6th Korea-Japan Joint Workshop
in Kobe on 29th August 2024.

Stress-induced anisotropy of small strain
shear modulus in saturated andunsaturated cohesive soils
Hirofumi TOYOTA
Department of Civil and Environmental Engineering
Nagaoka University of Technology1

Contents
Background and objectives
Experiment
Strain dependency of Gsec
Anisotropic G0
Normalization methods
Conclusions

2

Background
Saturated:

𝐾

Unsaturated: 𝐾𝜎𝜎𝜎𝜎

K or Knet > 1
Extensional

Anisotropic consolidation

𝑢𝑢Embankment

K or Knet
Intermediate

K or Knet < 1Compressional

Out of scopeIntermediate: shear stress or inclined loading
3

Objectives
To create different K or Knet-consolidated specimens(Anisotropic consolidation)
To measure G0 and Gsec
(Stress-induced anisotropy)
Normalize G0 to remove effects of K or Knet(for prediction)4

Apparatus used

Local small strain (LSS) measurement

Vertical displacement
meter

Vertical strain
Bender element
Load cell

Start time

Top cap
Bender element(Transmitter)

Δt

Porous disc

TargetTargetLtt

Arrival time
Time (msec)

80 mm

Horizontal proximity
sensorBender element(Receiver)

Vs=Ltt/tVoltage

Air pressure, ua

Vertical proximity
sensorHorizontal strain

Ceramic
disc

Unsaturated soils: Pressure plate method

TargetPedestal

Water pressure, uw
Drainage tube
Cell pressure

Outsideadjustment

5Specimen preparation
Remove the airfrom slurry

1D-consolidation byair pressure

VaneAir Pressure

Vacuum Pressure

Drain

Extracted soil
block

Flexible pipe
Acrylic cylinder
PistonSlurry
H=400 mm

Trimmed125 mm height
50 mm diameter

80 mm

Porous Stone Disk
TripodDrain
Step 1
Under Vacuum Process

Step 2
Under One Dimension
Pre-Consolidation ProcessMaterial used
Yoneyama silt3s=2.74 g/cm , wL=52 %, Ip=29100

Degree of saturation, Sr (%)

Percentage finer by mass

100
80
604020Silt

Clay00.001

0.01

Sand0.1

Grain size (mm)1pnet=300 kPa

Yoneyama silt
Pressure plate method
Drying (dehydration)90

pnet=100 kPa

80

70

60

1

10100

Matric suction, s (kPa)

1000

Stress path during experiment
800

Stress path, K=h'/v'
Knet=(hua)/(vua)

q=vh (kPa)

600
400

K or Knet
0.35,
1.0,0.43,2.0,0.6
3.0

K or Knet consolidation(Compressional)
Drained q-loadingp'=50 kPa

2000-200-400Drying, s=400 kPa

050100

K or Knet consolidation(Extensional)

150

200

250

Triaxialcompression

300350p'=(v'+2h')/3 or pnet=(v+2h)/3ua (kPa)400

Strain dependency of Gsec
Secant shear modulus, Gsec (MPa)

200

150

Yoneyama silt, K-consolidation
Triaxial compression
p'=300 kPa

100

Saturated soil(a) Saturated
Compresional consolidation
K=0.35
K=0.43
K=0.6
K=0.8
K=1.0
Extensional consolidation
K=1.5
K=2.0
K=3.05000.0001

0.001

0.01

Shear strain, s (%)

0.1𝐺∆𝑞3∆𝜀Strain dependency of Gsec
Secant shear modulus, Gsec (MPa)

300
250

Yoneyama silt, Knet-consolidation
Triaxial compressionpnet=300 kPa, s=400 kPa

200150Unsaturated soil(b) Unsaturated
Compresional consolidation
Knet=0.35
Knet=0.43
Knet=1.0
Extensional consolidation
Knet=2.0
Knet=3.0

100
5000.0001

0.001

0.01

Shear strain, s (%)

0.1𝐺∆𝑞3∆𝜀Anisotropic G0

LSS vs BE tests
220150Yoneyama silt, K-consolidation
Triaxial compression
p'=300 kPa(a) Saturated
BE test
LSS test

K=0.43 (=K0)

140130120
110
1000.0Extensional
consolidation

Compressional
consolidation

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Initial shear modulus, G0 (MPa)

