Study On The Reliability Of Flexural And Shear Capacity Formula Of Reinforced UHPC Members

Ultra-high performance concrete(UHPC)has been widely used in bridge engineer-ing,and many countries have put forward the design specifications and technical guide-lines for UHPC.In order to ensure that the UHPC structure in the bridge is in a reliable state,and the reinforced UHPC beams in the code meet the reliability requirements in flexural and shear state,the flexural and shear capacity formula and reliability of the reinforced UHPC beams in the codes of various countries are deeply analyzed:(1)In order to obtain material property variability parameters of UHPC,the test results of 648 cube compressive strength and 210 axial tensile initial crack strength at home and abroad are sorted out.The compressive strength and tensile strength of UHPC are in accordance with the normal distribution based on the fitting results,and the mean value and coefficient of variation of UHPC material strength drops when the strength level of UHPC increases.(2)Extensive collection of flexural and shear test beams was carried out,based on the published papers by researchers all over the world.By screening 187 flexural test beams and 371 shear test beams,the database of 105 flexural beams and 206 shear test beams is established.(3)Based on 105 reinforced UHPC flexural test beams in database I,the calcula-tion errors of various codes at home and abroad are analyzed,and the relationship between the parameters of flexural test beams and the calculation errors is discussed.The calculation errors and the variation coefficient of flexural capacity formula in Swiss code and FHWA report are the smallest.The accuracy and safety of the Chinese and French code formulas are better.The calculation error of flexural capacity is re-lated to the reinforcement ratio and tensile strength of UHPC:the higher the tensile strength,the lower the reinforcement ratio,and the greater the calculation error.(4)Based on 206 UHPC shear test beams in database II and database III,the cal-culation formulas of shear capacity of nine codes are compar ed,and the predicted and experimental values of shear capacity of beams without web reinforcement and beams with web reinforcement are compared.At the same time,the correlation between test beam parameters and calculation error in beams without web rein forcement is deeply analyzed.Compared with the flexural capacity,the predicted values of shear capacity of UHPC beams in various codes are relatively conservative,among which the formu-las of French code,Chinese code in process and steel fiber code are relatively accurate,while the formulas of the American code and the Swiss code have a large r deviation.The shear span ratio and reinforcement ratio have strong correlation with the calcula-tion error:In a certain range,the higher the reinforcement ratio,the lower the shear span ratio,and the greater the calculation error.(5)By using JC method and Monte Carlo important sampling method,the relia-bility of flexural and shear formulas in Chinese code,French code,Swiss code and American ACI code is studied.The reliability index of Swiss code is the highest and that of American code is the lowest,which is lower than the target value of 3.5 accord-ing to the results.And the reliability index of Swiss code is the highest and that of Chinese code is the lowest,which is lower than the target value of 4.7.The shear reli-ability indexes of Chinese codes in process,French codes and Swiss codes are lower than the corresponding flexural reliability indexes,while the American codes are on the contrary.The factors having greater effect on the reliability index of UHPC section are live load ratio and reinforcement ratio,while the influence of material strength can be ignored according to the sensitivity analysis of flexural reliability.When it comes to shearing,the influence of material strength and shear span ratio on the reliability index is limited,while the influence of stirrup ratio and live load ratio on the reliability index is significant.(6)Based on the comprehensive comparative analysis of flexural and shear relia-bility in various countries,the partial coefficient of UHPC materialγ_c=1.25 in the flex-ural capacity formula of Chinese code,and the reduction coefficient of matrix and fiber in the shear capacity formulaφ1=0.8,and the reduction coefficient of stirrupφ2=0.88are calibrated with the flexural target reliability indexβT=4.2 and shear target relia-bility index βT=4.7.Based on the target reliability indexβT=3.5,the flexural capacity reduction factor of American ACI codeφis calibrated to be 0.80.(7)Based on database II and database III,considering the influence o f shear span ratio and longitudinal reinforcement ratio,the modified shear capacity formula of re-inforced UHPC beam is proposed.Error analysis and reliability calculation show that the modified formula can effectively reduce the discreteness of calculati on,and the reliability index of beam with web reinforcement can meet the requirement of target reliability index βT=4.7.