Механика грунтов. Пьянков С.А - 47 стр.

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93
ɲɟɪɨɯɨɜɚɬɨɫɬɶɸ ɩɪɢɧɢɦɚɟɬɫɹ ɪɚɜɧɵɦ
M
; ɞɥɹ ɦɟɥɤɨɡɟɪɧɢɫɬɵɯ ɜɨɞɨɧɚɫɵɳɟɧɧɵɯ ɩɟɫɤɨɜ ɢ
ɩɪɢ ɜɢɛɪɚɰɢɨɧɧɵɯ ɧɚɝɪɭɡɤɚɯ
MZ
54,0
, ɝɞɟ
M
– ɪɚɫɱɟɬɧɨɟ ɡɧɚɱɟɧɢɟ ɭɝɥɚ ɜɧɭɬɪɟɧɧɟɝɨ
ɬɪɟɧɢɹ).
ɇɚ ɩɪɢɡɦɭ ɨɛɪɭɲɟɧɢɹ ɈȺȼ ɜ ɩɪɟɞɟɥɶ-
ɧɨɦ ɫɨɫɬɨɹɧɢɢ ɞɟɣɫɬɜɭɸɬ ɫɥɟɞɭɸɳɢɟ ɪɟ-
ɡɭɥɶɬɢɪɭɸɳɢɟ ɫɢɥɵ: ɫɨɛɫɬɜɟɧɧɵɣ ɜɟɫ ɝɪɭɧ-
ɬɚ
g
P
, ɪɟɚɤɬɢɜɧɵɣ ɨɬɩɨɪ ɫɬɟɧɤɢ
a
E , ɪɟɚɤ-
ɬɢɜɧɵɣ ɨɬɩɨɪ ɦɚɫɫɢɜɚ ɝɪɭɧɬɚ R ɧɢɠɟ ɩɨ-
ɜɟɪɯɧɨɫɬɢ ɫɤɨɥɶɠɟɧɢɹ Ⱥȼ, ɨɬɤɥɨɧɹɸɳɢɣɫɹ
ɨɬ ɧɨɪɦɚɥɢ ɧɚ ɭɝɨɥ
M
. Ɉɬɦɟɬɢɦ, ɱɬɨ ɡɧɚɱɟ-
ɧɢɟ ɭɝɥɚ ɧɚɤɥɨɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɫɤɨɥɶɠɟɧɢɹ
T
ɤ ɝɨɪɢɡɨɧɬɚɥɢ ɩɨɤɚ ɟɳɟ ɧɟɢɡɜɟɫɬɧɨ ɢ
ɩɪɢɧɢɦɚɟɬɫɹ ɩɪɨɢɡɜɨɥɶɧɨ. Ɉɩɪɟɞɟɥɢɜ ɢɡ
ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɫɨɨɛɪɚɠɟɧɢɣ ɜɟɥɢɱɢɧɭ
g
P
ɢ, ɡɧɚɹ ɧɚɩɪɚɜɥɟɧɢɟ ɨɫɬɚɥɶɧɵɯ ɭɫɢɥɢɣ,
ɦɨɠɧɨ, ɩɨɫɬɪɨɢɜ ɬɪɟɭɝɨɥɶɧɢɤ ɫɢɥ, ɨɩɪɟɞɟɥɢɬɶ ɜɟɥɢɱɢɧɵ
a
E ɢ
R
ɞɥɹ ɩɪɢɧɹɬɨɝɨ ɡɧɚɱɟɧɢɹ
T
(ɪɢɫ. 6.10, ɛ). Ɍɨɝɞɚ
)90sin(
)sin(
TMHZ
MT
$
g
a
P
E . (6.25)
Ɍɟɩɟɪɶ ɧɟɨɛɯɨɞɢɦɨ ɧɚɣɬɢ ɬɚɤɨɟ ɡɧɚɱɟɧɢɟ ɭɝɥɚ
T
, ɩɪɢ ɤɨɬɨɪɨɦ ɚɤɬɢɜɧɨɟ ɞɚɜɥɟɧɢɟ ɛɭɞɟɬ
ɦɚɤɫɢɦɚɥɶɧɵɦ. ɂɫɩɨɥɶɡɭɹ ɩɪɚɜɢɥɨ ɷɤɫɬɪɟɦɭɦɚ
0
T
d
dE
a
, ɨɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭɱɢɦ
)cos(cos
)(cos
)1(2
2
2
2
2
ZHH
HMJ
z
h
E
a
, (6.26)
ɝɞɟ
)cos()cos(
)sin()sin(
DHZH
DMZM
z .
