Introduction
The determination of upward conductive heat flow, one of the mechanisms of intra-terrestrial heat release, occupies a special place in the study of subglacial Lake Vostok in Antarctica. It is important not only for determining the genesis of the lake and the associated evolution of life on Earth, but also for reliably determining the heat flow from the Earth's interior, which plays a role in the evolution of the Antarctic crust and the formation of its morphology and physical properties. In real-world conditions, the presence of a global heterogeneous ice sheet with creep deformation, as well as structural and thermоphysical inhomogeneities in the Earth's crust (Yang & Song Reference Yang and Song2023), affects the geomechanical processes occurring under the influence of natural causes, which can be considered as a nonlinear dynamic system (close to fractal system). This is a process with non-constant and non-periodic variable trajectories. To establish the pattern of deformation of the ice sheet and its deflection in the area of Vostok Station, we used the obtained physical and mechanical properties of rocks of East Antarctica and elastic-plastic models of the medium, taking into account creep deformation for the ice sheet. Modelling of the geomechanical processes of the impacts of the glacial cover was considered over time as a linear dynamic system.
Study of the ice sheet and subglacial Lake Vostok in Antarctica has been undertaken using seismic and radar methods since 1960, when seismic sounding by the reflected wave method and determination of the glacier thickness and subglacial relief were carried out (Savatyugin & Preobrazhenskaya Reference Savatyugin and Preobrazhenskaya1999, Savatyugin et al. Reference Savatyugin, Verkulich, Masolov, Sheremetev, Lipenkov and Abyzov2003, Popov et al. Reference Popov, Masolov, Lukin and Popkov2012, Popov Reference Popov2021).
The native relief and depths of Lake Vostok, which is a depression in the form of a lowered block of the Earth's crust in an extended sub-meridional region of lithospheric destruction measuring ~310 × 100 km, have been established (Fig. 1; Savatyugin et al. Reference Savatyugin, Verkulich, Masolov, Sheremetev, Lipenkov and Abyzov2003, Popov & Lunev Reference Popov and Lunev2012, Popov Reference Popov2021). Eleven islands with a total area of 365 km2 have been identified in the water area. The area of the largest of them is 175 km2 (Popov et al. Reference Popov, Masolov, Lukin and Popkov2012).
Figure 1. Native relief and subglacial water bodies in the area of Lake Vostok: 1 = isohypses of native relief, cross-section of isolines at 150 m; 2 = sea level; 3 = shoreline of the lake; 4 = seismic profiles; 5 = shot points of the seismic reflection survey of the 46th Russian Antarctic Expedition (RAE). The bottom-left inset shows the layout of the used geophysical data; blue colour shows subglacial water bodies; domestic radar routes are shown in red colour (Popov & Lunev Reference Popov and Lunev2012).
Lake Vostok is an isolated water body with a water table area of 15 790 km2 and a water body volume of 6100 km3. Its altitude position varies from 600 to 150 m (Popov et al. Reference Popov, Masolov and Lukin2011, Reference Popov, Masolov, Lukin and Popkov2012, Popov & Lunev Reference Popov and Lunev2012). The average depth of the lake is ~400 m. In the master plan of the lake, the southern part of the lake, measuring 70 × 30 km, is the deepest, with an average depth of ~900 m and a maximum depth in the central part of up to 1200 m (Savatyugin et al. Reference Savatyugin, Verkulich, Masolov, Sheremetev, Lipenkov and Abyzov2003). The northern part of the lake, measuring 150 × 70 km, has an average depth of ~300 m and a maximum depth of up to 600 m (Popov et al. Reference Popov, Masolov and Lukin2011, Popov & Lunev Reference Popov and Lunev2012). The concentration of dissolved oxygen in the lake water is estimated at 27–1300 mg/l, which is 2–90 times higher than the oxygen content in water under normal conditions (Arapov et al. Reference Arapov, Lipenkov and Savatyugin2005).
The bottom of the part of Lake Vostok, which has been studied using seismic measurements, has the shape of a step-like bend with bottom depths of 4310–5040 m from the ice surface, where the eastern step (depth 4310 m) is raised relative to the western one by 140 m.
The greatest thickness of the water layer (1200 m) is found in the central part of profile S1 (Fig. 1; Masolov et al. Reference Masolov, Popov, Lukin and Popkov2010). The bottom of the lake in the upper part is seemingly covered with loose sediments with a thickness of 40–300 m (Leitchenkov et al. Reference Leitchenkov, Antonov, Luneov and Lipenkov2016).
The water area of Lake Vostok is represented by a hilly underwater plain. In the western area of Lake Vostok there is a mainly mountainous landscape with elevations of up to 1580 m, and in the eastern area there is hilly and flat terrain with elevation differences of 100 m on average (Popov & Lunev Reference Popov and Lunev2012). The crustal thickness is 34 km to the west of the Vostok trench and 36 km to the east (Popov et al. Reference Popov, Masolov, Lukin and Popkov2012).
At depths of 55–60 km below Lake Vostok a local geospatial region with increased geothermal flow along a transcrustal fault into the Earth's crust was presumed to have been identified (Isanina et al. Reference Isanina, Krupnova, Popov, Masolov and Lukin2009). The Vostok Basin may be reefogenic in nature, as the fault zones have not been traced above the basement, and it is possible that the ‘eastern ’ block is in a stretched state and the ‘western ’ block is in a compressed state (Isanina et al. Reference Isanina, Krupnova, Popov, Masolov and Lukin2009). At the same time, an increase in geothermal flow is possible in the area of the Vostok Basin and to the east of it (Popov et al. Reference Popov, Masolov, Lukin and Popkov2012).
In the ‘western ’ block, the upper boundary of the basement is located at a depth of 3500 ± 200 m. It is rough but not stratified (Isanina et al. Reference Isanina, Krupnova, Popov, Masolov and Lukin2009). The thickness of the bottom sediments varies, ranging from 40 to 300 m (Leitchenkov et al. Reference Leitchenkov, Antonov, Luneov and Lipenkov2016).
The thickness of the sedimentary rocks varies from 400 m in the north to 1000 m in the south. Below this boundary, a crystalline basement lies at depths of 3.8–5.0 km (Isanina et al. Reference Isanina, Krupnova, Popov, Masolov and Lukin2009). The sedimentary stratum consists of sediments from the Upper Proterozoic to the Jurassic inclusive and represents deposits of glacial and glacial-marine genesis, with the presence of siltstone-clay sediments with inclusions of coarse-grained material (diamectites; Grikurov et al. Reference Grikurov, Leichenkov, Kamenev, Mikhalsky, Golinsky and Masolov2003).
The crystalline basement is composed of a magmatized and granitized complex of gneisses and crystalline schists with a total thickness of 15–20 km.
Precambrian and Lower Palaeozoic intrusions of gabbroic-anorthosites and charnockite and Early Mesozoic intrusions of nepheline syenites are widespread in the crystalline basement (Pandey et al. Reference Pandey, Pant, Arora, Ferraccioli, Gupta and Joshi2023).
When opening the congelation ice layer with borehole 5G, small (0.1–1.0 cm) mineral inclusions captured by the glacier during its movement through the western shallow part of the lake were detected (Leitchenkov et al. Reference Leitchenkov, Antonov, Luneov and Lipenkov2016). Lake water samples (Lipenkov et al. Reference Lipenkov, Ekaykin, Alekhina, Shibaev, Kozachek and Vladimirova2017) obtained during the first opening of Lake Vostok on 5 February 2012 were studied previously (Litvinenko Reference Litvinenko2020).
Most of the bottom sediments accumulated in Lake Vostok and captured during the accretion of the lower ice layer in the form of small inclusions came from the western shore of the lake due to the exaration of the native glacier bed. These inclusions contain indirect information about its geological structure.
Studies of the core collected from borehole 5 G (Savatyugin et al. Reference Savatyugin, Verkulich, Masolov, Sheremetev, Lipenkov and Abyzov2003) showed that at a depth of 3538 m at the base of the glacial strata there is a 200 m-thick layer of accretion ice formed as a result of lake water freezing over the base of a slowly moving (3 m/year) glacier. The upper part of this layer (from 3538 to 3608 m) is saturated with solid (mineral), irregularly distributed (from 2 to 25 per 1 m of core) inclusions of 1–2 mm in size, which were captured during its formation, when the glacier crossed the shallow coastal area of the lake located to the north-west of the borehole (Savatyugin et al. Reference Savatyugin, Verkulich, Masolov, Sheremetev, Lipenkov and Abyzov2003). They actually reflect the composition of its bottom sediments, being carriers of unique information about the geological structure of the subglacial environment.
