Seismic stress state of a high earth dam using the spectroscopic method

. The reliable and safe operation of earth dams located in seismic regions of the Republic of Uzbekistan requires engineers and researchers to constantly improve the design normative methods for their calculation in order to identify safety margins and stability under various types of loads. A method is proposed for calculating the seismic stress state of an earth dam (on the example of the Pskem HPP being designed), based on the spectral method, in accordance with the current standards for the design of hydro-technical structures in seismic areas. Structural and piecewise non-homogeneous physical and mechanical characteristics of soils of the structure body were provided by Hydroproject JSC of the Republic of Uzbekistan. The results of the calculations show that under a horizontal seismic impact, the dam performs transverse oscillations. It was determined that the maximum vertical stresses are observed in the lower part of the upper slope, where the maximum hydrostatic pressure is reached. The maximum shear stresses appear at the base of the dam and on the surface of the downstream slope, where the risk of loss of strength under shear is greater.


Introduction
Dams are especially important hydro-technical structures.They play an important role in the life of the country, supplying fresh water and hydropower.
The territory of the Republic of Uzbekistan is divided into areas with seismicity of 7, 8, and 9 points.Therefore, possible earthquakes have a great impact on buildings and structures, including dams and reservoir structures.In Uzbekistan, there are 273 large and very important hydraulic structures of I, II, III categories, including 54 large dams -mostly earth and earth-fill ones.
An earthquake causes various dangerous displacements and stresses in reservoirs of the dams and their structures, and the presence of various damages in structures during operation leads to a decrease in their seismic resistance.If the technical condition of the dams of reservoirs located in seismically active zones is assessed in advance and measures are taken to eliminate their shortcomings, then the work performed will serve to reduce economic losses.
It is known that the dam must withstand static and dynamic (including seismic) loads that affect it during its operation.There are two types of deformations associated with earthfill dams: the first is the vertical subsidence caused by the weight of the dam, and the second is the horizontal deformation caused by the hydrostatic pressure of the reservoir; it occurs perpendicular to the main axis of the dam.Monitoring dam movement with surface or internal instrumentation is labor-intensive and time-consuming procedure.Satellite monitoring makes it possible to measure strains (settlements and displacements) of the dam soils at regular intervals, thereby helping to track small structural movements of the dam in order to prevent its failure before the damage is catastrophic and leads to an emergency.Therefore, continuous space monitoring of operating dams of reservoirs located in seismically active zones will serve to ensure seismic safety and reduce damage in case of possible earthquakes.
Lotfollah Emadali et al. [1] have shown that satellites provide accurate images of dam deformations.To monitor the Masjed-Soleiman dam located in southwestern Iran, they used images from the TerraSAR-X satellite made in German.This dam has been monitored over the past 15 years using classical geodetic methods that measure the horizontal and vertical deformation of the structure.By comparing data from the TerraSAR-X satellite with conventional sensor measurements recorded since 2000 (the year the dam was built), they found that satellite data provided more accurate information on deformation.It was found that the Masjed-Soleiman dam is rapidly deforming (up to 13 cm per year) and that serious cracks are appearing in the dam wall.For the Masjed-Soleiman dam, the damage was timely recorded, so satellite measurements can be used to identify damage on other dams.
In May 2020, the Sardoba reservoir (water-retaining earth dam) in the Syrdarya region (Uzbekistan) burst, as a result of which several settlements in the territory of Uzbekistan and Kazakhstan were flooded.In this regard, in order to avoid floods and other emergencies in Uzbekistan, since May 2023, a system of continuous space monitoring of the seismic resistance of reservoir dams has been launched.Therefore, the Agency for Space Research and Technology under the Cabinet of Ministers regularly submits space images and processed data to state bodies (responsible ministries and departments).With a special simulation program, it is planned to develop visual 3D models of the territories of the republic that are at risk of flooding when the dams of reservoirs burst as a result of an earthquake.Currently, the Agency for Space Research and Technology, the Academy of Sciences of the Republic of Uzbekistan, the Ministry of Emergency Situations, the Ministry of Water Resources, and the State Inspectorate for Control over the Safety of Water Facilities are jointly working on this issue.
Differential satellite interferometry (InSAR) can help monitor the displacements of the tops of large dams using spaceborne microwave sensors [2][3][4].Since the first experimental applications of these methods, accuracy and processing parameters have been improved and expanded, with the possibility of constructing long time series of observations for retrospective analysis using SAR data archives (Milillo [5]).