Ɏɨɪɦɭɥɚ (6.26) ɧɟɩɪɢɦɟɧɢɦɚ ɩɪɢ ɤɪɭɬɵɯ ɨɬɤɨɫɚɯ (
MD
! ), ɤɨɬɨɪɵɟ ɫɚɦɢ ɩɨ ɫɟɛɟ ɧɟɭɫ-
ɬɨɣɱɢɜɵ, ɢ ɞɥɹ ɫɬɟɧɨɤ ɫ ɨɱɟɧɶ ɩɨɥɨɝɨɣ ɡɚɞɧɟɣ ɝɪɚɧɶɸ (ɩɪɢ
$
65!
H
).
ȼ ɛɨɥɟɟ ɫɥɨɠɧɵɯ ɫɥɭɱɚɹɯ ɩɪɢɦɟɧɹɸɬɫɹ ɢ ɞɪɭɝɢɟ ɦɟɬɨɞɵ, ɜ ɱɚɫɬɧɨɫɬɢ ɝɪɚɮɢɱɟɫɤɢɣ ɦɟ-
ɬɨɞ Ʉ. Ʉɭɥɶɦɚɧɚ, ɩɨɡɜɨɥɹɸɳɢɣ ɪɟɲɚɬɶ ɡɚɞɚɱɭ ɩɪɢ ɧɟɩɪɨɢɡɜɨɥɶɧɨɦ ɨɱɟɪɬɚɧɢɢ ɩɨɜɟɪɯɧɨɫɬɢ
ɝɪɭɧɬɚ ɢ ɥɸɛɵɯ ɫɯɟɦɚɯ ɡɚɝɪɭɠɟɧɢɹ. ɗɬɨɬ ɦɟɬɨɞ ɩɨɞɪɨɛɧɨ ɪɚɫɫɦɨɬɪɟɧ ɜ ɥɢɬɟɪɚɬɭɪɟ, ɧɚɩɪɢ-
ɦɟɪ, ɜ ɭɱɟɛɧɢɤɚɯ Ȼ. ɂ. Ⱦɚɥɦɚɬɨɜɚ ɢ ɉ. Ʌ. ɂɜɚɧɨɜɚ.
Ɉɩɪɟɞɟɥɟɧɢɟ ɚɤɬɢɜɧɨɝɨ ɞɚɜɥɟɧɢɹ ɩɪɢ ɥɨɦɚɧɨɣ ɮɨɪɦɟ ɝɪɚɧɢ ɫɬɟɧɤɢ ɢ ɧɟɨɞɧɨɪɨɞ-
ɧɵɯ ɝɪɭɧɬɚɯ ɡɚɫɵɩɤɢ.
ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɫɬɟɧɤɚ ɢ ɝɪɭɧɬɵ ɡɚɫɵɩɤɢ ɪɚɡɞɟɥɹɸɬɫɹ ɩɨ ɝɨɪɢɡɨɧɬɚɥɢ ɧɚ ɨɬɞɟɥɶɧɵɟ ɭɱɚ-
ɫɬɤɢ, ɜ ɩɪɟɞɟɥɚɯ ɤɨɬɨɪɵɯ ɭɝɨɥ ɧɚɤɥɨɧɚ ɫɬɟɧɤɢ ɢ ɮɢɡɢɤɨ-ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɝɪɭɧ-
ɬɨɜ (
J
,
M
,
c
) ɩɨɫɬɨɹɧɧɵ. ɉɪɢ ɷɬɨɦ ɫɥɟɞɭɟɬ ɭɱɢɬɵɜɚɬɶ, ɱɬɨ ɧɢɠɟ ɭɪɨɜɧɹ ɩɨɞɡɟɦɧɵɯ ɜɨɞ ɡɧɚ-
ɱɟɧɢɟ ɭɞɟɥɶɧɨɝɨ ɜɟɫɚ ɝɪɭɧɬɚ ɩɪɢɧɢɦɚɟɬɫɹ ɫ ɭɱɟɬɨɦ ɜɡɜɟɲɢɜɚɸɳɟɝɨ ɞɟɣɫɬɜɢɹ ɜɨɞɵ.
