra – the widened shapes for Sites Classes D
and E are not inconsistent with Seed, Ugas and Lysmer (1976)
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ASCE 7-16 provisions for Site Classes D and E
• The provisions of ASCE 7-16, implemented in the2019 CBC and many other building codes, include raising
the value of Fa for Site Class C to 1.2 from 1.0, which lifts the flat top on the MCE and design response
spectra, and, most importantly, require a “ground motion hazard analysis” for structures on Site Class D
and E with S1 equal to or greater than 0.2 (that is most California sites). While there are some exceptions
allowed for Site Classes D and E, these are generally more onerous in terms of structural design and will
not be exercised by most structural engineers
• There are some issues related to this language for Site Classes D and E. The required “ground motion
hazard analysis” can be conducted using ground motion prediction equations (GMPEs) which are a
function of Vs30, however, for the San Francisco Bay Area there is uncertainty in the maximum
magnitudes of future earthquakes on the San Andreas and Hayward faults and because the uncertainty in
the GMPE’s is especially large for softer soil profiles the predicted values blow up at long return periods
and small probabilities of occurrence. The most rational way to comply with the new code requirements
is to use acceleration histories fitted to a Site Class B or C spectrum as input to a site response analysis at
an appropriate depth and to rely on this analysis to account for the effects of the site conditions on the
surface ground motions
17Page 17 of 57

Why are site response analyses conducted at the MCE level?
• Because the code says so (in Section 21.1.1)
• Hence the examples shown in this presentation are at the MCE level
• But the design level or DBE level is still a flat two-thirds of the MCE. Does this make any sense?
• Only on the basis that the code is necessarily simplified. Because soil behavior is nonlinear, the
relationship between the MCE and the DBE would logically vary with the amplitude of shaking (as is
illustrated later in this presentation). It would be more logical to conduct separate site response
analyses for the DBE using input motions that are two-thirds of the input motions used for the MCE
analyses. In special circumstances it might be worth seeking the approval of the Building Official to
conduct separate site response analyses at the DBE level
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Possible further improvements:
• It is intended that the next major update to the code will use a “multi-period” approach rather than the current “two-
period” approach using mapping by the USGS, Petersen et al. (2019), that provides spectral accelerations for 22 periods
and 8 values of Vs30. This should generally be an improvement, but the multi-period spectra may still be unnecessarily
conservative because of the large variability in softer soil sites
• One possibility would be to take the depth of the softer soils into account in those cases where there is a well-defined
impedance contrast. This can be accomplished by using the low-strain site period which is a function both of that depth
and the weighted average shear wave velocity to that depth
• In current discussions regarding the updating of Eurocode 8 (Pitilakis et al., and Paolucci, 2019), there is talk of using the
fundamental period to “seismic” bedrock, normally taken as a shear wave velocity of 800 m/sec , or the fundamental
period interpreted from microtremor measurements as part of the classification scheme, however, both these
alternatives are flawed
• But the low-strain site period to the depth of a strong impedance contrast could be established with some certainty if
that were a useful thing to do. For reference, the low-strain site periods that correspond to the existing site class
boundaries assuming a strong impedance contrast at a depth of 30 m or 100 feet are shown on the next slide …
19Page 19 of 57

Low strain site periods at soil class boundaries
Layer Boundary Vs in ft/sec T in seconds
A/B 5000 0.08
B/C 2500 0.16
C/D 1200 0.33
D/E 600 0.66
20Page 20 of 57

Two examples of nonlinear site response analyses for Site Class E:
• In order to explore the usefulness of using low-strain site period as the basis for site classification, we look at
the two Site Class E profiles that are shown on the next slide
• 301 Mission Street, San Francisco, (a.k.a. Millennium Tower)
Based on a profile developed by Slate Geotechnical Consultants and included in publicly available documents
but of uncertain accuracy, this site has a Vs30 = 538 ft/sec, which puts it in Site Class E. Over the full 240 feet
depth to Franciscan bedrock the weighted average shear wave velocity is 680 ft/sec and the low-strain site
period is 1.41 seconds
• A typical site in Foster City CA (slightly modified from a real site)
The depth to “bedrock” at this site is unknown but denser sands and gravels, equivalent to Site Class C are found
at a depth of 200 feet. The Vs30 = 449 ft/sec, a little lower than for the Millennium Tower, which pushes the site
further into Site Class E, but the low-strain site period over 200 feet is almost the same at 1.39 seconds
21Page 21 of 57

