Washington State Transportation Center (TRAC). Civil and ... (WSDOT) for nine soil groups representative of deposits that can be found in Washington State. These ..... for magnitude 6.5 earthquake and a hypocentral distance of 12 miles ..... Shock waves propagate outward from the focus through the body of the earth and.
SEISMIC RESPONSE SPECTRAREFINEMENT
WA-RD 333.1
Final Technical Report December 1994
.....
...,,. 1AI ......_State 'fffi, De,_.._t of 1'lwlsportatlon
Washington State Transportation Commission Planning and Programming Service Center
in cooperation with the U.S. Department of Transportation Federal Highway Administration
TECHNICAL REPORT STANDARD TITLE PAGE I~
1. REPQJtTNO.
''·
WA-RD 333.1
1'- Rl'.I'OllT D.
-B (;'I I
·~
.,.,
------------------=--. ' \." ------:,:c c~,.,
SHAKE [7) (a compuler program for linear earthquake response analysis for horizontally layered siles), and soil modulus and damping curves developed in the 1970's. The soil paramelers were corrclaiCd to Standard Penetration Test data (SPT) from 123 actual boring logs from all around Washington Stale. Recently, new dynamic moduli curves for cohesive soils were developed [1). These curves have been accepiCd as _more representative for the soil in the region. Also the computer code SHAKE, a frequency domain program, lends to attenuale high frequency components producing low frequency biases in the response spectra. New compuler codes have been developed to work on the time domain; DYNA1D [8], a computer program for nonlinear seismic sile response analysis, is used in this study to verify the results obtained by SHAKE. A significant problem in developing response spectra in Komher' s study was the lack of earthquake records at rock siles for subduction zone events. One such record was identified for a magnitude M 5.0 to M 5.5 event. Strong motion accelerations resulting from the Pender Island, British Colombia earthquake of May 1976 were recorded at the Lake Cowichan telecommunications station [9]. There are also several strong motion records for smaller earthquakes than the M 7.5 design earthquake. The unique data from these records can be used to evaluale the deconvolution technique to synthesize base accelcrograms. The objective of this study is to develop new responses for the same nine soil groups used in the previous study, representative of a design earthquake of M 7.5 for the Puget Sound region. The new dynamic moduli for cohesive soils is used. A Check on
7
the SHAKE results is provided by the use of DYNAlD code.
ORGt\NIZATION OF THE REroRT
This report is divided into five main sections. The INTRODUCJ10N contains material about the problem statement and the research objectives and approach. The
second section contains BACKGROUND material about the earthquake phenomenon, and the geology and seismicity of the Puget Sound. The third section contains details about the MODEL AND ANALYSIS and includes description of the programs SHAKE and DYNAID. Soil modeling for both codes and the associated input parameters arc also included in this section.
The fourth section contains the FINDINGS AND
INTERPRETATIONS. Soil amplification spectra for nine soil groups are presented in this section along with the base spectrum. Results of sensitivity study are presented in this section. Comparisons between the results of the linear analysis and the non-linear analysis are also presented along with comparisons with the current codes. The fifth section presents a comparison between the MAPS OF SEVERITY COEFFICIENT found in the AASHTO and WSOOT seismic design guidelines. Appendix A presents soil profiles used in the analysis and Appendix B contains curve ordinates developed in this study.
RESEARCH APPROACH
This research uses procedures followed by Gates [ IO] in developing soil amplification factors for California Department of Transportation (Ca!Trans ). First. the
8
peak rock acceleration is detcnnined from the seismologist's studies of fault activity and attenuation data as gathered from past events. In developing the seismogenic zones of the Pacific Northwest, Perkins et al. [II] used an approach relying on two different methods: the first method depends predominantly on historic seismic activity to develop a zoning rationale; the second method addresses the ongoing problem from a geological point of view. The use of geological
eviden~.
can identify currently seismic areas as areas of
potential activity if they lie along or within structural trends that have historic seismicity. Figure 2 shows a map of acceleration on rock with a 90% probability of not being exceeded in 50 years developed by Perkins et al. (1980) [II]. The base spectrum developed in the previous study [6] was adopted for this study. Komher selected a base spectrum based on anticipated ground shaking from the subduction zone earthquakes expected in Washington State. Various methods of finding an appropriate base motion were investigated. The Seed et al. stiff curve [12] was selected in Komher" s study to be appropriate as a target response spectrum in generating input motion for SHAKE. Figure 3 shows the-base spectrum used in this study with the AASHTO base spectrum for comparison. The soil amplification factors of the nine soil groups are developed using the computer codes SHAKE and DYNAID [7.8].
SHAKE and DYNAlD were used to
obtain the five percent damped acceleration response of the ground surface for the nine soil groups. Soil amplification spectra arc then obtained by dividing surface response by the response of the time history at a rock outcropping. Figure 4 schematically shows how the soil amplification factors were developed. The input model for SHAKE includes
9
FIGURE =:. Acceleration on rock with 90'K prohahility of not heing exceeded in 50 years deYelopcd hy Perkin> et al. in 19SO 16 ].
10
:z::
-.... 0
< a:::
--' ..... u
u
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Richter Magnitude
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fun.::ti,,n of Ri.:htcr
ma~nitudc.
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7
8
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FJGURE 6. Some of
\
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I I J
I I
Richter, Seed et al. [16) developed a chart for the average predominant periods of accelerations for various earthquakes as a function of the distance from the causative fauiL This chart is shown in Figure 7 Seed et al. [16) also developed attenuation relationships for values of maximum acceleration as functions of earthquake magnitude and distance from the causative fauiL
These relationships are shown in Figure 8.
Attenuation
relationships have also been developed by others. Most of these relationships are based upon data collected from California earthquakes. Earthquake-induced ground motion is a function of the source mechanics and the dynamic characteristics of the propagation media. The local geological and topographical conditions strongly affect the temporal and spatial behavior of the ground motion. Although it is accepted that ground motion reflects the geodynamic characteristics of the underlying soil layers, the significance of this influence has been a controversial issue in earthquake engineering and strong ground motion seismology [17].
Theoretical
calculations of the influence of the local soil conditions have been successfully correlated with strong ground motion or other macroseismic data from many locations where the local suhsoils are soft ( e.g., Mexico City, Caracas, San Francisco and several locations in Japan including Tokyo).
However, it has also been shown that ,except for data
recorded on deep and soft soil deposits. the peaks of ground motion spectra do not show any correlation with the ground characteristics. Seismic forces tend to dissipate or attenuate as they radiate outward from the causative fault; the peak ground acceleration varies as a function of the magnitude of the earthquake and the distance from the causative fault [ 14). The peak ground acceleration
17
1.:: 1.0
..,.., r
-: -
O.S
O.o
-
..,
-
0.~
0: 0
0
80
;:o
I 60
FIGURE 7. Average predominant periods of accelerations for various earthquakes as a function of the distance from the causative fault developed by Seeder al. [13].
