experimental study of the shear strength of un filled and rough rock

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  • 8/12/2019 Experimental Study of the Shear Strength of Un Filled and Rough Rock

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    T

    AD .............................................................................................................................

    1. D................................................................................................................................... 1

    1.1 B ....................................................................................................................................... 1

    1.2 O ........................................................................................................................................... 2

    2. A D ............................................................................................................................. 3

    2.1 I ...................................................................................................................................... 3

    2.2 B ............................................................................................... 3

    2.2.1 F .................................................................................................. 3

    2.2.2 S .................................................................................................................. 5

    2.3 P .............................................................................................. 5

    2.3.1 C ...................................................................................................................... 5

    2.3.2 P (1966) .......................................................................................................................... 6

    2.3.3 L A (1970) ............................................................................................. 6

    2.3.4 B (1977) (1997,) ........................................................................................... 7

    2.3.5 M (1992 & 1996) ...................................................................................................... 7

    2.3.6 K (1995) ..................................................................................................................... 7

    2.3.7 G (2001) ....................................................................................................................... 8

    2.3.8 R ..................................................................................................... 8

    3. A D .......................................................................................................................... 9

    3.1 I ...................................................................................................................................... 9

    3.2 P ............................................................................................................................. 9

    3.3 S ............................................................................................................... 10

    3.4 P ...................................................................................................................... 11

    3.5 T ............................................................................................................................ 12

    3.6 M ............................................................................................................................. 13

    3.7 F ....................................................................................................... 15

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    E

    4. A ................................................................................................................................. 18

    4.1 I .................................................................................................................................... 18

    4.2 T ..................................................................................................................................... 18

    4.3 A ........................................................................................................... 20

    4.4 T ................................................................................................................................... 21

    4.5 T ................................................................................................................................ 23

    4.6 T ...................................................................................................................................... 27

    4.7 A ............................................................................................................................ 32

    4.7.1 N ....................................................................................................... 32

    4.7.2 I ........................................................................................................ 32

    4.8 E JCS S .................................................................................. 34

    5. A A .......................................................................................................................... 35

    5.1 I .................................................................................................................................... 35

    5.2 S ................................................................................................................... 36

    5.3 P ................................................................................................... 38

    5.3.1 C ..................................................................................................... 38

    5.3.2 C ...................................................................................................... 40

    6. A AA ................................................................................................................... 43

    6.1 I .................................................................................................................................... 43

    6.2 A ............................................................................................................ 43

    6.3 A ....................... 45

    6.3.1 R S 1 .............................................................................................................. 45

    6.3.2 R S 2 .............................................................................................................. 46

    6.3.3 R S 3 .............................................................................................................. 47

    6.4 A ................................................................................................................... 49

    6.5 F ......................................................................................................... 51

    7. ................................................................................................................................... 52

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    T

    8. ...................................................................................................................................... 53

    AD

    A. R LDT .................................................................................................. I

    B. T ............................................................... III

    C. G .......................... ...................... ............. I

    D. G ..................................................

    E. F ............................................................... II

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    E

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    T

    AD

    F, I F J; .

    S, I CL, LT S S

    .

    F, E STEN AB

    .

    T "S H C SC". SC

    S E A, E S K

    L T, T R I T, C

    T . ..

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    C 1 I

    1

    1 D

    1.1

    R . T ,

    (P, 1966). T

    . T

    . T

    . I

    . R ,

    , . O

    . R

    , . I , I

    .

    O . I

    . T

    . I ,

    . T

    . I

    .

    I ,

    . T . O

    . E

    . A

    . E

    (JRC), (JCS) . I

    . A

    . T

    .

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    E

    2

    1.2

    T ,

    . T

    . T

    . T

    , ,

    . T , ,

    . M

    .

    A , . T

    . T

    , . T

    .

    I , I J (2009)

    . T J(2009).

    H, . M

    . T

    , .

    T . T

    . T

    . T

    . T

    .

    I I . I I . I , I

    J(2009). T

    . C

    . T

    .

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    C 2 L

    3

    2 A D

    2.1

    A ,

    . T

    . T , ,

    .

    T . E ,

    . T

    .

    I , ;

    . A, .

    2.2

    2.2.1 &

    T .

