Deformation behaviour of railway embankment ... - Liikennevirasto

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Figure 7.6:2 Relationship between permanent shear strain and the maximum stress
ratio of Equation 7.6:3 (Pappin 1979).
Other researchers have reported that the amount of permanent strain is determined by
how close the applied stresses are to the static failure stress. Barret and Smith (1976)
and Raymond and Williams (1978) made use of the stress ratio q max /q failure , in which q max
is the maximum deviator stress and q failure the deviator stress at failure (continuing along
the same stress path), to characterize the results of permanent deformation tests. Thom
(1988), on the other hand, suggested that permanent shear strain is better related to the
stress ratio (q max - q failure )/ q max .
Shaw (1980) attempted to apply the equation suggested by Pappin and to relate
permanent shear strain to stress path length and stress ratio, but found it inadequate as
the existence of stress paths with identical stress ratio but completely different strain
rates was proven possible. He then modified the equation above by replacing the stress
ratio variable with an expression which was a function of the minimum distance of the
applied stress path from the static failure envelope. Shaw reported that, generally, a
good correlation between predicted and experimental shear strains existed for the
crushed limestone of nominally 1 mm particle sized used in his study. However, when
the permanent strain programme conducted by Pappin on the well-graded material was
reanalysed using the modified equation, the results were not satisfactory. Shaw, too,
stated that modelling attempts on permanent volumetric strains were unsuccessful.
In a more recent study in France, Paute et al. (1993) defined a practical limit value to
the maximum permanent axial strain, the A-value as described before, and suggested
that it varies with the maximum shear stress ratio, q max /(p max +p * ), according to a
hyperbolic expression of the form given in the following equation: