. , 3/5/2004 8-1

8

8.

8.1 ( ) . , , . : 1. , .

2. ( ).

3. . , .

4. .

5. . 6. .

8.2 , : 1. (..

) .

2. (.. ).

( RMR) ( ). , (k) . (

. , 3/5/2004 8-2

- ) k = 0.10, 10% () . , , () 2%, 2.2% , 2.4% 2.6% . , . : ( )[ ]oeteoet ttkttk /log1)/log( +=+= k , t (t), e () , (to) . 1 2 t1 t2 t2=10xt1, : ek = 12 , (k) . , ( 1). , eoE / ( to) /E (t), :

( )oo ttkEE /log11

+= , n- ( o

n tt =10 ), to=1.2 (n = 1 1 , n = 2 10 n = 3 100 ) :

nkEE o += 1

1

:

/ k 1 10 100

0.02 0.980 0.961 0.943 0.05 0.952 0.909 0.870 0.10 0.909 0.833 0.769 0.15 0.870 0.769 0.690

30% .

. , 3/5/2004 8-3

8.3

8.3.1 : 1. ( ) . , , . , .

2. .

3. , ( " "). : () ,

Winkler .

() , .

. ( ) .

8.3.2 ( )

. , , . , .

. , 3/5/2004 8-4

8.3.2.1 RMR Unal (1983) RMR. :

tv Hp = BRMRHt

=100

100

: = = RMR = ( Bieniawski)

: vh pp = NGI ( ).

5-10 , NATM RMR>50 100 . , RMR>50.

8.3.2.2 NGI ( Q) (Q) :

=

SRFJ

JJ

JRQDQ w

a

r

n

: RQD = Rock Quality Designation ( ) Jn = Jr = Ja = Jw = SRF = (Stress Relief Factor)

( kg/cm2): 312132

= QJ

Jp n

rv

: vh pp = :

Q Q > 10 0.58

0.1 < Q < 10 0.74 Q < 10 1.0

NATM NGI. (Q>0.05).

. , 3/5/2004 8-5

Q 1.5 (b+h). Terzaghi 1940 5 , .

8.3.3

.

8.3.3.1 Terzaghi

8.3.3.1.1 (D < 2.5 B) , .

. , 3/5/2004 8-6

dz ( 1): dzdBdzB v 2+= :

+==+=

245tan2tan hbBKc vhh

:

=

+B

cBBK

dzd

vv 2tan2

: v(z=0) = q z :

( )zzv eBcqe += 121 tan2

BK= . () Terzaghi

(=1). (v) (v = q + z). ( z=D):

( )DDv eBcqep += 121 , (d) :

( )

+=2

45tan22

45tan2 cdpp vh (pv) .

1: Terzaghi.

. , 3/5/2004 8-7

8.3.3.1.2 (D > 2.5 B) , , . ( ) ( 2.5 ), q = (D - H), ( ):

( ) ( )p D H e cB

evH H= +

1 2

1

.

8.3.3.2 Protodyakonov ( )

( ) :

HBfp

=2

: B b h= + 2 45 2tan

: b, h = , . f = :

: f cc

= + tan , c =

: f c= 100

,

c ( kg/cm2)

2: Protodyakonov

. , 3/5/2004 8-8

(f) :

- f 10-20

, 8 , 5-6 , , 2-5

1.0-1.5* , 0.3-0.8*

* f : f = tan + c/c , Protodyakonov (D) Hp 2Hp. . ( ):

p Hv p,max = ( x) :

p px

Bv v=

,max 1 2

2

:

( )p H B bv p=

1

1

32

Terzaghi ( ). ( ), , :

pv 1.50 ph 0.2 1.2

Protodyakonov ( ) (RMR>40). ( ) .

. , 3/5/2004 8-9

8.3.4 , ( " "). : () ,

Winkler .

() , .

8.3.4.1 Winkler Winkler (r) () :

( )kE

Rr= +1 , k = (0.3-0.5)kr

: = = Poisson R = . , . ( Terzaghi RMR), Winkler () .

8.3.4.2 , . , . : 1. ( ). ( ).

. , 3/5/2004 8-10

2. . - . () .

, ( ) ( ). . (deconfinement) ( ).

() (, , ). ( ).

() . . .

. , : () ,

.

() . ()

. 3. . , . , . , : () .

. .

() . (

. , 3/5/2004 8-11

). , , ( ). , .

() / . , , , ( ) . . , , , .

() .

8.4

8.4.1 ' (.. ). , : 1. . ( ). , . , ( ) .

2. . . , .

. , 3/5/2004 8-12

. , (10-15 ) (100-500 ) . : 1. (30-100 ) .

2. . ( ) .

3. 1 , . , ( ) , .

8.4.2 , "" . (.. ). , . , : 1.

( ) (S) .

2. ( ) (S) .

1

. , 3/5/2004 8-13

, ( ) , ( ). , , (.. 10-15 ) . , .

8.4.3 () T.R. Kuesel: "Earthquake Design Criteria for Subways", Journal of the Structural Division, ASCE, Vol 95, No ST6, June 1969, pages 1213-1231. : 1. . 2. . .

8.4.3.1 ( ) (S) . () ( 3): () :

= txAux cos2sinsin () :

= txAuy cos2sincos :

=

=

. , 3/5/2004 8-14

sin =

cos = /cos = = 2f = (f = ) x = y =

( ) :

== txA

xux

x cos2coscossin2

:

cossin2 Ax =

, () :

yy u

xu

R 222

2

2 cos41

==

, ( ) () :

3:

. , 3/5/2004 8-15

=R

Bb

12

:

( ) 232

2

22 cos2coscos42

12

ABAB

RB

b =

==

, :

coscossin2 2

+

=+= BAbx . 2 (6) (), : /cos = 6, :

coscos

6sin2

+

= A

= 32, :

A2.5max =

= 32 . () Kuesel (1969) 4. () : 1. () 2. , :

gamaxmax = 4 ( , , ). Kuesel (1969) . Kuesel . . . 2/3 . 4 (max = 5.2 /) . , . : = V/f, (V ) (f ) 2

. , 3/5/2004 8-16

. 3 . , : = maxL, (L) . ' , , (max) (.. max < 10-4). : cross-hole: Vo = 600 m/sec ( ): f = 0.5 Hz , amax = 0.24 g.

50-75% (Vo) :

V=0.67*600=400 m/sec :

= V / f = 400 / 0.5 = 800 m Kuesel :

5maxmax

102.21000

24.009.01000

09.009.01000 ==== AA

: = 2.2 x 10 -5 x 80000 = 1.76 cm

3

0.001

0.01

0.1

1

100 1000 10000

Wa ve length (m)

1000

*A/(

* m

ax)

soft soilstiff soilsoft rockmedium rock

4: (A)

() (max) (Kuesel, 1969).

. , 3/5/2004 8-17

: max = 5.2 x 2.2 x 10-5 = 1.1 x 10-4 12 m, :

= maxL = 1.1 x 10-4 x 12000 = 1.4 mm

8.4.3.2 ' (SV) . Kuesel (1969) () :

max230.2

=VH

: ( ) ( ).

V ( m/sec) .

(u) (d) :

u = (H - d) .

. , 3/5/2004 8-18