A mechanism of rock failure at the walls of large caverns and by mhf39s

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									A mechanism of rock failure at the walls of
     large caverns and excavations

      A. V. Dyskin, E Sahouryeh, L. N. Germanovich




            The University of Western Australia


                                                     Slide 1
                              Plan
  Introduction
  Model of Crack Growth
  Rockburst Initiation
  Rockburst Initiation
  Conclusions




Geomechanics Group, UWA, Australia   Slide 2
                          Introduction




Geomechanics Group, UWA, Australia       Slide 3
                       Crack Growth
       2-D mechanism
                                                  Rock
                                                  mass
                                     Excavation
                                     surface



                                                    Initial (pre-
                                                    existing)
                                                    crack


                                                     Wing




                                                   Direction of
                                                   unstable
                                                   growth




Geomechanics Group, UWA, Australia                                  Slide 4
           3-D crack growth in uniaxial compression




                          No extensive growth

Geomechanics Group, UWA, Australia                    Slide 5
                                            Wing crack near free surface



                     2a              bL
                                                                    b
         a
                                                       2a
                                                       f

                       b  ( 0.6  0.8) a              b  ( 0.6  1) a
                       L  ( 0.6  2) a                    f  4a




Geomechanics Group, UWA, Australia                                         Slide 6
   3-D crack growth in biaxial compression




Geomechanics Group, UWA, Australia           Slide 7
                                  Crack Model
 Pz
                              Extensive wing
                              growth                                                  F


                                                                                          R
                                                                                 F
Py


(a)   Before testing                           (b)    After testing              (c) Model

 (Germanovich et al., 1996)
F  a 2 Pz sin 2  cos                             (1)

     KI=F(R)-3/2         (Cherepanov, 1979)                          Stable growth

Geomechanics Group, UWA, Australia                                                     Slide 8
                       Accounting for free surface

Srivastava & Singh (1969).


             F            5  R 3 
K I ( R)                1     (2)                   6
           (R ) 3 2       h 
                                                       4.8
                                                                        stable




                                           KI h3/2 F-1
 dK I
      0                             (3)                 3.6
 dR                                                                              unstable
                                                         2.4
Rcr = h(/5)1/3  0.85h              (4)                 1.2

K I  K Ic                           (5)                  0
                                                               0    1       2         3    4    5
      2                                                                        R/h
Fcr      K Ic h 3 2                 (6)
      2                                                        Critical radius



Geomechanics Group, UWA, Australia                                                        Slide 9
                         Rcr = h(/5)1/3  0.85h




                                       Rcr




Geomechanics Group, UWA, Australia                 Slide 10
       Rockburst Initiation                                     pz
      Averaging (1)             F     2
                                           3 a 2 Pz   (7)




                                                            h




H is minimum of :
•         stress concentration depth
•         depth of flaws                                         pz
Geomechanics Group, UWA, Australia                                    Slide 11
                                                   NAH
      ( x )  Phm in  x  1  Phm in  x  1   Phi  x
                                                     i 1
                                             NAH
                                                                        (8)
            NAH
                                      x
      1   (1  Phi  x)  1  1  
           i 1                     H                        e.g., Freudenthal, 1968)

For A1/2 , H >> 1/N1/3 and H >> hmin
            H                  H            NAH 1
                                      x
  hm in      ( x ) xdx  NA  1               xdx                (9)
                                0 
            0
                                      H
                 H                     1
                             
                             
                             H
             NAH  1                  NA
                                     2
  Substituting into (6)      Fcr         K Ic h 3 2
                                    2
    and using (7)         F  2 3 a 2 Pz

Geomechanics Group, UWA, Australia                                            Slide 12
                               3 2 K Ic
                    Pcr                               (10)         for unstable growth
                            4 5a 2 ( NA) 3 2
                    Pcr  Pwing
  Using Cherepanov’s, 1979 critertion of maximum circumferential stress
                                                                 2        a
                   3                                  K II        Pz            (11)
      Pwing           K Ic                                              
                4    a
                                           (12)

                   3                3         
      Pcr             K Ic max               , 1                                (13)
                                 5 ( NAa )       
                4    a                      32
                                                 
Normalising, following Dyskin et al. (1991),

                v 0  Na 3 ,     K Ic  2 t a                                    (14)

             Pcr  3          3            a 
                                                   3            
                        max                   v 0 3 2 ,   1                  (15)
             t               5                              
                     2
                                            A                
Geomechanics Group, UWA, Australia                                                 Slide 13
                                     Size Effect
             A 3 5
                       1/6
   1
             
                                                          (16)
 v 01 3     a    v 01 2
  3          Pcr       3 3 2
                               v 0 1 2                 (17)
   2          t        2 5
                                       P cr/ t

 v0~0.1                                     104
 0.46<A1/2/a<3.5,
                                                          v0=0.001
 2.7<Pcr/t<11.8                                 3
                                            10                 v 0=0.01
 v0~0.01
 0.99<A1/2/a<11,                                                     v 0=0.1
 2.7<Pcr/t>37,                             100


 v0~0.001                                   10
 2.1<A1/2/a<35
 2.7<Pcr/t>118
                                                  1
                                                      0   10         20        30   A 1/2/a
Geomechanics Group, UWA, Australia                                                   Slide 14
                         Rockburst Progression
(e.g., Timoshenko, 1959)

                 Eh3
  Pcr   2                                         (18)
            12(1  2 ) Rcr
                         2



Substituting (9), (10), (14) into (18)

           3
  Rcr               E 5             
 
  a       2
                                   v 01 / 2        (19)
              18 2 (1   2 ) t

From (18) and (19)
Pcr       27 2 (1   2 ) t                      (20)
                               v -1
t
                                  0
                5 2 E
inserting A=Rcr2 into (9), we have
                                           23
hmin       1      2E 5                        
                                             v04 3      (21)
 a          18 2 (1   2 ) t
                                      
                                       
 Geomechanics Group, UWA, Australia                               Slide 15
                         Conclusions
    The proposed model of rockburst initiation predicts the scale
     effect: the larger the area of stress concentration the smaller the
     magnitude of stress concentration required to initiate rockburst.



    The model relates rockburst initiation to the quality of the
     excavated surface: the smaller the crack concentration at the
     excavation wall, the higher the stress of rockburst initiation.




Geomechanics Group, UWA, Australia                                Slide 16

								
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