    , . T . T

    A C. T

    :

    A' :T .

    A' : T

    .

    ' :K .

    I , . I

    T (1925) B T (1950 1964).

    T :

    A ,

    .

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    E

    4

    C

    . T

    .

    T . T

    :

    = (2.1) .

    T , ..

    . T (2.1)

    A . T

    .

    T :

    = (2.2)

    .

    B (2.1) (2.2) :

    = (2.3)

    . I . T :

    = tan (2.4)

    I

    .

    M

    . I . T

    . A

    . I ,

    (G (1966) L T (1986)).

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    C 2 L

    5

    2.2.2

    A . I

    . I . I

    , . T .

    I . M . T

    B

    (1973) JRC, . O

    .

    A

    . T (RMS) (CLA) (T 1982). I , ,

    , , (SF),

    () () (P 1996).L, , M

    (1983); B S (1985); F (2003). T

    . S

    .

    I . T

    (M 1990).

    2.3

    T

    .

    2.3.1

    C

    . I C. I :

    = (2.5) , . I :

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    E

    6

    = tan (2.6)

    . T , C,

    .

    2.3.2 (1)

    P . H

    . H

    :

    = tan+ (2.7)

    . I . P . I

    . T :

    = c+ tan (2.8) c .

    2.3.3 (10)

    A L A (1970)

    . T :

    = (2.9):

    : P : E : A : S : B : D = arctan

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    C 2 L

    7

    .

    2.3.4 (1) (1 ,)

    A B C (1977)

    . I

    . I JRCJCS . T :

    = tan log + (2.10)

    ,

    .

    JRC 0 20,

    0 20 .

    JCS

    .

    (1997 ,) B . H

    JMC . JMC

    0 1 0 1 .

    2.3. (12 1)

    M (1996)

    . T :

    = tan + /1+ (2.11) , . T .

    .

    2.3. (1)

    K (1995) . I

    . T :

    = + log + (2.12) I , . ,

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    E

    8

    . SRP

    .

    2.3. (2001)

    G (2001)

    . H .

    T ATM A T S.

    T G (2001) . I :

    = tan 1 + (2.13) : = + (2.14) : = . 1 (2.15) .T . I .

    = (2.16) .2.3.

    I , . T

    . T (

    ). T

    , .

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    C 3 C

    9

    3 A D

    3.1

    I , J (2009) . T

    . T

    : , , , . E

    . T

    .

    3.2

    T

    , . T .S := + (3.1)T (P

    (1966)). I

    . T . T

    . F

    .

    F , . F, . T . T

    . T

    . T

    . A

    30 .

    A

    . I L A (1970), B (1973) B . (1981).

    P (1966), F (1990) G (2001)

    . I , ,

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    E

    10

    . T , ,

    .

    A J (2009),

    , .. 30, . 30

    . T

    70.

    T . T

    :

    =

    tan (3.2)

    .C (3.1) (3.2) :

    = tan+ (3.3)3.3

    I . T

    , ,

    . T

    . I ,

    , .

    I . L

    .

    T , . T

    ,

    (M 1983). R ,

    .

    F ,

    :

    = (3.4)

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    C 3 C

    11

    H H A . T

    :

    = (3.5) . T . T . H 1

    .

    H, H , ,

    . T

    () .

    = tan (3.6)

    3.4 A

    T G (2001). I ,

    . H

    . T

    , G, ,. T , :, = (3.7) , G 0.5 . C .T

    . I 3.1. T

    . A

    .

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    E

    12

    3.1

    T

    .

    I

    . T

    3.5

    T

    T

    T

    =

    . T,

    .

    .

    . T

    :

    , .

    ( 2006)

    .. I

    . C

    . T

    .

    (3.8)

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    C 3 C

    13

    T

    . T :

    , = (3.9)C (3.8) (3.9) :

    , = (3.10)A :

    (3.11)

    C (3.10) (3.11):

    , = (3.12)T . F :

    , = (3.13)3.6

    M

    .

    A .

    I . I

    :

    3.2 A

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    E

    14

    A

    . I . I

    :

    L , , L , ,

    3.3 A

    I , ,

    .

