1 Course Introduction
2 Topics Covered
• 2008 USGS Uniform Hazard Maps
• 2009 NEHRP Provisions Maps
• ASCE 7-10 Seismic Maps
• Determination of Ground Motion Values
• Horizontal Response Spectra
• Vertical Response Spectra
• Peak Ground Acceleration
• Selection and Scaling of Ground Motions
•
3 Topics Covered
• 2008 USGS Uniform Hazard Maps
• 2009 NEHRP Provisions Maps
• ASCE 7-10 Seismic Maps
• Horizontal Response Spectra
• Vertical Response Spectra
• Peak Ground Acceleration
• Selection and Scaling of Ground Motions
•
4 2008 USGS Maps
• Probabilistic
• Uniform Hazard (e.g. 2% in 50 year probability)
• Spectral Contours (T=0, 0.1, 0.2 sec…)
• 5 % Damping
• Site Class B/C Boundary
• Geomean Values
5 Obtaining 2008 Maps from
USGS Seismic Hazard Data Website
6 2008 USGS Seismic Hazard Maps
7 Obtain Accelerations for Given Lat-Lon
8 2009 NEHRP Maps
• Probabilistic / Deterministic (Separate Maps)
• Uniform Risk (Separate Maps)
• Spectral Contours (PGA, 0.1, 0.2 sec)
• 5 % Damping
• Site Class B/C Boundary
• Maximum Direction Values
9 2009 NEHRP Probabilistic Maps
•Probabilistic / Deterministic (Separate Maps)
•Uniform Risk (Separate Maps)
•Spectral Contours (PGA, 0.1, 0.2 sec)
•5 % Damping
•Site Class B/C Boundary
•Maximum Direction Values
10 Maximum Direction Conversion
11 Using the USGS Utility: 2009 NEHRP
12 Results from Detailed Report
13 Adjustment for Risk and Deterministic Cap
14 Adjustment for Risk
15 Adjustment for Deterministic Cap
16 2009 NEHRP Intermediate Results
17 2009 NEHRP Results
18 Summary of Differences between 2009 NEHRP and ASCE 7-10 Approaches
• NEHRP Starts with maximum direction maps and a uniform hazard and provides explicit values (CRS and CR1) for adjust to uniform risk.
• NEHRP Provides maps for deterministic cap
• When using NEHRP the user must manually (or via web utility) convert to MCER values.
• ASCE 7-10 Provides MCER values Directly
19 Using the USGS Utility: ASCE 7-10
20 ASCE 7-10 Results
21 Adjusting for Site Effects
2009 NEHRP and ASCE 7-10
22 Topics Covered
• 2008 USGS Uniform Hazard Maps
• 2009 NEHRP Provisions Maps
• ASCE 7-10 Seismic Maps
• Horizontal Response Spectra
• Vertical Response Spectra
• Peak Ground Acceleration
• Selection and Scaling of Ground Motions
•
23 Development of Design Spectrum
24 Development of Design Spectrum
25 Vertical Response Spectra
• New Chapter 23 of NEHRP Provisions
• Not yet incorporated into ASCE 7
26 Vertical Response Spectra
27 Peak Ground Acceleration
Section 11.8.3 of ASCE 7-10:
28 Peak Ground Acceleration
29 Topics Covered
• 2008 USGS Uniform Hazard Maps
• 2009 NEHRP Provisions Maps
• ASCE 7-10 Seismic Maps
• Horizontal Response Spectra
• Vertical Response Spectra
• Peak Ground Acceleration
• Selection and Scaling of Ground Motions
•
30 Selection and Scaling of Ground Motions
• Selection and Scaling procedures are Provided in Chapter 16 of ASCE 7-10: Response
History Analysis
• Chapter 16 is usually used in association with nonlinear analysis of special structures or structures that do not conform to certain requirements (e.g. height limitations) in ASCE 7-
10.
• This example will demonstrate procedure for a site in Seattle, Washington.
• Additional discussion of ground motion scaling and use in linear and nonlinear response history analysis is provided in Chapter 4 of P-751, Structural Analysis.
