Slip circle method

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Embankment failure body with slip circle, divided into lamellae

The slip circle method (English: "Method of Slices" and "general limit equilibrium method") is a method for calculating the stability of embankments in geotechnics ( slope failure verification).

The procedure

Forces on a lamella
Embankment breach with an approximately circular arc-shaped sliding surface

Since slipping down an embankment often results in circular arc-shaped sliding surfaces (especially clear in clay, where Alexandre Collin first observed this in the 1840s), circular fracture bodies are examined and therefore we speak of the slip circle method. In the calculation, a distinction is made between lamellar-free methods (here there is a single fracture body) and lamellar methods (in this case the fracture body is divided into a number of vertical disks, the lamellae). The methods are further subdivided according to the forces (dead weight, earth pressure, water pressure, buoyancy, traffic load, etc.) and resistances (friction, shear strength) and the mechanisms that are taken into account or neglected. The first to perform calculations using the slip circle method were Knut Petterson and Sven Hultin from the Gothenburg Port Authority in 1916. They calculated the slide of a quay wall in Gothenburg. Fellenius (and also Krey ) improved the process in the 1920s to such an extent that it is better known today as the Fellenius process or also as the Krey-Bishop process. Various authors later (in the 1950s and after) made contributions and improvements ( Otto Karl Fröhlich , Alan W. Bishop , Nilmar Janbu , Hubert Borowicka , etc.).

In addition to the slip circle process, there are also processes with polygonal slip surfaces, e.g. B. after Janbu. Also Morgenstern / Price have described a method for slope stability analysis (slats method non-circular fracture surfaces, no rotation, balance exactly met).

Today one finds in the DIN 4084 guidelines for terrain and slope failure calculations according to these methods.

In the case of a concrete proof of the stability of an embankment, the center point and the radius of the slip circles are varied step by step until the arc with the lowest and therefore decisive safety has been found.

Lamella-free process

In the lamellar-free method, the broken body is viewed as if it were slipping as a whole on an arcuate surface. All applied external forces are combined into one resulting force and compared with the resisting forces in the sliding plane. The stability is determined according to Fellenius for the determined slip circle from the ratio of the resisting forces to the acting forces and the torques around the center of the circle.

Lamella process

With the lamella method according to Krey / Bishop, the fracture body is divided into several vertical lamellae on which the various forces act. The balance of forces is formulated on each lamella. In addition to the forces mentioned above, there are also earth pressure forces on both sides of the lamellae. The forces of the lamellas are added to the total equilibrium.

An alternative method for calculating slopes is the kinematic element method .

literature

  • Konrad Simmer , Grundbau, Volume 1, Chapter 6.4 (Terrain and slope failure), 19th edition, Teubner 1994, pp. 211–232

Individual evidence

  1. ↑ SWEDISH GEOTECHNICAL SOCIETY ( Memento of the original from October 9, 2007 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. , and KE Petterson The early history of circular sliding surfaces , Geotechnique, Volume 5, 1955, pp. 275-296  @1@ 2Template: Webachiv / IABot / www.issmge.org
  2. ↑ Historical dams, Garbrecht 1987
  3. ^ Karl-Eugen Kurrer The History of the Theory of Structures. Searching for Equilibrium , Ernst & Sohn , Berlin 2018, p. 341ff
  4. ↑ Fellenius Earth Static Calculations with Friction and Cohesion , Ernst and Son, Berlin 1927, Fellenius Calculation of the Stability of Earth Dams , Transactions Second Congress on Large Dams, Washington DC, 1936, Volume 4, p. 445
  5. ↑ Krey: Earth pressure, earth resistance and bearing capacity of the subsoil, 5th edition, 1936, Ernst and Son, Berlin
  6. ↑ Fröhlich General Theory of Stability of Slopes , Geotechnique, Volume 5, 1955, p. 37, Basic features of a statics of earth embankments , Der Bauingenieur 1963, Issue 10
  7. ^ Bishop Use of the slip circle in the stability analysis of slopes , Geotechnique, Volume 5, 1955, p. 7
  8. ^ Janbu Stability analysis of slopes with dimensionless parameters , Harvard Soil Mechanics Series No. 46, 1954
  9. ↑ Borowicka The Stability of Slopes in Theory and Practice , Civil Engineer, Volume 40, 1965, p. 21, A statically flawless method for determining the stability of slopes , Der Bauingenieur 1970, Issue 9
  10. ↑ Morgenstern / Price, GEOTECHNIQUE. VOL. 15, 'NO.1, 1965: The analysis of the stability of general slip surfaces. Retrieved January 27, 2018 .

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