Formation of the Surfaces of Side Slopes of Embankments and Excavations

N. Sal'kov

doi:10.12737/18058

FORMATION OF THE SURFACES OF SIDE SLOPES OF EMBANKMENTS AND EXCAVATIONS Formation of the Surfaces of Side Slopes of Embankments and Excavations

АА Аа

Published in Geometry & Graphics · Volume 4, Issue 1 · Pages 55–63 · Rubric: Methodical questions of teaching

DOI: https://doi.org/10.12737/18058

Received: 02.03.2016 Accepted: 16.03.2016 Published: 16.03.2016 Language of publication: ru-RU

Authors

N. Sal'kov

Academic degree: candidate of technical sciences

Science rang: professor

MIREA – Russian technological university Russian Federation

ABSTRACT

Designing of surfaces attracted many experts in the field of applied geometry. However, there was paid quite little attention to the formation of the surfaces of side slopes of embankments and excavations, probably due to the belief that there was done possible and there is nothing more to consider. The problem was that the question of the side slopes from put or taken out ground coat was discussed in the all textbooks for the builders while occupying a very small number of pages and the tasks in these textbooks were on the one hand simple, on the other – completed. Unfortunately, these tasks’ solutions have one and the same defect: the lack of a systematic approach to the study of the slopes’ formation, and therefore this unfortunate mistake at the corners of building areas, which could not (and unfortunately) can´t see the developers of modern textbooks for builders and architects. This work is characterized by the presence of the system approach, which eliminates any mistakes in training and in operation of excavation. In this work the author gives the information on the building of slopes with filled soil for ground work. All the necessary for correct image in the drawing examples are given. As follows from the analysis the image of slopes of embankments in projections with numerical marks is identical to the image of excavations, only with a different sign of a numeric mark. Special attention was paid to the construction of embankments’ slopes and excavations on the corners of buildings, because all the modern textbooks contain annoying mistakes.

KEYWORDS

descriptive geometry, the formation of surfaces, image surfaces in the drawing, projections with numerical marks.

Text

Конструирование поверхностей привлекало многих специалистов [2–4; 6; 13; 15; 16; 18; 20–22; 24] в области прикладной геометрии.

Однако формированию поверхностей откосов насыпей и выемок уделялось совершенно мало внимания, видимо, из-за убежденности в том, что тут сделано все возможное [1; 5; 7–12; 14; 17; 23] и дальше рассматривать просто нечего. Дело скорее всего было в том, что откосы из насыпаемого или вынимаемого грунта рассматривались во всех учебниках для строителей, занимая при этом очень малое количество страниц, и задачи в этих учебниках были, с одной стороны, простыми, а с другой, как бы окончательно и однозначно решенными. К сожалению, решения этих задач имеют один и тот же недостаток: отсутствие системного подхода к рассмотрению формирования откосов, а отсюда — та досадная ошибка на углах строительных площадок, которую не могли и, к большому сожалению, не могут увидеть разработчики современных учебников для строителей и архитекторов. Об этой ошибке поговорим чуть позже, а сейчас приведем тот самый системный подход, который полностью исключает любые промахи в обучении и производстве земляных работ.

Характерны в этом случае данные табл. 1, показывающие, сколько в абсолютном и процентном отношении занимает глава о числовых отметках в том или ином учебнике. Учебники представлены для строителей и архитекторов.

1. Vinickij I.G. Nachertatel´naja geometrija [Descriptive geometry]. Moscow, Vysshaja shkola Publ., 1975. 280 p.

2. Gevorgyan V.V. Avtomatizatsiya karkasno-parametricheskogo metoda zadaniya i konstruirovaniya karkasov poverkhnostey. Kand. Diss. [Automation frame-parametric methods of defining and constructing frameworks surfaces. Cand. Diss.]. Odessa, 1978.

3. Gershman I.P. Konstruirovanie poverkhnostey putem vydeleniya ikh nepreryvnykh lineychatykh karkasov iz mnogoparametricheskikh mnozhestv liniy [Design surfaces by highlighting their non-continuous bar frames from a multivariate sets of lines]. Trudy UDN im. P. Lumumby. Moscow, 1967, V. 26: Matematika. I. 3: Prikladnaya geometriya. Pp. 33-47. (in Russian).

4. Grjaznov Ja.A. Otsek kanalovoj poverhnosti kak obraz cilindra v ras-slojaemom obrazovanii [Bay canal surface as a cylinder in rastlayamad education]. Geometrija i grafika [Geometry and graphics]. 2013, V. 1, I. 1, pp. 17-19. DOI:https://doi.org/10.12737/2077 (in Russian).

5. Dobrjakov A.I. Kurs nachertatel´noj geometrii [A course in descriptive geometry]. Moscow, Leningrad, Gos. izdatel´stvo literatury po stroitel´stvu i arhitekture Publ., 1952. 496 p.

6. Ivanov G.S. Konstruirovanie tekhnicheskikh poverkhnostey (matematicheskoe modelirovanie na osnove nelineynykh preobrazovaniy) [Design of technical surfaces (mathematical modelirovanie based on nonlinear transformations)]. Moscow, Mashinostroenie Publ., 1987.

7. Klimuhin A.G. Nachertatel´naja geometrija [Descriptive geometry]. Moscow, Strojizdat Publ., 1978. 334 p.

8. Koroev Ju.I. Nachertatel´naja geometrija [Descriptive geometry]. Moscow, KNORUS Publ., 2011. 432 p.

9. Kuznecov N.S. Nachertatel´naja geometrija [Descriptive geometry]. Moscow, Vysshaja shkola Publ., 1981. 262 p.

10. Kolotov S.M., Dol´skij E.E., Mihajlenko V.E. Kurs nachertatel´noj geometrii [A course in descriptive geometry]. Kiev, Gos. izdatel´stvo literatury po stroitel´stvu i arhitekture USSR Publ., 1961. 316 p.

