Environmental Engineering Reference
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General method for estimating the active and passive earth
pressures on retaining walls assuming different strength criteria
a. serrano
E.T.S.I.C.C.P., Universidad Politécnica de Madrid, Madrid, Spain
a. Perucho & M. conde
Laboratorio de Geotecnia, CEDEX, Madrid, Spain
aBsTRacT: a new method for estimating the earth pressures on retaining walls has been developed.
it is an extension of coulomb's earth pressure theory for non cohesive materials that can follow a non-
linear strength criterion. This was previously done by the authors (serrano et al, 2007) for some basic
assumptions that have now been extended. The method is valid for materials that may have either a linear
or non-linear strength criterion (parabolic or hoek-Brown), a non-horizontal surface and an earth-wall
friction angle. The method considers the material dilatancy. Moreover, the failure surface does not need
to be plane, as in previously developed methods, but its shape is obtained as a result of the calculus, by
applying euler's variational method that obtains the extremal force.
1
inTRoDUcTion
α
This study is an extension of coulomb's classic
method of calculating wall pressures on incoherent
materials with a non linear strength criterion
at the present time the calculation of pressures
on these materials requires a previous linearization
of the failure criterion. This linearization is always
problematical so its success depends on the elec-
tion of a carefully chosen range of stresses.
The fundamental hypothesis of the coulomb
method was abandoned -the adoption of a plane
for the failure surface- and now this surface is
obtained directly by euler's variational method
making the force extremal. Therefore it is nec-
essary to dispose of a calculation method for
non-linear media able of incorporating these new
failure surface.
The results of this study allow determination
of the pressures on walls due to materials such as
rockfills, highly fractured rock masses, pyroclasts,
etc., whose mechanical behaviour is clearly non
linear.
σ
H
τ
a)
b)
Figure 1.
Wall geometry (a) and geomechanical hypoth-
eses (b).
2. The earth surface is plane, forming an α angle
with the horizontal.
3. The wall has a vertical backfilling.
2.2
Geomechanical (cf Fig. 1b )
1. a wedge of earth limited by a surface passing
through the foot of the wall leaning against the
wall.
2. The earth is dry, i.e., pore pressures are not
taken into account. The calculation is done on
effective pressures.
3. The earth has a specific weight of γ.
4. The normal (σ) and tangential (τ) stresses acting
on the surface of the wedge can verify a failure
criterion of the type ( Fig. 2 ):
2
Basic hYPoTheses
2.1
Geometrical ( cf Fig. 1a )
1. The wall is assumed to be indefinite so that it is
a two-dimensional problem in plane deforma-
tion condition.
 
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