PSI - Issue 18

Kostina A. et al. / Procedia Structural Integrity 18 (2019) 293–300 Author name / Structural Integrity Procedia 00 (2019) 000–000

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performed by circulation of liquid refrigerant inside the pipes, the ground in near-wellbore domain is frozen and an ice-soil wall is established. Thus integrity of the freezing pipes determines fulfillment of design parameters of AGF process and safety of underground works. AGF is accompanied by a complex interaction between thermal, hydrodynamic and mechanical processes. Frost heave is an important phenomenon for geotechnical engineering induced by AGF. The conversion of soil pore water into ice causes a volumetric changes of the pore space (Sres et al. (2006)). The volume expansion induces frost-heaving pressure that has a significant influence on geotechnical structures. In Wang and Zhou (2018) a review of studies devoted to features of frost heave phenomenon in geotechnical applications is presented. It is noted that frost-heaving pressure is determined by a value of ice saturation and a freezing rate. In Han et al. (2015), Yang et al. (2006) the frost heave induced by AGF during a tunnel construction is considered. In Han et al. (2015) on the basis of in situ measured it is shown that the frost heave leads to a change of rock pressure acting on a tunnel. In Yang et al. (2006) analysis of an effect of design parameters of a tunnel excavation and AGF on the frost heave has been carried out by a numerical simulation. A serious issue in geotechnical engineering is related to an influence of the frost heave on underground pipes. Significant deformation of pipes could be induced if frost heave is nonhomogeneous along a buried pipeline (Li et al. (2018), Wu et al. (2010)). In Wu et al. (2010) an experimental system for AGF consisting of two pipes has been developed. The experimental data and a numerical simulation have shown that soil freezing leads to compressive stress around the pipes. Another process that induced by artificial freezing is thawing of soil. During the thawing a volume of frozen soil is changed due to the phase transition of ice to water and water flow out of the soil. As a result, the thaw settlement occurs (Li et al. (2018), Zhou and Tang (2015)). In Zhou and Tang (2015) an experimental study of the thaw settlement after AGF has been carried out. In Wen et al. (2010) an influence of the frost heave and the thaw settlement on a buried pipeline has been studied by a numerical simulation. In Li et al. (2018), Wen et al. (2010) it is noted that the frost heave causes in underground pipes larger deformation compared with the thaw settlement. The present work is devoted to study of mechanical behavior of steel freezing pipes during artificial freezing of rock mass and subsequent its thawing on the basis of a numerical simulation. To estimate pressure acting on the pipe by a surrounding soil, a thermo-hydro-mechanical model is used (Panteleev et al. (2017)). The constitutive relations of the model are derived within the framework of the linear theory of thermo-poroelasticity under the assumptions that the rock mass is layered linear isotropic porous media that undergoes small deformation. In Panteleev et al. (2017) it has been shown that the temperature distribution obtained by a numerical simulation of AGF is in good agreement with real monitoring data. Strength analysis of the freezing pipe is performed on the basis of linear elasticity with using a failure criterion proposed technical standard adopted by Russia. 2. Theoretical model Let us consider a thermo-hydro-mechanical model of artificial freezing process of rock mass (Panteleev et al. (2017)). It supposed that the rock mass is three-phase material that consists of a drained rock skeleton, water and ice in pore space. During the freezing water in pores is converted to ice at temperature of the phase transition. Rock skeleton is supposed to be a multi-layered poroelastic medium that undergoes small deformation. The model includes the energy conservation equation, the mass balance equation and the equilibrium equation. The phase transition is described by Stefan’s model with using the apparent heat capacity coefficient. Water flow is governed by Darcy’s law. The interaction between a fluid and a rock skeleton is described on the basis of Biot theory. A system of governing equations of the thermo-hydro-mechanical model has the following form:



,

(1)

v

( T     T 

) 0

, p f p f c T c   

t



p



t 



  f  v

f

S

,

(2)

f 

 



 

vol

f

B

t



