1、附录 A 外文翻译 Cellular Automata Approach to Durability Analysis of Concrete Structures in Aggressive Environments Abstract: This paper presents a novel approach to the problem of durability analysis and lifetime assessment of concrete structures(under the diffusive attack from external aggressive agents
2、. The proposed formulation mainly refers to beams and frames, but it can be easily extended also to other types of structures. The diffusion process is modeled by using cellular automata. The mechanical damage coupled to diffusion is evaluated by introducing suitable material degradation laws. Since
3、 the rate of mass diffusion usually depends on the stress state , the interaction between the diffusion process and the mechanical behavior of the damaged structure is also taken into account by a proper modeling of the stochastic effects in the mass transfer . To this aim, the nonlinear structural
4、analyses during time are performed within the framework of the finite element method by means of a deteriorating reinforced concrete beam element. The effectiveness of the proposed methodology in handling complex geometrical and mechanical boundary conditions is demonstrated through some application
5、s. Firstly, a reinforced concrete box girder cross section is considered and the damaging process is described by the corresponding evolution of both bending moment-curvature diagrams and axial force-bending moment resistance domains. Secondly, the durability analysis of a reinforced concrete contin
6、uous T - beam is developed. Finally, the proposed approach is applied to the analysis of an existing arch bridge and to the identification of its critical members. Introduction Satisfactory structural performance is usually described with reference to a specified set of limit states, which separate
7、desired states of the structure from the undesired ones. In this context, the main objective of the structural design is to assure an adequate level of structural performance for each specified limit state during the whole service life of the structure. From a general point of view, a structure is s
8、afe when the effects of the applied actions S are no larger than the corresponding resistance R. However, for concrete structures the structural performance must be considered as time dependent, mainly because of the progressive deterioration of the mechanical properties of materials which makes the
9、 structural system less able to withstand the applied actions. As a consequence, both the demand S and the resistance R may vary during time and a durability analysis leading to a reliable assessment of the actual structural lifetime Tashould be able to account for such variability (Sa1Ja and Vesika
10、ri 1996； Enright and Frangopol 1998a, 1998b). In this way, the designer can address the conceptual design process or plan the rehabilitation of the structure in order to achieve a prescribed design value Td of the structural lifetime. In the following, the attention will be mainly focused on the dam
11、aging process induced by the diffusive attack of environmental aggressive agents, like sulfate and chloride, which may lead to deterioration of concrete and corrosion of reinforcement ( CEB 1992 ) . Such process involves several factors, including temperature and humidity. Its dynamics is governed b
12、y coupled diffusion process of heat, moisture, and various chemical substances. In addition, damage induced by mechanical loading interacts with the environmental factors and accelerates the deterioration process ( Saetta et al. 1993 , Xi and Bazant 1999 ； Xi et al . 2000 ； Kong et al . 2002 ) . Bas
13、ed on the previous considerations, a durability analysis of concrete structures in aggressive environments should be capable to account for both the diffusion process and the corresponding mechanical damage, as well as for the coupling effects between diffusion, damage and structural behavior. Howev
14、er, the available information about environmental factors and material characteristics is often very limited and the unavoidable uncertainties involved in a detailed and complex modeling may lead to fictitious results. For these reasons, the assessment of the structural lifetime can be more reliably
15、 carried out by means of macroscopic models which exploit the power and generality of the basic laws of diffusion to predict the quantitative time-variant response of damaged structural systems. This paper presents a novel approach to the durability analysis of concrete structures under the environm
16、ental attack of aggressive agents The proposed formulation mainly refers to beams and frames, but it can be easily extended also to other types of structures. The analysis of the diffusion process is developed by using a special class of evolutionary algorithms called cellular automata, which are ma
17、thematical idealizations of physical systems in which space and time are discrete and physical quantities are taken from a finite set of discrete values. In principle, any physical system satisfying differential equations may be approximated as a cellular automaton by introducing discrete coordinate
18、s and variables, as well as discrete time steps. However, it is worth noting that models based on cellular automata provide an alternative approach to physical modeling rather than an approximation. In fact, they show a complex behavior analogous to that associated with differential equations, but b
19、y virtue of their simple formulation are potentially adaptable to a more detailed and complete analysis, giving to the whole system some emergent properties, self-induced only by its local dynamics (von Neumann 1966； Margolus and Toffoli 1987； Wolfram 1994, 2002； Adami1998). Noteworthy examples of c
20、ellular automata modeling of typical physical processes in concrete can be found in the eld of cement composites (Bentz and Garboczi 1992； Bentz et al. 1992,1994). Based on such an evolutionary model, the mechanical damage coupled to diffusion is then evaluated by introducing a degradation law of th
21、e effective resistant area of both the concrete matrix and steel bars in terms of suitable damage indices. Since the rate of mass diffusion usually depends on the stress state, the interaction between the diffusion process and the mechanical behavior of the damaged structure is also taken into accou
22、nt by a proper modeling of the stochastic effects in the mass transfer. To this aim, the nonlinear structural analyses during time are performed within the framework of the finite element method by means of a deteriorating reinforced concrete beam element (Bontempi et al. 1995；Malerba 1998； Biondini
23、 2000). The effectiveness of the proposed methodology in handling complex geometrical and mechanical boundary conditions is demonstrated through some applications. Firstly, a reinforced concrete box girder cross-section is considered and the damaging process is described by the corresponding evoluti
24、on of both bending momentcurvature diagrams and axial force-bending moment resistance domains. Secondly, the durability analysis of a rein-forced concrete continuous T-beam is developed. Finally, the proposed approach is applied to the analysis of an existing arch bridge and to the identification of
25、 its critical members. Diffusion Processes and Cellular Automata Modeling of Diffusion Processes The kinetic process of diffusion of chemical components in solids is usually described by mathematical relationships that relate the rate of mass diffusion to the concentration gradients responsible for
26、the net mass transfer (Glicksman 2000). The simplest model is represented by the Ficks first law, which assumes a linear relationship between the mass ux and the diffusion gradient. The combination of the Ficks model with the mass conservation principle leads to Ficks second law which, in the case of a single component diffusion in isotropic media, can be written as follows:
