1

2

2.1 , , , Atterberg. . , .

2.1.1 2.1.1.1 ( 2.1) - , , () ( ) / ( ). / . , , , , , , . , , , . , ( ), ( ), . , . , . , -

. 2.1:

2 2

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

2.1.1.2 , , , ( ) ( ). , , , . . , : 2 mm , 2mm 0.06 mm ( ), 0.06 mm 0.002 mm , , 0.002 mm ( 2.2).

, : , (5).

0.002 0.006 0.02 0.06 0.2 0.6 2 6 20 60 200 0.001 0.01 0.1 1 10 100

(mm) . 2.2:

3

( ) ( ). , , . ( ) ( ) ( ). , , . , ( ) . , . 2.3 , 0.1 m (1 m = 0.001 mm) () 0.3-1 m, 3-10. , . , 10-30, , 100. , . , , () , ( ) ( 2.4). , , , . , ( ) ( ) ,

. 2.3:

. 2.4:

4 2

. 2.3 m2/kg, 15000 m2/kg 800.000 m2/kg. H () () , ' , . , ( ). , -, .

2.1.1.3 , . , .., . , . . , , , , . ( 2.5) ', . , , , . , , . () , . . , .., ( ) , . , , ( ) (

. 2.5:

5

). , , , ( ) . , , ( ) . (.. ), ( .. ). , , . () . . , .. . , , . , , . , , . (.. ), , , ( ). - "" , ( 2.6).

. 2.6: ()

6 2

2.1.2 , , () / . 2.7 . V Vs Vv . ( Vw) ( Vg). (M) , , (W) : M ( ), Ms ( ), Mw ( ) Mg ( ). , ( ). , : 1. ,

:

VVn v=

. 2. ,

:

VVe

s

v= ( ):

een += 1 n

ne = 1 3. ,

:

VVS

v

w= ( )

. 0 100%. , () 1 (100%).

4. ,

. 2.7:

7

:

MMw

s

w= .

. () : ( M1) , ( M2). , :

MMMw2

21= 100M

MMw =2

21 (%)

5. , ( ) :

VM=

6. , :

VM

s

ss =

7. , ( ) :

VM

w

ww = = 1 Mg/m3

( ):

++=

ew

s 11 , ws Sew =

: (i) :

e1 sd += 1

. (ii) :

ee wssat +

+=1

S = 1. (iii) () :

e = wswsatb +

=1

: (1) : : 0,30 0,50 : 0,20 0,60 ( ) (2) : : 0,40 1,00 : 0,30 1,50 ( )

8 2

(3) : 0 1 (4) : 0 0,40 (40%) 0

1 (100%). (.. ) 5 (500%).

(5) ( Mg/m3 ): : 1,70 2,40 : 1,40 2,10 : 1,00 1,60. (6) : ( ):

s = 2,50 - 2,80 Mg/m3 2,50 Mg/m3.

2.2 - - (, ) , .

2.2.1 - (e), () . . . , . . , . (.. ). , . (Dr), :

100eeee Dminmax

maxr

(%) : e , ema

( ) emin

( ).

9

. , , . :

(%) - 0 - 15 15 - 35 35 - 65 65 - 85

85 - 100

2.2.2 () - u . . , (m), 10000 . . (British Standards), ( 2.2):

(mm)

60 20 20 6 6 2

2 0.6 0.6 0.2 0.2 0.06

0.06 0.02 0.02 0.006 0.006 0.002

- < 0.002 - : (20m ), , . ( ) " ", " ". (

10 2

2.8). ( ) . ASTM D422-1980. :

() (mm) 4 4.75 10 2 20 0.85 40 0.425 60 0.25

100 0.15 140 0.106 200 0.075

200 (0.06 mm). 200 . , ( ) , , . Stokes , , . , . , , ( ). 2.9, ( ). , ( ) . , D10 (

. 2.8:

11

10% ) D60 ( 60% ). , :

DDCu

10

60= . , Cu = 1. , Cu > 5, . , , Cu < 5, . , , .

2.3 , - . , , . ( ) ( ) , , . , ' - , - Atterberg. . ( ) . 2.10 (

. 2.9:

12 2

- ) . , , . , , : 1. :

( ) . , , .. .

2. : ( ) ( ) .

3. : , (-) (). .

4. : (). ( ) , , , .

: ws SL ( ), wp PL ( ) wL LL ( ). , Atterberg, . , , Casagrande ( 2.11) 25 . , 3 mm. ,

. 2.10:

13

, . , () : 1. , ..

, . (, .). , , , Van der Waals. , ( ). , () .

2. . . Stokes. , .

Atterberg , , . , . , (, , ) Atterberg. ,

. 2.11: Casagrande

14 2

, , . Atterberg. , : 1. :

ww I PI pLp = ,

( ) . , .

2. :

wwww = I LI

pL

pL

( w )

. , IL = 1, IL = 0. , IL 0 1 . , IL < 0 , IL > 1 .

Atterberg , ' , .. . , , , . , Atterberg () (.. , , , .), Atterberg.

