title: Ð§Ð¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ Ð³Ð¸Ð´ÑÐ¾ÑÐµÑ Ð½Ð¸ÑÐµÑÐºÐ¸Ñ ÑÑÐ½Ð½ÐµÐ»ÐµÐ¹ Ð¸ Ð¼Ð°ÑÑ Ð³Ð¾ÑÐ½ÑÑ Ð¿Ð¾ÑÐ¾Ð´
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Numerical modelling of the interaction between hydrotechnical tunnels and rock masses
Creators: name: ÐÐ¾Ð²Ð°Ð½Ð¾Ð²ÑÐºÐ°, Ð¢Ð°Ð¼Ð°ÑÐ°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2019
Subjects: Ð¢ÑÐ½Ð½ÐµÐ»Ð¸ Ð³Ð¸Ð´ÑÐ¾ÑÐµÑ Ð½Ð¸ÑÐµÑÐºÐ¸Ðµ
Ð§Ð¸ÑÐ»ÐµÐ½Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ
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ÐÐ¾ÑÐ½ÑÐµ Ð¿Ð¾ÑÐ¾Ð´Ñ
Ð³ÐµÐ¾ÑÐµÑ Ð½Ð¸ÑÐµÑÐºÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ
ÑÐºÑÑÑÐ°Ð¿Ð¾Ð»ÑÑÐ¸Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð²
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description: Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ Ð´Ð¸ÑÑÐµÑÑÐ°ÑÐ¸Ð¸ Ð¿ÑÐµÐ´Ð»Ð°Ð³Ð°ÐµÑÑÑ Ð¿ÑÐ¾ÑÐµÐ´ÑÑÐ° Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð³Ð¾ÑÐ½ÑÑ Ð¼Ð°ÑÑÐ¸Ð²Ð¾Ð² Ð² ÐºÐ°ÑÐµÑÑÐ²Ðµ ÑÐ¸ÑÐ¾ÐºÐ¾Ð¹ Ð¾ÑÐ½Ð¾Ð²Ñ Ð´Ð»Ñ ÑÑÑÐ¾Ð¸ÑÐµÐ»ÑÑÑÐ²Ð° ÑÐ»Ð¾Ð¶Ð½ÑÑ ÑÑÑÐ¾Ð¸ÑÐµÐ»ÑÐ½ÑÑ Ð¾Ð±ÑÐµÐºÑÐ¾Ð², ÑÐ°ÐºÐ¸Ñ ÐºÐ°Ðº Ð¿Ð»Ð¾ÑÐ¸Ð½Ñ, Ð³Ð¸Ð´ÑÐ¾ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ðµ ÑÑÐ½Ð½ÐµÐ»Ð¸ Ð¸ Ñ. Ð´. Ð¦ÐµÐ»Ñ ÑÐ¾ÑÑÐ¾ÑÐ»Ð° Ð² ÑÐ¾Ð¼, ÑÑÐ¾Ð±Ñ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½ÑÐ¼ Ð¾Ð±ÑÐ°Ð·Ð¾Ð¼ Ð¿ÑÐ¾Ð²ÐµÑÑÐ¸ Ð½ÐµÐ¾Ð±ÑÐ¾Ð´Ð¸Ð¼ÑÑ ÑÐ¸ÑÑÐµÐ¼Ð°ÑÐ¸Ð·Ð°ÑÐ¸Ñ Ð·Ð½Ð°Ð½Ð¸Ð¹ Ð¸ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ð¹ Ð² ÑÑÐ¾Ð¹ Ð¾Ð±Ð»Ð°ÑÑÐ¸ Ð¸ Ð¿ÑÐµÐ´Ð»Ð¾Ð¶Ð¸ÑÑ Ð½Ð¾Ð²ÑÐµ, Ð° ÑÐ°ÐºÐ¶Ðµ Ð¸Ð·Ð¼ÐµÐ½Ð¸ÑÑ ÑÐ¶Ðµ ÑÑÑÐµÑÑÐ²ÑÑÑÐ¸Ðµ Ð¿ÑÐ¾ÑÐµÐ´ÑÑÑ Ð¸ Ð¼ÐµÑÐ¾Ð´Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ.
ÐÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ð½ÑÐµ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð¸ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÐµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð±ÑÐ»Ð¸ ÑÑÐ¾ÑÐ¼Ð¸ÑÐ¾Ð²Ð°Ð½Ñ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ ÑÐ¾Ð±ÑÐ°Ð½Ð½ÑÑ Ð»Ð°Ð±Ð¾ÑÐ°ÑÐ¾ÑÐ½ÑÑ Ð¸ Ð¿Ð¾Ð»ÐµÐ²ÑÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ð¹ Ð³Ð¾ÑÐ½ÑÑ Ð¼Ð°ÑÑÐ¸Ð²Ð¾Ð² Ð½Ð° ÑÑÐ°ÑÑÐºÐ°Ñ Ð¿Ð»Ð¾ÑÐ¸Ð½Ñ Â«Ð¡Ð²ÐµÑÐºÐ° ÐÐµÑÐºÐ°Â» Ð² Ð ÐµÑÐ¿ÑÐ±Ð»Ð¸ÐºÐµ ÐÐ°ÐºÐµÐ´Ð¾Ð½Ð¸Ð¸. Ð¡Ð¾Ð±ÑÑÐ²ÐµÐ½Ð½ÑÐµ ÐºÐ¾ÑÑÐµÐ»ÑÑÐ¸Ð¸ Ð±ÑÐ»Ð¸ ÑÑÑÐ°Ð½Ð¾Ð²Ð»ÐµÐ½Ñ Ð¼ÐµÐ¶Ð´Ñ ÑÑÐ¸Ð¼Ð¸ Ð²ÑÐ¾Ð´Ð½ÑÐ¼Ð¸ Ð³ÐµÐ¾ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¼Ð¸ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ°Ð¼Ð¸. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐ¸Ð²ÐµÐ´ÐµÐ½ Ð¿ÑÐ¸Ð¼ÐµÑ ÑÐ¾ÑÐ¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¸ ÐºÐ¾Ð½ÑÐµÐ¿ÑÑÐ°Ð»ÑÐ½Ð¾Ð¹ Ð¼Ð°ÑÑÐ¸ÑÑ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð³Ð¾ Ð¿Ð°ÐºÐµÑÐ° Examine 2D, ÑÑÐ¾Ð±Ñ Ð¿Ð¾ÐºÐ°Ð·Ð°ÑÑ, ÑÑÐ¾ Ð¿ÑÑÐµÐ¼ Ð¿ÑÐ°Ð²Ð¸Ð»ÑÐ½Ð¾Ð³Ð¾ Ð²ÑÐ±Ð¾ÑÐ° Ð¸ Ð²Ð°ÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¾ÑÐ½Ð¾Ð²Ð½ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð² Ð´Ð¸Ð°Ð³Ð¾Ð½Ð°Ð»ÑÐ½Ð¾Ð¹ Ð¼Ð°ÑÑÐ¸ÑÑ, ÐºÐ¾ÑÐ¾ÑÑÐµ Ð²ÐºÐ»ÑÑÐ°ÑÑ ÐºÐ°ÑÐµÑÑÐ²Ð° Ð¸ ÑÑÐ»Ð¾Ð²Ð¸Ñ Ð¼Ð°ÑÑÐ¸Ð²Ð¾Ð² Ð³Ð¾ÑÐ½ÑÑ Ð¿Ð¾ÑÐ¾Ð´, Ð¼Ð¾Ð¶Ð½Ð¾ ÑÐµÐ°Ð»Ð¸ÑÑÐ¸ÑÐ½Ð¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°ÑÑ Ð¸ Ð¿ÑÐµÐ´Ð²Ð¸Ð´ÐµÑÑ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ Ð¿Ð¾ÑÐ¾Ð´Ñ â ÑÐ¾Ð¾ÑÑÐ¶ÐµÐ½Ð¸Ñ. ÐÐµÑÐ¾ÑÑÐ½Ð¾ÑÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð±ÑÐ» Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð³Ð¾ Ð¿Ð°ÐºÐµÑÐ° RocSupport, ÑÑÐ¾Ð±Ñ Ð¿ÑÐµÐ´Ð¾ÑÑÐ°Ð²Ð¸ÑÑ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½ÑÐµ ÑÐµÐºÐ¾Ð¼ÐµÐ½Ð´Ð°ÑÐ¸Ð¸ Ð´Ð»Ñ Ð¿ÑÐ¸ÐµÐ¼Ð»ÐµÐ¼Ð¾Ð³Ð¾ ÑÑÐ¾Ð²Ð½Ñ ÑÐ¸ÑÐºÐ° Ð´Ð»Ñ ÑÑÐ½Ð½ÐµÐ»ÐµÐ¹ Ð² ÑÐ²ÐµÑÐ´ÑÑ Ð¿Ð¾ÑÐ¾Ð´Ð°Ñ, Ð² ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²Ð¸Ð¸ Ñ ÑÐµÐºÐ¾Ð¼ÐµÐ½Ð´Ð°ÑÐ¸ÑÐ¼Ð¸ ÐÐ°ÑÑÐ¾Ð½Ð° Ð¸ ÐºÐ¾Ð½ÑÐµÐ¿ÑÐ¸ÐµÐ¹ ALARP.
