2145
Calculation of slopes stability based on the energy approach
Calcul de la stabilité des pentes sur la base de l’approche énerg
é
tique
Bogomolov A.N., Ushakov A.N., Bogomolova O.A.
Volgograd State University of Architecture and Civil Engineering, Volgograd, Russia
ABSTRACT: For quantitative evaluation of slope’s stability value safety factor coefficient K is used, defined by various known
methods. However, the results ensued in this way for identical objects may substantially differ. The reason for this are numerous
assumptions and simplifications adopted in the calculations. Approach based on the analysis of the stress fields and displacement of
soil mass points and principle of virtual displacements allows to get adequate results while solving the corresponding task. The used
method of sliding surface constructing ensures realization of minimal condition of K value at each point. Analysis of the stress-strain
state of homogeneous and heterogeneous slopes is accomplished by using finite element method (FEM), and the boundary conditions
imposed on the design scheme FEM are processed based on the analytical solutions of the first basic boundary value problem of
elasticity theory for homogeneous weight simply connected domain, get by the authors.
RÉSUMÉ : Pour l'évaluation quantitative de la stabilité des pentes on utilise la valeur du facteur de sécurité K, définie par diverses
méthodes connues. Cependant, les résultats obtenus de cette manière pour des objets identiques peuvent différer substantiellement.
Les raisons de cette situation sont de nombreuses hypothèses et simplifications adoptées dans les calculs. Obtenir des résultats
satisfaisants lors de la résolution du problème correspondant devient possible grace à l’aproche basée sur l’analyse des champs de
tensions et de déplacements des points du massif de sol et aussi sur le principe des déplacements virtuels. La méthode utilisée de la
construction de la surface de glissement assure l’accomplissement d’une condition de minimalité pour la valeur K dans chaque son
point. L'analyse de l'état précontraint et déformé des pentes homogènes et hétérogènes est realisée en utilisant la méthode des
éléments finis (FEM), tandis que les conditions aux limites, imposées au schema de calcul FEM, sont traitées sur la base des solutions
analytiques du premier problème aux limites faisant partie de la théorie de l'élasticité pour une domaine homogène simplement
connexe, obtenues par les auteurs.
KEYWORDS: slope, safety factor, stresses, displacements, work, restraining and moving forces
1. QUESTION STASUS
Principle of virtual displacements - one of the basic principles
of mechanics, evaluating general condition of equilibrium of the
mechanical system. It is widely used in static studies of material
systems, with the effect imposed on the system connections,
considered by adding appropriate reactions. This principle has
been used previously in the stability of slopes calculation
(Goldstein 1969, Dorfman 1975, Magdeev 1973, etc.), however,
movements of the points lied on the most probable slip surface,
are not appointed on the basis of the stress-strain state analysis
of near the slope area and arbitrarily vary in magnitude until the
condition K=Kmin is achieved.
In addition the following quite not correct assumptions can
be provided:
– sliding prism splits into separate blocks, the interaction
force and the friction between them is rarely taken into account;
orientation of this forces and the position of the points of their
application does not settle, and set arbitrarily to make a
statically indeterminate task about equilibrium of blocks,
statically determinate;
– the form and position of the fracture surface are taken in
advance, in the process of problem solving their direct link with
physical and mechanical properties of soils, slope geometry,
surface loads is not established;
– almost always only one (and approximately in the form of
bay weight) vertical
z component of the stress at near the slope
area is taken into account;
– semi-infinite slope is considered (the fact of stress
concentration in the transition region of the slope into the base
is left out of the account); well-known calculation methods
doesn’t allow to take into account mutual influence of
embankment’s slopes and excavations on their stability, as in
the design scheme base of the slope is not considered, and the
daily surface of the slope is infinite, etc. and so on;
– in stability calculation such important value as the
coefficient of lateral earth pressure ξo is not considered and etc.
All this makes it necessary to look for new solutions of the
slope’s stability problem, in particular, based on the analysis of
the stress-strain state.
Known method (Potapova 2001), when the value of K is
defined as algebraic sum of work of restraining and shearing
forces acting at the points of most likely slip line
,
)
cos
(
)
cos
(
сдi
i сдiF
удi
i удiF
сдiA
удiA
K
(1)
where
- restraining and shearing forces agreeably;
- complete movement;
- angles between
positive directions of the restraining and shearing forces and
direction of the total displacement vector, respectively, in the i-
th point of the sliding surface. Equation (1), in our opinion, is
not quite correct, because in this equation full displacements of
the points made of movements of the external load and dead
weight of the soil are taken into account. Movements from dead
weight of soil are formed during all period of the soil mass
existence, and therefore their true values cannot be reliably
сдiF удiF
;
i
сдi
удi
;
