Gravity-driven failure of shallow magma chamber roofs and formation of collapse calderas are commonly accompanied by ejection of large volumes of pyroclastic material to the Earth's atmosphere and thus represent severe volcanic hazards. In this respect, numerical analysis has proven as a key tool in understanding the mechanical conditions of caldera collapse. The main objective of this paper is to find a suitable approach to finite-element simulation of roof fracturing and caldera collapse during inflation and subsequent deflation of shallow magma chambers. Such a model should capture the dominant mechanical phenomena, for example, interaction of the host rock with magma and progressive deformation of the chamber roof. To this end, a comparative study, which involves various representations of magma (inviscid fluid, nearly incompressible elastic, or plastic solid) and constitutive models of the host rock (fracture and plasticity), was carried out. In particular, the quasi-brittle fracture model of host rock reproduced well the formation of tension-induced radial and circumferential fractures during magma injection into the chamber (inflation stage), especially at shallow crustal levels. Conversely, the Mohr–Coulomb shear criterion has shown to be more appropriate for greater depths. Subsequent magma withdrawal from the chamber (deflation stage) results in further damage or even collapse of the chamber roof. While most of the previous studies of caldera collapse rely on the elastic stress analysis, the proposed approach advances modeling of the process by incorporating non-linear failure phenomena and nearly incompressible behaviour of magma. This leads to a perhaps more realistic representation of the fracture processes preceding roof collapse and caldera formation.
Out of plane load bearing capacity of a masonry structure enhanced by surface render made of high performance lime-based mortar is investigated by numerical simulations using the finite element method (FEM). The response of the wall is simulated firstly without render (as a reference) then with surface render consisting of conventional lime mortar with increased tensile strength (by addition of the metakaolin) without fibers and finally with the proposed lime-metakaolin mortar reinforced with PVA fibers. The thickness of the surface render is considered in two configurations (20 mm and 40 mm). Material parameters of masonry units (bricks), joints (mortar between bricks) and conventional plain render are chosen with regard to investigations of historic structures (reported in the literature), material characteristics of fiber reinforced render are evaluated based on experiments or numerical simulations of these experiments. Using these parameters and characteristics, the numerical simulations of masonry wall subjected to out of plane bending are performed. The results allow us to identify influence of the thickness and the material of render on load-bearing and deformation capacity, failure mode and amount and width of cracks. The results show that the conventional plain mortar improves load-bearing capacity and deformation capacity proportionately to the thickness of render, but the response remains brittle. Fiber reinforced mortar significantly increases the deformation capacity and load-bearing capacity and the amount of absorbed energy is significantly improved.
The formation of a caldera poses a serious risk for the society and the environment. There are several established processes (mostly dealing with the conditions inside the reservoir), which must take place in order to reach a collapse leading to the caldera. The role of magma chamber geometry is investigated in this paper, exploiting the numerical modeling. The results indicates that the knowledge of the magmatic system dimensions can provide a helpful factor for an assessment of the caldera formation scenario.
The overall mechanical response of a fractured rock mass is, to a large extent, affected by naturally occurring fractures that exhibit sizes from millimeters to kilometers. Thus, in analysis of underground structures, such as tunnels, it is required that the fractures’ influence on the stress and deformation state in the vicinity of the structure is taken into account. In the present work, we examine the applicability of the statistical volume element (SVE) approach to determining the apparent stiffness tensor of an equivalent continuum representation of the fractured rock, which is then used in the framework of the finite element method. The equivalent continuum properties are determined by volume-averaging the effect of individual fractures that intersect the SVE, while the fractures are represented using the “parallel plate model”. Stochastically generated discrete fracture networks are used to represent the fractures’ geometry. Presently, we solve the problem linearly for an incremental change of the stress state. An application of the concept is demonstrated on simulation of tunnel excavation.
