Strength of earth dams considering the elastic-plastic properties of soils

The paper provides a detailed analysis of the current state of the problem. A mathematical model is presented to determine the dynamic behavior of earth dams, considering the viscoelastic properties of soil, using the hereditary Boltzmann-Volterra theory with the A.R. Rzhanitsyn kernel under periodic kinematic impacts. To solve the problems considered, the finite element method and complex arithmetics were used to reduce integrodifferential equations to a high-order complex algebraic equation. The accuracy of the methods was verified by solving test problems. Steadystate forced vibrations of the Pskem earth dam 195 m high are studied considering the real geometry and soil properties under resonant vibration modes. It was stated that the largest stress amplitudes in the body of the dam occur not only under the first resonance, but they can occur under other dense spectra of the eigenfrequencies of the dam, due to the interaction between close natural modes of vibration. The strength of various sections of the dam body was tested under kinematic impact using the Coulomb- Mohr theory of strength; the most dangerous sections of the dam were identified in terms of the highest stress.

Section: Introductionmentioning

confidence: 99%

Dynamic behavior of earth dams under different kinematic impacts

Mirsaidov

Toshmatov²

2023

“…In [19,20], a detailed review of known publications devoted to the study of the stress state and dynamic behavior of earth dams is presented, taking into account the elastic and elastoplastic properties of soil. A mathematical model was developed using the principle of virtual displacements to assess the stress-strain state of earth dams, considering the elasticplastic properties of soil under static loads.…”

Section: Introductionmentioning

confidence: 99%

Propagation of longitudinal waves in a linear viscoelastic medium

Khamidov,

Loginov,

Akbarov

2023

The article is devoted to the study of longitudinal wave propagation in a viscoelastic medium. A mathematical model of the problem of a linear viscoelastic medium was developed. The solution to the considered problems is reduced to the solution of a system of differential equations solved by the method of characteristics with the appropriate boundary conditions. The results are compared with known results obtained by other authors; a comparison shows the adequacy of the task posed. It was determined that the maximum values of stress, strain, and velocity of particles in viscous media vary according to a non-linear law. In the initial section of the medium and near it, first, the stress reaches its maximum, and then the strain and velocity of particles reach their maximum values.

“…-in [30][31][32][33][34][35], some results are given concerning the study of the stress-strain state and the dynamic behavior of an earth dam as a multilayer structure interacting with a ground base. The internal force factors and the strength of these structures are evaluated under various types of impacts.…”

mentioning

confidence: 99%

Nonlinear vibrations of earth structures

Mirsaidov,

Ishmatov,

Urinov

et al. 2023

This article offers a detailed analysis of the current state of plane structure dynamics, addressing the complexities posed by non-homogeneous materials exhibiting nonlinear elastic and viscoelastic properties during real-life operations. The study proposes a comprehensive mathematical model and algorithm to investigate the dynamic behavior of such structures, employing the non-linear hereditary Boltzmann-Volterra theory to describe viscoelastic material properties accurately. Nonlinear oscillatory systems are analyzed using Lagrange equations based on the d’Alembert principle. The problem is approached through a multi-step process. Initially, the linear elastic problem of the structure’s natural oscillations is solved to determine its natural frequencies and modes of oscillations. Subsequently, these eigenmodes are employed as coordinate functions to address forced nonlinear oscillations in viscoelastic non-homogeneous systems. The complexity of the problem necessitates solving a Cauchy problem comprising a system of nonlinear integrodifferential equations. To illustrate the methodology, the study examines the Gissarak earth dam, considering real operational conditions and nonlinear, viscoelastic material properties near resonant modes of vibrations. Utilizing numerical methods, the dynamic behavior of the structure is analyzed, assessing displacements and stress components at different time points under non-stationary kinematic action. Stress concentration regions within the structure are identified for resonant vibrations, allowing the evaluation of its strength. Furthermore, the impact of nonlinear elasticity and viscoelasticity on the structural dynamics is quantified. This research provides valuable insights into the behavior of plane non-homogeneous structures, considering real-world scenarios and material complexities, ultimately contributing to an improved understanding of structural dynamics and facilitating the identification and mitigation of potential structural challenges.