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A Review on Collapse Caldera Modelling 245

section, we review the contribution of current numerical models to caldera-
collapse studies (see Table 1 for a short description).
Ideally, the modelling of collapse calderas formation should be performed
considering physical processes that occur both inside and outside the magma
reservoir. Our understanding of this ‘fluid-structure’ interaction is, however, far
from complete. For simplification, models deal, in practice, with only a part of the
problem (chamber or surrounding rocks) at a time, i.e. focus on one domain and
incorporate simplistically the effect of the other. In this sense, theoretical models on
collapse calderas formation can be classified into two groups:
(i) models based on thermodynamics and fluid mechanics that aim to quantify
processes occurring inside the chamber prior to and during collapse (hereafter
termed magma chamber models), i.e. they analyse aspects such as the evolution
of pressure within a magma reservoir; and
(ii) models based on solid mechanics, exploring processes outside the chamber
(hereafter termed host rock models), i.e. they deal with aspects such as stress
conditions for the formation of fractures and faults in the host rocks.

3.1. Magma chamber models
This family of models is based on equations of state of magma combined with a
simple criterion for collapse, which is commonly defined as an underpressure
threshold (Druitt and Sparks, 1984; Bower and Woods, 1997, 1998; Martı ´ et al.,
2000; Roche and Druitt, 2001; Macedonio et al., 2005). Imposing mass
conservation, these models track pressure variations within the magma reservoir
as a function of erupted mass. They enable prediction of eruptive conditions that
satisfy the criteria for collapse based on parameters such as magma composition,
volatile content, host rock mechanics, or magma chamber geometry (mainly
dimensions and depth). It is important to note that this group of models simulate
implicitly the ‘classical’ caldera scenario, in which collapse results from critical
decompression of the magma reservoir. As such, these models simulate the
following succession: (i) a chamber pressure increase until P M W P L + DP START
(where P M , P L , and DP START stand for magma pressure, lithostatic pressure, and
critical overpressure respectively, see Figure 6); followed by (ii) eruption, during
which the conduit is enlarged by sidewall erosion (an open conduit is maintained
against lithostatic forces); and finally (iii) the onset of a piston-like collapse as soon
as the failure criteria is satisfied, i.e. when the chamber pressure drops below the
lithostatic value by a certain amount (Figure 6).
The main deliverable of these models is f, the percentage of magma volume that
must be erupted in order to reach critical underpressure. It is important to
understand that the removal of magma does not imply the creation of a ‘void
cavity’. In fact, since the magma’s bulk density decreases during decompression, due
to further exsolution of volatiles, the remaining magma reservoir can be envisaged
as a pressurised porous media which always fills its cavity as the eruption proceeds
due to its increasing void fraction (the exsolved gas volume fraction). For a given
chamber roof aspect ratio, the value of f depends on the volatile content, the