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Statistical Estimation of Soil Type UsingCross-plots of S-wave Velocity and
Resistivity in Japanese Levees
*Koichi Hayashi, Geometrics
Tomio Inazaki, PWRI Tsukuba Central Institute
Kaoru Kitao, CubeWorks
Takaho Kita, TK Ocean-Land Investigations
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 1
Outline of Integrated Geophysical Method forLevee Safety Assessment
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 2
• The method consists of a surface-wave method and
resistivity methods, such as a capacitively-coupled
resistivity method or an electro-magnetic method.
• The surface-wave method provides S-wave velocity
structure of levee body and fundation.
• The capacitively-coupled resistivity method or the
electro-magnetic method provides resistivity structure
of levee body and foundation.
• A cross-plot analysis of S-wave velocity and resistivity
estimates soil type of levee body and foundation.
Surface-wa e Method Using Land Streamer
"' Short.wavd ngth surfa<: wav s
)
3
Resistivity Method Using Capacitively
Coupled Resistivity (CCR)
Statistical Estimation of Soil Type Using Cross-plots of S-wave
In CCR, capacitors are used as
electrode and metallic stakes are
not used. The OhmMapper was
used as a CCR instrument
Velocity and Resistivity in Japanese Levees 4
S-wave Velocity and N-value
(blow-count) obtained by SPT
0.1
10
Clay
Sand
Gravel
Others
1
100
0 50 100 150 200 250
S-wave velocity (m/sec)
300 350 400
N-
valu
e
N= 1.7 ∗ 10−4 ∗ 𝑉�2.1
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 5
20% Grain Size (D20) and Resistivity
0.001
0.01
0.1
1
10
10 100 1000
Resistivity (ohm- m)
10000
D2
0
(mm
)
Clay
Sand
Gravel
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 6
7
S-wave velocity and Resistivity forLevee Safety
• From theArchie’s equation, resistivity of soil mainly indicates soil type.
• S-wave velocity is mainly affected by shear strength or porosity.
• Safety of levees can be evaluated by S-wave velocity andresistivity.
S-wave velocity
Resistivity
High
Low
Low High
Soil type
Sandy
Clayey
S-wave velocity
Low
Low High
Resistivity
High
Danger (loose, sandy)
Safety
Safe (tight, clayey )
Shear strength(degree of compaction)
High(tight)Low(loose)
S-wave velocity and Resistivity forLevee Safety
8Velocity and Resistivity in Japanese Levees
• A soil type (clay, sand or gravel) or grain size distribution (clay
contents or D20) is the most important information for levee safety
evaluation from an engineering point of view.
• The soil type or the grain size distribution is used in many engineering
analyses
• In most of such analyses, the soil type or the grain size distribution is
obtained by the borings or laboratory tests.
• Physical properties obtained through the geophysical methods (e.g. S-
wave velocity or resistivity) do not directly relate to the soil type and
the grain size distribution.
• We are going to estimate the soil type in terms of a statistical
approach using geophysical and geotechnical data collected in Japan.
Statistical Estimation of Soil Type Using Cross-plots of S-wave
9Velocity and Resistivity in Japanese Levees
Statistical Estimation of Soil Type
• Soil type of levee body and foundation is statistically
estimated using cross-plots of S-wave velocity and
resistivity in Japan
• S-wave velocity and resistivity are collected from
• surface wave methods and resistivity methods.
• Total survey line length of the geophysical methods is
about 600km on 37 rivers in Japan.
• The blow counts and soil types are collected from about
• 400 boring logs carried out on geophysical survey lines.