18
"' -
0.3
"' "
-"
.. ~
"J
·- o.: X
" ::;:
oL--....;..._...;..._.....:._......:...;..._.:....._~----__.
0
40 SO i :0 D:stancc irom causatJV\.' fault Ikm'
lt>O
FIGURE 8. Maximum acceleration as a function of magnitudes of earthquakes and distances from causative faults developed by Seed ct a!. [13).
19
alone does not completely define the rock accelerations at a site. The dynamic response of a system of simple single degn:e-of-fn:edom pendulums (response spectrum) is usually used to indicate the frequency content of a seismic evenL The shape of the response spectrum in rock is primarily controlled by the predominant period of spectra, which is the period of maximum spectral response.
In 1978 Paiwardan et al. [18] used ground motion data recorded during a number of earthquakes to develop attenuation relationships for peak acceleration, peak velocity and spectral ordinates at several periods for two categories of earthquakes: shallow-focus earthquakes, such as California earthquakes and those that occurred in parts of Japan; and subduction zone earthquakes such as those that occun:d offshore of Japan, South America, and the Puget Sound. Typically shallow-focus earthquakes occurred at depths less than 15 km.
Records obtained during earthquakes which occurred in subduction zones
typically occurred at depths greater than 25 km. Another study by ldriss [ 19] showed that the peak acceleration and spectral ordinates at short periods (less than 0.4 or 0.5 seconds) can be significantly higher for the subduction zone earthquakes than for the shallow-focus earthquakes. At longer periods (longer than 1.5 or 2 seconds), the spectral ordinates for the shallow-focus earthquakes can be significantly higher than those for the subduction zone earthquakes. These trends can be partially attributed to the fact that for deeper earthquakes, the dynamic stress drop must be greater than for shallower earthquakes. A higher dynamic stress drop results in higher peak acceleration. This illustrates the importance of recognizing whether a certain
20
event falls in the shallow-focus category or the subduction zone category. One of the most important factors in specifying earthquake ground motion is knowledge of seismic wave attenuation from the source in various geographic regions. One of the procedures followed for defining the seismic attenuation functions of an area is the use of observed strong ground motion acceleration-attenuation curves [20]. Such a family of acceleration attenuation _curves applicable for sites in the western United States were developed by Schnabel and Seed in 1973. Each site is assumed to be located on rock material having a shear wave velocity of at least 760 rnls at low strain levels. These curves are somewhat controversial in terms of whether or not they underestimate the peak ground acceleration inside 20 km range. In spite of this they are still used at the present time in many applications. In regional hazard analysis, zones of some severity coefficient, such as peak ground acceleration or intensity, are usually mapped [6]. The severity coefficient is used to scale a base response spectrum to represent the various strengths of earthquakes expected to occur.
Seismic source zones are defined based on the best available
information regarding the seismicity of the region. relation of the seismicity to geology and tectonics, the physical and temporal characteristics of earthquake source zones, ground motion attenuation. and influence of local site conditions [21). The first national earthquake zonation map was published in 1948. It divided the United States into zones numhcred 0 to 3, where 3 indicates the greatest damage potential. In 1976. Algcrrnisscn and Perkins [22) published a national seismic zonation map which presented peak acceleration values with 90 percent probability of nonexceedance in a 50
21
year period. The previous maps were based on a maximum intensity scale. In 1978, the Applied Technology Council (ATC) produced two new ground shaking maps. These maps are based largely on the map developed by Algennissen and Perkins. Two separate ground motion parameters; Effective Peak Acceleration (EPA) and Effective Peak Velocity (EPV), were defined based on spectral acceleration and on spectral velocity rather than actual peak accelerations and velocities [23].
The
Algennissen and Perkins approach was used in the AASHTO specifications for seismic design of highway bridges to produce contour maps for an acceleration coefficient which shows the relative severity of ground shaking. The acceleration coefficient is a response spectrum scaling factor for different ground shaking conditions [4,6]. Figure 9 shows AASHTO's map of acceleration coefficient. In 1976, Gates [10] developed seismic design guidelines for the California Department of Transportation (CaiTrans). These guidelines used base spectra developed by studies on California earthquakes and with peak ground acceleration as a severity coefficient A maximum elastic spectrum (5% damped) on rock can be obtained by multiplying the maximum expected bedrock acceleration by the ordinate of the normalized rock spectrum curve.
Soil amplification factors were developed based on computer
studies (SHAKE) and by actual recorded data. The design guidelines currently used in the AASHTO codes are based on Gates' procedures.
QEOI .OGY OF Pl JGET SOl JND
The Puget Sound region of western Washington State lies in a north-trending
..,.., -~
'
'
I .. -. ,
-'3
. ....
\ a ......
.
FlGl:RE 9. AASHTO">
m:1p
of acceleration coefficient !6].
-.
structural and topographic through between the Olympic Mountains on the west and the Cascade Range on the east Geological structure in the
ba.~in
is poorly characterized
because of thick accumulations of glacial deposits which mask the underlying bedrock structure (24]. Development of the crustal structure of western North America began more than 300 million years ago, but the structural identity of the Puget Lowland was established only as recently as 20 to 40 million years ago ( 14]. Once the large-scale structure of the Puget Lowland was established, the detailed, small-scale surface topography was shaped. This was accomplished primarily by surfacial processes. The most prominent process was glaciation during the ice age of only a few tens of thousands of years ago. About 3.50 million years ago there was a reorganization of the existing boundary on the oceanic plate somewhere west of the American Continent This was the earliest decipherable event in the structural evolution of the western edge of the Americas, including the Puget Sound. This event marked the first addition of new crustal material against the western margin of the continent and represented the beginning of convergent plate boundary processes that have continued
to
this day.
Figure 10 is a schematic
diagram of the evolution of the western North American boundary. The several advances and retreats of glaciers have reshaped the Puget Sound [21 ). The current shape of the Puget Sound is the result of scour during the glacial advancement from the north and deposition of glacial sediments during subsequent recession periods. Because of repeated glaciation, most of the sediments arc highly ovcrconsolidatcd. estimated the sediment thickness as high as J .3 km.
24
Recent studies have
Figure II shows the glacial
Trench
arc Back arc basin
(Pumaruy oceamc)
Back arc {i ransu,onal crust)
/~~
:;::::=:::~-- -. ~::__
13 Ar~ terrene
[j Contmenlill crus:
0
.
A~:~~ volc:an1S~
•- ....··-~
~
."\'t'L• il
·.• _,.
::if.J=.,
-.~.·
...