In [6,7], the destruction of the Sardoba dam in Uzbekistan was investigated.In [7], the studies were carried out on the basis of three sets of Earth observation data: (1) ICESat-2 data needed to understand the topographic features in the area under study; (2) SAR Sentinel-1 multi-geometric data to extract pre-crash strain along vertical and horizontal east-west directions; (3) Optical images from the Sentinel-2 satellites and Global Precipitation Measurement (GPM) products, used to study the state of the environment before the accident.The possible causes of the collapse are analyzed from the point of view of physical and human factors.The differential settlement of about 60 mm found by InSAR at the collapse site is an indication of internal embankment erosion, which is a physical factor contributing to the collapse.The opportunity to prevent the collapse was missed due to the limitations of traditional monitoring methods.The authors of [6] found that the Sardoba waterworks experienced continued subsidence and local nonuniform subsidence of ~4.7 cm near the breach using optical and SAR imagery and modeling tools.It was also found that secondary consolidation controls post-construction deformation.The researchers in [7] noted that neither ground-based observations nor GPM satellite products showed extreme precipitation in the region, which excludes the possibility of overflow caused by rains.The settlement rate of the embankment does not tend to decay, indicating that the dam is in the primary consolidation phase of full settlement.The maximum subsidence of ~270 mm (~0.8% of the dam height) has occurred on the north bank since the reservoir was flooded.Groups of authors [6,7] have shown that InSAR can recognize the precursor of failure by detecting surface movement and that deformation signals can help warn of risks and avoid damage to the dam.
Reference [8] presents the application of differential synthetic aperture radar (SAR) (DInSAR) interferometry algorithms for accurate monitoring of soil strain in earth dams.The authors of the article compared differential radar interferometry data and ground-based measurements while monitoring the displacement of the Conza dam located in the southern Apennines (Italy).The results showed a high agreement between the final InSAR offsets and the ground data, demonstrating the reliability of this method for accurate monitoring of civil infrastructure and high-risk dams in particular.
W. Zhou et al. [9] used the InSAR time series to monitor surface deformation of the Shuibuya dam.In this paper, the high correlation of 0.93 between InSAR and local ground monitoring confirmed the reliability of the InSAR method; the deformation history obtained from InSAR is also consistent with the settlement monitoring system in situ.In addition, InSAR results allow a continuous study of dam deformation over a wide area, including the entire surface of the dam as well as the adjacent area, which gives a clear picture of the continuous deformation of the dam.
Articles [10,11] present studies of the largest dam -Ataturk (Turkey) to determine the magnitude and direction of radial deformations using ERS, ENVISAT and Sentinel-1 satellite images.It is revealed that the movement from east to west is higher than the vertical movement.There is a maximum displacement of 10 mm/year in the direction of the line of sight on the crest of the dam for the period 2003-2010, decreasing down the slope.
Using three case studies of dam monitoring, the study in [12] discusses the advantages and disadvantages of using modern Global Positioning System (GPS) technology successfully applied in various 3D monitoring applications.
Since the full operation of the Three Georges dam, many landslides in its area had active deformations associated with fluctuations in the water level, which requires careful monitoring to prevent natural disasters [13].SAR pixel offset tracking is a powerful technique that can be used to measure large 2D offsets.As an improvement to this method, the Point Target Offset Tracking (PT) method focuses on stable point targets and thus provides measurements that are more reliable.
Chen Bingqian et al. [14] proposed a method that combines SAR data with 3D laser scanning point cloud data to improve strain detection gradient.The proposed method takes advantage of the high data density of the 3D laser scanning point cloud and the high accuracy of point positioning after 3D modeling.The proposed method was used in the study of large-scale deformation of an embankment dam located in the province of Shandong.
In [15], the dynamics of tailings consolidation subsidence in the Great Salt Lake, Utah region was investigated using big remote sensing data, including multi-temporal and multispace images SAR images of ENVISAT, ALOS PALSAR-1, and Sentinel-1A, and SRTM DEM and LIDAR DEM, as well as water level data.Displacement maps were obtained using the Interferometric Synthetic Aperture Radar (InSAR).InSAR can provide a complete spatial representation of subsidence rates to the millimeter with weekly or monthly updates.The results showed that high-resolution surface displacement measurements using InSAR could significantly improve understanding of tailings subsidence and facilitate monitoring of dam stability.
The purpose of continuous space monitoring of subsidence and displacements of operating dams of reservoirs located in seismically active zones is to analyze information that allows us to track and record the state of the dam and its changes with continuous display of the data obtained on the map, forecasting emergency situations that may develop on their basis, as well as comparison of the received data with calculations according to safety standards and assessment of their condition on the same day.
In recent years, large-scale comprehensive measures have been implemented in Uzbekistan to develop the fields of seismology, ensure seismic resistance and seismic safety of structures.At present, the consistent continuation of reforms in these areas, the introduction of new/improved calculation methods and solution algorithms, which make it possible to ensure the seismic safety of especially important hydraulic structures (including earth dams) and nearby settlements, are of great importance.

