PSI - Issue 32

A. Kostina et al. / Procedia Structural Integrity 32 (2021) 101–108 A. Kostina/ Structural Integrity Procedia 00 (2021) 000 – 000

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freezing pipes which are installed into the boreholes drilled around the intended mineshaft [1]. Circulation of low temperature brine inside the pipes turns surrounding water-saturated soil into a frozen state. Thus, the so-called frozen wall is formed. Three stages of AGF can be distinguished [2]. On the first stage a frozen wall is formed up to a thickness which is able to withstand a lateral pressure acting by surrounding soils and groundwater. On the second stage excavation works are conducted under the protection of the frozen wall. In this stage artificial freezing is performed only to maintain the desired thickness of the frozen wall. After shaft sinking and installation of the shaft lining, the third stage is initiated. In this stage the frozen ground is thawed due to the heat transfer from the surrounding soils and the sidewall of the shaft. Under external loading, frozen soils exhibit rheological behavior due to ice bonds between their grains. It has been shown that key factors determining rheological properties of frozen soils are dependent on value of negative temperature, ice and unfrozen water content as well as confining pressure [3-6]. Creep deformation of a frozen wall subjected to lateral pressure was studied in [7, 8]. In [7-9] the radial displacements of a frozen wall were estimated by Vaylov’s equation for attenuation creep stage. In [9 -10] rheological Nishihara model was modified to compute the deformation of a frozen wall during a non-attenuation creep process under high confining pressure. In order to describe a change in a stress-strain state of water-saturated soils during freezing and thawing processes thermo-mechanical and thermo-hydro-mechanical models are developed. In [11] thermo-mechanical model was proposed to study effects of frost heave and thaw settlement on mechanical behavior of buried oil pipeline. The ground deformations were incorporated into the model by additional components of volumetric strain which were dependent on frost heave and thaw settlement coefficients. Similar mathematical approach to evaluation of deformation induced by freezing and thawing of soil is employed in [12] for prediction of deformation at ground surface induced by AGF for tunnel construction. Also, in [13] the approach was applied to analysis of wellhead subsidence due to thawing of frozen soil during drilling operation in a cold region. Other way of estimation of additional volumetric strain induced by freezing and thawing is provided by a porosity rate function [14]. In [15] porosity rate function was used to investigate the effect of soil freezing on pipes of heat pump system. Thermo-hydro-mechanical model proposed in [16] expresses frost expansion and thaw contraction by quantity of heat inflow/outflow and effective mean stress. The model was applied for studying of a stress-strain state in pavement located above a box culvert during freezing-thawing process. In thermo-hydro-mechanical model developed by [17] volumetric strain of soil during freezing-thawing cycle was estimated by a change in total volumetric water content. Effect of frost heave on damage of concrete lining of a drainage trench along a railway embankment located in a warm permafrost region was analyzed using the model. Mechanical behavior of frozen and thawed soils can be described also with the poromechanics theory. Constitutive relations provided by the poromechanics theory were applied to thermo-hydro-mechanical model developed in [18]. The model was applied to a problem of freezing and thawing of a soil mass surrounding an energy pile. In [19] thermo hydro-mechanical model was proposed to study stability of a seasonally frozen soil layer of an open-pit mine slopes in permafrost regions. Special algorithm for calculation of latent heat due to water-ice phase change was developed. In this work thermo-hydro-mechanical simulation of the second stage of AGF in silt and sand stratums is performed. During this period of time the unsupported part of the frozen wall may be significantly deformed by the lateral pressure which can lead to loss of its stability. Moreover, shutdown of the cooling station (which is a common practice during drilling and blasting operations) can also induce thawing and, as a consequence, decrease in the thickness of the frozen wall as well as inrush of soil into the stope. Therefore, investigation of a stress-strain state of the soil is an important issue for a safe shaft sinking. It has been assumed that frozen wall losses bearing capacity when displacement of its unfixed section is less than 10 cm and shutdown time does not exceed four days. This time interval has been chosen as an upper bound for drilling and blasting operations. On the first step the problem of frozen wall formation was solved and distributions of pore pressure, ice content and temperature were defined. On the second step thawing of frozen ground was considered using the same model, distributions of the main parameters defined on the first step and appropriate boundary conditions which are described below. 2. Coupled thermo-hydro-mechanical model of freezing and thawing Mathematical model of soil freezing/thawing is based on mass, energy and momentum balance laws which are supplemented by Fourier’s law, Darcy’s law of filtration, Hook’s law for elastic strains and some additional equations