31 Ground Motion Nomenclature
• An “Event” refers to a given historical earthquake, such as the 1989 Loma Prieta California
Earthquake
• A “Record” refers to the recorded ground acceleration histories at a particular recording station, such as the Saratoga-Aloha Ave. recording of the Loma Prieta event.
• Each record has (usually) three “Components” consisting of two (usually) orthogonal components and one vertical component. The horizontal components are often, but not always, oriented in N-S and E-W directions. In some cases fault-normal and fault-parallel values are provided. Records can be transformed to any direction (e.g. N-S and E-W recordings can be transformed to fault-normal and fault-parallel given the orientation of the fault.
• A “Suite” of ground motions consist of three or more records.
32 Location of Site
33 Selection of Appropriate Records
• Select from records of events having magnitude, fault distance, and source mechanisms that control the maximum considered earthquake (MCE)
• Pertinent information can be obtained from “Deaggregtion” of the seismic hazard
•
34 Deaggreagtion of Hazard (2.0 sec Accel)
35 Deaggregation of Hazard (2.0 sec Accel)
36
37 Spectral Characteristics of Close and Far Records
38 Deaggregation of Hazard
(0.2 Sec Accel)
39 Source Mechanisms for Selected Records
40 Scaling Requirements
• 2D Analysis: The ground motions shall be
scaled such that the average of the 5% damped response spectra is not less than the design spectrum over the period range 0.2T to 1.5T.
• 3D Analysis: The ground motions shall be scaled such that the average of the SRSS spectra from all horizontal component pairs does not fall below the design spectrum over the period range 0.2T to 1.5T.
• At sites within 5 km of the active fault each pair of components shall be rotated to fault- normal and fault-parallel directions and shall be scaled such that the fault normal dominant component is not less than the MCER design spectrum over the period range 0.2 to 1.5T.
41 Ground Motion Scale Factors for 3D Analysis
42 Components of the Northridge Earthquake
43 Ground Motion Spectra
44 Response Spectra for Two Selected
Scaled Motions
45 SRSS Scaled Spectra and MCE Spectrum
46 Scaled Records and DBE Spectrum
47 Alternate Scaling
48 Questions
This topic covers Chapter 3 of FEMA P-751, Earthquake Ground Motion. The
chapter is presented in two parts, the first being the theoretical basis of the 2008
USGS, the maps in 2009 NEHRP, and the maps in ASCE 7-10. The second part
presents some examples for determining ground motion values for a site in Seattle,
Washington. This slide sets is a based primarily on the examples. Note that most
of the examples use various web-based utilities. It would be valuable for the
instructor to have access to the internet so that the applications can be
demonstrated live.
Earthquake Ground Motions -1
This slide presents a list of the topics covered.
Earthquake Ground Motions -2
This slide presents a list of the first several topics covered.
Earthquake Ground Motions -3
The maps in ASCE 7 and 2009 NEHRP are derived from the 2008 USGS maps.
The USGS maps are purely probabilistic, represent a uniform hazard, and are
based on geomean spectral values. The geomean is the square root of the product
of the spectral values for the two components, at a particular period. The 2009
maps are split into three parts: Uniform hazard maps that have been converted to
maximum direction ground motion, separate maps which provide coefficients to
convert to uniform risk, and additional maps provide deterministic caps. This
information must be combined to obtain the values of Ss and S1 that are provided
directly by ASCE 7-10.
Earthquake Ground Motions -4
This slide shows a screen captured from a web site developed by USGS. In this
instance the site was used to provide maps for the conterminous U.S. for a 2% in
50 year probability of occurrence. Maps for 0.2 second and 1.0 second periods are
specified. Maps are then downloaded as PDF files or Postscript files.
Earthquake Ground Motions -5
PDF files of the two requested maps are shown on this slide. Note that the maps
are not particularly useful from a design perspective, but do show in some detail the
distribution of shaking hazard across the U.S. In the western U.S. and certain
areas in the central and eastern U.S. the ground shaking can be violent, with peak
horizontal accelerations as high as 1.0 g. Peak ground acceleration is
approximately 0.4 times the 0.2 second spectral acceleration. USGS also provide
peak ground acceleration maps if needed.
