PEER Meeting, 02/15/05
SUMDES RESULTS COMPUTED FOR
TREASURE ISLAND AND GILROY_2 SITES
By Zhi-Liang Wang
1.
Introduction
Site response computed by SUMDES04:
 Use reference strain suggested by UCLA team
 Use estimated shear strength
 Ways to fit damping curve in non-linear analyses
2.
SUMDES Results Using Reference Strain Determined at G/Gmax = 0.5
Following suggestions by USLA team (Jonathan and Annie), reference strains are
determined at G/Gmax = 0.5 for the modulus reduction curves (T1, T2, G1 through G4)
applied for the two sites. For G2 and G3 curves, I estimated the reference strains as
0.102% and 0.125%.
I found that if we use the Stokoe’ approach to define the reference strain (a strain
corresponding to G/Gmax= 0.5 from a given modulus reduction curve) then, for the
bounding surface model (Wang, 1990), the model parameter hr= 0.7726.
In general, we can propose that for a given modulus reduction curve G/Gmax versus strain,
the reference strain can be defined by G/Gmax = a ( say 0.45 < a <0.55). For the Wang
model (1990, Eq.2.34, page 49, or, from SUMDES manual, page 33),
2 

Gmax    f [  ln( 1  )]
(1)
hr  f
f
Substituting the know relations:
G / Gmax  a   r /  r / Gmax
(2)
and maximum shear stress
 f   r Gmax
(3)
we have
2(a  ln( 1  a))
hr  
(1  a)
(4)
If we use a = 0.5 (following Stokoe), then hr = 0.7726 as a constant, but the reference
strain depends on the modulus reduction curves specified.
The given modulus and damping curves and the curve fittings using the above model
parameter hr = 0.7726 are shown in Figures 1 and 2.
Also shown in the two figures are modulus and damping for each soil layers computed
using program SHAKE. The computed surface response spectra are presented in Figures
3 and 4. The relatively lower response spectral values at Treasure Island site may due to
the higher damping as shown in Figure 1a.
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PEER Meeting, 02/15/05
Normalized Shear Modulus, G/Gmax
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0001
Treasure Island Site
T1: 0-44 feet (Darragn and Idriss, 1997)
Wang Model, hr=0.7726,
reference strain from G/Gmax=0.5
from SHAKE results
0.001
0.01
0.1
1
Effective Shear Strain Amplitude (%)
Material Damping Ratio (%)
Treasure Island Site
T1 Damping: 0-44 feet (Darragh and Idriss, 1997)
30
Wang Model
from SHAKE results
20
10
0
0.0001
0.001
0.01
Effective Shear Strain Amplitude (%)
Figure 1a. Model Simulation for T1 Curve
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Normalized Shear Modulus, G/Gmax
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0001
Treasure Island Site
T1: >44 feet (Darragn and Idriss, 1997)
Wang Model, hr=0.7726,
reference strain from G/Gmax=0.5
from SHAKE results
0.001
0.01
0.1
1
Material Damping Ratio (%)
Effective Shear Strain Amplitude (%)
Treasure Island Site
T1 Damping: >44 feet (Darragh and Idriss, 1997)
30
Wang Model
from SHAKE results
20
10
0
0.0001
0.001
0.01
Effective Shear Strain Amplitude (%)
Figure 1b. Model Simulation for T2 Curve
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PEER Meeting, 02/15/05
Normalized Shear Modulus, G/Gmax
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0001
Gilroy 2 Site
G1: 0-40 feet (Darragn and Idriss, 1997)
Wang Model, hr=0.7726,
reference strain from G/Gmax=0.5
from SHAKE results
0.001
0.01
0.1
1
Effective Shear Strain Amplitude (%)
Material Damping Ratio (%)
Gilroy 2 Site
G1 Damping: 0 - 40 feet (Darragh and Idriss, 1997)
30
Wang Model
from SHAKE results
20
10
0
0.0001
0.001
0.01
Effective Shear Strain Amplitude (%)