Young Bay Mud
Young Bay Mud
0
50
100
150
200
250
0 200 400 600 800 1000 1200 1400
Depth-feet
Shear Wave Velocity - feet/sec
Millennium Tower
0
20
40
60
80
100
120
140
160
180
200
0 200 400 600 800 1000 1200 1400
Depth-feet
Shear Wave Velocity - feet/sec
fill
Typical Foster City Site
Fill
Sand
Sand
Old Bay Clay
Sand
Old Bay Clay
Fill
Young Bay Mud
Sandy Clay
Old Bay Clay
Sand
Old Bay Clay
Sand
Old Bay Clay
22Page 22 of 57

Computed ground surface response spectra
• The ground surface 5 percent damped response spectra computed using the program TESS2 are
shown on the following slide
• Further details regarding TESS2 are provided below
• Again, the spectra are shown on a semi-log plot in order to go out to 10 seconds
• Comments on the results obtained follow the next slide
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24
Computed ground surface response spectra
Millennium Tower Foster City Site
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Comments on results
• Note that two effects are combined – the input motions for the Millennium Tower site are fitted to
the ASCE 7-16 Site Class B spectrum and those for Foster City are fitted to the higher amplitude
Site Class C spectrum, in addition to the two sites being somewhat different even though they have
the same low-strain site period
• But the upshot is that the results are quite different. The ground surface response spectra for the
Millennium Tower site fit within the new ASCE 7-16 Site Class D spectrum (although they exceed
the motions for which the retrofit is designed) while the ground surface response spectra for Foster
City at longer periods fall outside even the new ASCE 7-16 Site Class E spectrum
• Thus it would seem that use of the low-strain site period is not such a good idea. Site response is
too much impacted by nonlinear behavior, especially in soft soils, for this to be a useful parameter
25Page 25 of 57

Conclusions regarding Vs30
• It turns out that Vs30 is probably as good a measure as you can get for a basic site classification
which does not take the depth to any clear impedance contrast and the strength of shaking into
account
• But there can be great variability in the sites that fall within any site class, particularly for Site
Classes D and E
• Therefore there will be significant uncertainty in the GMPEs developed for these site classes in
particular
• Design using the standard code values for the various site classes will always be approximate and
greater precision will normally be obtained by running site response analyses. ASCE 7-16 allows the
use of site response analyses even when it does not require them
26Page 26 of 57

What about Site Class C?
• The previous slide only talks about Site Classes D and E because they are called out
for special studies in ASCE 7-16, but it is also true that there can be great variability
in the sites that fall within Site Class C, not only because of the wide variation of
Vs30 of 1200 to 2400 ft/sec but also because of the varying depth to a clear
impedance contrast
• The following slide shows the computed ground surface response spectra for
profiles typical of Palo Alto CA with assumed depths to the Franciscan formation
ranging from 75 feet to 900 feet, inputting Site Class B motions at the base of the
profile. It may be seen that, although all these profiles would be classified as Site
Class C, the effect of the depth to “bedrock” is quite significant, and while the
ASCE 7-16 spectrum represents a reasonable average of these motions, the actual
motions might be much higher or lower.
27Page 27 of 57

28
Variation in ground surface spectra for Site Class C with depth to “bedrock”
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Does this change the conclusion about Vs30?
• No, this just confirms that the depth to a clear impedance contrast is important,
which we already knew
• However, there are several problems with trying to include the depth to a clear
impedance contrast in a simple site classification scheme. One this that is would
require more extensive site investigations; another is what form would the
classification take; but the kicker is that the strength of shaking would still not be
taken into account
• So, Vs30 still reigns but better results can always be obtained by running a proper
nonlinear site response analysis
29Page 29 of 57

