Page 313 - Caldera Volcanism Analysis, Modelling and Response

288 Valerio Acocella

most numerical models, permit the study of discontinuous solutions, (i.e. the
development of faults) during the deformation process. Therefore, they are
particularly suitable to reconstruct mechanisms of deformation and associated
structural patterns. Another advantage is that the modelling does not require any
advanced analytical approach.
The greatest limitation concerns the current difficulty in simulating temperature
gradients. This may become relevant when dealing with magma-related processes,
such as caldera collapse, implying that a fundamental assumption in all the
performed experiments is the lack of a temperature control. Caldera collapse is
therefore studied simulating a system with two components, a magma chamber and
a brittle upper crust; the presence of a ductile crust overlying the magma chamber is
neglected. Another common assumption is that the simulated contraction of the
magma chamber, even though related to the extrusion of magma at surface, is not
simulated as such. In fact, rather than reproducing the development of a conduit
feeding a vent responsible for magma extrusion, these experiments are simply
focused on its effect.

2.2. Materials and scaling

The modelling is achieved through the attainment of the geometric, kinematic
and dynamic similarity with nature (Hubbert, 1937; Ramberg, 1981). This is
obtained through the definition of precise scaling proportions between model and
nature, which influence the choice of both the analogue materials and the
apparatus.
The brittle crust in the caldera experiments is usually simulated by sand, flour or
clay. The choice of any of these materials depends upon the imposed length ratio

between model and nature L (Merle and Vendeville, 1995, and references therein);
in fact, this ratio affects the cohesion of the crustal analogue to be chosen for

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modelling. In most experiments, for practical reasons, L B10 ; moreover, the

density ratio between rocks and most experimental materials is r B0.5 and the

gravity ratio between model and nature is g ¼ 1. Therefore, the corresponding

stress ratio between model and nature is s ¼ r g z B5 10 6 (Table 1). As the

cohesion c has the dimensions of stress, assuming a Mohr–Coulomb criterion and
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a cohesion cB10 Pa for the rocks, a material with cB50 Pa is required to simulate
the brittle crust. Therefore, the most suitable material to reproduce the behaviour
of the brittle crust is dry quartz sand, with a negligible cohesion (in the order of a
few Pa). In addition, dry sand has a Mohr–Coulomb failure criterion similar to the
rocks in the brittle crust, with an angle of internal friction fB301. Flour and clay
have slightly larger cohesion (1–3 orders of magnitude) and therefore are not ideal
crust analogues, at least with the imposed ratios. Nevertheless, if added in small
quantities (r10%) to sand, they may be useful in enhancing the resolution and
details of the structural features at surface (including the formation of subvertical
scarps and extension fractures).
The magma chamber responsible for collapse has been simulated by air (e.g.
Marti et al., 1994), water (e.g. Kennedy et al., 2004) and silicone (e.g. Roche et al.,
2000) in the various experimental sets. The main difference in these materials lies in