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226 Analysis and Design of Energy Geostructures

Figure 5.13 Volumetric response of coarse-grained soils subjected to temperature variations at dif-
ferent mean effective stresses. Redrawn after Ng, C.W.W., Wang, S.H., Zhou, C., 2016. Volume change
behaviour of saturated sand under thermal cycles. Géotech. Lett. 6 (2), 124 131.

characterising NC fine-grained soils (Ng et al., 2016). Yet, the discussed behaviour of
dense to loose coarse-grained soils is the inverse compared that characterising slightly
OC fine-grained soils, which show an initial expansion and a subsequent contraction
upon heating.
The significance of the thermal collapse of coarse-grained soils appears to depend
0
on the stress state, which can be quantified in terms of the mean effective stress, p .
Experimental evidence supporting the previous consideration is reported in Fig. 5.13
with reference to the results of Ng et al. (2016). Results are depicted in terms of the
relationship between thermally induced volumetric strain, ε v , and applied temperature
variation, ΔT. The relative density of the tested materials prior to heating is of
D R 5 20%. For the same relative density prior to heating, the thermal contraction
increases with the mean effective stress. In the considered example, thermally induced
volumetric contractions of 0.15% and 0.07% are observed at a mean effective stress of
200 and 50 kPa, respectively.
According to Ng et al. (2016), the observed volumetric behaviour of coarse-grained
soils under thermal loads cannot be explained by most thermomechanical constitutive
models (see, e.g. Hueckel and Borsetto, 1990; Cui et al., 2000; Laloui and François,
2009; Zhou and Ng, 2015). These models typically assume the stress history only to
characterise the nonisothermal volumetric soil behaviour and describe contractive and