title: ÐÐ»Ð¸ÑÐ½Ð¸Ðµ ÑÑÑÑÐºÑÑÑÑ Ð½Ð° Ð¾ÑÐ¾Ð±ÐµÐ½Ð½Ð¾ÑÑÐ¸ ÑÐ°Ð·ÑÑÑÐµÐ½Ð¸Ñ Ð³ÐµÑÐµÑÐ¾Ð³ÐµÐ½Ð½ÑÑ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»Ð¾Ð²: Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ Ð´Ð¸ÑÐºÑÐµÑÐ½ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð²
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: The Influence of Materials Structure on the Main Features of the Fracture Process in Rocks: Discrete Elements Method
Creators: name: ÐÐµÑÐ¸Ð½, ÐÐ¾Ð½Ð°
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: 2023
Subjects: ÐºÐ¾Ð¼Ð¿ÑÑÑÐµÑÐ½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð¼ÐµÑÐ¾Ð´ Ð´Ð¸ÑÐºÑÐµÑÐ½ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð²
ÑÐ°Ð·ÑÑÑÐµÐ½Ð¸Ðµ Ð³Ð¾ÑÐ½ÑÑ Ð¿Ð¾ÑÐ¾Ð´
Ð°ÐºÑÑÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÐ¼Ð¸ÑÑÐ¸Ñ
Ð¼ÐµÑ Ð°Ð½Ð¸ÑÐµÑÐºÐ¾Ðµ Ð½Ð°Ð³ÑÑÐ¶ÐµÐ½Ð¸Ðµ
computer modelling
discrete elemente method
rock fracture
acoustic emission
mechanical loading

description: Ð ÑÐ°Ð±Ð¾ÑÐµ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½ ÐÐµÑÐ¾Ð´ ÐÐ¸ÑÐºÑÐµÑÐ½ÑÑ Ð­Ð»ÐµÐ¼ÐµÐ½ÑÐ¾Ð² Ð´Ð»Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐ°Ð·ÑÑÑÐµÐ½Ð¸Ñ Ð² Ð³Ð¾ÑÐ½ÑÑ Ð¿Ð¾ÑÐ¾Ð´Ð°Ñ. ÐÑÐ»Ð° Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð° Ð¼Ð¾Ð´ÐµÐ»Ñ ÑÐ²ÑÐ·Ð°Ð½Ð½ÑÑ ÑÐ°ÑÑÐ¸Ñ (BPM âBonded Particle Model). Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð» Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÑÐµÑÑÑ Ð² Ð²Ð¸Ð´Ðµ ÑÐ¾Ð²Ð¾ÐºÑÐ¿Ð½Ð¾ÑÑÐ¸ Ð§Ð°ÑÑÐ¸Ñ (Ð¸Ð¼Ð¸ÑÐ¸ÑÑÑÑÐ¸Ñ Ð·ÑÑÐ½Ð° Ð¿Ð¾Ð»Ð¸ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ð¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»Ð°), ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐ¾ÐµÐ´Ð¸Ð½ÑÑÑÑÑ ÑÐ²ÑÐ·ÑÐ¼Ð¸ (Ð·Ð°Ð´Ð°ÑÑ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ðµ Ð¼ÐµÐ¶Ð´Ñ Ð·ÑÑÐ½Ð°Ð¼Ð¸ Ð¸ Ð¸Ð¼Ð¸ÑÐ¸ÑÑÑÑ Ð¼ÐµÐ¶Ð·ÑÑÐµÐ½Ð½ÑÐµ Ð³ÑÐ°Ð½Ð¸ÑÑ.) Ð Ð°Ð·ÑÑÑÐµÐ½Ð¸Ðµ ÑÐ²ÑÐ·ÐµÐ¹ Ð² Ð´Ð¸ÑÐºÑÐµÑÐ½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÐ°ÐºÐ¾Ð³Ð¾ ÑÐ¸Ð¿Ð° ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²ÑÐµÑ Ð¿Ð¾ÑÐ²Ð»ÐµÐ½Ð¸Ñ ÑÑÐµÑÐ¸Ð½. ÐÐ¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð»Ð¸ÑÑ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð¾Ð±ÑÐ°Ð·ÑÑ, ÑÐ¾ÑÑÐ¾ÑÑÐ¸Ðµ Ð¸Ð· Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»Ð¾Ð² Ñ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÐ¼Ð¸ ÑÐ¸Ð·Ð¸ÐºÐ¾-Ð¼ÐµÑÐ°Ð½Ð¸ÑÐµÑÐºÐ¸Ð¼Ð¸ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ°Ð¼Ð¸. ÐÑÐ»Ð¸ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ñ ÑÐ°ÑÐ°ÐºÑÐµÑÐ½ÑÐµ Ð¾ÑÐ¾Ð±ÐµÐ½Ð½Ð¾ÑÑÐ¸ ÑÐ°Ð·ÑÑÑÐµÐ½Ð¸Ñ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»Ð¾Ð², Ð¸Ð· ÐºÐ¾ÑÐ¾ÑÑÑ ÑÐ¾ÑÑÐ¾ÑÑ Ð¾Ð±ÑÐ°Ð·ÑÑ. ÐÑÐ»Ð¸ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ñ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ, ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ð½ÑÐµ Ð½Ð° Ð¯Ð Python, Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑÐ¸Ðµ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸ÑÑ Ð°Ð½Ð°Ð»Ð¸Ð· ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ° Ð¿Ð¾ ÑÐ°Ð·ÑÑÑÐµÐ½Ð¸Ñ Ð³Ð¾ÑÐ½ÑÑ Ð¿Ð¾ÑÐ¾Ð´. ÐÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ñ ÑÐ¿Ð¾ÑÐ¾Ð±Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐ°Ð·Ð²Ð¸ÑÐ¸Ñ Ð´ÐµÑÐµÐºÑÐ½Ð¾Ð¹ ÑÑÑÑÐºÑÑÑÑ Ð² Ð³Ð¾ÑÐ½ÑÑ Ð¿Ð¾ÑÐ¾Ð´Ð°Ñ Ð¿ÑÐ¸ Ð¸Ñ Ð½Ð°Ð³ÑÑÐ¶ÐµÐ½Ð¸Ð¸, Ð° ÑÐ°ÐºÐ¶Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð°Ð½Ð°Ð»Ð¾Ð³Ð° ÑÐ¸Ð³Ð½Ð°Ð»Ð¾Ð² Ð°ÐºÑÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð­Ð¼Ð¸ÑÑÐ¸Ð¸ (ÐÐ­). ÐÑÐ»Ð° Ð²ÑÑÐ²Ð»ÐµÐ½Ð° Ð´Ð²ÑÑÑÑÐ°Ð´Ð¸Ð¹Ð½Ð¾ÑÑÑ ÑÐ°Ð·ÑÑÑÐµÐ½Ð¸Ñ Ð³Ð¾ÑÐ½ÑÑ Ð¿Ð¾ÑÐ¾Ð´: Ð¿ÐµÑÐ²Ð°Ñ ÑÑÐ°Ð´Ð¸Ñ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸Ð·ÑÐµÑÑÑ Ð´ÐµÐ»Ð¾ÐºÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ð½ÑÐ¼ Ð¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÑÑÐµÑÐ¸Ð½, Ð²ÑÐ¾ÑÐ°ÑâÐ¾Ð±ÑÐµÐ´Ð¸Ð½ÐµÐ½Ð¸ÐµÐ¼ ÑÐ°ÑÑÐ¸ Ð´ÐµÑÐµÐºÑÐ¾Ð² Ð² Ð¼Ð°Ð³Ð¸ÑÑÑÐ°Ð»ÑÐ½ÑÑ ÑÑÐµÑÐ¸Ð½Ñ, Ð¿ÑÐ¸Ð²Ð¾Ð´ÑÑÑÑ Ðº ÑÐ°Ð·ÑÑÑÐµÐ½Ð¸Ñ Ð¾Ð±ÑÐ°Ð·ÑÐ°. Ð­ÑÐ¾Ñ ÑÐµÐ·ÑÐ»ÑÑÐ°Ñ ÑÐ¾Ð³Ð»Ð°ÑÑÐµÑÑÑ Ñ Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ð½Ð¾Ð¹ ÑÐ°Ð½ÐµÐµ Ð´Ð²ÑÑÑÑÐ°Ð´Ð¸Ð¹Ð½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»ÑÑ ÑÐ°Ð·ÑÑÑÐµÐ½Ð¸Ñ Ð³Ð¾ÑÐ½ÑÑ Ð¿Ð¾ÑÐ¾Ð´, ÑÑÐ¾ Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÐµÑ Ð³Ð¾Ð²Ð¾ÑÐ¸ÑÑ Ð¾ ÑÐ¾Ð¼, ÑÑÐ¾ ÐºÐ¾Ð¼Ð¿ÑÑÑÐµÑÐ½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð°Ð´ÐµÐºÐ²Ð°ÑÐ½Ð¾ Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÐµÑ Ð¿ÑÐ¾ÑÐµÑÑ ÑÐ°Ð·ÑÑÑÐµÐ½Ð¸Ñ. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ñ Ð²Ð°ÑÐ¸Ð°Ð½ÑÑ ÑÑÐ»Ð¾Ð¶Ð½ÐµÐ½Ð¸Ñ Ð´Ð¸Ð°Ð³ÑÐ°Ð¼Ð¼Ñ Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸ÑâÐ´ÐµÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ (Ð¿Ð¾ÑÐ²Ð»ÐµÐ½Ð¸Ñ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾ÑÑÐ¸) Ð² ÑÐ»ÑÑÐ°Ðµ Ð³ÐµÑÐµÑÐ¾Ð³ÐµÐ½Ð½ÑÑ Ð³Ð¾ÑÐ½ÑÑ Ð¿Ð¾ÑÐ¾Ð´.
description: Discrete Element Method is being used for modeling the fracture of rocks. For this purpose, Bonded Particle Model (BPM) is used. In BPM material is represented by a set of Particles (imitate the grains of polycrystalline material), connected with bonds (imitate the grain boundaries). The disruption of bonds in a discrete model of this type corresponds to an appearance of cracks. Cylindrical specimen, consisting of materials with various physical and mechanical properties are modeled. The characteristics of fracture of these materials are studied. Result analysis programs were developed in Python. Methods of modeling the evolution of defects (cracks) in rocks and modeling the parameters of the analog of acoustic emission are proposed. The two-stage process of rock fracture is shown: the first stage is a delocalized generation of cracks, the second oneâthe merge of the part of the defects into a single main crack, that results in a final destruction of the specimen. This result corresponds to a previously offered twoâstage model of rock fracture and lets us to claim that the offered computer model is adequate. Several variants of more complex stress-strain diagrams in case of heterogeneous rocks are presented.