Fuzzy modelling of powder snow avalanches

This paper examines powder snow avalanches by introducing a predetermined degree of variation, or fuzziness, in model parameters. Given a value of vagueness in the parameters, fuzzy set theory makes it possible to evaluate the vagueness in the results. The use of a more complex stochastic analysis can be avoided. Six parameters of the model are taken to be affected by a certain amount of uncertainty; the response of the numerical model is calculated by solving the fuzzy equations. In this way, it is possible to evaluate how the results are affected by a given change in the model parameters. The paper first presents a well-known avalanche model and its solution considering the influence of friction. A brief introduction of the fuzzy set is given with regard to the avalanche model mentioned. Later, the fuzzy solution of the model in terms of velocity and average pressure is calculated for three different levels of imprecision in the data. At the end, the results are presented and commented

Creep and Fracture in Concrete: A Fractional Order Rate Approach

The paper analyses the interaction between strain-softening and time-dependent behaviour in the case of quasi-static fracture of concrete. A viscous element based on a fractional order rate law is coupled with a micromecanical model for the fracture process zone. This approach makes it possible to include a whole range of dissipative mechanisms in a single rheological element. Creep fracture in mode I conditions is analysed through the finite element method, the cohesive (or fictitious) crack model and a new space and time integration scheme. The comparison with creep tests executed on three-point bending conditions shows a good agreement

Lifetime evaluation of concrete structures under sustained post-peak loading

Experimental tests on crack propagation in concrete under constant post-peak loading are simulated using the finite element method and the cohesive crack model, in both Mode I and Mixed-mode conditions. The time-dependent behaviour of concrete in the process zone is due to the interaction and growth of microcracks, a phenomenon which, for high constant load levels, turns out to be predominant over linear viscoelastic creep in the bulk material. In mechanical systems based on this type of material behaviour (creep and strain-softening taking place simultaneously), the initial value problem is non-parabolic, i.e., the error at one time level is affected by the accumulation of errors introduced at earlier time levels. Despite these difficulties, the scatter in numerical failure lifetime vs. load level turns out to be negligible in Mode I conditions and practically acceptable in Mixed-mode conditions. Therefore the time-dependent behaviour of the process zone can be inferred solely from the results of direct tensile tests

The cohesive frictional crack model applied to the analysis of the dam-foundation joint

The mechanical behaviour of dam-foundation joints plays a key role in concrete dam engineering since it is the weakest part of the structure and therefore the evolutionary crack process occurring along this joint determines the global load-bearing capacity. The reference volume involved in the above mentioned process is so large that it cannot be tested in a laboratory: structural analysis has to be carried on by numerical modelling. The use of the asymptotic expansions proposed by Karihaloo and Xiao at the tip of a crack with normal cohesion and Coulomb friction can overcome the numerical difficulties that appear in large scale problems when the Newton-Raphson procedure is applied to a set of equilibrium equations based on ordinary shape functions (Standard Finite Element Method). In this way it is possible to analyze problems with friction and crack propagation under the constant load induced by hydro-mechanical coupling. For each position of the fictitious crack tip, the condition K1=K2=0 allows us to obtain the external load level and the tangential stress at the tip. If the joint tangential strength is larger than the value obtained, the solution is acceptable, because the tensile strength is assumed negligible and the condition K1=0 is sufficient to cause the crack growth. Otherwise, the load level obtained can be considered as an overestimation of the critical value and a special form of contact problem has to be solved along the fictitious process zone. For the boundary condition analyzed (ICOLD benchmark on gravity dam model), after an initial increasing phase, the water lag remains almost constant and the maximum value of load carrying capacity is achieved when the water lag reaches its constant valu

Numerical modelling of ground-tunnel support interaction using bedded-beam-spring model with fuzzy parameters

The study of the ground-tunnel interaction by introducing a predetermined degree of variation (fuzziness) in some parameters of the chosen model is presented and discussed. This research comes from the consideration that tunnel model parameters and geometry are usually affected by a degree of uncertainty, mainly due to construction imprecision and the great variability of rock mass properties. The research has been developed by using the fuzzy set theory assuming that three model parameters are affected by a certain amount of uncertainty (defined by the so-called membership functions). The response of the numerical model is calculated by solving the fuzzy equations for different shapes of the membership functions. In order to investigate the effects of some model parameters, and to provide a simple procedure and tool for the designers, a study on the effect of tunnel boundary conditions, based on a fuzzy model, has been carried out using a simple but well known and widely used design method such as the bedded-beam-spring mode

Fracture Mechanics Characterization of an AnisotropicGeomaterial

Argillites are considered worldwide as potential host rock for high level radioactive waste given the low permeability and strong adsorption potential. However, the excavation of the galleries of a repository would produce a disturbed zone around the boundaries rich of new fractures which may enhance the conductivity of the rock along the gallery axis. Several mine-by experiments have been performed in underground rock labs to investi- gate the features of the disturbed zone. In Mont Terri URL (Kanton Jura, Switzerland) the EZ-B experiment was specifically conceived for the measurement of excavation induced fractures around a small chamber. The host rock of the URL is a particularly compact and resistant argillite, known as the Opalinus Clay (OPA) excavated and OPA samples were subjected to fracture mechanics tests at the rock mechanics lab of IGAG-CNR in Torino, Italy. The tests aimed at the understanding aspects of the fracturing process occurring in OPA of Mont Terri, which may be considered a transversely isotropic geomaterial, whose planes of isotropy coincide with the beddin