Methodology
To date, the current regulatory methods for calculating hydraulic structures, in particular earth dams for seismic effects, are based on a spectral method based on a one-dimensional model (a cantilever rod).The main disadvantage of this method is that it does not take into account the design features of the structure, as well as the piecewise non-homogeneous characteristics of soils that make up the body of the structure and its foundation.The proposed developed method and algorithm for solving seismic resistance problems for soil structures (dams, levees), based on the numerical solution to problems of the mechanics of a deformable rigid body (the finite element method), allows taking into account the above characteristics within the framework of the standards, and, in contrast to the current design standards [16] make a forecast of the stress state of the structure under certain loads.There are a large number of scientific publications in this direction concerning the seismic resistance of surface and underground structures [17][18][19][20][21][22][23][24][25].These publications propose methods for solving problems of seismic resistance of surface and underground structures using numerical methods within the framework of current design standards.
To calculate the earth dam for seismic impact, a spectral method was adopted, according to which the design seismic load Sik in the selected direction, applied to point k and corresponding to the i-th tone of natural oscillations of the structure, is determined by the following formula [16]: . ( In addition to various coefficients taken according to the KMK tables [16], this formula includes Qk -the weight of the structure, referred to point k; i -the dynamic coefficient representing the i-th frequency of natural vibrations of the structure, and nik -the i-th form of natural vibrations of the structure.Thus, the first step in calculating the seismic impact is to determine the dynamic characteristics of the structure -the frequencies and modes of natural oscillations.
When determining the dynamic characteristics of a plane model of the "damfoundation" system, the finite element method is also used, and the resolving system of equations, in this case, is represented as a homogeneous algebraic system [22]: where [K], [M] are the stiffness and mass matrices of the system obtained in the process of finite element discretization; ω are eigenfrequencies and {q} is the eigenform vector.The last two parameters are determined in the course of solving the eigenvalue problem (2).After finding them, the seismic load Si is determined (depending on the number of forms taken into account) and the solution to the problem of the stress-strain state of the dam under seismic impact is reduced to solving the following static problem: Below are the results of the calculation of the dam for seismic impact, taking into account the first form.
The geometric parameters of the earth dam model are as follows: height H=200 m; crest width 10 m; slope laying coefficients: upstream face m1=2.55,downstream face -m2=2.25, symmetrical core mя =0.2.The physical and mechanical characteristics of materials for each section of the dam are taken from the design documentation and are presented in Table 1.Characteristics required for calculation -Young's modulus E of soils was determined from a formula reflecting the velocity of transverse wave propagation , where vs=500 m/s; γ is the soil density of varying degrees of moisture content (Table 1); Poisson's ratio μ=0.3 for all types of soil.
The fundamental frequency obtained as a result of solving system (2) was ω1=0.728Hz and the corresponding period was T=1.37sec.The main mode of natural oscillations of the dam is shown in Fig. 1 and represents the shear of the dam in the transverse direction.The stress state of the dam caused by this seismic load is determined as a result of substituting the form vector η1 and dynamic factor 1~1/Т into the formula of seismic load S1 (1) and solving the resulting system (3).It should be noted that in addition to these parameters, the formula of seismic load (1) also includes other coefficients.Since the problem was solved in an elastic linear formulation, a change in these coefficients, causing a proportional change in the components of the stress-strain state of the system, does not affect the value of the safety factor K. This coefficient is expressed as a fraction, and a proportional increase in the numerator and denominator does not change the final value of the fraction.

