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Creep behavior of ice-soil retaining structure during shaft sinking
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ECF22 - Loading and Environmental effects on Structural Integrity ECF22 - Loading and Environmental effects on Structural Integrity
Creep behavior of ice-soil retaining structure during shaft sinking Creep behavior of ice-soil retaining structure during shaft sinking
XV Portuguese Conference on Fracture, February 2016, Paço de a a, PCF 2016, 10-12 a a b Arcos, Portugal
Kostina A.a, Zhelnin M.a,*, Plekhov O.a, Panteleev I.a, Levin L.b Kostina A. , Zhelnin M. *, Plekhov O. , Panteleev I. , Levin L.
Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science, Perm 614013, Russia Thermo-mechanical modeling ofAcademy a ofhigh pressure turbine blade of an Institute of Continuous Media Mechanics of the Ural Branch Russian Academy of 614007, Science, Russia Perm 614013, Russia Mining institute, Ural Branch of Russian of Sciences, Perm Mining institute, Ural Branch of Russian Academy of Sciences, Perm 614007, Russia airplane gas turbine engine a a
b b
Abstract Abstract P. Brandãoa, V. Infanteb, A.M. Deusc* The article is devoted to analysis of deformation of an ice-soil retaining structure during a vertical mine shaft sinking by applying a Department offreezing Mechanical Engineering, Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, The article isground devoted to analysis of deformation of anSuperior ice-soil retaining during a vertical mine shaft1, sinking applying the artificial technique. The Instituto analysis was performed bystructure finite element numerical simulation. Since by frozen soils Portugalby finite element numerical simulation. Since frozen soils the artificial ground properties, freezing technique. The analysis wasice-soil performed possess rheological creep deformation of the structure was considered. To determine the creep deformation, b IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, possess rheological properties, creep the ice-soil structure was considered. the creepcreep deformation, the Vaylov’s constitutive relations wasdeformation used. In theofrelations the creep behavior is describedTo bydetermine the Norton-Bailey law and Portugal the wasEngineering, used. the relations the creep behavior is described by Av. the Norton-Bailey creep law and the cVaylov’s volumetric creep strain is restricted to beInzero. The wall thickness ofUniversidade the ice-soil was estimated by1049-001 the Vaylov’s CeFEMA, constitutive Department ofrelations Mechanical Instituto Superior Técnico, destructure Lisboa, Rovisco Pais, 1, Lisboa, Portugal the volumetric creep strain is restricted to be zero. The wall thickness of the ice-soil structure was estimated by the Vaylov’s formula that is widely used in structural design of potash mines. As a result of the study, it was established that for time required formula that isinstallation widely usedat inlarge structural potash mines. a result of the study, it was established for time required for the lining depthsdesign of theofshaft sinking theAs creep deformation of the ice-soil structurethat exceeds admissible for theguaranteeing lining installation at the large depths ofprocess. the shaft sinking the creep deformation of the ice-soil structure exceeds admissible value safety of excavation Abstract value guaranteeing safety of the excavation process. © 2018 The Authors. Published by Elsevier B.V. © 2018 Thetheir Authors. Publishedmodern by Elsevier B.V. engine components are subjected to increasingly demanding operating conditions, operation, aircraft © During 2018 The under Authors. Published by B.V. Peer-review responsibility of Elsevier the ECF22 organizers. Peer-review under responsibility ofturbine the ECF22 organizers. especially the high pressure (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent Peer-review under responsibility of the ECF22 organizers. degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict Keywords: artificial ground freezing; mine shaft; creep deformation; numerical simulation the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation Keywords: artificial ground freezing; mine shaft; creep deformation; numerical simulation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were 1. obtained. Introduction The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D 1. rectangular Introduction block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall of displacement was observed, in particular at the trailing edge ofconstructed the blade. Therefore such a In theexpected mining behaviour industry, in theterms tendency to an increase of a quantity of vertical mine shafts under hard model be useful in the goal predicting blade life, a set of In thecan mining industry, the tendency toturbine an of agiven quantity ofFDR vertical mine great shaftsdepths. constructed hard hydrogeological conditions forof exploitation of increase mineral deposits occurring at data. extreme One ofunder universal
hydrogeological conditions exploitation of mineral deposits occurring at extreme great depths. One of universal and efficient technique for afor mine shaft sinking in weak, unstable, fluid-saturated soils is artificial ground freezing © 2016 The Authors. Published by Elsevier B.V. in weak, unstable, fluid-saturated soils is artificial ground freezing and efficient technique for(2013)). a mine shaftpurpose sinking (Andersland and Ladanyi The of the technique is formation prior to an excavation of a temporary Peer-review and under responsibility of the Scientific Committee of PCF 2016. (Andersland Ladanyi The purpose of withstands the technique formation to an excavation of filtration. a temporary ice-soil retaining structure (2013)). around the shaft, which rockispressure andprior eliminates groundwater ice-soil retaining structure around the shaft, which withstands rock pressure and eliminates groundwater filtration. Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.
