Improvements to the
Development of
Acceleration Design
Response Spectra
Nicholas E. Harman, M.S., P.E., SCDOT
Thanks
• Clemson University
– Dr. Ron Andrus
• Co-Principal Investigator
– Dr. Nadarajah Ravichandran
• Co-Principal Investigator
– Shimelies Aboye
• PhD Candidate
– Ariful Bhuiyan
• PhD Student
Background
• Kramer (1996) indicates that the effect of
local site conditions has been previously
noted.
– MacMurdo (1824) – 1819 Cutch, India EQ
– Mallet (1863) – 1857 Neapolitian EQ
• 2 EQ events emphasized the effect of
local site conditions on Site Amplification
– 1985 Michoacán, Mexico (aka Mexico City)
EQ
– 1989 Loma Prieta, California EQ
Michoacán, Mexico (aka Mexico
City) EQ
•
•
•
•
•
•
September 19, 1985
Mw = 8.1
R = 217 miles from Mexico City
Duration = 3 to 4 minutes
Fault displaced approximately 10 feet
Most of the damage was caused by
resonance between the soils, the
earthquake and the structures
Loma Prieta, California EQ
•
•
•
•
•
•
October 17, 1989
Mw = 6.9
R = 61 miles from San Francisco
Duration = 10 to 15 seconds
Maximum fault displacement 7.5 feet
Numerous bridges damaged
Results
• Based on the destruction for both EQ
events
– Rock Sites are stiffer
– Soil Sites tend to amplify the EQ motion
• Especially for soft sites
• To account for these different responses
based on site stiffness
– NEHRP recommendations were developed
NEHRP
• Each site is classified based on its
stiffness (aka Site Class)
– Stiffness can be measured using
• Vs
•N
• Undrained shear strength, Su
• Developed Site Amplification Factors (F)
– F factors based on
• Site stiffness
• Acceleration
Site Class
Source: AASHTO Guide Specifications for LRFD Seismic Bridge Design, 2nd Edition, 2014 Interim
Revisions, AASHTO
SC Practice
AVERAGE PROPERTIES IN TOP 100 FT (30 M) Below ZDTM
SITE CLASS
SOIL PROFILE
NAME
A
Hard Rock
B
Rock
C
Very Dense Soil and Soft
Rock
D
Stiff Soil
E
Soft Soil
F
Soils Requiring Site Specific
Response Evaluation
SITE STIFFNESS V
s
Vs > 5,000 ft/sec ( Vs>1500 m/sec)
2,500 
Vs  5,000 ft/sec (760  Vs  1500 m/sec)
1,200  Vs
 2,500 ft/sec (360  Vs
600  V  1,200 ft/sec (180 
s
 760 m/sec)
Vs  360 m/sec)
Vs < 600 ft/sec ( < 180 m/sec)
Any profile with more than 10 ft (3m) of soft clay defined as:
PI > 20; w > 40%; and   s u < 500 psf (25 kPa)
Any soil profile containing one or more of the following characteristics:
1.
Peats and/or highly organic clays (H>10 ft [3 m] of peat and/or
highly organic clay where H = thickness of soil)
2.
Very high plasticity clays (H>25 ft [8 m] with PI > 75)
3.
Very thick soft/medium stiff clays (H> 120 ft [36 m])
Definitions:
PI
= Plasticity Index (AASHTO T89, T90 or ASTM D 4318)
w
= Moisture Content (AASHTO T265 or ASTM D 2216)
= Average shear wave velocity for the upper 100 ft (30 m) below ZDTM. (ft/sec or m/sec)
= Average undrained shear strength ( ) for cohesive soils in the upper 100 ft (30 m) below ZDTM. (psf or kPa) (AASHTO T208 or T296 or ASTM D2166 or D2850)
ZDTM = Depth-to-motion is the location where the ground motion transmits the ground shaking energy to the structure.
Notes:
(1)
The shear wave velocity for rock, Site Class B, shall be either measured on site or estimated by a geotechnical engineer or engineering geologist/seismologist for competent rock with
moderate fracturing and weathering. Softer and more highly fractured and weathered rock shall either be measured on site for shear wave velocity or classified as Site Class C.
