Research On Damage Constitutive Theory Of Concrete And Its Application In Seismic Analysis Of Long-Span Bridge

Long-span concrete bridges, as lifeline engineering, are the throat of economic life line at the peacetime, and also are the inevitable roads to transport the disaster-relief materials together with the equipment and evacuate the people afflicted in the calamity. To a great extent, the post-seismic worsen state of long-span bridges will affect the succor of post-disaster. The constitutive relationship is the hypostasis among the reason which affect the responses of postquake structures, with excitation, boundary condition and structural style being given. For its innate defects and postnatal own mechanical behaviors, the damage models are rational and applicable to analyse the action of concrete materials as well as concrete structures in service.The object of this dissertation includes: research on damage mechanism of concrete material and the theoretical base of damage constitutive relationship, deduction of irreversible thermodynamic formulations of damage course, general dynamical damage model, and global damage index based on the equivalent free energy. The study on the damage behaviors and damage status of a long-span concrete bridge can be made in succession based on the theoretical model previous which can be helpful to assess the three levels of earthquake loss in the material, component and structure simultaneously. The quantificational measures can be supplied to the present rational design scheme at the stage of layout, the corresponding reinforcing measure of the existing bridges, and the rapid repair and reinforcement of those surviving structures according to the method in this essay. Consequently, analysis on seismic responses of large-scale complicated bridges and exploration of damage assessment of the system will be of practical and long-term strategic significance, which will ensure safe and reliable running of great bridges suffering intense seismic effect.In this essay, several aspects were analysed concerned with seismic weakened behaviors as following:1. Description of historical and actual study on the seismic breakage of bridge systems and damage constitutive models were supplied. With the characteristic of the issue to be faced to being considered, the corresponding research treatment and technical line were set down on the ground of the achievement published according to the specialty of the questions be suffered (Chapter one).2. The damage mechanism and analysis means of concrete material were described. The course of construction of damage mechanics model and the axiomatic were discussed. The expressions of the first and the second laws of thermodynamic theory were deducted. According, the key and difficult problems were pointed out (Chapter two).3. The modified Drucker-Prager yielding surface and the corresponding plastic potential function were expressed in view of the difference strength between tension and compression as well as the sensitivity to hydrostatic stress and nonassociative yielding flow. Appropriate formulations of Helmholtz free energy were formed based on elastic strain energy, and expressions of damage variable were recommended in virtue of the definition of fracture energy, then the relevant damage criteria and evolution equation were supplied. Thus the elastoplastic scalar-damage constitutive equations were deducted with the aid of the thermodynamics (Second and Third passage of Chapter three).4. Research on the strain rate dynamical damage theory was made to couple the damping process into the continuous tangent stiffness matrix, with the kinetic hardening effects being considered. The damping effect was included through viscoelastic constitutive (Fourth and Fifth passage of Chapter three).5. The algorithmic functions of stress, strain and damage variable were supplied on the ground of discrete time step. The two-step map returning method (closest project point method) which is rational for elastoplastic damage models based upon implicit backward Euler scheme was expressed according to the stress upgrade operation, with plastic potential being equivalent to the yielding function. The plastic parameter and consistent tangent stiffness tensor was deduced which meet the convergent condition supposition. The constitutive integral Jacobi matrix of plane stress and 3D beam elements were listed (Second passage of Chapter four).6. The user material subroutines(UMAT) of planestress element and 3D beam element were programmed in Fortran language based on the commercial code, then the access subroutines to fetch data from running process and postprocess results were compiled. The tests data published verified the models used in the dissertation (Third passage of Chapter four).7. The general frame of finite element method (FEM) to analyse the structural dynamic damage response was put forward. The Jacobi matrices in common use were given and the integral formulations of the section internal forces of the elastoplastic damage beam were deduced, from which the kinetic equation could be found. Simulation on the nonlinear seismic deterioration behaviors of a long-span cable-stayed concrete bridge were implemented using the program above. The damage variable evolution curves were obtained of the structural system subjected to seismic excitations (Chapter five).8. The damage index expression was deduced from the weights of element volumes of the damage variable and stress-strain state on the Gauss integral points as a result of the theory of equivalent of free energy between damaged states and undamaged status. The finite element method was also developed to find the degrading extent of structural components and the system. Damage assessment of the postseismic structure was performed on account of the standard refered to the publication, which suggested the rationality of the design scenario (Chapter six).9. Several constructive summings-up and the issues to be faced with the viable aspects were summarized on the ground of the theoretical and experimental research in this essay (Chapter seven).The following conclusions can be gained through the comparable results of calculation and the experiment:1. Damage axioms are the theoretical bases of damage mechanics, from which we can get general damage constitutive models with the essential materials theorems, thermodynamic rules and Noll's axioms being given;2. The key points of damage mechanical issues comprises of damage variable, damage potential function and damage evolution equation, solution of which means the complete of damage model;3. The damage model of constitutive equation and element as well as the algorithm in this essay are reasonable for consistency between the theoretical and experimental data.4. It is given great attention to that the safety and stability of long-span concrete bridge subjected to earthquake. So it is constructive for the reasonable design to develop advantage theoretical method by which the seismic response of complex structural system can be forecast and investigated.5. As a thermodynamic course, the damage process is irreversible and the damage variable is decreasing parameter with increment of load. When damage variable comes to be one, material failures on the integral point concerned.6. The global damage index is an average quantity of damage variable on the integral points respect to the weight of element volume. However, the index mentioned before is of evident physical mechanism and can describe the essence of structural weakening for the equivalent free energy theory being accepted. The previous model could be helpful to assess the three levels of earthquake loss in the material, component and structure simultaneously, which is of great theoretical importance for large-scale complicated structural engineering.7. The structural damping is included in the constitutive equation by strain rate effect, which is consistent with the physical mechanism and of strictly physical meaning.8. Investigation on concrete materials, especially on the damage behavior large-scale concrete structures, needs the support of plentiful experiment. Simulation based on the increasingly perfect and deepening theoretical models in the dissertation is an alternative with the lack of finance.