моделирование влияния скорости горных работ на прочность

Górnictwo i GeoinĪynieria • Rok 34 • Zeszyt 2 • 2010
Ⱥɥɟɤɫɟɣ ɂɜɚɧɨɜ*, ȿɥɟɧɚ ɋɞɜɢɠɤɨɜɚ*, Ⱥɥɟɤɫɚɧɞɪ ɒɚɲɟɧɤɨ**
ɆɈȾȿɅɂɊɈȼȺɇɂȿ ȼɅɂəɇɂə ɋɄɈɊɈɋɌɂ ȽɈɊɇɕɏ ɊȺȻɈɌ
ɇȺ ɉɊɈɑɇɈɋɌɖ ɉɈɊɈȾ ɂ ɍɋɌɈɃɑɂȼɈɋɌɖ ȼɕɊȺȻɈɌɄɂ
1. ɋɨɫɬɨɹɧɢɟ ɜɨɩɪɨɫɚ
ɉɪɨɝɧɨɡ ɩɨɜɟɞɟɧɢɹ ɝɨɪɧɵɯ ɩɨɪɨɞ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɬɟɦɩɨɜ ɨɱɢɫɬɧɵɯ ɪɚɛɨɬ ɹɜɥɹɟɬɫɹ
ɧɟɨɛɯɨɞɢɦɵɦ ɷɥɟɦɟɧɬɨɦ ɞɥɹ ɪɚɡɪɚɛɨɬɤɢ ɦɟɪɨɩɪɢɹɬɢɣ ɩɨ ɨɯɪɚɧɟ ɜɵɪɚɛɨɬɨɤ ɢ ɜɵɛɨɪɭ
ɫɪɟɞɫɬɜ ɤɪɟɩɥɟɧɢɹ. ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɧɟɬ ɟɞɢɧɨɝɨ ɦɧɟɧɢɹ ɨ ɬɨɦ ɤɚɤɨɜɨ ɜɥɢɹɧɢɟ
ɫɤɨɪɨɫɬɢ ɩɪɨɜɟɞɟɧɢɹ ɜɵɪɚɛɨɬɨɤ ɧɚ ɦɟɯɚɧɢɱɟɫɤɢɟ ɩɪɨɰɟɫɫɵ, ɤɨɬɨɪɵɟ ɩɪɢɫɯɨɞɹɬ ɜ ɩɨɪɨɞɧɨɦ ɦɚɫɫɢɜɟ. Ƚɢɩɨɬɟɬɢɱɟɫɤɢ ɦɨɠɧɨ ɩɪɟɞɩɨɥɨɠɢɬɶ, ɱɬɨ ɩɪɢ ɛɵɫɬɪɨɦ ɨɛɧɚɠɟɧɢɢ ɩɨɪɨɞ
ɜ ɦɚɫɫɢɜɟ ɩɪɨɢɫɯɨɞɹɬ ɬɟ ɠɟ ɩɪɨɰɟɫɫɵ, ɱɬɨ ɢ ɜ ɨɛɪɚɡɰɟ ɝɨɪɧɵɯ ɩɨɪɨɞ ɩɪɢ ɛɵɫɬɪɨɦ
ɩɪɢɥɨɠɟɧɢɢ ɧɚɝɪɭɡɤɢ ɧɚ ɢɫɩɵɬɚɬɟɥɶɧɨɦ ɩɪɟɫɫɟ. ɉɨɷɬɨɦɭ ɦɧɨɝɢɦɢ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɢɦɢ
ɤɨɥɥɟɤɬɢɜɚɦɢ ɢɡɭɱɚɥɫɹ ɜɨɩɪɨɫ ɨ ɜɥɢɹɧɢɢ ɫɤɨɪɨɫɬɢ ɧɚɝɪɭɠɟɧɢɹ ɧɚ ɩɪɨɰɟɫɫ ɪɚɡɪɭɲɟɧɢɹ
ɨɛɪɚɡɰɨɜ ɜ ɥɚɛɨɪɚɬɨɪɧɵɯ ɭɫɥɨɜɢɹɯ [1]. ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɜɵɩɨɥɧɟɧɨ ɨɛɨɛɳɟɧɢɟ ɢɡɜɟɫɬɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ ɢ ɩɪɟɞɥɨɠɟɧɚ ɦɟɬɨɞɢɤɚ ɭɱɟɬɚ ɫɤɨɪɨɫɬɢ ɩɪɨɜɟɞɟɧɢɹ ɜɵɪɚɛɨɬɨɤ ɩɪɢ
ɦɨɞɟɥɢɪɨɜɚɧɢɢ ɝɟɨɦɟɯɚɧɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɨɜ.
2. ȼɥɢɹɧɢɟ ɫɤɨɪɨɫɬɢ ɧɚɝɪɭɠɟɧɢɹ
ɧɚ ɩɪɨɱɧɨɫɬɶ ɩɨɪɨɞɧɵɯ ɨɛɪɚɡɰɨɜ
ȼ ɬɚɛɥɢɰɟ 1 ɩɪɢɜɟɞɟɧɵ ɨɫɧɨɜɧɵɟ ɪɟɡɭɥɶɬɚɬɵ, ɩɨɥɭɱɟɧɧɵɟ ɢɫɫɥɟɞɨɜɚɬɟɥɹɦɢ ɜ ɪɚɡɧɵɟ ɝɨɞɵ [1]. ȼ ɍɤɪɚɢɧɟ ɩɪɟɞɫɬɚɜɢɬɟɥɶɧɵɣ ɨɛɴɟɦ ɢɫɩɵɬɚɧɢɣ ɧɚ ɫɠɚɬɢɟ ɨɛɪɚɡɰɨɜ ɩɟɫɱɚɧɢɤɚ, ɚɥɟɜɪɨɥɢɬɚ, ɚɪɝɢɥɥɢɬɚ, ɭɝɥɹ ɜɵɩɨɥɧɟɧ ɫɨɬɪɭɞɧɢɤɚɦɢ ɂȽɌɆ ɇȺɇ ɍɤɪɚɢɧɵ [2].