11. Krylov N.N., Lobandievskij P.I., Mjen S.A., Nikolaev V.L., Ikonnikova G.S. Nachertatel´naja geometrija [Descriptive geometry]. Moscow, Vysshaja shkola Publ., 1977. 231 p.

12. Krylov N.N., Ikonnikova G.S., Nikolaev V.L., Lavruhina N.M. Nachertatel´naja geometrija [Descriptive geometry]. Moscow, Vysshaja shkola Publ., 1990. 240 p.

13. Podgornyy A.L. Geometricheskoe modelirovanie prostranstvennykh konstruktsiy. Dokt. Diss. [Geometric modeling of spatial structures. Doct. Diss.]. Moscow, 1975.

14. Russkevich N.L. Nachertatel´naja geometrija [Descriptive geometry]. Kiev, Vishha shkola Publ., 1978. 312 p.

15. Ryzhov N.N. Algoritmy perekhoda ot konstruktivnokinematicheskogo zadaniya poverkhnosti k analiticheskomu [The algorithms of the transition from structurally-kinematic-Denmark surface to analysis]. Trudy UDN im. P. Lumumby [Proceedings of the Peoples´ Friendship University named after P. Lumumba]. Moscow, 1971, V. 53, I. 4, pp. 17-25. (in Russian).

16. Ryzhov N.N., Lovetskiy K.P., Salkov N.A. Matematicheskoe modelirovanie proezzhey chasti avtomobil´nykh dorog [Mathematical modelling of the carriageway roads]. Moscow, MADI Publ., 1988. (in Russian).

17. Rynin N.N. Nachertatel´naja geometrija [Descriptive geometry]. Leningrad, Gosstrojizdat Publ., 1939. 448 p.

18. Salkov N.A. Modelirovanie avtovobil´nyh dorog [Modeling roads]. Moscow, INFRA-M Publ., 2012. Available at: http://www.znanium.com/catalog.php#none/

19. Salkov N.A. Nachertatel´naja geometrija: Osnovnoj kurs [Descriptive geometry. The main course]. Moscow, INFRA-M Publ., 2014. 235 p.

20. Salkov N.A. Parametricheskaja geometrija v geometricheskom modelirovanii [Parametric Geometry in Geometric Modeling]. Geometrija i grafika [Geometry and graphics]. 2014, V. 2, I. 3, pp. 7-13. DOI:https://doi.org/10.12737/6519 (in Russian).

21. Sokolova N.Yu. Parametrizatsiya figur i konstruirovanie ogibayushchey poverkhnosti [Parameterization of shapes and design envelope surface]. Trudy UDN im. P. Lumumby [Proceedings of the Peoples´ Friendship University named after P. Lumumba]. Moscow, 1975. V. 73. Mathematics. I. 5: Applied Geometry, pp. 29-39. (in Russian).

22. Yakunin V.I. Teoreticheskie osnovy formirovaniya modeley poverkhnostey [The theoretical basis for the formation of surface models]. Moscow, MAI Publ., 1985.

23. Timrot E.S. Nachertatel´naja geometrija [Descriptive geometry]. Moscow, Gos. izdatel´stvo literatury po stroitel´stvu, arhitekture i stroitel´nym materialam Publ., 1962. 280 p.

24. Umbetov N.S. Konstruirovanie jekvipotencial´noj poverhnosti [Equipotential surface design]. Geometrija i grafika [Geometry and graphics]. 2013, V. 1, I. 1, pp. 11-14. DOI:https://doi.org/10.12737/2075 (in Russian).

JATS XML

Zamestitel' glavnogo redaktora, chlen redsoveta

Vladimir Vyshnyepolskiy

Glavnyy redaktor

A. A. Ishchenko

Vypuskayuschiy redaktor

Dar'ya Sklyankina

501@infra-m.ru

Deputy editor-in-chief, member of the editorial Board

N. Sal'kov

nikolaysalkov@mail.ru

GOST

Sal'kov N. A. Formation of the Surfaces of Side Slopes of Embankments and Excavations // Geometry & Graphics. 2016. no. 1. pp. 55-63. DOI: https://doi.org/10.12737/18058. (Date of access 12.11.2026).

MLA

N. Sal'kov. "Formation of the Surfaces of Side Slopes of Embankments and Excavations." Geometry & Graphics 4.1 (2016): 55-63. DOI: https://doi.org/10.12737/18058.

APA

Sal'kov N. A. (2016). Formation of the Surfaces of Side Slopes of Embankments and Excavations. Geometry & Graphics, 4(1), 55-63. https://doi.org/10.12737/18058

Chicago

N. Sal'kov. "Formation of the Surfaces of Side Slopes of Embankments and Excavations." Geometry & Graphics 4, no. 1 (2016): 55-63. https://doi.org/10.12737/18058.

WIKI

{{cite journal | author = Sal'kov N. A. | title = Formation of the Surfaces of Side Slopes of Embankments and Excavations | journal = Geometry & Graphics | year = 2016 | volume = 4 | issue = 1 | pages = 55-63 | doi = 10.12737/18058 }}

Copy

Export: BibTeX EndNote RefMan RusMARC

FORMATION OF THE SURFACES OF SIDE SLOPES OF EMBANKMENTS AND EXCAVATIONS Formation of the Surfaces of Side Slopes of Embankments and Excavations

Confirmation