планирование эксперимента по исследованию напряженно

2015
ȼȿɋɌɇɂɄ ɉɇɂɉɍ
ɋɬɪɨɢɬɟɥɶɫɬɜɨ ɢ ɚɪɯɢɬɟɤɬɭɪɚ
ʋ1
DOI: 10.15593/2224-9826/2015.1.10
ɍȾɄ 624.137
Ⱥ.ɋ. Ʉɭɡɧɟɰɨɜɚ, Ⱥ.Ȼ. ɉɨɧɨɦɚɪɟɜ
ɉɟɪɦɫɤɢɣ ɧɚɰɢɨɧɚɥɶɧɵɣ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɢɣ ɩɨɥɢɬɟɯɧɢɱɟɫɤɢɣ ɭɧɢɜɟɪɫɢɬɟɬ,
ɉɟɪɦɶ, Ɋɨɫɫɢɹ
ɉɅȺɇɂɊɈȼȺɇɂȿ ɗɄɋɉȿɊɂɆȿɇɌȺ ɉɈ ɂɋɋɅȿȾɈȼȺɇɂɘ
ɇȺɉɊəɀȿɇɇɈ-ȾȿɎɈɊɆɂɊɈȼȺɇɇɈȽɈ ɋɈɋɌɈəɇɂə
ɇȺȽɊɍɀȿɇɇɈȽɈ ɆȺɋɋɂȼȺ ɎɂȻɊɈȺɊɆɂɊɈȼȺɇɇɈȽɈ
ȽɊɍɇɌȺ, ɇȺɏɈȾəɓȿȽɈɋə ɁȺ ɉɈȾɉɈɊɇɈɃ ɋɌȿɇɈɃ
ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɚɪɦɨɝɪɭɧɬɨɜɵɟ ɩɨɞɩɨɪɧɵɟ ɫɬɟɧɵ ɫɬɚɥɢ ɩɨɩɭɥɹɪɧɵɦ ɬɢɩɨɦ ɨɝɪɚɠɞɚɸɳɢɯ ɤɨɧɫɬɪɭɤɰɢɣ. ȼ ɤɚɱɟɫɬɜɟ ɚɪɦɚɬɭɪɵ ɦɨɝɭɬ ɩɪɢɦɟɧɹɬɶɫɹ ɦɟɬɚɥɥɢɱɟɫɤɢɟ ɫɟɬɤɢ, ɪɚɡɥɢɱɧɵɟ ɩɪɢɪɨɞɧɵɟ ɢɥɢ ɫɢɧɬɟɬɢɱɟɫɤɢɟ ɞɨɛɚɜɤɢ. Ɉɫɧɨɜɧɵɦɢ ɞɨɫɬɨɢɧɫɬɜɚɦɢ ɚɪɦɢɪɨɜɚɧɧɵɯ ɩɨɞɩɨɪɧɵɯ ɫɬɟɧ ɹɜɥɹɸɬɫɹ ɢɯ ɩɪɢɧɰɢɩɢɚɥɶɧɚɹ ɩɪɨɫɬɨɬɚ, ɥɟɝɤɨɫɬɶ ɜɨɡɜɟɞɟɧɢɹ, ɫɧɢɠɟɧɢɟ ɦɚɬɟɪɢɚɥɨɡɚɬɪɚɬ. ɉɨɦɢɦɨ ɚɪɦɢɪɨɜɚɧɢɹ ɥɢɧɟɣɧɵɦɢ ɦɚɬɟɪɢɚɥɚɦɢ ɫɭɳɟɫɬɜɭɟɬ ɬɟɯɧɨɥɨɝɢɹ ɜɧɟɞɪɟɧɢɹ
ɜ ɝɪɭɧɬ ɫɥɭɱɚɣɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɵɯ ɞɢɫɤɪɟɬɧɵɯ ɜɨɥɨɤɨɧ – ɮɢɛɪɨɜɨɟ ɚɪɦɢɪɨɜɚɧɢɟ. Ɏɢɛɪɨɝɪɭɧɬ
ɢɦɟɟɬ ɭɥɭɱɲɟɧɧɵɟ ɩɪɨɱɧɨɫɬɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɛɥɚɝɨɞɚɪɹ ɱɟɦɭ ɨɞɧɨɣ ɢɡ ɩɟɪɫɩɟɤɬɢɜ ɟɝɨ
ɩɪɢɦɟɧɟɧɢɹ ɹɜɥɹɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɜ ɤɚɱɟɫɬɜɟ ɨɛɪɚɬɧɨɣ ɡɚɫɵɩɤɢ ɪɚɡɥɢɱɧɵɯ ɨɝɪɚɠɞɚɸɳɢɯ
ɤɨɧɫɬɪɭɤɰɢɣ.
ȼ ɫɬɚɬɶɟ ɩɪɟɞɫɬɚɜɥɟɧ ɩɥɚɧ ɦɨɞɟɥɶɧɵɯ ɢ ɱɢɫɥɟɧɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɨ ɢɫɫɥɟɞɨɜɚɧɢɸ
ɧɚɩɪɹɠɟɧɧɨ-ɞɟɮɨɪɦɢɪɨɜɚɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɦɚɫɫɢɜɚ ɝɪɭɧɬɚ, ɚɪɦɢɪɨɜɚɧɧɨɝɨ ɞɢɫɤɪɟɬɧɵɦɢ ɜɨɥɨɤɧɚɦɢ ɩɨɥɢɩɪɨɩɢɥɟɧɚ, ɧɚɯɨɞɹɳɟɝɨɫɹ ɡɚ ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɨɣ. Ɋɚɡɪɚɛɨɬɚɧɚ ɩɪɨɝɪɚɦɦɚ ɢɫɩɵɬɚɧɢɣ, ɫɨɫɬɨɹɳɚɹ ɢɡ ɱɟɬɵɪɟɯ ɫɟɪɢɣ, ɩɨ ɢɫɫɥɟɞɨɜɚɧɢɸ ɜɥɢɹɧɢɹ ɫɥɟɞɭɸɳɢɯ ɮɚɤɬɨɪɨɜ: ɫɨɞɟɪɠɚɧɢɹ ɚɪɦɢɪɭɸɳɢɯ ɜɨɥɨɤɨɧ, ɬɨɥɳɢɧɵ ɚɪɦɢɪɭɸɳɟɝɨ ɫɥɨɹ, ɜɵɫɨɬɵ ɫɬɟɧɵ, ɪɚɫɩɨɥɨɠɟɧɢɹ ɮɭɧɞɚɦɟɧɬɚ. ȼ ɤɚɠɞɨɣ ɫɟɪɢɢ ɩɥɚɧɢɪɭɟɬɫɹ ɨɰɟɧɤɚ ɜɥɢɹɧɢɹ ɨɞɧɨɝɨ ɮɚɤɬɨɪɚ ɩɪɢ ɩɨɫɬɨɹɧɧɵɯ ɞɪɭɝɢɯ.
ȼ ɤɚɱɟɫɬɜɟ ɩɚɪɚɦɟɬɪɨɜ ɞɥɹ ɨɰɟɧɤɢ ɜɜɨɞɹɬɫɹ ɜɟɥɢɱɢɧɵ ɤɨɷɮɮɢɰɢɟɧɬɚ ɧɟɫɭɳɟɣ ɫɩɨɫɨɛɧɨɫɬɢ
(Ʉɇɋ) ɢ ɢɧɞɟɤɫɚ ɞɟɮɨɪɦɢɪɭɟɦɨɫɬɢ (ɂȾ). ɉɨɞɪɨɛɧɨ ɨɩɢɫɚɧɚ ɦɟɬɨɞɢɤɚ ɩɨɞɝɨɬɨɜɤɢ ɥɚɛɨɪɚɬɨɪɧɨɝɨ ɫɬɟɧɞɚ ɞɥɹ ɢɫɩɵɬɚɧɢɣ ɦɨɞɟɥɟɣ ɮɭɧɞɚɦɟɧɬɚ ɢ ɨɛɪɚɛɨɬɤɢ ɩɨɥɭɱɟɧɧɵɯ ɪɟɡɭɥɶɬɚɬɨɜ. Ⱦɥɹ ɢɫɤɥɸɱɟɧɢɹ ɜɨɡɦɨɠɧɨɣ ɨɲɢɛɤɢ ɪɟɡɭɥɶɬɚɬɵ ɥɚɛɨɪɚɬɨɪɧɵɯ ɢɫɩɵɬɚɧɢɣ ɩɥɚɧɢɪɭɟɬɫɹ ɩɪɨɜɟɪɢɬɶ
ɦɟɬɨɞɨɦ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɜ ɩɪɨɝɪɚɦɦɟ PLAXIS 2D. ɑɢɫɥɟɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɩɪɨɜɨɞɢɬɫɹ
ɚɧɚɥɨɝɢɱɧɨ ɩɪɨɝɪɚɦɦɟ ɥɚɛɨɪɚɬɨɪɧɵɯ ɢɫɩɵɬɚɧɢɣ. Ⱦɥɹ ɢɧɬɟɪɩɪɟɬɚɰɢɢ ɪɟɡɭɥɶɬɚɬɨɜ ɧɚ ɩɨɥɧɨɦɚɫɲɬɚɛɧɭɸ ɦɨɞɟɥɶ ɫɭɳɟɫɬɜɭɟɬ ɪɹɞ ɨɝɪɚɧɢɱɟɧɢɣ, ɫɜɹɡɚɧɧɵɯ ɫ ɦɚɫɲɬɚɛɧɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ ɷɤɫɩɟɪɢɦɟɧɬɚ. Ⱦɚɧɵ ɩɨɹɫɧɟɧɢɹ ɨ ɫɧɢɠɟɧɢɢ ɜɥɢɹɧɢɹ ɧɟɤɨɬɨɪɵɯ ɨɝɪɚɧɢɱɢɜɚɸɳɢɯ ɮɚɤɬɨɪɨɜ,
ɬɚɤɢɯ ɤɚɤ ɪɚɡɦɟɪ ɱɚɫɬɢɰ, ɩɥɨɬɧɨɫɬɶ ɝɪɭɧɬɚ, ɷɮɮɟɤɬ ɬɪɟɧɢɹ ɢ ɞɪ.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɩɥɚɧɢɪɨɜɚɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚ, ɩɨɞɩɨɪɧɚɹ ɫɬɟɧɚ, ɮɢɛɪɨɜɨɟ ɚɪɦɢɪɨɜɚɧɢɟ, ɱɢɫɥɟɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ, ɢɫɩɵɬɚɧɢɹ ɜ ɥɨɬɤɟ.
135
Ⱥ.ɋ. Ʉɭɡɧɟɰɨɜɚ, Ⱥ.Ȼ. ɉɨɧɨɦɚɪɟɜ
A.S. Kuznetsova, A.B. Ponomarev
Perm National Research Polytechnic University, Perm, Russian Federation
EXPERIMENTAL DESIGN TO INVESTIGATE THE STRESSSTRAIN BEHAVIOR OF LOADED FIBER REINFORCED SOIL
MASS ADJACENT TO RETAINING WALL
Currently reinforced walls have become a popular type of retaining structures. Metal mesh, various natural or synthetic additives can be used as the reinforcement. The main advantages of reinforced
retaining walls are their fundamental simplicity, ease of construction, economy. In addition to the linear
reinforcement there is a technology there randomly distributed discrete fiber are introduced into the soil
- fiber reinforcement. Fibersoil has improved strength characteristics, so one of the prospects of its application is to use as backfill of different retaining structures.
The article presents a plan model and numerical experiments to investigate the stress-strain
state of soil reinforced with discrete polypropylene fibers adjacent to the retaining wall. Test program
consisting of four series are developed to evaluate the effect of the following factors: the content of the
reinforcing fibers, the thickness of the reinforcing layer, the location of the foundation. Each series is
planned to study the response of one parameter while the other variable parameters are constant. In
order to evaluate the fiber-reinforced effects the bearing capacity ratio and deformability index are introduced. The method how to prepare the laboratory stand for testing models and the interpretation of the
results are described in detail. To exclude possible error in results of laboratory tests finite element
analysis is planned in program PLAXIS 2D. Numerical simulation is similar to the laboratory tests program. To interpret the results on full-scale model there are some limitations associated with the scaling
factors of the experiment. Explanations are given to reduce the influence of some limiting factors, such
as particle size, material density, the friction effect and etc.
