1. Statistical Estimation of Soil Type Using
Cross-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

2. Outline of Integrated Geophysical Method for
Levee 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.

3. Surface-wa e Method Using Land Streamer
"' Short.wavd ngth surfa<: wav s
)
3

4. 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

5. 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-
value
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

6. 20% Grain Size (D20) and Resistivity
0.001
0.01
0.1
1
10
10 100 1000
Resistivity (ohm- m)
10000
D20
(mm)
Clay
Sand
Gravel
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 6

7. 7
S-wave velocity and Resistivity for
Levee Safety
• From the Archie’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 and
resistivity.
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)

8. S-wave velocity and Resistivity for
Levee 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

9. 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

10. 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
1.1 BS
GS
6.6
S
8.0
GS
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
1.1 BS
GS
6.6
S
8.0
GS
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

11. 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
100
70
130
220
160
280
500
3602
4
6
8
9.9 S1-0G
6.6
S
8.0
GS
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
150
80
240
500
360
3000
1000
1020304050
2
4
6
8
9.9 S1-0G
1.1 BS
GS
6.6
S
8.0
GS
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

12. Cross-plot of Vs and Resistivity
100
Resistivity(m/sec)
1
10
100
1000
10000
0
S-wave velocity (m/sec)
10000
1
10
100
1000
0 100
Levee body
200 300 400 500
Foundation
200 300 400 500
Resistivity(m/sec)
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
243
247
262
134
134
134
Grave
l
Sand
Grave
l
Gravel
247 93 Sand
297 93 Gravel
Foundatio
n
311 80 Gravel
311 80 Gravel

13. Resistivity and S-wave velocity
from 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
Resistivity(ohm-
m)
C
S
G
O
1
10
100
1000
10000
0 50 100 150 200 250 300 350 400 450
500
Vs (m /sec)
Resistivity(ohm-
m)
Clay
Sand
Gravel
Others
Foundation
(saturated)
Levee body
(unsaturated)

14. 1
10
100
1000
10000
Clay
0 450
500
Resistivity(ohm-
m)
Vs (m/sec)
1
10
100
1000
10000
Sand
450 500
Resistivity(ohm-
m)
Vs (m/sec)
1
10
100
1000
10000
Resistivity(ohm-
m)
Vs (m/sec)
Gravel
1
10
100
1000
10000
0 50 100 150 200 250 300 350
400
Vs (m/sec)
450 500
Resistivity(ohm-
m)
1
10
100
1000
0 50 100 150 200 250 300
Vs (m/sec)
350 400 450 500
Resistivity(ohm-m)
Sand
1
10
100
1000
0 50 100 150 200 250
300
Vs (m/sec)
350 400 450
500
Resistivity(ohm-
m)
Cla
Fy
10000
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

15. 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 dlog10evs log10 fvs log10  gvs log10h
2 22 2
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees 15

16. 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

17. S-wave velocity and Resistivity
10000
1000
Resisivity(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
1
0 50 100 150 200 250 300 350
S-wave velocity (m/s)
:Clay
:Sand
Levee body
(1.0)
(2.0)

18. Resistivity(ohm-m)
Sand (2.0)
Clay (1.0)1
0 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 Approximation
Levee body

19. S-wave velocity and Resistivity
10000
1000
100
10
Resistivity(ohm-m)
:Clay (1.0)
:Sand (2.0)
:Gravel (3.0)
1
0 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

20. Sand (2.0)
Clay (1.0)1
0 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
Resistivity(ohm-m)
Polynomial Approximation
Foundation

21. Polynomial Approximation
Clay
Sand
Gravel
10000
1000
100
10
1
R
e
i
s
t
s
vi
ti
y
(
o
hm
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
Resistivity(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)

22. Polynomial Approximation of Soil Type
S  avs bvs clog10 dlog10evs log10 fvs log10  gvs log10h
2 22 2
Statistical Estimation of Soil Type Using Cross-plots of S-wave
Velocity and Resistivity in Japanese Levees
22
Levee body Foundation
a -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

23. Example of Estimation
S-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)
Resistivity
Elevation (m) Resistivity
(Ohm-m)
Levee body
Foundation

24. Example of Estimation
10000
1000
100
10
Resistivity(ohm-m)
10
1
0
Resistivity(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)

25. 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.

26. 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
Estimatedsoilparameter
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
Estimatedsoilparameter
Probability
40% 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

27. 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 and
resistivity, can be used not only for qualitative
interpretation but also quantitative engineering analyses,
such as slope stability or liquefaction analyses.
• Similar approaches can be applied to other purposes
besides levee inspection and other countries besides
Japan.
• It is important that any results of geophysical
investigations 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