Propagation velocity of magma intrusions, a new 2D numerical approach

<p>The tortuous travel of magma through the crust may sometimes result in volcanic eruptions at the surface. In the brittle crust, magma propagation usually occurs by fracturing the rock and opening its own way through them. This process of diking is controlled by the interaction of many complex physical processes including rock fracture, flow of compressible fluids, phase transitions, heat exchange. Current models of dikes consider either a fracturing-dominated approach, that neglects the viscous flow and allow to estimate the trajectory of dike propagation, or a viscous-dominated approach that neglects the fracturing at the dike tip allowing to infer the propagation velocity of the dike. Here we propose a new numerical approach aiming at modeling both the magma path and velocity. We start from a two-dimensional Boundary Element model solving for the trajectory of a quasi-static crack in an elastic medium subjected to external stress (Maccaferri et al, 2011), and implement the effects of the viscous fluid flow assuming a Poiseuille flow. We build on the previous work by Dahm (2000) but relaxing the assumption of stationarity, and thus allowing to take into account heterogeneous crustal stresses, complex dike paths, and dike velocity variations. The fluid flow results in a viscous pressure drop applied to the crack wall, which modifies the crack shape and contributes to the energy balance of the propagating dike. In fact, the energy dissipated by viscous flow is linearly dependant on the viscosity of the fluid and the crack velocity. It follows that the velocity can be inferred from the total energy budget by imposing that the viscous energy dissipation and the energy spent to fracture the rocks equals the strain-plus-gravitational energy release. However, the viscous dissipation strongly depends on the opening of each dislocation element, causing numerical instabilities in the calculation of the dike velocity due to the fracture closure at the dike tail. We will present first results of velocities derived with this approach considering only a static crack shape (that is to say neglecting the modification of the crack shape induced by the flow). We will discuss the influence of various parameters (crack size, Young’s modulus value...), and will compare the numerical velocities obtained with observations, first considering velocities measured in analogue experiments when injecting fluids of various viscosity (air and oils) in gelatin tanks, and secondly using diking events documented at basaltic volcanoes (such as Piton de la Fournaise (Réunion) and Mount Etna (Sicily)).</p>

SCC Growth Prediction for Surface Crack in Welded Joint Using Advanced FEA

Management of plant service life is a key issue for improving the safety of light water reactors. In boiling water reactor (BWR) plants, some incidents of intergranular stress corrosion cracking (IGSCC) of components in contact with the main coolant, such as a shroud support weld, have been reported in the past. When a crack is detected in a nuclear component, crack growth analysis is required as part of assessing the structural integrity of that component. In Japan, the “Rules on Fitness-for-Service for Nuclear Power Plants” of the Japan Society of Mechanical Engineers Code (JSME FFS Code) provides a simplified crack growth analysis method, assuming a semi-elliptical crack shape and calculating crack growth at the deepest and surface points of the crack. It is known, however, that the actual shape of the SCC is very likely to be different from a semi-ellipse due to the complex distribution of residual stress and the dependency of crack growth properties on the materials composing the welded joint, particularly in the case of a crack crossing the fusion line. Therefore, crack growth analysis techniques using finite element analysis (FEA) have recently been developed to analyze the crack growth behavior of a crack having a more detailed, natural shape. In crack growth analysis using the FEA technique, natural crack growth behavior in the materials composing the welded joint is estimated by using the reference curves of SCC. These reference curves are based on crack growth test data that are generally obtained with C(T) specimens prepared for homogeneous material. To demonstrate the applicability and adequacy of the analysis technique, it is important to validate the results of crack growth analysis using FEA. In this study, validation of the results of SCC crack growth analysis using FEA was conducted by comparison with the results of a SCC growth test. For the SCC growth test, a groove welded joint consisting of austenitic stainless steels was prepared. The welded joint was subjected to sensitizing heat treatment at 620°C for 24 h. A Lee-James specimen with a surface crack, whose crack plane crossed the fusion line between base and weld metals, was taken from the welded joint. After pre-cracking in air and in high-temperature water, the SCC crack growth test was conducted in a normal water chemistry (NWC) environment. Observation of the fracture surface revealed a transition from transgranular (TG) cracking to intergranular (IG) or interdendritic (ID) cracking, and broader IG morphology was observed on the base metal rather than on the weld metal due to a difference in the SCC growth sensitivity of both materials. On the other hand, a FEA model of the Lee-James specimen was prepared and SCC crack growth with a natural shape was analyzed by using FEA. Here, the observed crack front transitioning from TG to IG/ID was set as the initial crack front of the analysis. The reference curves of SCC growth rate for sensitized type 304 stainless steel and low carbon stainless steel in the JSME FFS Code were applied to the base metal and the weld metal of the specimen, respectively. A comparison of the analysis results with the fracture surface of the actual specimen confirmed that the analyzed crack shape generally showed good agreement with the observed crack shape on the fracture surface, although the analysis conservatively overestimated crack growth around surface points of the crack. Modification of the crack growth analysis was also investigated to obtain more accurate analysis results including around surface points of the crack.