ÐÐ¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÑ Ð¿Ð¾ÑÐ²Ð»ÐµÐ½Ð¸Ñ ÐºÑÑÐ¿Ð½ÑÑ Ð½ÐµÑÑÐ°Ð±Ð¸Ð»ÑÐ½ÑÑ Ð±Ð»Ð¾ÐºÐ¾Ð² Ð²Ð´Ð¾Ð»Ñ ÑÑÐ½Ð½ÐµÐ»Ñ Ð² Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð¾Ñ Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²ÐµÐ½Ð½Ð¾Ð¹ Ð¾ÑÐ¸ÐµÐ½ÑÐ°ÑÐ¸Ð¸ Ð¾ÑÐ½Ð¾Ð²Ð½ÑÑ ÑÐ¸ÑÑÐµÐ¼ ÑÑÐµÑÐ¸Ð½ ÑÐ°ÐºÐ¶Ðµ Ð°Ð½Ð°Ð»Ð¸Ð·Ð¸ÑÑÐµÑÑÑ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ UnWedge.
Ð Ð¸ÑÐ¾Ð³Ðµ, Ñ ÑÑÐµÑÐ¾Ð¼ Ð²ÑÐµÑ Ð¿ÑÐµÐ´ÑÐ´ÑÑÐ¸Ñ Ð°Ð½Ð°Ð»Ð¸Ð·Ð¾Ð² Ð¸ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð², Ð² Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ðµ Plaxis, ÐºÐ¾ÑÐ¾ÑÐ°Ñ ÑÐ°Ð±Ð¾ÑÐ°ÐµÑ Ð¿Ð¾ Ð¿ÑÐ¸Ð½ÑÐ¸Ð¿Ñ Ð¼ÐµÑÐ¾Ð´Ð° ÐºÐ¾Ð½ÐµÑÐ½ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð², Ð±ÑÐ»Ð° ÑÐ¾Ð·Ð´Ð°Ð½Ð° ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ, Ð´Ð»Ñ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¸Ñ Ð¾ÐºÐ¾Ð½ÑÐ°ÑÐµÐ»ÑÐ½ÑÑ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ð¹ Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ð¹ Ð¸ Ð´ÐµÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¹. Ð¢Ð°ÐºÐ¶Ðµ Ð² ÑÑÐ¾Ð¼ ÑÐ°Ð·Ð´ÐµÐ»Ðµ Ð±ÑÐ»Ð° ÑÑÑÐµÐ½Ð° ÑÐµÐ¹ÑÐ¼Ð¸ÑÐµÑÐºÐ°Ñ ÑÐ¸Ð»Ð°, ÑÐ¾Ð³Ð»Ð°ÑÐ½Ð¾ ÑÐ°ÐºÑÑ, ÑÑÐ¾ ÑÑÐ½Ð½ÐµÐ»Ñ ÑÐ°ÑÐ¿Ð¾Ð»Ð¾Ð¶ÐµÐ½ Ð² Ð°ÐºÑÐ¸Ð²Ð½Ð¾Ð¹ ÑÐµÐ¹ÑÐ¼Ð¸ÑÐµÑÐºÐ¾Ð¹ Ð·Ð¾Ð½Ðµ.
description: This thesis proposes methodology of modelling rock massifs as a wide basis for building complex construction facilities such as dams, hydrotechnical tunnels etc. The goal was to undertake, in a certain way, necessary systematization of knowledge and research in this field and to propose new as well as modify already existing procedures and methods of modelling. Proposed analytical and numerical models were formed based on gathered laboratory and field investigations of rock massifs on the localities of dam âSveta Petkaâ in Republic of Macedonia. Own correlations were established between these input geotechnical parameters. The work gives an example of forming a numerical model and conceptual interaction matrix by using a programme packet Examine 2D in order to show that by proper choice and varying of main elements of diagonal matrix, which include qualities and conditions of rock massifs in one hand and qualities of engineering activities, in the other hand, we can realistically examine and anticipate interaction rock â structure that is stress-strain behaviour of rock massif. 
Variational analysis was carried out with the help of the RocSupport program package in order to provide certain recommendations for an acceptable level of risk for tunnels in hard rocks, in accordance with Barton's recommendations and ALARP concept. The possibility of occurrence of large unstable blocks along the tunnel, depending on the spatial orientation of the main crack systems, is also analyzed using the UnWedge program.
Finally, taking into account all previous analyzes and results, a mathematical model was created in the Plaxis program, which works on the principle of finite element method, in order to obtain the final values of strains and deformations. Also in this section is the seismic force was taken in account, given the fact that the tunnel is located in an active seismic area.