Ȼɨɥɶɲɢɧɫɬɜɨ ɪɟɡɭɥɶɬɚɬɨɜ ɫɜɨɞɢɬɫɹ ɤ ɫɥɟɞɭɸɳɟɦɭ: ɜ ɞɢɚɩɚɡɨɧɟ ɫɤɨɪɨɫɬɟɣ
10-4–103 ɤɝ/ɫɦ2·ɫ ɞɥɹ ɝɨɪɧɵɯ ɩɨɪɨɞ ɭɫɬɨɣɱɢɜɨ ɩɪɨɹɜɥɹɟɬɫɹ ɬɟɧɞɟɧɰɢɹ ɤ ɭɜɟɥɢɱɟɧɢɸ
ɩɪɨɱɧɨɫɬɢ ɫ ɪɨɫɬɨɦ ɫɤɨɪɨɫɬɢ ɧɚɝɪɭɠɟɧɢɹ. ȼ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ ɷɬɨ ɭɜɟɥɢɱɟɧɢɟ
* Ʉɚɮɟɞɪɚ ɜɵɫɲɟɣ ɦɚɬɟɦɚɬɢɤɢ, ɇɚɰɢɨɧɚɥɶɧɵɣ ɝɨɪɧɵɣ ɭɧɢɜɟɪɫɢɬɟɬ, Ⱦɧɟɩɪɨɩɟɬɪɨɜɫɤ, ɍɤɪɚɢɧɚ
** Ʉɚɮɟɞɪɚ ɫɬɪɨɢɬɟɥɶɫɬɜɚ ɢ ɝɟɨɦɟɯɚɧɢɤɢ, ɇɚɰɢɨɧɚɥɶɧɵɣ ɝɨɪɧɵɣ ɭɧɢɜɟɪɫɢɬɟɬ, Ⱦɧɟɩɪɨɩɟɬɪɨɜɫɤ, ɍɤɪɚɢɧɚ
307
ɌȺȻɅɂɐȺ 1
Ɋɟɡɭɥɶɬɚɬɵ ɢɫɫɥɟɞɨɜɚɧɢɣ ɩɪɨɱɧɨɫɬɢ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɤɨɪɨɫɬɢ ɧɚɝɪɭɠɟɧɢɹ
ɂɫɫɥɟɞɨɜɚɬɟɥɢ
ɋɤɨɪɨɫɬɶ
ɧɚɝɪɭɠɟɧɢɹ,
ɤɝ/ɫɦ2·ɫ
Ɇɚɬɟɪɢɚɥ
ɨɛɪɚɡɰɚ
ɉɨɥɭɱɟɧɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɢ/ɢɥɢ ɫɞɟɥɚɧɧɵɟ ɜɵɜɨɞɵ
vn = 0, 005^log Vnh2 + 0, 075 log Vn + 1
v1
ɝɞɟ:
Ɇ.Ɏ. Ʉɭɧɬɵɲ
10-3–103
ɢɡɜɟɫɬɧɹɤ ın — ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɫɠɚɬɢɸ ɩɪɢ ɫɤɨɪɨɫɬɢ ɧɚɝɪɭɠɟɧɢɹ
Vn  1 ɤɝ/ɫɦ2·ɫ,
ı1 — ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɫɠɚɬɢɸ ɩɪɢ ɫɤɨɪɨɫɬɢ ɧɚɝɪɭɠɟɧɢɹ,
Vn = 1 ɤɝ/ɫɦ2·ɫ
vn = a + b log Vi
V0 ɝɞɟ:
Ɋ. ɏɨɭɩɟɪ
101–104
Ⱥ.ɂ. Ȼɟɪɨɧ
10-4–103
ɢɡɜɟɫɬɧɹɤ, ın= a + b · lgVi
ɩɟɫɱɚɧɢɤ, Ɉɬɦɟɱɚɟɬɫɹ ɛɨɥɟɟ ɢɧɬɟɧɫɢɜɧɨɟ ɜɥɢɹɧɢɟ ɞɥɹ ɫɥɚɛɵɯ
ɝɚɛɛɪɨ ɩɨɪɨɞ.
Ɏɨɧ Ɇ. ȼɚɜɪɨ
ɢ Ⱦɠ. Ɇɢɤɟɲɤɚ
ɞɜɚ
ɢɧɬɟɪɜɚɥɚ:
1) < 10,0
2) > 10,0
ɋ ɪɨɫɬɨɦ ɫɤɨɪɨɫɬɢ ɧɚɝɪɭɠɟɧɢɹ ɪɚɫɬɟɬ ɩɪɨɱɧɨɫɬɶ ɢ
ɝɥɢɧɢɫɬɵɣ
ɩɚɞɚɟɬ ɪɚɡɦɟɪ ɤɪɢɬɢɱɟɫɤɢɯ ɞɟɮɨɪɦɚɰɢɣ, ɨɬɦɟɱɚɟɬɫɹ
ɫɥɚɧɟɰ
ɢɡɦɟɧɟɧɢɟ ɦɨɞɭɥɹ ɭɩɪɭɝɨɫɬɢ
ȼ.Ⱥ. Ɇɚɧɫɭɪɨɜ
0–900
ɝɪɚɧɢɬ
a ɢ b — ɩɨɫɬɨɹɧɧɵɟ, ɫ ɪɚɡɦɟɪɧɨɫɬɶɸ ɧɚɩɪɹɠɟɧɢɣ,
Vɧ – ɫɤɨɪɨɫɬɶ ɧɚɝɪɭɠɟɧɢɹ ɨɛɪɚɡɰɚ,
V1 = 1 ɤɝ/ɫɦ2·ɫ.
ɢɡɜɟɫɬɧɹɤ, ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ ɫɤɨɪɨɫɬɢ ɧɚɝɪɭɠɟɧɢɹ ɪɚɫɬɟɬ ɩɪɨɱɧɨɫɬɶ
ɩɟɫɱɚɧɢɤ, ɨɛɪɚɡɰɚ. ȼɵɹɜɥɟɧ ɞɢɚɩɚɡɨɧ ɫɤɨɪɨɫɬɟɣ, ɝɞɟ ɨɬɦɟɱɚɟɬɫɹ
ɦɪɚɦɨɪ ɪɟɡɤɨɟ ɩɚɞɟɧɢɟ ɩɪɨɱɧɨɫɬɢ
ɨɩɢɫɵɜɚɟɬɫɹ ɥɨɝɚɪɢɮɦɢɱɟɫɤɨɣ ɡɚɜɢɫɢɦɨɫɬɶɸ. ɍɫɬɚɧɨɜɥɟɧɧɭɸ ɡɚɤɨɧɨɦɟɪɧɨɫɬɶ ɦɨɠɧɨ
ɨɛɴɹɫɧɢɬɶ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɩɪɨɱɧɨɫɬɢ.
