Механика грунтов. Пьянков С.А - 32 стр.

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63
Ɉɩɪɟɞɟɥɟɧɢɟ ɨɫɚɞɤɢ ɮɭɧɞɚɦɟɧɬɚ ɩɨ ɦɟɬɨɞɭ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɫɥɨɹ
(ɇ. Ⱥ. ɐɵɬɨɜɢɱ, 1934 ɝɨɞ)
Ɋɢɫ. 5.7. ɗɩɸɪɵ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɞɚɜɥɟɧɢɣ ɩɪɢ ɪɚɡɥɢɱɧɨɣ ɩɥɨɳɚɞɢ ɡɚɝɪɭɡɤɢ
ɉɪɢ ɛɨɥɶɲɟɣ ɩɥɨɳɚɞɢ ɡɚɝɪɭɡɤɢ ɝɥɭɛɢɧɚ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɞɚɜɥɟɧɢɣ ɢ ɨɛɴɟɦ ɝɪɭɧɬɚ,
ɩɨɞɜɟɪɝɚɸɳɢɣɫɹ ɞɟɮɨɪɦɚɰɢɢ, ɛɭɞɭɬ ɛɨɥɶɲɟ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɨɫɚɞɤɢ ɛɭɞɭɬ ɛɨɥɶɲɟ.
ɉɨɞ ɷɤɜɢɜɚɥɟɧɬɧɵɦ ɫɥɨɟɦ ɩɨɞɪɚɡɭɦɟɜɚɟɬɫɹ ɧɟɤɨɬɨɪɵɣ ɨɝɪɚɧɢɱɟɧɧɵɣ ɩɨ ɬɨɥɳɢɧɟ ɫɥɨɣ
ɝɪɭɧɬɚ, ɤɨɬɨɪɵɣ ɩɪɢ ɫɩɥɨɲɧɨɣ, ɪɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɧɚɝɪɭɡɤɟ, ɩɪɢɥɨɠɟɧɧɨɣ ɤ ɝɪɚ-
ɧɢɰɟ ɨɫɧɨɜɚɧɢɹ, ɞɚɟɬ ɡɧɚɱɟɧɢɟ ɨɫɚɞɤɢ, ɪɚɜɧɨɟ ɨɫɚɞɤɟ ɮɭɧɞɚɦɟɧɬɚ, ɢɦɟɸɳɟɝɨ ɨɝɪɚɧɢɱɟɧɧɵɟ
ɪɚɡɦɟɪɵ ɜ ɩɥɚɧɟ ɩɪɢ ɬɨɣ ɠɟ ɧɚɝɪɭɡɤɟ ɢ ɚɧɚɥɨɝɢɱɧɵɯ ɝɪɭɧɬɨɜɵɯ ɭɫɥɨɜɢɹɯ. Ⱦɪɭɝɢɦɢ ɫɥɨɜɚɦɢ,
ɜ ɞɚɧɧɨɦ ɦɟɬɨɞɟ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɚɹ ɡɚɞɚɱɚ ɪɚɫɱɟɬɚ ɨɫɚɞɨɤ ɦɨɠɟɬ ɡɚɦɟɧɹɬɶɫɹ ɨɞɧɨɦɟɪɧɨɣ.
ȼ ɫɥɭɱɚɟ ɨɞɧɨɪɨɞɧɨɝɨ ɨɫɧɨɜɚɧɢɹ ɝɪɭɧɬ ɦɨɞɟɥɢɪɭɟɬɫɹ ɫɩɥɨɲɧɵɦ ɥɢɧɟɣɧɨ ɞɟɮɨɪɦɢ-
ɪɭɟɦɵɦ ɬɟɥɨɦ. ɋɱɢɬɚɟɬɫɹ, ɱɬɨ ɨɫɚɞɤɚ ɨɫɧɨɜɚɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɫɟɦɢ ɤɨɦɩɨɧɟɧɬɚɦɢ
ɧɚɩɪɹɠɟɧɢɣ ɢ ɡɚɜɢɫɢɬ ɨɬ ɠɟɫɬɤɨɫɬɢ ɮɭɧɞɚɦɟɧɬɚ. ɍɱɢɬɵɜɚɟɬɫɹ ɬɚɤɠɟ ɛɨɤɨɜɨɟ ɪɚɫ-
ɲɢɪɟɧɢɟ ɝɪɭɧɬɚ ɨɫɧɨɜɚɧɢɹ.