* Corresponding author. Tel.: +7-342-237-8312; fax: +7-342-237-8487. * E-mail Corresponding Tel.: +7-342-237-8312; fax: +7-342-237-8487. address:author. [email protected] E-mail address: [email protected] 2452-3216 © 2018 The Authors. Published by Elsevier B.V. 2452-3216 © 2018 Authors. Published Elsevier B.V. Peer-review underThe responsibility of theby ECF22 organizers. * Corresponding Tel.: +351of218419991. Peer-review underauthor. responsibility the ECF22 organizers. E-mail address: [email protected] 2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. 10.1016/j.prostr.2018.12.260
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Kostina A. et al. / Procedia Structural Integrity 13 (2018) 1273–1278 Author name / Structural Integrity Procedia 00 (2018) 000–000
Thus the ice-soil wall is an important geotechnical construction, strength and reliability of that determine safety of the shaft sinking. Despite the long-term experience of using the artificial freezing technique, numerous accidents and technological problems arise under the excavation of mine shafts at great depths. To prevent emergencies and guarantee the fulfilment of designed characteristics of mine shafts it is required conduction of through studies of mechanical behavior of the ice-soil wall (Panteleev et al. (2017)). Frozen soils, because of the presence in them of ice and unfrozen water, possess clearly defined rheological properties such as development imperceptibly slow deformations (creep) and losing strength during a prolonged load action. In (Vyalov (1986), Razbegin et al. (1996), Arenson et al. (2007), Qi et al. (2013), Lai et al. (2013)) extensive reviews of experimental and theoretical studies related to frozen soils are presented. The Vyalov’s constitutive relations (Vyalov et al. (1962), Vyalov et al. (1979), Vyalov (1986)) give one of the basic mechanical model for describing rheological properties of frozen soils. According to the relations creep strain is described by the Norton-Bailey power law (Ottosen and Ristinmaa (2005)) in that a modulus depends on time and temperature and it is assumed that volume deformation under creep can be neglected. Experimental studies confirm that the theory allows one to describe of the creep in wide range of temperatures. In particular, in (Vyalov et al. (1962), Klein and Jessberger (1979), Eckardt (1982), Vyalov (1986)) an analysis of the experimental data of creep of various type of frozen soils in uniaxial compression and tensile tests has been conducted based on the theory. In (Vyalov et al. (1979)) theory has been justified by experimental results of uniaxial and triaxial compression tests performed for frozen dusty loam and two types of clay. Based on the theory the Vyalov’s formula for estimating of an optimal thickness of an ice-soil wall for that it can resist to given rock pressure has been derived (Vyalov et al. (1979)). This formula is widely used by engineers for design the ice-soil wall and determination of optimal parameters for the artificial ground freezing (Andersland and Ladanyi (2013)). However, the formula has been obtained analytically with strong assumptions, which could differ from real conditions under shaft construction. In recent times for prediction of a mechanical behavior of soils and a mine shaft during the excavation process and the installation of the shaft support applied numerical simulation. In (Judeel et al. (2012)) an elastic behavior of a cast iron tubbing lining during mine shaft construction has been researched. In (Fabich et al. (2015)) displacement of a shaft wall before installation of the shaft lining has been estimated with considering an ideal elasto-plastic behavior of soil and the Hoek-Brown strength criterion. In (Oreste et al. (2016), Spagnoli et al. (2017)) an approach for estimating radial loads on a vertical shaft lining and radial soil displacement during the excavation have been developed on the basis of the Mohr-Coulomb strength criterion. In (Schwamb and Soga (2015)) an analysis of monitoring data obtained at several shaft excavation levels has been numerically performed with using the Mohr-Coulomb and the Hoek-Brown failure criteria. In (Jia et al. (2008)) a numerical modelling of hydromechanical response of argillite during a shaft sinking have been carried out taking into account plastic and creep deformations. This work is devoted to verification of the Vyalov’s formula at various depth of a shaft sinking by finite element numerical modelling of a vertical mine shaft with the unsupported wall. The creep behavior of frozen soil was described by using the Vyalov’s constitutive relations. The mechanical properties were determined from experimental data for Callovian sandy loam as one of the most dangerous soil layer for a sinking. The rock pressure was estimated by applying a standard structural design approach (Farazi and Quamruzzaman (2013)) based on the Rankine’s theory (Terzaghi et al. (1996)). 2. Theoretical model According to (Vyalov et al. (1979)) a vertical mine shaft sinking by the artificial ground freezing technique is performed by the following way. An ice-soil retaining structure represented as an ice-soil cylinder is formed around the building mine shaft. As the shaft is sunk the outer surface of the cylinder is loaded by rock pressure P . However, the shaft sinking is carried out incrementally together with installation of the shaft lining that is supported the shaft wall. Therefore, a relatively small height h of the inner surface is unsupported. This part of the retaining structure is deformed under an effect of the pressure P within some time period t pr that is required for building of the lining. It is known because of creep of frozen soils even if plastic deformation of the ice-soil retaining structure does not occur, creep deformation of the cylinder wall could reach significant values. As a result, freezing columns could fail and the installation of the shaft lining could be complicated. Thus, the thickness of the cylinder wall is
