Geology Reference
In-Depth Information
Latent heat is released when ground freezes and is largely responsible for the “zero-
curtain” effect discussed in Chapter 3. Frozen soil thermal conductivity is greater
than that of unfrozen soil because ice conductivity is approximately 4 times that of
water; therefore, other things being equal, heat penetrates the ground more quickly when
frozen than when unfrozen. As a result, thermal conductivity is a major control over the
permafrost temperature gradient and the active-layer thickness (see below). Porosity infl u-
ences the degree of saturation of soil or rock, and moisture is described by its gravimetric
water content and bulk density. The latter is useful when discussing ground ice (see
Chapter 7).
Typical values for thermal conductivity and volumetric heat capacity are given in
Table 5.1. Figures 5.2A and 5.2B summarize the temperature dependence of thermal
conductivity of different materials of different grain size.
5.2.1. The Geothermal Regime
The growth of permafrost refl ects a negative heat balance at the surface of the earth. The
minimum time for the duration of permafrost is two years. Thus, if the ground freezes
one winter to a depth of 60 cm and only thaws during the following summer to a depth of
55 cm, 5 cm of permafrost comes into existence in the second year. If the climatic condi-
tions are repeated in following years, the layer of permafrost will thicken and extend
downwards from the base of the seasonal-frost layer. Ultimately, permafrost several hun-
dreds of meters in thickness can be formed.
The thickness to which permafrost develops is determined by a balance between the
internal heat gain with depth and heat loss from the surface. According to A. Lachenbruch
(1968), heat fl ow from the Earth's interior normally results in a temperature increase of
approximately 1 °C per 30-60 m increase in depth. This is known as the geothermal gradi-
ent (see Figure 5.1A). The permafrost base is indicated on Figure 5.1A. Also shown is the
thickness of a basal “cryopeg,” i.e. that part of permafrost that is unfrozen but at a tem-
perature
0 °C.
The amplitude of the surface seasonal temperature wave decreases with depth. This
can be expressed by the following equation:
<
Az
=
As e
.
−
z
πα
P
(5.1)
where
Az
is the amplitude of the temperature wave, at depth
z
,
As
is the amplitude of the
surface temperature wave (i.e. amplitude
is thermal diffusivity of the soil
or rock, and
P
is the period of the wave (one year). The depth of zero-annual amplitude
varies according to both air temperature and thermal diffusivity but generally occurs
within 20 m of the ground surface.
If the ground-surface temperature and geothermal gradients are known, it is possible
to calculate the ground temperature at any depth by using a one-dimensional heat fl ow
equation:
=
½ range),
α
Tz
=+×
Ts
Gg
Z
(5.2)
where
Tz
is the ground temperature (°C) at depth
Z
(m),
Ts
is the mean annual
ground surface temperature (°C),
Gg
is the geothermal gradient (°C m
−1
) (i.e. the tem-
perature increase over unit depth) , and
Z
is depth (m). For example, if
Ts
=
−
4 °C and
Gg
=
0.02° C/m, the temperature at 100 m depth is calculated as follows:
T
100
=
−
4
+
0.02
×
100
=
−
4
+
2
=
−
2 °C.
