Issue 53

A. Kostina et alii, Frattura ed Integrità Strutturale, 53 (2020) 394-405; DOI: 10.3221/IGF-ESIS.53.30 402 In addition to approximation (20), it is suggested that formula (4) can be modified as                                                        2 0 1 2 0 45 /2 1 0 45 / 2 1 1 1 2 45 / 2 tg p tg E a z c tg (21) The values of parameter z for sand, chalk and clay are given in Tab. 11. The calculated results are obtained for the designed thickness by Eqn. (21) and the numerical simulation results are shown for each material in Fig.5. The approximations are nonlinear, which is caused by the nonlinear dependence of stress on the radial coordinate and, as a consequence, on the desired ice wall thickness. The nonlinear character is determined by the material parameters of the soil, e.g., for chalk and sand, the curve is convex upwards and for clay – downwards. Chalk and sand exhibit similar cohesion values (6.2 and 6.33 MPa), and clay has significantly lower cohesion value (3.78 MPa). It is interesting that almost the same nonlinear behavior is observed for Eqn. (4). Sand Chalk Clay Z 1.140 0.198 0.153 Table 11: Values of the parameter z , entering Eqn. (21). (a) (b) (c) Figure 5 : Results of approximation of Eqn. (4) (curve 2) by function (21) (curve 1) for sand (a), chalk (b), clay (c). Markers – numerical solution.