Study of the interaction between roof bolting of the output and a breed array inclined to creep

The basic equations of the theory of linear hereditary creep are considered. An algorithm for determining the value of the anchor tension as a result of deformation of rocks in the bottom-hole zone of the barrel is presented. The area of the scope of roof bolting trunks in various breeds is defined. 1 Description of the method of calculation Consider the interaction between roof bolting in the bottom-hole zone of the barrel and a breed array that exhibits the properties of creep [1-4]. Apply the theory of linear hereditary creep proposed by L. Boltzmann and modified by Volterr. The creep of rocks is described by the Voltaire integral equation of the second kind            t d t t L E E t 0 0 , 1      (1) where σ (t), ε (t) – are stresses and strains at time t; τ – time before instant t; L(t τ) – the influence function (creep kernel). At constant stresses from the equation (2.53) we obtain


Description of the method of calculation
Consider the interaction between roof bolting in the bottom-hole zone of the barrel and a breed array that exhibits the properties of creep [1][2][3][4].
Apply the theory of linear hereditary creep proposed by L. Boltzmann and modified by Volterr.
The creep of rocks is described by the Voltaire integral equation of the second kind where σ (t), ε (t) -are stresses and strains at time t; τ -time before instant t; L(t -τ) -the influence function (creep kernel). At constant stresses from the equation (2.53) we obtain     .
Academician Zh. S. Yerzhanov showed that the deformation of rocks to a certain level of loading corresponds to the equation (1) with the core of Abel type where , α -creep characteristics obtained experimentally.
Academician Rabotnov U. N. showed that the problem of linear hereditary creep theory can be formally considered as the problem of elasticity theory, in which instead of elastic constants it is necessary to use temporal operators with creep kernel. Then the equation (2) can be represented as Prof. Linkov, A. M. and Ph. D. of engineering Amusin B. Z. proved that in the tasks of mechanics of underground structures in which boundary conditions and volume forces are time independent, the operator expressions for elastic constants can be replaced by algebraic expressions corresponding to the kernel of the integral equation (the method of variable modules).
Based on the above, the creep equation (3) looks like: where Фthe creep function: The time functions for the deformation modulus, shear modulus, and Poisson's ratio are: The time functions for the deformation modulus, shear modulus, and Poisson's ratio are: In the framework of the theory described above, we consider the interaction of anchors installed without tension from the bottom of the barrel, with the breed array.
As the bottom of the barrel moves away, the change in the stress-strain state of the massif is described by the expression Н   * . The coefficient α*, taking into account the lag of the considered point from the bottom, can be determined from the ratio [2][3][4] , where u0the starting array offset; u∞the full array offset; ldistance from the considered point to the bottom of the trunk; r0the radius of the barrel is rough; Hence we get The proportion of increment of the total coefficient α* at each time t, defining the distance l, will be    .  where rsthe radius of the bearing washer; l * =l/lz; lzthe length of the fixed part of the anchor; l'=l/aij; аijdistance from the j-th anchor to the anchor.

Calculation results
On the basis of the considered algorithm, the author determined the maximum application area of rigid anchors for three types of rocks (table. 1), for anchorage for the most frequently used parameters in practice: l=1,8 -2,2 m; Аа=3,14 sm 2 (the diameter of the rod 20 mm); lz=100 sm type of reinforcing steel used -А300, A400. The calculation was made for the barrel diameter of approximately 7.5 m with standard parameters of the tunneling cycle. where Srrod area, m 2 ; Rрthe calculated resistance of the rod material to tension for reinforcing steel of class А300 -Rр =270 МPа, А400 -Rр =340 МPа; mc-the working condition ratio, in dry wells mу=0,9; in wet wells mу=0,7 -0,8. The field of application is presented in the form of graphs in Fig. 1 -3.

Conclusions
From the graphs it can be seen that the tendency of rocks to creep largely determines the application area of anchors. In sandstones practically in all range of mountain-geological conditions it is possible to carry out fastening by rigid designs of anchors. In creep-prone mudstones and siltstones in a wide field there is a need to increase the strength characteristics of the anchors or the use of pliable structures.
The final determination of the necessary compliance of anchors in rocks prone to creep should be made on the basis of the results of full-scale measurements of the values of radial displacements in the bottom of the barrel [5][6][7].