We investigate the mechanism for initiating phreatic eruptions followi
ng the emplacement of a shallow magmatic intrusion into water-saturate
d permeable rock which contains subsidiary low-permeability crack netw
orks and disconnected cracks. Heat from the intrusion causes the local
groundwater to boil and ascend through the main permeable crack netwo
rk. As the ascending superheated steam heats the overlying rock, the w
ater in the subsidiary networks and disconnected cracks will boil. The
pressure exerted by the vapor in the subsidiary and disconnected crac
ks can lead to rapid horizontal crack propagation, resulting in an inc
rease in crack length by more than an order of magnitude. According to
the model, the eruption process starts near a free surface and migrat
es rapidly along thermoelastic isostresses as a result of multiple bre
akage of the thin surface layers above the cracks. For certain crack a
nd rock parameters, however, the crack propagation mechanism, instead
of leading to a dynamic eruption, may generate a highly cracked zone t
hat may be removed later by fluid transport processes. The proposed me
chanism gives rise to precursory phenomena observed in conjunction wit
h many phreatic eruptions. According to the model developed here, phre
atic eruptions are most likely to occur only for a rather restricted s
et of rock parameters. For example, the country rock should not be too
strong (sigma(t) congruent to 10 MPa) and should be characterized by
two-scale permeability structure involving a main crack network of rel
atively high permeability (greater than or similar to 10(-12) m(2)) an
d a subsidiary crack network with much lower permeability (< 10(-17) m
(2)). Moreover, the model works better if the mean crack aspect ratio
is relatively large (beta similar to 10(-1)) and the crack concentrati
on is not too low (Omega > 10(-2)). These restrictions may explain ind
irectly why phreatic eruptions are not ubiquitous in volcanic regions.