FIGl~RE 1'
Gla.:ial aJ,anccmcnt tbt afl'crtcd the
Pu~c:
S.nmJ [1-1:.
advancement that affected the Puget Sound. The underlying bedrock geology is thought to consist of Paleozoic and Mesozoic sedimentary and prc-Devonian crystalline rocks in the northern parts with Tertiary continental and marine sedimentary and volcanic rocks to the south.
SEISMICITY OF PIJGET SOUND
Historically the Puget Sound basin is the most seismically active area of Washington State. Two destructive earthquakes occurred there within the last forty years: the April 13, 1949 event,with a magnitude of 7.1 and epicenter near Olympia, and the April 29, 1965 event, with a magnitude of 6.5 and centered near Seattle [24].
The
primary cause of the seismicity of the entire western United States, including the Puget Sound, is the motion differential between the North American and the Pacific plates [5]. Figure 12 schematically illustrates the primary tectonic elements that interact in the northeast Pacific and western North America. Earthquakes originating within the Puget Sound area can be classified into two categories according to the focal depth: shallow-focus earthquakes with focal depths at approximately 20-30 km, and deeper focus earthquakes with focal depths between 40 and 70 km.
The subduction of the Juan de Fuca plate is currently active.
earthquakes occurring in the area are deep focus
evenL~
The largest
associated with this subduction
process [6]. However. most of the smaller earthquakes in Puget Sound occur at shallower depths and arc associated with the existence of the Puget Sound depression. Figure 1:.'1 shows how the subduction process might be occurring.
27
Explorer Ridge
Juan de Fuca plate
so•
-Q)
0
Rise
-
• • High Cascade 1 Volcanoes
•
Blanco Fracture Zone-"' Gordo Rise
,,~
.,........_..._,•....- Gordo basin
Mendocino fault}
Son Andreas fault
30'
600
BOO
0
::sr
~
40'
130'
11 0'
FJGL'RE 12. Primar~ tectonic clement' that interact in the Ih>rtheast Pa..:ilic and western
North
Arncric~
11 ].
OLUIIBIA
.,. l,.~--··a~~-Cl
~--~
PACIFIC
~
II'
PLATE
-
I I
! .,. __
._____
./
.
FIGURE
I~-
-:- .... -~·.· . -
The suhduuion process that affect the seismicity of the region 1::!1 ].
::!9
~ I
SUMMARY
In summary, earthquake induced ground motion is a function of the
SOII!l:e
mechanics and the dynamic properties of the propagatillg media. The local geological and topographical conditions strongly affect the temporal and spatial behavior of the ground motion. Attenuation relationships for ground motion developed by many researchers are
based on specific earthquakes recorded at specific locations, such as, California earthquakes. Washington State has a unique geology that is characterized by the thick deposits which resulted from the glaciation activity during the ice ages. Also, the seismicity of Washington State is unique; being affected by the subduction of Juan de Fuca plate beneath the American plate. Thus, a need for developing seismic response spectra that would reflect the unique geology and seismicity of Washington State is eminenL
In the next section the modeling and analysis procedures that were followed to come out with a family of seismic response spectra for Washington State are discussed in detail.
30
MODEL AND ANALYSIS
SHAKE Several methods for evaluating the effects of local soil conditions on ground response during earthquakes are presently .available. Most of these methods are based on the assumption that the main responses in a soil deposit are caused by the upward propagation of shear waves from the underlying bed formation [7].
1be analytical
procedure generally involves determination of the characteristics of the motion likely to develop in the rock formation underlying the site, determination of the dynamic properties of the soil deposit, and computing the response of the soil deposit to the base rock motion. Computer programs developed for this analysis are generally based on either the solution of the wave equation or on a lumped mass simulation. Some of these programs are based on constitutive modeling for the soil and use finite element analysis. The program SHAKE computes the responses in a system of homogeneous, viscoelastic layers of infinite horizontal extent subjected to vertically travelling shear waves. The program is based on the continuous solution of the wave equation adapted for use with transient motions through the Fast Fourier Transform Algorithm. It involves the iterative use of strain-compatible soil properties in a frequency-domain-based analysis to account for the nonlinearity of the shear modulus and damping rations [7,17]. Several assumptions are required for the analysis. Among those are the following: the soil system is assumed to extend infinitely; each layer in the system is completely defined by its value of shear modulus, critical damping ratio, density and thickness. The
31
strain dependence of modulus is accounted for by an equivalent linear procedure based on the average effective strain level computed for each layer.
DYNAID DYNAID [8] is a finite element computer program for nonlinear seismic site response analysis for dry, saturated, and partially saturated deposits. DYNAID allows site response analysis to be performed taking into account the nonlinear, anisotropic and hysteretic stress-strain behavior of the soil materials, and the effect of transient flow of the pore water through the soil strata. This program uses procedures based on field and constitutive equations which are general and applicable to multidimensional situations. The required material constitutive parameters are identified in terms of "classical" soil
mechanics parameters (elastic modulus, friction angles, permeabilities, etc).
In DYNAID, the semi-infinite domain is represented by finite element model. The site response calculations are performed for a given seismic input motion prescribed in the form of an acceleration, velocity, or displacement time histories applied at the base of the soil column. Special boundary conditions can be prescribed which allow the seismic input motion to be prescribed as an incident propagating motion, or as the sum of an incident and reflected motion. The finite soil column is modeled by using finite elements. For that purpose the horizontally-layered ground is divided into several finite elements. Each finite element is defined by two nodes. The nodes need not be equally spaced. Soil skeleton motions occur in both the horizontal and vertical directions.
32
Therefore two solid kinematic
degn:es of fn:edom are assigned to each node. Fluid motions can only occur in the vertical directions; therefore, for saturated deposits in which fluid motions can take place a third kinematic degree of fn:edom is assigned to the fluid motion in the vertical direction. Figure 14 shows modeling of the soil layers and input motion in DYNAID. A set of material properties is associated to each element. 1be material may be assumed linear or nonlinear. Nonlinear soil model is based on multi-yield levels plasticity constitutive theory. For detailed discussion of the theoretical background of the program DYNAID, the reader is referred to the program's technical documentation [8]. Output for DYNAlD consists of nodal, element stresses, strains, pore water pressures, time histories, etc. The results are post-processed using the graphics pastprocessor which allow selective plots of field components time histories, Fourier spectra, velocity spectra, etc., and spatial plots at selected time of field components variations.
MODE!
The SHAKE program requires as input, shear modulus vs. strain and damping ratio vs. strain curves, a description of the soil profile, and time history input at the base of the profile. The following discussion illustrates how the input requirements for SHAKE were selected. The shear modulus and damping in soil are important to the analysis of all soil vibration problems. In particular, the modulus and damping for small strain amplitudes arc necessary for the analysis of foundation vibrations. The modulus and damping for a range of strain amplitudes arc needed for the analysis of earthquakes effects. Strain
33
.