Implications of Sections 21.3 and 21.4 of ASCE 7-16
• But ASCE 7-16 imposes certain restrictions on the way that the results of site response analyses are used, as
illustrated on the next slide
• Absent these restrictions what would make the most sense is to use a conservative average or loose
envelope of the computed ground surface spectra as shown by the curved response spectrum on the next
slide
• But Section 21.4 states that Ss cannot be less than 90 percent of the maximum value of Sa and that S1 has to
be calculated in such a way that the lower blue spectrum on the following slide is obtained. Further, in
Section 21.3, the MCE and design spectra are limited to 80 percent of the code spectra so that the upper
blue spectrum would govern for periods up to about 3 seconds and the site-specific spectrum would govern
beyond that. This code provision is intended to prevent designers from using excessively low values as a
result of errors or other flaws in the site response analyses. That is not the case here.
• On projects where the 80 percent limitation is significant, the building official should be requested to waive
strict compliance with the code. See also Kumar et al. (2018) (but note that their computed spectra are in
fact impacted by erroneously adjusting the modulus reduction curves to match the static shear strengths
(see Slide 46 below)).
30Page 30 of 57

31
Illustration of construction of MCE response spectrum
in accordance with Section 21.4 of ASCE 7-16
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Sensitivity studies
• The sensitivity to further details of the analyses of the Foster City site are shown on subsequent
slides. The sensitivity is shown for two variations in the input motions – the amplitude of the input
motions and, for the actual MCE level of input motion, an increase in the shear wave velocity of the
young Bay Mud from the actual measured values
• What is not shown …
Base impedance ratio – this does not have so much effect when soil behavior is highly
nonlinear, but it can make a significant difference when due to lower input motions or stiffer
soils the behavior is more linear
Modulus reduction curves – these usually do not make that much difference unless they are
erroneously modified in order to match the static shear strength. See further discussion on this
subject below. Nonetheless, don’t use sand curves for clays, and vice versa!
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More on sensitivity …
• Effect of a single soft or liquefiable layer - this can have a really big impact just as the soft young Bay
Mud has a big impact on this problem. However, sometimes liquefaction does not have a much impact
on the surface response spectrum because the maximum response occurs before the full development
of excess pore pressures. An isolated stiff layer can also have a big effect – see below
• Sensitivity to overall increases or decreases, like + or – 10 percent, in shear wave velocity – it is
sometimes recommended or required that this be tested, but that is wrong if you have good measured
values of the shear wave velocity
• However, if shear wave velocities are interpreted from other data such as penetration resistance or
obtained from poorer measurements of shear wave velocity like seismic reflection or anything with a
passive source, such as microtremor based measurements, a + or - variation should be checked
• If there are multiple good measurements of shear wave velocity at the same site, in general they
should be averaged rather than analyzed separately because the adjacent columns of soil must move
together
33Page 33 of 57

The effect of different values of Vs in the yBM
34Page 34 of 57

The effect of the amplitude of the input motion
35Page 35 of 57

What if there is no strong impedance contrast?
• You can either just use the standard GMPEs or conduct site response analyses to
multiple depths to explore the sensitivity of the results to both the depth of the
profile and the assumed base shear wave velocity
• The following example is typical of many sites around the south end of San Francisco
Bay (commonly called Silicon Valley)
• The site conditions consist of a thin layer of Holocene fat clay underlain by late
Pleistocene clayey silts and silty clays. A typical shear wave velocity profile from a
seismic CPT sounding is shown on the next slide. The weighted average shear wave
velocity over 100 feet is 746 ft/sec so that the site falls towards the lower end of Site
Class D
36Page 36 of 57

100 feet
Shear Wave Profile at
Typical South Bay Site
37Page 37 of 57

Alternate One: Site response analyses with varying depths
• As shown on the next slide, a suite of motions fitted to the ASCE 7-16 MCE spectrum for Site Class C at
this location was propagated using TESS2 up through the profile first with the measured shear wave
velocities to a depth of 100 feet, then with the measured values extrapolated to 200 feet, and then 300
feet, but remaining in the range for Site Class D
• It can be seen that there is a significant effect of depth with the effective fundamental period moving to
longer periods and greater attenuation of shorter period motions with increasing depth
• While there is uncertainty that results from the site investigation not establishing whether of not there is
a strong impedance contrast at a reasonable depth, for design purposes it would however be reasonable
to assume an MCE spectrum using the ASCE 7-16 values at short periods and 80 percent of the ASCE 7-16
values at longer periods
38Page 38 of 57

