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An attempt at soil profiling on a river embankment using geophysical data*

Toru Takahashi

1,3

Tsuyoshi Yamamoto

2

1

Fukada Geological Institute, 2-13-12 Honkomagome, Bunkyo-ku, Tokyo 113-0021, Japan.

2

Kinki Regional Development Bureau, Ministry of Land, Infrastructure, Transport and Tourism, Osaka Godochosha, Bldg. No. 1, 1-5-44, Otemae, Chuo-ku, Osaka 540-8586, Japan.

3

Corresponding author. Email: [email protected]

Abstract. The internal structure of a river embankment must be delineated as part of investigations to evaluate its safety.

Geophysical methods can be most effective means for that purpose, if they are used together with geotechnical methods such as the cone penetration test (CPT) and drilling. Since the dyke body and subsoil in general consist of material with a wide range of grain size, the properties and stratification of the soil must be accurately estimated to predict the mechanical stability and water infiltration in the river embankment. The strength and water content of the levee soil are also parameters required for such prediction. These parameters are usually estimated from CPT data, drilled core samples and laboratory tests. In this study we attempt to utilise geophysical data to estimate these parameters more effectively for very long river embankments. S-wave velocity and resistivity of the levee soils obtained with geophysical surveys are used to classify the soils. The classi fication is based on a physical soil model, called the unconsolidated sand model. Using this model, a soil profile along the river embankment is constructed from S-wave velocity and resistivity pro files. The soil profile thus obtained has been verified by geotechnical logs, which proves its usefulness for investigation of a river embankment.

Key words: geophysical data, resistivity, river embankment, S-wave velocity, soil profiling, unconsolidated sand model.

Introduction

In Japan recent localised torrential rainfall events have often caused serious damage to river embankments, as seen in the Maruyama River flood in 2004. They have brought much public attention to the present state of river embankments, and to their investigation for safety evaluation and strengthening. In such investigations the internal structure of the earthen embankments must be delineated for further analyses. Geophysical methods can be one of the most effective tools for that purpose because of their quick and non-destructive subsurface profiling capability (Asch et al., 2008; Inazaki et al., 2008; Niederleithinger et al., 2008).

River embankments are usually artificial constructions, which may have been built up from individual dykes over periods of hundreds of years. Because the dyke body and subsoil in general consist of materials with a wide range of grain size, which is one of the major controlling parameters of mechanical and hydrogeological characteristics of the river embankment, the properties and stratification of the soil must be accurately estimated to predict the mechanical stability of the embankment and water in filtration in it. The strength and water content of the levee soil making up each dyke are also parameters required for such prediction. These parameters are usually estimated from cone penetration test (CPT) data, drilled core samples, and laboratory tests. These point-based measurements, in general, cannot be conducted at many locations due to economic and time constraints. Geophysical methods can interpolate between such measurements at discrete locations. If the properties and stratification of the soil can be estimated from geophysical data together with CPT and drilling data, soil pro filing of an

entire length of the river embankment can be very effectively conducted.

We, therefore, have tried to develop an interpretation technique for geophysical data, combined with CPT and drilling data, to produce profiles of the stratification of properties of the levee soil. In this paper, we describe this method of soil profiling, using S-wave velocity and resistivity data and a soil physical model, and present an actual field example of a soil profile of a river embankment using the data obtained in experimental geophysical surveys at the Uji River in Kyoto Prefecture, Japan.

Experimental field data at the Uji River

In the experimental surveys at the Uji River, we pro filed the 9 m high and 500 m long dyke body and underlying subsoil with several geophysical methods in order to evaluate the applicability of each method and their integration to river embankment investigation (Yamamoto et al., 2008). Geophysical methods tested were the seismic reflection and surface wave methods, electrical and electromagnetic methods and the continuous and pulse wave type ground penetrating radars. Among them, S-wave velocity profiling with the seismic surface wave method (Hayashi and Suzuki, 2004) and resistivity pro filing with the capacitively- coupled resistivity method (Groom et al., 2009) are used for soil pro filing in this study, because S-wave velocity and resistivity are strongly related to the strength and grain size of the levee soil, respectively. Figure 1 shows these two profiles as well as the geotechnical data acquired at the same time. In this embankment,

*Part of this paper was presented at the 9th SEGJ International Symposium (2009).

