Seepage consolidation under space deformation of elastic half-space
The process of seepage consolidation of elastic saturated half-space under the action of an arbitrary normal load on its surface was investigated in the case of space deformation. The fluid and skeleton grains were assumed to be incompressible. The purpose of the study was to obtain analytical formu...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2019-09-01
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| Series: | Учёные записки Казанского университета. Серия Физико-математические науки |
| Subjects: | |
| Online Access: | https://kpfu.ru/uz-eng-phm-2019-3-3.html |
| _version_ | 1797963790492368896 |
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| author | A.V. Kosterin E.V. Skvortsov |
| author_facet | A.V. Kosterin E.V. Skvortsov |
| author_sort | A.V. Kosterin |
| collection | DOAJ |
| description | The process of seepage consolidation of elastic saturated half-space under the action of an arbitrary normal load on its surface was investigated in the case of space deformation. The fluid and skeleton grains were assumed to be incompressible. The purpose of the study was to obtain analytical formulas for the main characteristics of consolidation. To fulfill this purpose, a mathematical model of consolidation with the use of the compatibility equation was proposed. The sum of the effective normal stresses was found as a solution to the first boundary value problem for the heat equation in a half-space. Then the first boundary value problem for an auxiliary function satisfying the Laplace equation was solved. This made it possible to obtain explicit expressions for the fluid pressure and the sum of the total normal stresses. Finally, the surface settlement of the half-space was determined. To illustrate the proposed approach, examples of determining the characteristics of consolidation with load on the surface of a half-space, load over the areas of a circle and a square were given. The maximum settlement of the square centre was determined. The obtained results can be used as tests when applying numerical methods for solving the problems of seepage consolidation. |
| first_indexed | 2024-04-11T01:33:49Z |
| format | Article |
| id | doaj.art-87a1263da7744e2abee69ee4d02fd081 |
| institution | Directory Open Access Journal |
| issn | 2541-7746 2500-2198 |
| language | English |
| last_indexed | 2024-04-11T01:33:49Z |
| publishDate | 2019-09-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета. Серия Физико-математические науки |
| spelling | doaj.art-87a1263da7744e2abee69ee4d02fd0812023-01-03T09:16:00ZengKazan Federal UniversityУчёные записки Казанского университета. Серия Физико-математические науки2541-77462500-21982019-09-01161335536410.26907/2541-7746.2019.3.355-364Seepage consolidation under space deformation of elastic half-spaceA.V. Kosterin0E.V. Skvortsov1Kazan Federal University, Kazan, 420008 RussiaKazan Federal University, Kazan, 420008 RussiaThe process of seepage consolidation of elastic saturated half-space under the action of an arbitrary normal load on its surface was investigated in the case of space deformation. The fluid and skeleton grains were assumed to be incompressible. The purpose of the study was to obtain analytical formulas for the main characteristics of consolidation. To fulfill this purpose, a mathematical model of consolidation with the use of the compatibility equation was proposed. The sum of the effective normal stresses was found as a solution to the first boundary value problem for the heat equation in a half-space. Then the first boundary value problem for an auxiliary function satisfying the Laplace equation was solved. This made it possible to obtain explicit expressions for the fluid pressure and the sum of the total normal stresses. Finally, the surface settlement of the half-space was determined. To illustrate the proposed approach, examples of determining the characteristics of consolidation with load on the surface of a half-space, load over the areas of a circle and a square were given. The maximum settlement of the square centre was determined. The obtained results can be used as tests when applying numerical methods for solving the problems of seepage consolidation.https://kpfu.ru/uz-eng-phm-2019-3-3.htmlconsolidationelastic semi-spaceloadpressure |
| spellingShingle | A.V. Kosterin E.V. Skvortsov Seepage consolidation under space deformation of elastic half-space Учёные записки Казанского университета. Серия Физико-математические науки consolidation elastic semi-space load pressure |
| title | Seepage consolidation under space deformation of elastic half-space |
| title_full | Seepage consolidation under space deformation of elastic half-space |
| title_fullStr | Seepage consolidation under space deformation of elastic half-space |
| title_full_unstemmed | Seepage consolidation under space deformation of elastic half-space |
| title_short | Seepage consolidation under space deformation of elastic half-space |
| title_sort | seepage consolidation under space deformation of elastic half space |
| topic | consolidation elastic semi-space load pressure |
| url | https://kpfu.ru/uz-eng-phm-2019-3-3.html |
| work_keys_str_mv | AT avkosterin seepageconsolidationunderspacedeformationofelastichalfspace AT evskvortsov seepageconsolidationunderspacedeformationofelastichalfspace |