    A , :

    (3.14)T

    . A , :

    (3.15) . T

    :

    (3.16) , . H . C (3.15) (3.16) :

    (3.17)

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    C 3 C

    15

    . T

    .

    J (2009) ,

    :

    ( (3.18) .

    T

    . T (3.18)

    . I , =0 .

    O , ( )

    . T

    . T (3.18)

    . I , =1

    .

    I .

    , :

    (3.19) , 2 2 .3.7

    A , J (2009)

    . B, .

    1 :

    t(+ (3.3)2 :

    (3.5)

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    E

    16

    3 :

    t( (3.6)4 : ( (3.7)5 :

    , = (3.13)6 :,= , (3.18)T , J(2009),

    . (3.7) (3.13) :

    = 10 (3.20)C (3.5), (3.6) (3.20),

    :

    ,=0,5 tan 10

    (3.21)

    C (3.5), (3.6), (3.18) (3.21),

    :

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    C 3 C

    17

    rt 2 5 t 10

    (3.22)

    E (3.22) :

    = 10 (3.23)E (3.23) J(2009) . T

    5.

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    E

    18

    4 A

    4.1

    I ,

    J (2009) . T

    . E

    .

    T L T. T

    280 280

    ISRM (ISRM 1981).

    4.2

    T E S AB. E

    251414 20 . I ,

    . H,

    . T 4

    . A ,

    . F , 1, 2 3. A ,

    T 4.1.

    4.1 .

    () ()

    1 10.40 10.15

    2 12.52 11.51

    3 13.71 12.93

    T

    . P F 4.1.

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    C 4 S

    19

    4.1 .

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    E

    20

    4.3 A

    B ,

    . I

    . S 1 , S 2

    S 3 .

    4.2

    250 . ( (2009)).

    A , . A,

    .

    A F 4.2, , =0 =0.6

    =0.6 =1.0

    . C, =0, =0.4,

    =0.75 1, 2 3 . T F 4.8.

    ,

    . T 35 . S, .

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    C 4 S

    21

    A, ,

    . T :

    (3.19) 2 0.5 = 2 120 .

    T 4.2

    :

    4.2 .

    D ()

    ()

    , ()1 0 30 65 0

    2 0.4 22.5 57.5 5

    3 0.75 15 50 30

    T , . I E (3.19). F S 1,

    , . ,=0. H, T 4.2, 5 30 S 2 S 3 .I , 3 MP . I 0.1 /

    5 .

    4.4

    D , . T

    3 MP .

    T . F S 1,

    . H,

    2 3.

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    E

    22

    I F 4.3, . T 0.5 3

    2 3 . T .

    10 .40

    10 .15

    0.50

    12 .02

    11 .51

    3.00

    10 .71

    12 .93

    S A M P L E 1 S A M P L E 2 S A M P LE 3

    4.3 ().

    T , 3 MP.

    T 4.3 :

    4.3 .

    () () A (2) ()

    1 10.40 10.15 105.56 31.72 12.02 11.51 138.35 41.5

    3 10.71 12.93 138.48 41.5

    T

    . A

    . T ,

    . T

    . F 4.4 S 1.

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    C 4 S

    23

    4.4 . 1.

    I 21.5

    . T

    . I 8 N 1 3 8.5 N

    S 2. T T 4.4.

    4.4 .

    () A () ()

    1 31.7 8 39.72 41.5 8.5 50

    3 41.5 8 49.5

    4.5

    T 500 N

    . A F 4.5.

    0

    5

    10

    15

    20

    25

    30

    35

    21.25 21.00 21.00 20.02 19.93 21.03 21.62 21.84

    (

    )

    ()

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    E

    24

    4.5

    T F 4.6,

    4.6 ( (2009)) (0)

    (1) , (2) , (3) , (4) , (5)

    , (6) & (7) , (8) ( . 2005)

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    C 4 S

    25

    4.7 ( . 2005)

    T LDT (L D T)

    . T 4 LDT, .

    S 5 0.1

    /. D 0.5

    0.0017 /.

    T :

    1. C .

    2. P .

    3. A

    . T .

    4. A (2 3 N),

    .

    5. LDT .

    6. A .

    7. A .

    8. S .

    T 3 F 4.8.

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    E

    26

    4.8 1(), 2() 3 () .

