Scientific journal

European Journal of Natural History

ISSN 2073-4972

ИФ РИНЦ = 0,301

To evaluate the degree of oscillation of crack that is formed in fragile environment from a straight direction, comparative research to define tension that arise in its peak and in different distances from it. Marble has been selected as the destructed material. The problem was solved considering three possible ways to impact it: with fluids, plastic substances, and also with gads trough spurs and cracks that are described by similar geometric parameters. The following data was used in the calculation:

• pressure that is necessary to create in a spur to initiate and continue the destruction process (no less) - 45 MPa;
• spur radius - 25 mm;
• length of the formed crack - 0,2 m;
• utmost stretching tension for marble - σp = 20 MPa;
• utmost cramping tension for marble - σc = 160 MPa;
• coefficients of friction against a crack walls: liquids - 0; plastic substances - 1; gads - 0;
• coefficients of a crack filling: liquids - 1; plastic substances - 0,6; gads - 0.

The objective of our calculations was to define horizontal σx and vertical σy stretching tensions. The goal was being solved using the necessary systems of differencial equations of the second order that were realized in means of computer modelling Comsol Multiphysics 3.5a.

The main differential characteristics of destruction of a fragile environment by liquids are an absolute filling of cracks by the destructing matter and equal pressure degrees at all points according the law of Pascal. Hermetization of a spur collar was not considered. The calculations show that the destruction of marble with liquids goes under maximum horizontal pressured up to 102,5 MPa, and vertical - up to 110 MPa. Maximum horizontal oscillation equals ± 20 mm, and vertical - ±75 mm per each 200 mm of the formed crack length.

The schematics of destruction of a fragile environment with plastic substances is characterized by partial filling of the formed crack with them and different pressure along its length that decreases from the peak point in accordance with the logarithmic law. Hermetization as a spur collar was not considered. The calculations show that destruction of marble with plastic substances goes under maximum horizontal pressure up to 88 MPa, and verti-
cal - up to 110 MPa. Maximum horizontal oscillation equals ±14 mm, and vertical - ±75 mm per each 200 mm of the formed crack length.

The schematics of destruction of a fragile environment with gads is characterized by an absence of crack filling and impact upon the destructed object only in points of contact with the gad. In this case no destructing matter fills a spur and a crack, formed with a gad. The calculations show that destruction of marble with gads goes under maximum horizontal pressure up to 102,5 MPa, and verti-
cal - up to 110 MPa. Maximum horizontal oscillation equals ±20 mm, and vertical - ±75 mm per each 200 mm of the formed crack length.

On the foundations of the circle of works we can conclude that:

1. During the destruction of marble through spurs by short cracks (up to 200 mm) with liquids or gads vertical (up to 110 MPa) and horizontal (up to 102,5 MPa) pressures that arise in a fragile environment and also oscillations of the formed cracks from their straight direction in vertical (±75 mm) and horizontal (±75 mm) axis are same.
2. In case of destruction of marble through spurs by short cracks (up to 200 mm) with plastic substances horizontal pressures that arise in a fragile environment decrease by 14,1% (down to 88 MPa), and oscillations of the formed cracks from the straight horizontal direction decrease by 30% (down to ±14 mm).
3. The lowest degree of horizontal pressure that arise in a fragile environment (down to 88 MPa in marble) that is destructed with plastic substances through spurs explains the minimal interval of oscillations of the formed cracks from a straight direction in vertical axis (down to ±14 mm), compared to usage of liquids and gads for the same purpose.