ȼ ɦɟɬɨɞɟ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɫɥɨɹ ɤɨɧɟɱɧɭɸ ɨɫɚɞɤɭ ɮɭɧɞɚɦɟɧɬɚ ɨɩɪɟɞɟɥɹɸɬ ɜ ɪɟɡɭɥɶɬɚɬɟ
ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɬɟɨɪɢɢ ɭɩɪɭɝɨɫɬɢ ɨ ɞɟɮɨɪɦɢɪɨɜɚɧɢɢ ɭɩɪɭɝɨɝɨ ɩɨɥɭɩɪɨɫɬɪɚɧɫɬɜɚ ɩɨɞ ɞɟɣɫɬ-
ɜɢɟɦ ɪɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɨɣ ɧɚɝɪɭɡɤɢ ɩɨ ɮɨɪɦɭɥɟ
s = h
e
·m
v
·p
0
, (5.5)
ɝɞɟ m
v
– ɤɨɷɮɮɢɰɢɟɧɬ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɫɠɢɦɚɟɦɨɫɬɢ ɝɪɭɧɬɚ;
p
0
– ɞɨɩɨɥɧɢɬɟɥɶɧɨɟ ɞɚɜɥɟɧɢɟ ɩɨ ɩɨɞɨɲɜɟ ɮɭɧɞɚɦɟɧɬɚ;
h
e
– ɦɨɳɧɨɫɬɶ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɫɥɨɹ ɝɪɭɧɬɚ:
h
e
= A·Ȧ·b, (5.6)
b – ɲɢɪɢɧɚ ɩɨɞɨɲɜɵ ɮɭɧɞɚɦɟɧɬɚ; Ȧ – ɤɨɷɮɮɢɰɢɟɧɬ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɮɨɪɦɵ ɩɨɞɨɲɜɵ ɢ
ɠɟɫɬɤɨɫɬɢ ɮɭɧɞɚɦɟɧɬɚ; Ⱥ – ɤɨɷɮɮɢɰɢɟɧɬ, ɡɚɜɢɫɹɳɢɣ ɨɬ ɤɨɷɮɮɢɰɢɟɧɬɚ ɛɨɤɨɜɨɝɨ ɪɚɫɲɢɪɟɧɢɹ
ɝɪɭɧɬɚ Ȟ:
A = (1–Ȟ)
2
/(1–2Ȟ). (5.7)
ɉɪɨɢɡɜɟɞɟɧɢɟ A·Ȧ ɧɚɡɵɜɚɸɬ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɫɥɨɹ, ɤɨɬɨɪɵɣ ɧɚɯɨɞɹɬ
ɩɨ ɬɚɛɥɢɱɧɵɦ ɞɚɧɧɵɦ.
Ɇɟɬɨɞ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɫɥɨɹ ɩɨɡɜɨɥɹɟɬ ɨɩɪɟɞɟɥɹɬɶ ɨɫɚɞɤɭ ɫɥɨɢɫɬɨɝɨ ɨɫɧɨɜɚɧɢɹ ɫ ɢɫ-
ɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɢɛɥɢɠɟɧɧɨɝɨ ɪɟɲɟɧɢɹ.
Ɍɚɤ, ɜ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɫɠɢɦɚɟɦɭɸ ɬɨɥɳɢɧɭ ɨɫɧɨɜɚɧɢɹ, ɜɥɢɹɸɳɭɸ ɧɚ ɨɫɚɞɤɭ ɮɭɧɞɚ-
ɦɟɧɬɚ, ɩɪɢɧɢɦɚɸɬ ɪɚɜɧɨɣ H
c
= 2h
e
, ɚ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɜɟɪɬɢɤɚɥɶɧɵɯ ɧɚɩɪɹ-
ɠɟɧɢɣ – ɩɨ ɬɪɟɭɝɨɥɶɧɨɣ ɷɩɸɪɟ (ɪɢɫ. 5.8, ɚ). ȼɟɪɲɢɧɭ ɬɪɟɭɝɨɥɶɧɨɣ ɷɩɸɪɵ ɧɚɩɪɹɠɟɧɢɣ ɧɚɡɧɚ-
ɱɚɸɬ ɧɚ ɝɥɭɛɢɧɟ ɇ
ɫ
, ɚ ɨɫɧɨɜɚɧɢɟ ɷɩɸɪɵ ɪ
0
– ɩɨɞ ɩɨɞɨɲɜɨɣ ɮɭɧɞɚɦɟɧɬɚ. Ƚɪɭɧɬɵ, ɧɚɯɨɞɹɳɢɟ-
b
1
b
2
P=0,2 Ɇɉɚ
P=0,2 Ɇɉɚ
h
p1
h
p2
P=0,2 Ɇɉɚ
P=0,2 Ɇɉɚ
Ʌɢɧɢɢ ɪɚɜɧɵɯ ɜɟɪɬɢɤɚɥɶɧɵɯ ɞɚɜɥɟɧɢɣ
64
ɫɹ ɜ ɩɪɟɞɟɥɚɯ ɝɥɭɛɢɧɵ ɫɠɢɦɚɟɦɨɫɬɢ ɬɨɥɳɢ, ɫɱɢɬɚɸɬɫɹ ɨɞɧɨɪɨɞɧɵɦɢ ɫ ɨɫɪɟɞɧɟɧɧɵɦɢ ɯɚɪɚɤ-
ɬɟɪɢɫɬɢɤɚɦɢ.