Kostina A. et al. / Procedia Structural Integrity 13 (2018) 1273–1278 Author name / Structural Integrity Procedia 00 (2018) 000–000
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determined in order to maximal displacement max is not exceeded. The three-dimensional theoretical model for describing a stress-strain state of the ice-soil retaining structure is written as:
div σ 0
(1)
σ С : ε ε cr
ε
(2)
1 T grad u grad u 2
(3)
where σ – Cauchy stress tensor [Pa], ε – full strain tensor, ε cr – creep strain tensor, u –displacement vector [m]. It is assumed that the ice-soil retaining structure is a hollow cylinder with inner radius rin and wall thickness E . The outer surface of the cylinder is loaded by the rock pressure P , the top and bottom cylinder ends are fixed in longitudinal direction by the lining and frozen soil, correspondingly, and the circle at the topcrend is fixed in all directions by the tubbing. On the basis of the Vyalov’s constitutive relations the creep strain ε of frozen soils in uniaxial stress conditions is described by the Norton-Bailey creep law. For multiaxial stress conditions with the assumption that the volumetric creep strain equals zero this law can be generalized as:
cr eff
1 A( ) effm
cr m eff
m m
m
(4)
cr [2 / 3(εcr : εcr )]1/2 – the effective creep strain rate, eff [3 / 2(dev(σ) : dev(σ))]1/2 – the effective where eff A( ) 1/ m ( 1) k / m , t – time [h], [Pa∙hλ∙(C)-k], – temperature of the soil [C]. stress, By solving the problem (1-3) analytically with some assumptions, the main from which are that instantaneous elastic deformation is neglected, radial stress equals zero on the inner cylinder surface, shear stress linearly varies near the cylinder ends and equals zero on the inner surface, radial displacement on the top end equals zero and the stress-strain state is considered only at the last time moment, in (Vaylov et al. (1962)) the engineering formula for the optimal thickness E of the ice wall was obtained:
1 1 m 1 m (1 m) Ph E rin 1 m 1 1 m 2 max rin A( )t pr 3
(5)
3. Numerical simulations To estimate adequacy of (5) in this study the problem (1-4) was solved numerically. The numerical modelling was carried out for Callovian sandy loam as one of the most dangerous soil layer for a shaft sinking. The creep parameters characterizing rheological properties of the soil were estimated on the basis of experimental measurements of creep strain on time (Vaylov et al. (1962)). The data was obtained from a uniaxial compression test of a cylindrical rod with the ratio of the radius to the height equal 0.5 one of the ends of that was loaded by pressure equal 3 MPa during 12 hours. The temperature of the soil was 10 C. To identify the properties, the analytical relationship of the creep strain on time obtained by integration (4) was used. In table 1 identified values of the parameters are presented. Table 1. Creep parameters for Callovian sandy loam at -10 C. , MPa∙hλ∙(C)-k
k
m
0.9
0.89
0.27
0.1
Kostina A. et al. / Procedia Structural Integrity 13 (2018) 1273–1278 Author name / Structural Integrity Procedia 00 (2018) 000–000
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In figure 1 the experimental data for the Callovian sandy loam, the curve obtained from the analytical dependence and the curve obtained from a three-dimensional numerical simulation for the identified values are presented. The numerical simulation was performed for the mentioned experimental conditions with using the constitutive relation (4). As it can be seen the analytical curve is in good agreement with the numerical one. From figure 1 it could be concluded that (4) allows describing the primary nonstationary creep stage with a deceasing deformation rate and the secondary stationary creep stage with an almost constant rate, but it is not able to quality characterize the tertiary creep stage related to progressive flow with an increasing rate. The geometrical parameters for the mine shaft sinking were defined as rin 5.25 m, h 5 m, max 0.1 m on the basis of documentations used for structural design of potash mines in Belarus. The time required for lining installation was assumed t pr 12 h. The rock pressure acting on the ice-soil retaining structure was estimated by the standard engineering formula (Farazi and Quamruzzaman (2013))
P Pl Pw
(6)
Pw w g ( H H w ) – hydrostatic pressure, H , H w where Pl l Hg Tan[(900 ) / 2] – effective lateral pressure, – depths of a soil layer and a groundwater level, [m], γl, γw – average density of rock soils and density of water, [kg/m3], – friction angle, [deg], g – the gravitational acceleration. The expression for Pl is based on the Rankine’s theory (Terzaghi et al. (1996)). In this study it was assumed that H w 1.5 , l 2 103 . For the sandy loam 32 (Vaylov et al. (1962)). In figure 2 (a) relationship of the rock pressure to the depth is presented. Figure 2 (a) shows values of the thickness E of the ice-soil cylinder given by (5) for H equal 100, 115, 250, 500 and 1000 m. Figure 2 (b) presents maximal values u2,max of the second displacement component u2 in depending on H obtained by numerical solving (1)–(4). As can be seen u2,max nonlinearly increases with the depth and reaches 8.8 m at the depth 1000 m. Despite on the significance wall thickness reaching to 104.1 m at 1000 m, the maximal admissible displacement Δmax is not exceeded only for the depths less than 115 m. At that u2,max equals 0.08 m at the depth 100 m.
a
b
Fig. 1. (a) relationship between 33 and t (markers – the experimental data, dash line – the analytical curve, solid line – the numerical one); (b) relationship between rock pressure P and depth H .
a
b
Fig. 2. (a) values of thickness E and (b) values of u2,max in depending on depth H .