Keywords: experimental design, retaining walls, fiber reinforcement, numerical modeling, soil
box testing.
Ɉɫɨɛɨɟ ɦɟɫɬɨ ɜ ɫɬɪɨɢɬɟɥɶɧɨɣ ɩɪɚɤɬɢɤɟ ɡɚɧɢɦɚɟɬ ɩɪɨɟɤɬɢɪɨɜɚɧɢɟ
ɫɨɨɪɭɠɟɧɢɣ, ɧɚɯɨɞɹɳɢɯɫɹ ɧɚ ɤɪɭɬɵɯ ɝɪɭɧɬɨɜɵɯ ɨɬɤɨɫɚɯ, ɢɥɢ ɩɪɨɟɤɬɢɪɨɜɚɧɢɟ ɡɟɦɥɹɧɵɯ ɫɨɨɪɭɠɟɧɢɣ, ɬɚɤɢɯ ɤɚɤ ɞɚɦɛɵ, ɩɥɨɬɢɧɵ, ɧɚɫɵɩɢ,
ɝɥɭɛɨɤɢɟ ɤɨɬɥɨɜɚɧɵ. Ɉɬ ɬɨɝɨ, ɧɚɫɤɨɥɶɤɨ ɤɚɱɟɫɬɜɟɧɧɨ ɛɭɞɟɬ ɩɨɞɝɨɬɨɜɥɟɧ ɩɪɨɟɤɬ ɬɚɤɨɝɨ ɫɬɪɨɢɬɟɥɶɧɨɝɨ ɨɛɴɟɤɬɚ, ɚ ɬɚɤɠɟ ɨɬ ɫɬɟɩɟɧɢ ɜɧɢɦɚɧɢɹ
ɤ ɨɫɨɛɟɧɧɨɫɬɹɦ ɝɪɭɧɬɚ ɜɨ ɦɧɨɝɨɦ ɡɚɜɢɫɢɬ ɞɨɥɝɨɜɟɱɧɨɫɬɶ ɩɨɫɬɪɨɣɤɢ
ɢ ɛɟɡɨɩɚɫɧɨɫɬɶ ɟɟ ɷɤɫɩɥɭɚɬɚɰɢɢ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɩɟɪɜɨɨɱɟɪɟɞɧɨɣ ɡɚɞɚɱɟɣ ɢɧɠɟɧɟɪɨɜ-ɝɟɨɬɟɯɧɢɤɨɜ ɹɜɥɹɟɬɫɹ ɨɰɟɧɤɚ ɭɫɬɨɣɱɢɜɨɫɬɢ ɝɪɭɧɬɨɜɨɝɨ
ɦɚɫɫɢɜɚ. ɇɚɪɭɲɟɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɝɪɭɧɬɚ ɧɚ ɨɬɤɨɫɟ ɢɥɢ ɜ ɬɟɥɟ ɡɟɦɥɹɧɨɝɨ
ɫɨɨɪɭɠɟɧɢɹ ɦɨɠɟɬ ɩɪɢɜɟɫɬɢ ɤ ɫɟɪɶɟɡɧɵɦ ɩɨɫɥɟɞɫɬɜɢɹɦ ɢ ɞɚɠɟ ɤɚɬɚɫɬɪɨɮɚɦ. ȿɫɥɢ ɧɟɭɤɪɟɩɥɟɧɧɵɣ ɝɪɭɧɬɨɜɵɣ ɨɬɤɨɫ ɢɦɟɟɬ ɩɪɟɞɟɥɶɧɭɸ ɤɪɭɬɢɡɧɭ, ɜɨɡɧɢɤɚɟɬ ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɭɫɬɪɨɣɫɬɜɚ ɨɝɪɚɠɞɚɸɳɢɯ ɤɨɧɫɬɪɭɤɰɢɣ, ɬɚɤɢɯ ɤɚɤ ɩɨɞɩɨɪɧɵɟ ɫɬɟɧɵ. Ɉɫɧɨɜɧɨɟ ɧɚɡɧɚɱɟɧɢɟ ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɵ – ɭɤɪɟɩɥɟɧɢɟ ɝɪɭɧɬɚ ɧɚ ɨɬɤɨɫɚɯ, ɫɤɥɨɧɚɯ, ɚ ɬɚɤɠɟ ɩɪɟɞɨɬɜɪɚɳɟɧɢɟ
136
ɉɥɚɧɢɪɨɜɚɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚ ɩɨ ɢɫɫɥɟɞɨɜɚɧɢɸ…
ɨɛɪɭɲɟɧɢɹ ɢ ɫɩɨɥɡɚɧɢɹ ɝɪɭɧɬɚ ɧɚ ɭɱɚɫɬɤɚɯ, ɪɚɫɩɨɥɨɠɟɧɧɵɯ ɩɨ ɛɟɪɟɝɚɦ
ɪɟɤ, ɨɡɟɪ ɢ ɩɪɭɞɨɜ. ɇɚ ɭɫɬɨɣɱɢɜɨɫɬɶ ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɵ, ɩɨɦɢɦɨ ɝɟɨɦɟɬɪɢɱɟɫɤɢɯ ɨɫɨɛɟɧɧɨɫɬɟɣ ɢ ɫɜɨɣɫɬɜ ɦɚɬɟɪɢɚɥɚ, ɢɡ ɤɨɬɨɪɨɝɨ ɨɧɚ ɢɡɝɨɬɨɜɥɟɧɚ, ɫɭɳɟɫɬɜɟɧɧɨɟ ɜɥɢɹɧɢɟ ɨɤɚɡɵɜɚɸɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɝɪɭɧɬɚ ɨɛɪɚɬɧɨɣ ɡɚɫɵɩɤɢ. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɟɤɨɦɟɧɞɚɰɢɹɦɢ ɋɉ 43.133330.2012
«ɋɨɨɪɭɠɟɧɢɹ ɩɪɨɦɵɲɥɟɧɧɵɯ ɩɪɟɞɩɪɢɹɬɢɣ» ɞɥɹ ɫɧɢɠɟɧɢɹ ɞɚɜɥɟɧɢɹ
ɝɪɭɧɬɨɜɨɣ ɜɨɞɵ ɧɚ ɩɨɞɩɨɪɧɵɟ ɫɬɟɧɵ ɜ ɤɚɱɟɫɬɜɟ ɨɛɪɚɬɧɨɣ ɡɚɫɵɩɤɢ ɫɥɟɞɭɟɬ ɩɪɢɦɟɧɹɬɶ ɝɪɭɧɬɵ ɫ ɯɨɪɨɲɢɦɢ ɮɢɥɶɬɪɚɰɢɨɧɧɵɦɢ ɫɜɨɣɫɬɜɚɦɢ
(ɩɟɫɱɚɧɵɟ ɢɥɢ ɤɪɭɩɧɨɨɛɥɨɦɨɱɧɵɟ).
ȼ ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɚɤɬɢɜɧɨ ɩɪɢɦɟɧɹɸɬɫɹ ɚɪɦɨɝɪɭɧɬɨɜɵɟ ɩɨɞɩɨɪɧɵɟ ɫɬɟɧɵ, ɜ ɤɨɬɨɪɵɯ ɝɪɭɧɬ ɨɛɪɚɬɧɨɣ ɡɚɫɵɩɤɢ ɹɜɥɹɟɬɫɹ ɧɟɨɬɴɟɦɥɟɦɨɣ
ɱɚɫɬɶɸ ɤɨɧɫɬɪɭɤɰɢɢ. ȼ ɤɚɱɟɫɬɜɟ ɚɪɦɢɪɭɸɳɢɯ ɷɥɟɦɟɧɬɨɜ ɜɵɫɬɭɩɚɸɬ ɦɟɬɚɥɥɢɱɟɫɤɢɟ ɫɟɬɤɢ, ɚ ɬɚɤɠɟ ɪɚɡɥɢɱɧɵɟ ɩɪɢɪɨɞɧɵɟ ɢɥɢ ɫɢɧɬɟɬɢɱɟɫɤɢɟ
ɞɨɛɚɜɤɢ (ɩɥɚɫɬɦɚɫɫɵ, ɝɟɨɫɢɧɬɟɬɢɱɟɫɤɢɟ ɦɚɬɟɪɢɚɥɵ, ɬɨɧɤɢɟ ɫɬɚɥɢ). Ɍɟɯɧɨɥɨɝɢɹ ɫɬɪɨɢɬɟɥɶɫɬɜɚ ɚɪɦɨɝɪɭɧɬɨɜɨɣ ɤɨɧɫɬɪɭɤɰɢɢ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɩɨɫɥɨɣɧɨɣ ɭɤɥɚɞɤɟ ɭɩɥɨɬɧɟɧɧɨɝɨ ɝɪɭɧɬɚ ɢ ɚɪɦɚɬɭɪɵ. ȼ ɤɚɱɟɫɬɜɟ ɨɛɥɢɰɨɜɤɢ ɦɨɝɭɬ ɜɵɫɬɭɩɚɬɶ ɛɟɬɨɧɧɵɟ ɛɥɨɤɢ, ɩɚɧɟɥɢ, ɝɢɛɤɢɟ ɝɟɨɬɟɤɫɬɢɥɶɧɵɟ ɦɚɬɟɪɢɚɥɵ, ɝɚɛɢɨɧɵ. Ɍɚɤ, ɜ ɉɟɪɦɢ ɜɟɪɬɢɤɚɥɶɧɚɹ ɩɨɞɩɨɪɧɚɹ ɫɬɟɧɤɚ ɛɵɥɚ
ɜɨɡɜɟɞɟɧɚ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɫɬɚɥɶɧɨɣ ɚɪɦɚɬɭɪɧɨɣ ɫɟɬɤɢ ɫ ɪɚɡɦɟɪɨɦ
ɹɱɟɣɤɢ 100×100 ɦɦ, ɤɨɬɨɪɚɹ ɡɚɚɧɤɟɪɢɜɚɥɚɫɶ ɡɚ ɛɟɬɨɧɧɵɟ ɛɥɨɤɢ ɨɛɥɢɰɨɜɤɢ. ȼ ɤɚɱɟɫɬɜɟ ɨɛɪɚɬɧɨɣ ɡɚɫɵɩɤɢ ɛɵɥɚ ɩɪɟɞɭɫɦɨɬɪɟɧɚ ɬɳɚɬɟɥɶɧɨ ɭɩɥɨɬɧɟɧɧɚɹ ɩɟɫɱɚɧɨ-ɝɪɚɜɢɣɧɚɹ ɫɦɟɫɶ. ȼɵɫɨɬɚ ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɤɢ ɫɨɫɬɚɜɢɥɚ 10 ɦ [1].
Ɉɫɧɨɜɧɵɦɢ ɞɨɫɬɨɢɧɫɬɜɚɦɢ ɤɨɧɫɬɪɭɤɰɢɣ ɫ ɩɪɢɦɟɧɟɧɢɟɦ ɚɪɦɢɪɨɜɚɧɢɹ ɹɜɥɹɸɬɫɹ ɢɯ ɩɪɢɧɰɢɩɢɚɥɶɧɚɹ ɩɪɨɫɬɨɬɚ, ɥɟɝɤɨɫɬɶ ɜɨɡɜɟɞɟɧɢɹ,
ɫɧɢɠɟɧɢɟ ɦɚɬɟɪɢɚɥɨɡɚɬɪɚɬ. ɉɪɢ ɝɪɚɦɨɬɧɨɦ ɩɪɨɟɤɬɢɪɨɜɚɧɢɢ ɢ ɫɬɪɨɢɬɟɥɶɫɬɜɟ ɩɪɢɦɟɧɟɧɢɟ ɚɪɦɨɝɪɭɧɬɨɜɵɯ ɤɨɧɫɬɪɭɤɰɢɣ ɫɩɨɫɨɛɧɨ ɪɟɲɢɬɶ
ɛɨɥɶɲɢɧɫɬɜɨ ɡɚɞɚɱ ɫɨɜɪɟɦɟɧɧɨɣ ɝɟɨɬɟɯɧɢɤɢ.
