THE PROPAGATION OF SEISMIC WAVES IN THE SUBTERRANEAN AQUIFERS DURING TRAIN TRANSIT

MINISTRY OF HIGHER EDUCATION, SCIENCE AND INNOVATIONS OF THE REPUBLIC OF UZBEKISTAN Samarkand State Architecture and Construction University, Samarkand, Uzbekistan. PROBLEMS OF ARCHITECTURE AND CONSTRUCTION (Scientific and technical journal) 2025, VOLUME-03, ISSUE-04. ПРОБЛЕМЫ АРХИТЕКТУРЫ И СТРОИТЕЛЬСТВА (научно-технический журнал) 2025, ТОМ 3, ВЫПУСК 45383. ME’MORCHILIK VA QURILISH MUAMMOLARI , 2025, 3-JILD, 4-SON, ISSN: 2091-5004, e-ISSN:2901-7845 https://portal.issn.org/resource/ISSN/2091-5004 Samarkand, 2025 PROBLEMS OF ARCHITECTURE AND CONSTRUCTION (Scientific and technical journal) 2025 № ISSUE 4 E-ISSN: 2901-7845, ISSN: 2091-9004, https://portal.issn.org/resource/ISSN/2091-5004 83 THE PROPAGATION OF SEISMIC WAVES IN THE SUBTERRANEAN AQUIFERS DURING TRAIN TRANSIT. Fakhriddin Sharafitdinovich Yuldashev1 1PhD, Senior Lecturer, Department of Mechanics, Namangan State Technical University, 1 ORCID: 0000-0002-3572-1639 Abstract. This paper presents a three-dimensional numerical study of ground vibration propagation induced by railway train movement. The dynamic load generated by a moving freight train is modeled as a time-dependent force acting on the track structure. The problem is solved using the finite element method with irregular tetrahedral elements to accurately represent the soil domain. The influence of key physical and mechanical soil parameters on vibration intensity is investigated. Ground vibration responses are evaluated at various distances from the railway track to assess attenuation characteristics. Keywords: railway transport, ground vibration, finite element analysis, soil dynamics, elasticity theory, boundary conditions, wave velocity. Annotatsiya. Ushbu maqolada temir yo‘l poezdi harakati natijasida yuzaga keladigan yer vibratsiyalarining uch o‘lchovli raqamli tadqiqoti taqdim etilgan. Harakatlanuvchi yuk poezdi tomonidan hosil qilingan dinamik yuk, yo‘l inshootiga ta’sir etuvchi vaqtga bog‘liq kuch sifatida modellashtirilgan. Masala tuproq maydonini aniq ifodalash uchun noaniq tetraedral elementlardan foydalangan holda tugallangan elementlar usuli yordamida yechilgan. Vibratsiya intensivligiga ta’sir qiluvchi asosiy fizik va mexanik tuproq parametrlarining ta’siri o‘rganilgan. Yer vibratsiyalari temir yo‘l izidan turli masofalardagi nuqtalarda baholangan va attenuatsiya xususiyatlari aniqlangan. Kalit so‘zlar: temir yo‘l transporti, tuproq vibratsiyalari, elementlar usuli bo‘yicha tahlil, tuproq dinamikasi, elastiklik nazariyasi, chegaraviy shartlar, to‘lqin tezligi. Аннотация. В данной статье представлен трёхмерный численный анализ распространения вибраций грунта, вызванных движением железнодорожного поезда. Динамическая нагрузка, создаваемая движущимся грузовым поездом, моделируется как зависящая от времени сила, действующая на конструкцию пути. Задача решена с использованием метода конечных элементов с неравномерными тетраэдральными элементами для точного представления области грунта. Исследуется влияние ключевых физических и механических параметров грунта на интенсивность вибраций. Реакции грунта на вибрации оцениваются на различных расстояниях от железнодорожного пути для анализа характеристик затухания. Ключевые слова: железнодорожный транспорт, вибрации в грунте, анализ методом конечных элементов, динамика грунта, теория упругости, граничные условия, скорость распространения волн. Introduction. Vibrations and noise generated by transport systems, particularly railway traffic, often exceed permissible sanitary standards and pose a potential risk to nearby buildings and infrastructure. Numerous experimental observations and field surveys confirm that this issue remains