Long-term monitoring of earth dam of the Charvak hydroelectric power plant (HPP) considering the water level of the reservoir

. A numerical method for determining the settlement and stress-strain state (SSS) of high earth dam of the Charvak hydroelectric power plant is developed based on the finite element method (FEM). The results were compared with the available data from long-term field observations and with records of continuous geodetic monitoring of the dam behavior based on processed space radar images obtained from the Sentinel-1 satellite. To conduct calculations, OJSC Gidroproekt of the Republic of Uzbekistan provided the structural and piecewise non-homogeneous physical and mechanical characteristics of soil of the structure body. The results of calculations of vertical displacements, normal stresses, and pore pressure were compared with field observation data for the section in which the corresponding control and measuring equipment was installed. A cause-and-effect relationship was identified between the water level in the reservoir and the deformation of the dam. The difference between the theoretical results obtained and field observations was up to 10%. A comparison of the results obtained using the finite element analysis calculations (taking into account the level of water filling in the reservoir) with the actually measured deformations of the dam during the filling of the reservoir, and with processed space monitoring data depending on the time of year, showed a good agreement between the measured and calculated displacements.


Introduction
Dams are large hydraulic structures and are among the most important engineering structures.They are used for water supply, agricultural purposes, and hydroelectric engineering.However, most of these dams were built before the introduction of seismic regulations or during a period when the seismicity of dam sites was estimated approximately and thus was often underestimated or even completely ignored [1].Therefore, many earth dams currently in operation were not designed to withstand earthquakes or were designed for seismic intensity below the currently estimated one.Accidents in these structures can be significant and comparable to the consequences of natural disasters.
The impact of earthquakes on dams has been documented in several studies [2 -5].Rare cases of dam failure during or immediately after a seismic event were mostly caused by severe earthquakes and manifested in soil liquefaction of foundations or embankments.However, permanent displacements and deformations, ground mass motion, and crack development were widely observed even during moderate seismic events without soil liquefaction [6].
Analysis of the seismic behavior of earth dams at the screening level is generally performed by estimating the residual displacements caused by the earthquake using simplified Newmark-type calculations.They include conventional coupled or uncoupled analysis of rigid blocks sliding and coupled analysis of the stick-slip motion taking into account soil compliance and nonlinear behavior [7].
As was noted in [8], an important role in the reduction in shear strength that can occur in dam soils plays the need for further clarification and high-level analysis to assess the influence of the vertical component of ground motion and excess pore pressure on the magnitude of dam displacement caused by an earthquake.The authors of [1] believe that crest settlement can be considered a reliable indicator of seismic performance since it reflects the overall seismic response of the dam and is appropriate for assessing the level of damage caused by an earthquake.
In accordance with the standards for the safe and reliable operation of high earth dams erected in seismic regions (in our case, the area has a seismic magnitude of 8-9), it is necessary to provide continuous monitoring of the structure conditions to ensure that the stability and serviceability are guaranteed against the expected ground motions characterized by a relatively low or high probability of emergencies arising due to uncontrolled water discharge during extreme (unlikely) events, as well as to ensure the operability of the dam and adjacent structures during possible earthquakes.
For more reliable information about the deformed state of the dam body (crest and slopes) and its dynamics under various loads, in addition to the above, the method of space synthetic aperture radar interferometry (SAR, InSAR) is proposed, which is a new space geodetic tool for monitoring deformations on Earth surface.Unlike conventional pointbased observation methods, InSAR provides observations at large spatial scales over long periods, providing a more complete analysis of the deformation characteristics of the dam and its surroundings.
In recent years, satellite data has been widely used as a useful complement to conventional methods of monitoring dams to ensure their safety.Due to its ability to provide wide and relevant geospatial information, remote sensing is becoming an important technology for managing natural hazards such as earthquakes, volcanic eruptions, floods, or landslides, etc.
Soil subsidence is another type of hazard that develops over large time scales and is characterized by smaller but consistent changes.Soil subsidence is more common in urban and suburban areas, caused by various reasons such as water resource exploitation or mining [9].Subsidence of dam sections (which may result in water overtopping) can affect the risk of flooding and cause damage to downstream infrastructure.Therefore, the phenomenon of subsidence should be given the same importance as the other hazardous events mentioned above.
Changes in structures or associated dam infrastructures, including crest and slopes, can be effectively captured using satellite inferometry synthetic aperture radar (InSAR) techniques, particularly, Muti-Temporal InSAR time series analysis.Today, with the availability of space-based satellites with high spatial resolution SAR imagery and short revisit times, this technology is a powerful, cost-effective way to monitor displacements of a dam structure and its surroundings at the millimeter level.Moreover, the potential of the method increases since the Sentinel-1 Copernicus C-band SAR satellites have two advantages: a revisit time of 6 days and the availability of free data [10].
Differential satellite interferometry (InSAR) can help monitor displacements of the upper parts of large dams registered by space-based microwave sensors [11 -13].
ReMoDams is a Spanish research project aimed to monitor the deformation of several earth-fill dams using advanced InSAR time series methods.One of these dams is the Arenoso Dam, located in the province of Cordova (southern Spain).This dam has been monitored using Sentinel-1 SAR data since the mission began in 2014 [10].
