Page 278 - Caldera Volcanism Analysis, Modelling and Response

A Review on Collapse Caldera Modelling 253

2004) is to assume that tensional fractures are produced when:

s 3 T 0 (2)
whereas shear fractures occur if:
(3)
s 1 s 3 S 0
where T 0 and S 0 represent the tensile and the shear strength of the embedding
crust, respectively. Equation (2) is the Griffith failure criteria for brittle materials
under a tensional regime (s 1 +3s 3 o0), whereas Equation (3) reflects a limit of the
Mohr–Coulomb shear failure criteria near the brittle-ductile transition. Hence,
the above expressions can be considered as end-members of the combined Griffith/
Mohr–Coulomb failure criteria for brittle materials. Using these criteria, tensional
fractures are produced in a plane perpendicular to s 3 , whereas a conjugate pair of shear
fractures occurs in the plane s 1 s 3 forming angles of 7451 with respect the s 1
direction.
Once a fracture criteria and a crustal rheology is defined, we can use models to
assess the likelihood of a collapse formation depending on load conditions, magma
chamber geometry, and crustal properties (homogeneous, horizontal layering, etc.).
Thus, in contrast to magma chamber models, host rock models are based on stress-field
computations to analyse distinct collapse scenarios defined by different load conditions
such as magma chamber overpressure (e.g. Komuro et al., 1984; Chery et al., 1991;
Gudmundsson et al., 1997; Gudmundsson, 1998; Burov and Guillou-Frottier, 1999;
Guillou-Frottier et al., 2000; Gray and Monaghan, 2004; Gudmundsson, 2008),
underpressure (e.g. Druitt and Sparks, 1984; Folch and Martı ´, 2004; Gudmundsson
2008), or the existence of regional tectonic stress such as horizontal tension or regional
doming (e.g. Gudmundsson, 1998; Gudmundsson et al., 1997; Gudmundsson, 2008).
Figure 8 shows the general sketch of the scenario contemplated by this group of
models. The main findings of models can be summarised as follows:

(1) Formation of ring faults considering underpressure load conditions.
All results from models employing purely elastic and homogeneous rheology
agree that spherical magma chambers are unlikely to generate ring faults
because the maximum tensile stress at the ground surface is much lower than
the chamber’s underpressure, and the maximum shear stress occurs at the centre
of the chamber rather than at its margins. However, for a fixed underpressure,
increasing the chamber’s eccentricity entails an increase of tensional stresses at
surface and a progressive shift of the maximum shear stress towards the chamber
margins. This suggests that sill-like chambers having a certain eccentricity and
subjected to sufficient underpressure can induce dyke injection (Gudmundsson,
2008), ring-fault formation (Gudmundsson, 1998; Folch and Martı ´, 2004), or a
combination of both. Thus, Folch and Martı ´ (2004) propose that the formation
of calderas by underpressure may be governed by two different mechanisms
strongly controlled by the chamber geometry (Figure 9). For very eccentric
geometries, ring faults would form as a consequence of the flexural bending of
the chamber roof. This would be the mechanism related to the formation of