 ASEG/SEGJ/KSEG 2010 10.1071/EG09049 0812-3985/10/010102

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three portions have been excavated and later back- filled in the past, to build and remove water gates across the dyke body.

The location of the reclaimed portions, as well as geologically estimated soil layer boundaries, is overlain on the profiles in this figure.

The geotechnical data are employed for soil physical modelling and verifying geophysical data, and include the radioisotope (RI) cone penetration test, Swedish weight sounding, and drilling, with the standard penetration test. The RI cone consists of three probes, which are a mechanical probe measuring cone resistance, friction, and pore pressure, a density probe measuring soil density, and a neutron probe measuring water content of soil (Shibata et al., 1992). The cone resistance

can be converted to the ‘N-value’, which is strongly related to S-wave velocity, and density is used to estimate porosity of soil.

The converted N-value and porosity thus obtained are used for soil physical modelling as described below. In this experiment, the RI cone test data were acquired at four different locations along the geophysical measurement line on the top of the dyke.

The converted N-value and porosity logs are shown in Figure 2.

These logs were acquired through the 9 m high dyke body, except in the uppermost part (0–2 m) that has been artificially consolidated. It is seen that the data for the upper 2 –5 m, consisting of clayey sand, and the lower 6–9 m, of sand, show clear difference in both properties, due probably to change of soil stratification.

Fig. 1. S-wave velocity (top) and resistivity (middle) profiles along the 500 m long river embankment used in this study.Geotechnical logs obtainedby four RI cone tests and six Swedish weight soundings, as well as three N-value logs from standard penetration tests, are also shown at the bottom. A sketch of the reclaimed portions and geologically estimated soil layer boundaries is overlain on these profiles.

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Levee soil modelling

Several soil physical models for granular materials have been proposed to represent unconsolidated sand/clay mixtures (for example, Marion et al., 1992). These can possibly be used to model soft soils. In this study, we tried to use the unconsolidated sand model (the friable sand model) (Avseth et al., 2005) to model the soils of the river embankment because this model has been often used for modelling shallow marine sediments or soft sedimentary rocks. The model schematically illustrated in Figure 3 represents poorly sorted sands with clay particles deposited in the pore space. The additional clay decreases the porosity and slightly increases the stiffness of the sand.

Unconsolidated sand model (Friable sand model)

Following Dvorkin et al. (2002), we describe how to determine the model parameters of the unconsolidated sand model as below.

In modelling the bulk (K

dry

) and shear (G

dry

) moduli of dry soil with porosity () are first estimated with the Hashin-Shtrikman lower bound (Hashin and Shtrikman, 1963) given as

K

dry

¼

’’0

K

HM

þ

43

G

HM

þ 1 

0

K

s

þ

43

G

HM

( )

 4 3 G

HM

G

dry

¼

’’0

G

HM

þ Z þ 1 

0

G

s

þ Z

( )

1

Z

Z ¼ G

HM

6

9K

HM

þ 8G

HM

K

HM

þ 2G

HM

 

ð1Þ

where

K

HM

¼ n

2

ð1  ’

0

Þ

2

G

2s

18 p

2

ð1  n

s

Þ

2

P

( )

1

3

G

HM

¼ 5  4n

s

5ð2  n

s

Þ

 

3n

2

ð1  ’

0

Þ

2

G

2s

2p

2

ð1  n

s

Þ

2

P

( )

1

3

ð2Þ

are the bulk and shear moduli, respectively, of the sand/clay mixture at the critical porosity of 