Marco Corsetti et al. [11] applied an improved DInSAR (Differential Interferometric Synthetic Aperture Radar) method called Small BAseline Subset (SBAS) to monitor the Genzano di Lucania earth dam and the Corbara gravity dam.Analysis of DInSAR data covering a period of 15 years (1992-2007) clearly indicates the settlement of the Genzano earth-fill dam with a maximum average rate of 1.55 mm/year as a result of the consolidation process.A data set of 35 images of the Corbara dam was also obtained, from 2010 to 2014 using the COSMO SkyMed sensor (ASI source).All points were found to have a velocity between -1.00 and 1.00 mm/year.It was shown that the Corbara Dam did not experience significant vertical displacements during the analyzed period, but only small periodic displacements due to changes in reservoir water levels and temperature variations.
In [12], the surface displacement of the La Pedrera reservoir dam (southeast Spain) was measured using satellite differential interferometry synthetic aperture radar (SAR).Based on a dataset consisting of ERS-1, ERS-2 and Envisat-ASAR imagery, a displacement of approximately 13 cm along the satellite line visibility was recorded between August 1995 and May 2010.Joint analysis of historical instrumental surveys and data obtained using DInSAR, allowed the authors to identify the long-term process of deformation of the dam surface.DInSAR data were used to calculate the long-term settlement of the La Pedrera Dam.
The destruction of the Sardoba Dam in Uzbekistan was studied in [14 -16].The Sardoba Dam is located on the left bank of the Syrdarya River.The Sardoba Reservoir was intended for irrigation and hydropower engineering purposes.
On May 1, 2020, at about 6:00 a.m.local time, a catastrophic collapse occurred at the Sardoba Dam site in the Syrdarya region of Uzbekistan (Fig. 1b) [14].The breach was located near the bend of the western front of the dam, where the dam changes its strike from ~N45•W to ~N0•W (Fig. 1).
The developing breach of the dam resulted in two water releases around 8:58 a.m.(Figure 1c) and finally created a breach section approximately 260 meters long (Figure 1d).The flood and subsequent mudflow killed six people, injured more than 50, forced the evacuation of at least 100,000 people in the Syrdarya River basin, and caused enormous environmental damage and economic losses [15].Most of the reservoir's volume was exhausted, and on May 3, 2020, the flood spread further north, to the southern territory of Kazakhstan [16].Economic losses amounted to approximately US$ 1 billion, including damage to households, infrastructure, and agricultural lands.Ten months after the incident, a new arc-shaped dam was built to repair the breach (Fig. 1e) [14].SAR surveys from two Sentinel-1 orbits were used to map the spatiotemporal deformation of the dam.Multi-temporal InSAR observations demonstrated wellconstrained deformation of the peripheral U-shaped dam from May 2015 to December 2020 (Fig. 2) [14].Based on InSAR analysis, significant non-uniform settlement of up to 4.7 cm was identified near the breach site in the years before the breach date.This significant nonuniform settlement during the secondary consolidation period reflects potential defects in the underlying wall of the dam (caused by construction quality) [15].Transverse cracks resulting from non-uniform settlement could be further eroded by water if the hydraulic shear stresses exceeded the critical shear stress of the filled materials.Further development of these cracks can lead to the formation of seepage, i.e. suffusion (ground motion) [14].
An assessment of the risks of a breakthrough of the Sardoba Reservoir was also conducted by the Geospatial Agency "Innoter" (https://innoter.com/projects/otsenka-riskovproryva-damb-vodokhranilishch/)using free-of-charge space radar images obtained from the Sentinel-1 satellite.A study of the territory of the Sardoba Reservoir (Uzbekistan) before the dam breach (August 2017 -May 2020) is presented in Fig. 3.A graph of the displacement of the earth's surface before the dam collapsed was plotted.As can be seen from the graph, the displacement over three years reached 90 mm.A study of displacements after the repair of the dam (May 2020 -June 2022) (Fig. 4) was also conducted.Displacement graphs that show displacements of up to 30 mm over two years were plotted.preceded by a critical settlement; after repair of the dam, the displacement remains, though in smaller values.
Thus, non-uniform settlement of dams during or after construction can lead to crack formation below the reservoir level and, as a result, to uncontrolled seepage and the onset of internal erosion of the embankment.Therefore, the settlement pattern is critical for safety monitoring.
Space monitoring of the state of the Charvak reservoir was conducted by the Center for Space Monitoring and Geoinformation Technologies.Space radar images obtained from the Sentinel-1 satellite were used in the study.The layout of the Charvak earth dam is shown in Fig. 5.The dam is located on the Chirchik River (not far from Tashkent city).It includes a centrally symmetrical core (of loam), filters serving as two-layer transition zones (of sand and gravel materials) and retaining prisms (of stones).The base of the dam consists of limestones [17].From the analysis of graphs obtained from satellite images (not presented here due to confidentiality), it follows that the displacements have a cyclicity, depending on the area of the water surface (which depends on the time of year).Maximum amplitudes are observed in the upper part of the dam.
Space observations should be combined with geodetic monitoring data to analyze the correlation between deformation, hydrological conditions, and environmental factors [18].
To conduct theoretical calculations on predicting the stress-strain state of a dam under various types of loads to which it is exposed, it is necessary to know the design features and piecewise non-homogeneous physical and mechanical characteristics of soils of the body and base of the dam; they are also important for estimating settlement using numerical calculation methods, for example, the method of finite elements (FEM) [19].Today, FEM is widely used in solving problems of above-ground and underground structures [20 -25].These publications propose methods for solving the problems of the stress-strain state of structures under various loads to which they are subject, including seismic ones.In this regard, this article compares satellite images with field observation data and the results of theoretical calculations obtained by FEM, using as an example the Charvak hydroelectric power plant.