    2 3 .

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    C 4 S

    27

    4.6

    T T 4.5. T

    ,

    , , , , , N , .T . T

    . T

    (4.1)

    rt

    (4.1)

    . T 0.1 . T LDT. T

    . T , 0 5 .T 4.5 . G F 4.9 F 4.14. I

    F 4.15 . T

    LDT A A.

    4.5 1, 2 3.

    ()

    ()

    ,()

    ()

    ()

    ()

    ()

    ,()

    1 2.28 5.35 0.84 66.88 13.96 39.76 36.82 1.11

    2 2.39 2.60 3.96 47.31 5.0 41.99 13.55 0.54

    3 2.42 3.33 4.63 54.02 0.61 43.64 15.43 4.95

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    E

    28

    4.9 (

    4.10

    10

    0

    10

    20

    30

    40

    50

    60

    70

    0 1

    A()

    0

    10

    20

    30

    40

    50

    60

    0 1

    )

    .

    2 3

    D ()

    2 3

    D ()

    1.

    1.

    4 5

    N

    D

    T

    4 5

    S L (N)

    N L (N)

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    4.11 (

    4.12

    20

    10

    0

    10

    20

    30

    40

    50

    0 1

    A()

    0

    10

    20

    30

    40

    0 1

    )

    .

    2 3

    D ()

    2 3

    D ()

    C 4 S

    29

    2.

    2.

    4 5

    N

    D

    T

    4 5

    S L (N)

    N L (N)

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    E

    30

    4.13 (

    4.14

    20

    10

    0

    10

    20

    30

    40

    50

    60

    0 1

    A()

    0

    10

    20

    30

    40

    50

    0 1

    )

    .

    2 3

    ()

    2 3

    ()

    3.

    3.

    4 5

    N

    D

    T

    4 5

    S L (N)

    N L (N)

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    C 4 S

    31

    4.15 .

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    E

    32

    4.7 A

    I ,

    .

    4..1

    I

    . F S 1 ,

    39.7 N 24 N . T

    .A , 2.3 2.4 MP

    3 MP .

    F S 3, 30 . ,

    LDT . T LDT

    . A ,

    LDT 2 3. T

    3.

    I S 1 3

    . T .

    4..2

    T 4.6 F 4.16 . I

    S 1 , .

    T S 2 3 ,

    LDT S 3.

    4.6 .

    A A 1 66.9 36.8

    2 47.3 13.6

    3 54 15.4

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    C 4 S

    33

    4.16 .

    R S 1, F 4.9

    . I . T

    . I

    0.2 1 . T

    .

    R S 2, F 4.11

    . A 4 . I

    ,

    . H,

    . T S 2

    5 .

    R S 3, F 4.13 3 . A LDT,

    . T S 2

    . H .

    I ,

    .

    0

    10

    20

    30

    40

    50

    60

    70

    80

    1 2 3

    A()

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    E

    34

    4.8 E C

    S JCS, ,

    B C (1977). T

    S R F 4.17.

    4.17 .

    T .

    , . T 10

    . O ,

    . T B C (1977). T :

    og( 88 + (4.2) JCS. S (N/3), 27 N/3.T 10 T 4.7.

    4.7

    1 2 3 4 5 7 8 9 10

    40 42 46 38 44 40 44 40 50 45

    A ,

    S 45.8.

    (4.2), 125 MP.

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    C 5 O

    35

    5 CA CA

    5.1

    I , ,

    , H ,

    . T

    . T .

    T S L

    ATOS III, F 5.1. I ,

    , 4

    . C .T 50 .

    5.1 A ( )

    T

    . T

    .

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    E

    36

    T

    MATLAB (M

    F

    5.2

    5.2

    I H

    . T

    L

    T 5.1. T

    . T

    2007). T

    S 1 F

    1

    H

    2

    0.5

    . T

    2 . T S 2 3 A

    0.5 0.5 .

    5.2.

    .

    ,

    . H,

    16 . T

    S 1 B.

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    C 5 O

    37

    5.1 1.

    A, . T . T

    H .

    F 5.3 S 1. T S 2

    3 A C. T T

    5.2.

    5.3 1.