0

in the Hertz –Mindlin model (Mavko et al., 2009). K

s

, G

s

and n

s

are the bulk and shear moduli and Poisson’s ratio of the mixture itself, respectively, P is the confining pressure and n is the coordination number. The bulk and shear moduli of the mixture itself are defined by the Voigt-Reuss- Hill average of those for sand and clay (Mavko et al., 2009) as

K

s

¼ fð1CÞK

sand

þCK

clay

gþ 1C K

sand

þ C

K

clay

 

1

" #

2

G

s

¼ fð1CÞG

sand

þCG

clay

gþ 1C G

sand

þ C

G

clay

 

1

" #

2

; ð3Þ

where C is the clay content, and K

sand

and G

sand

are the bulk and shear moduli of the sand, and K

clay

and G

clay

are those of the clay, respectively.

Once the bulk and shear moduli of the dry soil are determined as above, those of saturated soil are given by the Gassmann ’s equation (Mavko et al., 2009) as

K

sat

¼ K

dry

þ ð1 

KKdry

s

Þ

2

Kf

þ

1’K

s



KKdry2 s

;

G

sat

¼ G

dry

ð4Þ

where K

f

is the bulk modulus of pore fluid (water). As the shear modulus is in general unchanged by fluid saturation, the shear modulus of the saturated rock is equal to that of the dry rock.

Using the moduli calculated as above, the elastic properties of the soil are derived as

M ¼ K

sat

þ 3

4 G

sat

: P-wave modulus ð5Þ

G ¼ G

sat

: shear modulus ð6Þ

V

P

¼ ffiffiffiffiffiffiffiffiffiffi M =r

p : P-wave velocity ð7Þ

V

S

¼ ffiffiffiffiffiffiffiffiffi p G=r

: S-wave velocity ð8Þ

r ¼ ’r

f

þ ð1  ’Þr

s

: density; ð9Þ where r

f

and r

s

are the densities of the pore fluid and sand/clay mixture, respectively.

0

1

2

3

4

5

6

7

8

9

0 10 20 30 40 50

Converted N-value

Depth (m)

RI-1 RI-2 RI-3 RI-4

0

1

2

3

4

5

6

7

8

9

0 20 40 60 80

Porosity (%)

Depth (m)

RI-1 RI-2 RI-3 RI-4

Fig. 2. Depth profiles of N-value (left) converted from cone resistance data and porosity (right) obtained with the four radioisotope (RI) cone tests (RI-1, RI-2, RI-3 and RI-4) on the top of the river embankment.

Sand Clay

Fig. 3. Schematic diagram of the unconsolidated sand model. This model represents poorly sorted sands with clay particles deposited in the pore space.

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Modelling of levee soil

Since S-wave velocity is strongly related to the strength of the levee soil, S-wave velocity is employed to model the levee soil with the unconsolidated sand model in this study. The model parameters are generally determined based on a relationship between seismic velocity and porosity (Mavko et al., 2009). In this study the optimum unconsolidated sand model is, therefore, determined first using the estimated S-wave velocity and porosity data obtained in the RI cone tests. Then the resistivity data obtained by the electrical method are incorporated into the model using a correlation of measured data of resistivity and porosity, because resistivity is one of the most sensitive geophysical parameters to the soil type and can be easily measured by using the electrical and electromagnetic methods.

The S-wave velocity and resistivity diagram thus obtained is applied to soil classi fication for constructing a soil profile of the river embankment. This workflow is shown in Figure 4 and its details are explained below.

Figure 5 shows the crossplot of N-value and porosity obtained in the RI cone tests at four different locations on the dyke body shown in Figure 1. The N-value is converted to S-wave velocity using the correlation (Figure 6) of measured N-values and S-wave velocity values extracted from the S-wave velocity pro file shown in Figure 1. Figure 7 is the crossplot of the S-wave velocity thus converted versus porosity. Using equations (1) through (4), and (6), (8), and (9) for S-wave, the S-wave velocity is calculated as a function of porosity with different clay contents. The calculated curves with four clay contents (0, 30, 60 and 100%) in this case are overlain on the measured data as shown in Figure 8. The parameters used in this model calculation are summarised in Table 1. It is clearly seen that the calculated model curves cover the measured data range well, indicating that the unconsolidated sand model can be applied to modelling of soft soils.