Ɉɫɚɞɤɭ ɫɥɨɢɫɬɨɝɨ ɨɫɧɨɜɚɧɢɹ ɬɚɤɠɟ ɜɵɱɢɫɥɹɸɬ ɩɨ ɮɨɪɦɭɥɟ (5.5), ɫ ɬɨɣ ɥɢɲɶ ɪɚɡɧɢɰɟɣ,
ɱɬɨ ɜ ɧɟɣ ɢɫɩɨɥɶɡɭɸɬ ɫɪɟɞɧɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɫɠɢɦɚɟɦɨɫɬɢ, ɨɩɪɟɞɟɥɹɟɦɵɣ ɢɡ
ɭɫɥɨɜɢɹ, ɱɬɨ ɜ ɩɪɟɞɟɥɚɯ ɫɠɢɦɚɟɦɨɣ ɬɨɥɳɢ ɩɨɥɧɚɹ ɨɫɚɞɤɚ ɪɚɜɧɚ ɫɭɦɦɟ ɨɫɚɞɨɤ, ɜɯɨɞɹɳɢɯ ɜ
ɧɟɟ ɫɥɨɟɜ. ɋɪɟɞɧɢɣ ɤɨɷɮɮɢɰɢɟɧɬ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɫɠɢɦɚɟɦɨɫɬɢ ɧɚɯɨɞɹɬ ɢɡ ɜɵɪɚɠɟɧɢɹ
ivi
n
i
i
e
vm
zmh
h
m
¦
1
2
2
1
, (5.8)
ɝɞɟ h
i
– ɜɵɫɨɬɚ i-ɝɨ ɫɥɨɹ ɝɪɭɧɬɚ ɜ ɩɪɟɞɟɥɚɯ ɫɠɢɦɚɟɦɨɣ ɬɨɥɳɢ;
m
vi
– ɤɨɷɮɮɢɰɢɟɧɬ ɨɬɧɨɫɢɬɟɥɶɧɨɣ ɫɠɢɦɚɟɦɨɫɬɢ i-ɝɨ ɫɥɨɹ;
z
i
– ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɧɢɠɧɟɣ ɬɨɱɤɢ ɬɪɟɭɝɨɥɶɧɨɣ ɷɩɸɪɵ ɞɨ ɫɟɪɟɞɢɧɵ i-ɝɨ ɫɥɨɹ (ɪɢɫ. 5.8).
Ɇɟɬɨɞ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɫɥɨɹ ɩɨɡɜɨɥɹɟɬ ɪɚɫɫɱɢɬɵɜɚɬɶ ɨɫɚɞɤɭ ɫ ɭɱɟɬɨɦ ɜɥɢɹɧɢɹ ɞɪɭɝɢɯ,
ɪɹɞɨɦ ɪɚɫɩɨɥɨɠɟɧɧɵɯ ɮɭɧɞɚɦɟɧɬɨɜ ɫ ɩɨɦɨɳɶɸ ɦɟɬɨɞɚ ɭɝɥɨɜɵɯ ɬɨɱɟɤ, ɨ ɤɨɬɨɪɨɦ ɭɠɟ ɝɨɜɨ-
ɪɢɥɨɫɶ ɜɵɲɟ.
Ɋɢɫ. 5.8. Ɋɚɫɱɟɬɧɚɹ ɫɯɟɦɚ ɤ ɦɟɬɨɞɭ ɷɤɜɢɜɚɥɟɧɬɧɨɝɨ ɫɥɨɹ ɩɪɢ ɫɥɨɢɫɬɨɦ ɩɥɚɫɬɨɜɚɧɢɢ ɝɪɭɧɬɨɜ
Ɂɚɬɭɯɚɧɢɟ ɨɫɚɞɤɢ ɜɨ ɜɪɟɦɟɧɢ
Ɂɚɬɭɯɚɧɢɟ ɨɫɚɞɤɢ ɝɪɭɧɬɨɜ ɜɨ ɜɪɟɦɟɧɢ (ɢɯ ɤɨɧɫɨɥɢɞɚɰɢɹ) ɹɜɥɹɟɬɫɹ ɫɥɨɠɧɵɦ ɩɪɨɰɟɫɫɨɦ,
ɧɚ ɤɨɬɨɪɵɣ ɨɤɚɡɵɜɚɸɬ ɜɥɢɹɧɢɟ ɜɨɞɨɩɪɨɧɢɰɚɟɦɨɫɬɶ, ɫɬɪɭɤɬɭɪɚ, ɩɨɪɨɜɨɟ ɞɚɜɥɟɧɢɟ, ɩɨɥɡɭ-
ɱɟɫɬɶ ɫɤɟɥɟɬɚ ɝɪɭɧɬɚ, ɫɠɢɦɚɟɦɨɫɬɶ ɫɚɦɢɯ ɦɢɧɟɪɚɥɶɧɵɯ ɱɚɫɬɢɰ, ɜɨɞɵ ɢ ɡɚɳɟɦɥɟɧɧɨɝɨ ɜɨɡɞɭ-
ɯɚ, ɭɫɥɨɜɢɹ ɧɚɝɪɭɠɟɧɢɹ, ɚ ɬɚɤɠɟ ɝɟɨɥɨɝɢɱɟɫɤɨɟ ɫɬɪɨɟɧɢɟ ɩɥɨɳɚɞɤɢ.
