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Physical hydrogeology 49

BO X
Continued
2.7

that the thermal waters attain a maximum temperature between Carboniferous limestone outcrop in the Mendip Hills (see Sec-
64°C and 96°C, the uncertainty depending on whether chalcedony tion 2.7), 15–20 km south and south-west of Bath, in order to drive
or quartz controls the silica solubility. Using an estimated geother- recharge down along a permeable pathway and then up a possible
−1
mal gradient of 20°C km , Andrews et al. (1982) calculated a thrust fault to the springs themselves. The structural basin contain-
circulation depth for the water of between 2.7 and 4.3 km from ing the Carboniferous limestone lies at depths exceeding 2.7 km at
these temperatures. The natural groundwater head beneath central the centre of the basin, sufficient for groundwater to acquire the
Bath is about 27–28 m above sea level, compared with normal necessary temperature indicated by its silica content. This ‘Mendips
spring pool levels at about 20 –m. For this head to develop, Burgess Model’ for the origin of the Bath hot springs is summarized by
et al. (1980) argued that the recharge area is most likely the Andrews et al. (1982) and shown in Fig. 3.

Fig. 3 Conceptual model for the origin of the Bath thermal springs. The numbers shown in squares indicate: (1) recharge (9–10°C) at
the Carboniferous limestone/Devonian sandstone outcrop on the Mendip Hills; (2) flow down-dip and downgradient; (3) possible
4
downward leakage from Upper Carboniferous Coal Measures; (4) possible leakage of very old He-bearing groundwater from Devonian
sandstone and Lower Palaeozoic strata; (5) storage and chemical equilibration within the Carboniferous limestone at 64–96°C; (6) rapid
ascent, probably along Variscan thrust faults re-activated by Mesozoic tectonic extension; (7) lateral spread of thermal water into Permo-
Triassic strata at Bath; and (8) discharge of the thermal springs at Bath (46.5°C). After Andrews et al. (1982).

If the total stress does not change (dσ = 0), then from dV =−βV dP eq. 2.31
T w w w
a knowledge that P = ρgψ and ψ = h − z (eq. 2.22),
w
with z remaining constant, then, using equation 2.25: Recognizing that the volume of water, V , in the total
w
unit volume of aquifer material, V , is nV where n is
T T
dσ = 0 − ρgdψ =−ρgdh eq. 2.29 porosity, and that dP = ρgdψ or −ρg for a unit decline
e
in hydraulic head (where ψ = h − z (eq. 2.22), with z
For a unit decline in head, dh =−1, and if unit volume remaining constant), then for unit volume, V = 1,
T
is assumed (V = 1), then equation 2.28 becomes: equation 2.31 gives:
T
dV = α(1)(−ρg)(−1) = αρg eq. 2.30 dV =−βn(1)(−ρg) = βnρg eq. 2.32
w w
The water produced by the expansion of water is Finally, the volume of water that a unit volume of
found from equation 2.26 thus: aquifer releases from storage under a unit decline in