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 u2 in the ice-soil retaining structure at t 12 h and H 100 m. It can be seen that the distribution is non uniform along the cylinder height and u2 takes a maximum value at the bottom cylinder base. Also u2 does not equal to zero at the top cylinder base. Figure 3 (b) shows the curve of development u2,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 t 12 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. 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 were 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 u 2 in the ice-soil cylinder at 12 h and (b) evolution of u2,max in time for the case H 100 m.
a
b
Fig. 4. Profiles of stress components along height l ( l 0 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
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Kostina A. et al. / Procedia Structural Integrity 13 (2018) 1273–1278 Author name / Structural Integrity Procedia 00 (2018) 000–000
volumetric creep strain equals zero. However, in soils effects of dilatancy and compaction accompany the volumetric creep strain. Both process leads to increase of soil strength that could contribute to decrease of the creep deformation rate. Finally, for shaft sinking at large depths design parameters should be determined based on numerical modelling. For example, it was established that at depth 250 m the ice-soil cylinder with the wall thickness given by the Vaylov’s formula can satisfy the deformation criterion if its height is less than 0.5 m. Acknowledgements This research was supported by 17-11-01204 project (Russian Science Foundation). References Andersland O.B., Ladanyi B., 2013. An introduction to frozen ground engineering. Chapman and Hall, New York. Panteleev I., Kostina A., Zhelnin M., Plekhov A., Levin L., 2017. Intellectual monitoring of artificial ground freezing in the fluid-saturated rock mass. Procedia Structural Integrity, 5, 492–499. Vyalov S.S., 1986. Rheological fundamentals of soil mechanics. Elsevier, Amsterdam, the Netherlands. Razbegin V.N., Vyalov S.S., Maksimyak R.V., Sadovskii A.V., 1996. Mechanical properties of frozen soils. Soil Mechanics and Foundation Engineering 33(2), 35–45. Arenson L.U., Springman S.M., Sego D.C., 2007. The rheology of frozen soils. Applied Rheology, 17(1), 12147. Qi J., Wang S., Yu F, 2013. A Review on Creep of Frozen Soils, in “Constitutive Modeling of Geomaterials”. In. Yang Q., Zhang J.M., Zheng H., Yao Y. (Ed.). Springer, Berlin, Heidelberg, pp. 129–133. Lai Y., Xu X., Dong Y., Li S., 2013. Present situation and prospect of mechanical research on frozen soils in China. Cold Regions Science and Technology, 87, 6–18. Vyalov S.S., Gorodetsky, S.E., Zaretsky Yu.K., Gmoshinsky V.G, Grigoreva V.G., Pekarskaya N.K., Shusherina E.P., 1962. Strength and Creep of Frozen Soils and Design of Ice—Soil Retaining Structures. U.S.S.R. Acad. Press, Moscow (in Russian). Vyalov S.S., Zaretsky Y.K., Gorodetsky S.E., 1979. Stability of mine workings in frozen soils. Engineering Geology, 13(1-4), 339-351. Ottosen N.S., Ristinmaa M., 2005. The Mechanics of Constitutive Modeling. Elsevier, Amsterdam. Klein J., Jessberger H.L., 1979. Creep stress analysis of frozen soils under multiaxial states of stress. Engineering Geology, 13, 353–365. Eckardt H., 1982. Creep tests with frozen soils under uniaxial tension and uniaxial compression, in “Proceedings of the 4th Canadian Permafrost Conference”. In: French H.M. (Ed.). Calgary, Alberta. National Research Council of Canada, pp. 394–405. Judeel G.duT., Keyter G.J., Harte N.D., 2012. Shaft sinking and lining design for a deep potash shaft in squeezing ground in "Harmonising Rock Engineering and the Environment”. In: Qian Q., Zhou Y. (Ed.). Taylor & Francis Group, London, pp. 1697–1704. Fabich S., Bauer J., Rajczakowska M., Świtoń S. (2015). Design of the shaft lining and shaft stations for deep polymetallic ore deposits: Victoria Mine case study. Mining Science, 22, 121 – 140 Oreste P., Spagnoli G., Bianco L.L., 2016. A combined analytical and numerical approach for the evaluation of radial loads on the lining of vertical shafts. Geotechnical and Geological Engineering, 34(4), 1057-1065. Spagnoli G., Oreste P., Bianco L.L., 2017. Estimation of shaft radial displacement beyond the excavation bottom before installation of permanent lining in nondilatant weak rocks with a novel formulation. International Journal of Geomechanics, 17(9), 04017051. Schwamb T., Soga K., 2015. Numerical modelling of a deep circular excavation at Abbey Mills in London. Géotechnique, 65(7), 604-619. Jia Y., Bian H.B., Duveau G., Su K., Shao, J.F, 2008. Hydromechanical modelling of shaft excavation in Meuse/Haute-Marne laboratory. Physics and Chemistry of the Earth, Parts A/B/C, 33, S422-S435. Farazi A. H., Quamruzzaman C., 2013. Structural design of frozen ground works for shaft sinking by practicing artificial ground freezing (AGF) method in Khalashpir coal field. International Journal of Engineering and Science, 2(3), 69-74. Terzaghi K., Peck R. B., Mesri G.,1996. Soil mechanics in engineering practice. John Wiley & Sons, New York.
