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GEO5

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Shape of Subsidence Trough

The program offers two particular shapes of subsidence troughs - according to Gauss or Aversin.

Curve based on Gauss

A number of studies carried out both in the USA and Great Britain proved that the transverse shape of subsidence trough can be well approximated using the Gauss function. This assumption then allows us to determine the horizontal displacement at a distance x from the vertical axis of symmetry as:

where:

Si

-

settlement at point with coordinate xi

Smax

-

maximum terrain settlement

Linf

-

distance of inflection point

Curve based on Aversin

Aversin derived, based on visual inspection and measurements of underground structures in Russia, the following expression for the shape of subsidence trough:

kde:

Si

-

settlement at point with coordinate xi

Smax

-

maximum terrain settlement

L

-

reach of subsidence trough

Literature:

Széchy, Károly, The art of tunelling, Budapest : Akadémiai Kiadó, 1966.