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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Figure 3 (a) presents distribution of the component 2 u in the ice-soil retaining structure at 100 H  m. It can be seen that the distribution is non uniform along the cylinder height and u 2 takes a maximum value at the bottom cylinder base. Also u 2 does not equal to zero at the top cylinder base. Figure 3 (b) shows the curve of development u 2 ,max in time. This curve qualitatively coincides with the curve in figure 1 (a). Profiles of axial and shear components  22 ,  23 of the stress tensor at 12 t  h along the height on the inner surface of the cylinder are presented in figure 4 (a), (b). The component  22 takes a nonzero constant value at most part of the considered segment. At the same time, the component  23 equals zero at this part and linearly decreases near the bottom cylinder end. 12 t  h and

4. Conclusions

Deformations of the ice-soil retaining structure consisting of the frozen Callovian sandy loam with the wall thickness given by the Vaylov’s formula w ere studied at depths from 100 m to 1000 m of mine shaft sinking by the numerical modelling. Creep strain of the frozen soil was estimated on the basis of the Vaylov’s constitutive relations.

a

b Fig. 3. (a) distribution of 2 u in the ice-soil cylinder at 12 h and (b) evolution of 2, max u in time for the case

100 H  m.

a

b

Fig. 4. Profiles of stress components along height l (

0 l  m corresponds to the top end) on the inner surface of the cylinder (a)

22  , (b) 23  .

It was established that the admissible displacement of the ice-soil cylinder is not exceeded only for depths less than 115 m while the estimated wall thicknesses for the considered depths reach to 104.1 m. Also it was shown that the assumptions of the Vaylov’s formula concerning to values of the radial stress and displacement on the inner surface and the top end of the ice-soil cylinder are not satisfied. At the same time, the assumption relating to shear stress takes zero value on the inner surface is fulfilled on most part of the surface. One of the possible reason on that the ice-soil cylinder with the significant wall thickness is not able to satisfy of the deformation criterion is in estimation of the rock pressure by (6). In the deformation process of the frozen soil the encircling unfrozen rock massif is also deformed, as a result its stress-strain state is changed that leads to alteration of the rock pressure. Another reason is related to the Vaylov’s constitutive relations. It is assumed that the