Results for Input at 100 feet
Results for Input at 200 feet Results for Input at 300 feet
Fit of Input Motions
39Page 39 of 57

Alternate Two: Site-specific hazard analysis
• It has already been noted that for the San Francisco Bay Area there is uncertainty in the maximum
magnitudes of future earthquakes on the San Andreas fault and also that the uncertainty in GMPE’s is
especially large for softer soil profiles so that the predicted values blow up at small probabilities of
occurence
• The South Bay site is located on the margin of San Francisco Bay where the deterministic evaluation of
seismic hazard governs over a probabilistic evaluation so that the magnitude used for future
earthquakes on the San Andreas fault is quite critical
• The mean + one standard deviation spectra using PEER NGA West 2 GMPEs, rotated to the “maximum
direction” as required by ASCE 7-16, are shown on the next slide for both magnitude 7.8 and 8.25
• It may be seen that even the magnitude 7.8 spectrum exceeds the minimum code spectrum at
medium to long periods
40Page 40 of 57

41
Results obtained from site-specific hazard evaluation
Page 41 of 57

But, a caution …
• If there really is a throughgoing very soft or a very stiff layer in the profile (as opposed
to a lens), this can increase the cyclic shear strains and the damping, further reduce
short period motions, and amplify long period motion
• This is illustrated on the next slide which shows the same results as above for the TESS2
analyses of the 200-foot profile with the addition of a run for one pair of motions in
which the stiffness of the third layer from the bottom is arbitrarily increased, as if there
is a sand and gravel layer before Site Class C materials are encountered
• It may be seen that the cyclic shear strain in Layer 18 is reduced when Vs is increased,
but that the cyclic shear strains below and, particularly, above that layer are increased
as a result of the reflection of energy by the stiffer layer
42Page 42 of 57

Cyclic shear strains (percent)
Best estimate Stiff layer 18
43
With stiff layer 18
Page 43 of 57

Recapitulation re site classes and ASCE 7-16
• The existing site classes based on Vs30, while not perfect, are not so bad
• There are basically two kinds of sites – those with a strong impedance contrast at a
reasonable depth and those without
• Where there is a clear impedance contrast it will generally be advantageous to
conduct site-specific site response analyses using Site Class B or C motions as input
• Even for those sites without a clear impedance contrast it may be advantageous to
conduct site-specific site response analyses because of the conservatism in hazard
analyses using GMPEs for soil sites
• It may be necessary to request a waiver from the Building Official for a departure from
literal compliance with the code more frequently than has been the case in the past
44Page 44 of 57

General issues involved in the conduct of site response analyses
• Even though we assume vertically propagating shear waves for the purpose of these analyses, that will never be the whole
truth
• Even if soil layering is perfectly horizontal, it is a good idea to increase the shear wave velocity in the bottom layer of the
analytical model so that excessive cyclic shear strains do not develop in that layer, since motions will not in fact be purely
vertical
• Keep lateral variation in mind. If for instance the site, or some portion of it is located in a paleo channel backfilled with softer
soils, a site response analysis for that profile alone might be misleading since all adjacent columns have to move together
• Thin layer problems. Beware modelling what are in fact lenses, such as a basal sand fill at the bottom of a paleo channel, as
continuous layers. Through-going soft or liquefiable layers should however be included in the model because they can
significantly affect site response, as can isolated stiffer layers
• Conduct sensitivity studies as appropriate - even with a superior site investigation there is always a need for some judgement
- beware of automation!
45Page 45 of 57

What about equivalent linear analyses?
• Equivalent linear analyses were a brilliant idea at the time - 50 years ago - but it is time to move on
• Equivalent linear analyses exaggerate the site response at the “equivalent linear natural period” of the site, and overdamp
the motions at other periods
• Equivalent linear analyses did have the advantage of more inherent stability because of the overdamping, but that is a high
price to pay for getting the wrong answer
• They also allowed “deconvolution” of surface motions to a “base” motion, but those base motions were very artificial. It is
in fact possible to easily perform “deconvolution” using nonlinear analyses using a simple iterative process that results in
much more realistic base motions - see Pyke (2019)
• Equivalent linear analyses neglected the effects of both excess pore pressure development (liquefaction) and cyclic
softening of clays. There is now an emerging consensus that only by conducting nonlinear effective stress analyses can we
understand site response, especially where development of excess pore pressures is an issue. See Cubrinovski (2019),
Hutabarat and Bray (2019), Kramer (2019) and Olson et al.(2010)
46Page 46 of 57