It was found that mineral inclusions are agglomerates formed as a result of coagulation of clay-mica minerals (0.3–0.5 μm in size). Illite and chlorite predominate among the clay minerals, with fragments (usually subrounded and angular) of rock-forming and accessory minerals present. Quartz of 10–100 μm, tourmaline (~70 μm), epidote, zircon and hornblende (50–100 μm) and rutile, dolomite and iron hydroxides were reliably identified. It was found that the general dimensionality of the substance composing the solid inclusions corresponds to the pelite-siltstone fraction of sediments. There is a large gravity anomaly near the lake. The presence of this anomaly and clay particles in the ice suggests that this part is composed of sedimentary rocks, possibly of Permian-Triassic age (Leitchenkov et al. Reference Leitchenkov, Antonov, Luneov and Lipenkov2016).
The angular shape of the quartz and accessory minerals testifies to glacial transport of fragmental material. Through the discovery of zircon it was possible to determine the age of the rocks subjected to exaration, which are 1.74 billion years old, corresponding to the time of formation of metamorphic complexes of the Proterozoic mobile belt of the Antarctic crystalline shield.
Russian studies and studies conducted by other nations have shown good agreement regarding water and sediment thicknesses between the gravity model and seismic measurements, which confirms two basic facts about Lake Vostok: the lake consists of sedimentary rocks and the lake bottom is covered with a layer of unconsolidated sediment that does not exceed 300 m in the southern basin and thickens to almost 400 m in the northern basin.
The ice cover above the lake has a layered, sub-horizontal structure of the distribution of the parameters of material composition, petrophysical and petrographic properties and the velocity and direction of flow of ice masses (Fig. 2). Up to a depth of 3539 m, the ice cover is composed of ice of atmospheric origin, but deeper than 3539 m and down to the contact of the glacier with the surface of lake water at a depth of 3769.3 m, the glacial cover is composed of congelation (lake) ice formed from the water of the subglacial reservoir (Fig. 2).
Figure 2. Layers of ice with different rheological properties in the ice-sheet section in the area of Vostok Station. The profile of ice velocity V relative to the surface is plotted based on the data from geophysical studies of a deep borehole.
Ice is not an absolutely solid body. Even at low pressure it exhibits plastic properties. This means that it changes its shape or flows without turning into a liquid. Experimental and calculated data of the physical properties of ice (Epifanov Reference Epifanov2007, Tsyganova et al. Reference Tsyganova, Popov, Salamatin and Lipenkov2010, Vasilev et al. Reference Vasilev, Dmitriev and Lipenkov2016) are shown in Table I.
Table I. Average physical and mechanical characteristics of ice.
The mechanical properties of ice depend on its structure, porosity, salinity and temperature (Higashi et al. Reference Higashi, Koinuma and Mae1964, Jones & Glen, Reference Jones and Glen1969a,Reference Jones and Glenb, Michel & Ramseier Reference Michel and Ramseier1971, Nanthikesan & Shyam Sunder Reference Nanthikesan and Shyam Sunder1994).
Structural transformations in the Antarctic glacier strata were studied as a result of analysis of a core from borehole 5 G at a depth of 3769.3 m (Lipenkov et al. Reference Lipenkov, Polyakova, Duval and Preobrazhenskaya2007, Reference Lipenkov, Lukin, Bulat, Vasiliev, Ekaikin, Leichenkov and Kotlyakov2011). A general tendency of ice crystal size to increase with depth was established (Fig. 3). The sizes of the crystals do not exceed 5 mm up to a depth of 2500 m, and then significant growth in is observed. At the same time, the orientation of the main axes of the crystals also changes.
Figure 3. Change in ice-grain size with depth (Lipenkov et al. Reference Lipenkov, Polyakova, Duval and Preobrazhenskaya2007).
Experimental studies have shown that the limit to ice fluidity also increases with decreasing temperature: as the temperature drops from -1.7°C to -20°C, the limit to ice fluidity increases by more than 200%, and down to -30°C it increases by 300%. The deformation curve has an elastic-plastic form with a pronounced yield area (Glazovsky et al. Reference Glazovsky, Epifanov and Yuryev2008).
Methodology
On the basis of published and experimental data on the ice cover and underlying rock, the native relief and the depths of the subglacial Lake Vostok (Ravich & Kamenev Reference Ravich and Kamenev1972, Grikurov et al. Reference Grikurov, Leichenkov, Kamenev, Mikhalsky, Golinsky and Masolov2003, Savatyugin & Preobrazhenskaya Reference Savatyugin and Preobrazhenskaya1999, Arapov et al. Reference Arapov, Lipenkov and Savatyugin2005, Popov et al. Reference Popov, Masolov and Lukin2011, Popov & Lunev Reference Popov and Lunev2012), a three-dimensional model has been built, in which an elastic model of medium deformation and an elastic-plastic model of medium deformation based on the modified von Mises yield criterion have been used in the numerical modelling of the stress-strain state of the ice cover, Lake Vostok waters and the underlying rock. The substantiation of long-term deformation characteristics of the ice has been performed on the basis of the adopted rheological model (Ashby & Duval Reference Ashby and Duval1985, Shyam Sunder & Wu Reference Shyam Sunder and Wu1990).