... . ..
--
:
.
·..
·-·
.
' . ... .. .
·- . t
2
1
t
3
Solid/Fluid
H
Kl NEMATICS
i
~--
..I JN:::IDENT •I"'"~. r: T•T \....'""\ ...~,1 .......
y
FIGL'RE 1-t. Scmi-in1initc layered 'oil profile and Finite Element me'h 1~1.
X
amplitude, effective mean principal stress and void ratio are the most important factors that affect shear modulus and damping of cohesionless soils. The above factors along with the degree of saturation are the most important factors that affect shear modulus and damping for cohesive soils [25]. In 1970, Seed and Idriss [26] developed curves giving shear moduli and damping values as function of shear strain for both cohesive and cohesionless soil. 'These curves were used in the previous study [6]. The shear modulus vs. strain curve for cohesionless soils was represented by Seed and ldriss by the following equation: I
G ; 1000 K2 (a • "J 2 where k 2 is a function of the void ratio and strain amplitude and
(2)
a,•." is the effective
mean principal stress. For practical purposes, values for k 2 may be determined from a correlation with the void ratio or the relative density and the strain amplitude of the motion. Values of k 2 usually lie in the range 30 to 75 for loose to dense sands. The damping ratio vs strain curves for sands were developed by Seed and Idriss [26] based on the work done by Hardin and Dmevich [25]. They concluded that the shear strain, effective mean principal stress, void ratio, and number of cycles were very important factors influencing the damping ratios of sands. Figure 15 shows the shear modulus and average damping ratio of sand as function of shear strain as presented by Seed and ldriss. Accurate determination of the shear modulus of saturated clays is complicated by
35
5:~----~-------;------~----~
K~
'
c~~----~------~----~----~ :o-; 10- 3 1o-: 1(;-: SHEAR STRAIN- PERCENT
::a
I
:4
=
:o I Il
I I
I
I
:6
l2
/ 1/ /\ I
I
0
I
'
i
''
I I
;
'!'
i
:
I'
I
'
I I I ~
X I
I
-
!
J
/
I
i
I
'
I
I
I I:
I
'
I
II
;
l
FIGURE 1~. Shear mo.:luli and damping ratio for sands fmm Seed and ldriss
1:7J.
the large effects of strain amplitude and sample disturbance on modulus values [26]. Besides the effects of strain amplitude and disturbance, the moduli for different clays clearly depend on their relative strengths and stiffnesses. Hardin and Dmevich [25] expressed these effects in terms of the effective mean principal stress, void ratio, overconsolidation ratio, and effective stress strength parameters. Seed and ldriss [26] concluded that the effects of variations in clay characteristics on the shear moduli can be taken into account with reasonable degree of accuracy by normalizing the shear modulus, G, with respect to the undrained shear strength,
s•.
GIS. can be expressed as a function
of shear strain. Damping ratio curves were also developed by Seed and ldriss using data from previous investigations. Approximate upper and )ower bound relationship between damping ratio and shear strain were developed and a representative average relationship for all of the test data were obtained. Figure 16 shows the shear moduli and damping curves for saturated clays as presented by Seed and Idriss in 1970. These curves were used in the previous study [6]. As mentioned in earlier sections, new curves for shear modulus of saturated clays were recently reported by Sun et al. [1).
They concluded that unlike the modulus
reduction curves reported for a variety of sands which show a relatively small variation from one sand to another, the modulus reduction curves for clays are highly variable. The rate of modulus reduction with shear strain (which is normally shown on a plot of GIG,... vs. strain, where G...,. is the low strain modulus for a shear strain of the order of 0.0001 percent) is related to the characteristics of each individual clay. After examining many factors that might influence the form of the normalized modulus reduction relationships
37
l :.:.:~ ,..---~:-----.,---~-----:-----,
-
-V')
~
rac~,-------~--------~~----1 I
'
I
.!.. ·~~I------~----~------~----------~ ..... -. _., -
•"
• - - .i
J.
SHEAR STRAIN - PERCENT
1-
3
,..... < :::::
I
I
I
I
I /
I
30
u
0
I
20
0
I
I
I
I
I
I
I
1/
i
0
'
r
1.
I
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/
1/ I I
!
:0-.-
I
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.... -
'
-~
1
-
SHE:l.R STRAIN- PERCE:\:T
FJGCRE I 6. Shear moduli and Jampinf rati
,:;,
0.2
C5
C4
80
GJ
t___L_J~~~~~-L-J~-LI~~~_L_J~~~~~-LI-11~1~1-I_iiJil ~~~----~ cz
0.0
I
10 -·
1
I
•I
1 1 II I I
I 0 -•
I·
I
1- 1 I I I
II
10
I
-I
CJ I
11111111
1 0 _,
__
I
Shear Strain, percent !·!(il 1RI: 17. Normalized modulus reduction relationship for clays with different plasticity indices (1].
I
I !IIlii
10
to geophysical description of the soils, approximate layering, depths of water table, Standard Penetration Test blow counts (SPT), and undrained shear strength where clays or organics were present in the deposits. The soil profiles were up to ISO feet in depth and the SPT values were up to 100 blows per fooL Converting these data to the form required by SHAKE program required identifying the soil as sand or clay. and then correlating the field and laboratory data to dynamic input parameters. Komher investigated several relationships that correlate lowstrain shear modulus to the Standard Penetration Test values (SPT). Ohsaki and Iwasaki's [27] relationship for uncorrected blow counts were chosen. This equation is expressed as follows: (3)
where G.,.. is the shear modulus at low strain levels in tsf and N is the SPT number in blows per foot. This relationship was chosen since the correlation coefficient with downhole velocity studies is high and the results are consistent with the results obtained by other researchers [28]. The low strain shear modulus G.,.. can then be converted to the k, coefficient using the equation:
K,
G.,..
=---,
(4)
(cr ')' M
dividing k 2 by 61 will give the proper multiplying factor for SHAKE [6]. Komher also used the undrained shear strength, where available, for correlation with shear modulus for cohesive soils. The ratio G...,/S. was found based on average
41
values from the variational relationships provided (29] (see Figure 18). The a..JS. value was multiplied by by dividing
s. to get better estimates for a_.