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ECF22 - Loading and Environmental effects on Structural Integrity ECF22 - Loading and Environmental effects on Structural Integrity
Creep behavior of ice-soil retaining structure during shaft sinking Creep behavior of ice-soil retaining structure during shaft sinking
XV Portuguese Conference on Fracture, February 2016, Paço de a a, PCF 2016, 10-12 a a b Arcos, Portugal
Kostina A.a, Zhelnin M.a,*, Plekhov O.a, Panteleev I.a, Levin L.b Kostina A. , Zhelnin M. *, Plekhov O. , Panteleev I. , Levin L.
Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science, Perm 614013, Russia Thermo-mechanical modeling ofAcademy a ofhigh pressure turbine blade of an Institute of Continuous Media Mechanics of the Ural Branch Russian Academy of 614007, Science, Russia Perm 614013, Russia Mining institute, Ural Branch of Russian of Sciences, Perm Mining institute, Ural Branch of Russian Academy of Sciences, Perm 614007, Russia airplane gas turbine engine a a
b b
Abstract Abstract P. Brandãoa, V. Infanteb, A.M. Deusc* The article is devoted to analysis of deformation of an ice-soil retaining structure during a vertical mine shaft sinking by applying a Department offreezing Mechanical Engineering, Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, The article isground devoted to analysis of deformation of anSuperior ice-soil retaining during a vertical mine shaft1, sinking applying the artificial technique. The Instituto analysis was performed bystructure finite element numerical simulation. Since by frozen soils Portugalby finite element numerical simulation. Since frozen soils the artificial ground properties, freezing technique. The analysis wasice-soil performed possess rheological creep deformation of the structure was considered. To determine the creep deformation, b IDMEC, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, possess rheological properties, creep the ice-soil structure was considered. the creepcreep deformation, the Vaylov’s constitutive relations wasdeformation used. In theofrelations the creep behavior is describedTo bydetermine the Norton-Bailey law and Portugal the wasEngineering, used. the relations the creep behavior is described by Av. the Norton-Bailey creep law and the cVaylov’s volumetric creep strain is restricted to beInzero. The wall thickness ofUniversidade the ice-soil was estimated by1049-001 the Vaylov’s CeFEMA, constitutive Department ofrelations Mechanical Instituto Superior Técnico, destructure Lisboa, Rovisco Pais, 1, Lisboa, Portugal the volumetric creep strain is restricted to be zero. The wall thickness of the ice-soil structure was estimated by the Vaylov’s formula that is widely used in structural design of potash mines. As a result of the study, it was established that for time required formula that isinstallation widely usedat inlarge structural potash mines. a result of the study, it was established for time required for the lining depthsdesign of theofshaft sinking theAs creep deformation of the ice-soil structurethat exceeds admissible for theguaranteeing lining installation at the large depths ofprocess. the shaft sinking the creep deformation of the ice-soil structure exceeds admissible value safety of excavation Abstract value guaranteeing safety of the excavation process. © 2018 The Authors. Published by Elsevier B.V. © 2018 Thetheir Authors. Publishedmodern by Elsevier B.V. engine components are subjected to increasingly demanding operating conditions, operation, aircraft © During 2018 The under Authors. Published by B.V. Peer-review responsibility of Elsevier the ECF22 organizers. Peer-review under responsibility ofturbine the ECF22 organizers. especially the high pressure (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent Peer-review under responsibility of the ECF22 organizers. degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict Keywords: artificial ground freezing; mine shaft; creep deformation; numerical simulation the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation Keywords: artificial ground freezing; mine shaft; creep deformation; numerical simulation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were 1. obtained. Introduction The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D 1. rectangular Introduction block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall of displacement was observed, in particular at the trailing edge ofconstructed the blade. Therefore such a In theexpected mining behaviour industry, in theterms tendency to an increase of a quantity of vertical mine shafts under hard model be useful in the goal predicting blade life, a set of In thecan mining industry, the tendency toturbine an of agiven quantity ofFDR vertical mine great shaftsdepths. constructed hard hydrogeological conditions forof exploitation of increase mineral deposits occurring at data. extreme One ofunder universal
hydrogeological conditions exploitation of mineral deposits occurring at extreme great depths. One of universal and efficient technique for afor mine shaft sinking in weak, unstable, fluid-saturated soils is artificial ground freezing © 2016 The Authors. Published by Elsevier B.V. in weak, unstable, fluid-saturated soils is artificial ground freezing and efficient technique for(2013)). a mine shaftpurpose sinking (Andersland and Ladanyi The of the technique is formation prior to an excavation of a temporary Peer-review and under responsibility of the Scientific Committee of PCF 2016. (Andersland Ladanyi The purpose of withstands the technique formation to an excavation of filtration. a temporary ice-soil retaining structure (2013)). around the shaft, which rockispressure andprior eliminates groundwater ice-soil retaining structure around the shaft, which withstands rock pressure and eliminates groundwater filtration. Keywords: High Pressure Turbine Blade; Creep; Finite Element Method; 3D Model; Simulation.