relevant, especially in densely populated areas. Since soil acts as a transmitting medium for vibration energy from the source to surrounding structures, understanding the mechanical behavior of ground materials is essential for reliable vibration assessment. Vibrations propagating through near-surface soil layers may alter stress–strain states and negatively affect the durability of engineering structures located close to railway lines. This study focuses on the numerical investigation of vibration propagation caused by freight train movement and evaluates how different soil properties influence vibration levels at various distances from the track. Research Methodology. The key feature of the approach we are considering is its capacity to effectively address issues by incorporating soil PROBLEMS OF ARCHITECTURE AND CONSTRUCTION (Scientific and technical journal) 2025 № ISSUE 4 E-ISSN: 2901-7845, ISSN: 2091-9004, https://portal.issn.org/resource/ISSN/2091-5004 84 characteristics. It enables us to simulate large regions within a short period, resulting in a reduction of computation time when dynamically assessing the response at observation points situated between 10 and 100 meters away from railway tracks in the case under analysis. In this investigation, we compared outcomes obtained for two varieties of soil conditions. The elastic-perfectly plastic Coulomb-Mohr model represents one of the most extensively utilized models of soil behavior. Its primary benefit is that the source data is readily available, which is invariably included in conventional engineering and geological records. E - represents the modulus of elasticity in MPa, ν - represents Poisson's ratio, φ - represents the angle of internal friction in degrees, C - represents specific adhesion in kPa, and ψ - represents the dilatation angle in degrees. The Coulomb-Mohr model is used to describe the behavior of soil. Deformation in soil is linear, and it is directly proportional to the stress level σ and varies according to the soil modulus E. Researchers studying soil and structural properties under dynamic loading conditions use elastoplastic and viscoplastic models. The latter provides more accurate results but is more difficult to apply. A nonlinear soil expansion model takes into account wave propagation and interactions with buildings and structures, yielding wave parameters that differ significantly from those of ideal elastic and nonlinear elastic medium models. The problem involves vibration levels in the ground caused by railway train movement. A model was created using an unpaved foundation 200 m wide, 100 m long, and 50 m deep. The influence of groundwater was not taken into account, and soil characteristics were selected based on Tables 1 and 2 for illustration. To create the railway track, a design was used that followed the standards for railway track construction, as illustrated in Figure 1. Figure 1. Drawing construction of the base for a railway train In accordance with the drawing, a protective layer 1 meter thick and a ballast base 50 centimeters thick are laid on the ground starting from a mark 0 meters above the surface on which the railway track (sleepers and rails) are designed. The movement of a freight train weighing 120 tons with cargo is being studied. The cargo transport is moving at a speed of 100 kilometers per hour. Since the selected area has a length of 100 meters, the vibration acting on the soil base will continue until the freight transport has completely passed through. To solve this problem, we will use the finite element method. The study area will be divided into 7,875 finite elements. The shapes of these finite elements will be chosen in the form of irregular tetrahedra. It is believed that the dynamic loads from the train tracks can affect the ground base. In this study, we will consider the action of eight concentrated loads along the z-axis, moving at a certain speed along the y-axis. We will determine the movement and speed of the resulting nodes in the soil, considering the physical and mechanical properties of the material. In this problem, we will replace the infinite half-space with a finite parallelepiped [3, 4, 5, 6]. Conditions will be set on the faces of the parallelepiped, where the continuation of the medium will be discarded: PROBLEMS OF ARCHITECTURE AND CONSTRUCTION (Scientific and technical journal) 2025 № ISSUE 4 E-ISSN: 2901-7845, ISSN: 2091-9004, https://portal.issn.org/resource/ISSN/2091-5004 85 𝜎𝑥=𝑎𝜌𝑉𝑝𝑢󰇗 𝜏𝑦𝑧=𝑏𝜌𝑉𝑠𝑢󰇗 𝜏𝑧𝑦=𝑏𝜌𝑉𝑠𝑤󰇗} 𝜎𝑦=𝑎𝜌𝑉𝑝𝑣󰇗 𝜏𝑥𝑧=𝑏𝜌𝑉𝑠𝑤󰇗 𝜏𝑧𝑥=𝑏𝜌𝑉𝑠𝑢󰇗} 𝜎𝑧=𝑎𝜌𝑉𝑝𝑤󰇗 𝜏𝑥𝑦=𝑏𝜌𝑉𝑠𝑢󰇗 𝜏𝑦𝑥=𝑏𝜌𝑉𝑠𝑣󰇗} (1) the dynamic model of the problemsolving field is shown in Fig. 2. Fig.2. A model in which the domain is divided into finite elements. The fundamental equation that describes the motion of an object under the influence of a force as a function of time can be expressed in the following form: [𝑀]{𝑢󰇘}+[𝐶]{𝑢󰇗}+[𝐾]{𝑢}={𝐹} , ( 2 ) The arrangement of [M]- the mass matrix, {u}- the displacement vector, [C] - the damping matrix, which also includes boundary conditions, [K]- the stiffness matrix, and {F}- the load vector are the most important components of the analysis. The {u}- movement, {u  }- speed, and {u  } acceleration of these elements can change over time during dynamic analysis. In principle, all models can be employed for dynamic analysis regardless of whether the soil is in a dry state or not. The presence or absence of groundwater in the study area during data collection is irrelevant for this purpose. Plaxis 3D allows for the resolution of issues related to both the existence and absence of water levels. The matrix [𝑴] is based on information about the mass of materials, including soil, water, and other components. For numerical simulation of dynamics, it is important to ensure the stability and accuracy of calculations. The Newmark numerical integration method helps in this. The properties of soil and other materials are presented in Tables 1, 2 and 3. Table - 1. Physical and mechanical properties of materials Parameter Unit of meas urem ent Des ign atio n Sandy loam Loesslike loam General properties The soil model – – MohrCoulo mb MohrCoulom b Type of material behavior – – Draine d Drained The specific gravity of the soil above the groundwater level 𝑘𝑁 𝑚3 ⁄ 𝛾𝑢𝑛𝑠𝑎𝑡 16 14,70 The specific gravity of the soil below the groundwater level 𝑘𝑁 𝑚3 ⁄ 𝛾𝑠𝑎𝑡 18 16,80 Mechanical parameters Young's modulus (constant value) 𝑘𝑁 𝑚2 ⁄ 𝐸′𝑟𝑒𝑓 60000 95000 The Poisson's ratio – 𝑣/ 𝑣𝑢𝑟 0.32 0,35 Coupling (permanent 𝑘𝑁 𝑚2 ⁄ 𝑐′𝑟𝑒𝑓 6 5,6 Angle of internal friction ° 𝜑′ 22 25 Dilatation angle ° 𝜓 1 0 PROBLEMS OF ARCHITECTURE AND CONSTRUCTION (Scientific and technical journal) 2025 № ISSUE 4 E-ISSN: 2901-7845, ISSN: 2091-9004, https://portal.issn.org/resource/ISSN/2091-5004 86 Table - 2. Features of the ballast layer Physical and mechanical properties of rails and sleepers Table - 3. The rail The sleepers Specific gravity [kN/m3] 78 25 Type of section User – defined Defined Cross sectional area m2 0,0077 0,0513 Moment of inertia 𝐼2 𝑚4 0,00000513 0,000245 𝐼3 𝑚4 0,00003005 0,02530 Young's Module ν 200 000 000 360 000 Results and discussions. a) The location of the railway track, and the movements of the load in a designated limited area Fig. 2. Vibration levels in each node of the model being tested Ballast layer Features stylnig Unit of measureme nt Protective layer Balast № 1 2 3 The soil model – Mohr-Coulomb Mohr-Coulomb Type of material behavior – Drained Drained The specific