Retaining Wall Calculation

2

,

,

2012

3

- . , - , (-: . . , . . , . . , . . , . . , 1992 ., 2011 .). - ; - : www.buildcalc.ru. , . . ..., . ..

1 ................ 4

........................................................................................................ 5

2 .................................................................................................................................... 5

3. ....................................................................................................................................... 9

3.1 ....................................................................................................... 9

3.2. ( . . ) ........................................................ 12

4. .................... 14

4.1. ........................................................ 14

4.1.1. .......................................................................... 14

4.1.2. .............................................. 15

4.1.3. ............................................................... 15

4.2. ........................................................ 16

5. ................................................................ 16

5.1. ................................................................................. 16

5.2. ................ 17

5.3. .................... 18

5.4. ( . . ) .................................................................................................................................. 20

5.5. , ........................ 20

5.6. .................................................. 24

......................................................................................... 24

5.7. .................................................................... 25

4

5.8. , , : www.BuildCalc.ru .................................................................................................................... 26

5.8.1. : www.BuildCalc.ru .................................................... 26

5.9. ............................................................................................................................... 30

6 . ............................... 34

........................................................................................................... 34

................................................................................................................. 35

( ) ....................... 35

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(, ) ............................................... 38

................................................................................................................. 42

( ) ........................................................................... 42

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( ) ............................................................................................. 43

1

- - .

, - . - .

. 1. . 2.

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, . 6.

. 7. . 8.

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- .

1. .. . ( ). -, , 2009, http://www.buildcalc.ru/Books/2009062801/Default.aspx

2. .., .., .. - . . -, , 2011.

3. .., .. . - . -, , 1992.

4. .. . . . -. 2010. http://www.zimbelmann.ru/education/solid-and-granular-media/manuals/manual_21.html

2

, . - . - , . , ; - . -, (. 1).

) )

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)

. 1. : ; ; ; 1 ;

2 ; 3 ; 4 ; 5 ; 6

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G G , . , , - .

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. 3.

U

, - . -

z - , z, . (- ) -

, = = = 0:

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tg

a

(2.1)

, .

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. - . . . .

9

(1736-1806). .

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3.

3.1

:

= z , (3.1)

, /3;

10

z ,

, , ( . 4); ,

,)cos(cos

)(cos

)1(

12

2

2

Zaa (3.2)

.coscos

sinsin

a

aZa

(3.3)

. 2. (3.2)(3.5)

. - .

1 . , - /.

:

= cos ( + ); (3.4)

= sin ( + ). (3.5)

. 4 , , - q . . 4, , . 4, , , . - . 4, - .

-, /3 . - , :

= 2

1 2 ; (3.6)

= cos ( + ); (3.7)

= sin ( + ). (3.8)

q - :

11

.

qh

(3.9)

e e e e

e

..

B

e

E

Ea

e2e2ea2A

E

E

. 4.

:

1 = h , (3.10)

2 = (h + ) . (3.11)

Hee

E aaa

2

21

(3.12)

, -

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3

30

hH

hHHh

(3.13)

.

(3.7), (3.8).

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, d, :

= z , (3.14)

z , , ;

( ),

= tq2 (45

0 +/2), (3.15)

, - d.

(3.15) = 0, = 0 = 0, . . , , , - , , , . -

- 0,33:

.2

2

dE

(3.16)

d/3 .

3.2. ( . . )

(. 5) ( ). -

h.

1 + . 1 2 -, . 2 D1 (2 = AD1). D , D1D - 1. , D1D D1 - . DD1, DD1 D1 , . , -

l , 1 , , - + h .

= D1 DD2 . (3.17)

13

90

ea

ea2

ea1

D

D1

D2B1

B2

h

H

A

B

K90

5. .. .

, ,

.

h

2

2

(3.18)

.21

h

h

(3.19)

, , 1

.2

21

(3.20)

5 %.

14

4.

4.1.

4.1.1.