2.4 . , , . , .., , ' . , ( ) ,

15

. : . Atterberg, , . . , " " (Unified Soil Classification System). 200 ( ) 4 ( ), Atterberg " Casagrande", 2.12. , - 50%. - (C), - (M). , LL = 50% (H), LL = 50% (L). 2.1 .

2.5

. .

. 2.12: Casagrande

16 2

. , . , .

17

18 2

2.1 , 2000 , 2.1-1. (), : : = 1.85 Mg/m3, : w = 9%, : = 2.70 Mg/m3. 18 . w = 12% , = 1.90 Mg/m3. : 1. (

). 2.

, (12%). : 1. : 20+29 = 38 m, : 0.5(20+38)6 = 174 m2 : V = 174 2000 = 348000 m3. , , :

42101

17029011

1 .e e

.. e

=+=+= : VV / = 0.421. , : V = 348000 = + VV . , :

V = 103102 m3, V = 244898 m3. , : =VV = 244898 m3. , :

5910090170285111 . e

e...

ew =+=

++=

VV / = 0.591 : V = 0.591244898 = 144735 m3. , :

+= VVV = 144735 + 244898 = 389633 m3 , : A = 389633 / 18 = 21646 m2, 22 . 2. (V w ) V :

ww

www Vw V VV

MMw ===

2.1-1: 2.1

19

: 001702244898090

... = V w = 59510 m3.

( ):

001702244898120

... = V w = 79347 m3.

, : Vw = 79347 - 59510 = 19837 m3.

2.2 , , (.. ) . , , , : ()

()

. . : () () . : Atterberg 16 . , ( ). Atterberg 2.2-1.

2.2-1

LL (%)

PL (%)

PI (%) 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16

31 35 36 34 32 31 37 33 34 38 30 36 33 32 35 34

14 16 15 14 17 16 18 12 15 14 13 17 12 11 16 15

17 19 21 20 15 15 19 21 19 24 17 19 21 21 19 19

: 33.81 14.69 19.12 : 2.33 1.97 2.38

20 2

2.2-1, : PI = LL - PL. ( x ) (s) :

( )=

=

=

=N

ii

N

ii

xxN

s

xN

x

1

22

1

11

1

N = 16 . " ". , , ( ) . , .., 24%. , .., 24% ( ). , , , 24% (: PI < 24%), PI > 24%. , , ( 16 ), 24% , . , Atterberg . Atterberg ( ) . , x ( ) xo ( 24%) :

[ ] [ ] %202.005.2p38.2

12.1924ppp ==>=

>=

>=> z -z s

xxs

xx xx oo

2% , )/sx-(xz . , 2% ( 2% ) 24%. (2%) , (PI < 24%) . " " , ( ). , 90%, , 90% () . , () . ,

21

(x) (), (N) ( x ) (s), :

Nsx t = (2.2-1)

t-Student, (N-1) . , [-to, to], : p[-to < t < to] = 0.90. Student 15 (N = 16 ) 90% : to = 1.753. : -to < t < to , ( 2.2-1):

tNs

x t oo

22 2

, , ( .. ). (EC-7). , . ( ), 2.2-1. (PI) , (PIc ) 5% , : p [ PI > PIc ] = 0.05. , , x ( ) (). x N , ( x ) (s). (xc) (x) : () (.. > 10) , , :

Nsx t =

t-Student 1 , tc, : p[t > tc] = 0.05. , N = 16 , tc = 1.753. (xc) :

tNs

|xx|c

c = , :

Ns

txx cc = (2.2-3) , , :

16201638275311219 ....

Ns

txx cc =+=+= , PIc = 20.16%, 19.12%. : (2.2-3) . .., :

Ns

tcc = ( ) s . () (.. < 10) , Student ( ), Chebyshev, :

23

h

Nshx

292p =

+>

, : 05.092 2 =h , : h = 2.11, : :

Nshxxc +=

: Nshxxc =

: 2.2-1, : 17%, 19%, 21%, 20%, 15% : x = 18.4% : s = 5.8%, :

% 923585112418 . ... IP c =+=

15 (PIc = 20.16%), , . 2.3 1. () . 50.70 gr. , ( ) 105oC 24 . , 45.99 gr. 18.90 gr. . 2. 37.6 gr ( ). ( ), ( = 0.90 gr/cm3) . 40.9 gr. , ( ) , 16.5 gr. 2.70 Mg/m3, : () . () . () . () . () . : 1. :

= 50.70 - 18.90 = 31.80 gr :

= 45.99 - 18.90 = 27.09 gr , () :

= 31.8 - 27.09 = 4.71 gr :

24 2

0927714.. =

= w

= 0.174 = 17.4 %

2.() : = 40.90 - 37.60 = 3.30 gr

:

900303.. = = V

= 3.67 cm3

( ) . , . , V :

1516940673 .-. = .+V

: V = 20.73 cm3 : . () :

73206037..

V == = 1.814 Mg/m3

() :

174016037

1 ..

w +=+= = 32.03 gr

:

73200332..

V == = 1.545 Mg/m3

() e : 1

1=+=

e e1

: e = 2.70 / 1.545 - 1 = 0.748. n :

748017480

1 ..

ee n +=+= = 0.428

() S :

ww e

w S eSw ==

: 17480

1740702

=.

..S = 0.628 = 62.8 % .

25