The SHAKE factor was obtained
a_ by 2300 since SHAKE was formulated under the assumption that G-'S•
is equal to 2300 under low strain levels. As mentioned earlier, an earthquake record at rock site for a subduction zone earthquake was identified. Strong motion accelerations resulting from the magnitude 5.5 Pender Island, British Columbia earthquake of May 1976 were recorded at lake Cowichan telecommunication stations along with other soil sites in the region [9]. This record and the soil profiles where the strong motion was recorded were used in the non-linear analysis (DYNAlD) and compared with the results of the linear analysis (SHAKE). These time histories were used as the bedrock motion in the program DYNAlD to calculate surface response of several soil profiles in the area. The modeling parameters
for DYNAlD were correlated to the soil properties available for the proftles used in the analysis. The calculated surface motions were compared with the actual motions recorded for the 1976 Pender Island earthquake to estimate the accuracy of the modeling procedure and input parameters. With this knowledge, the second stage of the analysis could be undertaken. This involved subjecting the profiles developed in the first stage to the design earthquakes of the Puget Sound and then comparing the response of these profiles with the response of the nine soil groups of Washington Stale. Because of the necessity of comparison between the recorded and measured responses of the Pender Island earthquakes, the soil profiles used in the analysis were limited to those where surface records had been obtained. Three sites satisfied this
42
-=-2200-
-!
Gmax/Su """!''~"~""·I~_ _,,n,.,..., '
1
I
_;\----L----+------l-----t--------j
-
v: X
"'
4
5
Undraine::: Shear
F!Gl'RE l S. Variation of Gnu/S, a, a fun.:tion of undrained ~hear strcn~th 16.::!9].
43
criterion (9]: Roberts Bank, Annacis Island, and Brighouse Library of Richmond, British Columbia.
These three sites are widely spaced across the area; their profiles are
representative of the soils usually found throughout Vancouver and the Puget Sound regions.
The difference between these three soil profiles and the Washington State
profiles is in the depth. The Vancouver profiles range from approximately 315 to 670 feet in depth while the Washington State profiles were much shallower. This difference would result in more amplification of the propagating waves in the Vancouver profiles compared to the Washington State profiles. The three profiles and the soil models which were used in the non-linear analysis are shown in Figures 19 through 21.
INJ>liT TIME HISTORY In an attempt to select proper time histories that would represent the anticipated ground motion due to Washington State earthquakes, Komher investigated two possible methods; deconvolution of the available strong ground-motions time histories recorded in Washington State using SHAKE, and using predictive equations to get appropriate target response spectra which would be used to attain simulated time histories. Earthquakes induced ground motions that affect Washington State could be represented by a single spectrum scaled by the appropriate severity coefficient, since the soil amplification factors are dependent on the strength of the record and since the strength of the record is defined by the severity coefficient. As stated earlier, Washington State earthquakes are unique in nature. Therefore, some important factors must be considered when selecting appropriate time histories for
44
•
Sand)" Sill
9.0 m
II
10 9
8 Sand
7
51.0 m
•
t•
6
5 4
Sandy Sill
~5.0
• •
m
1..
FIGL"RE llJ. R,,hcns Bank sDil profile and Finite Element model.
45
3
-'
4.0m
II 10 9
Sandy Sill
8 36.0m
Sand
7
6
5
T •I • I
55.0 m Sandy Sill
•I
1
•
I
I~! I
FIGCRE 20. An:1a~i' Island soil profile and Finite E!cmcn: moJcl.
46
4
3
,
C'bv.:~·
.tO.O •
I
S.h
•
s..c~
l t
I I
8
7
•
6
•
5
•
4
•
a,~-
I
Q(IO m :
! I
I
• :I.
•
Cb,q- Silt
65.0•
FIGL:RE
II 10
Brig house ,;1il profile anJ Finite Element mnJcl.
47
Washington State Earthquakes: the range of magnitudes and focal depths which can be expected to occur in this area; and the differences in spectral shapes associated with different epicentral distances. Studies on the seismicity of Washington State [2,3] suggested that a magnitude 8 earthquake at a depth of approximately 31 miles (50 km) would be a reasonable estimate of the largest design earthquake in this area in light of the reasonable recurrence interval for such earthquakes. This choice of seismic source parameters is based on geologic and geomorphic evidence of subduction zone events in the Puget Sound region. Deconvolution of the strong-motion records from actual Washington State events was considered in choosing input time histories for SHAKE and DYNAID.
The
problems associated with this approach are mainly the tendency of SHAKE to produce unrealistically large high frequency components at the base spectrum, and the Jack of sufficient strong motion records from the region. The use of a limited number of records may lead to serious misrepresentation of the motions that could be expected in future earthquakes. Another problem with using actual records is that the response is earthquake site specific. This means that for each site different earthquake motions would have to be used to obtain a realistic range of responses [6]. Joyner and Boore [30] developed empirical equations for predicting earthquake response spectra in terms of magnitude, distance, and site conditions by analyzing horizontal pseudo-velocity response at 5 percent damping for 64 earthquake records in Western North America. These equations do not consider the difference in spectral shape between deep and shallow focus earthquakes resulting from reduced inelastic attenuation,
48
greater stress drop and general suppression of surface waves for earthquakes with the increase in focal depths [ 19).
This results in an increase in the high frequency
components and a decrease in the longer period components of ground motion from subduction zone earthquakes compared to shallow-focus earthquakes [6]. This trend is illustrated in Figure 22 by comparing the response of deep and shallow earthquakes from predictive equations [30,31,6]. Other researchers provided similar predictive equations for rock and soil sites [32,33,34). Normalized curves from predictive equations provided by Crouse, Vyas and Kawashima for a magnitude 8 earthquake at a depth of 50 km (31 miles) were compared to the spectra provided by Seed and ldriss [ 12] in Figure 23. Upon comparison, the Seed stiff curve, scaled by 0.2 was selected to be a target spectrum in the program SIMQUAKE to simulate acceleration time histories to be used in the SHAKE and DYNAID analysis [35]. This scaling factor represents the average range of strengths of ground motion expected from the predictive equations. Actual rock records from the 1976 Pender Island earthquake were used in the analysis that involved the Vancouver soil profiles.
BASE SPECTRJJM
The base spectrum selected to represent Puget Sound earthquakes is a modified Seed et a!. 50 percent stiff curve. This curve was modified with the assumptions made in the AASHTO guidelines [4). The modification addresses the increase in the response spectrum ordinates at longer periods because of concerns with inelastic response of longer period bridges [6]. The AASHTO guidelines state the spectra should be about 50 percent
49
.
''l 0.8
:z
-..... 0
< a::
.....
....J
D
0
l
·j
DEEP
rocus
SHAllOW
.ll
erioc (sec)
FIGURE 33. Amplification spectra scaled by 0.:! for Group 9 soils.
63
~.o
6.0 5.4
4.8 Ql
~ 0 Cl. ~
(/)
.....Ql
"0 a; N
0
E ~
0
4.2
36 30 2.4 1 .8
z
j . ::
0.5
oc
0.0
0.4
0.8
1.2
1 .6
2.0
2.4
2.8
Period (sec)
FIGURE 34. Normalized response scaled by 0.2 for Group I soils.