Earthquake Ground Motions -6
This slide a screen capture for a USGS utility that provides geomean spectral
acceleration by Longitude and Latitude. The given location is in Seattle,
Washington. These values provided are purely probabilistic, and are based on a
2% in 50 year seismic hazard. Note that longitude must be entered as a negative
number because Seattle is west of the prime meridian.
Earthquake Ground Motions -7
The 2009 NEHRP provides three sets of maps that are used to provide design
values. The first set is a based on a uniform hazard, but has been converted from
geomean to maximum direction by use of a simple approximation. The second set
of maps provide risk coefficients that are used to convert the maximum direction
uniform hazard values to uniform risk values. The final set of maps is used to
provide a “deterministic cap”
on the probabilistic values where the probabilistic
values are greater than the deterministic values.
Earthquake Ground Motions -8
This slide shows the 2009 NEHRP Uniform Hazard maps which are based on
maximum direction motions without a probabilistic cap. Maps are shown are for a
2% in 50 year hazard and for spectral accelerations at periods of 0.2 seconds and
1.0 seconds.
Earthquake Ground Motions -9
The maps that are shown on this page are the 2009 NEHRP Uniform Hazard
Maximum Direction maps. These are obtained by multiplying values on the
corresponding 2008 BSSC 0.2 second spectral values by 1.1, and the 2008 USGS
1.0 second spectral values by 1.3. This is an approximation to the maximum
direction values.
Earthquake Ground Motions -10
The USGS Utility can be used to obtain values from the 2009 NEHRP Maps. This
slide shows a screen capture of the U.S. Seismic Design Maps Web Application,
with the Seattle ordinates of 47.65 Lat and -122.3 Lon keyed in.
Earthquake Ground Motions -11
The Detailed Report from the web application shows the 2009 NEHRP maps
together with the computed values S sub SUH and S sub 1UH, where the “UH”
in
the subscript stands for Uniform Hazard”. As can be seen the results are the same
as computed “by hand”
on Slide 10.
Earthquake Ground Motions -12
The next step to obtain the ASCE 7 values is to adjust for Uniform Risk by
multiplying the Uniform Hazard values by Risk Coefficients. There is one map for
0.2 sec Risk Coefficients, and one Map for 1.0 sec Risk Coefficients.
Earthquake Ground Motions -13
Before the final ASCE 7-10 mapped values can be determined, it is necessary to
make sure the probabilistic Uniform Risk values do not exceed the deterministic
cap values. 2009 NEHRP Provides the maps of the deterministic caps.
Earthquake Ground Motions -14
This slide shows the deterministic contours for the 0.2 second acceleration.
Earthquake Ground Motions -15
Finally, the values of S sub S and S sub 1 can be found. Values computed by hand
are shown.
Earthquake Ground Motions -16
The values computed by the USGS Application are the same as those computed by
hand, as shown on this screen capture from the detailed report.
Earthquake Ground Motions -17
A summary of the differences between the 2009 NEHRP and the ASCE 7-10 Maps
is provided on this slide.
Earthquake Ground Motions -18
The USGS Utility can be used to determine the ASCE 7 Design Values (S sub s
and S sub 1) directly. The slide shows a screen capture of the utility with the
pertinent information keyed in for the Seattle location. Note again the negative
value entered for longitude.
Earthquake Ground Motions -19
The results from the USGS Utility are provided by the screen captures shown on
this slide.
Earthquake Ground Motions -20
The USGS Web application also provides the interpolated values of the site
coefficients F sub a and F sub v. Using these values, S sub MS and Sub sub M1
are obtained, where the “M”
stands for Maximum Considered Earthquake. Dividing
these values by 1.5 provides the Design values S sub DS and S sub D1.
Earthquake Ground Motions -21
This slide presents a list of the next three topics covered.