3. ɂɡɦɟɧɟɧɢɹ ɩɪɨɱɧɨɫɬɢ ɝɨɪɧɵɯ ɩɨɪɨɞ ɫ ɬɨɱɤɢ
ɡɪɟɧɢɹ ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɩɪɨɱɧɨɫɬɢ
ȼ [2] ɨɛɨɫɧɨɜɚɧɚ ɜɟɪɨɹɬɧɨɫɬɧɚɹ ɦɨɞɟɥɶ ɪɚɡɪɭɲɟɧɢɹ ɨɛɪɚɡɰɚ, ɤɚɤ ɩɪɨɰɟɫɫ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɪɚɡɪɵɜɚ ɫɜɹɡɟɣ. ɉɨɤɚɡɚɧɨ, ɱɬɨ ɟɫɥɢ ɩɪɢ ɫɤɨɪɨɫɬɢ ɧɚɝɪɭɠɟɧɢɹ v0
ɜɟɪɨɹɬɧɨɫɬɶ ɪɚɡɪɭɲɟɧɢɹ ɪɚɜɧɚ F(ı), ɬɨ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɫɤɨɪɨɫɬɢ ɜ n ɪɚɡ ɜɟɪɨɹɬɧɨɫɬɶ
ɪɚɡɪɭɲɟɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɚɤ ɜɟɪɨɹɬɧɨɫɬɶ ɩɪɨɢɡɜɟɞɟɧɢɹ n ɧɟɡɚɜɢɫɢɦɵɯ ɫɨɛɵɬɢɣ, ɬɨ
ɟɫɬɶ ɫɨɫɬɚɜɥɹɟɬ Fn(ı), ɝɞɟ n = vn/v0. ɉɟɪɟɣɞɟɦ ɬɟɩɟɪɶ ɤ ɨɩɢɫɚɧɢɸ ɮɭɧɤɰɢɢ F(ı), ɝɞɟ
ı — ɦɚɤɫɢɦɚɥɶɧɚɹ ɩɪɨɱɧɨɫɬɶ ɢɡ ɜɫɟɯ ɜɨɡɦɨɠɧɵɯ ɡɧɚɱɟɧɢɣ ɩɪɨɱɧɨɫɬɢ ɫɜɹɡɟɣ, ɬɨ ɟɫɬɶ
— ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɜ ɜɵɛɨɪɤɟ. ɂɡɜɟɫɬɧɨ [3], ɱɬɨ, ɟɫɥɢ ɷɥɟɦɟɧɬɵ ɜɵɛɨɪɤɢ ɩɨɞɱɢɧɹɸɬɫɹ ɡɚɤɨɧɭ ɪɚɫɩɪɟɞɟɥɟɧɢɹ, ɤɨɬɨɪɨɟ ɢɦɟɟɬ ɜɢɞ ɷɤɫɩɨɧɟɧɬɵ ɜ ɨɛɥɚɫɬɢ ɧɚɢɛɨɥɶɲɢɯ
ɡɧɚɱɟɧɢɣ ɢ ɧɟ ɨɝɪɚɧɢɱɟɧɨ ɫɩɪɚɜɚ (ɬɚɤɢɦɢ ɹɜɥɹɸɬɫɹ ɷɤɫɩɨɧɟɧɰɢɚɥɶɧɨɟ, ɧɨɪɦɚɥɶɧɨɟ,
ɝɚɦɦɚ-ɪɚɫɩɪɟɞɟɥɟɧɢɟ), ɬɨ ɦɚɤɫɢɦɚɥɶɧɵɟ ɡɧɚɱɟɧɢɹ ɜ ɜɵɛɨɪɤɟ ɨɩɢɫɵɜɚɸɬɫɹ ɡɚɤɨɧɨɦ
Ƚɭɦɛɟɥɹ ɫ ɮɭɧɤɰɢɟɣ ɜɟɪɨɹɬɧɨɫɬɢ:
308
v n
F^vh = exp `- exp `- - jj
d
(1)
Ɂɞɟɫɶ ȝ, į — ɩɚɪɚɦɟɬɪɵ ɮɨɪɦɵ ɢ ɦɚɫɲɬɚɛɚ, ɤɨɬɨɪɵɟ ɨɩɪɟɞɟɥɹɸɬɫɹ ɱɟɪɟɡ ɫɪɟɞɧɸɸ
ɜɵɛɨɪɨɱɧɭɸ ı̄ ɢ ɫɬɚɧɞɚɪɬ ɨɬɤɥɨɧɟɧɢɹ S: ȝ = ı̄ – 0,577 į, į = 1,288 S.
Ɍɨɝɞɚ:
F n ^vh = exp c- exp c-
v - ^ n + d ln nh
mm
d
(2)
Ɏɭɧɤɰɢɹ Fn(ı) ɢɦɟɟɬ ɬɨɬ ɠɟ ɫɚɦɵɣ ɬɢɩ, ɱɬɨ ɢ F(ı), ɨɬɥɢɱɚɟɬɫɹ ɬɨɥɶɤɨ ɡɧɚɱɟɧɢɹɦɢ
ɜɯɨɞɹɳɢɯ ɜ ɧɟɟ ɩɚɪɚɦɟɬɪɨɜ, ɤɨɬɨɪɵɟ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɪɚɜɧɵ:
nn = n + d ln ^ nh
(3)
dn = d
(4)
ɋ ɭɱɟɬɨɦ, ɱɬɨ ȝ = ı̄ – 0,577 į ɢ įn = į ɩɨɥɭɱɟɧɨ ɫɨɨɬɧɨɲɟɧɢɟ:
vn = v + 1, 288S ln vn
v0
(5)
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɟɲɟɧɢɟ ɜɟɪɨɹɬɧɨɫɬɧɨ-ɫɬɚɬɢɫɬɢɱɟɫɤɨɣ ɡɚɞɚɱɢ ɬɚɤɠɟ ɩɪɢɜɨɞɢɬ
ɤ ɥɨɝɚɪɢɮɦɢɱɟɫɤɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɩɪɨɱɧɨɫɬɢ ɨɬ ɫɤɨɪɨɫɬɢ ɧɚɝɪɭɠɟɧɢɹ, ɩɪɢɱɟɦ ɩɚɪɚɦɟɬɪɵ
ɭɪɚɜɧɟɧɢɹ ɪɟɚɥɶɧɨ ɦɨɝɭɬ ɛɵɬɶ ɩɨɥɭɱɟɧɵ ɩɭɬɟɦ ɫɬɚɧɞɚɪɬɧɨɣ ɨɛɪɚɛɨɬɤɢ ɫɬɚɬɢɫɬɢɱɟɫɤɢɯ
ɞɚɧɧɵɯ. ɍɪɚɜɧɟɧɢɟ (5) ɦɨɠɧɨ ɩɪɢɜɟɫɬɢ ɤ ɜɢɞɭ:
vn = 1 + 1, 288h ln vn
v0
v
(6)
ɝɞɟ Ș = S/ı — ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɜɚɪɢɚɰɢɹ ɩɪɨɱɧɨɫɬɢ. Ʉɚɤ ɜɢɞɧɨ ɢɡ ɝɪɚɮɢɤɚ (ɪɢɫ. 1), ɭɜɟɥɢɱɟɧɢɟ
ɫɤɨɪɨɫɬɢ ɧɚɝɪɭɠɟɧɢɹ ɫɭɳɟɫɬɜɟɧɧɨ (ɛɨɥɟɟ ɱɟɦ ɜ 2 ɪɚɡɚ) ɭɜɟɥɢɱɢɜɚɟɬ ɩɪɨɱɧɨɫɬɶ ɬɟɯ ɩɨɪɨɞ,
ɞɥɹ ɤɨɬɨɪɵɯ ɯɚɪɚɤɬɟɪɟɧ ɡɧɚɱɢɬɟɥɶɧɵɣ (> 0,3) ɫɬɚɬɢɫɬɢɱɟɫɤɢɣ ɪɚɡɛɪɨɫ ɡɧɚɱɟɧɢɣ ɩɪɨɱɧɨɫɬɢ
ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɪɟɞɧɟɝɨ, ɬ.ɟ. ɞɥɹ ɫɬɪɭɤɬɭɪɧɨ ɧɟɨɞɧɨɪɨɞɧɨɣ ɩɨɪɨɞɧɨɣ ɫɪɟɞɵ.