3.2
3.5
4.0
6.0 5.4 4.8 (1) Ill
c
4.2
0
Q.
Ill (1)
c::
"0 (1) N
0
3.6 3.0 ') 4
~.
E 1 .8 0 z ~
1 .2
0.6 0.0 0.0
0.4
0.8
1.2
1 .6
2.0
2.4
2.8
Perioo (sec)
FIGURE 35. Nonnalizcd response scaled hy 0.::! for Group ::! soils.
-:, ')
3.6
4.0
4.0
35 3.2 v
"'c:
2.8
.,c.v
24
"0
20
0
c:: v
N
0
1.6
~
c: 0
z
1 .2
0.8 04
00 1""\ "' u.v
o.~
08
, .., I
• ..:..
1 .6
2.0
2.4
2.8
3.2
Period (sec)
FIGURE 36. Normalized response scaled by 0.2 for Group 3 soils.
3.6
4.0
6.0 5.4 4.8 CIJ 1/)
c: a. 1/)
4.2
0
CIJ
3.6
a:: -o
3.0
"'0
2.4
....
, .8
CIJ
c: ~
0
z
, .2
0.6 0.0 C.C
0.4
0.8
1.2
, .6
2.0
2.4
2.8
Period (sec)
FIGURE 37. Normalized response scaled hy 0.2 for Group 4 soils.
67
3.2
3.6
4.0
6.0 5.4 4.8 4l
II)
c
4.2
a. II)
3.6
0
4l
a::
"
w
N
0
3.0 2.4
E 1 .8 0 ~
z
1 .2
0.6 00 0.0
04
08
1.2
1 .6
2.0
2.4
2.8
Period (sec)
FlGURE 38. Normalized response scaled by 0.:! for Group 5 soils.
68
3.2
3.5
4.0
6.0
54
.
4.8 1-
.
QJ
Ill
c
4:2
0
a.
Ill
QJ
0: ""0
3.6 t30
QJ
"' 24 0 ~
t: ~
0
z
1 .8
1:2 0 6
I
00 OQ
.
0.4
0.8
1 .2
1. 6
?O -·
.'"'4 . . . . .'"'8 .
Perioo (sec)
FIGURE 39. Normalized response scaled by 0.2 for Group 6 soils.
~..2 -
3.6
4.0
6.0 5.4
~
4.8
~
(I)
Vl
.
4.2
c 0
c.. Vl
(I)
c::
3.6
"'0
3.0
"'0
2.4
E ...
1 .8
~
(I)
0
z
-
1.2 0.6
o.oL---~--------------------~------~------~ 0.0 0.4 0.8 1 .2 1 .6 2.0 2.4 2.8 3.2 3.5 4.:) Period (sec)
FIGURE 40. Normalized response scaled hy 0.2 for Group 7 soils.
70
6.0 5.4
4.8 probability of not being exceeded in 50 years was adopted in the 1991 addition of AASHTO Standard Specifications for Seismic Design of Highway Bridges [4]. This section illustrates the model and procedures followed in producing the new map with concentration on the Pacific Northwest region.
THE 1991 AASHTO MAP-MODEl.
The concept of hazard mapping used here is to assume that earthquakes are exponentially distributed with respect to magnitude and randomly distributed with respect to time. Seismicity is modeled by grouping it into discrete areas termed seismic zones. A seismic zone is defined as a geologic feature or group of features throughout which the style of deformation and tectonic setting are similar and a relationship between this deformation and historic earthquake activity can be inferred [36].
DEVELOPMENT OF PROBABII ISTIC QROJJNO MOTION MAPS
Producing of probabilistic ground motion maps usually requires three steps:
91
dcterminatim of seismic source area; study the statistical characteristics of historical earthquakes in each seismic source area: calculation and mapping of the extreme
cumulative probability of ground motion during certain periods of time. The procedure for developing probabilistic ground motion maps is illustrated in Figure SS [21]. Earthquakes within a given seismic source can be modeled in three different ways:
point sources wbere the fault rupture length is small compared with the used map scale, finite rupture lengths, or as mixed source. The boundaries of a source zone are defined based on historic seismicity and the interpretation of a variable geologic and tectonic
evidence where possible. Once the source zone has been defined, the magnitude-recurrence relationships are
defined for each source zone as:
Log N =a - b M
(5)
where N is the number of earthquakes in a given magnitude range, M, per unit time and a and b are constants to be determined. If the seismicity of individual source zones in a region is low, the b-value in equation S is determined by considering the seismicity of a group of source zones. The a-value for each source zone is determined by fining a time with slope b through the seismicity data for each zone. The spatial occurrence of future activity is assumed to be uniform within a given source zone. Thus if the source zone is divided into n subzones and the number of occurrences for a given magnitude range is N, the number of earthquakes likely to occur in each subdivision, n, for the given magnitude range is N/n.
92
t
z
Si
J
;'
(B)
MAGNITUDE-
o.a c
-
.2 0
..... •
.!!
~
0
-'• --
1.0 c
0
c
. ;:
..
E £ 0.8 2
'
2
2
2
0
i
Yl
""i
0.6
..
!
0.4
-
0.2
{!
" 2
""-
2 46102040 100 Distance (miles l
0~
0
-
(C)
(0)
0
Acceleration
Acceleration Eleaents of the ba:ard calculation: lA)
Typ1cal source areas and £Tid of po1nts at computed.
l ~I
SutistlCal anal)"SlS of seismic-ay data and typical
iC)
Cu::ulative conditlonal probability distribution of accelnauon.
'~·:
The Ut!"eme p·o'bat:-1! 1ty F t).pc>!-UT-t
tlt1CS
{T).
max,
~hich
the ha:ard is to ag~nuatlon
la) for \"arious ac:celera-:.:.on!- and t
FIGL'RE 55. Dc,·c]opmcnt of ground motion map 1211.
b~
curves.
H seismicity is distributed along a fault of length L, the distribution of eanhquakes is somewhat more complicated. Mark (38] suggested the following relationship between fault length and magnitude:
Log L
= 1.9IS + 0.389 M
r-
(~....
(10)
or
..,
R(a) ~----
'
ln[F.,.Ja))
Thus for extreme probability of 0.90 and exposure time of 10 years the return period Ry(a)
= 94.9 years.
95
SEISMIC SOURCE ZONES IN 1HE PACIFIC NORTHWEST
1be probabilistic ground motion calculations use, as input, a model of future seismicity. This model consists of source zones and their associated rates of activity for earthquakes of various magnitudes up to the maximum magnitude assumed for each zone.
