Granular Mechanics of the Rankine’s Lateral Pressure on Retaining Walls Under General Conditions

Calixtro Yanqui

doi:10.1007/978-3-031-12851-6_26

Granular Mechanics of the Rankine’s Lateral Pressure on Retaining Walls Under General Conditions

Calixtro Yanqui

Departamento Académico de Ingeniería Civil

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Rankine’s theory of lateral pressure in granular backfill is based on the hypothesis that the slip lines are straight. Despite this hypothesis, the achievement of the equations for the case of sloping wall and backfill is relatively difficult. However, when using the principles of granular mechanics, this problem is simplified to an elementary exercise in Statics. The definition of the associated and conjugate bands allows finding the global contact forces in any rhombic element of an infinite slope, under the condition that it obeys the Mohr-Coulomb law of plasticity. Knowing the contact area between a band and the back side of the retaining wall, the lateral pressure of the backfill is obtained, which is found to increase linearly with depth and depends on sines and cosines of the inclination angles of the back face, the slope of the backfill, and the angle of the associated bands. The lateral force is attained by integrating the pressure along the back face of the retaining wall, and can be verified with those resultants obtained previously by using the theory of plasticity. Granular mechanics allows for the complete generalization of the Rankine’s theory by means of very simple calculations.

Original language	English
Title of host publication	Challenges and Innovations in Geomechanics - Proceedings of the 16th International Conference of IACMAG - Volume 3
Editors	Marco Barla, Alessandra Insana, Alice Di Donna, Donatella Sterpi
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	211-218
Number of pages	8
ISBN (Print)	9783031128509
DOIs	https://doi.org/10.1007/978-3-031-12851-6_26
State	Published - 2023
Event	6th International Conference of the International Association for Computer Methods and Advances in Geomechanics, IACMAG 2022 - Turin, Italy Duration: 30 Aug 2022 → 2 Sep 2022

Publication series

Name	Lecture Notes in Civil Engineering
Volume	288 LNCE
ISSN (Print)	2366-2557
ISSN (Electronic)	2366-2565

Conference

Conference	6th International Conference of the International Association for Computer Methods and Advances in Geomechanics, IACMAG 2022
Country/Territory	Italy
City	Turin
Period	30/08/22 → 2/09/22

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

Chains of forces
Friction soil-wall
Packings
Rankine’s theory
Soil statics

Access to Document

10.1007/978-3-031-12851-6_26

Cite this

Yanqui, C. (2023). Granular Mechanics of the Rankine’s Lateral Pressure on Retaining Walls Under General Conditions. In M. Barla, A. Insana, A. Di Donna, & D. Sterpi (Eds.), Challenges and Innovations in Geomechanics - Proceedings of the 16th International Conference of IACMAG - Volume 3 (pp. 211-218). (Lecture Notes in Civil Engineering; Vol. 288 LNCE). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-12851-6_26

Yanqui, Calixtro. / Granular Mechanics of the Rankine’s Lateral Pressure on Retaining Walls Under General Conditions. Challenges and Innovations in Geomechanics - Proceedings of the 16th International Conference of IACMAG - Volume 3. editor / Marco Barla ; Alessandra Insana ; Alice Di Donna ; Donatella Sterpi. Springer Science and Business Media Deutschland GmbH, 2023. pp. 211-218 (Lecture Notes in Civil Engineering).

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abstract = "Rankine{\textquoteright}s theory of lateral pressure in granular backfill is based on the hypothesis that the slip lines are straight. Despite this hypothesis, the achievement of the equations for the case of sloping wall and backfill is relatively difficult. However, when using the principles of granular mechanics, this problem is simplified to an elementary exercise in Statics. The definition of the associated and conjugate bands allows finding the global contact forces in any rhombic element of an infinite slope, under the condition that it obeys the Mohr-Coulomb law of plasticity. Knowing the contact area between a band and the back side of the retaining wall, the lateral pressure of the backfill is obtained, which is found to increase linearly with depth and depends on sines and cosines of the inclination angles of the back face, the slope of the backfill, and the angle of the associated bands. The lateral force is attained by integrating the pressure along the back face of the retaining wall, and can be verified with those resultants obtained previously by using the theory of plasticity. Granular mechanics allows for the complete generalization of the Rankine{\textquoteright}s theory by means of very simple calculations.",

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Yanqui, C 2023, Granular Mechanics of the Rankine’s Lateral Pressure on Retaining Walls Under General Conditions. in M Barla, A Insana, A Di Donna & D Sterpi (eds), Challenges and Innovations in Geomechanics - Proceedings of the 16th International Conference of IACMAG - Volume 3. Lecture Notes in Civil Engineering, vol. 288 LNCE, Springer Science and Business Media Deutschland GmbH, pp. 211-218, 6th International Conference of the International Association for Computer Methods and Advances in Geomechanics, IACMAG 2022, Turin, Italy, 30/08/22. https://doi.org/10.1007/978-3-031-12851-6_26

Granular Mechanics of the Rankine’s Lateral Pressure on Retaining Walls Under General Conditions. / Yanqui, Calixtro.

Challenges and Innovations in Geomechanics - Proceedings of the 16th International Conference of IACMAG - Volume 3. ed. / Marco Barla; Alessandra Insana; Alice Di Donna; Donatella Sterpi. Springer Science and Business Media Deutschland GmbH, 2023. p. 211-218 (Lecture Notes in Civil Engineering; Vol. 288 LNCE).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Yanqui C. Granular Mechanics of the Rankine’s Lateral Pressure on Retaining Walls Under General Conditions. In Barla M, Insana A, Di Donna A, Sterpi D, editors, Challenges and Innovations in Geomechanics - Proceedings of the 16th International Conference of IACMAG - Volume 3. Springer Science and Business Media Deutschland GmbH. 2023. p. 211-218. (Lecture Notes in Civil Engineering). https://doi.org/10.1007/978-3-031-12851-6_26

Granular Mechanics of the Rankine’s Lateral Pressure on Retaining Walls Under General Conditions

Abstract

Publication series

Conference

Bibliographical note

Keywords

Access to Document

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