Determination of stresses in concrete lining with rock-bolt in case of exhaustion of rock-bolt supporting strength

The article deals with the solution of analytical problem of flat axisymmetric elasticity theory, when rock-bolt supporting strength is exhausted. Expression for determination of stresses in concrete lining is deduced, where pressure increasing at exploitation have regarded. This methodology can be used at blueprint stage and preliminary calculation during mining operations. Further evaluation of concrete lining strength and geophysical probe of rock is needed for the preliminary calculation.


Introduction
Lining of the mining shaft must have an adequate load-carrying capacity and imperviousity for overall life of shaft. Different factors exercise the influence on durability, which can make operating parameters of lining worse.
At shaft excavation, support setting is in arrears of excavation by 20 -25 m. Borehole zone is fixed by rock-bolt. During these operations forms a bilayer lining, which includes outer layer of hardened rock mass and inner layer of concrete lining.
The inner layer of concrete lining is contacts with atmospheric environment of mine shaft, which corrosive properties are defined by: amplitude attributes, air-flow resistance of frames, temperature and etc. Analysis of these factors can be examined in researches [1][2][3][4][5].
The water can affect a concrete lining outer layer and rock-bolt. Analysis of corrosion processes, defects and damages in lining, examination of influence on lining load-capacity can be found in researches [6][7][8][9][10]. Exploration and empirical research illustrates that service life of rock-bolt is three-four time lower than service life concrete lining. On operational phase at one point rock-bolt loses its functionality, which leads to an increase in the load on the concrete lining and a change in the stress-strain state. Methodology of analysis this process must be refined.

Computational model
Let's consider interaction between concrete lining and rock mass, which is fixed by rock-bolt on operational phase. Circle of rock mass that fixed by rock-bolt is certain layer. It is aquasihemogeneous layer with Еstr and Rstr parameters (where Еstr is elasticity modulus and Rstr is rock mass strength fixed by rock-bolt). The axisymmetric problem of stress-deformed state of infinite plane, that relaxed by circular perforation in equal parameters of stress pattern is considered.

Results
In case of loss of rock-bolt functionality, parameters of layer 2 ( fig. 1) lead to rock mass loading-out and stress parameters change. These may be written as: Where λlateral earth pressure coefficient; γweight of incumbent rock mass; Нdepth of mine shaft; αrbloading-out coefficient of support, based on the fact that shaft excavation is in arrears of excavation and fixed rock-bolt influence on rock mass.
For determination parameter αrb let's analyze the dynamic of movement in contour line of mine shaft. Summary fractional rock mass contour line movement before concrete lining setting may be written as [12]: where u0 -Initial displacements before fixing rock-bolt; urbmine shaft contour line displacement after fixing rock-bolt and before concrete lining setting; u∞total displacements of relaxed mine. Thus , 1 * 0 where α *coefficient in accordance with [1]. Value parameter krb determined with numerical model study of bottom shaft zone, which has fixed rock mass layer, width equal rock-bolt length lrb and instantiated of elasticity model

Krb·Е0.
As a result of data handling, will have correlation connection for determinating parameter krb: where Doutside of shaft timber diameter, m; l0 -Concrete lining arrearage from bottom shaft, m. Equivalent stresses applied at infinite, is given as where 0coefficient equals at plane deformation: 0coefficient equals at plane deformation.
Radial stresses on outline section of mine shaft (with rock mass contact) equal Where K0stress transfer coefficient through infinite layer of rock mass until rock-bolt strength loss: 0stress transfer coefficient through infinite layer of rock mass after rock-bolt strength loss: where G0rock mass shear modulus; G2layer 2 shear modulus fixed by rock-bolt; G ' 2layer 2 shear modulus after rock-bolt strength loss; с2=(r1+l)/r1; K2stress transfer coefficient through layer 2 that fixed by rock-bolt: G1concrete shear modulus; 1transverse deformation coefficient.
Average normal tangential stresses in lining of mine determined from the formula where Strength condition for lining , mb R   (13) where Rbestimated concrete compressive resistance.

Conclusions
In connection with the problem solution of flat axisymmetric elasticity theory we generated a method of determining stresses in lining during rock-bolt support strength loss. This method can be used at a blueprint stage and preliminary calculation during operation of mining venture. Further evaluation of concrete lining strength and geophysical probe of rock is needed for the preliminary calculation. This equates to implementation of advanced lining enforcement measures.