In the next step, the porosity is converted to resistivity using the correlation of the measured data to obtain an S-wave velocity

Crossplotting of the converted N-values versus porosities obtained with RI cone tests (Fig. 5)

Estimation of Vs from N-value using the correlation of the measured data (Fig. 6)

Crossplotting of Vs versus porosity to make a soil physical model (Fig. 7)

Application of the unconsolidated sand model based on the Vs and porosity crossplot (Fig. 8)

Estimation of resistivity from porosity using the correlation of the measured data (Fig. 9)

Crossplotting of Vs versus resistivity to make the Vs-Resistivity diagram (Fig. 10)

Soil classification with the Vs versus Resistivity diagram (Fig. 11)

Construction of a soil profile using the Vs and resistivity profiles (Fig. 12)

Fig. 4. Workflow for soil profiling using S-wave velocity and resistivity profile together with the radioisotope (RI) cone test data.

0 5 10 15 20 25 30 35 40

20 30 40 50 60 70 80

Porosity (%)

Converted N-Value

RI-1 RI-2 RI-3 RI-4

Fig. 5. Crossplot of the converted N-value versus porosity obtained in the radioisotope (RI) cone tests at four different locations, RI-1 to RI-4.

Vs = 139.2N**0.1665

10 100 1000

1 10 100

N-Value

S-wave velocity (m/s)

Fig. 6. Correlation of S-wave velocity values extracted from the S-wave velocity profile with N-values obtained in the radioisotope (RI) cone tests, the Swedish weight soundings and the Standard penetration tests on the river embankment. The regression curve, VS= 139.2N0.1665, is used for estimating VSfrom the N-value.

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versus resistivity crossplot. Figure 9 shows the correlation of resistivity data extracted from the resistivity profile shown in Figure 1 and porosities at the four RI cone test locations. Although the data for RI-3 have some scatter, this figure indicates that resistivity decreases as porosity decreases. As the levee soil is unsaturated (the groundwater level is around 13 m in depth at this

site), it can be interpreted from the model schematically shown in Figure 3 that an increase in the proportion of clay particles with lower resistivity reduces both porosity and resistivity of the sand/clay mixture.

Using this relation, the porosity is converted to resistivity to obtain an S-wave velocity versus resistivity crossplot as shown in Figure 10. In this figure, the data are labelled by soil type, which is identified from drilled core samples obtained in the dyke body.

The soil of the dyke body at this site is classified into three types, clayey gravel, sand, and clayey sand. This figure clearly shows that the model calculation curves with different clay contents match very well with the actual soil types. It also means that this S-wave velocity–resistivity diagram can be utilised for soil classi fication of the river embankment.

Field example of soil profile

Based on the S-wave velocity–resistivity diagram shown in Figure 10, the levee soil is classi fied into three types of soils:

sand with clayey gravel, sand/clayey sand mixture, and clayey sand. In addition, the reclaimed soil has much lower resistivity than the natural levee soil. Therefore the soil whose resistivity is less than 80 W-m is classified as reclaimed, within the earlier excavations. Figure 11 shows the S-wave velocity –resistivity diagram used in the soil profiling of the embankment, in which the data are divided into four classes corresponding to each soil type.

Using this diagram, S-wave velocity and resistivity profiles shown in Figure 1 are converted to a soil pro file as shown in Figure 12. The geotechnical logs and the sketch of the reclaimed portions and the soil layer boundaries are overlain for verifying the soil profile estimated from geophysical data. The estimated soil profile clearly discriminates between reclaimed and natural soils except for the deeper part around the distance of 300 m, where the original dyke body was composed of clay, as identified in the excavation. The clay dyke body probably has very low resistivity. The estimated soil profile also delineates three distinct soil layers, each of which can be interpreted as the dyke bodies at present and in the past.