Methodology
A plane-deformable model (a cross-section) of an earth dam located on an elastic foundation is examined.The structure is considered under static loading (its own weight, hydrostatic water pressure).The non-homogeneous composition of soil of the dam body (the presence of a core) is taken into account.The mathematical formulation of the plane elastic statics problem includes: -differential equilibrium equations: where -boundary conditions: on the surface of the upstream slope: . where n is the normal vector to the surface.
An account for hydrostatics on the surface of the upstream slope of the dam, located in a homogeneous incompressible fluid of the reservoir, leads to the setting of a pressure on the surface of the slope that increases linearly with depth: where z is the depth measured from the free surface of water; g is the free-fall acceleration; ρ -is the density.
The base is considered rigid, which is expressed in the absence of horizontal and vertical virtual displacements: .0 ; 0 : 0 In accordance with the developed methodology and algorithm for solving the problem using the numerical method, the problem is reduced to a system of homogeneous linear equations relative to displacements of nodal points.Next, the Cauchy relations and Hooke's law are applied [25 -26].

Analysis of results
As an example of the calculation, the channel section of the Charvak earth dam with a height of 169 m was chosen; the ratio of slopes is 1.8, the ratio of core is -0.The distribution of isolines of horizontal displacements shows that the central axis of the dam under the influence of its own weight is vertical (there are no horizontal displacements in the center), and the largest values (±37 cm) are observed in the upper parts of the upstream and downstream slopes.
As seen from Fig. 6, water pressure mainly affects the sections of the upstream pool, where the values of horizontal displacements increase by 3 times.Note that when considering the weight of the dam soil only, the values of vertical displacements are an order of magnitude higher than horizontal ones and reach the maximum value (approximately 4 m) at the crest of the dam.Besides, the magnitudes of the   The patterns of normal stresses in the body of the dam obtained considering the forces of gravity and hydrostatics, show that their values increase by several times, especially in the upstream pool.A comparison of the distribution of isolines of shear stresses in the body of the dam under gravity and hydrostatic forces and the case when only gravity forces were taken into account shows that the zero line is displaced towards the upstream pool.