Initial shear modulus, G0 (MPa)160210(b) Unsaturated

Yoneyama silt, Knet-consolidation
Triaxial compressionpnet=300 kPa, s=400 kPa

200
190
180
170
160
0.0

Compressional
consolidation

0.5

BE test
LSS test

Extensional
consolidation

1.0

1.5

2.0

2.5

3.0

Stress ratio, K=h'/v'

Net stress ratio, Knet=(hua)/(vua)

Saturated soil

Unsaturated soil

3.5

Void ratio function, F(e)1.0Void ratio, e

0.9

Yoneyama silt
After K or Knet-consolidationp' or pnet=300 kPa, s=400 kPa

𝐹 𝑒

0.8

0.7
Compressional
consolidation

0.6
0.0

0.5

1.0

1.5

Reported byHardin and Black (1968 and 1969)

Saturated
Unsaturated

Extensional
consolidation

2.0

2.5

K=h'/v' or Knet=(hua)/(vua)

3.0

2.973 𝑒1 𝑒

3.5

Normalized G0 by F(e)100(a) Saturated

Yoneyama silt, K-consolidation
BE test, p'=300 kPa

60

K=0.43 (=K0)

Normalized G0: G0/F(e)2F(e)=(2.973e) /(1+e)

50

40Compressional
consolidation

30
0.0

0.5

Extensional
consolidation

1.0

1.5

2.0

2.5

Stress ratio, K=h'/v'

Saturated soil

3.0

3.5

Normalized shear modulus, G0 (MPa)Normalized shear modulus, G0 (MPa)70(b) Unsaturated

Yoneyama silt, Knet-consolidation
BE test, pnet=300 kPa, s=400 kPa

90Normalized G0: G0/F(e)2F(e)=(2.973e) /(1+e)

8070Extensional
consolidation

Compressional
consolidation

60
0.0

0.5

1.0

1.5

2.0

2.5

3.0

Net stress ratio, Knet=(hua)/(vua)

Unsaturated soil

3.5

Stress functions
Unsaturated soil

Saturated soil

𝐺𝐺𝐴𝐹 𝑒 𝑝𝑝𝑝𝑛0.5

Reported by
Hardin and Richart (1963) andHardin and Drnevich (1972)

𝑆 𝐹 𝑒 𝑂𝐶𝑅 𝑝𝑛0.25,𝜎𝑛𝜎0.25

Reported by
Hardin and Blandford (1989) andJamiolkowski et al. (1995)

Normalized G0 by F(e) and stress function
400600(a) Saturated

Yoneyama silt, K-consolidation
BE test, p'=300 kPa

1ninjninj

v' h' )Normalized G0: G0/(F(e)pa2F(e)=(2.973e) /(1+e), ni=0.25, nj=0.25350
300
250
2000.0Compressional
consolidation

0.5

Extensional
consolidation

1.0

1.5

2.0

2.5

3.0

3.5

Normalized shear modulus, G0 (MPa)Normalized shear modulus, G0 (MPa)

450

550

Yoneyama silt, Knet-consolidation
BE test, pnet=300 kPa, s=400 kPa(b) UnsaturatednNormalized G0: G0/(F(e)pa(pnet/pa) )2F(e)=(2.973e) /(1+e), n=0.5

500
450
400
350
0.0

Compressional
consolidation

0.5

Extensional
consolidation

1.0

1.5

2.0

2.5

3.0

Stress ratio, K=h'/v'

Net stress ratio, Knet=(hua)/(vua)

Saturated soil

Unsaturated soil

3.5

Conclusions• Very small shear strain: G0 is strongly affected by anisotropic stress conditions inthe saturated cohesive soil. However, those were not significant for theunsaturated cohesive soil.
• Shear strain greater than 0.03%: The trends of Gsec are changed from the trendsof G0. Degradation with shear strain is large in small K value.
• The values of G0 under anisotropic stress conditions are normalized successfullyusing the void ratio function and the stress function.

16Recommended normalized functions
𝐹 𝑒

2.973 𝑒1 𝑒.

𝑝𝑝

Unsaturated soil

𝐺𝐴𝐹 𝑒 𝑝Saturated soil

𝐺𝑆 𝐹 𝑒 𝑝 . 𝜎.

𝜎.

Thank you for your kind attention!