Issue 53

A. Kostina et alii, Frattura ed Integrità Strutturale, 53 (2020) 394-405; DOI: 10.3221/IGF-ESIS.53.30 403 A comparison of the results of approximation by Eqn. (4) shows that in case of piecewise-linear dependence (20) they are in rather good qualitative and quantitative agreement. A deficiency of this approach is the necessity of calculating four material parameters, as well as the intervals for determining piecewise-linear correction coefficients. Therefore, it is advisable to use formula (21) in order make rapid estimation for the designed ice wall thickness. In this case, it is necessary to determine only one material parameter, whereas formula (20) can be used when there is a need for more accurate calculation. Comparative analysis of Vyalov’s formulas for ultimate displacements and stresses Fig. 6 presents the calculation results for ice wall thickness obtained for sand, chalk and clay by Eqns. (1)-(2) recommended for ultimate displacement calculations and by Eqns. (3)-(4) - for strength calculations. Apart from these formulas, this figure also shows the calculation results obtained by Eqn. (20) and by the equation which is a modification of relation (1) [12]:                                  1 1 1 1 1 ( ) 1 2 , m m m p m p h a E g p A t T a (22) where the material function g ( p ) is dependent on the value of the load acting on the ice wall and determined by applying the numerical simulation results. The function for the materials under study was taken from [12]. (a) (b) (c) Figure 6 : Dependence of the designed ice wall thickness on the load for sand (a), chalk (b), clay (c): curve 1 – Eqn. (1), curve 2 – Eqn. (2), curve 3 – Eqn. (3), curve 4 – Eqn. (1), curve 5 – Eqn. (20), curve 6 – Eqn. (22). For sand (Fig.6a), the maximum discrepancy between Eqns. (4) and (20) is 1.49m, which corresponds to the load of 889 М P а . Analogous thicknesses are determined using Eqns. (3) and (22) for the load less than 4.889 М P а . Besides, for the load not exceeding 3.222 М P а , the thickness calculated by Eqn. (2) is close to the value obtained by Eqns. (3) and (22). Eqn. (2)