My preferred program - TESS2 - bi-directional
nonlinear effective stress site response analyses
• The same explicit finite difference solutions for response and redistribution and dissipation of excess pore
pressures as TESS
• Simple hyperbolic soil model – see Pyke (1979, 1993, 2004,2020)
• Computes excess pore pressures following Seed, Martin and Lysmer (1976)
• Computes seismic settlements following Pyke (1973) and Seed, Pyke and Martin (1978)
• Runs two horizontal components simultaneously, adds excess pore pressures and redistributes them, and
adds settlements or latent settlements. See:
https://www.linkedin.com/pulse/further-updated-presentation-improved-analyses-settlement-robert-pyke/
47Page 47 of 57

Ease of use features of TESS2
• Selection and modification of site-specific input motions now much easier thanks to the PEER
strong motion database etc.
• Users basically only have to specify shear wave velocity, soil type and undrained shear strength or
apparent relative density for each soil layer
• Most or all of the other required soil properties have defaults that are built in, although,
importantly, the user can specify site specific data if this is available
• In particular, default relationships for the increase in resistance to liquefaction with various aspects
of “ageing” are built into the program as a function of either time or MEVR (see Bwambale and
Andrus, 2019)
• However, the user still has to think about the depositional environment, the age of the deposit,
and how to subdivide the profile into layers
48Page 48 of 57

Some issues involved in nonlinear site response analyses
• Even though soils exhibit a constant secant shear modulus at shear strains less than about 10-3 percent, they still
exhibit low-strain damping
• Many nonlinear programs introduce some low-strain damping as a result of the solution technique that is
employed and may also allow the user to specify viscous damping in order to eliminate chatter at higher
frequencies. But neither of these techniques is a reliable method of modelling the real low-strain material damping
• TESS2 employs a solution scheme that does not introduce any damping and is therefore able to match elastic
solutions exactly. But TESS2 also contains a unique scheme to generate realistic damping at small strains which
results from rate of loading effects. Occasionally high frequency chatter can still be seen in TESS2 results but this
can be suppressed by increasing the low-strain damping or it can be filtered out
• Some programs or soil models limit the implied value of the shear strength at large strains to the “static” or
monotonic loading shear strength, see for instance Stewart and Kwok (2008), Hashash et al. (2010), Kumar et al.
(2018) (although Stewart and Kwok do at least suggest adjusting the shear strength for rate of loading effects). This is WRONG and
leads to excessively nonlinear behavior and excessive damping. There is nothing wrong with the implied shear
strength at large shear strains being up to several times greater than the conventional shear strength under
monotonic loading because of both rate of loading and repeated loading effects. In site response analyses we are
not concerned with failure under montonic loading
49Page 49 of 57

More about damping in nonlinear analyses
• Large strain damping does not need to be specified separately in nonlinear analyses because hysteretic damping is
developed automatically as a result of tracing nonlinear shear stress – shear strain loops. But note that these will be
irregular loops, as shown on the following slide for cases with and without initial shear stresses and that the loops are
not necessarily closed
• Because the stress strain loops are irregular and the style of loading is likely different from that in laboratory tests, there
is no point trying to match the damping exactly to element test results in the laboratory
• Indeed, there will be damping mechanisms in the field associated with non-horizontal soil layers and reflections and
refractions which suggest that the damping generated by nonlinear soil models should be greater than that observed in
laboratory tests (Pyke, 2004). This conclusion is confirmed by Afshari and Stewart (2019) who found that a better fit is
obtained to vertical array data using larger values of damping than are observed in laboratory element tests
• Although it is possible in the HDCP soil model that is used in TESS2 to modify the basic shape of the shear stress – shear
strain curves from a plain hyperbola (Pyke, 2020), use of a plain hyperbolic shape which gives greater values for
hysteretic damping than observed in laboratory element tests appears to be part of the reason that TESS and TESS2
have had some success in matching motions recorded in vertical arrays
• The discussion of the HDCP model by Hashash et al. (2010) is totally erroneous
50Page 50 of 57

51
Illustration of damping generated by HDCP soil model with and without an initial shear stress
Page 51 of 57

Other benefits of nonlinear site response analyses:
• See my three papers in the 7th International Conference on Earthquake Geotechnical Engineering
held in Rome, Italy, June 2019, or my presentation on LinkedIn:
https://www.linkedin.com/pulse/further-updated-presentation-improved-analyses-settlement-
robert-pyke/
for examples of nonlinear site response analyses that include modeling of liquefaction and seismic
settlement. These examples show not only how one can obtain much more accurate and less
conservative evaluations of liquefaction and seismic settlement but also much improved estimates of
ground surface motions.
• See also https://www.linkedin.com/pulse/improved-analysis-potential-lateral-spread-earthquakes-
robert-pyke for an expanded presentation on using 1D analyses to estimate potential lateral
spreading displacements. This presentation also includes more detailed discussion of the HDCP soil
model.
52Page 52 of 57

But don’t get carried away!
• Even the best nonlinear effective stress analyses using TESS2 are approximate and
don’t fall into the trap of believing that they are precisely correct, although they
will provide useful guidance as long as you don’t make basic errors (like forcing the
modulus reduction curves to match the “static” shear strengths, or ignoring
“ageing” effects and making overly conservative assumptions about excess pore
pressure development)
• In view of that, should we not run parametric studies on the major variables and
envelope the results? No, at least not necessarily, that may add unnecessary
conservatism to the overall results. A best estimate is good enough when the input
motions under ASCE 7-16 will already be 2475-year return period or median plus
one standard deviation ground motions.
53Page 53 of 57

Conclusions
• There is generally a benefit that is obtained by conducting site-specific nonlinear effective stress
site response analyses rather than just relying on GMPEs, especially for softer soil sites
• It is now practical to conduct nonlinear effective stress analyses in everyday geotechnical
engineering practice
• But there is a companion requirement to conduct more thorough site investigations
• Judgment is still required in conducting analyses / beware of automation
• Conduct of site-specific site nonlinear effective stress site response analyses is in any case desirable
to obtain more accurate, less conservative evaluations of the potential for liquefaction, seismic
settlement and lateral spreading
54Page 54 of 57

References 1
• Afshari, K. and Stewart, J.P., “Insights from Calffornia Vertical Arrays on the Effectiveness of Ground Response Analysis with Alternative Damping Models”, Bulletin of the Seismological
Society of America, Vol. 109 No.4, 2019
• ATC-3-06 , “Tentative Provisions for the Development of Seismic Regulations for Buildings “, Applied Technology Council, 1978
• Boulanger, R. W., and DeJong, J. T., “Inverse Filtering Procedure to Correct Cone Penetration Data for Thin-layer and Transition Effects.” Proc., Cone Penetration Testing 2018, Hicks,
Pisano, and Peuchen, eds., Delft University of Technology, The Netherlands, 2018
• Boulanger, R.W., et al., “Evaluating Liquefaction and Lateral Spreading in Interbedded Sand, Silt and Clay Deposits Using the Cone Penetrometer”, Geotechnical and Geophysical Site
Characterization 5, Australian Geomechanics Society, Sydney, Australia, 2016
• Bwambale, B., and Andrus, R.D., “State of the art in the assessment of aging effects on soil liquefaction”, Soil Dynamics and Earthquake Engineering, 125, 2019
• Cubrinovski, M., Keynote Lecture 09, “Key aspects in the engineering assessment of soil liquefaction”, Proc. 7th International Conference on Earthquake Geotechnical Engineering,
Rome, June 2019
• Dobry, R., Borcherdt, R.D., et al., “New Site Coefficients and Site Classification System Used in Recent Building Seismic Code Provisions”, Earthquake Spectra, Volume 16, No.1, February
2000
• Hashash, Y.M.A., et al., “Recent advances in non-linear site response analyses”, 5th Int. Conf. on Recent Advances in Earthquake Engineering and Soil Dynamics, San Diego, May 2010
• Hutabarat, D., and Bray, J.D., “Effective stress analysis of liquefiable site in Christchurch to discern the characteristics of sediment ejecta”, Proc. 7th International Conference on
Earthquake Geotechnical Engineering, Rome, June 2019
• Idriss, I.M., Dobry, R., and Singh, R.D., “Nonlinear Behavior of Soft Clays”, Journal of Geotechnical Engineering, ASCE, Vol.104, No.11, December 1978
• Kramer, S., Keynote Lecture 08, “The use of numerical analysis in the interpretation of liquefaction case histories”, Proc. 7th International Conference on Earthquake Geotechnical
Engineering, Rome, June 2019
• Kircher and Associates, “Investigation of an identified short-coming in the seismic design procedures of ASCE 7-10 and development of recommended improvements for ASCE 7-16”
Report to Building Seismic Safety Council National Institute of Building Sciences Washington, D.C., March 15, 2015
• Kumar, P. et al., “Comparison of Code-Based Design Spectra and Site-Specific Response Spectra in San Francisco”, ASCE Geotechnical Special Publication No. 291, Geotechnical
Earthquake Engineering and Soil Dynamics V, Austin 2018
• Olson, S.M., et al. “Nonlinear Site Response Analysis with Pore-Water Pressure Generation for Liquefaction Triggering Evaluation”, Journal of the Geotechnical and GeoEnvironmental
Division, ASCE, Vo. 146, No. 2, 2020
• Pitilakis, K. et al. “Towards the rvision of EC8: Proposal for an alternative site classification scheme and associated desihn response spectra considering complex subsurface geometry”,
55Page 55 of 57