gravity of the soil above the groundwater level 𝑘𝑁 𝑚3 ⁄ 22 19 The specific gravity of the soil below the groundwater level 𝑘𝑁 𝑚3 ⁄ 23 21 Angle of internal friction 𝜑′ 40 35 Dilatation angle 𝜓 15 5 Coupling (permanent 𝑐′𝑟𝑒𝑓 30 30 Young's modulus (constant value) 𝐸′𝑟𝑒𝑓 55000 50000 The Poisson's ratio 𝑣/ 𝑣𝑢𝑟 0.25 0,3 b) Coordinates of the location of the observed points in the area under consideration c) Moving the points in the direction of the axis PROBLEMS OF ARCHITECTURE AND CONSTRUCTION (Scientific and technical journal) 2025 № ISSUE 4 E-ISSN: 2901-7845, ISSN: 2091-9004, https://portal.issn.org/resource/ISSN/2091-5004 87 The graphs in Figures 3 and 5 are detailed, showing the fluctuations resulting from the movement of a train on the ground at different distances from a railway track. To analyze the differences in the levels of vibration propagation between the two cases, we analyzed the oscillation rate at several points: 10 m and 100 m from the railway track.. Fig.3. Graph of the time dependence of the rate of fluctuations occurring in sandy loam soil. Fig.4. Graph of the time dependence of the rate of fluctuations occurring in loess-like loamy soil at various distances. Fig.5. Graph of the dependence on the time of movement of vibrations, in comparison with sandy loam and loess-loamy soil Conclusions. A comparative analysis of the findings obtained from the resolution of issues pertaining to vibration transmission in two distinct types of soil substrates, namely sandy loam and loess-loamy, has been conducted. The investigation reveals that the transmission of vibrations through soil and structures is contingent upon the characteristics of the soil, including its elastic modulus, Poisson's ratio, and density. Upon comparing the outcomes for the various soil types, it was observed that the velocity of wave transmission varies. The acquired data indicates a second-order velocity of propagation. When comparing the results to those obtained for sandy loam, it can be seen that the velocity at 20.22 cm will increase by 14.95%, at 49.86 cm it will increase by 39.29%, and at 75.68 cm it will rise by 21.69%, compared to the values obtained for loess-loam. The velocities at these distances will be 71.73%, 12.38%, and 48.37% higher, respectively, than the corresponding values for sandy loam. At 20.22 meters, the velocity will be 60.64 percent higher; at 49.86 meters, it will only be PROBLEMS OF ARCHITECTURE AND CONSTRUCTION (Scientific and technical journal) 2025 № ISSUE 4 E-ISSN: 2901-7845, ISSN: 2091-9004, https://portal.issn.org/resource/ISSN/2091-5004 88 5.45 percent higher; and at 75.68 m, it will decrease by 17.2 percent compared to values for sandy loams. From this, we can conclude that when studying the propagation of vibrations in soils, it is important to consider the actual physical parameters. Based on the results obtained, we can state that the level of vibrations resulting from vehicle traffic largely depends on the properties of the soil. Therefore, when performing calculations, it is critical to take into account both the physical and mechanical properties of the ground. References [1] Il'ichev V.A., Yuldashev S.S., Saidov S.M. Propagation of vibration from trains in relation to track position //Soil Mechanics and Foundation Engineering. – 1999. – Т. 36. – №. 2. – С. 55-56. [2] Lysmer J., Kyhlemeyer L. Finite Dynamic Model for Infinite Media // Jour Engineering Mechanics Division.ASCE. 1969. Vol. 95.NoEM4.August.P. 859 – 887. [3] Mirsaidov, M., Boytemirov, M., & Yuldashev, F. (2022). Estimation of the Vibration Waves Level at Different Distances. In Proceedings of FORM 2021: Construction the Formation of Living Environment (pp. 207-215). Springer International Publishing.