PDF Advanced Soil Mechanics I - Seoul National University

SNU Geotechnical and Geoenvironmental Engineering Lab.

b) K0 – consolidation condition.

In field → K0 – state.

In lab → Generally isotropic state (triaxial test) to simplify the field conditions.

< For sedimented soils>

∗ Field : During sedimentation and subsequent loading (no lateral strain), soil structure is formed to resist efficiently to vertical loading.

( → anisotropy )

SNU Geotechnical and Geoenvironmental Engineering Lab.

∗ Lab : During consolidating for undisturbed anisotropic samples isotropically, soil structure can be altered to have isotropic-inclined characteristics. And total confining stress ^{' (} 3^')/3

' 2 '

1 σ σ

σ + +

=

p is different from (larger than) that in field.

­ The effect of isotropic consolidation on undrained behavior of N.C. or lightly O.C.

clays. ( K0 < 1 → p’iso > p’Ko and rearrange of soil structure during isotropic consolidation (more isotropic structure) )

⇒ Comparing the shear behaviors under isotropic consolidation with those under K0-consolidation

⇒ Subsequent shearing also induces structure rearrangement to activate the effective resistance to the given shearing mode.

SNU Geotechnical and Geoenvironmental Engineering Lab.

(1) Compression shearing.

Soil structure: needs more strain to the peak and develops higher excess pore pressure and lower su.

Higher p’ induces higher su and possibly higher excess pore pressure during shearing.

(2) Extension shearing.

Soil structure: increases su, and possibly ( but not significantly ) less strains to the peak and lower excess pore pressure.

Higher p’ induces higher su and higher excess pore pressure.

(3) Isotropic consolidation has no effect on φ’ .

SNU Geotechnical and Geoenvironmental Engineering Lab.

SNU Geotechnical and Geoenvironmental Engineering Lab.

SNU Geotechnical and Geoenvironmental Engineering Lab.

SNU Geotechnical and Geoenvironmental Engineering Lab.

∗ The Effect of Isotropic Consolidation on Shearing Behavior.

Triaxial Compression Trialxial Extension Soil

Structure Change

su ↓ ( Stiffness ↓ ) ( ue ↑ )

su ↑ ( Stiffness ↑ ) ( ue ↓ )

Increasing p’ su ↑

ue (↑)

su ↑ ue (↑)

∗ Anisotropy of su (for NC or lightly OC clays).

( ) ( )

( ) ( )

u E u E

u C i u C Ko

s s

s s

   

  >  

   

SNU Geotechnical and Geoenvironmental Engineering Lab.

∗ Mayne (1985), for 42 soil types,

For comp. ,

( s

u

/ σ '

vc

)

Ko

≈ 0.87 ( s

u

/ σ '

vc

)

iso

For ext. ,

( s

u

/ σ '

vc

)

Ko

≈ 0.60 ( s

u

/ σ '

vc

)

iso

∗ Sivakugan and et al.

Base on using K0 (=1-sinφ’) and pore pressure parameter at failure, Af for isotropic and K0 – consolidation;

^{0 0 ,}

(

^{, 0 0}

)

0 0 ,

' 2(1 )

(1 )

2(1 )

'

u

vc CKoUC f i

f i u f Ko

vc CIUC

s

K K A

A K K

K K A

s σ

σ

 

 

+ −

 

= − +

+ −

 

 

 

SNU Geotechnical and Geoenvironmental Engineering Lab.

∗ Wroth

^{' 3 2 sin '}₃

(

^{1 2}

)

'

u

vc CKoUC u

vc CIUC

s

a s

σ φ

σ

Λ

 

 

−

 

= −

 

 

 

where

c r

C

a Λ = − C

−

= − 1

) ' sin 2 3 ( 2

' sin

3 ,

φ φ

∗ For heavily OC clays

K₀ =(1−sin

φ

)(OCR)^sinφ ⇒ For OCR = 4, K₀ ≈1 So, the higher OCR (<4), the lower anisotropy.

SNU Geotechnical and Geoenvironmental Engineering Lab.

2) Shearing Conditions.

a) Anisotropy

2 types 1) Material → Inherent anisotropy.

2) K0 ≠ 1 → Stress system anisotropy .

→ Caused by tendency of clay particles to become horizontally oriented during deposition (1 – D Compression).

Anisotropy will affect

→ φ’ , c’ ⇒ φ’ext > φ’com (?).

→ su.

→ Deformation parameters (σ - ε response).

→ Pore pressure response.

SNU Geotechnical and Geoenvironmental Engineering Lab.

As the direction of major principal stress changes, anisotropy of undrained strength (su(β)/su(0)) is shown as,

0000 45454545 90909090 1.01.01.0

1.0 OC clayOC clayOC clayOC clay

NC clay NC clay NC clay NC clay

TXC TXC TXC

TXC DSSDSSDSSDSS TXETXETXETXE Su(0)

Su(0) Su(0) Su(0) Su(Su(

Su(Su(ββββ⁾⁾⁾⁾ ββββ

σ σ σ σ_1f1f1f1f σσσ

σ_{1f1f 1f1f} σσσσ_1f1f1f1f σ σσ σ_{1f1f 1f1f}

) 0 (

) (

u u

s s β

SNU Geotechnical and Geoenvironmental Engineering Lab.