1be seismicity is assumed to be uniformly distributed within each zone. The size of the source zone is determined by the amount of geological and seismological information available, seismic history, and the scale of mapping. Unlike the coastal parts of California where individual seismogenic faults and general Cenozoic tectonic development are well known, the Pacific Northwest lacks a detailed regional tectonic model for Cenozoic tectonics. An important question related to the tectonic development of the Pacific Northwest is the origin of deep focus earthquakes in the Puget Sound area.
As mentioned in previous sections, many
researchers provided geophysical, stratigraphic, or tectonic arguments in favor of the subduction of Juan de Fuca plate beneath the west coast. The rate of subduction, the degree of coupling and the shape of subduction are all still a matter of debate[21]. Instead of developing regional tectonic model, observations on the geographical distribution of seismicity as it relates to geological features are useful. The youngest orogenic province in the region is the Cascade Range which has large volumes of Quaternary Volcanic rocks. Within the Puget Sound area, zones boundaries are based on seismicity alone as there are no dominant faults on known specific geologic structures that govern the spatial pattern of seismicity. The Puget Sound zones are within a broad region that encloses the Pugct Sound-Willamette Depression [36].
96
In northeastern Oregon and southeastern Washington, seismic zones have a northwest trend that is sub-parallel to the Intermountain Seismic Belt in western Montana. Figure 56 shows a map of nineteen seismic source zones in the Pacific Northwest [39]. The estimates of uncertainty for fault rupture length relationships used for the maps were based on the following relationship which was provided by Mark [38].
ATIENl!ATION The acceleration attenuation relationships for the western United States provided
by Schnabel and Seed [40] were used in producing the new maps. In the Puget Sound
area, the Schnabel and Seed curves were modified to reflect the greater focal depths of earthquakes originating at this region.
Figure 57 shows acceleration attenuation
relationships applicable for the western United States given by Schnabel and Seed. The velocity attenuation used in the preparation of the maps was developed by Perkins and Harding [41] using a data set and methods of analysis similar to that of Schnabel and Seed [40]. The current AASHTO map of acceleration coefficient is shown in Figure 19.
WSDOT MAP OF ACCEI ERATIQN COEFFICIENT The map of acceleration coefficient currently used by WSDOT was developed by Higgins et al. 1988 [21]. This map is based on the maps of peak acceleration and velocity on rock for the Pacific Northwest developed by Perkins et al. in 1980 [11]. The Perkins et al. [ 11] maps display peak accelerations and velocities for return periods of 100, 500 and 2500 years based on 19 source zones. Discrimination of these
97
FIGURE 56. Seismic source zones in the Pacific !\orthwest [:'19].
98
08
07
06
•
; 0~
!
p ••v o•
-·
~
I'-~ ::-.....
"" !"-..
v
•
~
~
~
"""' ""oz 0
~
I
0
,~
~
~" ~ ....
""
~~
~ ~~
~
""'~ 0
F:::::r-- ~""' ~ t:--"' ~ -
2
r~~
•00
FIGURE 57. Acceleration attenuation curves for the Pacific Nonhwcst [40].
99
zones followed a method based on integrating historic seismicity with available geologic information [11]. Because many seismogenic zones do not have enough earthquakes to
make a reliable estimate of the underlying rates of seismic activity, Perkins et al. combined all of the seismogenic zones into one of five groups. The appropriate group was determined by contiguousness and general tectonic character. Recurrence rates were calculated for each group based on the relationship:
Log N
EQ
(11)
+b M,
where N is the annual occurrence rate, Ms is surface wave magnitude, and a and b are regression constants. Acceleration attenuation relationships based on these developed by Schnabel and Seed [40] were used. The velocity attenuation curves were developed similarly to the
acceleration attenuation curves of Schnabel and Seed. After reviewing all the efforts of producing seismic zonation mapping applicable
to the Pacific Northwest, Higgins et al. [21] chose the maps of peak acceleration and velocity on rock developed by Perkins et al. in 1980 [ 11] to be the basis of developing a new map for the specific use of WSDOT. The Perkins et al. maps were chosen in Higgins et al. study for two reasons: they are considered an improvement over the original 1976 maps, and they express velocity in the same probabilistic terms as acceleration, making it possible to develop a velocity-related acceleration. The purpose of the velocity-related acceleration coefficient,
A..
is to account for
the slower attenuation of velocity than acceleration with distance from the source, and to consider the influence of velocity on the damage of long period structures at a distance 100
from the source. Higgins et al. argued that a map of A, could be developed based on the work of Perkins et al., and such a map would provide greater accuracy than the existing AASHTO codes. Higgins et al. suggested that the A, contours can be constructed based on the velocity contours by multiplying the alv ratio at a source by the velocity contour value located at some distance from the source, generating an acceleration coefficient attenuated at the same rate as velocity; i.e., velocity-related acceleration coefficient. For multiple source zones both acceleration and velocity attenuation are dependent on magnitude, and the v/a ratio also varies with magnitude. Thus, the a/v ratio used to transform the velocity contours to A, contours will vary with the statistical parameters of the seismic source zone influencing the contour at a particular location. If a velocity contour is influenced by more than one seismic source zone and the influencing zones have different statistical parameters, the v/a ratio applied to the contour will vary. Usually this will require a shift in the contour location [21]. Higgins et al. obtained values of a, v, and v/a at various distances from the source for magnitudes of 5.6, 6.6, and 7.6 from the velocity and acceleration attenuation curves used in Perkins et al. study [II]. Using the data and procedures explained above, Higgins et al. constructed the velocity-related acceleration coefficient map of Washington State. This map is shown in Figure 58.
DISCUSSION It is useful to point out that the old editions of the AASHTO specifications
incorporated maps that showed contours of velocity-related acceleration coefficient and
101
'' ,, '
'
I
()lt.AA!O&AN
,,,
r.c. tN~O(.It
J/'(JI/ANC
It)
0 0
• ADAM$
rnttf•AN
I J
'!10''"' ,cau 0
0
J0
-i(;-- "'ioiiM
M)
10
.,- ito
FIGURE 5R, Vcfocity-rclatcd accclcrntion coefficient map of Washington State (21).
~,..
not expected peak ground acceleration.
This acceleration coefficient was developed
specifically as a response spectrum scaling factor for a combination of rock and stiff soil conditions (Applied Technology Council, [23]). The map of acceleration coefficient found
in the old editions of the AASHTO specifications is shown in Figure 59. On the other band, the maps found in the 1991 editions of the AASHTO specifications and based on
the maps developed by Algennissen and others [37] show expected peak acceleration and velocity on rock. The maps of peak ground acceleration developed by Perkins et al. [II] in 1980 are based in the same model and methodology that were followed by Algennissen and otbers[37] to produce the 1982 national maps. This means that the 1991 ASSHTO maps and the current WSDOT maps are based on the same basic model. The authors feel that the new AASHTO maps represent a step foreword because they were developed with a deeper understanding of the seismicity of the region. The remaining task is to develop a map of velocity-related acceleration coefficient using a method similar to the procedures followed by Higgens et al. to be used according to the methodology of the AASHTO guidelines.