Analysis of the Results
The isolines of displacements, stresses and the safety factor of the dam under seismic impact are shown in Fig. 2. Here, the hydrostatic load on the upstream side is also taken into account.The obtained calculation results obtained show that the dam performs transverse oscillations under horizontal seismic impact (Fig. 1).Here, horizontal stresses х (Fig. 2, c) reach ±1.6 MPa on the slopes, where the "+" sign indicates extension of the upstream slope, and the "-" sign indicates compression of the downstream slope.The maximum vertical stresses у are observed in the lower part of the upstream slope (-1.5 MPa) (Fig. 2), where the maximum hydrostatic pressure is reached.The maximum shear stresses (about 3 MPa) (Fig. 2) appear at the base of the dam and on the surface of the downstream slope, where the risk of loss of strength under shear is greater.Nevertheless, the safety factor K (Fig. 2, f) remains quite high (K>1), which indicates a sufficient safety margin for the slopes of the Pskem dam.

Conclusion
This article is a continuation of our research in the field of seismic resistance of hydrotechnical structures.In recent years, Uzbekistan has paid special attention to ensuring seismic resistance and seismic safety of structures, including reservoirs of the dams.The practice of early forecasting and seismic risk assessment at reservoir dams was introduced.A system of continuous space monitoring of the seismic resistance of reservoir dams was launched.The presence and operation of a space monitoring system for deformations and displacements of reservoir dams will prevent a future recurrence of a tragedy similar to the breakthrough of one of the dams of the Sardoba reservoir (Uzbekistan) on May 01, 2020.
Thus, continuous space monitoring of reservoir dams is relevant and vital.In addition, based on the provided satellite imagery and processed data, it is possible to prevent the damage that may occur in the event of an earthquake and assess the risk of possible earthquakes in advance, so that the responsible ministries and departments can develop appropriate protection measures by organizing rescue work for breakthrough situations.
Note that space-monitoring data must comply with calculations according to safety standards.In this regard, in this paper, an improved calculation method is proposed and a set of applied programs for calculating earth dams for seismic effects is developed, which combines the solution to problems of determining dynamic characteristics by numerical method with current regulatory methods.The proposed calculation method is applied to the Pskem dam when solving the problem of assessing the strength of an earth dam under the main static and seismic loads, taking into account the design features of the dam, soil moisture content, and hydrostatics.

Fig. 1 .
Fig. 1.The first mode of natural oscillations of the Pskem dam with a frequency ω=0.728Hz and a period T=1.37 sec

Fig. 2 .
Fig. 2. Components of the stress-strain state in the dam under seismic action and hydrostatic pressure on the upstream side

Table 1
Estimated characteristics of soils in the body and foundation of the projected Pskem dam (Uzbekistan)