References 2
• Paolucci, R., “Site classificationand site effects in the seismic norms: Work in progress for the revision of Eurocode 8”, Proc. 7th International Conference on Earthquake Geotechnical
Engineering, Rome, June 2019
• Petersen, M.D., et al., “The 2018 update of the US National Seismic Hazard Model: Overview of model and implications”, Earthquake Spectra, electronic pre-print,
https://journals.sagepub.com/doi/full/10.1177/8755293019878199
• Pilz, M., et al., “Does the 1D assumption hold for real sites? An analysis of KiK-net site responses and implications for ground motion modelling”, Proc. 7th International Conference on
Earthquake Geotechnical Engineering, Rome, June 2019
• Pyke, R., "Non-linear Soil Models for Irregular Cyclic Loadings," Journal of the Geotechnical Engineering Division, ASCE, Volume 105, No. GT6, June 1979.
• Pyke, R., “Evolution of Soil Models Since the 1970s.”, Opinion Paper, International Workshop on Uncertainties in Nonlinear Soil Properties and their Impact on Modeling Dynamic Soil
Response, Sponsored by the National Science Foundation and PEER Lifelines Program PEER Headquarters, UC Berkeley, March 18-19, 2004
• Pyke, R., et al., “Modeling of Dynamic Soil Properties”, Appendix 7.A, Guidelines for Determining Design Basis Ground Motions, Report No. TR-102293, Electric Power Research
Institute, November 1993
• Pyke, R., “Improved analyses of earthquake-induced liquefaction and settlement”, Proc. 7th International Conference on Earthquake Geotechnical Engineering, Rome, June 2019
• Pyke, R., “ An iterative procedure to obtain compatible base motions for defined ground surface motions using nonlinear site response analysis procedures”, in preparation, 2019
• Pyke, R., “Why the HDCP soil model is wrongly named but works very well!”, presentation in preparation, 2020
• Seed, H.B., Martin, P.P., and Lysmer, J., “Pore Pressure Changes During Soil Liquefaction”, Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 102, No.GT4, April 1976
• Seed, H.B., Pyke, R., and Martin, G.R., "Effect of Multi-directional Shaking on Pore Pressure Development in Sands," Journal of the Geotechnical Engineering Division, ASCE, Vol. 104,
No. GT1, January 1978.
• Seed, H.B., Ugas, C., and Lysmer, J., “Site-dependent spectra for earthquake-resistant design”, Bulletin of the Seismological Society of America, Vol. 66. No.1, 1976
• Stewart, J.P.., and Kwok, A.O.L., “Nonlinear seismic ground response analysis: code usage protocols and verification against vertical array data”, ASCE Special Geotechnical Publication
181, Geotechnical Earthquake Engineering and Soil Dynamics V, Sacramento 2008
56Page 56 of 57

The End!
If you have any comments or questions, please write to me at: bobpyke@attglobal.net
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