• The total number of extracted data is about 4000.Statistical Estimation of Soil Type Using Cross-plots of S-wave
Example of Geophysical Sections
-6
-4
-2
-0
2
4
6
8
10
12
14
16
Depth
(m)
-100
12
14
16
018
2
4
6
8
100 183.4 0 500 700 900 1100 1300 1500 1700 1900 2100 2300 2500 2700 2900 3100
Distance (m)
S-wave velocity section
500
360
280
220
160
130
100
70
40
(m/s)
S-wave velocity
1020304050
9.9 S1-0G
1.1BS
GS
6.6S
8.0GS
10.6
GS
-6
-4
-2
-0
2
4
6
8
10
12
14
16
Depth
(m)
-100 100 183.4 0 500
12
14
16
018 700 900 1100 1300 1500 1700 1900 2100 2300 2500 2700
Distance (m)
2900 3100
Resistivity section
3000
1000
500
360
240
150
80
40
10
Ohm-m
Resistivity
1020304050
2
4
6
8
9.9 S1-0G
1.1BS
GS
6.6S
8.0GS
10.6
GS
S-wave velocity
Resistivity
Levee body (unsaturated)
Foundation (saturated)
Levee body (unsaturated)
Foundation (saturated)
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 10
Extracting Vs, Resistivity and Soil type
6
8
10
12
14
16
-6
Depth
(m)
-100 100 183.4 0 500
12
14
16
018 700 900 1100 13700.3 1500 17006 1900
8.3Distance (m2)3
9.3 20
10.3 24
12.3 29
13.3 33
14.3 31
15.3 35
16.3 19
2100 23202002500 2700 2190304 3100
S-wave velocity section
(m/s)
40
10070
130
220160
280
5003602
4
6
8
9.9 S1-0G
6.6S
8.0GS
10.6
GS
-6
-4
-2
-0
2
4
6
8
10
12
14
16
Depth
(m)
-100 100 183.4 0 500
12
14
16
018 700 900 1100 1300 1500 1700 1900 2100 2300 2500 2700 2900 3100
Distance (m)
Resistivity section
10
Ohm-m
sistivity
40
15080
240
500360
3000
1000
1020304050
2
4
6
8
9.9 S1-0G
1.1BS
GS
6.6S
8.0GS
10.6
GS
Levee body3.3 8 220 339 Gravel
4.4 10 259 378 Gravel
5.5 8 223 262 Gravel
6.3 8 223 262 Gravel
Foundation
Sand
243 134 Gravel
247 134 Gravel
247 93 Sand
Gravel
311 80 Gravel
311 80 Gravel
307 80 Gravel
307 73 Gravel
307 73 Gravel
17.3 39 307 73 Gravel
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 11
Depth N-value S-wave velocity Resistivity Soil type-4
-2(m) (m/sec) (ohm-m)
S-
wave velocity
-0
2
1.1BS
1020304050
1.3 42 230 226 Gravel
4 GS
2.3 9 230 256 Gravel
Re
11.3 20 297 93
Cross-plot of Vs and Resistivity
100
Re
sist
ivit
y(m
/se
c)
1
10
100
1000
10000
0
S-wave velocity (m/sec)
10000
1
10
100
1000
0 100
Levee body200 300 400 500
Foundation200 300 400 500
Re
sist
ivit
y(m
/se
c)
S-wave velocity (m/sec)
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 12
Sand
Gravel
Sand
Gravel
S-wave velocity Resistivit
y
Soil type
(m/sec) (ohm-m)
230
230
226
256
Grave
l
Grave
l
220 339 Gravel Levee
body
259 378 Gravel
223 262 Gravel
223
220
243247
262
134
134134
Grave
l
Sand
Grave
lGravel
247 93 Sand
297 93 GravelFoundation
311 80 Gravel
311 80 Gravel
307 80 Gravel
Resistivity and S-wave velocityfrom 400 Boring Logs
13
1
10
100
1000
10000
0 50 100 150 200 250 300 350 4
Vs (m/sec)
lay
and
ravel
thers
00 450 500
Re
sist
ivit
y(o
hm
-m
)
C
S
G
O
1
10
100
1000
10000
0 50 100 150 200 250 300 350 400 450 500
Vs (m /sec)
Res
isti
vity
(oh
m-
m)
Clay
Sand
Gravel
Others
Foundation
(saturated)
Levee body
(unsaturated)
1
10
100
1000
10000
Clay
0 450 500
Re
sist
ivit
y(o
hm
-m
)
Vs (m/sec)
1
10
100
1000
10000
Sand
450 500
Re
sist
ivit
y(o
hm
-m
)
Vs (m/sec)
1
10
100
1000
10000
Re
sist
ivit
y(o
hm
-m
)
Vs (m/sec)
Gravel
1
10
100
1000
10000
0 50 100 150 200 250 300 350 400
Vs (m/sec)
450 500
Re
sist
ivit
y(o
hm
-m
)
1
10
100
1000
0 50 100 150 200 250 300
Vs (m/sec)
350 400 450 500
Re
sist
ivit
y(o
hm
-m)
Sand
1
10
100
1000
0 50 100 150 200 250 300
Vs (m/sec)
350 400 450 500
Re
sist
ivit
y(o
hm
-m
)
ClaFy10000
S-wave velocity and Resistivity
10000
Gravel
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 14
oundation
Levee body
Clay Sand Gravel
Polynomial Approximation of Soil Type• Polynomial approximation (curved plane) is used to
estimate the soil type from the correlation between S-wave
velocity and resistivity.
• In the approximation, the soil type is represented by
discontinuous numbers one (clay), two (sand) and three
(gravel).
• Polynomial equation is a function of S-wave velocity (Vs)
and resistivity () and yields a continuous value S between
one and three.
• Coefficients of equation are optimized by least squares
method.
