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Abstract: 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 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 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 value. [Copyright &y& Elsevier]

Abstract: 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, Brühwiler 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 Brühwiler and Saouma [Brühwiler E, Saouma VE. Water fracture interaction in concrete. Part I: Fracture properties. Am Concr Inst J 1995;92:296–303; Brühwiler 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 dilatancy. [Copyright &y& Elsevier]

The purpose of this study is to examine the numerical simulation of concrete specimens under high loading rates in tension. The data found in the literature are described: they show an increase in compressive and tensile strength as a function of the loading rate. To study this behaviour, we focused our attention on the assessment of the consistency model through the simulation of many experimental results related to a wide range of strain rates. In particular, the tests on unnotched and notched specimens performed at Delft University in recent years are examined. The proposed model is able to describe the increase in strength due to a high loading rate by an appropriate choice of the viscosity parameter. [Copyright &y& Elsevier]

The paper analyses the behaviour of concrete in the case of quasi-static fracture. The attention is focused on the interaction between strain-softening and time-dependent behaviour: a viscous rheological element (based on a fractional order rate law) is coupled with a micromechanical 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 and the cohesive (or fictitious) crack model. The comparison with creep tests executed on three-point bending conditions (three different load levels) shows a good agreement both in terms of failure-lifetime, and, load–displacement. [Copyright &y& Elsevier]

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 micromechanical 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. [Copyright &y& Elsevier]

The present paper is a review of the research works carried out on the cohesive crack model and its applications at the Politecnico di Torino during the last decade. The topic encompasses experimental, numerical and theoretical aspects of the cohesive crack model. The research work followed two main directions. The early work concerns the development and the implementation of the cohesive crack model, which has been shown to be able to simulate experiments on concrete specimens and structures. It is referred to as the dimensional analysis approach, since it succeeds in capturing the ductile-to-brittle transition by increasing the structural size owing to the different physical dimensions of two material parameters: the tensile strength and the fracture energy.On the other hand, the later research direction aims at extending the classical cohesive model to quasi-brittle materials showing (as they often do) fractal patterns in the failure process. This approach is referred to as the renormalization group (or fractal) approach and leads to a scale-invariant cohesive crack model. This model is able to predict the size effects even in tests where the classical approach fails, e.g. the direct tension test.The two research paths, therefore, complete each other, allowing a deeper insight into the ductile-to-brittle transition usually detected when testing quasi-brittle material specimens or structures at different size-scales. [Copyright &y& Elsevier]