Ɋɢɫ. 6.10. ɋɯɟɦɚ ɞɟɣɫɬɜɢɹ ɫɢɥ ɧɚ ɫɬɟɧɤɭ:
ɚ – ɫ ɲɟɪɨɯɨɜɚɬɨɣ ɧɚɤɥɨɧɧɨɣ ɝɪɚɧɶɸ
ɛ – ɬɪɟɭɝɨɥɶɧɢɤ ɪɚɜɧɨɞɟɣɫɬɜɭɸɳɢɯ ɫɢɥ
94
Ɋɢɫ. 6.11. ɉɨɫɬɪɨɟɧɢɟ ɷɩɸɪɵ ɚɤɬɢɜɧɨɝɨ
ɞɚɜɥɟɧɢɹ ɩɪɢ ɥɨɦɚɧɨɣ ɮɨɪɦɟ ɡɚɞɧɟɣ ɝɪɚɧɢ
ɫɬɟɧɤɢ ɢ ɧɟɨɞɧɨɪɨɞɧɵɯ ɝɪɭɧɬɚɯ ɡɚɫɵɩɤɢ
ɉɨɫɬɪɨɟɧɢɟ ɷɩɸɪɵ ɚɤɬɢɜɧɨɝɨ ɞɚɜɥɟɧɢɹ
ɜɵɩɨɥɧɹɟɬɫɹ, ɧɚɱɢɧɚɹ ɫ ɜɟɪɯɧɟɝɨ ɭɱɚɫɬɤɚ ɫɬɟɧɤɢ,
ɩɪɢɱɟɦ ɞɥɹ ɤɚɠɞɨɝɨ ɭɱɚɫɬɤɚ ɢɫɩɨɥɶɡɭɟɬɫɹ
ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɟ ɢɡ ɩɪɢɜɟɞɟɧɧɵɯ ɜɵɲɟ ɪɟɲɟɧɢɣ.
ȼɥɢɹɧɢɟ ɜɵɲɟɥɟɠɚɳɢɯ ɝɪɭɧɬɨɜ ɡɚɫɵɩɤɢ ɩɪɢ
ɨɩɪɟɞɟɥɟɧɢɢ ɚɤɬɢɜɧɨɝɨ ɞɚɜɥɟɧɢɹ ɜ ɩɪɟɞɟɥɚɯ
ɤɚɠɞɨɝɨ ɭɱɚɫɬɤɚ, ɪɚɫɩɨɥɨɠɟɧɧɨɝɨ ɧɢɠɟ,
ɭɱɢɬɵɜɚɟɬɫɹ ɤɚɤ ɪɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɚɹ ɧɚ-
ɝɪɭɡɤɚ
q
.
ɉɪɢɦɟɪ ɬɚɤɨɝɨ ɩɨɫɬɪɨɟɧɢɹ ɩɨɤɚɡɚɧ ɧɚ
ɪɢɫ. 6.11, ɚ. Ɋɚɜɧɨɞɟɣɫɬɜɭɸɳɚɹ ɷɩɸɪɵ ɚɤɬɢɜɧɨɝɨ
ɞɚɜɥɟɧɢɹ
a
E ɧɚ ɤɚɠɞɨɦ ɭɱɚɫɬɤɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ
ɩɥɨɳɚɞɶ ɷɬɨɣ ɷɩɸɪɵ, ɚ ɬɨɱɤɚ ɟɟ ɩɪɢɥɨɠɟɧɢɹ
ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɰɟɧɬɪɭ ɬɹɠɟɫɬɢ ɷɩɸɪɵ.