ɉɪɢ ɨɱɢɫɬɧɨɣ ɜɵɟɦɤɟ ɭɝɥɹ ɫɤɨɪɨɫɬɶ ɨɛɧɚɠɟɧɢɹ ɝɨɪɧɵɯ ɩɨɪɨɞ, ɚ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ,
ɢ ɫɤɨɪɨɫɬɶ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɹ ɧɚɩɪɹɠɟɧɢɣ ɜ ɩɨɪɨɞɧɨɦ ɦɚɫɫɢɜɟ ɫɨɩɨɫɬɚɜɢɦɚ ɫɨ
ɫɤɨɪɨɫɬɶɸ ɧɚɝɪɭɠɟɧɢɹ ɥɚɛɨɪɚɬɨɪɧɵɯ ɨɛɪɚɡɰɨɜ ɧɚ ɢɫɩɵɬɚɬɟɥɶɧɨɦ ɩɪɟɫɫɟ. ɍɫɥɨɜɧɨ
ɜɵɞɟɥɟɧɧɵɣ ɛɟɫɤɨɧɟɱɧɨ ɦɚɥɵɣ ɫɬɪɭɤɬɭɪɧɵɣ ɷɥɟɦɟɧɬ ɦɚɫɫɢɜɚ ɢɫɩɵɬɵɜɚɟɬ ɧɚɝɪɭɡɤɭ ɨɬ
ɫɢɥ ɝɨɪɧɨɝɨ ɞɚɜɥɟɧɢɹ, ɟɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɩɨɞɨɛɧɨ ɫɨɩɪɨɬɢɜɥɟɧɢɸ ɩɨɪɨɞɧɨɝɨ ɨɛɪɚɡɰɚ
ɡɚɜɢɫɢɬ ɨɬ ɫɤɨɪɨɫɬɢ ɧɚɝɪɭɠɟɧɢɹ.
ɉɪɢ ɷɬɨɦ, ɫɤɨɪɨɫɬɶ ɩɪɢɥɨɠɟɧɢɹ ɧɚɝɪɭɡɤɢ ɜ ɦɚɫɫɢɜɟ ɫɨɩɨɫɬɚɜɢɦɚ ɫɨ ɫɤɨɪɨɫɬɶɸ
ɧɚɝɪɭɠɟɧɢɹ ɥɚɛɨɪɚɬɨɪɧɵɯ ɨɛɪɚɡɰɨɜ. ɍɪɚɜɧɟɧɢɟ (6) ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɤɨɪɪɟɤɬɢɪɨɜɚɬɶ
309
Ɋɢɫ. 1. ɂɡɦɟɧɟɧɢɟ ɩɪɨɱɧɨɫɬɢ ɩɨɪɨɞ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɤɨɪɨɫɬɢ ɩɪɢɥɨɠɟɧɢɹ ɧɚɝɪɭɡɤɢ:
ɪɹɞ 1 — Ș = 0,2; ɪɹɞ 2 — Ș = 0,3; ɪɹɞ 3 — Ș = 0,4; ɪɹɞ 4 — Ș = 0,5
ɩɪɟɞɟɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɩɪɨɱɧɨɫɬɢ, ɩɨɥɭɱɟɧɧɨɟ ɥɚɛɨɪɚɬɨɪɧɵɦ ɩɭɬɟɦ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ
ɫ ɪɟɚɥɶɧɵɦɢ ɭɫɥɨɜɢɹɦɢ ɞɨɛɵɱɢ ɭɝɥɹ ɢ ɨɯɪɚɧɵ ɜɵɪɚɛɨɬɨɤ.
4. Ʉɪɢɬɟɪɢɣ ɩɪɨɱɧɨɫɬɢ ɩɨɪɨɞ ɫ ɭɱɟɬɨɦ
ɫɤɨɪɨɫɬɢ ɩɪɢɥɨɠɟɧɢɹ ɧɚɝɪɭɡɤɢ
Ɂɨɧɚ ɪɚɡɪɭɲɟɧɢɹ ɜ ɤɪɨɜɥɟ ɢ ɩɨɱɜɟ ɩɥɚɫɬɚ ɦɨɠɟɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɚ ɤɚɤ ɫɨɜɨɤɭɩɧɨɫɬɶ
ɬɨɱɟɤ, ɜ ɤɨɬɨɪɵɯ ɜɵɩɨɥɧɹɟɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟ:
ve $ Rc `1 + 1, 288h ln vn j
v0
(7)
ɝɞɟ ıe — ɷɤɜɢɜɚɥɟɧɬɧɨɟ ɧɚɩɪɹɠɟɧɢɟ, ɨɩɪɟɞɟɥɹɟɦɨɟ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɜɵɛɪɚɧɧɨɣ
ɬɟɨɪɢɟɣ ɩɪɨɱɧɨɫɬɢ. ȼ ɱɚɫɬɧɨɫɬɢ, ɫɥɨɠɧɨɟ ɧɚɩɪɹɠɟɧɧɨɟ ɫɨɫɬɨɹɧɢɟ ɦɨɠɟɬ ɛɵɬɶ
ɫɜɟɞɟɧɨ ɤ ɷɤɜɢɜɚɥɟɧɬɧɨɦɭ ɨɞɧɨɨɫɧɨɦɭ ɧɚɩɪɹɠɟɧɢɸ ɧɚ ɨɫɧɨɜɟ ɬɟɨɪɢɢ ɩɪɨɱɧɨɫɬɢ
ɉ.ɉ.Ȼɚɥɚɧɞɢɧɚ [4]:
ve =
^} - 1h^v1 + v2 + v3h
+
2}
^} - 1h2 ^v1 + v2 + v3h2 + 4} 6^v1 - v2h2 + ^v2 - v3h2 + ^v3 - v1h2 @
+
2}
(7)
ɝɞɟ:
ı1, ı2, ı3 — ɝɥɚɜɧɵɟ ɧɚɩɪɹɠɟɧɢɹ,
Rp, Rc — ɩɪɟɞɟɥɵ ɩɪɨɱɧɨɫɬɢ ɧɚ ɨɞɧɨɨɫɧɨɟ ɪɚɫɬɹɠɟɧɢɟ ɢ ɫɠɚɬɢɟ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ,
ȥ = Rp/Rc — ɩɨɤɚɡɚɬɟɥɶ ɯɪɭɩɤɨɫɬɢ ɦɚɬɟɪɢɚɥɚ.
310
ɍɫɥɨɜɢɹ (7) ɢ (8) ɨɬɪɚɠɚɸɬ ɪɟɚɥɶɧɭɸ ɞɢɧɚɦɢɤɭ ɨɛɪɚɡɨɜɚɧɢɹ ɩɨɥɨɫɬɟɣ ɜ ɦɚɫɫɢɜɟ
ɩɨɪɨɞ.
5. ɑɢɫɥɟɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɇȾɋ ɩɨɪɨɞɧɨɝɨ ɦɚɫɫɢɜɚ
ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɫɤɨɪɨɫɬɹɯ ɨɱɢɫɬɧɨɝɨ ɡɚɛɨɹ
ȼɥɢɹɧɢɟ ɫɤɨɪɨɫɬɢ ɩɨɞɜɢɝɚɧɢɹ ɨɱɢɫɬɧɨɝɨ ɡɚɛɨɹ ɧɚ ɫɨɫɬɨɹɧɢɟ ɩɨɪɨɞ ɤɪɨɜɥɢ ɥɚɜɵ ɩɪɨɚɧɚɥɢɡɢɪɨɜɚɧɨ ɞɥɹ ɭɫɥɨɜɢɣ ɲɚɯɬɵ «ɒɚɯɬɟɪɫɤɚɹ Ƚɥɭɛɨɤɚɹ» Ƚɉ «ɒɚɯɬɟɪɫɤȺɧɬɪɚɰɢɬ».