, ma min , - :

;1

g

R

A

N

(4.1)

;11maxg

c R

W

M

A

N

(4.2)

011min W

M

A

NP (4.3)

N1 1 , ( . 2);

W , 3;

, 2 ;

R , , (4.6);

g , 1,4; , 1

1,2 pma.. ( )

A = b 1, (4.4)

b , . , 3,

.6

1 2bW

(4.5)

, ,

15

R = 1.7 {R0 [1 + k1 (b 2)] + k2 (d 3)}, (4.6)

R0 , - , - (. 14) . 5, 6;

, - /3,;

d , ;

k1, k2 , . 7.

4.1.2.

,

1

1

nz

u m

M

M

(4.7)

u1 - ( . 2);

z1 ; m , -

0,8;

n , 1,1.

4.1.3.

,

1

1

nz

m

Q

Qr

(4.8)

Qr1 , ;

Qz1 , - ;

m , 0,9;

n , 1,1.

16

4.2.

NII .

,0

e (4.9)

II

II

N

Me 0 NII -

II ;

=W/A ;

= 0,8 ( ).

5.

5.1.

:

= 1 ; b = 3 ; = 6 ; d = 1,5 ; = +10.

:

, = 18 /3;

= 28; = 1; = + 8; =0,7 0=6 .

():

= 21,0 /3; = 0,16; s = 27,5 /

3;

L = 0,33;

17

= 0,15;

=21; =81 ;

0=28 .

q = 40 . . , -

, ( -) , - .

5.2.

:

;/ 1,1816,01

0,21

1

3

d

;342,05,27

1,1811

s

dn

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342,0

1

n

ne

05,015,033,0

15,016,0

pL

p

LI

.18,015,033,0 pLpI

(. . 1, 2, 3 2.02.01-83*) http://elima.ru/scripts/ground.php

18

( . 1) , (. 2) . . 5 -

R0 = 500 . -

:

R = 1,7 {R0 [1 + k1 (b 2)] + k2 (d 3)},

k1 = 0,04 k2 = 2,0 . 7;

R = 1,7 { 500 [1 + 0,04 (3 2)] + 2,0 18 (1,5 3)} = 884 .

2 18 (1,5 3) , d < 3,0 .

, -

;w

S

e

wS

w /3,;

. 3, 4 ,

R0 (. 6).

5.3.

q = 40 :

22,218

40

qh

:

;

coscos

cos

1

12

2

2

a

z

;169,0810cos110cos

828sin128sin

coscos

sinsin

a

aZa

19

.477,0

110cos10cos

1018cos

169,01

1222

a

Za a .

:

1 = . h

. a = 18

. 2,22

. 0,477 = 19,06 /;

2 = . (h + )

. a

= 18(2,22 + 6)

. 0,477 = 70,58 /.

. 9,26862

58,7006,19

2

21

Hee

E aaa

- :

1 = 1 . cos (+) = 19,06 . cos (10 + 1) = 18,71 /:

2 = 2 . cos (+) = 70,58 . cos (10 + 1) = 70,57 /;

1 = 1 . sin (+) = 19,06 . sin (10 + 1) = 3,64 /;

2 = 2 . sin (+) = 70,58 . sin (10+1) = 13,47 /.

-

; 8,26762

57,7071,18

2

21

Hee

E arar

. 3,5162

47,1364,3

2

21

= . d

. tg

2 (45 +/2) = 18 . 1,5 . tg2 (45 + 28/2)= 74,78 /.

, ,

. 1,562

28452

5,118

245

2

22

2

2

tgtgd

E

, 3,

= 0,33 . 56,1 = 18,5 .

20

. 6.

5.4. ( . . )

.

(. 7)

F = 5,9 5,6

2

= 16,4 2.

, + hp ,

= . F = 18

. 16,4 = 295,2 .

, , , , :

2 =

2

p

h =

2 295,2

6 2,22

= 71,82 ;

1 =

2np

p

h

h

= 71,82

.

2,22

6 2,22= 19,40 /.

, ,

=

1 2

2

. =

19,4 71,82

2

. 6 = 273,7 .

, ,

273,7 268,9

268,9

. 100 = 1,8 %,

.

5.5. ,

, , (4.1)(4.3). (. 1).

