Page 197 - Analysis and Design of Energy Geostructures

170 Analysis and Design of Energy Geostructures

Eq. (4.79) implies that only a proportion of the strain is blocked, that is
ε 5 ε 2 ε th ð4:80Þ
th
th
b o f
In other words, the response of the energy pile is governed by a certain degree of
freedom, defined as (Laloui et al., 2003)

ε th
DOF 5 o with 0 # DOF # 1 ð4:81Þ
ε th
f
The blocked thermally induced strain induces an observed thermally induced stress
that can be calculated as

σ 5 Eε 5 E ε 2 ε th 5 E ε 1 αΔT 5 EαΔTð1 2 DOFÞ ð4:82Þ
th
th
th
th
o b o f o
Eq. (4.82) is the simplified one-dimensional formulation of the generalised thermo-
elastic stress strain relation expressed in Eq. (4.52). Fig. 4.17 shows the impact of the
degree of freedom of the energy pile on the development of the average thermally
induced deformation, ε , and stress, σ . The higher the restraint provided by the
th
th
o o
presence of the surrounding ground and the superstructure, the greater the thermally
induced stress and the lower the thermally induced strain. The opposite is true for the
lower pile restraint.

Figure 4.17 Impact of the system restraint on the thermally induced strain and stress in energy
piles. Modified after Rotta Loria, A.F., 2019. Performance-based design of energy pile foundations. DFI
J. 12 (2), 94 107.