Transcript Regression Equations for Estimating Shear

Comparing Liquefaction Evaluation
Methods Using Penetration-VS
Relationships
Ronald D. Andrus
Clemson University
with
P. Piratheepan, Brian S. Ellis, Jianfeng Zhang,
and C. Hsein Juang
U.S.-Taiwan Workshop on Soil Liquefaction
National Chiao Tung University, Hsin-Chu, Taiwan
November 3-5, 2003
Acknowledgements
• The U.S. Geological Survey (USGS) and the South
Carolina Department of Transportation (SCDOT) funded
part of this work
• Many individuals assisted with data collection, including:
T. L. Holzer, M. J. Bennett, J. C. Tinsley, & T. E. Noce of USGS
T. N. Adams of SCDOT
T. J. Casey & W. B. Wright of Wright Padgett Christopher
W. M. Camp & E. Cargill of S&ME, Inc.
F. Syms of Bechtel Savannah River, Inc.
S. L. Gassman of University of South Carolina
Database
• Data from California, South Carolina,
Canada, Japan, and Taiwan
• 45 Holocene (< 10,000 years) soil layers,
and 55 older soil layers
• Only sands with FC ≤ 20 % or Ic ≤ 2.25
• All measurements below water table
• Both non-liquefied and liquefied sites
Criteria for Selecting Data
• Thick, uniform soil layers based on CPT data,
or several SPT and VS measurements
• Penetration test within 6 m of Vs test
• At least 2 Vs measurements and corresponding
test intervals within layer
• Time history records used for Vs determination
have “easy picks” for shear wave arrivals; if
time histories are not available, at least 3 Vs
measurements within layer
Corrected S-Wave Velocity
VS1 csa1  Ka1VS1 cs  Ka1KcsVS1
where
VS1 = stress-corrected VS
(VS1)cs = stress- and fines content-corrected VS
Kcs = fines content correction factor (Juang et al. 2002)
Ka1 = age correction factor (Andrus & Stokoe 2000)
Cyclic Resistance Ratio, CRR
Three Curves for Evaluating
Liquefaction Resistance
0.6
0.6
M W = 7.5
D 50 = 0.25-2 mm
M W = 7.5
0.5
0.5
0.4
Robertson
& Wride
0.3
(1998)
0.3
Modified 0.2
Seed et al.
(1985) 0.1
0.2
0.1
0.5
0
0.4
0.3
Andrus
& Stokoe
(2000)
0.1
No Liquefaction
0
10 20 30 40 50
Liquefaction
0.2
No Liquefaction
0
M W = 7.5
Liquefaction
Liquefaction
0.4
0.6
0
No Liquefaction
0
50 100 150 200 250 100
150
200
250
Corrected SPT Blow Corrected CPT Tip
Corrected S-Wave
Count, (N 1 )60cs
Resistance, (q c1N )cs Velocity, (V S1 )csa1 , m/s
Corrected S-Wave Velocity,
(VS1 )cs , m/s
SPT – VS Relationships for
Holocene Sands
300
Mean for Holocene data:
0.253
(V S1 )cs = 87.7[(N 1 )60cs ]
250
Implied from
CRR curves
200
Age, years
< 500 > 500
Yound
Old
Non-liquefied
YL
LiquefiedO L
150
100
0
10
20
30
40
50
60
Corrected SPT Blow Count, (N 1 )60cs
Corrected S-Wave Velocity,
(VS1 )cs , m/s
CPT - VS Relationships for
Holocene Sands
300
250
Age,
Yound years
Old
L
<YO500
> 500
L
Non-liquefied
Liquefied
Implied from
CRR curves
200
150
Mean for Holocene data:
0.213
(V S1 )cs = 67.6[(q c1N )cs ]
100
0
50
100
150
200
250
300
Corrected CPT Tip Resistance, (q c1N )cs
Corrected SPT Blow
Count, (N1 )60cs
CPT – SPT Relationships for
Holocene Sands
60
50
40
Age,
Youndyears
Old
< 500
> 500
YL
OL
Non-liquefied
Liquefied
Implied from
CRR curves
30
20
Mean for Holocene data:
0.779
(N 1 )60cs = 0.488[(q c1N )cs ]
10
0
0
50
100
150
200
250
300
Corrected CPT Tip Resistance, (q c1N )cs
VS – CRR Equation
(Andrus & Stokoe 2000)
 VS 1 csa1 
 0.022

 100 

1
1 
 2.8


 215 VS 1 csa1 215
2
CRR7.5cs
where
CRR7.5cs = CRR curve for MW = 7.5 and FC ≤ 5 %
(VS1)csa1 = corrected VS
New SPT – CRR Equation

CRR7.5cs  0.0169  N 1 60cs

0.506

1
1 
 2.8


0.253
215
 215 87.7 N 1 60cs 
where
CRR7.5cs = CRR curve for MW = 7.5 and FC ≤ 5 %
(N1)60cs = corrected SPT blow count
New CPT – CRR Equation