S avs bvs clog10 d log10evs log10 fvs log10 gvs log10h2 22 2
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 15
Soil Type and Represented Numbers
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 16
Soil type Represented
number
Number of data
Levee
body
Foundation
Clay 1.0 221 915
Sand 2.0 199 2145
Gravel 3.0 143 425
Total - 563 3485
S-wave velocity and Resistivity
10000
1000
Resis
ivity
(ohm
-m)
400 450 500
:Gravel (3.0)100
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 17
10
10 50 100 150 200 250 300 350
S-wave velocity (m/s)
:Clay
:Sand
Levee body
(1.0)(2.0)
Resis
tivity
(ohm
-m)
Sand (2.0)
Clay (1.0)10 50 100 150 200 250 300 350 400 450 500
S-wave velocity (m/s)
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 18
:Clay (1.0):Sand (2.0):Gravel(3.0)
Gravel (3.0)
10000
1000
100
10
Polynomial ApproximationLevee body
S-wave velocity and Resistivity
10000
1000
100
10
Resis
tivity
(ohm
-m)
:Clay (1.0):Sand (2.0):Gravel (3.0)
10 50 100 150 200 250 300 350 400 450 500
S-wave velocity (m/s)
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 19
Foundation
Sand (2.0)
Clay (1.0)10 50 100 150 200 250 300 350 400 450 500
S-wave velocity (m/s)
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 20
:Clay (1.0):Sand (2.0)
:Gravel (3.0)
Gravel (3.0)
10000
1000
100
10
Resis
tivity
(ohm
-m)
Polynomial ApproximationFoundation
Polynomial Approximation
Clay
Sand
Gravel
10000
1000
100
10
1
R
e
is
tsvi
tiy(ohm
m-
)
400 450 5000 50 100 150 200 250 300 350
S-wavevelocity(m/s)
400 450 500
:Clay
:Sand
:Gravel
Clay
Sand
Gravel
10000
1000
100
10
1
Resis
tivity (
ohm
-m)
0 50 100 150 200 250 300 350
S-wavevelocity(m/s)
:Clay
:Sand
:Gravel
Clay
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 21
Sand
Gravel
Gravel
Sand
Clay
Foundation
(saturated)
Levee body
(unsaturated)
Polynomial Approximation of Soil Type
S avs bvs clog10 d log10evs log10 fvs log10 gvs log10h2 22 2
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 22
Levee body Foundationa -0.0000062
b -0.0072263
c 0.5333744
d -1.5275230
e 0.0000016
f -0.0025515
g 0.0111545
h 1.7115340
a -0.0000002
b 0.0019388
c 0.0938875
d -0.5366671
e -0.0000064
f 0.0001980
g 0.0032458
h 1.4068120
Example of EstimationS-wave velocity
Elevation (m) S-wave velocity
Levee body
Foundation
Distance (m)
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 23
Distance (m)
(m/sec)
ResistivityElevation (m) Resistivity
(Ohm-m)
Levee body
Foundation
Example of Estimation10000
1000
100
10
Resis
tivity
(ohm
-m)
10
1 0
Resis
tivity
(ohm
-m)
10000
1000
100
Levee body Foundation
Elevation (m)
Gravel (3.0)Levee body
Foundation
Soil type
Sand (2.0)
Clay (1.0)
Distance (m)
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 24
50 100 150 200 250 300 350 400 450 500 1 0 50 100 150 200 250 300 350 400 450 500
S-wave velocity (m/s) S-wave velocity (m/s)
Accuracy of Estimation
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 25
• Accuracy of estimation can be statistically
evaluated by comparing the estimated soil
parameter with actual soil.
• Data were grouped into four groups (1.0 to 1.5, 1.5
to 2.0, 2.0 to 2.5, 3.0 to 3.5) by the estimated soil
parameter.
• In each group, the numbers of actual soil type (clay,
sand, gravel) were counted as probability.
0% 20% 80% 100%
Soil type
Clay(1.0)
Sand(2.0)
Gravel(3.0)2.0 to 2.5
2.5 to 3.0
Proportion Fo
Esti
mat
edso
ilp
aram
ete
r
Levee body
Accuracy of Estimation
Statistical Estimation of Soil Type Using Cross-plots of S-wave
1.5 to 2.0
2.0 to 2.5
2.5 to 3.0
Proportion
Esti
mat
edso
ilp
aram
ete
r
Probability40% 60%
1.0 to 1.5
1.5 to 2.0
Levee body Foundation
0% 20% 80% 100%
1.0 to 1.5
undation
Soil type
Clay(1.0)
Sand(2.0)
Gravel(3.0)
Probability
40% 60%
Velocity and Resistivity in Japanese Levees 26
27Velocity and Resistivity in Japanese Levees
Conclusions• The soil type of levee body and foundation was
statistically predicted using the cross-plots of S-wave velocity and of resistivity.
• The results imply that the physical properties obtained by geophysical methods, such as S-wave velocity andresistivity, can be used not only for qualitativeinterpretation but also quantitative engineering analyses,such as slope stability or liquefaction analyses.
• Similar approaches can be applied to other purposesbesides levee inspection and other countries besidesJapan.
• It is important that any results of geophysicalinvestigations are saved as a standard format and registered in database with adequate geotechnical or geological information.
Statistical Estimation of Soil Type Using Cross-plots of S-wave