Granular Materials in Civil Engineering: Recent Advances in the Physics of Their Mechanical Behavior and Applications to Engineering Works - Multiscale Geomechanics: From Soil to Engineering Projects - page 61

τ

b

σ

with b < 1 (De Mello's
criterion [DEM 77]), the scale effect rule leads to the following expression of the
shear strength envelope:

In the particular case of a power law

() .
n

= A σ

n

−− 3 ( 1) b −− 3 1) b

 

D D

m m

b

[3.32]

σ

()

=

1

()

= A

1

G

0

σ



σ



n G G

1

n



0

n



D

G

0

D

0 0

It shall be outlined that, in this particular condition of a power law, the scale
effect incidence is only on coefficient A , but not exponent b .

3.2.2.3.3. Shear strength envelope σ 1 = h (σ 3 ,D) - Hoek-Brown's criterion

If the expression of the shear strength envelope of material G 0 is given by

σ = h

(,

σ D )

[3.33] ( )

10

G M a x

then, for the same characteristics of material G 1 as the ones given above, combining
equations [3.29] and [3.33] gives the expression of the shear strength envelope of
material G 1 :

− 3 3

[3.34]

  D

m

D

m

σ σ =

1

⋅  h

3 .

1

D

 

() G

1

0

1



D



D

0 0

In the case of Hoek-Brown's criterion [HOE 80]:

a

σσ

with a <1 ,

s

σσσ =

+

σ

m

3

+

1 3 c

HB

σ

c

The scale effect rule leads to the following expression of the shear strength
envelope:

a

( 0 G

− 3

3

 

σσ

 

D D

D

m

[3.35]

m
1 1

σ σ =σ σ σ

3

+ m +

() G

   

G G G

11 3 0

HB

0 0

σ D

 

G ) 0

0 0