Stress reorientation effects

We want to evaluate the change in strength caused by the rotation of principal stress direction (⇐ stress system induced anisotropy due to K0≠1).

SNU Geotechnical and Geoenvironmental Engineering Lab.

Point A

2 ) (

2

3 1 3

1f f f

su σ σ σ −σ

− =

=

Look at N.C. clays (c’=0), based on Mohr-coulomb criteria to define failure,

' 3 '

1 3

' ( 1 )

sin

f f

f

σ σ

σ φ σ

+

= −

0 ' 0

0p u

K +

0 '

0 u

p + σ_1f

f

σ3

Init. Fail.

SNU Geotechnical and Geoenvironmental Engineering Lab.

By Algebra,

⁾

sin 1

sin ( 2 )

( '

' '

3 3

1 φ

σ φ σ

σ − _f = _f − --- ① Where

σ

₃^'_f =

σ

_3f − ∆ −u u₀

' '

3i u0 3 u u0 3i 3 u

σ σ σ σ

= + + ∆ − ∆ − = + ∆ − ∆ We know : ∆

σ

¹ =

σ

¹_f − p^0' −u⁰

0 ' 0 0 3

3 = _f −K p −u

∆σ σ

∆ u = B ( ∆ σ

₃

+ A ( ∆ σ

₁

− ∆ σ

₃

))

(for saturated soil, B=1)

)]

( [

) (

0 ' 0 0 3

0 ' 0 1

' 0 0 3

0 ' 0 0 3

' 0 0

3 '

3 '

3

u p K u

p A

u p K

u p K p

K

u

f f

o f

f i

f

+ +

−

−

− +

−

−

−

−

− +

=

∆

−

∆ +

=

σ σ

σ σ σ σ

σ

σ₃^' _f = K₀p₀^' − A(σ_1f −σ_3f − p₀^' + K₀p₀^' ) --- ②

SNU Geotechnical and Geoenvironmental Engineering Lab.

Sub. ② → ①.

)

' sin 1

' sin )]( 2

) ((

[ )

( _{1 3 0 0}^' _{1 3 0}^' _{0 0}^'

φ σ φ

σ σ

σ − _f = K p − A − _f − p +K p −

⁾

' sin 1

' sin )]( 2 (

[ ') sin 1

' sin 1 2

( )

( _{1 3 0 0}^' ₀^' _{0 0}^'

φ φ φ

σ φ

σ = − − + −

+ −

− A K p A p K p

f

⇒ )

' sin 2 sin

1

' )]( sin

1 (

2 [ ) (

0 ' ' 0

0 '

0 3 1

φ φ

σ φ σ

K A A p K

s p

f u

+

− −

−

=







=

−

NC clays (typical values) For φ^'=30°

K0 = 0.5

Af=1 ⇒ _'

0 . 3

0

p =

s

_u

SNU Geotechnical and Geoenvironmental Engineering Lab.

Point B

0 ' 0 0 1

1 = _f −K p −u

∆σ σ , 0

' 0 3

3 = _f − p −u

∆σ σ , ' '

' 0

'

0 1 sin 2 sin

sin )]

1 ( 1 [

φ φ

φ A K A p

s_u

+

−

−

= −

NC clays (typical values) For φ^'=30°

K0 = 0.5

Af=1 ⇒ ' ^0.17 0

p = s_u

Question :

φ

com^'

= φ

ext^'

(?)

_, (A_f )compression =(Af )extension

(?)

0 ' 0

0p u

K +

0 '

0 u

p + σ_3f

f

σ1

Init. Fail.

SNU Geotechnical and Geoenvironmental Engineering Lab.

Example of undrained strength anisotropy

⇒ Combined effect of inherent and stress system anisotropy A : 0.37

' 0

p = s_u

B : ' ^0.30

0

p = s_u

0 90

1.0

0.8 SanFrancisco Bay Mud

su(β=0)

(A) (B)

f

σ1

f

σ1

SNU Geotechnical and Geoenvironmental Engineering Lab.

Plane strain tests vs. Triaxial tests.

Plane strain tests comparing to triaxial tests gives;(the effect of intermediate stress σ2)

① Slight increase (5± %) in su.

Loading direction su(TX)/su(PL) β=0° 0.92±0.5 (5 clays) β=90° 0.82±0.2 (4 clays)

② Increase φ’ by 2±2°.

③ Lower strain at failure and increase tendency of the strain softening in plain strain tests, perhaps because of the more general formation of failure plane.

SNU Geotechnical and Geoenvironmental Engineering Lab.

b) Aging effect.

Aging → increase undrained strength, owing to decrease of e.

In lab → one log cycle of time for secondary compression is required for aging.

SNU Geotechnical and Geoenvironmental Engineering Lab.

c) Rate of shearing.

SuSu SuSu

Rate of Rate of Rate of Rate of Shearing Shearing Shearing Shearing 0.5%/hr

0.5%/hr 0.5%/hr

0.5%/hr 5%/hr5%/hr5%/hr5%/hr

Conventional test Conventional test Conventional test Conventional test

(s_u)conventional test = 1.3 s_u(0.5%/hr) s_u

conventional test