PSI - Issue 32

A. Yu. Shumikhina et al. / Procedia Structural Integrity 32 (2021) 224–229 A.Yu. Shumikhina/ Structural Integrity Procedia 00 (2019) 000–000

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2. Methodology The parametric support of the model is important both during mathematical modelling and the construction of constitutive relations that reflect the deformation processes of the undermined rock mass (Baryakh A.A., Samodelkina N.A. 2009). The parametric support is the availability of reli-able information about the structure of the considered section of the mass, and the quantitative es-timation of the model parameters. As a rule, the geomechanical analysis of safe mining conditions for productive strata is based on a priori geological information obtained from the drilling of explora-tion wells on a 1x1 km grid. This does not allow the lateral variability of the physical and mechani-cal properties of the waterblocking stratum (WS) to be considered in calculation scheme of mathe-matical modelling. Complex geophysical studies must be performed to define the structural features of the WS. Their interpretation makes it possible to form an appropriate physical and geological model of the salt mass, with its subsequent transformation into a geomechanical calculation scheme (Baryakh et al. 2017). It is preferrable in seismic geomechanical studies to carry out the first stage of seismic surveys before the stoping. At later stages, this helps to easily separate the contribution of natural and man-induced factors to changes of the parameters of wave fields, which increases the reliability of the constructed physical and geological models and geomechanical calculations based on them. It is not always possible to implement this control option. To determine the genesis of ge-ophysical anomalies, rules have been developed for the joint interpretation of the results of seismic geomechanical studies. Based on the numerous results of seismic geomechanical studies, we found a consistency of the changes in the components of the stress field and the velocities of seismic waves: the zones of the abutment rock pressure corresponded to an increase in the velocities of elastic vibrations, and the unloading areas corresponded to a decrease in their values. To determine the origin of the iden-tified anomalies, several stages of seismic geomechanical studies were proposed. During the first stage, a preliminary geomechanical calculation was performed for an averaged physical-geological model, which did not consider the factor of lateral variability of the physical properties of the rocks. The consistency of the lateral change in the vertical stress and the velocities of the elastic waves recorded in the selected elements of the section were analysed based on these calculation results. The violation of the correspondence between an increase in the compressive stresses and an increase in velocities was interpreted as indicating the presence of areas of man-induced disturbances; low-speed zones corresponding to areas of an insignificant stress changes were considered to be naturally weakened ones. Based on this joint analysis of the seismic and geomechanical data, the parameters of the mathematical model were adjusted and a recalculation was made, which enabled an estima-tion of the rock mass state. The mathematical modelling was carried out in a two-dimensional elastoplastic formula-tion for the conditions of the plane-strain state (Fadeev 1987). Estimation of changes in the state of the WS during the displacement process was based on the analysis of the formation of subvertical fractures in the undermined mass. The Mohr-Coulomb criteria (Kuznetsov 1947) and ultimate ten-sile stresses were used to analyse the discontinuity of the WS layers. To describe the deformation progress in the undermined mass within time, a rheological approach was used based on a modification of the well-known method of alternating deformation moduli (Amusin 1973). In this modification (Baryakh et al. 2005), the method of alternating the deformation moduli characterises the deformation of only the mined layers, but not all the elements of the geological section. At the same time, changes of the deformation moduli in time are com-pletely determined by the graphs of the subsidence increase in the earth’s surface (Baryakh A.A., Telegina E.A. 2005). To analyse the situation at the current time, the determination of the creep function Ф(t) was based on the actual graphs of the subsidence increase of the earth’s surface, see Fig. 1:

( )

0 ν η t

( ) t Φ =

(1)

where the subsidence values ( ) t η were found through the surveying, and 0 v were elastic displacements related to the goaf formation.