(2)
The hard rock, Site Class A, category shall be supported by shear wave velocity measurements either on site or on profiles of the same rock type in the same formation with an equal
or greater degree of weathering and fracturing. Where hard rock conditions are known to be continuous to a depth of 100 feet (30m) below ZDTM, surficial shear wave velocity
measurements may be extrapolated to assess shear wave velocities.
(3)
Site Classes A and B should not be used when there is more than 10 feet (3m) of soil between the rock surface and the depth-to-motion, ZDTM. When rock is encountered within the
100 feet (30m) below the depth-to-motion, ZDTM, and the soil layer is more than 10 feet (3m) use the Site Class pertaining to the soil above the rock.
(4)
A Site Class F is not required if a determination is made that the presence of such soils will not result in a significantly higher response of a bridge. Consideration of the effects of
depth-to-motion, ZDTM, shall be taken into account when making this determination. Such a determination must be approved by the PCS/GDS.
Spectral Accelerations
• Once Site Class determined
• Determine Spectral Accelerations (PSA)
for
– PGA
– SS
– S1
• Spectral Accelerations developed at B-C
Boundary or Hard Rock surface
– VsB-C > 2,500 ft/sec
– VsHR >11,500 ft/sec
Site Amplification Factors
• F factors are determined using
–𝐹=
𝑆𝑠𝑖𝑡𝑒
𝑆𝑜𝑢𝑡𝑐𝑟𝑜𝑝
– Ssite – Spectral Acceleration at a selected
period at the ground surface
– Soutcrop – Spectral Acceleration at a selected
period at the soft-rock outcrop
• F factors for the short (0.2 sec) (Fa) and
long (1.0 sec) (Fv) periods were developed
• Fa and Fv were developed empirically using
strong motion records from Treasure and Yerba
Buena Islands in San Francisco Bay
– PGA ~0.1g
• For strong levels of shaking one-dimensional
equivalent linear and non-linear site response
analyses were performed.
• These are the factors currently in use
• Fa was developed for a spectral period ranging
from 0.1 to 0.5s
• Fv was developed for a spectral period ranging
from 0.4 to 2.0s
• FPGA is equal to Fa
Site Amplification Factors
• Determine F using PSA and Site Class
Source: AASHTO Guide Specifications for LRFD Seismic Bridge Design, 2nd Edition, 2014 Interim Revisions, AASHTO
3-Point ADRS
• Develop the 3-point ADRS Curve using
the above information to determine
– 𝑃𝐺𝐴 = 𝐴𝑠 = 𝐹𝑃𝐺𝐴 ∗ 𝑃𝐺𝐴𝐵−𝐶
– 𝑆𝐷𝑆 = 𝐹𝑎 ∗ 𝑆0.2𝐵−𝐶 = 𝐹𝑎 ∗ 𝑆𝑠𝐵−𝐶
– 𝑆𝐷1 = 𝐹𝑣 ∗ 𝑆1𝐵−𝐶
– 𝑇𝑠 =
𝑆𝐷1
𝑆𝐷𝑆
and 𝑇𝑜 = 0.2 ∗ 𝑇𝑆
Concerns
• The existing F factors were developed for
– Relatively thin soil profiles (~200 feet)
– Soft rock (Vs = 2,500 to 5,000 ft/sec)
– Relatively low accelerations (PGA ~0.1g)
• South Carolina has
– Soil profiles in excess of 1,000 ft
– Hard rock (Vs = 8,200 to 11,000 ft/sec)
– Accelerations at the B-C Boundary in excess
of 0.6g
• Concerns confirmed in a paper by Kimball
and Costantino (2000)
– F factors at SRS lower than used by NEHRP
• SCDOT has enough site-specific seismic
response analyses showing dramatic
decreases in ADRS curves to show F
factors may be conservative
– Decreases in some case on the order of 50%
• ∴ SCDOT contracted with Clemson
