Issue 44

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

   

   

 C C 22 2 

1

3





C

3

2







C

2



   22

 C C

C C

2

11

11 21

3

(30)

   

    

2

 cl





c

c

csc

t

t

2

0

0





 

csc





2 2

2 2 2 2





+1

2

 cl





 sin cos







c

sin

cl

t

cl

0

From Eq. (30), micromechanics-based three-dimensional long-term strength criterion of rocks expressed by long-term uniaxial compressive strength of rocks can written as                          A A A A A 4 3 2 1 1 3 2 1 3 3 1 3 4 1 3 5 0 (31)

where





2

                     C C C 11 21 22

 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



1)si

n











 

 

2

2

2

2

2

2



 2 +2 c

 

 +1 +2



 sin cos 





sin

cos

2

3



     2  

2



2

2

2

2

 







 sin cos



 



C c

cos

sin

3

2

3

2 3





     

   

    

2

 cl





c

c

csc

 

t

t

2

0

0

 



C

csc

4





2 2

2 2 2 2





+1

2





 cl





 sin cos



c

sin

cl

t

cl

0

It is observed from Eq. (31) that 



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



  1 3

fracture criterion, the long-term uniaxial compressive strength  cl

, the short-term uniaxial tensile strength  t

, the time

iu f t 0 ( ) , the dip angle of penny-shaped microcracks θ and Poisson’s ratio  .

factor

Assumed that

    C C 11 21

2





0 ,

,

    cl 2

 m n



C s 22

    cl m n 2 



C s

3

3

3

Eq.(31) can be simplified to:

      s m n 3 1 3 2     cl

2

2















  









  





(32)

s

s

s

m n

0

cl

cl

cl

3 1 3

2

3

where s n , and m are the strength parameters which are determined by experiments.

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