ɇɟɫɦɨɬɪɹ ɧɚ ɛɨɥɶɲɨɣ ɨɩɵɬ ɩɪɢɦɟɧɟɧɢɹ ɚɪɦɨɝɪɭɧɬɨɜɵɯ ɤɨɧɫɬɪɭɤɰɢɣ ɜɨ ɦɧɨɝɢɯ ɨɛɥɚɫɬɹɯ ɩɪɨɦɵɲɥɟɧɧɨɝɨ ɢ ɝɪɚɠɞɚɧɫɤɨɝɨ ɫɬɪɨɢɬɟɥɶɫɬɜɚ,
ɫɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɫɭɳɟɫɬɜɭɟɬ ɧɟɞɨɫɬɚɬɨɱɧɨ ɢɡɭɱɟɧɧɚɹ ɬɟɯɧɨɥɨɝɢɹ
ɫɦɟɲɢɜɚɧɢɹ ɝɪɭɧɬɚ ɫ ɞɢɫɤɪɟɬɧɵɦɢ ɜɨɥɨɤɧɚɦɢ, ɬɚɤ ɧɚɡɵɜɚɟɦɨɟ ɮɢɛɪɨɚɪɦɢɪɨɜɚɧɢɟ. Ʉɨɧɰɟɩɰɢɹ ɮɢɛɪɨɜɨɝɨ ɚɪɦɢɪɨɜɚɧɢɹ ɩɨɞɫɤɚɡɚɧɚ ɩɪɢɪɨɞɨɣ.
ɉɪɢɦɟɪɨɦ ɟɫɬɟɫɬɜɟɧɧɨɝɨ ɜɤɥɸɱɟɧɢɹ ɫɥɭɱɚɣɧɨ ɨɪɢɟɧɬɢɪɨɜɚɧɧɵɯ ɜɨɥɨɤɨɧ ɜ ɝɪɭɧɬ ɹɜɥɹɸɬɫɹ ɤɨɪɧɢ ɪɚɫɬɟɧɢɣ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɤɨɪɧɢ ɪɚɫɬɟɧɢɣ
ɭɥɭɱɲɚɸɬ ɫɞɜɢɝɨɜɭɸ ɩɪɨɱɧɨɫɬɶ ɝɪɭɧɬɚ ɢ ɨɛɟɫɩɟɱɢɜɚɸɬ ɭɫɬɨɣɱɢɜɨɫɬɶ
ɩɪɢɪɨɞɧɵɯ ɫɤɥɨɧɨɜ [2].
137
Ⱥ.ɋ. Ʉɭɡɧɟɰɨɜɚ, Ⱥ.Ȼ. ɉɨɧɨɦɚɪɟɜ
Ɋɟɡɭɥɶɬɚɬɵ ɥɚɛɨɪɚɬɨɪɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɣ [2–6] ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ
ɜɨɥɨɤɧɚ ɮɢɛɪɵ, ɜɧɟɞɪɟɧɧɵɟ ɜ ɝɪɭɧɬ, ɩɨɜɵɲɚɸɬ ɩɪɨɱɧɨɫɬɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɟɫɱɚɧɨɝɨ ɝɪɭɧɬɚ. ɋɨɜɦɟɫɬɧɚɹ ɪɚɛɨɬɚ ɨɬɞɟɥɶɧɵɯ ɜɨɥɨɤɨɧ
ɢ ɱɚɫɬɢɰ ɝɪɭɧɬɚ ɫɩɨɫɨɛɫɬɜɭɟɬ ɩɨɹɜɥɟɧɢɸ ɭ ɧɟɫɜɹɡɧɨɝɨ ɝɪɭɧɬɚ ɭɞɟɥɶɧɨɝɨ ɫɰɟɩɥɟɧɢɹ ɢ ɭɜɟɥɢɱɟɧɢɸ ɭɝɥɚ ɜɧɭɬɪɟɧɧɟɝɨ ɬɪɟɧɢɹ. Ɍɚɤɨɣ ɦɚɬɟɪɢɚɥ
ɢɦɟɟɬ ɯɨɪɨɲɢɟ ɮɢɥɶɬɪɚɰɢɨɧɧɵɟ ɫɜɨɣɫɬɜɚ ɢ ɛɭɞɟɬ ɨɤɚɡɵɜɚɬɶ ɦɟɧɶɲɟɟ
ɚɤɬɢɜɧɨɟ ɞɚɜɥɟɧɢɟ ɧɚ ɨɝɪɚɠɞɟɧɢɹ ɡɚ ɫɱɟɬ ɭɜɟɥɢɱɟɧɧɨɝɨ ɡɧɚɱɟɧɢɹ ɭɝɥɚ
ɜɧɭɬɪɟɧɧɟɝɨ ɬɪɟɧɢɹ ɢ ɭɞɟɥɶɧɨɝɨ ɫɰɟɩɥɟɧɢɹ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɨɞɧɨɣ ɢɡ
ɩɟɪɫɩɟɤɬɢɜɧɵɯ ɨɛɥɚɫɬɟɣ ɩɪɢɦɟɧɟɧɢɹ ɬɚɤɨɝɨ ɦɚɬɟɪɢɚɥɚ ɦɨɠɟɬ ɫɬɚɬɶ
ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɟɝɨ ɜ ɤɚɱɟɫɬɜɟ ɨɛɪɚɬɧɨɣ ɡɚɫɵɩɤɢ ɪɚɡɥɢɱɧɵɯ ɨɝɪɚɠɞɚɸɳɢɯ ɤɨɧɫɬɪɭɤɰɢɣ [3].
Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɯɚɪɚɤɬɟɪɚ ɪɚɛɨɬɵ ɦɚɫɫɢɜɚ ɝɪɭɧɬɚ, ɚɪɦɢɪɨɜɚɧɧɨɝɨ ɞɢɫɤɪɟɬɧɵɦɢ ɜɨɥɨɤɧɚɦɢ ɩɨɥɢɩɪɨɩɢɥɟɧɚ, ɧɚɯɨɞɹɳɟɝɨɫɹ ɡɚ ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɨɣ, ɢ ɩɨɥɭɱɟɧɢɹ ɷɦɩɢɪɢɱɟɫɤɢɯ ɡɚɜɢɫɢɦɨɫɬɟɣ ɜɥɢɹɧɢɹ ɪɚɡɥɢɱɧɵɯ ɮɚɤɬɨɪɨɜ ɧɚ ɩɨɜɟɞɟɧɢɟ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɤɨɧɫɬɪɭɤɰɢɢ ɧɟɨɛɯɨɞɢɦɨ
ɩɪɨɜɟɫɬɢ ɨɩɪɟɞɟɥɟɧɧɵɣ ɨɛɴɟɦ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɣ.
ɐɟɥɶɸ ɞɚɧɧɨɣ ɪɚɛɨɬɵ ɹɜɥɹɟɬɫɹ ɫɨɫɬɚɜɥɟɧɢɟ ɩɪɨɝɪɚɦɦɵ ɥɚɛɨɪɚɬɨɪɧɵɯ
ɢ ɱɢɫɥɟɧɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɞɥɹ ɞɚɥɶɧɟɣɲɟɝɨ ɢɫɫɥɟɞɨɜɚɧɢɹ ɜɨɡɦɨɠɧɨɫɬɢ ɩɪɢɦɟɧɟɧɢɹ ɢ ɜɥɢɹɧɢɹ ɨɛɪɚɬɧɨɣ ɡɚɫɵɩɤɢ ɢɡ ɮɢɛɪɨɚɪɦɢɪɨɜɚɧɧɨɝɨ
ɝɪɭɧɬɚ ɜ ɚɤɬɢɜɧɨɣ ɡɨɧɟ. Ɉɩɬɢɦɚɥɶɧɨɟ ɩɥɚɧɢɪɨɜɚɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚ
ɩɪɟɞɩɨɥɚɝɚɟɬ ɨɞɧɨɜɪɟɦɟɧɧɨɟ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɟ ɢɡɦɟɧɟɧɢɟ ɜɫɟɯ ɜɯɨɞɧɵɯ ɩɚɪɚɦɟɬɪɨɜ, ɜɥɢɹɸɳɢɯ ɧɚ ɤɚɱɟɫɬɜɨ ɢɫɫɥɟɞɭɟɦɨɝɨ ɦɚɬɟɪɢɚɥɚ, ɢ ɩɨɡɜɨɥɹɟɬ ɭɫɬɚɧɨɜɢɬɶ ɩɨ ɫɩɟɰɢɚɥɶɧɨ ɫɮɨɪɦɭɥɢɪɨɜɚɧɧɵɦ ɩɪɚɜɢɥɚɦ ɡɚɜɢɫɢɦɨɫɬɶ ɦɨɞɟɥɢ ɤɚɱɟɫɬɜɚ ɦɚɬɟɪɢɚɥɚ ɨɬ ɷɬɢɯ ɩɚɪɚɦɟɬɪɨɜ [7].
ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɢɫɫɥɟɞɨɜɚɧɢɹ ɦɨɞɟɥɢ ɧɚɝɪɭɠɟɧɧɨɝɨ ɦɚɫɫɢɜɚ
ɝɪɭɧɬɚ ɡɚ ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɨɣ ɛɭɞɭɬ ɩɪɨɜɨɞɢɬɶɫɹ ɧɚ ɦɚɬɟɪɢɚɥɶɧɨɬɟɯɧɢɱɟɫɤɨɣ ɛɚɡɟ ɷɤɫɩɟɪɬɧɨɣ ɥɚɛɨɪɚɬɨɪɢɢ ɤɚɮɟɞɪɵ «ɋɬɪɨɢɬɟɥɶɧɨɟ
ɩɪɨɢɡɜɨɞɫɬɜɨ ɢ ɝɟɨɬɟɯɧɢɤɚ» ɉɟɪɦɫɤɨɝɨ ɧɚɰɢɨɧɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɨɝɨ ɩɨɥɢɬɟɯɧɢɱɟɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ.
ȼ ɦɨɞɟɥɶɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɚɯ ɩɪɢɦɟɧɹɟɬɫɹ ɩɟɫɱɚɧɵɣ ɝɪɭɧɬ, ɮɢɡɢɱɟɫɤɢɟ ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɤɨɬɨɪɨɝɨ ɛɵɥɢ ɩɨɥɭɱɟɧɵ ɩɨ
ɪɟɡɭɥɶɬɚɬɚɦ ɥɚɛɨɪɚɬɨɪɧɵɯ ɢɫɩɵɬɚɧɢɣ (ɬɚɛɥ. 1) [8].
Ⱦɥɹ ɚɪɦɢɪɨɜɚɧɢɹ ɢɫɩɨɥɶɡɭɟɬɫɹ ɩɨɥɢɩɪɨɩɢɥɟɧɨɜɚɹ ɮɢɛɪɚ ɤɪɭɝɥɨɝɨ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɞɥɢɧɨɣ 12 ɦɦ. ɉɨɥɢɩɪɨɩɢɥɟɧɨɜɨɟ ɜɨɥɨɤɧɨ ɹɜɥɹɟɬɫɹ ɷɮɮɟɤɬɢɜɧɨɣ ɚɪɦɢɪɭɸɳɟɣ ɞɨɛɚɜɤɨɣ ɞɥɹ ɛɟɬɨɧɚ ɢ ɧɚɢɛɨɥɟɟ ɩɨɩɭɥɹɪɧɵɦ ɦɚɬɟɪɢɚɥɨɦ, ɩɪɢɦɟɧɹɟɦɵɦ ɜ ɤɚɱɟɫɬɜɟ ɮɢɛɪɨɜɨɝɨ
ɚɪɦɢɪɨɜɚɧɢɹ ɝɪɭɧɬɨɜ [5]. Ⱦɢɚɦɟɬɪ ɷɥɟɦɟɧɬɚɪɧɨɝɨ ɮɢɛɪɨɜɨɥɨɤɧɚ ɫɨ138
ɉɥɚɧɢɪɨɜɚɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚ ɩɨ ɢɫɫɥɟɞɨɜɚɧɢɸ…
ɫɬɚɜɥɹɟɬ 0,025–0,035 ɦɦ, ɩɥɨɬɧɨɫɬɶ ɜɨɥɨɤɨɧ 0,91 ɝ/ɫɦ3. Ɇɨɞɭɥɶ ɭɩɪɭɝɨɫɬɢ ɩɪɢ ɢɡɝɢɛɟ ɢɫɩɨɥɶɡɭɟɦɨɝɨ ɩɨɥɢɩɪɨɩɢɥɟɧɨɜɨɝɨ ɜɨɥɨɤɧɚ ɧɟ
ɦɟɧɟɟ 1050 Ɇɉɚ.
Ɍɚɛɥɢɰɚ 1
Ɏɢɡɢɱɟɫɤɢɟ ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɟɫɱɚɧɨɝɨ ɝɪɭɧɬɚ
ʋ
ɩ/ɩ
1
2
3
4
5
6
7
8
9
10
ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ
Ɂɧɚɱɟɧɢɹ
ɉɨ ɝɪɚɧɭɥɨɦɟɬɪɢɱɟɫɤɨɦɭ ɫɨɫɬɚɜɭ ɩɨ ȽɈɋɌ 25100–2011
ɉɨ ɨɞɧɨɪɨɞɧɨɫɬɢ ɩɨ ȽɈɋɌ 25100–2011
ɍɞɟɥɶɧɵɣ ɜɟɫ ɝɪɭɧɬɚ Ȗ, ɤɇ/ɦ3
ɍɞɟɥɶɧɵɣ ɜɟɫ ɬɜɟɪɞɵɯ ɱɚɫɬɢɰ Ȗs, ɤɇ/ɦ3
ɍɞɟɥɶɧɵɣ ɜɟɫ ɫɭɯɨɝɨ ɝɪɭɧɬɚ Ȗd, ɤɇ/ɦ3
Ʉɨɷɮɮɢɰɢɟɧɬ ɩɨɪɢɫɬɨɫɬɢ ɟ
Ʉɨɷɮɮɢɰɢɟɧɬ ɮɢɥɶɬɪɚɰɢɢ Kɮ, ɦ/ɫɭɬ
ɍɝɨɥ ɜɧɭɬɪɟɧɧɟɝɨ ɬɪɟɧɢɹ ij, ɝɪɚɞ
ɍɞɟɥɶɧɨɟ ɫɰɟɩɥɟɧɢɟ ɫ, ɤɉɚ
Ɇɨɞɭɥɶ ɨɛɳɟɣ ɞɟɮɨɪɦɚɰɢɢ ȿɨ, Ɇɉɚ
ɉɟɫɨɤ ɦɟɥɤɨɡɟɪɧɢɫɬɵɣ
ɉɟɫɨɤ ɨɞɧɨɪɨɞɧɵɣ
16,4
26,0
16,3
0,6
2,6
33
3
33
Ⱦɥɹ ɥɚɛɨɪɚɬɨɪɧɵɯ ɢɫɩɵɬɚɧɢɣ ɦɚɥɨɦɚɫɲɬɚɛɧɵɯ ɦɨɞɟɥɟɣ ɛɭɞɟɬ
ɢɫɩɨɥɶɡɨɜɚɬɶɫɹ ɫɬɟɧɞ, ɤɨɧɫɬɪɭɤɰɢɹ ɤɨɬɨɪɨɝɨ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 1.
ɋɬɟɧɞ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɩɥɨɫɤɢɣ ɥɨɬɨɤ ɫ ɩɪɨɡɪɚɱɧɵɦɢ ɩɟɪɟɞɧɟɣ ɢ
ɡɚɞɧɟɣ ɫɬɟɧɤɚɦɢ, ɜɵɩɨɥɧɟɧɧɵɦɢ ɢɡ ɨɪɝɫɬɟɤɥɚ ɬɨɥɳɢɧɨɣ 50 ɦɦ. Ⱦɥɹ
ɢɫɤɥɸɱɟɧɢɹ ɩɪɨɝɢɛɚ ɩɪɨɡɪɚɱɧɵɯ ɫɬɟɧɨɤ ɩɪɢɦɟɧɟɧɵ ɞɜɟ ɫɬɚɥɶɧɵɟ ɪɟɲɟɬɤɢ, ɜ ɭɡɥɚɯ ɤɨɬɨɪɵɯ ɧɚɯɨɞɹɬɫɹ ɨɩɨɪɧɵɟ ɲɚɣɛɵ. ɋɬɟɧɞ ɢɦɟɟɬ ɨɛɳɢɟ
ɝɚɛɚɪɢɬɵ 1200×2100×1000 ɦɦ, ɲɢɪɢɧɚ ɥɨɬɤɚ ɪɟɝɭɥɢɪɭɟɬɫɹ ɜ ɩɪɟɞɟɥɚɯ
156–300 ɦɦ [9]. Ⱦɚɧɧɨɟ ɨɛɨɪɭɞɨɜɚɧɢɟ ɩɪɟɞɧɚɡɧɚɱɟɧɨ ɞɥɹ ɜɵɩɨɥɧɟɧɢɹ
ɥɚɛɨɪɚɬɨɪɧɵɯ ɢ ɧɚɭɱɧɨ-ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɢɯ ɪɚɛɨɬ ɢ ɩɨɡɜɨɥɹɟɬ ɩɪɨɜɨɞɢɬɶ ɜ ɭɫɥɨɜɢɹɯ ɩɥɨɫɤɨɣ ɢ ɨɫɟɫɢɦɦɟɬɪɢɱɧɨɣ ɞɟɮɨɪɦɚɰɢɢ ɢɫɩɵɬɚɧɢɹ
ɦɨɞɟɥɢ ɥɟɧɬɨɱɧɨɝɨ ɮɭɧɞɚɦɟɧɬɚ, ɪɨɥɶ ɤɨɬɨɪɨɝɨ ɢɝɪɚɟɬ ɠɟɫɬɤɢɣ ɲɬɚɦɩ.
ȼɧɟɲɧɹɹ ɧɚɝɪɭɡɤɚ ɫɨɡɞɚɟɬɫɹ ɭɫɬɚɧɨɜɤɨɣ ɫɬɟɩɟɧɹɦɢ ɩɪɢ ɩɨɦɨɳɢ ɤɨɦɩɪɟɫɫɨɪɚ ɩɨɞ ɭɩɪɚɜɥɟɧɢɟɦ ɩɧɟɜɦɨɰɢɥɢɧɞɪɚ, ɢ ɦɨɠɟɬ ɩɪɢɤɥɚɞɵɜɚɬɶɫɹ
ɤɚɤ ɜɞɚɜɥɢɜɚɸɳɟɟ, ɬɚɤ ɢ ɜɵɞɟɪɝɢɜɚɸɳɟɟ ɭɫɢɥɢɟ ɜɟɪɬɢɤɚɥɶɧɨ ɢɥɢ ɧɚɤɥɨɧɧɨ, ɫ ɭɝɥɨɦ ɧɚɤɥɨɧɚ ɞɨ 60° ɨɬ ɜɟɪɬɢɤɚɥɢ. ȼɟɪɬɢɤɚɥɶɧɨɟ ɩɟɪɟɦɟɳɟɧɢɟ ɦɨɞɟɥɢ ɮɭɧɞɚɦɟɧɬɚ ɢɡɦɟɪɹɟɬɫɹ ɞɚɬɱɢɤɨɦ ɩɟɪɟɦɟɳɟɧɢɹ, ɚ ɧɚɝɪɭɡɤɚ – ɞɚɬɱɢɤɨɦ ɫɢɥɵ. ɍɩɪɚɜɥɟɧɢɟ ɩɪɨɰɟɫɫɨɦ ɢɫɩɵɬɚɧɢɣ ɜɵɩɨɥɧɹɟɬɫɹ
ɚɜɬɨɦɚɬɢɱɟɫɤɢ, ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɨɝɪɚɦɦɵ Geotek-Ⱥɋɂɋ3.2 [10].
ɉɪɟɢɦɭɳɟɫɬɜɚɦɢ ɬɚɤɨɣ ɤɨɧɫɬɪɭɤɰɢɢ ɹɜɥɹɸɬɫɹ ɛɨɥɶɲɚɹ ɬɨɱɧɨɫɬɶ ɫɧɢɦɚɟɦɵɯ ɩɨɤɚɡɚɧɢɣ, ɚɜɬɨɦɚɬɢɱɟɫɤɚɹ ɝɟɧɟɪɚɰɢɹ ɨɬɱɟɬɨɜ, ɩɨɞɝɨɬɨɜɤɚ ɪɟ139
Ⱥ.ɋ. Ʉɭɡɧɟɰɨɜɚ, Ⱥ.Ȼ. ɉɨɧɨɦɚɪɟɜ
ɡɭɥɶɬɚɬɨɜ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɞɥɹ ɞɚɥɶɧɟɣɲɟɝɨ ɪɚɫɱɟɬɚ. ȼ ɦɨɞɟɥɶɧɵɯ ɢɫɩɵɬɚɧɢɹɯ ɞɥɹ ɫɧɢɠɟɧɢɹ ɷɮɮɟɤɬɚ ɬɪɟɧɢɹ ɫɬɟɧɵ ɢɫɩɵɬɚɬɟɥɶɧɨɝɨ ɫɬɟɧɞɚ
ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɫɦɚɡɚɬɶ ɦɚɫɥɨɦ [11].
ȼ ɩɥɚɧɢɪɭɟɦɨɦ ɷɤɫɩɟɪɢɦɟɧɬɟ ɛɭɞɟɬ ɪɚɫɫɦɚɬɪɢɜɚɬɶɫɹ ɦɨɞɟɥɶ
ɮɭɧɞɚɦɟɧɬɚ, ɪɚɫɩɨɥɨɠɟɧɧɨɝɨ ɧɚ ɝɪɭɧɬɨɜɨɦ ɦɚɫɫɢɜɟ ɡɚ ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɨɣ. ɋɯɟɦɚ ɢɫɩɵɬɚɧɢɣ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ. 2.
Ɋɢɫ. 1. ɋɬɟɧɞ ɞɥɹ ɢɫɩɵɬɚɧɢɣ ɦɨɞɟɥɟɣ ɮɭɧɞɚɦɟɧɬɨɜ:
1, 2 – ɩɟɪɟɞɧɹɹ ɢ ɡɚɞɧɹɹ ɫɬɟɧɤɢ; 3 – ɫɬɚɥɶɧɚɹ ɪɟɲɟɬɤɚ;
4 – ɨɩɨɪɧɚɹ ɲɚɣɛɚ
Ɋɢɫ. 2. ɋɯɟɦɚ ɦɨɞɟɥɶɧɵɯ ɢɫɩɵɬɚɧɢɣ: H – ɜɵɫɨɬɚ ɫɬɟɧɵ;
h – ɬɨɥɳɢɧɚ ɚɪɦɢɪɭɟɦɨɝɨ ɫɥɨɹ; X – ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɮɭɧɞɚɦɟɧɬɚ ɞɨ ɫɬɟɧɵ
140
ɉɥɚɧɢɪɨɜɚɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚ ɩɨ ɢɫɫɥɟɞɨɜɚɧɢɸ…
Ɋɚɡɦɟɪ ɮɭɧɞɚɦɟɧɬɚ, ɮɭɧɤɰɢɸ ɤɨɬɨɪɨɝɨ ɜɵɩɨɥɧɹɟɬ ɠɟɫɬɤɢɣ ɲɬɚɦɩ,
ɛɭɞɟɬ ɫɨɫɬɚɜɥɹɬɶ 50×156 ɦɦ. Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɭɫɥɨɜɢɣ ɩɥɨɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ ɞɥɢɧɚ ɮɭɧɞɚɦɟɧɬɚ ɪɚɜɧɚ ɲɢɪɢɧɟ ɥɨɬɤɚ. ȼɫɟ ɢɫɩɵɬɚɧɢɹ ɩɪɨɜɨɞɹɬɫɹ
ɩɪɢ ɧɟɩɨɞɜɢɠɧɨɦ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɨɜɟɪɯɧɨɫɬɢ ɝɪɭɧɬɚ ɲɬɚɦɩɟ. ɋ ɰɟɥɶɸ
ɧɚɢɛɨɥɶɲɟɝɨ ɩɪɢɛɥɢɠɟɧɢɹ ɤ ɪɟɚɥɶɧɵɦ ɭɫɥɨɜɢɹɦ ɲɟɪɲɚɜɚɹ ɩɨɜɟɪɯɧɨɫɬɶ
ɮɭɧɞɚɦɟɧɬɚ ɞɨɫɬɢɝɚɟɬɫɹ ɩɭɬɟɦ ɩɪɢɫɨɟɞɢɧɟɧɢɹ ɤ ɲɬɚɦɩɭ ɧɚɠɞɚɱɧɨɣ ɛɭɦɚɝɢ [11].