ɒɚɯɬɚ ɪɚɡɪɚɛɚɬɵɜɚɟɬ ɩɥɚɫɬ «Ɏɨɦɢɧɫɤɢɣ» (h8). ɇɟɩɨɫɪɟɞɫɬɜɟɧɧɚɹ ɢ ɨɫɧɨɜɧɚɹ ɤɪɨɜɥɹ
ɩɪɟɞɫɬɚɜɥɟɧɚ ɫɥɚɧɰɟɦ ɝɥɢɧɢɫɬɵɦ, ɩɟɫɱɚɧɨ-ɝɥɢɧɢɫɬɵɦ, ɚ ɬɚɤɠɟ ɩɟɫɱɚɧɵɦ. Ⱦɨɛɵɱɚ ɭɝɥɹ
ɩɪɨɢɡɜɨɞɢɬɫɹ ɜ ɤɨɦɩɥɟɤɫɧɨ-ɦɟɯɚɧɢɡɢɪɨɜɚɧɧɵɯ ɥɚɜɚɯ. ɋɤɨɪɨɫɬɶ ɩɨɞɜɢɝɚɧɢɹ ɨɱɢɫɬɧɨɝɨ
ɡɚɛɨɹ ɫɨɫɬɚɜɥɹɟɬ 22–25 ɦɟɬɪɨɜ ɜ ɦɟɫɹɰ. Ƚɥɭɛɢɧɚ ɜɟɞɟɧɢɹ ɪɚɛɨɬ ɧɚ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ
ɭɱɚɫɬɤɟ ɫɨɫɬɚɜɥɹɟɬ 1386 ɦɟɬɪɨɜ. Ɉɯɪɚɧɚ ɩɨɞɝɨɬɨɜɢɬɟɥɶɧɵɯ ɜɵɪɚɛɨɬɨɤ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ
ɰɟɥɢɤɚɦɢ ɲɢɪɢɧɨɣ 10 ɦ.
Ɇɟɬɨɞɨɦ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɦɨɞɟɥɢɪɨɜɚɥɨɫɶ ɬɪɟɯɦɟɪɧɨɟ ɧɚɩɪɹɠɟɧɧɨ-ɞɟɮɨɪɦɢɪɨɜɚɧɧɨɟ ɫɨɫɬɨɹɧɢɟ (ɇȾɋ) ɨɛɥɚɫɬɢ, ɜɤɥɸɱɚɸɳɟɣ ɨɱɢɫɬɧɭɸ ɢ ɩɨɞɝɨɬɨɜɢɬɟɥɶɧɭɸ
ɜɵɪɚɛɨɬɤɢ (ɪɢɫ. 2).
ɐɟɥɶɸ ɱɢɫɥɟɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɹɜɥɹɥɨɫɶ ɨɩɪɟɞɟɥɟɧɢɟ ɝɟɨɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɬɭɚɰɢɢ, ɩɪɢ ɤɨɬɨɪɨɣ ɩɪɨɢɫɯɨɞɢɬ ɩɟɪɜɢɱɧɨɟ ɨɛɪɭɲɟɧɢɟ ɤɪɨɜɥɢ ɥɚɜɵ ɩɨɡɚɞɢ ɨɱɢɫɬɧɨɝɨ
ɡɚɛɨɹ. ɂɦɢɬɢɪɨɜɚɥɫɹ ɩɨɲɚɝɨɜɵɣ ɨɬɯɨɞ ɥɚɜɵ ɨɬ ɪɚɡɪɟɡɧɨɣ ɩɟɱɢ ɧɚ ɪɚɫɫɬɨɹɧɢɟ 10,
20, 30 ɦ ɫ ɰɟɥɶɸ ɨɩɪɟɞɟɥɢɬɶ ɤɪɢɬɢɱɟɫɤɢɣ ɪɚɡɦɟɪ ɜɵɪɚɛɨɬɚɧɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ, ɩɪɢ
ɤɨɬɨɪɨɦ ɩɪɨɢɡɨɣɞɟɬ ɩɟɪɜɢɱɧɨɟ ɨɛɪɭɲɟɧɢɟ. ɇɚ ɩɟɪɜɨɦ ɷɬɚɩɟ ɪɚɫɱɟɬɨɜ ɩɪɟɞɟɥ ɩɪɨɱɧɨɫɬɢ ɧɚ ɫɠɚɬɢɟ ɩɪɢɧɢɦɚɥɫɹ ɪɚɜɧɵɦ ɫɪɟɞɧɟɦɭ ɜɵɛɨɪɨɱɧɨɦɭ Rc, ɨɩɪɟɞɟɥɟɧɧɨɦɭ ɩɪɢ
ɫɬɚɧɞɚɪɬɧɵɯ ɢɫɩɵɬɚɧɢɹɯ ɨɛɪɚɡɰɨɜ ɩɨɪɨɞ ɧɚ ɨɞɧɨɨɫɧɨɟ ɫɠɚɬɢɟ. ɋ ɭɱɟɬɨɦ ɤɨɷɮɮɢɰɢɟɧɬɚ ɫɬɪɭɤɬɭɪɧɨɝɨ ɨɫɥɚɛɥɟɧɢɹ (ɞɥɹ ɞɚɧɧɵɯ ɭɫɥɨɜɢɣ ɨɧ ɪɚɜɟɧ 0,5) ɩɪɨɱɧɨɫɬɶ ɩɨɪɨɞ
ɨɫɧɨɜɧɨɣ ɤɪɨɜɥɢ ɫɨɫɬɚɜɥɹɟɬ 34 Ɇɉɚ.
Ɋɢɫ. 2. Ɋɚɫɱɟɬɧɚɹ ɫɯɟɦɚ ɫɨɩɪɹɠɟɧɢɹ ɩɨɞɝɨɬɨɜɢɬɟɥɶɧɨɣ ɜɵɪɚɛɨɬɤɢ ɢ ɥɚɜɵ ɫ ɪɚɡɪɟɡɨɦ
ɜ ɡɨɧɟ ɜɟɞɟɧɢɹ ɨɱɢɫɬɧɵɯ ɪɚɛɨɬ ɢ ɤɨɧɟɱɧɨɷɥɟɦɟɧɬɧɚɹ ɚɩɩɪɨɤɫɢɦɚɰɢɹ ɢɫɫɥɟɞɭɟɦɨɣ ɨɛɥɚɫɬɢ:
1 — ɨɫɧɨɜɧɚɹ ɤɪɨɜɥɹ, 2 — ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɚɹ ɤɪɨɜɥɹ, 3 — ɩɥɚɫɬ ɭɝɥɹ,
4 — ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɚɹ ɩɨɱɜɚ, 5 — ɨɫɧɨɜɧɚɹ ɩɨɱɜɚ, 6 — ɜɵɪɚɛɨɬɚɧɧɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ
311
Ⱥɧɚɥɢɡɢɪɨɜɚɥɨɫɶ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɤɨɦɩɨɧɟɧɬɨɜ ɬɟɧɡɨɪɚ ɧɚɩɪɹɠɟɧɢɣ ɜ ɪɚɡɥɢɱɧɵɯ
ɫɟɱɟɧɢɹɯ ɥɚɜɵ, ɧɚɯɨɞɹɳɢɯɫɹ ɜ ɪɚɡɥɢɱɧɵɯ ɭɫɥɨɜɢɹɯ ɧɚɝɪɭɠɟɧɢɹ ɜɫɥɟɞɫɬɜɢɟ ɜɥɢɹɧɢɹ
ɩɨɞɝɨɬɨɜɢɬɟɥɶɧɨɣ ɜɵɪɚɛɨɬɤɢ. ɇɚɢɛɨɥɟɟ ɯɚɪɚɤɬɟɪɧɵɦ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɩɪɨɹɜɥɟɧɢɹ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɝɨ ɷɮɮɟɤɬɚ ɹɜɥɹɟɬɫɹ ɫɟɱɟɧɢɟ ɥɚɜɵ ɩɥɨɫɤɨɫɬɶɸ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɥɢɧɢɢ
ɡɚɛɨɹ (ɩɚɪɚɥɥɟɥɶɧɨɣ ɨɫɢ ɩɨɞɝɨɬɨɜɢɬɟɥɶɧɨɣ ɜɵɪɚɛɨɬɤɢ), ɨɬɫɬɨɹɳɟɣ ɩɪɢɦɟɪɧɨ ɧɚ 2 ɦɟɬɪɚ
ɨɬ ɰɟɥɢɤɚ. ɇɚ ɪɢɫ. 3 ɩɨɤɚɡɚɧɨ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɝɨɪɢɡɨɧɬɚɥɶɧɵɯ ɧɨɪɦɚɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ
ɜ ɷɬɨɦ ɫɟɱɟɧɢɢ ɩɪɢ ɪɚɡɦɟɪɟ ɜɵɪɚɛɨɬɚɧɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɚ = 30 ɦ. ȼ ɤɪɨɜɥɟ ɜɵɪɚɛɨɬɤɢ
ɹɜɧɨ ɜɢɞɧɚ ɡɨɧɚ ɪɚɫɬɹɝɢɜɚɸɳɢɯ ɧɚɩɪɹɠɟɧɢɣ, ɞɨɫɬɢɝɚɸɳɚɹ ɜ ɰɟɧɬɪɟ ɜɵɪɚɛɨɬɤɢ ɜɵɫɨɬɵ
4 ɦ ɩɨ ɧɨɪɦɚɥɢ ɤ ɩɥɚɫɬɭ.