1

, , , ,

21

G = [o1 3 (0,5 1,5 10 )

2

tq

(6 1,5)] . 24 = 175

G = 1,1 . 175 =

= 192,5 0,1 19,3

G = [(1,5 . 3) (

1,5 101,5)

2

otq]

. 24 =

= 103,3

G = 1,1. 103,3 =

= 113,6 0,05 + 5,7

= 267,8 =1,2 267,8 = 321,4 2,4 + 771,3

= 51,3 = 1,2 51,3 = 61,6 1,15 73,9

= 18,5 = 1 18,5 = 18,5 0,5 9,3

. 1 f = 1,1 ; f = 1,2 , . ,

( . 8). -

. .

. 6. (/)

22

. 7. . . . .

23

. 8. , , ,

.

N1 = 192,5 + 113,6 + 61,6 = 367,7 .

1 = 19,3 + 5,7 + 771,3 73,9 9,3 = 674,5 .

(4.4) (4.5):

= b . 1 = 3 . 1 = 3 2;

W = 21 3

6

= 1,5 3.

24

= 1N

A=

367,7

3= 122,6 ;

ma

min = 1 1 367,7 674,5 122,6 449,7

3 1,5

N M

A W ;

ma = 572,3 , min = 327,1 .

. 8. :

= 122,6 < 884

1,4 = 631,4 ;

m = 572,3 < 1,2 884

1,4

= 757,7 ;

min = 327,1 < 0.

, . . - , .

5.6.

- (4.7). - (. 2).

. 2 -

( 1 . 8), f = 0,9 .

1

1

771,4 0,81,38 0,73,

559,3 1,1

z

. . (4.7) .

(4.8) 1 2.

25

2

,

,

,

,

z1

1

G = 175

G = 103,3

= 267,8 = 51,3 = 18,5

G = 0,9 175 = 157,5

G = 0,9 103,3 = 93

= 1,2 267,8 = 321,4 = 1,2 51,3 = 61,6 = 1 18,5 = 18,5

1,60

1,45

2,40

2,65

0,50

252

134,8

163,2

9,3

771,4

559,3 771,4

1rQ = E = 321,4 18,5 = 302,9 .

1zQ = (Gc + G + ) = 0,3 (157,5 + 93 + 61,6) = 93,6 .

= 0,3 (. 8):

1

1

r

z

Q

Q =

302,9

93,6= 3,24 >

0,9

1,1 = 0,82,

. . (4.8) .

5.7.

II NII (4.9)

f = 1 . 1.

0 = II

II

M

N=

175 0,1 103,3 0,05 267,8 2,4 51,3 1,15 18,5 0,5

175 103,3 51,3

=

= 1,68 ;

21 3 1

6 3 1

W

A

0,5 ;

0

1,68

0,53,36 > = 0,8,

. . .

26

5.8. , ,

: www.BuildCalc.ru

[1] - http://www.buildcalc.ru/Books/2009062801/Default.aspx. - , - ( -) - .

(BRWL) - - http://www.buildcalc.ru/Calculations/Brwl/Default.aspx

(BRWL) - 2.02.01-83*, :

1. (R) - - .

2. (S) ( II ).

3. (.) ( I ) .

4. (.), (Pmin) (max) - .

BRWL, , , , - .

5.8.1. :

www.BuildCalc.ru

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-. (. 9) , - () .

27

. 9. .

- - . 10 . ( ) - , .

(. 10), 5.1, 5.2.

, . 10, -, . (), - . 2.02.01-83*( http://files.stroyinf.ru/Data1/2/2015/) , - .

28

. 10. .

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29

. 11. ,

(. 12). . - 1, 1,5 1,5 . - 3,0 .

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(. 13) - . - . .

1 .

30

, 1 (5.5), , .

N = 192,5+61,6 = 254,1 .

, , -, :

= -19,3+771,3-73,9-9,3=668,8 .

(. 13) - , .

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. 13 , -, .. - , .

, (BRWL) -

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: , . .

5.9.

, - . .

, . - ,

31

. , .

