1.2 Shear Strength of Granular Soils

(1)

SNU Geotechnical and Geoenvironmental Engineering Lab.

1.2 Shear Strength of Granular Soils

(1) Drained shear strength (φ’,c’

(=0)

)

(ue=0)

Parameters affecting drained strength 1) density

2) mineral composition 3) grain size distribution

φ’(well graded) > φ’(poorly graded) 4) grain shape

φ’ (angular particle) > φ’(rounded particle)

(2)

Components of drained strength - Energy is expended in 2 ways.

1) overcome frictional resistance of soil 2) expand soil against confining pressure.

(+ particle breakage, particle rearrangement)

(3)

Taylor and Bishop (Direct shear)

- For dense sand,

frictional

x

∆ y

∆

∆x

(−)

(+)

y

∆ τe= shear stress component due to volumetric expansion

e x n y

τ σ

∆ ⋅ ∆ = ∆ ⋅ ∆

e n

y τ σ ^∆x

∆ = ∆ ⋅

∆

y V =∆

∆

N

τ

x H =∆

∆

T

∆x

residual

τ

e

(4)

- Similar development can be made for TXC (based on drained test.) ( 3 3^'

'

σ σ

σ

_c = _c = = ₎

H y

a

= ∆

=ε ε₁

DS

τ

σ

n

TXC

σ

¹₍₌

σ

₁_e +

σ

₁_R₎

σ

₃

σ3

σ

∆

y H

∆

(5)

--- Eq. (1)

component of

σ

₁

ε

vol

due to vol. expansion

0 1 3

1 d V

dV

e σ ε

σ =

0 1 3 1 1

1

1 d V

dV

e

R σ σ σ σ ε

σ = − = − --- Eq. (2) component of

σ

1 due to mineral friction φ^’ at constant volume

and particle rearrangement

1 1 3

0

( )

e

d dV σ ε =σ V

σ3

σ

∆

y H

∆

(6)

Recall,

( ) tan

²

( 45

⁰

' / 2 )

3

1

φ

σ

_f

= +

) 2 / ' 45 ( tan )

( ² ⁰

3 1

R f

R φ

σ

σ = +

∴ --- Eq. (3)

φ^’^CV(φ^’ at constant volume) And from Eq.(2)

, )

(

0 1 3

1 3

1

V d

R dV

ε σ

σ σ

σ = −

Therefore,

f f f

R V

dV

d 







− 







=  +

0 1

3 0 1

2

) ( ) 1

2 / ' 45 (

tan σ ε

φ σ

(7)

Component of friction angle

3 components

' ' '

_E

φ

µ

φ φ

R e

φ '

CV = (zero overall volume change) + +

(1 component)

φ '

B

-

φ '

_µvalues (Terzaghi, peck, and Mesri, table 19.1)

(8)

- Breakage component (

φ

'B_{) of}

φ '

For quartz sands, σ3 > 500psi, φ'B becomes important.

For chlorite sands,

σ

3 > 50psi, φ'B becomes important.

- Accordingly,

For low σ3_, φ'_CV _and φ_E are important.

For high

σ

3_, φ'_CV _and

φ

_B are important.

(9)

- For a given σσσσ33c’33

( Redrawn after Rowe(1962) )

(10)

To test our hypothesis

Run tests on dense samples with varying σσσσ3333’.

3

2 1

1 2

3 (-)

(+)

εa

Increasing σ₃^'

V V

∆

εa

'

σ3

φ'

breakage particle

φ'

CV

φ'

1 2 3

'

φ1

'

φ2 '

φ3 3

1 σ

σ −

(11)

The effect of relative density or void ratio, grain shape, grain size distribution, and particle size on

φ '

By Cassagrande (Holtz and Kovacs, Table 11-2) (Holtz and Kovacs, Table 11-3)