Page 303 - Analysis and Design of Energy Geostructures

Thermomechanical behaviour of single energy piles 279

6.7 Thermally and mechanically induced vertical displacement
variations

The application of thermal loads along energy piles involves at best a linear distribu-
tion of the vertical displacement with depth and at worst a notably nonlinear distribu-
tion of the vertical displacement (becoming more pronounced with increasing pile
compressibility and slenderness) (Rotta Loria et al., 2018). This consideration is appli-
cable to the analysis of both rigid and deformable piles whether they have a predomi-
nantly floating or end-bearing character. In general, heating thermal loads cause
energy pile head heaves while cooling thermal loads cause energy pile head settle-
ments. The reason for this is due to the fact that thermal loads applied to energy piles
generally involve two pile portions that displace in opposite directions from the so-
called null point of the vertical displacement (located at a depth, z NP;w )(Laloui et al.,
2003a). The location of the null point depends on the end-restraint conditions
(Mimouni and Laloui, 2014; Rotta Loria et al., 2015; Sutman et al., 2018). For an
infinitely rigid base, the null point is located at the toe of energy piles. For an infinitely
rigid slab, the null point is located at the pile head. In practice the null point is located
somewhere along the length of the energy pile and always closer to the region of the
system characterised by the higher restraint.
An example of the head heave of an energy pile free to move vertically at its head
under the application of a heating passive cooling cycle is shown in Fig. 6.7 with ref-
erence to the results presented by Laloui et al. (2003a). An average temperature varia-

tion along an energy pile free to move vertically at its head of ΔT 5 22 Ccan
cause a vertical head displacement of approximately w h 524 mm. Higher head displa-
cements can be expected for energy piles resting on stiff soil strata compared to energy
piles floating in soft ground (the significant value of head displacement discussed with
reference to the considered case is to be associated with the former situations). This
phenomenon can be associated with the lower location of the null point in the former
case compared to the latter for the same applied temperature variation. Higher energy
pile displacements can be expected for longer piles. The reason for this is because,
although the thermally induced deformation is independent of the pile length, the ther-
mally induced displacement of energy piles is proportional to their length.
In contrast to the previous behaviour, the application of mechanical loads at the
head of energy piles involves an approximately constant distribution of the vertical dis-
placement with depth as well as a comparable distribution of shear stress (Rotta Loria
et al., 2018). This consideration is particularly applicable to the analysis of rigid piles
with a predominantly frictional character but is also acceptable for most piles.
Compressive mechanical loads applied at the head of piles involve energy pile head
settlements, while tensile mechanical loads involve energy pile head heaves. In particu-
lar, unless dealing with the phenomenon of negative skin friction, the action of