ɉɨɞɩɨɪɧɚɹ ɫɬɟɧɚ ɛɭɞɟɬ ɦɨɞɟɥɢɪɨɜɚɬɶɫɹ ɩɪɢ ɩɨɦɨɳɢ ɫɬɚɥɶɧɨɣ ɩɥɚɫɬɢɧɵ ɞɥɢɧɨɣ 750 ɦɦ ɢ ɬɨɥɳɢɧɨɣ 3 ɦɦ. ɉɥɚɫɬɢɧɚ ɛɭɞɟɬ ɡɚɝɥɭɛɥɟɧɚ
ɜ ɩɟɫɱɚɧɵɣ ɝɪɭɧɬɚ ɧɚ 500 ɦɦ. Ɉɫɧɨɜɚɧɢɟ ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɵ ɧɟɨɛɯɨɞɢɦɨ
ɭɦɟɧɶɲɢɬɶ ɞɥɹ ɛɨɥɟɟ ɥɟɝɤɨɝɨ ɩɨɝɪɭɠɟɧɢɹ ɜ ɝɪɭɧɬ. Ⱦɥɹ ɫɧɢɠɟɧɢɹ ɷɮɮɟɤɬɚ ɬɪɟɧɢɹ ɫɬɚɥɶɧɚɹ ɩɥɚɫɬɢɧɚ ɞɨɥɠɧɚ ɛɵɬɶ ɝɥɚɞɤɨ ɨɬɩɨɥɢɪɨɜɚɧɚ [11]. Ⱦɥɹ
ɮɢɤɫɚɰɢɢ ɛɨɤɨɜɨɝɨ ɨɬɤɥɨɧɟɧɢɹ ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɵ ɩɨɞ ɧɚɝɪɭɡɤɨɣ ɨɬ ɮɭɧɞɚɦɟɧɬɚ ɧɟɨɛɯɨɞɢɦɨ ɭɫɬɚɧɨɜɢɬɶ ɞɚɬɱɢɤɢ ɥɢɧɟɣɧɵɯ ɩɟɪɟɦɟɳɟɧɢɣ.
ɉɪɟɞɩɨɥɚɝɚɟɬɫɹ ɭɫɬɚɧɨɜɤɚ ɱɟɬɵɪɟɯ ɞɚɬɱɢɤɨɜ ɩɨ ɜɵɫɨɬɟ ɜ ɰɟɧɬɪɟ ɫɬɟɧɵ.
Ɏɢɛɪɨɝɪɭɧɬ ɝɨɬɨɜɢɬɫɹ ɢɡ ɫɦɟɫɢ ɡɚɞɚɧɧɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɜɨɥɨɤɨɧ
ɩɨɥɢɩɪɨɩɢɥɟɧɚ ɢ ɩɟɫɤɚ ɨɩɬɢɦɚɥɶɧɨɣ ɜɥɚɠɧɨɫɬɢ, ɧɚɣɞɟɧɧɨɣ ɢɡ ɢɫɩɵɬɚɧɢɣ ɫɬɚɧɞɚɪɬɧɨɝɨ ɭɩɥɨɬɧɟɧɢɹ. ȼ ɦɨɞɟɥɶɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɚɯ ɩɪɢɧɢɦɚɟɬɫɹ ɩɪɨɰɟɧɬɧɨɟ ɫɨɞɟɪɠɚɧɢɟ ɮɢɛɪɵ kɮ, ɪɚɜɧɨɟ 0,5; 1,0; 1,5 ɨɛɴɟɦɧɵɯ
ɩɪɨɰɟɧɬɚ, ɤɨɬɨɪɨɟ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
kɮ =
Vɮ
mɮ ⋅ ȡ ɩ
⋅100 % =
⋅100 %,
Vɩ
mɩ ⋅ ȡɮ
(1)
ɝɞɟ V ɮ , mɮ , ȡɮ – ɨɛɴɟɦ, ɦɚɫɫɚ ɢ ɩɥɨɬɧɨɫɬɶ ɩɨɥɢɩɪɨɩɢɥɟɧɨɜɨɣ ɮɢɛɪɵ;
V ɩ , mɩ , ȡ ɩ – ɨɛɴɟɦ, ɦɚɫɫɚ ɢ ɩɥɨɬɧɨɫɬɶ ɩɟɫɱɚɧɨɝɨ ɝɪɭɧɬɚ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ.
Ɂɚɩɨɥɧɟɧɢɟ ɫɬɟɧɞɚ ɩɟɫɤɨɦ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɨɫɥɨɣɧɨ ɦɟɬɨɞɨɦ
ɪɚɫɫɟɢɜɚɧɢɹ ɩɨ ɜɨɡɞɭɯɭ. Ⱦɥɹ ɞɨɫɬɢɠɟɧɢɹ ɡɚɞɚɧɧɨɣ ɩɥɨɬɧɨɫɬɢ ɨɫɧɨɜɚɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɨɩɪɟɞɟɥɢɬɶ ɜɵɫɨɬɭ ɩɚɞɟɧɢɹ ɱɚɫɬɢɰ
ɩɟɫɤɚ. ɉɪɟɞɩɨɥɚɝɚɟɦɨɟ ɪɚɫɩɨɥɨɠɟɧɢɟ ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɵ ɮɢɤɫɢɪɭɟɬɫɹ
ɧɚ ɫɬɟɧɤɚɯ ɫɬɟɧɞɚ. Ʉɨɝɞɚ ɫɬɚɥɶɧɚɹ ɩɥɚɫɬɢɧɚ ɭɫɬɚɧɨɜɥɟɧɚ ɜ ɝɪɭɧɬ, ɧɟɨɛɯɨɞɢɦɨ ɤɨɧɬɪɨɥɢɪɨɜɚɬɶ ɟɟ ɜɟɪɬɢɤɚɥɶɧɨɫɬɶ ɩɪɢ ɩɨɦɨɳɢ ɠɟɫɬɤɨɝɨ ɤɨɧɬɟɣɧɟɪɚ ɫɨ ɫɬɨɪɨɧɵ ɩɚɫɫɢɜɧɨɣ ɡɨɧɵ ɢ ɩɪɨɞɨɥɠɚɬɶ ɡɚɫɵɩɤɭ ɩɟɫɤɚ ɦɟɬɨɞɨɦ ɪɚɫɫɟɢɜɚɧɢɹ ɞɨ ɧɭɠɧɨɣ ɨɬɦɟɬɤɢ ɜ ɚɤɬɢɜɧɨɣ ɡɨɧɟ. Ⱥɪɦɢɪɨɜɚɧɧɨɟ
ɮɢɛɪɨɣ ɨɫɧɨɜɚɧɢɟ ɭɤɥɚɞɵɜɚɟɬɫɹ ɫ ɭɩɥɨɬɧɟɧɢɟɦ ɩɪɢ ɩɨɦɨɳɢ ɬɪɚɦɛɨɜɤɢ. ɉɨɫɥɟ ɩɨɞɝɨɬɨɜɤɢ ɚɪɦɢɪɨɜɚɧɧɨɝɨ ɨɫɧɨɜɚɧɢɹ ɩɨɜɟɪɯɧɨɫɬɶ ɝɪɭɧɬɚ
ɜɵɪɚɜɧɢɜɚɟɬɫɹ ɢ ɲɬɚɦɩ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɜ ɧɭɠɧɨɟ ɩɨɥɨɠɟɧɢɟ. Ʉɨɝɞɚ
141
Ⱥ.ɋ. Ʉɭɡɧɟɰɨɜɚ, Ⱥ.Ȼ. ɉɨɧɨɦɚɪɟɜ
ɦɨɞɟɥɶ ɩɨɥɧɨɫɬɶɸ ɫɨɛɪɚɧɚ, ɤɨɧɬɟɣɧɟɪ ɭɞɚɥɹɟɬɫɹ, ɚ ɧɚ ɫɬɚɥɶɧɭɸ ɩɥɚɫɬɢɧɭ ɭɫɬɚɧɚɜɥɢɜɚɸɬɫɹ ɞɚɬɱɢɤɢ ɩɟɪɟɦɟɳɟɧɢɣ [11].
ȼ ɦɚɥɨɦɚɫɲɬɚɛɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɹɯ ɩɥɚɧɢɪɭɟɬɫɹ ɩɪɨɜɟɫɬɢ ɱɟɬɵɪɟ
ɫɟɪɢɢ ɢɫɩɵɬɚɧɢɣ ɞɥɹ ɢɡɭɱɟɧɢɹ ɜɥɢɹɧɢɹ ɪɚɡɥɢɱɧɵɯ ɮɚɤɬɨɪɨɜ. Ɍɚɤ, ɩɟɪɜɚɹ ɫɟɪɢɹ ɢɫɩɵɬɚɧɢɣ (ɫɟɪɢɹ Ⱥ) ɛɭɞɟɬ ɩɪɨɜɟɞɟɧɚ ɛɟɡ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɚɪɦɢɪɨɜɚɧɢɹ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɞɚɧɧɵɯ ɞɥɹ ɫɪɚɜɧɟɧɢɹ. ɐɟɥɶɸ ɞɚɥɶɧɟɣɲɢɯ
ɫɟɪɢɣ (B, C, D) ɛɭɞɟɬ ɹɜɥɹɬɶɫɹ ɢɡɭɱɟɧɢɟ ɜɥɢɹɧɢɹ ɪɚɡɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɧɚ
ɩɨɜɟɞɟɧɢɟ ɮɭɧɞɚɦɟɧɬɚ ɢ ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɵ. ȼ ɤɚɱɟɫɬɜɟ ɜɚɪɶɢɪɭɟɦɵɯ
ɩɚɪɚɦɟɬɪɨɜ ɜ ɦɨɞɟɥɶɧɵɯ ɢɫɩɵɬɚɧɢɹɯ ɩɪɢɧɢɦɚɟɬɫɹ ɫɨɞɟɪɠɚɧɢɟ ɚɪɦɢɪɭɸɳɢɯ ɜɨɥɨɤɨɧ kɮ (%), ɨɬɧɨɲɟɧɢɟ ɬɨɥɳɢɧɵ ɚɪɦɢɪɭɟɦɨɝɨ ɫɥɨɹ ɤ ɜɵɫɨɬɟ ɫɬɟɧɵ h/ɇ (ɞ. ɟɞ.), ɨɬɧɨɲɟɧɢɟ ɪɚɫɫɬɨɹɧɢɹ ɨɬ ɮɭɧɞɚɦɟɧɬɚ ɞɨ ɫɬɟɧɵ
ɤ ɜɵɫɨɬɟ ɫɬɟɧɵ ɏ/ɇ (ɞ. ɟɞ.). ɉɥɚɧɢɪɭɟɬɫɹ, ɱɬɨ ɪɟɡɭɥɶɬɚɬɨɦ ɤɚɠɞɨɣ ɫɟɪɢɢ ɢɫɩɵɬɚɧɢɣ ɛɭɞɟɬ ɨɰɟɧɤɚ ɜɥɢɹɧɢɹ ɨɞɧɨɝɨ ɩɚɪɚɦɟɬɪɚ, ɨɫɬɚɥɶɧɵɟ ɩɚɪɚɦɟɬɪɵ ɩɪɢ ɷɬɨɦ ɨɫɬɚɸɬɫɹ ɩɨɫɬɨɹɧɧɵɦɢ. ɉɪɨɝɪɚɦɦɚ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɩɪɢɜɟɞɟɧɚ ɜ ɬɚɛɥ. 2.