Modeling water penetration at dam-foundation joint

When fracture occurs in a concrete dam, the crack mouth is typically exposed to water. Very often this phenomenon occurs at the dam-foundation joint and is driven also by the fluid pressure inside the crack. Since the joint is the weakest point in the structure, this evolutionary process determines the load bearing capacity of the dam. In this paper the cracked joint is analyzed through the cohesive model proposed by Cocchetti et al. [Cocchetti G, Maier G, Shen X. Piecewise linear models for interfaces and mixed mode cohesive cracks. J Engng Mech (ASCE) 2002;3:279-98.], which takes into account the coupled degradation of normal and tangential strength. The water pressure inside the crack, which reduces fracture energy and increases the driving forces, is analyzed through the model proposed by Reich et al. [Reich W, Bruhwiler E, Slowik V, Saouma VE. Experimental and computational aspects of a water/fracture interaction. In: Bourdarot E, Mazars J, Saouma V, editors, Dam Fracture and Damage, The Netherlands: Balkema; 1994. p. 123-31.] and Bruhwiler and Saouma [Bruhwiler E, Saouma VE. Water fracture interaction in concrete. Part II: Fracture properties. Am Concr Inst J 1995;92:296-303; Bruhwiler E, Saouma VE. Water fracture interaction in concrete. Part II: Hydrostatic pressure in cracks. Am Concr Inst J 1995;92:383-90.]. Some numerical results are presented which refer to the benchmark problem proposed in 1999 by the International Commission On Large Dams. During the evolutionary process the horizontal dam crest displacement has been found to be a monotonic increasing function of the external load multiplier. As the fictitious process zone moves from the upstream to the downstream edge a transition occurs in the path of crack formation: the initial phase is dominated by the opening displacement, on the contrary afterwards the shear displacement dominates. Therefore, crack initiation does not depend on dilatancy. On the contrary the load carrying capacity depends on dilatanc

Numerical modelling of ground-tunnel support interaction using bedded-beam-spring model with fuzzy parameters

The study of the ground-tunnel interaction by introducing a predetermined degree of variation (fuzziness) in some parameters of the chosen model is presented and discussed. This research comes from the consideration that tunnel model parameters and geometry are usually affected by a degree of uncertainty, mainly due to construction imprecision and the great variability of rock mass properties. The research has been developed by using the fuzzy set theory assuming that three model parameters are affected by a certain amount of uncertainty (defined by the so-called membership functions). The response of the numerical model is calculated by solving the fuzzy equations for different shapes of the membership functions. In order to investigate the effects of some model parameters, and to provide a simple procedure and tool for the designers, a study on the effect of tunnel boundary conditions, based on a fuzzy model, has been carried out using a simple but well known and widely used design method such as the bedded-beam-spring model

Sub-critical cohesive crack propagation with hydro-mechanical coupling and friction

Looking at the long-time behavior of a dam, it is necessary to assume that the water can penetrate a possible crack washing away some components of the concrete. This type of corrosion reduces the tensile strength and fracture energy of the concrete compared to the same parameters measured during a short- time laboratory test. This phenomenon causes the so called sub-critical crack propagation. That is the reason why the International Commission of Large Dams recommends to neglect the tensile strength of the joint between the dam and the foundation, which is the weakest point of a gravity dam. In these conditions a shear displacement discontinuity starts growing in a point, called Fictitious Crack Tip (shortened FCT),which is still subjected to a compression stress. In order to manage this problem, in this paper the cohesive crack model is re-formulated with the focus on the shear stress component. In this context, the classical Newton-Raphson method fails to converge to an equilibrium state. Therefore the approach used is based on two stages : (a) a global one in which the FCT is moved ahead of one increment; (b) a local one in which the non-linear conditions occurring in the Fracture Process Zone are taken into account. This two-stage approach, which is known in the literature as a Large Time Increment method, is able to model three different mechanical regimes occurring during the crack propagation between a dam and the foundation rock

Hacking the Higher Education: Experiences from EduHack Course

At present e-learning courses have increased their importance but only a few universities use them, so it is crucial to explore the best ways of using this method for education. This paper is the result of a collaboration among some university teachers that recently have taken part to the EduHack course. The article aims to share their experience with a wider scientific community in order to promote a reflection on e-learning tools and methods specifically reserved for university teaching. This study highlights the structure and the organization of the EduHack course and presents Drag&Fly, the project idea developed by the authors during the collaborative part of the course, called EduHackathon. Some proposals to enhance the experience of participation are discussed by answering the following questions: What feelings did the EduHack course convey? What were its main strengths? What could be improved? Using concepts and categories of analysis widespread in the pragmatic theoretical tradition and adopting a qualitative analysis method based on the reconstruction of the experience through the participants’ observation, the Authors will analyze the learning generated by participating in the EduHack course. Its transformative potential will be investigated, as well as the possibility of changing the teachers’ approach to the design and implementation of a higher educational e-learning course