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Strain Response Envelopes for low cycle loading processes
Enveloppe de réponse d´allongement pour chargements cycliques de basse intensité
Hettler A., Danne St.
Chair of Soil-Mechanics and Foundation Engineering, University of Dortmund
ABSTRACT: To look onto the stress-path-dependent strain behaviour at low-cycle loading, drained, stress-controlled triaxial-tests
have been carried out. Here the focus was to investigate strain-response envelopes which result from applying relatively small stress
increments of ≤ 50 kN/m², to the soil-specimen. It is found that quasi-elastic behaviour can already occur at low numbers of cycles.
The shapes of the obtained strain-response-envelopes are similar to symmetrical ellipses. It can be observed, that the size of the
ellipses decreases with increasing mean pressure p. The major axis of the ellipses rotates depending on the initial stress state
=q/p,
indicating a stress-induced anisotropy. Preloading seems to have little effect on the stiffness or the directions of the quasi-elastic
strains.
RÉSUMÉ : Afin d´analyser le comportement de dilatation résultant des chemins de contrainte pour un nombre réduit de cycles de
chargement, des essais triaxiaux drainés ont été réalisés. Le thème central est l´analyse des enveloppes des réponses d´allongement ,
en employant des incréments de contrainte relativement petits de ≤ 50 kN/m². Il s´est avéré, que le sable manifeste un comportement
quasi élastique après un nombre de cycles réduit. La forme des enveloppes de réponse d´allongement est celle des ellipses
symétriques. Les diamètres des ellipses se réduisent, lorsqu´on augmente la pression moyenne. Les axes majeurs des ellipses changent
d´inclination en fonction de la contrainte initiale η=p/q, indiquant une anisotropie causée par la contrainte. Il apparait qu´un
chargement préliminaire a peu d´influence sur la rigidité et les directions des allongements quasi-élastiques.
KEYWORDS: low cycle loading processes, triaxial tests, strain response envelopes
1
INTRODUCTION
Due to quasi-static loading with cyclic progression there are
plastic, i.e. irreversible, and elastic, i.e. reversible deformations
in the soil, without reaching fully elastic behaviour. In the
quasi-elastic regime the material behaves asympotically elastic.
Goldscheider (1978) describes this behaviour as “material
shakedown”.
Considering the number of cycles one can distinguish
between high cycle and low cycle loading processes.
Effects of wind load on foundations of wind energy plants,
vehicle crossing on foundation constructions, vibrating of
foundation-elements e.g. retaining-wall-elements or grouted
piles can be related to high cycle loading. The number of cycles
N during these processes is very high (N >> 50). Due to the
accumulation of numerical errors and a high computing time an
implicit calculation of displacements, where the deformations
during one cycle are calculated separately and accumulated, is
not adequate. Instead, deformations due to high cycle loading
are calculated by using explicit models. Here the calculation of
irreversible strains can be treated similar to creep deformations
under constant loads (Wichtmann et al., 2005).
Low cycle loading processes can be defined for a lower
number of cycles with N
≤
50, Danne & Hettler (2011).
Deformations in this case are usually calculated implicitly, i.e.
for each cycle separately and then accumulated.
Subject of this article are low cycle loading processes, where
it is assumed that inertial forces are negligible (Hettler, 1981).
Un- and reloading for example, occurring during the
construction phase of multiple braced excavation walls, produce
stress paths quite similar to those of cyclically loaded systems at
the first cycles before reaching shakedown. Therefore, these
processes are also included within the scope of low cycle
loading.
An external cyclic load on a foundation for example does not
lead to cyclic behaviour right from the beginning. This is the
case only after a certain number of cycles.
Some examples for low cycle loading processes and related
un- and reloading processes are:
construction stages of multiple braced or anchored
excavation walls
braced excavation with force-controlled struts (to control
deformations)
temperature exposure of struts
filling and emptying of locks or silos during first utilisation
phase
summer-/winter position of abutments of integral bridges
due to temperature differences
The simplified consideration of a soil element behind a
strutted retaining wall shows, that monotonous stress-paths as
well as repeated low cycle loading process with various
directions can occur (figure 1).
Figure 1: Typical stress-paths in a soil-element behind an excavation-
wall
In front of the embedded part of the wall stress-paths are
similar, but extension may be important instead of compression.
Element tests investigating the stress-strain behaviour of
soils must therefore take into account any stress-path and
repeated un- and reloading processes when contributing
successfully to the development of new or further developed
constitutive equations. It is also obvious, that stress states in