Earthquake Ground Motions -22
This slide shows the basic design spectrum, which is Figure 11.4-1 from ASCE 7
10. This spectrum would be used in Modal Response Spectrum Analysis as
described in Section 12.9 of ASCE 7-10. The shape of this spectrum can be traced
back to work done by Newmark in the 1960’s. The Constant Velocity label
indicates that if the spectrum were to be converted to a velocity spectrum, this
segment of the spectrum would be constant. Similar for the Constant Displacement
branch. Note the unit inconsistency of the values; for example, the division by T in
the constant velocity region produces units inconsistency if the units of seconds are
attached to T.
Earthquake Ground Motions -23
This slide shows the calculation of the intermediate values needed to construct the
design spectrum. Also shown is the long period transition map which provides the
periods at which the constant displacement branch of the spectrum governs. For
the location in Seattle, T sub L is 6 seconds. This represents (approximately) a
building that is 30 to 40 stories in height, and is thus the spectrum beyond T sub L
is not likely to control for most buildings.
Earthquake Ground Motions -24
The 2009 NEHRP Provisions provide a means for computing a vertical design
spectrum. The spectrum contains four branches, as shown. Note that the period
shown in the plot and used in the calculations is the vertical period of vibration of
the structure. For vertical periods beyond 2 seconds (not likely for most buildings) a
site specific analysis must be used to determine the vertical spectral values. The
procedure for computing the vertical response spectrum is not adopted for use in
ASCE 7-10.
Earthquake Ground Motions -25
This slide shows the computation steps for the vertical acceleration for the Seattle
Site.
Earthquake Ground Motions -26
ASCE 7-10 provides a means to calculate the Peak Ground Acceleration. This
values is used in determination of the potential for liquefaction. The PGA values are
provided by the Map of Figure 22-7, or by the USGS Utility.
Earthquake Ground Motions -27
Computation of the MCE level PGA is shown for the Seattle site. The calculation
was done using the USGS application, as indicated by the screen capture. Note
that the mapped value of PGA, 0.521 g, is the same as provided by the USGS
maps, not adjusted for maximum and not adjusted for risk.
Earthquake Ground Motions -28
This slide presents a list of the topics covered, and indicates that the next topic
covered (the last topic) is Ground Motion Selection and Scaling. Selection and
Scaling of ground motions is required whenever a response history analysis is to be
used.
Earthquake Ground Motions -29
The slide provides several important points regarding selection and scaling of
ground motions.
Earthquake Ground Motions -30
This slide provides nomenclature used in ground motion selection and scaling.
Earthquake Ground Motions -31
In the following example we will describe the procedures for selecting a suite of
motions for the site in Seattle.
Earthquake Ground Motions -32
The first bullet is taken directly from Chapter 16 of ASCE 7-10. While there are
thousands of recordings available (e.g. from the PEER NGA site), it is often difficult
to find a suitable number of records that match the criterion listed. The USGS utility
for hazard deaggregation provides information that can be used to detect the
appropriate types of ground motions (but not the actual recordings themselves).
Earthquake Ground Motions -33
This slide is a screen capture of the results of the deaggregation for ground motions
that affect the 2.0 second spectral acceleration for the site on Site Class C soils,
and a 2% probability of occurrence (consistent with the MCE). The three axes are
the distance from the site, the magnitude of the ground motion, and the percent
contribution to 2.0 second spectral acceleration. In this case, there appear to be a
cluster of events, 0 to 100 km from the site with a maximum magnitude of about 7
and which have moderate contribution. Somewhat further away (100 to 200 km)
are higher magnitude events that contribute even more significantly to the 2.0
spectral acceleration.
Earthquake Ground Motions -34
This slide shows the 2.0 second deaggregation information on a map of the area
surrounding the site.
Earthquake Ground Motions -35
The same USHS utility can provide deaggregation information at any period. In
these screen captures the contribution to the 0.2 second spectral acceleration is
shown. Note how the importance of the close-by motion has increased
dramatically when compared to the deaggregation for the 2.0 second acceleration.