Figure 2a. Model Simulation for G1 Curve
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PEER Meeting, 02/15/05
Normalized Shear Modulus, G/Gmax
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0001
Gilroy 2 Site
G2: 40-80 feet (Darragn and Idriss, 1997)
Wang Model, hr=0.7726,
reference strain from G/Gmax=0.5
from SHAKE results
0.001
0.01
0.1
1
Material Damping Ratio (%)
Effective Shear Strain Amplitude (%)
30
Gilroy 2 Site
G2 Damping: 40 - 80 feet (Darragh and Idriss, 1997)
Wang Model
from SHAKE results
20
10
0
0.0001
0.001
0.01
Effective Shear Strain Amplitude (%)
Figure 2b. Model Simulation for G2 Curve
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PEER Meeting, 02/15/05
Normalized Shear Modulus, G/Gmax
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0001
Gilroy 2 Site
G3: 80-130 feet (Darragn and Idriss, 1997)
Wang Model, hr=0.7726,
reference strain from G/Gmax=0.5
from SHAKEresults
0.001
0.01
0.1
1
Material Damping Ratio (%)
Effective Shear Strain Amplitude (%)
30
Gilroy 2 Site
G3 Damping: 80 - 130 feet (Darragh and Idriss, 1997)
Wang Model
from SHAKE results
20
10
0
0.0001
0.001
0.01
Effective Shear Strain Amplitude (%)
Figure 2c. Model Simulation for G3 Curve
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PEER Meeting, 02/15/05
Normalized Shear Modulus, G/Gmax
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0001
Gilroy 2 Site
G4: >130 feet (Darragn and Idriss, 1997)
Wang Model, hr=0.7726,
reference strain from G/Gmax=0.5
from SHAKE results
0.001
0.01
0.1
1
Effective Shear Strain Amplitude (%)
Material Damping Ratio (%)
Gilroy 2 Site
G4 Damping: >130 feet (Darragh and Idriss, 1997)
30
Wang Model
from SHAKE results
20
10
0
0.0001
0.001
0.01
Effective Shear Strain Amplitude (%)
Figure 2d. Model Simulation for G4 Curve
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0.8
Treasure Island Site
from SUMDES04, Reference Strains Based on G/Gmax=0.5
from SUMDES04, Estimated Strength
from SHAKE
0.7
Pseudo Spectral Acceleration (g)
0.6
0.5
0.4
0.3
0.2
0.1
0
0.01
1
0.1
10
Period (second)
Figure 3. . Comparison of Computed Response Spectra for Treasure Island Site
0.8
Gilroy 2 Site
Surface Response Spectrum from SUMDES04
Surface Response Spectrum from SHAKE
0.7
Pseudo Spectral Acceleration (g)
0.6
0.5
0.4
0.3
0.2
0.1
0
0.01
0.1
1
10
Period (second)
Figure 4. Comparison of Computed Response Spectra for Gilroy_2 Site
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3
SUMDES Results Using Estimated Shear Strength
The plasticity models implemented in SUMDES use the soil strength as a basic model
parameter. In the model 6, a simplified version of the bounding surface model (Wang,
1990, Wang et al., 1990), the input parameters are c, , Gmax and hr. For each of the soil
layers, we can use c = Su and  =0, then the model parameter hr can be calibrated using a
program HRW6NEW.EXE.
For an example, I estimated soil strengths for the Treasure Island site,
a) Top sand layer: strength is correlated with given blow count SPT. (See EPRI
Manual).  =32 degree was selected.
b) Young Bay Mud: based on recent UCB fast loading test on YBM samples
(Riemer and Faris, 2003), Su/v=0.44 was selected.
c) Old Bay Clay: based on recent Fugro and Earth Mechanics (1998) test report,
average Su/v=0.59 from 13 triaxial tests. Su/v=0.50 was selected for a 1_D
simple shear condition.
The model simulations are shown in Figures 5 and 6 for T1 and T2 respectively based on
given strength values. The computed surface response spectrum is also presented in
Figure 3 for comparison with those using reference strain approach.