103
!
•
,.. .,. . .... ... .... ,..
.
. •••
• ,. •
"
~
•
OREGON
•J"
--
CALIFORNIA
FIGURE 59. Acceleration on rock with 909< probability of not being exceeded in 50 years developed by Perkin~ ct al. in 1980 Ill].
104
ACKNOWLEDGMENT
The authors would like to thank the many people from various agencies who
contributed to this study. Special thanks is made to Ms. Karen Komher and Dr. C. B. Crouse.
Also, a great amount of gratitude must be given to Mr. Myint Lwin and the
Washington State Department of Transportation for their assistance and patience in completion of this projecL
105
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Seed, H.B. Ugas, C., and Lysmer,J., "Site-Dependent Spectra for Earthquake
106
Resistant Design," Bulletin of the Seismological Society of America Vol. 66, No. I, pp. 22I-234, February, I976. 13. Das, B.M., Fundamentals of SoU Dynamics, The university of Texas at El Paso, Texas I983. I4.
Bums, Robert, The Shape and Fonn of Puget Sound, Washington SeaGrant Program, University of Washington Press, Seattle, I985.
IS. Gutenberg, B., and Richter, C.F, "Earthquake Magnitude, Intensity, Energy and Acceleration," Bulletin of the Seismological Society of America, Vol. 46(2), pp. 105-146, 1972. I6. Seed, H.B., ldriss, I.M., and Keifer, F.W., "Characteristics of Rock Motions During Earthquakes," Journal of the SoU Mechanics and Foundation Division ASCE, Vol 95, No. SMS, September, I969. I7. Erdik, M., Site Response Analysis, Earthquake Engineering Research Center, Middle East Technical University, Ankara, Turkey. I8. Patwardhan, A., Sadigh, K., Idriss, I.M., and Youngs, R., "Attenuation of Strong Ground Motion--Effect of Site Conditions, Transmission Path Characteristics, and Focal Depths," Bn!letin of the Seismological Society of America, 1978. 19. ldriss, I.M., "Characteristics of Earthquake Ground motions," Procrcdings of the ASCE Geotechnical Engineering Division Specialty Conference on Earthquake Engineering and Soil Dynamics, pp. 1151-1365, Pasadena, California, June 19-21, 1978.
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107
24. Crossen, Roben S., "Small Earthquakes, Structure and Tectonics of the Puget Sound Region, • Bulletin of the seismological Society of America, Vol. 62, No. 5, pp. 1133-1171, October, 1972. 25.
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I
Mc•snn:ments and parameter Effects, Il Design Equations and Curyes, Technical
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SoU
Dynamics D Recent
Adyances
in
Gmnnd ..Motion
Eyaluatjon,
Geotechnical Special Publication No. 20, A.S.C.E., pp. 389-404, June, 1988. 29.
Egan. J.A., and Ebling, R.M., "Variation of Small-strian Shear Modulus with undrained Shear Strength of Clay," proceedings of Second International Conference on SoU Dynamics and Earthquake Engineering, on board the liner, the Queen Elizabeth 2, New York to Southampton, Vol. 2, pp. 27-36, June/July, 1985.
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Byas, Y.K., Crouse, D.B., and Schell, B.A., "Regional Design Ground Motion Criteria for the Southern Bearing Sea," Seventh International Conference on Offshore Mechanics and Arctic Engineering, Vol. I, pp. 187-193, Houston, Texas, February, 1988.
33. Kawashima. K., Aisawa, K., and Takahashi, K., "Attenuation of Peak Ground Motion and Absolute Acceleration Response Spectra," Proceedings of the Eighth Wodd Conference of Earthquake Engineering, Vol. II, pp. 247-264, San Francisco, California, July 21-28, 1984.
108
34. Crouse, C.B., and Eeri, M., "Ground-Motion Attenuation Equations for Earthquakes on the Cascadia Subduction Zone, • Earthquake: Sprara, Vol. 7, No. 2, pp. 201236, May, 1991. 35. Vanmarcke, E.H. et al., SIMQJJKE· A Program for Artificial Motion C.cneration, Department of Civil Engineering, Massachusetts Institute of Technology, November, 1976. 36. Algermissen, S. T. et al., Probabilistic Estimateg of maximum Arp:leration and Velocity in Rock in the Contiguous United Sta~eg, USGS Open File Report 821033, 1982. 37. Federal Emergency Management Agency, NEHRP Recommended Provisions for the Deye)opment of Seismic Regulation for New Buildings, Building Seismic Safty Counce!, Washington, D.C., 1988. 38. Mark, K.R., "Application of Linear Statistical Models of Earthquakes Magnitude Versus Fault Length in Estimating Maximum Expectable Earthqualces, • CICOlogy. Vol. 5, pp. 464-466, August 1977. 39. Hays, W. W., "Evaluation of Earthquake Hazards and Risk in the Puget Sound and Portland Areas," Procerrlings of Conference Xl.ii, U.S. Geological Survey Open File Report 88-541, 1988. 40.
Schnabel, Per B. and Seed, H.B., "Acceleration in Rock for Earthquakes in the Western United States," Bulletin of the Seismologic Society of America, Vol. 63, No. 2, pp. 501-516, April1973.
41. Perkins, D.M. et al.,"A Provisional Peak Velocity Attenuation Compatible with the Schnabel-Seed Acceleration Attenuation.", Seismic Hazard Stt1dies in the United Slale.s, edited by S. T. Algermissen, USGS Professional Paper. Denver, 1988.
109
Appendix A SoU Prorues from Washington State The first line gives number of layers in profile, the first submerged layer, and name of profile. 1be subsequent lines give the layer number, soil type (1 for clay, 2 for sand, and 3 for bed rock), layer thickness in ft, maximum shear modulus in psf, and unit weight in
pcf.
110
GROUP!
6
2 3 4 5 6
1 2
3
5.
8. 7. 2 5. 2 10. 3 0.
:
II
2 3 4
5 6 7 8 9 10 II
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2 5. 1 5.
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110. 115. 115. !20. !35. 140.
5
profile 007 A
I 2 3 4
2400. 2400.
5
2400.
3070. 5!80. 5800. 4000.
5560. 3300.
6000. 10000.
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6 7
I
2 3 4
5 4
4
profile 014A
2
6.
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8
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7
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7
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8
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9
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5 6 7 8 9 10 11 12
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·Appendix B Curve Ordinates This appendix gives the curve ordinates for the basic spectrum, the nine groups soil amplification spectra and normalized response. The curves shown in the FINDINGS AND IMPLEMENTATION OF TilE RESULTS section were smoothed using spline-fitting.
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