In the elastic model of medium deformation, the relationship between deformations ɛ and stresses σ (Eq. 1) is written through the elasticity matrix [D], which includes a set of coefficients determining the behaviour of the medium:
$$\rm \bf \sigma = [ {\rm\bf D} ] {\rm \bf \varepsilon }.$$The elasticity matrix for an isotropic linear-deformation medium is written in the following form (Eq. 2):
$$[{\bf D}] = \displaystyle{{{\rm E}_{\rm y}} \over {(1 + {\rm \nu })(1-2{\rm \nu })}}\left[ {\matrix{ {1-{\rm \nu }} & {\rm \nu } & {\rm \nu } & 0 & 0 & 0 \cr {\rm \nu } & {1-{\rm \nu }} & {\rm \nu } & 0 & 0 & 0 \cr {\rm \nu } & {\rm \nu } & {1-{\rm \nu }} & 0 & 0 & 0 \cr 0 & 0 & 0 & {\displaystyle{{1-2{\rm \nu }} \over 2}} & 0 & 0 \cr 0 & 0 & 0 & 0 & {\displaystyle{{1-2{\rm \nu }} \over 2}} & 0 \cr 0 & 0 & 0 & 0 & 0 & {\displaystyle{{1-2{\rm \nu }} \over 2}} \cr } } \right],$$where Eу is the modulus of elasticity and ν is Poisson's ratio.
The elastic-plastic model of medium deformation based on the modified von Mises yield criterion is written in the following form (Eq. 3):
$${\rm \sigma }_y = q, \;$$where σy is the boundary value of tensile stresses corresponding to the true limit to the fluidity of the ice and q is the normal stress intensity.
For volumetric stress conditions (Eq. 4):
$$q = \displaystyle{{\sqrt 2 } \over 2}\sqrt {{( {{\rm \sigma }_1-{\rm \sigma }_2} ) }^2 + {( {{\rm \sigma }_2-{\rm \sigma }_3} ) }^2 + {( {{\rm \sigma }_3-{\rm \sigma }_1} ) }^2} .$$To describe the rheological processes in the ice cover, the double power law model is used, which provides the most complete description of the development of long-term deformations characteristic of the second stage of creep (i.e. the stage of steady-state creep).
The model makes it possible to take into account the influence of the intensity of tangential stresses on the rate of development of creep deformations, as well as the influence of temperature. For ice, the dependence of the creep strain rate on its state is transformed to the following form (Eq. 5; Protosenya & Katerova Reference Protosenya and Katerov2023):
$$\dot{\varepsilon }^{vp} = A_1 exp\left({-\displaystyle{{B_1} \over {\theta -\theta_Z}}} \right)\left({\displaystyle{{q_k} \over {\sigma_{\rm o}}}} \right)^{C_1} +\; A_2 exp \left({-\displaystyle{{B_2} \over {\theta -\theta_Z}}} \right)\left({\displaystyle{{q_k} \over {\sigma_{\rm o}}}} \right)^{C_2}, \;$$where A 1, A 2, B 1, B 2, C 1 and C 2 are rheological model parameters determined experimentally, θ is ice temperature, θz is absolute zero temperature, σ 0 is a control parameter (taken to be equal to 1 MPa) and qk is the intensity of tangential stress.
The parameters of the accepted models of material deformation are presented in Table II.
Table II. Physical and mechanical characteristics of the materials. The indicators are taken approximately and will be clarified based on the results of laboratory tests. The numerators show the instantaneous values of the indicators and the denominators show long-term values.
The described models are implemented in the SIMULIA Abaqus CAE software package.
Two finite-element models in planar-strain (Fig. 4a) and spatial (Fig. 4b) settings have been built to predict the stress-strain state of the ice sheet, Lake Vostok waters and the underlying rocks. The construction of the geometry of the models was carried out on the basis of geophysical survey data with some simplifications, which would not have a significant impact on the results of the prediction of the stress-strain state.
Figure 4. a. Planar and b. special finite-element models for forecasting the stress-strain state of the ice cover in Lake Vostok waters and the underlying rocks.