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PEER Meeting, 02/15/05
Normalized Shear Modulus, G/Gmax
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0001
Treasure Island Site
T1: 0-44 feet (Darragn and Idriss, 1997)
Wang Model, hr calibrated for given strengths
from SHAKE results
0.001
0.01
0.1
1
Material Damping Ratio (%)
Effective Shear Strain Amplitude (%)
30
Treasure Island Site
T1 Damping: 0-44 feet (Darragh and Idriss, 1997)
Wang Model
from SHAKE results
20
10
0
0.0001
0.001
0.01
0.1
Effective Shear Strain Amplitude (%)
Figure 5. Model Simulations Based on Given Strengths for T1 Curve
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PEER Meeting, 02/15/05
Normalized Shear Modulus, G/Gmax
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0001
Treasure Island Site
T1: >44 feet (Darragn and Idriss, 1997)
Wang Model, hr calibrated for given strengths
from SHAKE results
0.001
0.01
0.1
1
Material Damping Ratio (%)
Effective Shear Strain Amplitude (%)
30
Treasure Island Site
T1 Damping: >44 feet (Darragh and Idriss, 1997)
Wang Model
from SHAKE results
20
10
0
0.0001
0.001
0.01
0.1
Effective Shear Strain Amplitude (%)
Figure 6. Model Simulations Based on Given Strengths for T2 Curve
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4.
Damping Curve in Non-linear Analyses
For a skeleton or backbone curve with shear strength as an upper limit (or an asymptotic
line), the damping will approach 2/ (or 63%) as a limit for very large strains. That
means it is impossible to fit the given damping curve that normally is about 25 to 30
percent at large strain level. There are two ways to fit the damping curve. The first way is
that define a backbone curve that does not use the strength limit. For example, the so
called Martin-Davidenkov model implemented in a modified DESRA program (MADES,
by C.M. Mok and C.Y. Chang, Geomatrix). In such a model three parameters are used to
reasonably fit modulus reduction and damping curves. But, the drawback is that there is
no strength limit, so that at high acceleration input motions it may compute much higher
shear stresses than the soil strength allowed like often is the case in a program using
elastic model (e.g., SHAKE).
The second way is to modify the Masing rule that is always used in the unloading and reloading cases. Masing rule is simply a doubled backbone (or skeleton) curve for
unloading. A generalized Masing rule was proposed in 1980 by Wang et al. (1980, also
see Finn, 1982). That model exactly fits a modulus and damping curves using the
generalized Masing rule.
Skeleton (or backbone) curve:
  f ( )
Unloading-reloading (Masing curve):
 m
2
 f(
(5)
 m
2
)
(6)
Generalized Masing curve with damping correction:
   m  k ( m )[ 2 f (
 m
2
)  G ( m )(   m )]  G ( m )(   m )
(7)
in which k(m) is the damping correction factor that is the ratio of the given damping and
the damping computed from the given modulus reduction curve, f()/Gmax, using the
original Masing curve Eq.(6) at strain level m.
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References
Finn, W.D.L., 1982, “Soil Liquefaction Studies in the People’s Republic of China”, Soil
Mechanics – Transient and Cyclic Loads.
Wang, Z.L., H. Qing-Yu, and Z. Gen-Shou., 1980, “Wave Propagation Method of Site
Seismic Response by a Visco-Elastoplastic Model,” Proceedings: Seventh World
Conference on Earthquake Engineering, v. 2, p. 279-386.
Wang, Z.L., 1990, “Bounding Surface Hypoplasticity Model for Granular Soils and its
Applications,” Ph.D. Thesis, University of California at Davis. (Dissertation
Information Service, Order No. 9110679, Ann Arbor, MI 48106.)
Wang, Z.L, Y.F. Dafalias, and C.K. Shen, 1990, “Bounding Surface Hypoplasticity
Model for Sand," Journal of Engineering Mechanics, American Society of Civil
Engineering, vol. 116, no. 5, p. 983-1001, 1990.
Figure 7. Generalized Masing Curve, Wang et al. (1980)
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