Issue 44

X.-P. Zhou et alii, Frattura ed Integrità Strutturale, 44 (2018) 64-81; DOI: 10.3221/IGF-ESIS.44.06

From Eq. (27), three-dimensional long-term strength criterion expressed by the short-term uniaxial compressive strength of rocks can be denoted by                          A A A A A 4 3 2 1 1 3 2 1 3 3 1 3 4 1 3 5 0 (28)

where





2

                       

 A C C C C A C C C A C C C C C C C C A C C C C A C C C C C C C C 1 11 4 11 21 2 2 11 22 4 2 3 11 3 4 11 21 4 11 3 4 22 4 11 3 3 11 21 3 4 11 3 4 4 4 2 2 4 2                    5

2

 

 

22

2

4

     2 ( sin



C C C

1)sin

11



21









 

  2

2

2

2

2

2

2



 sin cos 



 2 +2cos c

 

 +1 +







sin

2 

2

2

2

3



2 2 sin





   c

 

2

2

2

   







 

  



C

cos

sin

cos

3

2 3

2

3



   

    

2







c

c

csc

 

2

c

0

0



 

C

csc

4





2 2

2 2 2 2

 c



+1

2

 c



 c

 sin cos







c

sin

0

It is observed from Eq. (28) that 

 1 3 

 is related to the friction coefficient  , the coefficient  of mixed-mode



, the time

fracture criterion, the short-term uniaxial compressive strength  c

, the short-term uniaxial tensile strength  t

iu f (0) , the dip angle of penny-shaped microcracks θ and Poisson’s ratio  .

factor

If the long-term uniaxial compressive strength of rocks is known, three-dimensional long-term strength criterion of rocks can be expressed by long-term uniaxial compressive strength of rocks. Therefore, for the long-term uniaxial compressive condition    cl 1 ,   2 0 ,   3 0 , we can obtain the rate of change constant     1 cos /     1 cos / at  t t 0 as,

   

    

2

 cl





c

c

csc





cos

t

t

2

(29)

0

0





 

csc









2 2

2 2 2 2





+1

2

1

 cl





 sin cos







c

sin

cl

t

cl

0

 0 (2 ) 2 ( )   t iu f t

,  cl is the long-term uniaxial compressive strength of rocks, iu f t 0

( ) is the time factor when

 t 0

c

where

 t t 0 , t 0 is the time of creep failure of rocks under uniaxial compressive loads. Substituting Eq. (29) into Eq. (23) yields:

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