PSI - Issue 32

60 S. Yu. Devyatkov et al. / Procedia Structural Integrity 32 (2021) 56–63 S. Yu. Devyatkov / Structural Integrity Procedia 00 (2019) 000 – 000 5 where is the shear stiffness of the contact, is the shear stiffness of the contact in the softening region, is the peak strength of the contact, and ∗ is the residual strength. The ultimate resistance of the contact to shear (the peak strength) was calculated using the Coulomb equation: ൌ ൅ ǡ where is the adhesion factor of the contact, and is the inner friction angle of the contact. When tensile stresses were applied to the contact, it was assumed that the contact opened and its shear and normal stiffness decreased to zero ( ൌ ൌ Ͳ ). The properties of the clay contacts in salt rockswere taken from laboratory data (Baryakh et al. 2011). It was assumed that the clay interlayers that developed in the roof of the longwall face were degassed as a result of overworking. In view of this, the computation allowed for the opening of only the clay contacts present in the longwall soil. Preliminary calculations showed that accounting for one or two clay layers in the soil may not be sufficient to identify the main laws of behaviour. However, the introduction of a larger number of contacts significantly increases the convergence time for the problem. The best option therefore seemed to be to include the first three clay layers of the soil in the model, and these were implemented in the computations as described below. 3. Results of Mathematical Modelling The mathematical modelling results show that during the face advance in the soil of the mine working, a zone of plastic deformation associated with the formation of the opening mode fractures is localised. Caving of the roof rocks begins to occur when the length of the worked-out space is about 5 m (Fig. 3a). As the length of the worked-out space increases (Fig. 3b – d), the jointing section in the soil expands and the volume of the caved roof rocks increases. When the size of the worked-out space is more than 20 m (Fig. 3e – f), the jointing section in the soil is stabilised in depth, and its increase along the lateral direction is then recorded. For a decompaction coefficient of 1.1, the worked-out area fills with caved rocks, and this prevents the further development of rock jointing zones in the roof. Rocks up to and including the position of the clay-carnallite member are therefore very prone to caving. It should be noted that for a significantly greater length of the worked-out space, fracturing and possible caving of the roof can also affect the overlying strata. In general, there is a periodicity in the nature of the rock mass destruction in the vicinity of the worked-out area. We first recorded an increase in the jointing zones in the soil and the volume of the caved rocks in the roof. The worked-out space then filled with the caved rocks, preventing a further increase in the jointing zones in the vertical direction. This process was then repeated. According to our computations, the properties of the rocks caved from the roof (i.e., those filling the worked-out longwall space) are critical factors affecting the nature of the mass deformation. Depending on the deformation properties of the caved rocks, the calculated subsidence value of the earth surface changed significantly. In our mathematical model, we assumed that these were an order of magnitude smaller than the corresponding indicators of the rock mass. Fig. 4 shows the calculated subsidence along the benchmark (Fig. 1) during the face advance, for various properties of the caved rocks (curves 2 – 5). As expected, a greater decrease in relation to the properties of the enclosing rocks causes maximum subsidence of the earth surface, and there is an increase in the subsidence gradient when the longwall face passes the area where the benchmark is located. It can clearly be seen that the subsidence curves have similar shapes, and that the subsidence varies over a wide range. It can also be observed that these subsidence curves differ from the data obtained from mine surveying (Curve 1), which indicates that when the longwall face passes the benchmark area, there is a sharp increase in the subsidence gradient.