Ɍɚɛɥɢɰɚ 2
ɉɚɪɚɦɟɬɪɵ ɩɪɨɝɪɚɦɦɵ ɢɫɩɵɬɚɧɢɣ
ɋɟɪɢɹ
ɂɫɫɥɟɞɭɟɦɵɣ ɮɚɤɬɨɪ
Ⱥ
B
ɇɟɚɪɦɢɪɨɜɚɧɧɨɟ ɨɫɧɨɜɚɧɢɟ
ɋɨɞɟɪɠɚɧɢɟ ɜɨɥɨɤɨɧ
C
Ɍɨɥɳɢɧɚ ɚɪɦɢɪɭɟɦɨɝɨ ɫɥɨɹ
D
Ɋɚɫɩɨɥɨɠɟɧɢɟ ɮɭɧɞɚɦɟɧɬɚ
ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɬɟɧɵ
ɉɨɫɬɨɹɧɧɵɟ
ɩɚɪɚɦɟɬɪɵ
ɏ/ɇ = 0,6; h/ɇ = 0,3
ɏ/ɇ = 0,6; h/ɇ = 0,3
ɏ/ɇ = 0,6; kɮ = 0,5
ɏ/ɇ = 0,6; kɮ = 1,0
ɏ/ɇ = 0,6; kɮ = 1,5
h/ɇ = 0,3; kɮ = 0,5
h/ɇ = 0,3; kɮ = 1,0
h/ɇ = 0,3; kɮ = 1,5
ȼɚɪɶɢɪɭɟɦɵɟ
ɩɚɪɚɦɟɬɪɵ
–
kɮ = 0,5; 1,0; 1,5
h/ɇ = 0,1; 0,2; 0,3; 0,4; 0,5
h/ɇ = 0,1; 0,2; 0,3; 0,4; 0,5
h/ɇ = 0,1; 0,2; 0,3; 0,4; 0,5
ɏ/ɇ = 0,4; 0,6; 0,8; 1,0
ɏ/ɇ = 0,4; 0,6; 0,8; 1,0
ɏ/ɇ = 0,4; 0,6; 0,8; 1,0
ɉɨ ɪɟɡɭɥɶɬɚɬɚɦ ɦɨɞɟɥɶɧɵɯ ɢɫɩɵɬɚɧɢɣ ɧɚ ɫɬɟɧɞɟ ɛɭɞɭɬ ɩɨɥɭɱɟɧɵ
ɤɪɢɜɵɟ ɡɚɜɢɫɢɦɨɫɬɢ «ɧɚɝɪɭɡɤɚ – ɨɫɚɞɤɚ» ɜ ɚɤɬɢɜɧɨɣ ɡɨɧɟ. Ɇɚɤɫɢɦɚɥɶɧɚɹ ɧɟɫɭɳɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɨɫɧɨɜɚɧɢɹ ɛɭɞɟɬ ɨɩɪɟɞɟɥɹɬɶɫɹ ɤɚɤ ɩɢɤɨɜɚɹ
ɬɨɱɤɚ ɧɚ ɤɪɢɜɨɣ, ɩɨɫɥɟ ɤɨɬɨɪɨɣ ɩɪɨɢɡɨɲɥɨ ɪɚɡɪɭɲɟɧɢɟ. Ⱦɥɹ ɨɰɟɧɤɢ
ɜɥɢɹɧɢɹ ɮɢɛɪɨɜɨɝɨ ɚɪɦɢɪɨɜɚɧɢɹ ɧɚ ɧɟɫɭɳɭɸ ɫɩɨɫɨɛɧɨɫɬɶ ɭɥɭɱɲɟɧɧɨɝɨ ɨɫɧɨɜɚɧɢɹ ɜɜɟɞɟɦ ɛɟɡɪɚɡɦɟɪɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɧɟɫɭɳɟɣ ɫɩɨɫɨɛɧɨɫɬɢ
Ʉɇɋ, ɤɨɬɨɪɵɣ ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
max
Rɚɪɦ
Ʉɇɋ = max ,
Rɧɟɚɪɦ
142
(2)
ɉɥɚɧɢɪɨɜɚɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚ ɩɨ ɢɫɫɥɟɞɨɜɚɧɢɸ…
max
max
ɝɞɟ Rɚɪɦ
ɢ Rɧɟɚɪɦ
– ɦɚɤɫɢɦɚɥɶɧɚɹ ɧɟɫɭɳɚɹ ɫɩɨɫɨɛɧɨɫɬɶ ɜ ɫɥɭɱɚɟ ɚɪɦɢ-
ɪɨɜɚɧɧɨɝɨ ɢ ɧɟɚɪɦɢɪɨɜɚɧɧɨɝɨ ɨɫɧɨɜɚɧɢɹ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɤɉɚ.
Ⱦɪɭɝɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɮɢɛɪɨɚɪɦɢɪɨɜɚɧɧɨɝɨ ɨɫɧɨɜɚɧɢɹ ɛɭɞɟɬ ɢɧɞɟɤɫ ɞɟɮɨɪɦɚɬɢɜɧɨɫɬɢ (ɂȾ), ɨɩɪɟɞɟɥɹɟɦɵɣ ɞɥɹ ɨɰɟɧɤɢ ɟɝɨ ɩɥɚɫɬɢɱɧɨɫɬɢ:
ɂȾ =
S ɚɪɦ
,
S ɧɟɚɪɦ
(3)
ɝɞɟ Sɚɪɦ ɢ Sɧɟɚɪɦ – ɨɫɚɞɤɚ ɩɨɜɟɪɯɧɨɫɬɢ ɜ ɚɤɬɢɜɧɨɣ ɡɨɧɟ ɩɪɢ ɦɚɤɫɢɦɚɥɶɧɨɣ ɧɟɫɭɳɟɣ ɫɩɨɫɨɛɧɨɫɬɢ ɚɪɦɢɪɨɜɚɧɧɨɝɨ ɢ ɧɟɚɪɦɢɪɨɜɚɧɧɨɝɨ ɨɫɧɨɜɚɧɢɹ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɦɦ.
Ɋɟɡɭɥɶɬɚɬɵ ɦɨɞɟɥɶɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɨ ɤɚɠɞɨɣ ɫɟɪɢɢ ɢɫɩɵɬɚɧɢɣ ɛɭɞɭɬ ɫɮɨɪɦɢɪɨɜɚɧɵ ɜ ɜɢɞɟ ɬɚɛɥ. 3.
Ɍɚɛɥɢɰɚ 3
ɉɪɢɦɟɪ ɡɚɩɢɫɢ ɪɟɡɭɥɶɬɚɬɨɜ ɦɨɞɟɥɶɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ
Ɇɚɤɫɢɦɚɥɶɧɵɣ ɛɨɤɨɜɨɣ
Ɉɫɚɞɤɚ ɩɪɢ ɩɢɤɨɜɨɣ
Ɂɧɚɱɟɧɢɟ
Rmax,
ɩɪɨɝɢɛ ɩɪɢ ɩɢɤɨɜɨɣ
ɧɟɫɭɳɟɣ ɫɩɨɫɨɛɧɨɫɬɢ,
ɜɚɪɶɢɪɭɟɦɨɝɨ
ɤɉɚ
ɧɟɫɭɳɟɣ ɫɩɨɫɨɛɧɨɫɬɢ, ɦɦ
ɩɚɪɚɦɟɬɪɚ
ɦɦ
Ʉɇɋ
ɂȾ
ɋ ɰɟɥɶɸ ɞɨɩɨɥɧɟɧɢɹ ɪɟɡɭɥɶɬɚɬɨɜ ɥɚɛɨɪɚɬɨɪɧɵɯ ɢɫɩɵɬɚɧɢɣ ɧɟɨɛɯɨɞɢɦɨ ɩɪɨɜɟɫɬɢ ɬɚɤɠɟ ɱɢɫɥɟɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ
ɤɨɧɫɬɪɭɤɰɢɢ. ɑɢɫɥɟɧɧɵɣ ɚɧɚɥɢɡ ɛɭɞɟɬ ɨɫɭɳɟɫɬɜɥɟɧ ɦɟɬɨɞɨɦ ɤɨɧɟɱɧɵɯ
ɷɥɟɦɟɧɬɨɜ ɜ ɩɪɨɝɪɚɦɦɟ PLAXIS 8.2. Ɋɚɡɦɟɪɵ ɢ ɝɟɨɦɟɬɪɢɹ ɮɭɧɞɚɦɟɧɬɚ
ɢ ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɵ ɫɨɯɪɚɧɹɸɬɫɹ ɚɧɚɥɨɝɢɱɧɵɦɢ ɦɨɞɟɥɢ ɜ ɥɚɛɨɪɚɬɨɪɧɵɯ ɢɫɩɵɬɚɧɢɹɯ. Ɋɚɡɦɟɪɵ ɪɚɛɨɱɟɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ ɧɟɨɛɯɨɞɢɦɨ ɜɵɛɢɪɚɬɶ ɞɨɫɬɚɬɨɱɧɨ ɛɨɥɶɲɢɦɢ, ɱɬɨɛɵ ɝɚɪɚɧɬɢɪɨɜɚɬɶ ɨɬɫɭɬɫɬɜɢɟ ɜɥɢɹɧɢɹ
ɝɪɚɧɢɰ ɧɚ ɪɟɡɭɥɶɬɚɬɵ ɪɚɫɱɟɬɨɜ.
ɉɪɨɝɪɚɦɦɚ PLAXIS 2D ɩɪɟɞɥɚɝɚɟɬ ɲɢɪɨɤɢɣ ɫɩɟɤɬɪ ɪɚɫɱɟɬɧɵɯ
ɦɨɞɟɥɟɣ ɝɪɭɧɬɚ. Ⱦɥɹ ɞɚɥɶɧɟɣɲɢɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɦɟɬɨɞɨɦ ɤɨɧɟɱɧɵɯ
ɷɥɟɦɟɧɬɨɜ ɛɭɞɟɬ ɜɵɛɪɚɧɚ ɧɟɥɢɧɟɣɧɚɹ ɦɨɞɟɥɶ Ɇɨɪɚ – Ʉɭɥɨɧɚ ɛɥɚɝɨɞɚɪɹ
ɫɜɨɟɣ ɩɪɨɫɬɨɬɟ, ɩɪɚɤɬɢɱɟɫɤɨɣ ɡɧɚɱɢɦɨɫɬɢ ɢ ɧɚɥɢɱɢɸ ɧɟɨɛɯɨɞɢɦɵɯ ɩɚɪɚɦɟɬɪɨɜ. ɉɚɪɚɦɟɬɪɵ ɮɢɛɪɨɩɟɫɤɚ, ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɱɢɫɥɟɧɧɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ, ɛɭɞɭɬ ɩɨɥɭɱɟɧɵ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɥɚɛɨɪɚɬɨɪɧɵɯ ɢɫɩɵɬɚɧɢɣ
ɩɨ ɦɟɬɨɞɭ ɬɪɟɯɨɫɧɨɝɨ ɫɠɚɬɢɹ. Ɍɪɟɯɨɫɧɵɟ ɢɫɩɵɬɚɧɢɹ ɩɨɡɜɨɥɹɸɬ ɧɚɢɛɨɥɟɟ ɬɨɱɧɨ ɫɦɨɞɟɥɢɪɨɜɚɬɶ ɧɚɩɪɹɠɟɧɧɨ-ɞɟɮɨɪɦɢɪɨɜɚɧɧɨɟ ɫɨɫɬɨɹɧɢɟ
ɝɪɭɧɬɚ ɜ ɦɚɫɫɢɜɟ ɢ ɩɨɥɭɱɢɬɶ ɤɚɤ ɩɪɨɱɧɨɫɬɧɵɟ, ɬɚɤ ɢ ɞɟɮɨɪɦɚɰɢɨɧɧɵɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɝɪɭɧɬɚ.
143
Ⱥ.ɋ. Ʉɭɡɧɟɰɨɜɚ, Ⱥ.Ȼ. ɉɨɧɨɦɚɪɟɜ
Ʌɢɧɟɣɧɨ-ɭɩɪɭɝɢɣ ɯɚɪɚɤɬɟɪ ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɤɢ ɢ ɮɭɧɞɚɦɟɧɬɚ ɦɨɞɟɥɢɪɭɟɬɫɹ ɤɚɤ ɷɥɟɦɟɧɬ «ɩɥɢɬɚ». ȼɡɚɢɦɨɞɟɣɫɬɜɢɟ ɦɟɠɞɭ ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɨɣ, ɮɭɧɞɚɦɟɧɬɨɦ ɢ ɨɤɪɭɠɚɸɳɢɦ ɝɪɭɧɬɨɦ ɦɨɞɟɥɢɪɭɟɬɫɹ ɩɪɢ ɩɨɦɨɳɢ
ɢɧɬɟɪɮɟɣɫɧɵɯ ɷɥɟɦɟɧɬɨɜ, ɪɚɫɩɨɥɚɝɚɸɳɢɯɫɹ ɧɚ ɤɨɧɬɚɤɬɟ ɦɟɠɞɭ ɞɜɭɦɹ
ɥɸɛɵɦɢ ɨɛɴɟɤɬɚɦɢ. ɉɚɪɚɦɟɬɪɵ ɢɧɬɟɪɮɟɣɫɚ ɜ ɩɪɨɝɪɚɦɦɟ PLAXIS ɯɚɪɚɤɬɟɪɢɡɭɸɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɫɧɢɠɟɧɢɹ ɩɪɨɱɧɨɫɬɢ ɢ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ
ɫɩɪɚɜɨɱɧɵɦ ɦɚɬɟɪɢɚɥɚɦ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɦɚɬɟɪɢɚɥɚ ɷɥɟɦɟɧɬɚ. ɇɚɝɪɭɡɤɚ
ɧɚ ɮɭɧɞɚɦɟɧɬ ɡɚɞɚɟɬɫɹ ɤɚɤ ɪɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɚɹ.
ɑɢɫɥɟɧɧɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɩɪɨɜɨɞɢɬɫɹ ɚɧɚɥɨɝɢɱɧɨ ɩɪɨɝɪɚɦɦɟ ɥɚɛɨɪɚɬɨɪɧɵɯ ɢɫɩɵɬɚɧɢɣ. ɋɪɚɜɧɟɧɢɟ ɪɟɡɭɥɶɬɚɬɨɜ ɪɚɫɱɟɬɚ ɦɟɬɨɞɨɦ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɢ ɦɨɞɟɥɶɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɩɨɡɜɨɥɢɬ ɢɡɛɟɠɚɬɶ ɜɨɡɦɨɠɧɵɯ ɨɲɢɛɨɤ ɩɪɢ ɩɪɨɜɟɞɟɧɢɢ ɢɫɩɵɬɚɧɢɣ ɜ ɥɚɛɨɪɚɬɨɪɧɵɯ ɭɫɥɨɜɢɹɯ.
ɂɫɩɵɬɚɧɢɹ ɦɚɥɨɦɚɫɲɬɚɛɧɵɯ ɦɨɞɟɥɟɣ ɮɭɧɞɚɦɟɧɬɨɜ ɢ ɞɪɭɝɢɯ
ɤɨɧɫɬɪɭɤɰɢɣ ɱɚɫɬɨ ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɥɹ ɨɰɟɧɤɢ ɢɯ ɧɟɫɭɳɟɣ ɫɩɨɫɨɛɧɨɫɬɢ
ɢ ɞɟɮɨɪɦɚɰɢɨɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɜɫɥɟɞɫɬɜɢɟ ɧɟɜɨɡɦɨɠɧɨɫɬɢ ɩɪɨɜɟɞɟɧɢɹ ɢɫɩɵɬɚɧɢɣ ɜ ɧɚɬɭɪɚɥɶɧɭɸ ɜɟɥɢɱɢɧɭ. ɋɥɟɞɭɟɬ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɩɪɢ
ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɦɨɞɟɥɟɣ ɫɭɳɟɫɬɜɭɟɬ ɪɹɞ ɬɪɭɞɧɨɫɬɟɣ ɩɪɢ ɢɧɬɟɪɩɪɟɬɚɰɢɢ
ɪɟɡɭɥɶɬɚɬɨɜ ɜ ɧɚɬɭɪɧɵɟ ɭɫɥɨɜɢɹ, ɫɜɹɡɚɧɧɵɯ ɫ ɦɚɫɲɬɚɛɧɵɦɢ ɤɨɷɮɮɢɰɢɟɧɬɚɦɢ. Ⱦɥɹ ɦɚɥɨɦɚɫɲɬɚɛɧɵɯ ɦɨɞɟɥɟɣ ɞɨɥɠɟɧ ɛɵɬɶ ɭɱɬɟɧ ɪɹɞ ɜɚɠɧɵɯ ɮɚɤɬɨɪɨɜ, ɬɚɤɢɯ ɤɚɤ ɪɚɡɦɟɪ ɱɚɫɬɢɰ, ɩɥɨɬɧɨɫɬɶ ɝɪɭɧɬɚ, ɬɟɯɧɨɥɨɝɢɹ
ɫɬɪɨɢɬɟɥɶɫɬɜɚ, ɠɟɫɬɤɨɫɬɶ ɦɚɬɟɪɢɚɥɨɜ ɢ ɞɪ.
ɗɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɭɫɬɚɧɨɜɥɟɧɨ, ɱɬɨ ɪɚɡɦɟɪ ɱɚɫɬɢɰ ɧɟ ɨɤɚɡɵɜɚɟɬ
ɜɥɢɹɧɢɟ ɧɚ ɧɟɫɭɳɭɸ ɫɩɨɫɨɛɧɨɫɬɶ ɩɪɢ ɩɟɪɟɯɨɞɟ ɨɬ ɦɚɥɨɦɚɫɲɬɚɛɧɨɣ
ɦɨɞɟɥɢ ɜ ɬɨɦ ɫɥɭɱɚɟ, ɤɨɝɞɚ ɨɬɧɨɲɟɧɢɟ D50/B ɦɟɧɶɲɟ 0,1 (ɝɞɟ D50 –
ɞɢɚɦɟɬɪ ɱɚɫɬɢɰ, ɦɟɧɶɲɟ ɤɨɬɨɪɨɝɨ ɜ ɧɚɜɟɫɤɟ ɝɪɭɧɬɚ ɫɨɞɟɪɠɢɬɫɹ 50 %
ɢ ɛɨɥɟɟ ɱɚɫɬɢɰ ɩɨ ɦɚɫɫɟ, ȼ – ɲɢɪɢɧɚ ɮɭɧɞɚɦɟɧɬɚ) [11]. ȼ ɩɥɚɧɢɪɭɟɦɨɦ
ɷɤɫɩɟɪɢɦɟɧɬɟ ɷɬɨ ɨɬɧɨɲɟɧɢɟ ɫɨɫɬɚɜɢɬ 0,006. Ⱦɪɭɝɨɣ ɪɟɤɨɦɟɧɞɚɰɢɟɣ
ɤ ɦɚɥɨɦɚɫɲɬɚɛɧɵɦ ɢɫɫɥɟɞɨɜɚɧɢɹɦ ɹɜɥɹɟɬɫɹ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɛɨɥɟɟ ɪɵɯɥɨɝɨ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɪɟɚɥɶɧɵɦɢ ɭɫɥɨɜɢɹɦɢ ɩɟɫɤɚ, ɩɨɷɬɨɦɭ ɭɤɥɚɞɤɚ
ɩɟɫɱɚɧɨɝɨ ɝɪɭɧɬɚ ɜ ɥɨɬɨɤ ɛɭɞɟɬ ɨɫɭɳɟɫɬɜɥɹɬɶɫɹ ɛɟɡ ɭɩɥɨɬɧɟɧɢɹ.
Ⱦɥɹ ɜɵɩɨɥɧɟɧɢɹ ɭɫɥɨɜɢɹ ɩɥɨɫɤɨɣ ɞɟɮɨɪɦɚɰɢɢ ɬɪɟɧɢɟ ɦɟɠɞɭ ɝɪɭɧɬɨɜ ɢ ɫɬɟɧɤɚɦɢ ɥɨɬɤɚ ɞɨɥɠɧɨ ɛɵɬɶ ɪɚɜɧɨ ɧɭɥɸ [11]. Ⱦɥɹ ɷɬɨɣ ɰɟɥɢ ɝɥɚɞɤɢɟ ɫɬɟɧɤɢ ɥɚɛɨɪɚɬɨɪɧɨɝɨ ɫɬɟɧɞɚ ɞɨɥɠɧɵ ɛɵɬɶ ɩɨɤɪɵɬɵ ɦɚɫɥɨɦ ɞɥɹ
ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɫɧɢɠɟɧɢɹ ɷɮɮɟɤɬɚ ɬɪɟɧɢɹ. Ɍɚɤɠɟ ɞɨɥɠɧɚ ɛɵɬɶ ɪɚɜɧɚ ɧɭɥɸ ɢ ɩɪɨɞɨɥɶɧɚɹ ɞɟɮɨɪɦɚɰɢɹ. ɗɬɨ ɭɫɥɨɜɢɟ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɤɨɧɫɬɪɭɤɰɢɟɣ ɫɬɟɧɞɚ, ɧɚ ɫɬɟɧɤɚɯ ɤɨɬɨɪɨɝɨ ɭɫɬɚɧɨɜɥɟɧɵ ɫɬɚɥɶɧɵɟ ɪɟɲɟɬɤɢ ɫ ɨɩɨɪɧɵɦɢ ɲɚɣɛɚɦɢ ɜ ɭɡɥɚɯ.
