671017.pdf

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Shear

stren gt

h

rat

io

at

fai

lure

Fabri

c

ani

sot

ropy

Fabric anisotropy

Bedding angle (Deg)

Shear stren gth ratio at failure

0. 9


1. 0


2. 1


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(a)

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0. 4


1. 6


2. 8


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8. 0

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Shear

stren gt

h

rat

io

at

fai

lure

Fabri

c

ani

sot

ropy

Bedding angle (Deg)

Fabric anisotropy

Shear stren gth ratio at failure

(b)

3. 
   


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    0. 5
    0. 6
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    1. 
       
    
    
    
    

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Shear

st

ren gt

h

rat

io

at

fai

lure

Fabri

c ani

sot

ropy

Bedding angle (Deg)

Fabric anisotropy

Shear stren gth ratio at failure

(c)

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    1. 00
    
    
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Shear

st

ren gt

h

rat

io

at

fai

lure

Fabri

c ani

sot

ropy

Bedding angle (Deg)

Fabric anisotropy

Shear stren gth ratio at failure

(d)

Figure 1: Samples with휙휇=52∘and푟 1 /푟 2 = 1.1(a),휙휇=26∘and푟 1 /푟 2 = 1.1(b),휙휇=52∘and푟 1 /푟 2 = 1.4(c), and휙휇=26∘and푟 1 /푟 2 = 1.4
(d).

6. Fabric Evolution

The parameters훼and휃푓show the status of the fabric and
its evolution. These parameters have a great influence on
the behavior of the dilatancy equation. Shaverdi et al. [ 29 ]
proposed an equation which can predict the magnitude of훼
and휃푓in the presence of the noncoaxiality between stress and
fabric. This equation is obtained from the microlevel analysis.
To c a l c u l a t e t h e훼parameter, the magnitude of the shear to
normal stress ratio on the spatially mobilized plane (SMP)
must be determined. In the triaxial case, for example,휏/푝may
be obtained from the following equation [ 30 ]:

휏

푝

=√

휎 1

휎 3

−√

휎 3

휎 1

. (19)

The parameters훼and휃푓may be obtained from the fol-

lowing equations in the presence of noncoaxiality [ 29 ]:

훼=

(휏/푝)cos휙휇mob−sin휙휇mob

sin(2휃푓+휙휇mob)−((휏/푝)cos(2휃푓+휙휇mob))

,

(20)

휃̇푓=휃̇휎+(^1

2

)⋅푑휂⋅(휃휎−휃푓), (21)

where the dot over휃shows the variation. The most important

parameter in the above equation is the interparticle mobilized