* Corresponding author. Tel.: +7-342-237-8312; fax: +7-342-237-8487. * E-mail Corresponding Tel.: +7-342-237-8312; fax: +7-342-237-8487. address:author. [email protected] E-mail address: [email protected] 2452-3216 © 2018 The Authors. Published by Elsevier B.V. 2452-3216 © 2018 Authors. Published Elsevier B.V. Peer-review underThe responsibility of theby ECF22 organizers. * Corresponding Tel.: +351of218419991. Peer-review underauthor. responsibility the ECF22 organizers. E-mail address: [email protected] 2452-3216 © 2016 The Authors. Published by Elsevier B.V.
Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. 10.1016/j.prostr.2018.12.260
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Kostina A. et al. / Procedia Structural Integrity 13 (2018) 1273–1278 Author name / Structural Integrity Procedia 00 (2018) 000–000
Thus the ice-soil wall is an important geotechnical construction, strength and reliability of that determine safety of the shaft sinking. Despite the long-term experience of using the artificial freezing technique, numerous accidents and technological problems arise under the excavation of mine shafts at great depths. To prevent emergencies and guarantee the fulfilment of designed characteristics of mine shafts it is required conduction of through studies of mechanical behavior of the ice-soil wall (Panteleev et al. (2017)). Frozen soils, because of the presence in them of ice and unfrozen water, possess clearly defined rheological properties such as development imperceptibly slow deformations (creep) and losing strength during a prolonged load action. In (Vyalov (1986), Razbegin et al. (1996), Arenson et al. (2007), Qi et al. (2013), Lai et al. (2013)) extensive reviews of experimental and theoretical studies related to frozen soils are presented. The Vyalov’s constitutive relations (Vyalov et al. (1962), Vyalov et al. (1979), Vyalov (1986)) give one of the basic mechanical model for describing rheological properties of frozen soils. According to the relations creep strain is described by the Norton-Bailey power law (Ottosen and Ristinmaa (2005)) in that a modulus depends on time and temperature and it is assumed that volume deformation under creep can be neglected. Experimental studies confirm that the theory allows one to describe of the creep in wide range of temperatures. In particular, in (Vyalov et al. (1962), Klein and Jessberger (1979), Eckardt (1982), Vyalov (1986)) an analysis of the experimental data of creep of various type of frozen soils in uniaxial compression and tensile tests has been conducted based on the theory. In (Vyalov et al. (1979)) theory has been justified by experimental results of uniaxial and triaxial compression tests performed for frozen dusty loam and two types of clay. Based on the theory the Vyalov’s formula for estimating of an optimal thickness of an ice-soil wall for that it can resist to given rock pressure has been derived (Vyalov et al. (1979)). This formula is widely used by engineers for design the ice-soil wall and determination of optimal parameters for the artificial ground freezing (Andersland and Ladanyi (2013)). However, the formula has been obtained analytically with strong assumptions, which could differ from real conditions under shaft construction. In recent times for prediction of a mechanical behavior of soils and a mine shaft during the excavation process and the installation of the shaft support applied numerical simulation. In (Judeel et al. (2012)) an elastic behavior of a cast iron tubbing lining during mine shaft construction has been researched. In (Fabich et al. (2015)) displacement of a shaft wall before installation of the shaft lining has been estimated with considering an ideal elasto-plastic behavior of soil and the Hoek-Brown strength criterion. In (Oreste et al. (2016), Spagnoli et al. (2017)) an approach for estimating radial loads on a vertical shaft lining and radial soil displacement during the excavation have been developed on the basis of the Mohr-Coulomb strength criterion. In (Schwamb and Soga (2015)) an analysis of monitoring data obtained at several shaft excavation levels has been numerically performed with using the Mohr-Coulomb and the Hoek-Brown failure criteria. In (Jia et al. (2008)) a numerical modelling of hydromechanical response of argillite during a shaft sinking have been carried out taking into account plastic and creep deformations. This work is devoted to verification of the Vyalov’s formula at various depth of a shaft sinking by finite element numerical modelling of a vertical mine shaft with the unsupported wall. The creep behavior of frozen soil was described by using the Vyalov’s constitutive relations. The mechanical properties were determined from experimental data for Callovian sandy loam as one of the most dangerous soil layer for a sinking. The rock pressure was estimated by applying a standard structural design approach (Farazi and Quamruzzaman (2013)) based on the Rankine’s theory (Terzaghi et al. (1996)). 2. Theoretical model According to (Vyalov et al. (1979)) a vertical mine shaft sinking by the artificial ground freezing technique is performed by the following way. An ice-soil retaining structure represented as an ice-soil cylinder is formed around the building mine shaft. As the shaft is sunk the outer surface of the cylinder is loaded by rock pressure P . However, the shaft sinking is carried out incrementally together with installation of the shaft lining that is supported the shaft wall. Therefore, a relatively small height h of the inner surface is unsupported. This part of the retaining structure is deformed under an effect of the pressure P within some time period t pr that is required for building of the lining. It is known because of creep of frozen soils even if plastic deformation of the ice-soil retaining structure does not occur, creep deformation of the cylinder wall could reach significant values. As a result, freezing columns could fail and the installation of the shaft lining could be complicated. Thus, the thickness of the cylinder wall is