144
ɉɥɚɧɢɪɨɜɚɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚ ɩɨ ɢɫɫɥɟɞɨɜɚɧɢɸ…
ɉɥɚɧɢɪɭɟɦɵɟ ɢɫɫɥɟɞɨɜɚɧɢɹ ɧɚɰɟɥɟɧɵ ɧɚ ɨɰɟɧɤɭ ɪɚɛɨɬɵ ɤɨɧɫɬɪɭɤɰɢɢ ɧɚɝɪɭɠɟɧɧɨɝɨ ɝɪɭɧɬɨɜɨɝɨ ɦɚɫɫɢɜɚ ɮɢɛɪɨɚɪɦɢɪɨɜɚɧɧɨɝɨ ɝɪɭɧɬɚ
ɡɚ ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɨɣ. ɉɨɥɭɱɟɧɧɵɟ ɪɟɡɭɥɶɬɚɬɵ ɫɬɚɧɭɬ ɢɫɯɨɞɧɵɦɢ ɞɚɧɧɵɦɢ ɞɥɹ ɩɨɞɛɨɪɚ ɨɩɬɢɦɚɥɶɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɩɨɥɧɨɦɚɫɲɬɚɛɧɨɝɨ ɷɤɫɩɟɪɢɦɟɧɬɚ ɢ ɩɨɥɭɱɟɧɢɹ ɷɦɩɢɪɢɱɟɫɤɢɯ ɡɚɜɢɫɢɦɨɫɬɟɣ ɜɥɢɹɧɢɹ ɪɚɡɥɢɱɧɵɯ
ɮɚɤɬɨɪɨɜ ɧɚ ɩɚɪɚɦɟɬɪɵ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɫɢɫɬɟɦɵ. ɉɨɷɬɨɦɭ ɞɚɧɧɵɟ,
ɩɨɥɭɱɟɧɧɵɟ ɢɡ ɩɪɨɜɟɞɟɧɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ, ɫɥɟɞɭɟɬ ɫ ɨɫɬɨɪɨɠɧɨɫɬɶɸ
ɢɫɩɨɥɶɡɨɜɚɬɶ ɩɪɢ ɩɟɪɟɯɨɞɟ ɤ ɧɚɬɭɪɧɵɦ ɭɫɥɨɜɢɹɦ, ɭɱɢɬɵɜɚɹ ɜɫɟ ɦɚɫɲɬɚɛɧɵɟ ɤɨɷɮɮɢɰɢɟɧɬɵ. Ʉɪɨɦɟ ɬɨɝɨ, ɞɥɹ ɨɛɨɛɳɟɧɢɹ ɪɟɡɭɥɶɬɚɬɨɜ ɧɟɨɛɯɨɞɢɦɨ ɭɱɢɬɵɜɚɬɶ ɢ ɞɪɭɝɢɟ ɮɚɤɬɨɪɵ, ɩɨɦɢɦɨ ɬɟɯ, ɤɨɬɨɪɵɟ ɪɚɫɫɦɚɬɪɢɜɚɸɬɫɹ ɜ ɞɚɧɧɨɣ ɪɚɛɨɬɟ. Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɛɨɥɟɟ ɬɨɱɧɵɯ ɩɚɪɚɦɟɬɪɨɜ,
ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ, ɫɥɟɞɭɟɬ ɪɚɫɫɦɨɬɪɟɬɶ ɬɚɤɠɟ ɜɥɢɹɧɢɟ
ɬɢɩɚ ɦɚɬɟɪɢɚɥɚ ɡɚɫɵɩɤɢ, ɦɚɬɟɪɢɚɥɚ ɚɪɦɢɪɭɸɳɢɯ ɜɨɥɨɤɨɧ, ɠɟɫɬɤɨɫɬɢ
ɩɨɞɩɨɪɧɨɣ ɫɬɟɧɤɢ, ɭɫɥɨɜɢɣ ɧɚɝɪɭɠɟɧɢɹ ɢ ɬ.ɞ.
Ȼɢɛɥɢɨɝɪɚɮɢɱɟɫɤɢɣ ɫɩɢɫɨɤ
1. ɉɨɧɨɦɚɪɟɜ Ⱥ.Ȼ. Ɋɟɤɨɧɫɬɪɭɤɰɢɹ ɩɨɞɡɟɦɧɨɝɨ ɩɪɨɫɬɪɚɧɫɬɜɚ:
ɭɱɟɛ. ɩɨɫɨɛɢɟ ɞɥɹ ɫɬɭɞɟɧɬɨɜ, ɨɛɭɱɚɸɳɢɯɫɹ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ 653500
«ɋɬɪɨɢɬɟɥɶɫɬɜɨ». – Ɇ.: ɂɡɞ-ɜɨ Ⱥɋȼ, 2006. – 231 ɫ.
2. Diambra A., Ibraim E. Fibre reinforced sands: experiments and
modeling // Geotextiles and geomembranes. – 2010. – ʋ 28. – C. 238–250.
3. Ʉɭɡɧɟɰɨɜɚ Ⱥ.ɋ., ɉɨɧɨɦɚɪɟɜ Ⱥ.Ȼ. Ʌɚɛɨɪɚɬɨɪɧɵɟ ɢɫɫɥɟɞɨɜɚɧɢɹ
ɩɪɨɱɧɨɫɬɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɮɢɛɪɨɚɪɦɢɪɨɜɚɧɧɨɝɨ ɩɟɫɤɚ ɪɚɡɥɢɱɧɨɣ
ɫɬɟɩɟɧɢ ɜɨɞɨɧɚɫɵɳɟɧɢɹ // ȼɟɫɬɧɢɤ ɝɪɚɠɞɚɧɫɤɢɯ ɢɧɠɟɧɟɪɨɜ. – 2014. –
ʋ 6. – ɋ. 127–132.
4. Park T., Tan S.A. Enhanced performance of reinforced soil walls
by the inclusion of short fiber // Geotextiles and geomembranes. – 2005. –
ʋ 23. – C. 348–361.
5. Hejazi S.M., Sheikhzadeh M. A simple review of soil reinforcement by using natural and synthetic fibers // Construction and Building Materials. – 2012. – ʋ 30. – C. 101–116.
6. Michalowski R.L. Failure of Fiber-Reinforced Granular Soils //
Journal of Geotechnical Engineering. – 1996. – ʋ 122. – C. 226–234.
7. Ʉɭɡɧɟɰɨɜɚ Ⱥ.ɋ., ɉɨɧɨɦɚɪɟɜ Ⱥ.Ȼ. ɉɥɚɧɢɪɨɜɚɧɢɟ ɢ ɩɨɞɝɨɬɨɜɤɚ
ɷɤɫɩɟɪɢɦɟɧɬɚ ɬɪɟɯɨɫɧɨɝɨ ɫɠɚɬɢɹ ɝɥɢɧɢɫɬɨɝɨ ɝɪɭɧɬɚ, ɭɥɭɱɲɟɧɧɨɝɨ ɮɢɛɪɨɜɵɦ ɚɪɦɢɪɨɜɚɧɢɟɦ // ȼɟɫɬɧɢɤ ɉɟɪɦɫɤɨɝɨ ɧɚɰɢɨɧɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚ145
Ⱥ.ɋ. Ʉɭɡɧɟɰɨɜɚ, Ⱥ.Ȼ. ɉɨɧɨɦɚɪɟɜ
ɬɟɥɶɫɤɨɝɨ ɩɨɥɢɬɟɯɧɢɱɟɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ. ɋɬɪɨɢɬɟɥɶɫɬɜɨ ɢ ɚɪɯɢɬɟɤɬɭɪɚ. – 2013. – ʋ 1. – ɋ. 151–161.
8. ɉɥɚɧɢɪɨɜɚɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚ ɩɨ ɢɫɫɥɟɞɨɜɚɧɢɸ ɧɚɩɪɹɠɟɧɧɨɞɟɮɨɪɦɢɪɨɜɚɧɧɨɝɨ ɫɨɫɬɨɹɧɢɹ ɩɟɫɱɚɧɨɝɨ ɝɪɭɧɬɨɜɨɝɨ ɨɫɧɨɜɚɧɢɹ ɫ ɩɨɦɨɳɶɸ ɲɬɚɦɩɨɜɵɯ ɢɫɩɵɬɚɧɢɣ / Ⱦ.Ⱥ. Ɍɚɬɶɹɧɧɢɤɨɜ, Ʉ.ɉ. Ⱦɚɜɥɹɬɲɢɧ,
ə.Ⱥ. Ɏɟɞɨɪɨɜɵɯ, Ⱥ.Ȼ. ɉɨɧɨɦɚɪɟɜ // ȼɟɫɬɧɢɤ ɉɟɪɦɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ
ɬɟɯɧɢɱɟɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ. ɋɬɪɨɢɬɟɥɶɫɬɜɨ ɢ ɚɪɯɢɬɟɤɬɭɪɚ. – 2011. –
ʋ 1. – ɋ. 105–109.
9. ɂɥɥɚɪɢɨɧɨɜ ɋ.Ɉ., Ʉɚɥɨɲɢɧɚ ɋ.ȼ. ɂɡɭɱɟɧɢɟ ɜɥɢɹɧɢɹ ɨɛɴɟɤɬɨɜ
ɧɨɜɨɝɨ ɫɬɪɨɢɬɟɥɶɫɬɜɚ ɧɚ ɨɫɚɞɤɭ ɨɫɧɨɜɚɧɢɹ ɫɭɳɟɫɬɜɭɸɳɟɣ ɡɚɫɬɪɨɣɤɢ
ɧɚ ɨɫɧɨɜɟ ɦɨɞɟɥɶɧɨɝɨ ɷɤɫɩɟɪɢɦɟɧɬɚ // ȼɟɫɬɧɢɤ ɉɟɪɦɫɤɨɝɨ ɧɚɰɢɨɧɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɨɝɨ ɩɨɥɢɬɟɯɧɢɱɟɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ. ɍɪɛɚɧɢɫɬɢɤɚ. – 2013. – ʋ 4. – ɋ. 116–123.
10. Ʉɨɛɵɳɚ Ɉ.ȿ., Ȼɨɱɤɚɪɟɜɚ Ɍ.Ɇ. Ɇɨɞɟɥɢɪɨɜɚɧɢɟ ɩɪɨɬɢɜɨɤɚɪɫɬɨɜɨɣ ɡɚɳɢɬɵ // ȼɟɫɬɧɢɤ ɉɟɪɦɫɤɨɝɨ ɧɚɰɢɨɧɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɨɝɨ ɩɨɥɢɬɟɯɧɢɱɟɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ. ɋɬɪɨɢɬɟɥɶɫɬɜɨ ɢ ɚɪɯɢɬɟɤɬɭɪɚ. –
2013. – ʋ 1. – ɋ. 124–135.
11. Nasr A.M. Behavior of strip footing on fiber-reinforced cemented
sand adjacent to sheet pile wall // Geotextiles and geomembranes. – 2014. –
ʋ 42. – C. 599–610.
References
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ɉɨɥɭɱɟɧɨ 26.01.2015
ɋɜɟɞɟɧɢɹ ɨɛ ɚɜɬɨɪɚɯ
Ʉɭɡɧɟɰɨɜɚ Ⱥɥɥɚ ɋɟɪɝɟɟɜɧɚ (ɉɟɪɦɶ, Ɋɨɫɫɢɹ) – ɚɫɩɢɪɚɧɬ ɤɚɮɟɞɪɵ
«ɋɬɪɨɢɬɟɥɶɧɨɟ ɩɪɨɢɡɜɨɞɫɬɜɨ ɢ ɝɟɨɬɟɯɧɢɤɚ» ɉɟɪɦɫɤɨɝɨ ɧɚɰɢɨɧɚɥɶɧɨɝɨ
ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɨɝɨ ɩɨɥɢɬɟɯɧɢɱɟɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ (614990, ɝ. ɉɟɪɦɶ,
Ʉɨɦɫɨɦɨɥɶɫɤɢɣ ɩɪ., 29, e-mail: koallita@yandex.ru).
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Ⱥ.ɋ. Ʉɭɡɧɟɰɨɜɚ, Ⱥ.Ȼ. ɉɨɧɨɦɚɪɟɜ
ɉɨɧɨɦɚɪɟɜ Ⱥɧɞɪɟɣ Ȼɭɞɢɦɢɪɨɜɢɱ (ɉɟɪɦɶ, Ɋɨɫɫɢɹ) – ɞɨɤɬɨɪ
ɬɟɯɧɢɱɟɫɤɢɯ ɧɚɭɤ, ɩɪɨɮɟɫɫɨɪ, ɡɚɜɟɞɭɸɳɢɣ ɤɚɮɟɞɪɨɣ «ɋɬɪɨɢɬɟɥɶɧɨɟ
ɩɪɨɢɡɜɨɞɫɬɜɨ ɢ ɝɟɨɬɟɯɧɢɤɚ» ɉɟɪɦɫɤɨɝɨ ɧɚɰɢɨɧɚɥɶɧɨɝɨ ɢɫɫɥɟɞɨɜɚɬɟɥɶɫɤɨɝɨ ɩɨɥɢɬɟɯɧɢɱɟɫɤɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ (614990, ɝ. ɉɟɪɦɶ, Ʉɨɦɫɨɦɨɥɶɫɤɢɣ ɩɪ., 29, e-mail: spstf@pstu.ru).
About the authors
Alla S. Kuznetsova (Perm, Russian Federation) – Postgraduate student, Department of Building Production and Geotechnics, Perm National
Research Polytechnic University (29, Komsomolsky av., Perm, 614990,
Russian Federation, e-mail: koallita@yandex.ru).
Andrei B. Ponomarev (Perm, Russian Federation) – Doctor of Technical Sciences, Professor, Head of Department of Building Production and
Geotechnics, Perm National Research Polytechnic University (29, Komsomolsky av., Perm, 614990, Russian Federation, e-mail: spstf@pstu.ru).
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