    1

    = 0.19370.9083

    R = 0.99991

    = 0.19360.908

    R = 0.9999

    0.10

    1.00

    10.00

    1 10 100

    ()

    A ()

    S1

    S1 L

    () ()

    1

    2

    () () 2

    () ()

    0.5 1 0.380 20.797 0.190 0.380 20.797 0.190

    1 2 0.367 20.168 0.367 0.367 20.163 0.367

    2 4 0.346 19.060 0.691 0.345 19.009 0.689

    4 8 0.323 17.875 1.290 0.323 17.880 1.290

    8 16 0.302 16.799 2.415 0.301 16.762 2.410

    16 32 0.278 15.515 4.442 0.277 15.504 4.438

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    E

    38

    5.2

    .

    1 2 3

    0.194 0.194 0.147 0.147 0.152 0.156

    0.908 0.908 0.752 0.756 0.780 0.770 0.999 0.999 0.994 0.995 0.995 0.9955.3

    .3.1

    P

    . T

    0.5 0.5 . T , . 5.1, , .

    cos90 = | ||||| (5.1)A ,

    . T 0.5

    0.5 . ,

    ; , C.

    T

    . A

    . T . I

    ,

    0. I, , , 180.

    T T 5.3.

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    C 5 O

    39

    5.3 .

    1 2 3

    () 0 180 0 180 0 180

    A (A) 0.615 0.617 0.548 0.540 0.476 0.479

    A() 0.663 0.670 0.603 0.612 0.500 0.528

    2.765 2.820 3.704 4.206 3.648 5.354 58.286 58.553 47.904 52.338 48.918 64.312 0.987 0.987 0.993 0.995 0.990 0.989/ 21.080 20.763 12.933 12.444 13.409 12.012A T 5.3, 0.5. T . T

    . T S 1 S 2 3. T

    F 5.4 S

    1 . T S 1 , S 2 S 3

    A D.

    I F 5.4 T 5.3

    . T

    .

    5.4

    1.

    0 10 20 30 40 50 600

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    0.7

    Measured dip angle()

    Pote

    ntialcontactarea

    ratio

    Actual

    Regression

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    E

    40

    T F 5.5 S 1

    . T A E.

    5.5 1 ( )

    .3.2

    I T 5.3

    0.5. T (

    ). H, S 1

    0.5. A ,

    T 5.4. T

    .

    5.4 .

    1 2 3

    () 5.3 1.3 0.7

    () 5.3 1.3 0.7

    S

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    C 5 O

    41

    T ,

    . T T 5.5. A ,

    0.5. I 2 3 ;

    .

    5.5

    .

    1 2 3

    () 0 180 0 180 0 180A (A) 0.502 0.502 0.508 0.502 0.496 0.497

    A() 0.523 0.530 0.551 0.562 0.524 0.553 2.647 2.705 3.692 4.193 3.663 5.408 49.240 49.467 45.935 50.274 50.004 65.867 0.987 0.987 0.993 0.996 0.991 0.989/ 18.602 18.287 12.442 11.990 13.651 12.179

    T ,

    S 1 . I

    F 5.6.

    5.6

    1 .

    0 5 10 15 20 25 30 35 40 45 500

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    0.7

    Measured dip angle ()

    Potentialc

    ontactarea

    ratio

    Actual

    Regression

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    E

    42

    F 5.7 S 1

    . T . T

    . T 5, .

    5.7 ()

    () 1 ( ).

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    C 6

    43

    ECA AA

    .1

    T . T

    . T

    . T

    . T

    .

    .2 A

    T ,

    , H

    .

    I , E 6.1

    , .. 2 3.

    10

    (6.1)

    S =0 , E 6.2 S 1.

    = 10 (6.2)A, 35 . T

    () (). I

    .

    A . T

    T 6.1.

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    E

    44

    6.1

    . A .

    C A A

    1 66.88 66.43 66.00 66.22 69.32 68.95 69.14

    2 47.31 52.31 50.07 51.19 52.51 50.34 51.43

    3 54.02 60.44 55.87 58.16 61.57 55.57 58.57

    S T 6.1, :

    F S 2 3,

    ,

    (1.3 0.7) . T S 1 5.3. F S 2 3,

    . T

    ( ), . T

    . S

    1 , ,

    .