Ɋɢɫ. 3. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɝɨɪɢɡɨɧɬɚɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɜɨɤɪɭɝ ɨɱɢɫɬɧɨɣ ɜɵɪɚɛɨɬɤɢ
ɩɪɢ ɲɢɪɢɧɟ ɜɵɪɚɛɨɬɚɧɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ 30 ɦ. 1 — ɡɨɧɚ ɪɚɫɬɹɝɢɜɚɸɳɢɯ
ɝɨɪɢɡɨɧɬɚɥɶɧɵɯ ɧɚɩɪɹɠɟɧɢɣ ɜ ɤɪɨɜɥɟ ɜɵɪɚɛɨɬɤɢ
ɇɚ ɪɢɫ. 4 ɬɨɱɤɚɦɢ ɩɨɤɚɡɚɧɵ ɷɥɟɦɟɧɬɵ, ɜ ɤɨɬɨɪɵɯ ɜɵɩɨɥɧɹɟɬɫɹ ɭɫɥɨɜɢɟ (7). ȼɢɞɧɨ,
ɱɬɨ ɨɛɥɚɫɬɶ ɪɚɡɪɭɲɟɧɢɹ ɩɪɢ ɞɚɧɧɨɦ ɪɚɡɦɟɪɟ ɜɵɪɚɛɨɬɚɧɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɢɦɟɟɬ
ɮɨɪɦɭ ɫɜɨɞɚ, ɩɨɱɬɢ ɫɨɜɩɚɞɚɸɳɭɸ ɫ ɨɛɥɚɫɬɶɸ ɪɚɫɬɹɝɢɜɚɸɳɢɯ ɧɚɩɪɹɠɟɧɢɣ. Ɉɛɥɚɫɬɶ
ɪɚɡɪɭɲɟɧɢɹ ɨɯɜɚɬɵɜɚɟɬ ɩɪɚɤɬɢɱɟɫɤɢ ɩɨɥɧɨɫɬɶɸ ɨɫɧɨɜɧɭɸ ɤɪɨɜɥɸ.
Ɋɢɫ. 4. Ɉɛɥɚɫɬɶ ɪɚɡɪɭɲɟɧɢɹ ɜ ɤɪɨɜɥɟ ɨɱɢɫɬɧɨɣ ɜɵɪɚɛɨɬɤɢ
ɩɪɢ ɫɭɳɟɫɬɜɭɸɳɢɯ ɬɟɦɩɚɯ ɩɨɞɜɢɝɚɧɢɹ ɨɱɢɫɬɧɨɝɨ ɡɚɛɨɹ (22–25 ɦ ɜ ɦɟɫɹɰ)
312
Ɍɚɤɚɹ ɫɢɬɭɚɰɢɹ ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɚɤ ɤɪɢɬɢɱɟɫɤɚɹ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɦɨɦɟɧɬɭ ɨɛɪɭɲɟɧɢɹ ɤɪɨɜɥɢ, ɤɨɝɞɚ ɜɟɫ ɩɨɪɨɞ ɜ ɩɪɟɞɟɥɚɯ ɡɨɧɵ ɪɚɡɪɭɲɟɧɢɹ ɩɪɟɜɨɫɯɨɞɢɬ ɫɢɥɵ ɫɰɟɩɥɟɧɢɹ
ɫ ɦɚɫɫɢɜɨɦ. Ʉɪɨɦɟ ɬɨɝɨ, ɪɚɫɱɟɬɵ ɧɚ ɨɫɧɨɜɟ ɞɚɧɧɨɣ ɬɪɟɯɦɟɪɧɨɣ ɱɢɫɥɟɧɧɨɣ ɦɨɞɟɥɢ
ɩɨɡɜɨɥɢɥɢ ɡɚɮɢɤɫɢɪɨɜɚɬɶ ɨɛɥɚɫɬɢ ɪɚɡɪɭɲɟɧɢɹ ɧɚɞ ɬɨɪɰɟɜɵɦɢ ɭɱɚɫɬɤɚɦɢ ɜɵɪɚɛɨɬɤɢ,
ɜɵɫɨɬɨɣ ɞɨ 6 ɦɟɬɪɨɜ. Ɋɚɡɪɭɲɟɧɢɟ ɤɪɚɟɜɵɯ ɭɱɚɫɬɤɨɜ ɫɨɡɞɚɸɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɭɫɥɨɜɢɹ ɞɥɹ
ɨɛɪɭɲɟɧɢɹ ɩɨɪɨɞ ɜ ɜɵɪɚɛɨɬɚɧɧɨɟ ɩɪɨɫɬɪɚɧɫɬɜɨ. Ɋɟɡɭɥɶɬɚɬɵ ɱɢɫɥɟɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ
ɩɨɞɬɜɟɪɠɞɚɸɬɫɹ ɞɚɧɧɵɦɢ ɨ ɜɟɥɢɱɢɧɟ ɲɚɝɚ ɨɛɪɭɲɟɧɢɹ ɧɚ ɲɚɯɬɟ «ɒɚɯɬɟɪɫɤɚɹ-Ƚɥɭɛɨɤɚɹ»
ɩɨ ɩɥɚɫɬɭ h8, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɤɨɬɨɪɨɣ ɲɚɝ ɩɟɪɜɢɱɧɨɝɨ ɨɛɪɭɲɟɧɢɹ ɬɚɤɠɟ ɫɨɫɬɚɜɥɹɟɬ
28–30 ɦ.