100 150 200 250 300 350 400

20 30 40 50 60 70 80

Porosity (%)

S-wave velocity (m/s)

RI-1 RI-2 RI-3 RI-4

Fig. 7. Crossplot of S-wave velocity derived from N-value versus porosity.

100 150 200 250 300 350 400

20 30 40 50 60 70 80

Porosity (%)

S-wave velocity (m/s)

RI-1 RI-2 RI-3 RI-4 Model (C=0%) Model (C=30%) Model (C=60%) Model (C=100%)

Fig. 8. S-wave velocity versus porosity curves calculated with the unconsolidated sand model for four different clay contents (0, 30, 60 and 100%) overlain on the same measured data as those in Figure 7. C is the clay content.

Table 1. Parameters used in the model calculation. The elastic properties of sand and clay follow those in Mavko et al. (2009).

n 5 Coordination number

0 0.8 Critical porosity of the sand/clay mixture

Kclay 21 GPa Bulk modulus of clay

Gclay 7 GPa Shear modulus of clay

Ksand 36.6 GPa Bulk modulus of sand (quartz) Gsand 45 GPa Shear modulus of sand (quartz)

Kf 2.2 GPa Bulk modulus of water

50 100 150 200 250 300

30 40 50 60 70

Porosity (%)

Resistivity (Ω-m)

RI-1 RI-2 RI-3 RI-4

Fig. 9. Correlation of resistivity from the electrical survey and porosity of the radioisotope (RI) cone tests. Resistivity values plotted here are taken from the resistivity profile at the same positions as the porosity measurements of the RI cone tests. In this study a simple linear regression, R = 6.0*P-140 (R and P are resistivity and porosity, respectively) is used for transforming porosity to resistivity, because both data ranges are very limited.

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Conclusions

We have attempted soil profiling of a river embankment using S-wave velocity and resistivity pro files together with the RI cone test and drilling data. The unconsolidated sand model for the granular materials is applied to the actual levee soils to make an S-wave velocity–resistivity diagram for classifying the levee soil.

The soil pro file obtained from S-wave velocity and resistivity profiles of the river embankment is verified by the geotechnical logs, which demonstrates that the geophysical soil profiling is a promising technology for investigation of river embankments.

Acknowledgments

The data used in this study were acquired in the research project‘Study on geophysical methods and instruments for investigation of river embankments’ by Kinki Technical Office, Kinki Regional Development Bureau, MLIT,

being supervised by the Kyoto University River Embankment Research Consortium chaired by Professor Yuzuru Ashida.

References

Asch, T. H., Deszcz-Pan, M., Burton, B., Ball, L., Kress, W., and Vrabel, J., 2008, Geophysical Characterization of a Levee With DC Resistivity and Electromagnetic Measurements: Proceedings of the 21st Annual Symposium on the Application of Geophysics to Engineering and Environmental Problems (SAGEEP), 21, 739–748.

Avseth, P., Mukerji, T., and Mavko, G., 2005, Quantitative seismic interpretation: Cambridge University Press.

Dvorkin, J., Mavko, G., and Mukerji, T., 2002, Rock physics reservoir characterization– approaches and methods tutorial: Stanford University.

Groom, D., Yamashita, Y., Konishi, C., and Hayashi, K., 2009, Application of capacitively-coupled resistivity method to site investigation:

Proceedings of 8th SEGJ International Symposium.

100 150 200 250 300 350 400

0 50 100 150 200 250 300 350 400

Converted resistivity (Ω-m)

S-wave velocity (m/s)

Model (C=0%) Model (C=30%) Model (C=60%) Model (C=100%) clayey gravel sand clayey sand

Fig. 10. Crossplot of S-wave velocity versus resistivity converted from porosity with the model calculation curves. The data are indicated in three different soil types (clayey gravel, sand, and clayey sand). The model curves are calculated for the same clay contents as those in Figure 8.