    T ; ,

    . T T 6.2.

    6.2

    . .

    I T 6.2

    . S 1 ,

    . S 2 S 3

    . I

    . F 6.1

    .

    C

    1 66.9 66.2

    2 47.3 51.2

    3 54.0 58.2

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    C 6

    45

    6.1 .

    .3 A

    I ,

    . I

    , =0 =1 (.. ) (3.9), 2 2 . E . I .

    .3.1 1

    F 6.2 S 1. T 66.88

    0.84 . T 66.43

    0.5 . I F 6.2

    . T . T

    .

    0

    10

    20

    30

    40

    50

    60

    70

    80

    1 2 3

    A

    ()

    S T C M

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    E

    46

    6.2 1.

    .3.2 2

    F 6.3 S 2. T 47.31

    3.96 . H, ;

    2. A , B (1982)

    0.01L, L .

    T 1.2 . S 1.2

    .

    A , 51.17

    1.2 . R ,

    . H, . T

    S 1.

    0

    10

    20

    30

    40

    50

    60

    70

    80

    0 1 2 3 4 5

    ()

    ()

    Conceptual ModelShear Test

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    C 6

    47

    6.3 2.

    .3.3 3

    F 6.4 S 3. T 54.02

    4.63 . , S 2

    . S .

    R , 53.13 1.3

    . A S 2, . H,

    . T ; S

    3 (=1).

    0

    10

    20

    30

    40

    50

    60

    0 1 2 3 4 5

    ()

    ()

    Conceptual ModelShear Test

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    E

    48

    6.4 3.

    T 6.3 . F S 1,

    . H S 2 3 . T

    .

    6.3

    ()

    ()

    D

    ()

    D

    ()

    1 66.88 66.43 0.84 0.5

    2 47.31 51.17 3.96 1.2

    3 54.02 53.13 4.63 1.3

    0

    10

    20

    30

    40

    50

    60

    0 1 2 3 4 5

    ()

    ()

    Conceptual Model

    Shear Test

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    C 6

    49

    .4 A

    I ,

    . I

    (G E 2000; K E 1995).

    T ,

    . I

    . I

    . T

    .

    6.4 . A

    .

    1 31.4 31.0

    2 16.2 15.1

    3 26.1 20.9

    F 6.5 6.7 (

    ) . L ,

    :

    S 1

    .

    S 2 .

    S 3

    .

    I .

    F ,

    . F ,

    . T

    . T

    .

    H ,

    .

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    E

    50

    6.5

    1.

    6.6

    2.

    S

    S

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    C 6

    51

    6.7

    3.

    S

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    E

    52

    7 CC

    T .

    T

    . T ,

    . T

    .

    T . T

    .

    T , ,

    . T

    1% (B 1982)

    T

    . I ,

    . F , . H,

    , .

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    R

    53

    8 EEECE

    B, S.C. (1980). E S S E S S,

    D R J. D T, D E S, T

    L.

    B, S.C.; L, A.C.; B, N.R., (1981). E

    , I. J. R M. M. S.

    B, N., (1973). A .

    E G, . 7, N. 4, . 287332.

    B, F.P.; D. T, (1950). T F L S,P I, O P, L.

    B, F.P.; D. T, (1964). T F L S,

    P II, O P, L.

    EROCK 2010, R M C E E, J .

    F, N., (2003). T S M, M

    T S R F. P. D. T, R I

    T, L R E, S, S.

    F, .A., (1990). F M S S J

    A. I: R J.

    G, G., (2001) S

    . D T, EPFL, L.

    G, J.A.; , J.B. (1966). C N F S.

    P R S L. S A, M

    P S.

    J, F, (2009). S S R R J S S

    A C D, D T, R I T.

    K, P.H.S.., S, G., H, T.H. M, R.M., (1995). N

    C .

    L, B., A, G. (1970). S

    , P 11 .S. S R M.

  • 8/12/2019 Experimental Study of the Shear Strength of Un Filled and Rough Rock

    62/72

    E

    54

    L, J.M., T L.., (1986). T E N S R

    A C D F S R. P & A. G.

    M, M., (1992). T N, N

    .

    M, A., (1990). A .

    M, B.B., (1983). T . N : . H. F,

    M (2007) M, 7.4.0.287, N M, SA.