ɋɨɜɪɟɦɟɧɧɵɟ ɭɫɥɨɜɢɹ ɬɪɟɛɭɸɬ ɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɨɣ ɪɚɛɨɬɵ ɞɨɛɵɜɚɸɳɢɯ ɩɪɟɞɩɪɢɹɬɢɣ, ɚ ɫɨɜɪɟɦɟɧɧɨɟ ɨɛɨɪɭɞɨɜɚɧɢɟ ɩɪɨɟɤɬɢɪɭɟɬɫɹ ɫ ɭɱɟɬɨɦ ɫɤɨɪɨɫɬɧɨɝɨ ɪɟɠɢɦɚ
ɞɨɛɵɱɢ. Ɉɩɪɟɞɟɥɢɦ ɜɨɡɦɨɠɧɵɟ ɢɡɦɟɧɟɧɢɹ ɝɟɨɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɬɭɚɰɢɢ ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ
ɬɟɦɩɨɜ ɨɱɢɫɬɧɵɯ ɪɚɛɨɬ ɜ ɭɫɥɨɜɢɹɯ ɲɚɯɬɵ «ɒɚɯɬɟɪɫɤɚɹ-Ƚɥɭɛɨɤɚɹ». ɍɜɟɥɢɱɟɧɢɟ
ɫɤɨɪɨɫɬɢ ɨɛɧɚɠɟɧɢɹ ɩɨɪɨɞ ɩɨɜɥɟɱɟɬ ɫɨɝɥɚɫɧɨ (6) ɢɡɦɟɧɟɧɢɟ ɢɯ ɩɪɨɱɧɨɫɬɢ. ɇɚɩɪɢɦɟɪ,
ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɫɤɨɪɨɫɬɢ ɪɚɛɨɬɵ ɞɨɛɵɱɧɨɝɨ ɨɛɨɪɭɞɨɜɚɧɢɹ ɜ 3 ɪɚɡɚ ɩɪɨɱɧɨɫɬɶ ɩɨɪɨɞ
ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (6) ɭɜɟɥɢɱɢɬɫɹ ɜ 1,5–1,7 ɪɚɡ, ɬ.ɟ. ɞɨ ɡɧɚɱɟɧɢɹ Rn = 51–58 Ɇɉɚ. ɉɪɢ
ɬɚɤɨɦ ɡɧɚɱɟɧɢɢ ɩɪɨɱɧɨɫɬɢ ɪɚɡɦɟɪ ɜɵɪɚɛɨɬɚɧɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɚ = 30 ɦ ɭɠɟ ɧɟ ɹɜɥɹɟɬɫɹ
ɤɪɢɬɢɱɟɫɤɢɦ. Ɂɨɧɚ ɪɚɡɪɭɲɟɧɢɹ ɨɯɜɚɬɵɜɚɟɬ ɬɨɥɶɤɨ ɱɚɫɬɶ ɨɫɧɨɜɧɨɣ ɤɪɨɜɥɢ ɢ ɜɟɫ ɩɨɪɨɞ,
ɡɚɤɥɸɱɟɧɧɵɣ ɜ ɷɬɨɣ ɡɨɧɟ ɧɟɞɨɫɬɚɬɨɱɟɧ ɞɥɹ ɩɪɟɨɞɨɥɟɧɢɹ ɫɢɥ ɫɰɟɩɥɟɧɢɹ (ɪɢɫ. 5).
Ɋɢɫ. 5. Ɋɚɫɩɪɟɞɟɥɟɧɢɟ ɪɚɡɪɭɲɟɧɧɵɯ ɷɥɟɦɟɧɬɨɜ ɜ ɤɪɨɜɥɟ ɨɱɢɫɬɧɨɣ ɜɵɪɚɛɨɬɤɢ
ɩɪɢ ɭɜɟɥɢɱɟɧɢɢ ɫɤɨɪɨɫɬɢ ɨɛɧɚɠɟɧɢɹ ɩɨɪɨɞ (ɩɨɞɜɢɝɚɧɢɟ ɨɱɢɫɬɧɨɝɨ ɡɚɛɨɹ 60 ɦ ɜ ɦɟɫɹɰ)
ȼ ɬɨɪɰɟɜɵɯ ɱɚɫɬɹɯ ɜɵɪɚɛɨɬɤɢ ɧɟ ɧɚɛɥɸɞɚɟɬɫɹ ɫɭɳɟɫɬɜɟɧɧɵɯ ɡɨɧ ɪɚɡɪɭɲɟɧɢɹ, ɱɬɨ
ɬɚɤɠɟ ɫɧɢɠɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɨɛɪɭɲɟɧɢɹ. ɉɨɲɚɝɨɜɵɦ ɦɨɞɟɥɢɪɨɜɚɧɢɟɦ ɭɜɟɥɢɱɟɧɢɹ ɜɵɪɚɛɨɬɚɧɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɩɨɡɚɞɢ ɥɚɜɵ ɛɵɥɨ ɭɫɬɚɧɨɜɥɟɧɨ, ɱɬɨ ɤɪɢɬɢɱɟɫɤɚɹ ɫɢɬɭɚɰɢɹ ɩɪɢ
ɞɚɧɧɨɣ ɫɤɨɪɨɫɬɢ ɨɛɧɚɠɟɧɢɹ ɫɨɡɞɚɟɬɫɹ ɩɪɢ ɪɚɡɦɟɪɟ ɜɵɪɚɛɨɬɚɧɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ 40–45 ɦ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɟɞɥɨɠɟɧɧɵɣ ɚɥɝɨɪɢɬɦ ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧ ɞɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɭɜɟɥɢɱɟɧɢɹ ɫɤɨɪɨɫɬɢ ɨɛɧɚɠɟɧɢɹ ɩɪɢ ɨɰɟɧɤɟ ɝɟɨɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɬɭɚɰɢɢ ɜɛɥɢɡɢ
ɨɱɢɫɬɧɨɣ ɢ ɩɨɞɝɨɬɨɜɢɬɟɥɶɧɨɣ ɜɵɪɚɛɨɬɨɤ.
Ȼɟɡɭɫɥɨɜɧɨ, ɡɚɜɢɫɢɦɨɫɬɶ (7) ɨɬɪɚɠɚɟɬ ɬɨɥɶɤɨ ɥɢɲɶ ɫɬɨɯɚɫɬɢɱɟɫɤɭɸ ɩɪɢɪɨɞɭ
ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɹ ɩɪɨɱɧɨɫɬɢ ɫɜɹɡɟɣ ɧɚ ɭɪɨɜɧɟ ɤɪɢɫɬɚɥɥɢɱɟɫɤɨɣ ɪɟɲɟɬɤɢ ɦɚɬɟɪɢɚɥɚ.
313
ȼ ɪɟɚɥɶɧɨɫɬɢ ɧɚ ɝɟɨɦɟɯɚɧɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɵ ɜ ɩɨɪɨɞɧɨɦ ɦɚɫɫɢɜɟ ɨɤɚɡɵɜɚɟɬ ɜɥɢɹɧɢɟ
ɛɟɫɱɢɫɥɟɧɧɨɟ ɦɧɨɠɟɫɬɜɨ ɮɚɤɬɨɪɨɜ. ȼɵɞɟɥɢɬɶ ɫɪɟɞɢ ɧɢɯ ɜɥɢɹɧɢɟ ɫɤɨɪɨɫɬɢ ɨɛɧɚɠɟɧɢɹ
ɩɨɪɨɞ ɨɱɟɧɶ ɫɥɨɠɧɨ. Ɇɨɠɧɨ ɬɨɥɶɤɨ ɧɚɛɥɸɞɚɬɶ ɪɟɡɭɥɶɬɚɬ ɷɬɨɝɨ ɜɥɢɹɧɢɹ in situ, ɧɚɤɚɩɥɢɜɚɹ ɢ ɨɛɨɛɳɚɹ ɫɬɚɬɢɫɬɢɱɟɫɤɢɟ ɞɚɧɧɵɟ.
