Page 100 - Analysis and Design of Energy Geostructures

72 Analysis and Design of Energy Geostructures

The hypothesis for geomaterials to be characterised by only one fluid phase of
water or air, which involves completely dry or fully saturated conditions with water,
may be approximate to describe practical problems. While theories and modelling
approaches are available to address this problem (see, e.g. Fredlund et al., 1993), they
currently remain out of the scope of this book. Table 3.1 reports a summary of so-
called index properties that relate the phases, masses M i (or weights W i ) and volumes
V i of geomaterials.
In addition to the previous hypotheses, unless otherwise specified, reference is
made in the following to materials that are isotropic, that is characterised by properties
that are the same in all directions in space. When dealing with soil, rock and concrete,
the hypothesis of isotropy may be approximate in some cases. However, when applied
with judgement, the considered assumption has been largely proven to be effective in
modelling the behaviour of materials and the related physical phenomena, and for this
reason it is employed in the following.
Once effective properties are defined for continua, interest may lie in determining
equivalent properties of composite materials, such as reinforced concrete. In those situations
it is assumed that the equivalent property @ of a composite material can be determined
from the average of the effective properties @ i of thesinglematerials i over representative
dimensions x i (lengths, surfaces, volumes) characterising the composite material of interest
with reference to the total reference dimension x. This approach involves

X
@ 5 @ i x i ð3:1Þ
x
i

3.3 Principles of heat transfer

Heat transfer is the physical phenomenon for which energy is transferred between any two
particles of matter that are at different temperatures. There are three modes of heat transfer
considered in the following: conduction, convection and radiation. Additional heat transfer
phenomena caused, for example by latent processes thatresultfromphase variations of
material constituents exist. However, from an engineering perspective, latent heat transfer
processes are considered negligible for the analysis and design of energy geostructures.

Heat transfer phenomena can be quantified and analysed in terms of suitable rate
equations. These equations express the amount of thermal energy transferred per unit
time. Heat transfer cannot be measured directly. However, its occurrence can be
quantified through a measurable scalar quantity, that is the temperature, T.
Temperature is the variable governing heat transfer. Knowledge of the temperature
distribution within a region allows calculating the heat flow within this region
(Hermansson et al., 2009). The analysis of the heat transfer in any medium is therefore
strictly related to the determination of the temperature distribution within the medium
that is subjected to certain boundary and initial conditions.