    P, T.T.; H, S.R.; L, A.C., (1995). A

    . 18 I. C R M,

    T, J.

    P, F.D., (1966). M ,

    P.D. T, . I.

    S, D., M, L., N, E., (2005). L T

    R J D S, T C, R M

    R E.

    T, K. (1925). E, F D, .

    T, T.R. (1982) R S. L: L.

    , J. (1997). J M , P A: J

    M C (JMC).

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    A

    I

    AE A, E EA E

    A.1 4 1.

    A.2 4 2.

    0.5

    0.0

    0.5

    1.0

    1.5

    2.0

    0 1 2 3 4 5

    C

    ()

    ()

    LDT1

    LDT2

    LDT3LDT4

    0.5

    0.0

    0.5

    1.0

    1.5

    2.0

    2.5

    3.0

    3.5

    0 1 2 3 4 5

    C()

    ()

    LDT1LDT2LDT3LDT4

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    E

    II

    A.3 4 3.

    3

    4

    5

    6

    7

    8

    0 1 2 3 4 5

    C()

    ()

    LDT2

    LDT3

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    A

    III

    AE B, ABE AE E A EE AE BAE

    E

    B.1 2.

    () ()

    2

    2 A() () 2 A() ()

    0.5 1 0.269 15.051 0.134 0.269 15.040 0.134

    1 2 0.253 14.187 0.253 0.253 14.203 0.253

    2 4 0.224 12.604 0.447 0.224 12.642 0.449

    4 8 0.189 10.692 0.755 0.189 10.725 0.7588 16 0.151 8.576 1.206 0.151 8.598 1.210

    16 32 0.114 6.492 1.821 0.116 6.600 1.851

    B.2 3.

    () ()

    3

    2 A() () 2 A() ()

    0.5 1 0.280 15.642 0.140 0.286 15.982 0.143

    1 2 0.266 14.880 0.266 0.269 15.072 0.2692 4 0.240 13.490 0.480 0.241 13.561 0.482

    4 8 0.206 11.613 0.822 0.206 11.651 0.825

    8 16 0.170 9.637 1.358 0.169 9.603 1.354

    16 32 0.130 7.401 2.078 0.128 7.294 2.048

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    E

    I

    AE C, A AE E A EE AE BAE

    E

    .1 2.

    .2 3.

    2

    = 0.14710.7519

    R = 0.9943 2

    = 0.14680.7557

    R = 0.9948

    0.1

    1.0

    10.0

    1 10 100

    ()

    A ()

    S2

    S2 L

    3

    = 0.15220.78

    R = 0.9952 3

    = 0.15560.7701

    R = 0.9951

    0.1

    1.0

    10.0

    1 10 100

    ()

    A ()

    S3

    S3 L

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    A

    AE , A EA CAC AEA A AA

    EAE AE

    .1

    1.

    .2

    2.

    0 10 20 30 40 50 600

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    0.7

    Measured dip angle ()

    Potentialc

    ontactarea

    ratio

    Actual

    Regression

    0 5 10 15 20 25 30 35 40 45 500

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    0.7

    Measured dip angle ()

    Poten

    tialcontactarea

    ratio

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    E

    I

    .3

    2.

    .4 3.

    0 10 20 30 40 50 60

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    0.7

    Measured dip angle ()

    Potentialcontactarea

    ratio

    Actual

    Regression

    0 5 10 15 20 25 30 35 40 45 500

    0.05

    0.1

    0.15

    0.2

    0.25

    0.3

    0.35

    0.4

    0.45

    0.5

    Measured dip angle(

    Potentialcontactarea

    ratio

    Actual

    Regression

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    A

    II

    .5

    3.

    0 10 20 30 40 50 60 70

    0

    0.1

    0.2

    0.3

    0.4

    0.5

    0.6

    0.7

    Measure dip angle ()

    Potentialcontactarea

    ratio

    Actual

    Regression

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    E

    III

    AE E, E EAE AE AA EA EC

    .1

    1 ( )

    .2

    2 ( ).

    S

    S

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    A

    I

    .3

    2 ( ).

    .4

    3 ( ).

    S

    S

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    E

    .5

    3 ( ).

    S