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| Titel |
A new computational method based on the minimum lithostatic deviation (MLD) principle to analyse slope stability in the frame of the 2-D limit-equilibrium theory |
| VerfasserIn |
S. Tinti, A. Manucci |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1561-8633
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| Digitales Dokument |
URL |
| Erschienen |
In: Natural Hazards and Earth System Science ; 8, no. 4 ; Nr. 8, no. 4 (2008-07-16), S.671-683 |
| Datensatznummer |
250005641
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| Publikation (Nr.) |
 copernicus.org/nhess-8-671-2008.pdf |
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| Zusammenfassung |
| The stability of a slope is studied by applying the principle of the minimum
lithostatic deviation (MLD) to the limit-equilibrium method, that was
introduced in a previous paper (Tinti and Manucci, 2006; hereafter quoted as
TM2006). The principle states that the factor of safety F of a slope is the
value that minimises the lithostatic deviation, that is defined as the ratio
of the average inter-slice force to the average weight of the slice. In this
paper we continue the work of TM2006 and propose a new computational method
to solve the problem. The basic equations of equilibrium for a 2-D vertical
cross section of the mass are deduced and then discretised, which results in
cutting the cross section into vertical slices. The unknowns of the problem
are functions (or vectors in the discrete system) associated with the
internal forces acting on the slice, namely the horizontal force E and the
vertical force X, with the internal torque A and with the pressure on the
bottom surface of the slide P. All traditional limit-equilibrium methods make
very constraining assumptions on the shape of X with the goal to find only one
solution. In the light of the MLD, the strategy is wrong since it can be
said that they find only one point in the searching space, which could
provide a bad approximation to the MLD. The computational method we propose
in the paper transforms the problem into a set of linear algebraic
equations, that are in the form of a block matrix acting on a block vector,
a form that is quite suitable to introduce constraints on the shape of X, but
also alternatively on the shape of E or on the shape of X. We test the new
formulation by applying it to the same cases treated in TM2006 where X was
expanded in a three-term sine series. Further, we make different assumptions
by taking a three-term cosine expansion corrected by the local weight for
X, or for E or for A, and find the corresponding MLDs. In the illustrative
applications given in this paper, we find that the safety factors associated
with the MLD resulting from our computations may differ by some percent from
the ones computed with the traditional limit-equilibrium methods. |
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