Kostina A. et al. / Procedia Structural Integrity 13 (2018) 1273–1278 Author name / Structural Integrity Procedia 00 (2018) 000–000
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determined in order to maximal displacement max is not exceeded. The three-dimensional theoretical model for describing a stress-strain state of the ice-soil retaining structure is written as:
div σ 0
(1)
σ С : ε ε cr
ε
(2)
1 T grad u grad u 2
(3)
where σ – Cauchy stress tensor [Pa], ε – full strain tensor, ε cr – creep strain tensor, u –displacement vector [m]. It is assumed that the ice-soil retaining structure is a hollow cylinder with inner radius rin and wall thickness E . The outer surface of the cylinder is loaded by the rock pressure P , the top and bottom cylinder ends are fixed in longitudinal direction by the lining and frozen soil, correspondingly, and the circle at the topcrend is fixed in all directions by the tubbing. On the basis of the Vyalov’s constitutive relations the creep strain ε of frozen soils in uniaxial stress conditions is described by the Norton-Bailey creep law. For multiaxial stress conditions with the assumption that the volumetric creep strain equals zero this law can be generalized as:
cr eff
1 A( ) effm
cr m eff
m m
m
(4)
cr [2 / 3(εcr : εcr )]1/2 – the effective creep strain rate, eff [3 / 2(dev(σ) : dev(σ))]1/2 – the effective where eff A( ) 1/ m ( 1) k / m , t – time [h], [Pa∙hλ∙(C)-k], – temperature of the soil [C]. stress, By solving the problem (1-3) analytically with some assumptions, the main from which are that instantaneous elastic deformation is neglected, radial stress equals zero on the inner cylinder surface, shear stress linearly varies near the cylinder ends and equals zero on the inner surface, radial displacement on the top end equals zero and the stress-strain state is considered only at the last time moment, in (Vaylov et al. (1962)) the engineering formula for the optimal thickness E of the ice wall was obtained:
1 1 m 1 m (1 m) Ph E rin 1 m 1 1 m 2 max rin A( )t pr 3
(5)
3. Numerical simulations To estimate adequacy of (5) in this study the problem (1-4) was solved numerically. The numerical modelling was carried out for Callovian sandy loam as one of the most dangerous soil layer for a shaft sinking. The creep parameters characterizing rheological properties of the soil were estimated on the basis of experimental measurements of creep strain on time (Vaylov et al. (1962)). The data was obtained from a uniaxial compression test of a cylindrical rod with the ratio of the radius to the height equal 0.5 one of the ends of that was loaded by pressure equal 3 MPa during 12 hours. The temperature of the soil was 10 C. To identify the properties, the analytical relationship of the creep strain on time obtained by integration (4) was used. In table 1 identified values of the parameters are presented. Table 1. Creep parameters for Callovian sandy loam at -10 C. , MPa∙hλ∙(C)-k
k
m
0.9
0.89
0.27
0.1
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In figure 1 the experimental data for the Callovian sandy loam, the curve obtained from the analytical dependence and the curve obtained from a three-dimensional numerical simulation for the identified values are presented. The numerical simulation was performed for the mentioned experimental conditions with using the constitutive relation (4). As it can be seen the analytical curve is in good agreement with the numerical one. From figure 1 it could be concluded that (4) allows describing the primary nonstationary creep stage with a deceasing deformation rate and the secondary stationary creep stage with an almost constant rate, but it is not able to quality characterize the tertiary creep stage related to progressive flow with an increasing rate. The geometrical parameters for the mine shaft sinking were defined as rin 5.25 m, h 5 m, max 0.1 m on the basis of documentations used for structural design of potash mines in Belarus. The time required for lining installation was assumed t pr 12 h. The rock pressure acting on the ice-soil retaining structure was estimated by the standard engineering formula (Farazi and Quamruzzaman (2013))
P Pl Pw
(6)
Pw w g ( H H w ) – hydrostatic pressure, H , H w where Pl l Hg Tan[(900 ) / 2] – effective lateral pressure, – depths of a soil layer and a groundwater level, [m], γl, γw – average density of rock soils and density of water, [kg/m3], – friction angle, [deg], g – the gravitational acceleration. The expression for Pl is based on the Rankine’s theory (Terzaghi et al. (1996)). In this study it was assumed that H w 1.5 , l 2 103 . For the sandy loam 32 (Vaylov et al. (1962)). In figure 2 (a) relationship of the rock pressure to the depth is presented. Figure 2 (a) shows values of the thickness E of the ice-soil cylinder given by (5) for H equal 100, 115, 250, 500 and 1000 m. Figure 2 (b) presents maximal values u2,max of the second displacement component u2 in depending on H obtained by numerical solving (1)–(4). As can be seen u2,max nonlinearly increases with the depth and reaches 8.8 m at the depth 1000 m. Despite on the significance wall thickness reaching to 104.1 m at 1000 m, the maximal admissible displacement Δmax is not exceeded only for the depths less than 115 m. At that u2,max equals 0.08 m at the depth 100 m.
a
b
Fig. 1. (a) relationship between 33 and t (markers – the experimental data, dash line – the analytical curve, solid line – the numerical one); (b) relationship between rock pressure P and depth H .
a
b
Fig. 2. (a) values of thickness E and (b) values of u2,max in depending on depth H .