Ɉɛɨɛɳɟɧɧɨɟ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ ɡɚɬɭɯɚɧɢɹ ɨɫɚɞɤɢ ɜ ɡɚɦɤɧɭɬɨɦ ɜɢɞɟ ɢɡ-ɡɚ ɫɥɨɠɧɨɫɬɢ ɩɪɨ-
ɢɫɯɨɞɹɳɢɯ ɩɪɨɰɟɫɫɨɜ ɜ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɨɬɫɭɬɫɬɜɭɟɬ. ȼ ɪɚɫɱɟɬɧɵɟ ɦɨɞɟɥɢ, ɫɯɟɦɵ ɢ ɦɟɬɨɞɵ
ɜɜɨɞɹɬɫɹ ɪɚɡɥɢɱɧɵɟ ɞɨɩɭɳɟɧɢɹ, ɩɪɟɞɩɨɫɵɥɤɢ ɢ ɭɩɪɨɳɟɧɢɹ, ɩɪɢɟɦɥɟɦɵɟ ɬɨɥɶɤɨ ɞɥɹ ɨɬɞɟɥɶ-
ɧɵɯ ɝɪɭɧɬɨɜ ɢ ɭɫɥɨɜɢɣ ɢɯ ɧɚɝɪɭɠɟɧɢɹ.
ɇɚɢɛɨɥɟɟ ɩɪɨɫɬɨɣ, ɞɨɜɟɞɟɧɧɨɣ ɞɨ ɪɚɛɨɱɟɝɨ ɫɨɫɬɨɹɧɢɹ, ɹɜɥɹɟɬɫɹ ɮɢɥɶɬɪɚɰɢɨɧɧɚɹ ɬɟɨɪɢɹ
ɤɨɧɫɨɥɢɞɚɰɢɢ (ɭɩɥɨɬɧɟɧɢɹ) ɝɪɭɧɬɨɜ. ȼ ɷɬɨɣ ɬɟɨɪɢɢ ɝɪɭɧɬɵ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɜ ɫɨɫɬɨɹɧɢɢ
«ɝɪɭɧɬɨɜɨɣ ɦɚɫɫɵ», ɬ. ɟ. ɫ ɩɨɥɧɵɦ ɧɚɫɵɳɟɧɢɟɦ ɩɨɪ ɫɜɨɛɨɞɧɨɣ ɝɪɚɜɢɬɚɰɢɨɧɧɨɣ ɜɨɞɨɣ ɢ ɩɪɢ
ɨɬɫɭɬɫɬɜɢɢ ɫɢɥ ɫɰɟɩɥɟɧɢɹ. ɋɤɨɪɨɫɬɶ ɡɚɬɭɯɚɧɢɹ ɨɫɚɞɤɢ ɡɚɜɢɫɢɬ ɨɬ ɫɤɨɪɨɫɬɢ ɜɵɞɚɜɥɢɜɚɧɢɹ
(ɮɢɥɶɬɪɚɰɢɢ) ɜɨɞɵ ɢɡ ɩɨɪ ɭɩɥɨɬɧɹɟɦɨɝɨ ɝɪɭɧɬɚ. Ɋɟɲɟɧɢɟ ɩɨɥɭɱɟɧɨ ɞɥɹ ɨɞɧɨɦɟɪɧɨɣ ɡɚɞɚɱɢ ɫ
ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɢ ɬɪɟɭɝɨɥɶɧɨɣ ɷɩɸɪɚɦɢ ɭɩɥɨɬɧɹɸɳɢɯ ɞɚɜɥɟɧɢɣ ɜ ɩɪɟɞɩɨɥɨɠɟɧɢɢ, ɱɬɨ ɬɨɤ

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