Dynamic response of an isotropic elastic half-plane with shear modulus varying with depth to a load moving on its surface

Muho, Edmond V.; Beskou, Niki D.

doi:10.1016/j.trgeo.2019.100248

Cited by 19 publications

(10 citation statements)

References 27 publications

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“…The soil stresses are expressible in terms of displacements for the present anisotropic and nonhomogeneous half-plane case as [41] (9) (10) (11) and for the half-space as [34] (12)…”

Section: Problem Descriptionmentioning

confidence: 99%

“…In the above equations, and are elastic constants which are expressible in terms of the engineering constants as [34] (18…”

Section: Problem Descriptionmentioning

confidence: 99%

“…[29][30][31]. 5) Works associated with an isotropic, continuously non-homogeneous elastic half-space or half-plane under dynamic stationary or moving with constant speed [32][33][34]. 6) Works associated with a transversely isotropic (or cross-anisotropic), continuously nonhomogeneous, viscoelastic half-space [35,36] under stationary dynamic.…”

Section: Introductionmentioning

confidence: 99%

“…Most of all the other methods used in the aforementioned works employ integral transform methods (mainly Fourier and Hankel transforms) and this requires numerical integration or complicated analytical inversion techniques instead of simple series evaluation in the present case. This complex Fourier series method has been successfully used by Siddharthan et al [37] and Theodorakopoulos [38] in connection with moving loads on poroelastic half-planes and Beskou et al [39] and Muho and Beskou [40] in connection with moving loads on anisotropic homogeneous half-plane and isotropic nonhomogeneous half-plane, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Analytical/Numerical Solutions to the Problem of the Dynamic Response of an Elastic Plate on a Continuously Non-Homogeneous Cross-Anisotropic Viscoelastic Soil to a Moving Load

Beskou¹,

Muho²

2021

Proceedings of the 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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In this work the problem of the dynamic response of a flexural elastic plate on a continuously nonhomogeneous viscoelastic cross-anisotropic half-plane or half-space soil medium to a line or rectangular load moving with constant speed is determined analytically/numerically. Soil nonhomogeneity is associated with elastic moduli increasing with depth. Plate viscous damping is considered, and the viscoelastic effects of the soil are introduced via hysteric damping. The solution of the problem is obtained with the aid of the complex Fourier series method involving the horizontal coordinates and the time. Employment of this method reduces the partial differential equations of motion for the soil and the plate to ordinary differential equations with variable coefficients and an algebraic equation, respectively. Those ordinary differential equations are solved by the method of Frobenius. Verification of the solutions is done by means of comparisons with known existing analytical solutions for the special cases of isotropy and homogeneity with or without the plate.

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“…The soil stresses are expressible in terms of displacements for the present anisotropic and nonhomogeneous half-plane case as [41] (9) (10) (11) and for the half-space as [34] (12)…”

Section: Problem Descriptionmentioning

confidence: 99%

“…In the above equations, and are elastic constants which are expressible in terms of the engineering constants as [34] (18…”

Section: Problem Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analytical/Numerical Solutions to the Problem of the Dynamic Response of an Elastic Plate on a Continuously Non-Homogeneous Cross-Anisotropic Viscoelastic Soil to a Moving Load

Beskou¹,

Muho²

2021

Proceedings of the 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…In our opinion, it is advisable to consider the possibility of accounting the velocity of soil masses displacement when calculating the stability coefficient of the soil bed, reinforced with geosynthetic materials by the method [20,21], and also to propose a variational method for determining the most dangerous sliding surface. The use of this method makes it possible, when calculating the most dangerous sliding surface, to take into account additional efforts from: reinforcing materials, soil rheological properties [22 -24], as well as dynamic loading [25].…”

Section: Relevancementioning

confidence: 99%

Ensuring the sustainability of the motorway subgrade in the zones of underground mining operations

et al. 2019

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The article describes a variational method for calculating the motorway subgrade stability. The application of this method allows to quickly and accurately determine the most dangerous sliding surface with a minimum coefficient of stability. The purpose of the article is to improve the variational method for calculating the motorway subgrade stability. The article proposes to apply this method in the calculation of the transport earthwork structures, located in the area of mining operations, where there is a danger of failed subsidence. Underground mining operations have a significant impact on the vertical bent curves of a motorway, that leads to the modification of the subgrade geometric dimensions in the negative direction. This is the cause of sharp fluctuations in the values of local curvature and the radii of vertical curves. The use of variational method for calculating the motorway subgrade stability will allow to take into account the velocity of the saturated soil mass movement and the change in the geometric parameters caused by the underground mining operations. The advantages of this method include the possibility to consider the efforts from geosynthetic materials, recommended to use for strengthening the basement and slopes of the subgrade, the rheological properties of the soil, and the load from the vehicle moving along the surface. In the process of research, regulatory documents on the calculation of the stability of road structures reinforced with geosynthetic materials were studied. The identified shortcomings of the existing regulatory documents allowed to conclude that it is necessary to consider the velocity of the saturated soil mass movement caused by the underground mining operations when calculating the stability coefficient of soil structures.

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Simplified models for determining the response of an isotropic, continuously nonhomogeneous half-plane to a moving distributed line load

2019

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Dynamic response of an isotropic elastic half-plane with shear modulus varying with depth to a load moving on its surface

Cited by 19 publications

References 27 publications

Analytical/Numerical Solutions to the Problem of the Dynamic Response of an Elastic Plate on a Continuously Non-Homogeneous Cross-Anisotropic Viscoelastic Soil to a Moving Load

Analytical/Numerical Solutions to the Problem of the Dynamic Response of an Elastic Plate on a Continuously Non-Homogeneous Cross-Anisotropic Viscoelastic Soil to a Moving Load

Ensuring the sustainability of the motorway subgrade in the zones of underground mining operations

Simplified models for determining the response of an isotropic, continuously nonhomogeneous half-plane to a moving distributed line load

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