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Figure 3 (a) presents distribution of the component u2 in the ice-soil retaining structure at t 12 h and H 100 m. It can be seen that the distribution is non uniform along the cylinder height and u2 takes a maximum value at the bottom cylinder base. Also u2 does not equal to zero at the top cylinder base. Figure 3 (b) shows the curve of development u2,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 t 12 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. 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 were 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 u 2 in the ice-soil cylinder at 12 h and (b) evolution of u2,max in time for the case H 100 m.
a
b
Fig. 4. Profiles of stress components along height l ( l 0 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
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volumetric creep strain equals zero. However, in soils effects of dilatancy and compaction accompany the volumetric creep strain. Both process leads to increase of soil strength that could contribute to decrease of the creep deformation rate. Finally, for shaft sinking at large depths design parameters should be determined based on numerical modelling. For example, it was established that at depth 250 m the ice-soil cylinder with the wall thickness given by the Vaylov’s formula can satisfy the deformation criterion if its height is less than 0.5 m. Acknowledgements This research was supported by 17-11-01204 project (Russian Science Foundation). References Andersland O.B., Ladanyi B., 2013. An introduction to frozen ground engineering. Chapman and Hall, New York. Panteleev I., Kostina A., Zhelnin M., Plekhov A., Levin L., 2017. Intellectual monitoring of artificial ground freezing in the fluid-saturated rock mass. Procedia Structural Integrity, 5, 492–499. Vyalov S.S., 1986. Rheological fundamentals of soil mechanics. Elsevier, Amsterdam, the Netherlands. Razbegin V.N., Vyalov S.S., Maksimyak R.V., Sadovskii A.V., 1996. Mechanical properties of frozen soils. Soil Mechanics and Foundation Engineering 33(2), 35–45. Arenson L.U., Springman S.M., Sego D.C., 2007. The rheology of frozen soils. Applied Rheology, 17(1), 12147. Qi J., Wang S., Yu F, 2013. A Review on Creep of Frozen Soils, in “Constitutive Modeling of Geomaterials”. In. Yang Q., Zhang J.M., Zheng H., Yao Y. (Ed.). Springer, Berlin, Heidelberg, pp. 129–133. Lai Y., Xu X., Dong Y., Li S., 2013. Present situation and prospect of mechanical research on frozen soils in China. Cold Regions Science and Technology, 87, 6–18. Vyalov S.S., Gorodetsky, S.E., Zaretsky Yu.K., Gmoshinsky V.G, Grigoreva V.G., Pekarskaya N.K., Shusherina E.P., 1962. Strength and Creep of Frozen Soils and Design of Ice—Soil Retaining Structures. U.S.S.R. Acad. Press, Moscow (in Russian). Vyalov S.S., Zaretsky Y.K., Gorodetsky S.E., 1979. Stability of mine workings in frozen soils. Engineering Geology, 13(1-4), 339-351. Ottosen N.S., Ristinmaa M., 2005. The Mechanics of Constitutive Modeling. Elsevier, Amsterdam. Klein J., Jessberger H.L., 1979. Creep stress analysis of frozen soils under multiaxial states of stress. Engineering Geology, 13, 353–365. Eckardt H., 1982. Creep tests with frozen soils under uniaxial tension and uniaxial compression, in “Proceedings of the 4th Canadian Permafrost Conference”. In: French H.M. (Ed.). Calgary, Alberta. National Research Council of Canada, pp. 394–405. Judeel G.duT., Keyter G.J., Harte N.D., 2012. Shaft sinking and lining design for a deep potash shaft in squeezing ground in "Harmonising Rock Engineering and the Environment”. In: Qian Q., Zhou Y. (Ed.). Taylor & Francis Group, London, pp. 1697–1704. Fabich S., Bauer J., Rajczakowska M., Świtoń S. (2015). Design of the shaft lining and shaft stations for deep polymetallic ore deposits: Victoria Mine case study. Mining Science, 22, 121 – 140 Oreste P., Spagnoli G., Bianco L.L., 2016. A combined analytical and numerical approach for the evaluation of radial loads on the lining of vertical shafts. Geotechnical and Geological Engineering, 34(4), 1057-1065. Spagnoli G., Oreste P., Bianco L.L., 2017. Estimation of shaft radial displacement beyond the excavation bottom before installation of permanent lining in nondilatant weak rocks with a novel formulation. International Journal of Geomechanics, 17(9), 04017051. Schwamb T., Soga K., 2015. Numerical modelling of a deep circular excavation at Abbey Mills in London. Géotechnique, 65(7), 604-619. Jia Y., Bian H.B., Duveau G., Su K., Shao, J.F, 2008. Hydromechanical modelling of shaft excavation in Meuse/Haute-Marne laboratory. Physics and Chemistry of the Earth, Parts A/B/C, 33, S422-S435. Farazi A. H., Quamruzzaman C., 2013. Structural design of frozen ground works for shaft sinking by practicing artificial ground freezing (AGF) method in Khalashpir coal field. International Journal of Engineering and Science, 2(3), 69-74. Terzaghi K., Peck R. B., Mesri G.,1996. Soil mechanics in engineering practice. John Wiley & Sons, New York.