100 150 200 250 300 350 400

0 50 100 150 200 250 300 350 400

Converted resistivity (Ω-m)

S-wave velocity (m/s)

Model (C=30%) Model (C=60%) Model (C=100%) clayey gravel sand clayey sand

Sand with clayey gravel

Sand/clayey sand mixture

Clayey sand Reclaimed

soil

Fig. 11. Soil type classification based on the S-wave velocity–resistivity diagram. The soil is classified into four types: sand with clayey gravel, sand/

clayey sand mixture, clayey sand, and reclaimed soil, based on the diagram.

4

3 2 1

Fig. 12. Soil profile of the dyke body estimated from S-wave velocity and resistivity profiles using the S-wave velocity–resistivity diagram shown in Figure 11.

Four soil types are indicated in colour. Geotechnical logs and the sketch of the reclaimed portions and geologically estimated soil layer boundaries are overlain on the profile for verifying it.

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Hashin, Z., and Shtrikman, S., 1963, A variation approach to the elastic behaviour of multiphase materials: Journal of the Mechanics and Physics of Solids, 11, 127–140. doi: 10.1016/0022-5096(63)90060-7

Hayashi, K., and Suzuki, H., 2004, CMP cross-correlation analysis of multi-channel surface wave data: Exploration Geophysics, 35, 7–13.

doi: 10.1071/EG04007

Inazaki, T., Hayashi, K., Watanabe, F., Matsuo, K., Tokumaru, T., and Imamura, S., 2008, Ground truth verification of an integrated geophysical investigation for the assessment of an earthen levee:

Proceedings of the 21st Annual Symposium on the Application of Geophysics to Engineering and Environmental Problems (SAGEEP), 21, 731–738.

Marion, D., Nur, A., Yin, H., and Han, D., 1992, Compressional velocity and porosity in sand-clay mixtures: Geophysics, 57, 554–563. doi: 10.1190/

1.1443269

Mavko, G., Mukerji, T., and Dvorkin, J., 2009, The rock physics handbook, second edition: Cambridge University Press.

Niederleithinger, E., Weller, A., Lewis, R., Stötzner, U., Fechner, Th., Lorenz, B., and Nießen, J., 2008, Evaluation of geophysical methods for river embankment investigation: Proceedings of 4th International Symposium of Flood Defense.

Shibata, T., Mimura, M., Shrivastava, A., and Nobuyama, M., 1992, Moisture measurement by neutron moisture cone penetrometer; Design and application: Soil and Foundation, 32, 58–67.

Yamamoto, T., Kodan, E., Itokawa, M., Kyoto University River Embankment Research Consortium, 2008, Study on applicability of geophysical methods and instruments for investigation of river embankment by Kinki Technical Office, MLIT, in the state of the art of applications of geophysical methods, SEG Japan (in Japanese).

Manuscript received 10 September 2009; accepted 27 November, 2009.

http://www.publish.csiro.au/journals/eg

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恂庲痖斲͑ 沖巒庂͑ 決殯穢͑ 儛套͑ 皦檗͑ 涋埮彺壊͑ 沗昷͑