CRR7.5cs  0.0101 qc1 N cs

0.426

1
 2.8
 215 67.6 qc1 N cs

1 


0.213
215

where
CRR7.5cs = CRR curve for MW = 7.5 and IC ≤ 1.64
(qc1N) cs = corrected CPT tip resistance
Cyclic Resistance Ratio, CRR
NEW CRR Curves Based on
Penetration – VS Equations
0.6
0.6
M W = 7.5
D 50 = 0.25-2 mm
M W = 7.5
0.5
0.5
Liquefaction
0.4
Robertson
& Wride
0.3
(1998)
New
0.2
CRR
Curve 0.1
No Liquefaction
10 20 30 40 50
Andrus
& Stokoe
(2000)
No Liquefaction
0
0
0
0.3
New 0.2
CRR
Curve 0.1
No Liquefaction
0
0.5
Liquefaction
0.4
Modified
Seed et al.
0.3
(1985)
0.1
M W = 7.5
Liquefaction
0.4
0.2
0.6
0
50 100 150 200 250 100
150
200
250
Corrected S-Wave
Corrected SPT Blow Corrected CPT Tip
Resistance, (q c1N )cs Velocity, (V S1 )csa1 , m/s
Count, (N 1 )60cs
Cyclic Resistance Ratio, CRR
Comparison of CRR Curves with
Liquefaction Probability = 26 %
0.6
0.6
0.6
Youd & Noble (1997)
0.5
0.4
0.3
0.2
0.1
0.0
0.5
New CRR
Curve
Juang
Cetin et al.
et al.
(2000)
(2002)
Liao
Model 1
et al.
(1988)
Toprak
et al. (1999)
Juang et al.
(2002) Model 2
0
10
20
New CRR Curve
30
40
0.5
Juang et al.
(2002)
Model 2
0.4
0.3
Toprak
et al.
(1999)
0.2
0.1
50
Corrected SPT Blow
Count, (N 1 )60cs
0
0
0.4
0.3
Juang 0.2
et al.
(2002) 0.1
Model 1
0
Juang et al.
(2002) Model 2
Andrus &
Stokoe
(2000);
Juang et al.
(2002)
Model 3
50 100 150 200 250 100
Juang et al.
(2002) Model 1
150
200
250
Corrected CPT Tip
Corrected S-Wave
Resistance, (q c1N )cs Velocity, (V S1 )csa1 , m/s
Corrected S-Wave Velocity,
(VS1 )cs , m/s
SPT - VS Relationships
for Older Sands
350
300
Implied from
CRR curves
250
Mean for Holocene data:
(V S1 )cs = 87.7[(N 1 )60cs ]0.253
200
150
Ten Mile Hill
OL
(Liquefied)
100
0
10
20
30
40
50
60
Corrected SPT Blow Count, (N 1 )60cs
Corrected S-Wave Velocity,
(VS1 )cs , m/s
CPT - VS Relationships
for Older Sands
350
Mean for Holocene data:
(V S1 )cs = 67.6[(q c1N )cs ]0.213
300
250
200
Non-Liq Liq
150
Merritt Sand
WandoYound
OldHill
Ten Mile
YL
OL
Dry Branch
Series7
TaiwanSeries8
Sand
Implied from
CRR curves
100
Series9
0
50
100
150
200
250
300
Corrected CPT Tip Resistance, (q c1N )cs
Corrected SPT Blow
Count, (N1 )60cs
CPT – SPT Relationships
for Older Sands
60
Mean for Holocene data:
0.779
(N 1 )60cs = 0.488[(q c1N )cs ]
50
40
Implied from
CRR curves
30
20
10
Ten Mile Hill
OL
(Liquefied)
0
0
50
100
150
200
250
300
Corrected CPT Tip Resistance, (q c1N )cs
Age Scaling Factor, ASF
Age Scaling Factors for
Penetration – VS Equations
1.8
1.6
ASF = 0.073log(age)+0.92
Merritt Sand
R 2 = 0.843
Wando
1.4
Dry
Branch
100-500
years
1.2
Ten Mile Hill
1.0
0.5-10 ka
< 100 years
0.8
0
10
1.E+00
2
10
1.E+02
4
10
1.E+04
Age,years
years
Age,
SPT-VS data
CPT-VS data
6
10
1.E+06
8
10
1.E+08
Age Correction Factors
Time
(years)
1
10
100
1,000
10,000
100,000
Age Correction Factor,
Ka1 (≈ 1/ASF)
1.09
1.01
0.94
0.88
0.83
0.78
Conclusions
• For the compiled Holocene data, the VS-based CRR
curve by Andrus and Stokoe is on average more
conservative than the SPT- and CPT-based curves.
• Values of VS from liquefied sands are lower than those
from non-liquefied sands with similar penetration
resistances.
• The penetration-VS equations developed for Holocene
sands change by a factor of about 0.073 per log cycle
of time, based on data from non-liquefied sands.
• The VS-based CRR curve is characterized for soils
with age of roughly 10 years; and new age scaling
factors are proposed.