PSI - Issue 13

Kostina A. et al. / Procedia Structural Integrity 13 (2018) 1273–1278 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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In figure 1 the experimental data for the Callovian sandy loam, the curve obtained from the analytical dependence and the curve obtained from a three-dimensional numerical simulation for the identified values are presented. The numerical simulation was performed for the mentioned experimental conditions with using the constitutive relation (4). As it can be seen the analytical curve is in good agreement with the numerical one. From figure 1 it could be concluded that (4) allows describing the primary nonstationary creep stage with a deceasing deformation rate and the secondary stationary creep stage with an almost constant rate, but it is not able to quality characterize the tertiary creep stage related to progressive flow with an increasing rate. The geometrical parameters for the mine shaft sinking were defined as 5.25 in r  m, 5 h  m, 0.1 max   m on the basis of documentations used for structural design of potash mines in Belarus. The time required for lining installation was assumed 12 pr t  h. The rock pressure acting on the ice-soil retaining structure was estimated by the standard engineering formula (Farazi and Quamruzzaman (2013)) w w w P g H H    – hydrostatic pressure, H , w H – depths of a soil layer and a groundwater level, [m], γ l , γ w – average density of rock soils and density of water, [kg/m 3 ],  – friction angle, [deg], g – the gravitational acceleration. The expression for l P is based on the Rankine’s theory ( Terzaghi et al. (1996)). In this study it was assumed that 1.5 w H  , 3 2 10 l    . For the sandy loam 32   (Vaylov et al. (1962)). In figure 2 (a) relationship of the rock pressure to the depth is presented. Figure 2 (a) shows values of the thickness E of the ice-soil cylinder given by (5) for H equal 100, 115, 250, 500 and 1000 m. Figure 2 (b) presents maximal values u 2 ,max of the second displacement component u 2 in depending on H obtained by numerical solving (1) – (4). As can be seen u 2 ,max nonlinearly increases with the depth and reaches 8.8 m at the depth 1000 m. Despite on the significance wall thickness reaching to 104.1 m at 1000 m, the maximal admissible displacement Δ max is not exceeded only for the depths less than 115 m. At that u 2 ,max equals 0.08 m at the depth 100 m. l w P P P   (6) where 0 Tan[(90 ) / 2]   l l P Hg   – effective lateral pressure, ( )

a b Fig. 1. (a) relationship between 33  and t (markers – the experimental data, dash line – the analytical curve, solid line – the numerical one); (b) relationship between rock pressure P and depth H .

b Fig. 2. (a) values of thickness E and (b) values of 2, max u in depending on depth H .

a