University to study SC specific F factors
SC General Geology
Piedmont
Coastal Plain
Clemson’s Approach
• Investigate and recommend F factors for
the Coastal Plain and the Piedmont
• Investigate period shifting observed by
SCDOT in site-specific seismic response
analysis
• Look at the applicability of continuing the
use of Site Class determination using only
the upper 100 feet of a site instead of
something deeper
• Investigate the existing Site Class system
as applied to SC
• Provide procedures so engineers can
understand the repercussions of the new
ADRS curves on design
• Develop spreadsheet to determine F
factors
F Factor Determination
• One-dimensional equivalent linear
analysis (SHAKE ~36,000 runs)
• One-dimensional total stress non-linear
analysis (D-MOD ~12,000 runs)
• Earthquake histories were developed
using SCENARIO_PC (2006)
• NEHRP Fa and Fv based on spectral
period ranges of 0.1 – 0.5s and 0.4 – 2.0s,
respectively (Borchedt (1994))
• Narrower period ranges allow of better
spectral acceleration prediction
• Therefore period ranges of:
– ≤ 0.01
PGA
– 0.01 – 0.4
T0.2
T0.6
– 0.41 – 0.8
T1.0
– 0.81-1.2
T1.6
– 1.21 – 2.0
T3.0
– 2.01 – 4.0
• F is controlled by:
– Vs100 – Shear wave velocity for top 100 feet
– Tm – Mean predominant period used to
present period (frequency) of ground motion
– T330 – Proxy variable for site fundamental
period
– KH – Dimensionless adjustment coefficient to
account for shallow soft rock (B-C Boundary)
– Soutcrop – Spectral acceleration at outcrop at a
specific spectral period
• Tm – Increases with increasing distance
from the epicenter (R) and depth to hard
rock (ZHR)
– R comes from USGS Deaggregation Charts
– ZHR – Scenario_PC
• 𝑇𝑚 = 0.102 ∗
𝑍𝐻𝑅
1000
+ 0.301 ∗
𝑅
1000
+ 0.233
• T330 – Site period to a depth of 330 feet
– 𝑇330 =
4∗330
𝑉𝑠330
=
1320
𝑉𝑠330
Research Results
• Vs100 – F data pairs have 3 general
features
– Increasing trend in F as Vs100 increases from
a very low value
– A zone of peak F values depending on Soutcrop
– Decreasing trend in F as Vs100 increases
beyond the zone of peak F values
Procedure
• Obtain from field testing or existing
geologic information
– Vs100
– Vs330 or T330
– ZHR
– ZB-C
• Obtain from ground motions
– Soutcrop or PSAoutcrop
–R
– Tm
Peak Site Factor Determination
• 𝐹𝑃 = 𝑥1 𝑒𝑥𝑝
• 𝑉𝑠100𝑃 =
𝑥2 𝑆𝑜𝑢𝑡𝑐𝑟𝑜𝑝
𝑔
𝑇𝑚 𝑥3
𝑇330
𝑆𝑜𝑢𝑡𝑐𝑟𝑜𝑝 𝑥5 𝑇𝑚 𝑥6
𝑥4
𝑔
𝑠
+ 1 𝐾𝐻1
𝐾𝐻2
• x1, x2, x3, x4, x5, x6 – Regression
coefficients
• Once FP and Vs100P are determined then
the median Vs100 - F relationship can be
determined
• For Vs100 < Vs100P and all T
–𝐹=
𝐹𝑃
𝑉𝑠100𝑃
𝑉𝑠100
• For Vs100 ≥ Vs100P
– T < 0.2s
•𝐹=
𝐹𝑃 −1 2500−𝑉𝑠100
2500−𝑉𝑠100𝑃
– T ≥ 0.2s
• 𝐹 = 𝑎 + 𝑏𝑒 𝑐𝑉𝑠30
+1
• a – regression coefficient
• 𝑏=
• 𝑐=
1−𝑎
𝑒 760𝑐
ln
unitless
1−𝑎
𝐹𝑃 −𝑎
760−𝑉𝑠30𝑃
• 𝑉𝑠30𝑃 =
𝑉𝑠100𝑃
3.28
units of s/m
and 𝑉𝑠30 =
𝑉𝑠100
3.28
Results
• The F factors determined using this new
procedure result in
– F factors more similar to those developed
using site response analyses
– F factors are far more dependent on Vs then
indicated using NEHRP/AASHTO
– Anticipated differences between site response
analyses and 3 point method should be
greatly reduced
Example
• Questions?