Toru Takahashi

1

, Tsuyoshi Yamamoto

2



1 㨂┾⻫㧎G 㕂㥶㰖㰞㡆ῂ㏢G 2 ῃ䏶ᾦ䐋㎇ ⁒₆㰖⹿㩫゚ῃ



殚͑ 檃౐ G Ⴏᣫ⯲ ⧢ⲯ○⯞ 㡣ႚ㧲ዊ ⮞㨎▶ Ⴏᣫ⯲ ᕎ√ሆⴊḖ ⧦⧞⨖ 㧶᝾. Ṧ⨗ ῖṆ㕪╆ ⃃ℯⰎ ㏲ᆚⰟ❶㩲(cone

penetration test; CPT)ᆖ ❶㈮(drilling)⫚ Ⴓ⯚ ⹚₲ᆏ㧳ዊℯᆖ 㨂፲ Ⰾ⭃ᢶ᝾Ἆ Ⴏᣫ⯲ ⧢ⲯ○ 㡣ႚḖ ⮞㨎 ႚⰿ 㭂ᆖⲛⰒ

⃃ℯⰎ ᢺ ⚲ Ⱒ᝾. ṿ╛ㅎᔲ 㧲㋏㘺ᜮ Ⱆ₲ⲛ⯖ᳶ ᝾⨫㧶 ℮⮞⯲ ⰟᡞḖ Ⴐᜮ ῖ⹢᥾ᳶ ሆ○ᢲ⩎ Ⱒ⯖⁚ᳶ Ⴏᣫ⩪▶

ῖ⯲ ㌂㛆 ₩ ዊᅞⲛ ⧢ⲯ○⯞ ⪢㊻㧲ዊ ⮞㨎▶ᜮ 㘺⨫⯲ 㝓○ ₩ ㋏╛ሆⴊḖ ⲯ㫯㰢 㡣ႚ㨎⨖Ṧ 㧶᝾. Ⰾ ⪊ሆ⩪▶ᜮ Ṿ⭊ ዎ Ⴏᣫ⩪ រ㧲⪆ Ⰾᲆ㧶 ⅚⚲᥾⯞ Ṿ⭊ 㭂ᆖⲛ⯖ᳶ ⧦⧞ᕎዊ ⮞㧲⪆ ῖṆ㕪╆ ⰪᵦḖ Ⰾ⭃㧶᝾. ῖṆ㕪╆

⃃ℯ⯖ᳶ ㊻ⲯᢶ Ⲷ⃃ 㘺⨫⯲ S㞦 ☧ᡞ⫚ Ⲟዊ⋞Ⲛ㨇⯞ Ⰾ⭃㧲⪆ 㘺⨫⯞ ∞ᷲ㧶᝾. Ⰾᲆ㧶 ∞ᷲᜮ ₒᅺᅊ ╆⹢㘺 ὂ᠒ (unconsolidated sand model)Ⰾᰖ ∢Ṇᜮ ῖṆⲛ 㘺⨫ ὂ᠒⩪ ዊㆢ㧶᝾. Ⰾᲆ㧶 ὂ᠒⯞ Ⰾ⭃㧲⪆ S㞦 ☧ᡞ⫚ Ⲟዊ⋞Ⲛ㨇 ⴟគἎᡞᳶ√㗊 Ⴏᣫ⯞ ᧊ᰖ 㘺⨫ ⴟគἎᡞႚ Ṧ᥾⩎⹞᝾. Ⰾᲆ㧶 㘺⨫ ⴟគἎᡞᜮ Ⴏᣫ ⴊ╆⩪ រ㨎 ኒ ⮺⭃○Ⰾ Ⰾₒ ᄚ⸷ᢶ ⹚₲ᆏ㧳 ᄚ㋏Ⱚᵦ(geotechnical logs)⩪ ⯲㨎 ᄚ⸷ᢲ⩎ ⫮᝾.

渂殚檺౐ⶒⰂ䌦㌂G 㧦⬢SG ゚㩖䟃SG ṫ⚧SGz 䕢G ㏣☚SG 䏶㟧G 㫛┾Ⳋ☚SG ⹎ἶἆG ㌂㰞䏶G ⳾◎G

수치

Fig. 1. S-wave velocity (top) and resistivity (middle) pro files along the 500 m long river embankment used in this study.Geotechnical logs obtainedby four RI cone tests and six Swedish weight soundings, as well as three N-value logs from standard penetrati
Fig. 2. Depth pro files of N-value (left) converted from cone resistance data and porosity (right) obtained with the four radioisotope (RI) cone tests (RI-1, RI-2, RI-3 and RI-4) on the top of the river embankment.
Fig. 5. Crossplot of the converted N-value versus porosity obtained in the radioisotope (RI) cone tests at four different locations, RI-1 to RI-4.
Table 1. Parameters used in the model calculation. The elastic properties of sand and clay follow those in Mavko et al
+2

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