Issue 53

A. Kostina et alii, Frattura ed Integrità Strutturale, 53 (2020) 394-405; DOI: 10.3221/IGF-ESIS.53.30 398 M ATERIALS AND METHOD he allowable ice wall thickness was determined for three typical materials: sand, chalk and clay. We considered the bed rock depth values of 100m, 200m, 300m, and 500m. Tabs. 1 and 2 give the mechanical parameters of the soil in thawed and frozen states which were provided by the Institute of Nature Management of the NAS of Belarus. The parameters of the frozen soil were obtained at T =-8 0 C and for load duration of 12 h. These data were used for calculating the load acting on the ice wall according to formulas (15) – (18). The obtained data are given in Tabs. 3-5. Soil E ′ , GPa  с , kPa  , 0 Sand 0.32 0.3 9.6 30 Chalk 0.3 0.35 1 31.5 Clay 0.364 0.18 105 25 Table 1: M echanical parameters for the soil in thawed state . Soil E ′ , GPa  с , MPa  , 0  s , MPa Sand 5.3 0.18 6.33 37 4.4 Chalk 2.5 0.15 6.20 24 7 Clay 1.7 0.17 3.78 10 2.2 Table 2: M echanical parameters for the soil at T =-8 0 C . Load 100 m 200 m 300 m 500 m p, MPa 1.557 3.222 4.889 8.222 p ′ , MPa 2 4 6 10 Table 3: Loads acting on the frozen sand ice wall Load 100 m 200 m 300 m 500 m p, MPa 0.626 1.253 1.881 3.135 p ′ , MPa 2 4 6 10 Table 4: Loads acting on the frozen chalk ice wall. Load 100 m 200 m 300 m 500 m p, MPa 0.678 1.490 2.301 3.925 p ′ , MPa 2 4 6 10 Table 5: Loads acting on the frozen clay ice wall. The finite-element method was used for the solution of boundary value problem. The examined area was divided into rectangular elements. We controlled the convergence of the numerical solution based on a series of calculations on grids with elements of different sizes for the clay layer at a depth of 200m. The sizes of elements in the ice wall area with no mine working support (lining) varied from 1.28 to 0.02m. The relative error err i is defined by the formula