1 . 1, -, ; - , - .

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(. 1 5.5), :

N = 192,5+61,6 +113,6= 367,7 . -

(4.3),

min = 0.

. 17293,0184184

93,0

1846

37,3676

fB

f

B

M

bNM

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BRWL - .

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:

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1,50

32

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172,00

H,

- -

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,

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e W IL E -

1 1,5

18 28 0 0,7 - - 6000 0,3

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H, 1,

/3 2,

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1 1,50 16,36 18,00 25,45 28,00 0,00 0,00 1,30 1,26 1,10

2 10,00 19,09 21,00 18,26 21,00 54,00 81,00 1,25 1,08 1,10

: 2,00

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, /3: 10,00

I- - , /3:

16,36

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18,00

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R, : 776,18

( ) P, : 1 360,08

33

N, : 4 080,24

Pmin, : 0,03

P., : 114,70

Pmax, : 229,37

S, : 2,37

: 10,67

. 1.14. ( ). BRWL

(http://www.buildcalc.ru/Calculations/Brwl/Help.aspx) .

(. 14) - 2.02.01-83*, .. - Pmin >0, , , .. .

- S=2,37 1 ( - I ).

2,4 (. 8) -

, = 184/2,4 = 76,7 , 3,5 . (3.2), (3.3).

- ?

, , . -.

1. ; = 28 ( ). , -

.

= 3034 ; = 3236 ; - = 3538; = 3840. - = = 40.

2. . = 1, . - . -

= 0,5 = 20. = .

34

3. , ( < 0) .

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6 .

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4. , - ; .

5. ? ?

6.

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9. ( )? ?

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35

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; , . 13.

? 14. (4,3) (4,9)? 15.

? 16.

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(

)

, - .

(. 1). (. 2). ,

(. 3). -

(. 4). , 1234. ,

. 1 = 1 ; b = 3 . .; . 2 = 19 /3;

= 29 . .; . 3 ( ); = 19,8 /3;

= 0,1 . .; . 4 q = 50 . . 1 -

, . 1.

36

q

a

H

b

d

0.50

. 1.

. 2 -

. - , .

. 2.

.

, - , .

- .

38

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1

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0,07 < Ip 0,17

Ip > 0,17

2

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IL < 0

0 IL 1

IL > 1 :

IL < 0

0 IL 0,25

0,25 < IL 0,50

0,50 < IL 0,75

0,75 < IL 1

IL > 1

3

Sr

0 < Sr 0,5

0,5 < Sr 0,8

0,8 < Sr 1

39

4

,

< 0,55 0,55 0,70 > 0,70

< 0,60 0,60 0,75 > 0,75 < 0,60 0,60 0,80 > 0,80

5

R0 () ,

() IL

0 0,1 0,2 0,3 0,4 0,5 0,6

( Ip 0,05)

0,5

0,7

350

400

300

250

250

200

200

150

150

100

100

( 0,10 Ip 0,15)

0,5

0,7

1,0

400

350

300

350

300

250

300

250

200

250

200

150

200

150

100

150

100

100

( I 0,20)

0,5

0,6

0,8

1,1

600

500

400

300

450

350

300

250

350

300

250

200

300

250

200

150

250

200

150

100

200

150

100

150

100

Ip 0,050,10

0150,20 R0, . 5, .

40

R0 (IL < 0) -

R0 = 1,5 Rn

1000 , 2000 ,

3000 ; Rn -.

6

R0 ,

R0

-

:

:

:

350

300

250

200

150

200

150

100

, . 6, - 100 %, -, 60 %, , .

41

7

k1 k2

k1, 1

k2

, , ,

,

0,10

0,08

0,06

0,04

0,02

3,0

2,5

2,0

2,0

1,5

8

( , . .):

-

0,25

0,30

0,30

0,40

0,50

0,60

42

( )

________

_________

_____________

-

201

43

( )

_________________

_________________

__________________

q =

H =

a =

b =

d =

0.50

/3

/3

q

b w

s /3

d wL

wP

_______________ ____________

Retaining Wall Calculation

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