Earthquake Ground Motions -36
Similar information is shown on this plot, which shows response spectra for large
distant earthquakes, for moderate close-by earthquakes, and the code design
spectrum. The moderate, close-by earthquake dominates at lower periods, and the
large distant earthquake dominates at the longer periods. The smooth ground
motion curves were obtained from ground motion models called “attenuation
relationships”.
Earthquake Ground Motions -37
The deaggregation utility provides detailed information on how different types of
earthquake contribute to the hazard. A portion of the the text file that is provided
with the deaggregation is shown.
Earthquake Ground Motions -38
The information shown on the previous slide can be used to create a graph as
shown on the bottom of the current slide. As can be seen, the Cascadia subduction
zone dominates at longer periods, and has relatively low influence at short periods.
The influence of the deep intraplate events is just the opposite; dominant at lower
periods and waning at longer periods. The shallow crustal contribution is
somewhat constant along all periods.
Earthquake Ground Motions -39
This slide provides a summary of the ASCE 7-10 ground motions scaling
requirements. The strikeouts and rewording in the last bullet are discussed in the
text of the example.
Earthquake Ground Motions -40
The table provides seven records that fit the characteristics derived from the
deaggregation. As may be seen, the sources types, magnitudes, and distances are
consistent with the deaggregation. (Other pertinent information, not shown in the
example, is the site class at the recording station. This should be consistent with
the site class for the building under consideration). Note that all distances are
greater than 5km, so it is not necessary to rotate the components to fault-normal,
fault parallel, or to find the dominant component.
Earthquake Ground Motions -41
These ground motion acceleration histories are fault normal (upper) and fault
parallel (lower). The orbit plot (lower right corner of slide) shows that the motions in
the two directions are largely out of phase, and that the maximum resultant
acceleration occurs at a 45 degree rotation.
Earthquake Ground Motions -42
This slide shows the 5% damped response spectra for both components of each
record, together with the MCE Target Spectrum. The plot on the left shows the
unscaled records, and the plot on the right shows the record with the scale factors
shown in the last column of the table. The vertical lines in the scaled plot indicates
the period range over which the scaling applies, where the structural period is 2.3
seconds.
Earthquake Ground Motions -43
This slide shows the response spectra for two of the scaled records. Each
individual component is shown, as is the SRSS and the MCE target spectrum. The
individual component spectra as well as the SRSS spectra have a shape that is
consistent with the target spectrum over the indicated period range.
Earthquake Ground Motions -44
The plot on this slide shows the scaled SRSS spectra for the seven events,
together with the average of the SRSS (heavy red line), and the target MCE
spectrum (heavy black line). As can be seen, the Average SRSS falls above the
target spectrum over the indicated period range, with the match point at about
T=1.0 sec. Note that one of the SRSS spectra (for GM 7) has high amplitude at
T=0.5 seconds. Thus, this record will have a larger higher mode influence than will
the other records. Note also that the ordinate for GM 1 is nearly twice the ordinate
of the design spectrum at the period of 2.3 seconds.
Earthquake Ground Motions -45
This plot shows the individual MCE scaled components together with the DBE
target spectrum. On the average, the MCE scaled records are a good match for the
DBE target spectrum, thus little additional scaling would be required if was desired
to re-scale for analysis in 2-Dimensions, where the average of the individual
component spectra is used instead of the average of the SRSS spectra.
Earthquake Ground Motions -46
In the Chapter 3 example the method for determining the individual record scale
factors was not mentioned. In fact, there are an infinite number of sets of factors
that will fit the ASCE 7 criterion. In this slide, an approach is used where the SRSS
spectra are first scaled to match the target spectra at the design period (2.3 sec in
this example), and then re-scaled such that the average of the SRSS spectra does
not fall below the target over the period range 0.2 to 1.5 T. As may be seen, the fit
is much better near the target period, but a few of the individual records have
relatively low acceleration at the lower periods.
Earthquake Ground Motions -47
Slide to initiate questions from participants.
Earthquake Ground Motions -48