Issue 53

A. Kostina et alii, Frattura ed Integrità Strutturale, 53 (2020) 394-405; DOI: 10.3221/IGF-ESIS.53.30 400 h ′ , m Sand Chalk Clay 100 0.304 0.171 0.404 200 0.595 0.340 0.910 300 0.860 0.508 1.441 500 1.330 0.838 2.582 Table 8: Ice wall thickness calculated by formula (4). A comparison of the ice wall thickness values found during the numerical solution of problem (5)-(18) with the results obtained by Eqns. (3) and (4) is illustrated in Fig.3. For all materials under study, Eqn. (3) shows the most distinction from the numerical simulation results (Fig. 3a). The greatest ice wall thickness reserve is seen for clay and sand, especially, for the layers at a depth of 500 m. This is because the ice wall is subjected to maximum loads at this depth. In this case, the deviations from the numerical results obtained for clay and sand are the greatest, 12.8 m and 13.7m, respectively. (a) (b) Figure 3: Difference between the designed ice wall thickness obtained via numerical simulations and the analytical estimations for the ice wall thickness found by Eqns. (3) (a) and (4) (b). It was found that the results of numerical simulations of the ice wall thickness for chalk and sand are higher than the estimations obtained by Eqn. (4) (Fig.3 b). The most distinction from the numerical simulation results is 1.49m for sand at a depth of 300 m and 0.242 for chalk at a depth of 300 m. A comparison of the same results but obtained for clay shows that the numerical calculations give the higher ice wall thickness values for the material at depths of 100-200 m. At depths of 300-500 m, the simulation results are comparable with those obtained by formula (4); the relative error does not exceed 2.8%. Modification of Eqn. (4) Analysis of the obtained results has revealed that Eqn. (4) has the best correlation with the numerical simulation results. This equation was modified here in order to get a more accurate description of the relation between the designed ice wall thickness and the applied load. The modification made it possible to minimize the difference between the calculation results obtained by this formula and the numerical simulation data. Thus, we have                                                        2 0 1 2 0 45 /2 1 0 45 / 2 1 1 1 2 45 / 2 tg p tg E k a d c tg (20) where k and d are the piecewise constants 1 1 2 2 2 3 , ,         k p p p k k p p p