The problem has been solved in a gravitational setting with the following boundary conditions: displacements along the lower boundary of the model are prohibited in all directions; displacements along the lateral boundaries of the model are prohibited in the direction normal to these boundaries; and displacements along the upper boundary of the model are not limited.
The planar model dimensions are: width = 90 km and height = 10 km. The geometry is divided into triangular quadratic finite elements. The dimensions of the spatial model are: length = 2360 km, width = 2360 km and height = 10 km. The geometry is divided into tetrahedral quadratic finite elements.
Numerical modelling of the stress-strain state forecast of the considered system has been performed in the following sequence: formation of the initial stress state before the formation of the ice cover; and formation of the stress state of the considered system in the process of ice-cover formation.
Determination of rock properties
In the study of the physical and mechanical properties of rocks, due to the limited volume of the samples taken and their non-standard shape, methods of testing samples of regular (cylindrical) and irregular shapes with spherical indenters have been used.
The research has been carried out according to the standard methodology (GOST 24941-81) and supplemented with data for determining the complex of mechanical parameters according to the improved methodology developed in the laboratory of physical and mechanical properties of St Petersburg Mining University. Elastic-wave velocities were measured in the samples beforehand and then tested in controlled deformation mode.
The following indicators of physical and mechanical characteristics of the samples have been determined: density of regular-shaped samples (volume density), propagation velocities of elastic longitudinal (VP) and transverse waves (VS), strength limits for uniaxial compression (σcj) and tension (σр), brittleness index (Bi), cohesion (C) in volumetric compression and the corresponding angle of internal friction (φ) and deformation characteristics - moduli of total deformation and elasticity, transverse deformation coefficients, modulus of bearing capacity decline and residual strength. Statistical processing of the test results has been performed.
Sample descriptions are given in Table III.
Table III. Brief description of the selected samples.
Results
As a result of laboratory studies of 10 samples of bedrock from East Antarctica, new information on lithologic differences of the basement has been obtained, and the presence of Permo-Triassic sedimentary deposits in the synrift complex has been established.
The test results from the 10 samples represented by magmatic, metamorphic and sedimentary rocks collected in East Antarctica (Prince Charles Mountains region) are shown in Table IV. The complex of the physical and mechanical parameters of the rocks determined from the results of tests of irregularly shaped specimens with spherical indenters is presented: strength limits under uniaxial tension (σp) and compression (σcj), brittleness index (Bi), ultimate shear strength without normal stresses (cohesion; C0) and the corresponding angle of internal friction (φ0), cohesion (C) under volumetric compression and the corresponding angle of internal friction (φ), modulus of elasticity (Eу) and Poisson's ratio (μ) and residual strength under uniaxial compression (σR). Statistical data processing has been performed.
Table IV. Results of testing the irregularly shaped samples with spherical indenters and their statistical processing.
aThe average values of the indicators.
bRoot mean square deviations of the indicators.
cCoefficients of variation (%).
dNumber of determinations.
The results of calculations and of predicting the stress-strain state of the system ‘ice sheet-lake-underlying rocks’ are presented in the form of diagrams of the distribution of vertical and horizontal stresses, as well as in the form of diagrams of the resultant absolute deformations and diagrams of plastic deformations.
The results of calculations in the planar-deformation setting (Fig. 5) allow us to make a judgement about the character of the ice-cover deflection over Lake Vostok and changes in the stress state of the water in the lake. It has been established that the potential deflection of the ice cover can reach 250 m with the accepted mechanical characteristics of ice and water bulk modules.
Figure 5. Distribution pattern in the planar deformation setting in the ice cover of the waters of Lake Vostok and underlying rocks: а. vertical stress (MPa), b. horizontal stress (MPa), c. resultant absolute deformation (m) and d. plastic deformations (fractions of a unit).
The influence of changes in the long-term ice deformation modulus in the range of 250–1000 MPa and the water bulk modulus range of 2100–3000 MPa is described by a non-linear relationship, with increasing ice-cover deflection values as the deformation modulus decreases (Fig. 6).
Figure 6. Variation of the maximum value of the ice-cover deflection depending on the long-term deformation modulus of ice and bulk modulus of water in Lake Vostok.
The largest deflection is observed above the centre of Lake Vostok. The stress distribution patterns suggest a complex character of stress distribution in the system under consideration in the vicinity of the lake. The plastic deformation zone is formed at the edge areas of the lake, and, as the results show, it does not extend to the entire height of the ice cover.
The results of calculations performed in the spatial setting are presented in the form of profiles of vertical and horizontal stress distribution and resulting absolute and plastic deformations (Fig. 7). Taking into account the complex geometry of Lake Vostok allowed us to clarify the character of formation of the stress-strain state of the ice cover. In general, it is possible to note qualitative and quantitative convergence of the modelling results in planar and spatial settings.
Figure 7. Spatial distribution patterns in the ice cover of the Lake Vostok waters and underlying rocks: а. vertical stress (MPa), b. horizontal stress (MPa), c. resultant absolute deformation (m) and d. plastic deformations (fractions of a unit).
Discussion
To verify the reliability and correctness of the results of the numerical modelling, the geomechanical model has been verified using the data from experimental tests of bedrock samples and field observations in borehole 5G, drilled to a depth of 3769.3 m to the surface of Lake Vostok.
The geometric dimensions of the spatial model were chosen to achieve a calculation error of no more than 1% at the model boundaries.
The averaged rheological parameters that take into account the influence of the maximum creep strain rate (A1 and A2), the non-linear dependence between the initial velocity and stresses (C1 and C2) and the dependence of the creep strain rate on temperature (B1 and B2) are selected with the necessary accuracy to describe the ice sheet deformation process based on field observations in borehole 5G.
The stress values at the contact of the glacier with the lake according to the results of numerical modelling have been determined in the range of 32.0–35.0 MPa, and in the area of borehole 5 G to be 34.60 MPa, which satisfactorily correlates with the experimental data regarding the glacier pressure at the contact with the lake of 33.78 ± 0.05 MPa obtained from the results of measuring the ice-core density from borehole 5 G (Lipenkov et al. Reference Lipenkov, Turkeev, Vasilev, Ekaykin and Poliakova2021).The slight discrepancy in the results is due to the averaging in the model of the rheological properties of ice by layer, as well as the fractal properties of ice crystals and changes in temperature along the depth of the ice cover.
Conclusions
A new three-dimensional geomechanical model of the system ‘glacier-subglacial lake-bedrock ’ has been developed, which allows for modelling changes in the stress-strain state of the system, taking into account the drilling of deep boreholes.
For the first time a set of physical and mechanical characteristics of the rocks of East Antarctica (the region of Prince Charles Mountains), including volume density, propagation velocities of elastic longitudinal and transverse waves, ultimate strength under uniaxial compression and tension, brittleness coefficient, cohesion under bulk compression and the corresponding angle of internal friction, as well as deformation characteristics (modules of general strain and elasticity, coefficients of transverse deformation, modulus of bearing capacity decline and residual strength), have been experimentally determined.
Numerical modelling has shown that the deflection of the ice cover at given ice characteristics can reach a value of 250 m or more. Changes in the mechanical characteristics of the ice cover can significantly affect this value.
It has been noted that the stresses in the waters of Lake Vostok are distributed according to the hydrostatic law, while the stresses in the ice cover are distributed according to a law similar to the hydrostatic law. The zones of development of plastic deformations of the ice cover over Lake Vostok have been determined. It is shown that plastic deformations in the ice cover are localized in the areas along the perimeter of the lake, and the maximum intensity of their distribution is confined to the lower and upper layers of the ice cover.
The data obtained provide satisfactory convergence with the results of in situ observations obtained during drilling of the ultra-deep borehole and penetration into the subglacial Lake Vostok at a depth of 3769.3 m.
The established regularities of stress-strain state formation in the elements of the system under consideration can be used as input data for modelling borehole drilling processes, as well as for forecasting the main parameters of the natural environment in the subglacial Lake Vostok and the underlying rock necessary for the design and effective operation of unique research equipment and instrumentation.
In further studies it is planned to experimentally specify the structure and strength-deformation characteristics of the ice cover, as well as the underlying rocks, and to reveal the influence of deep geothermal flows, which will make it possible to improve the three-dimensional geomechanical model of the system ‘glacier-subglacial lake-bedrock ’ and to consider it as a dynamic non-linear system in the large-scale study of the subglacial Lake Vostok.
Author contributions
Both authors have contributed equally to the paper. Both authors have read and agreed to the published version of the manuscript.
Acknowledgements
The authors would like to thank Professor M.A. Karasev for his help in preparing the calculations and the anonymous reviewers for their helpful comments to improve the paper.
Financial support
This research was performed under the theme ‘Fundamental Interdisciplinary Research on Geological Formations of Antarctica’.
Competing interests
The authors declare none.
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