Bolatova A.B., YElgazinov D.S.
The East Kazakhstan state technical university named
aftor D.Serikbaev
THEORETICAL SUBSTANTIATIONS OF RELIABILITY OF UNDERGROUND DESIGNS FOR
STRATIFIED SYSTEMS OF WORKING OUT OF ORE BODIES WITH THE BOOKMARK
By working out of firm
minerals by underground way the difficult system of underground constructions
presented by extended mountain developments, variously focused in space is
created. The network of mountain developments of any mine or mine together with
hollow sites (HS) represents a difficult engineering construction which
naturally requires an estimation of level of its reliability on an interval of
time of its functioning for mining operations.
Without stopping on
details of the description of underground constructions, we will note their one
general property – it should be steady (not destroyed) on some quite certain
time T.
Hence, the basic characteristic of their stability it is necessary to
accept size of their probability not destructions on Ò, i.e.
Ðí=1-Ðâ (1)
Where Ðâ – probability
of destruction of an underground design.
Condition of loss of
stability various be whole can it is presented by crossing of two random
variables:
Ðâ=
(2)
Where - function of
distribution normal to section took pressure in its least diameter or width,
ÌÏà;
- Function of distribution of durability of breeds took on compression, ÌÏà.
The population means and
dispersion is defined on known analytical dependences for various hypotheses of
formation of loading on took. These hypotheses in article are not discussed.
Also are defined on the basis of experimental data on samples taking into
account the real environment.
Besides catastrophic
refusals by deposit working out by underground way there are refusals to which
number we carry most often shown:
- Destruction single
columnical or tape it is whole;
- Stability loss at
planimetric a file on a breast of a face and from sides of developments;
- A collapse of a roof
of developments.
Probability of
destruction of the single it is whole it is defined by crossing of function of
distribution (2) where and dispersions of parameters and define a population
mean under known formulas.
Stability loss at
planimetric a file is predicted by crossing of random variables: functions
distribution pressure, perpendicular to a breast of a face and sides of
mountain developments and durability of breeds on rupture. The probability of a
collapse of breeds of a roof on expression is similarly defined:
(3)
Let's consider further
algorithm of definition of probabilities of display of catastrophic and usual
refusals at crossing considered above random variables.
Let's designate the
right parts of an inequality (1), (2), (3) functions of density of distribution
of probabilities, and left – functions then all possible outcomes of definition
of reliability of underground constructions will be expressed by following set
of analytical formulas: (pic. 1 – 6).
Let's consider various
outcomes:
(4)
(5)
(6)
Then reliability to be
defined under the following formula:
(7)
Reliability for this
case will be expressed in a kind:
(8)
For this kind it is had:
(9)
And at last a case 6,
when
Reliability we will
write down in a kind:
(10)
Here in formulas
designations are accepted:
j(Sïð) = j(S) - function of
distribution of loadings on at planimetric a file (normal, tangents),
Here we consider all
cases of crossing of sizes y(S¢) è j(S).
{y(S¢) Ç j(S)}. (11)
We develop universal
methods of calculation of sizes of reliability (Ðí) (7¸10) for the normal law
of distribution j(S) è y(S¢) äëÿ êîìïüþòåðíûõ
òåõíîëîãèé óïðàâëåíèÿ.
Basically, random
variables j(S), y(S¢) can be distributed
under any known law which parameters can be defined or theoretically a method
of statistical tests, or experimentally.
To the simplified
estimation of reliability of designs of underground constructions probably to
apply the elementary laws of distribution:
The equiprobable:
; (12)
The triangular:
; (13)
; (14)
The truncated normal:
(15)
With parameters:
(16)
With led norm to unit
the area F1 = 0,999, similarly for y(S¢).
The specified laws of
distribution (12), (15) allow to receive formulas (10) 
(12) for Ðí
in an explicit form.
The schedule of possible
crossings of random variables will be presented in the following articles.
According to the results
resulted above in basic parameters for research of reliability (stability) of
an artificial concrete roof and an artificial file, supporting a roof of
chambers are:
1. 
- Strength of a file
of a bookmark on a stretching, is defined in vitro
, ÌÏà or òñ/ì2 (17)
where, 
- Relative density
bookmark a file,
- Safety factor
factor; òñ/ì3;
L – Flight of the
chamber, ì;
hí – Height
of a layer of a bookmark, ì;
2. Loading on artificial
ceiling bookmarks which works on a file stretching. This size is recommended to
be defined under the formula of prof. N.S.Bulychyov.
Ð
= 
, òñ/ì2 (18)
where, 
=òñ/ì3; b =
ì; Ñ = òñ/ì2; Õ è tg φ – the dimensionless;
Laboratory researches
durabilitical characteristics bookmark a file allow to estimate them during all
period firming and normal work in the form of two components:
- Durability bookmark a file on compression (on samples) - 
;
- Durability bookmark a file on rupture (on samples) - 
It is necessary to pay attention that working off of deposits of
valuable ores is made by descending layers when techniques and people work in
the chamber with an artificial file of a roof. Clearly that reliability of a
roof (bookmark) should be enough high. By data statisticians of work of
Bakyrchiksky gold mining mine reliability of Ðç of
an artificial roof in function from factor of a stock of Êç
of its durability us will be investigated in an interval:
0,9≤Ðç≤0,99 (19)
2≤Êç≤14
1. Universal mathematical models with stochastic
statement for definition of reliability of underground constructions, in
particular for artificial bookmark files are received by a theoretical way.
2. Settlement models for definition of stability
artificial bookmark files are received.
3. Stochastic laws for reliability of an artificial
roof from factor of a stock of its breaking strength are deduced.
The literature list
1. N.S.Bulychyov
of underground constructions (in examples and problems), Bowels, Moscow, 1989.
314 p.
2. E.I.system's
Horns the analysis in mining. Alma-Ata. 1976. 206 p.
3. Rogov
E.I., Gritsko G. I, Vylegzhanin V. N. Mathematical models of adaptation of
processes and colliery subsystems. Alma-Ata, 1979. 208 p.