Ⱥɜɬɨɪɚɦɢ ɩɪɨɚɧɚɥɢɡɢɪɨɜɚɧɵ ɞɚɧɧɵɟ ɨ ɩɟɪɜɢɱɧɵɯ ɨɛɪɭɲɟɧɢɹɯ ɤɪɨɜɥɢ ɨɱɢɫɬɧɵɯ
ɜɵɪɚɛɨɬɨɤ ɧɚ ɲɚɯɬɚɯ Ƚɉ «ɒɚɯɬɟɪɫɤȺɧɬɪɚɰɢɬ» [4] ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɫɤɨɪɨɫɬɹɯ ɩɨɞɜɢɝɚɧɢɹ
ɨɱɢɫɬɧɨɝɨ ɡɚɛɨɹ. Ⱦɚɧɧɵɟ ɢɦɟɸɬ ɡɧɚɱɢɬɟɥɶɧɵɣ ɪɚɡɛɪɨɫ, ɨɞɧɚɤɨ ɧɚ ɤɨɪɪɟɥɹɰɢɨɧɧɨɦ
ɩɨɥɟ ɦɨɠɧɨ ɜɵɞɟɥɢɬɶ ɥɢɧɢɸ ɬɪɟɧɞɚ, ɤɨɬɨɪɚɹ ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɤɨɪɪɟɥɹɰɢɢ
R² = 0,464 ɨɩɢɫɵɜɚɟɬɫɹ ɥɨɝɚɪɢɮɦɢɱɟɫɤɨɣ ɡɚɜɢɫɢɦɨɫɬɶɸ: a = 0,224lnV + 6,888. ɋɥɚɛɚɹ
ɤɨɪɪɟɥɹɰɢɨɧɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɨɬɪɚɠɚɟɬ ɭɩɨɦɹɧɭɬɨɟ ɜɵɲɟ ɦɧɨɠɟɫɬɜɨ ɪɚɡɥɢɱɧɵɯ
ɜɥɢɹɸɳɢɯ ɮɚɤɬɨɪɨɜ, ɨɞɧɚɤɨ ɨɛɳɚɹ ɬɟɧɞɟɧɰɢɹ ɭɤɚɡɵɜɚɟɬ, ɱɬɨ ɞɥɹ ɞɚɧɧɨɣ ɝɪɭɩɩɵ ɲɚɯɬ
ɭɜɟɥɢɱɟɧɢɟ ɫɤɨɪɨɫɬɢ ɨɱɢɫɬɧɵɯ ɪɚɛɨɬ ɨɛɭɫɥɚɜɥɢɜɚɟɬ ɭɜɟɥɢɱɟɧɢɟ ɲɚɝɚ ɩɟɪɜɢɱɧɨɝɨ (ɝɟɧɟɪɚɥɶɧɨɝɨ) ɨɛɪɭɲɟɧɢɹ ɤɪɨɜɥɢ ɥɚɜɵ. ɍɜɟɥɢɱɟɧɢɟ ɤɪɢɬɢɱɟɫɤɨɝɨ ɪɚɡɦɟɪɚ ɜɵɪɚɛɨɬɚɧɧɨɝɨ
ɩɪɨɫɬɪɚɧɫɬɜɚ a ɫɜɹɡɚɧɨ ɫ ɢɡɦɟɧɟɧɢɟɦ ɩɪɨɱɧɨɫɬɢ ɩɨɪɨɞ. ɇɚ ɷɬɨ ɭɤɚɡɵɜɚɟɬ ɨɛɳɢɣ
ɯɚɪɚɤɬɟɪ ɡɚɜɢɫɢɦɨɫɬɟɣ (6) ɢ (7).
6. ȼɵɜɨɞɵ
ɍɜɟɥɢɱɟɧɢɟ ɬɟɦɩɨɜ ɨɱɢɫɬɧɵɯ ɪɚɛɨɬ ɜ ɭɝɨɥɶɧɵɯ ɲɚɯɬɚɯ ɨɛɭɫɥɨɜɥɢɜɚɟɬ ɭɜɟɥɢɱɟɧɢɟ
ɫɤɨɪɨɫɬɢ ɨɛɧɚɠɟɧɢɹ ɩɨɪɨɞ, ɱɬɨ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɨɡɧɚɱɚɟɬ ɭɜɟɥɢɱɟɧɢɟ ɫɤɨɪɨɫɬɢ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɹ ɧɚɩɪɹɠɟɧɢɣ ɜ ɫɬɪɭɤɬɭɪɧɵɯ ɷɥɟɦɟɧɬɚɯ ɩɨɪɨɞɧɨɝɨ ɦɚɫɫɢɜɚ ɜɛɥɢɡɢ
ɨɛɧɚɠɟɧɢɹ. ɍɜɟɥɢɱɟɧɢɟ ɫɤɨɪɨɫɬɢ ɩɟɪɟɪɚɫɩɪɟɞɟɥɟɧɢɹ ɧɚɩɪɹɠɟɧɢɣ ɜ ɩɨɪɨɞɚɯ ɜɵɡɵɜɚɟɬ
ɢɯ ɭɩɪɨɱɧɟɧɢɟ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɬɪɭɤɬɭɪɧɵɯ ɨɫɨɛɟɧɧɨɫɬɟɣ ɩɨɪɨɞ. ɉɪɟɞɥɨɠɟɧɚ
ɦɟɬɨɞɢɤɚ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɇȾɋ ɩɨɪɨɞɧɨɝɨ ɦɚɫɫɢɜɚ ɫ ɭɱɟɬɨɦ ɭɜɟɥɢɱɟɧɢɹ ɫɤɨɪɨɫɬɢ
ɨɛɧɚɠɟɧɢɹ.
ɅɂɌȿɊȺɌɍɊȺ
[1] Mansurov V.A.: Povedenie gornyh porod pri razlichnyh skorostjah nagruzhenija. Frunzev Izdatel’stvo, Ilim, 1982. s. 84
[2] Skipochka S.I., Usachenko B.M., Kuklin V.Ju.: Elementy geomehaniki porodnogo massiva pri
vysokih skorostjah podviganija lav. Dnepropetrovsk, ChP Lira LTD, 2006. s. 248
[3] Han G., Shapiro S.: Statisticheskie modeli v inzhenernyh zadachah. Mir, 1969. s. 388
[4] Shashenko A.N., Sdvɭzhkova E.A., Gapeev S.N.: Deformiruemost’ i prochnost’ massivov gornyh porod: Monografija. Nacional’nyj gornyj universitet, 2008. s. 224
[5] Ivanov O.S.: Analiz faktoriv vplyvu na krok obvalennja porid pokrivli lavy v umovah vysokogo stupenju metamorfizmu porid. Naukovi praci Donec’kogo nacional’nogo tehnichnogo
universytetu. Serija „Girnycho-geologichna“ Redkol.: Bashkov Je. O. ta inshi., Vypusk 10
(151), 2009. s. 148–152