PSI - Issue 32

M. Zhelnin et al. / Procedia Structural Integrity 32 (2021) 71–78 M. Zhelnin/ Structural Integrity Procedia 00 (2021) 000–000

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Fig. 3 shows profiles of displacement between the inner side of the shaft lining and the middle part of the frozen wall. At the middle part of the frozen wall, the displacement reaches the maximum value. Within the frozen soil, thawed soil and the shaft lining the displacement varies almost linear. In thawed soil, the slope of the linear segment of the displacement profile is larger than in the frozen soil. As the stiffness of the shaft lining is high, the slope is minimal throughout to its thickness. In spite of the maximum equivalent strain in thawed soil is attained after 125 days of the thawing, the maximum value of the displacement near the concrete shell and the inner side of the shaft lining is observed after 250 days of the process. Thus, the displacement in the shaft lining rises with the time of the thawing.

Fig. 3. Profile of the radial displacement along the line segment from the inner side of the shaft lining to the middle part of the frozen wall.

In the next step, elasto-plastic behavior in the concrete shell and cement grouted soil is studied after the thawing of the frozen wall. Boundary conditions are presented in Fig. 1(b). Fig. 4 shows distributions of the von Mises stress and mechanical pressure (negative mean stress) around the mineshaft. The maximum value of the von Mises stress and the mechanical pressure is reached in the cast-iron tubbing due to its higher stiffness. From the cast-iron tubbing the von Mises stress reduces and attains minimum value in the sand. The mechanical pressure in the concrete shell is less than in the grouted soil in spite of the higher stiffness of the concrete and can be attributed to elasto-plastic behavior of concrete.

(a)

(b)

Fig. 4. Distributions of the von Mises stresss, MPa (a) and mechanical pressure, MPa (b) around the mineshaft

Fig. 5 presents distribution of the equivalent and volumetric part of the plastic strain in the concrete shell and grouted sand. There are no plastic strains at the outer side of the grouted soil. In the grouted soil the equivalent plastic strain attains the maximum value. In the concrete shell the equivalent plastic strain is distributed uniformly. The equivalent plastic strain in the concrete shell is less by 42% compared to the maximum value. Distribution of the volumetric plastic strain shows dilation in the grouted sand. According to the Drucker-Prager yield criterion, the dilation is induced by shear stress evolved in the grouted sand due to the lateral pressure. At the same time, the plastic volumetric strain in the concrete shell is negative, so it contracts under the compressive loading.