Topology Search Of Load Path And Truss Model Of Bearing Capacity For Corroded Concrete Beam Bridges

The safe operation of bridges is an important strategic demand for the healthy development of national economy and society.Concrete beam bridges account for a large proportion of the existing bridges in China.Under the long-term action of the adverse environment,the concrete beam bridges are prone to appear the concrete cracking and strand corrosion,which will cause the damage such as the deterioration of material property and bond behavior,affecting the normal use of the structure.It is necessary to evaluate and maintain the structure to ensure its service safety.The load path of corroded concrete bridges is of great significance for describing the force transmission mechanism,evaluating the structural performance and guiding the structural maintenance.The present study aims at studying the load path of corroded reinforced concrete(RC)structure and corroded prestressed concrete(PC)structure.The generation method of the load path for corroded RC structures,the bond degradation for corroded strands and multi-strand tendons,the development law of the load path for corroded PC structure under the bond degradation,and the optimal load path-based truss model for predicting the bearing capacity of corroded concrete structures,are mainly studied.The main works of this research are as follows:(1)A generation method of load paths for corroded RC structures is presented based on the automatic stiffness adjustment method.The search of load path for corroded RC structure is a nonlinear topology optimization problem.The conversion of material density during the nonlinear topology optimization results in the excessive distortion of minimum-density elements,which will lead to the numerical instability in load path searching.An automatic stiffness adjustment method is first proposed to overcome the numerical instability in load path searching.The multi-proportional growth strategy of the minimum-density element stiffness is developed according to the change of the maximum strain.On this basis,a generation method of load paths for corroded RC structures is presented by considering the material properties loss and bond degradation.The design sensitivity in the form of the corrosion-damaged strain energy is then derived based on the adjoint variable method.Finally,the effectiveness of the proposed method is illustrated by the numerical examples.The load paths of corroded RC beams under various corrosion levels are studied.(2)A bond strength analytical model of corroded strands is established by considering the non-uniform mechanical interlock.The bond degradation of corroded strands will affect the load path of PC structures.The interaction between the helical strand and concrete will cause the non-uniform mechanical interlock force at the interface.First,the expression of bond stress under the non-uniform mechanical interlock force is derived based on the three-dimensional force characteristics at the spiral bond interface of steel strand.The effects of the chemical adhesive force,confinement force and expansion force on the bond strength of corroded strand are considered.Then,a theoretical model on the bond strength of corroded strand is established by considering the non-uniform mechanical interlock force.Finally,the proposed model is verified by comparing with the experimental bond strength of corroded strand.The effect of the mechanical interlock on the bond strength of strand is quantified.(3)A bond-slip model of multi-strand tendons based on the interface equivalent principle is established in this study.The bond behavior between corroded tendons and grout is the key factor to generate the load path of post-tensioned PC structure.An interface equivalent principle,considering the effects of the quantity,the arrangement and the space of strands,is firstly presented to determine the effective bond interface between tendons and surrounding grout.Then,the maximum bond stress of the multi strand tendons provided by the interface is derived and incorporated into the existing bond stress-slip relationship to characterize the bond of multistrand tendons.Subsequently,a pull-out numerical model incorporating the considered effects is developed to predict pullout forces-slip response for tendons.Finally,a direct pull-out test on three strands tendons is designed to verify the proposed model by comparing with the numerical and experimental results.The proposed model is also validated against the previous experiment on seven strand tendons.(4)A generation method of the optimal load path for corroded PC structures is proposed by considering the bond degradation.First,the modelling methods of corroded material properties,bond degradation,shape preservation of local area and prestressing force in PC structure are introduced.Then,the local automatic stiffness adjustment method of the minimum density element is developed to overcome the numerical instability during the search of load path.Subsequently,the optimization formula for the problem of the load path search is given by considering the bond degradation,and the sensitivity formula of corroded PC structure is derived based on the adjoint method.Finally,the effectiveness of the proposed method is illustrated by the numerical examples of pretensioned and post-tensioned PC structures.The load paths distribution of PC structures under different loads,corrosion rates and local damage positions are discussed.(5)A method of determination the truss model based on the optimal load path of corroded concrete structures is presented.The load paths of corroded RC beams,considering the various shear span-depth ratios,stirrup ratios and loading methods,are first studied based on the proposed generation method of load paths.The truss model incorporating multiple variableinclination struts is then developed based on the load paths of corroded RC beams.Subsequently,the limiting failure criteria of the proposed model and the inclination angles of concrete struts are presented to estimate the shear capacity of corroded RC beams.Finally,the proposed model is verified by comparing with the experimental results of uncorroded and corroded RC beams.The load path-based truss model of corroded PC structure can be determined according to the same method.