Comparison of numerical results with field observation data
The records of deformation monitoring consist of accurate, correct data from a large number of monitoring stations installed along the crest and observation gallery of the dam and records of soil settlements registered using surface marks.
When comparing the results of the displacements and stresses obtained, the site of the Charvak earth dam (131 m high) was taken as an example, due to the fact that control and measuring equipment (CME) was installed there during construction -soil dynamometers (SD), piezodynamometers (PD) (Fig. 11).High earth-rock dams are generally built with a loamy core containing pores in the clay soil, so the pore pressure, which arises during filling of the reservoir and operation of the hydraulic structure, should be taken into account according to ShNK standards [26].Pore pressure is calculated using various methods, with and without considering soil consolidation.A comparison of the results of calculations of horizontal and vertical stresses in the body of an earth dam with the available field data shows a difference of 5% and 9%, respectively, for section 6, considering pore pressure (Fig. 12, 13).The studies conducted prove that residual pore pressure is present at these elevations and forms the core of the pore pressure, and the consolidation process occurs at the sea level elevation of 780.0 m and located almost at the base of the dam.Consequently, at this mark the maximum pressure from the dam core, retaining prisms, and, accordingly, pressure in the reservoir are observed.
A comparison of the results of calculations of vertical displacements with field data showed a difference of 8% for the same section.
Comparison of the calculation results with field observation data to determine the dam settlement when filling the reservoir showed their complete coincidence, which proves the reliability of the calculation program developed.

Conclusion
A static problem was solved to study displacements (horizontal, vertical), normal (horizontal, vertical), and shear stresses of the Charvak earth dam; the problem was solved within the framework of a plane problem of elasticity theory.A corresponding analysis of the results obtained was made.
A comparison of the results of calculations of horizontal and vertical stresses in an earth dam with field data showed a difference of 5% and 9%, respectively, for the dam section considering pore pressure.
A comparison of the results of calculated values of the maximum horizontal and vertical displacements in the body of the earth dam with field data showed a difference of 14% and 8%, respectively, for the dam section under consideration.
According to the calculated numerical results for determining the stress-strain state of the earth dam, it is possible to determine the reliability of the operating facilities.
The Charvak hydroelectric power plant has been in operation for more than 50 years, therefore the changes in deformation are insignificant and mainly related to the water level; this is confirmed by the analysis of space monitoring, theoretical calculations, and field measurements.

Fig. 1 .
Fig. 1.Study area and satellite observations of the dam breach.(a) Regional conditions and data coverage.Black, magenta, orange, and green rectangles outline frames of Sentinel-1, Sentinel-2, Landsat-8, and PlanetScope images, respectively.The red rectangle represents our study area.(b) Condition of the reservoir the day before the breach.(c) Enlarged view of the ongoing breach (8:58 a.m., May 1, 2020).(d) Enlarged view after the dam collapse (May 4, 2020).(e) Image of March 11, 2021: the erected arc-shaped dam spanning the breach [14].

Fig. 5 .
Fig. 5. Layout of high earth dam of the Charvak hydroelectric power plant components of the stress which are functions of coordinates; X, Y are the projections of external forces onto the coordinate axes.
cosines of the area of the upstream slope; in the absence of hydrostatic pressure, stresses cosines of the area of the downstream slope.If hydrostatics is not taken into account, then the static boundary conditions on the crest and slopes are represented as:

Fig. 6 .
Fig. 6.Isolines of horizontal displacements u (m) in the body of an earth dam under gravity and hydrostatic forces (normal water level (NWL) -163m)

Fig. 7 .
Fig. 7. Isolines of vertical displacements v (m) in the body of an earth dam under gravity and hydrostatic forces (NWL -163m).

E3S
Web of Conferences 462, 02050 (2023) AFE-2023 https://doi.org/10.1051/e3sconf/202346202050horizontaland vertical displacements of the dam indicate that the structure is flattening (the crest is lowering and the slopes are bulging); this is evidenced by significant vertical displacements of the crest and different signs of horizontal displacements of the left and right parts of the structure.Mainly such deformation (horizontal tension) is observed in the upper third of the structure, which can lead to a loss of strength.

Fig. 10 .
Fig. 10.Isolines of shear stresses τxy (t/m 2 ) in a dam on a rigid foundation under gravity and hydrostatic forces (NWL -163m)The distribution fields of the displacement components and the stress state of a flat almost symmetrical structure under the influence of only symmetrical (relative to the vertical axis) load (of its own weight), are also almost symmetrical, which indicates the reliability of the results obtained.

Fig. 11 .
Fig. 11.Layout of normal stress sensors in the core and transition layers of the dam: 1 -stress sensor; 2 -core; 3 -transition layers; 4 -pore pressure sensor The calculated components of the stress state -normal (horizontal) stresses in the body of the dam under its own weight and hydrostatics when filling up to 125 m of the NWL, are shown in Fig. 12.The readings of the soil dynamometer (SD) and piezodynamometer (PDmeasuring pore pressure) and the time of an earth dam operation are shown in Fig. 13.

Fig. 12 .Fig. 13 .
Fig. 12. Calculated diagrams of horizontal stresses σх (t/m 2 ) in the body of the earth dam at the sea level elevation 780.0 m