Ɉɩɪɟɞɟɥɟɧɢɟ ɩɚɫɫɢɜɧɨɝɨ ɞɚɜɥɟɧɢɹ.
Ʉɚɤ ɭɤɚɡɵɜɚɥɨɫɶ ɜɵɲɟ, ɩɚɫɫɢɜɧɨɟ ɞɚɜɥɟɧɢɟ ɜɨɡɧɢɤɚɟɬ ɩɪɢ ɩɟɪɟɦɟɳɟɧɢɢ ɫɬɟɧɤɢ ɜ ɫɬɨ-
ɪɨɧɭ ɝɪɭɧɬɚ ɡɚɫɵɩɤɢ. ɏɚɪɚɤɬɟɪɧɵɣ ɩɪɢɦɟɪ ɬɚɤɨɝɨ ɫɥɭɱɚɹ ɩɨɤɚɡɚɧ ɧɚ ɪɢɫ. 6.12, ɚ. ɉɨɞ ɞɟɣɫɬ-
ɜɢɟɦ ɚɤɬɢɜɧɨɝɨ ɞɚɜɥɟɧɢɹ ɫɩɪɚɜɚ ɨɬ ɫɬɟɧɤɢ ɨɧɚ ɫɬɪɟɦɢɬɫɹ ɩɟɪɟɦɟɫɬɢɬɶɫɹ ɜɥɟɜɨ. ɗɬɨɦɭ ɫɨɨɬ-
ɜɟɬɫɬɜɭɟɬ ɩɚɫɫɢɜɧɨɟ ɞɚɜɥɟɧɢɟ ɝɪɭɧɬɚ, ɪɚɫɩɨɥɨɠɟɧɧɨɝɨ ɫɥɟɜɚ ɨɬ ɫɬɟɧɤɢ. ɉɪɢ ɞɜɢɠɟɧɢɢ ɜɟɪ-
ɬɢɤɚɥɶɧɨɣ ɝɥɚɞɤɨɣ ɫɬɟɧɤɢ ɧɚ ɝɪɭɧɬ ɝɥɚɜɧɵɟ ɧɚɩɪɹɠɟɧɢɹ ɦɟɧɹɸɬɫɹ. Ɍɟɩɟɪɶ ɭɠɟ
ɩx
VVV
1
ɹɜɥɹɟɬɫɹ ɦɚɤɫɢɦɚɥɶɧɵɦ, ɚ z
z
JVV
3
ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ ɩɪɢɝɪɭɡɤɢ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɡɚɫɵɩɤɢ
ɫɥɟɜɚ – ɦɢɧɢɦɚɥɶɧɵɦ ɝɥɚɜɧɵɦ ɧɚɩɪɹɠɟɧɢɟɦ (ɪɢɫ. 6.12, ɛ). Ɍɨɝɞɚ, ɚɧɚɥɨɝɢɱɧɨ (6.13) ɢ (6.21),
ɭɫɥɨɜɢɟ ɩɪɟɞɟɥɶɧɨɝɨ ɪɚɜɧɨɜɟɫɢɹ ɩɪɢɦɟɬ ɜɢɞ:
ɞɥɹ ɫɵɩɭɱɢɯ ɝɪɭɧɬɨɜ
)
2
45(
2
31
M
VV
$
tg ; (6.27)
ɞɥɹ ɫɜɹɡɧɵɯ ɝɪɭɧɬɨɜ
)
2
45(2)
2
45(
2
31
MM
VV
$$
tgctg
. (6.28)
Ɋɢɫ. 6.12. ɋɯɟɦɚ ɞɟɣɫɬɜɢɹ ɚɤɬɢɜɧɨɝɨ ɢ ɩɚɫɫɢɜɧɨɝɨ ɞɚɜɥɟɧɢɹ ɧɚ ɫɬɟɧɤɭ

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