Research On Deformation Limits And Restoring Force Models Of Steel Reinforced Concrete Columns And Shear Walls

The performance-based seismic design and evaluation method has been well-known by scholars and designers and has been widely used.The quantification of component performance is the key for achieving the design and evaluation of component-level seismic performance.On the other hand,steel-reinforced concrete（SRC）components have been widely adopted in practical engineering and have become one of the main types of load-bearing components,due to their high bearing capacity and high ductility.To meet the needs of engineering,it is necessary to accurately quantify the performance levels of SRC components.However,a reasonable and accurate deformation index system for SRC components has not been established.Therefore,to promote the application of performance-based seismic design and evaluation method in SRC structures,this paper systematically studied the performance levels and deformation index limits of SRC columns and shear walls,and established their restoring force models.The work and main conclusions of this paper are as follows:（1）The performance level division method and deformation limit calculation method of SRC components were proposed.SRC components can be divided into six performance levels（PLs）before the failure state,namely no damage,slight damage,mild damage,moderate damage,relatively severe damage,and severe damage,and denoted as PL1 through PL6respectively.The drift is selected as the component deformation index,and the drift limits（performance points）of the six PLs are determined by the characteristic points on the skeleton curve.The drift limit of PL1,θ₁,is taken as the equivalent yield point,and the drift limit of PL5,θ₅,adopts the drift ratio where a 20 percent degradation occurs in lateral strength.The drift limit of PL6,θ₆,employs the lower drift ratio corresponding to either the axial failure or the 50%drop of the lateral strength,whichever is less.Furthermore,the drift limits of PL2,PL3,and PL4,θ₂,θ₃,andθ₄,are taken as each of the quartiles betweenθ₁ andθ₅,respectively.The damage extent corresponding to each PL was described according to the test conducted by the author.The mean absolute value of the relative errors between drift limits calculated using backbone curves and those derived from damage states does not exceed 23.42%.It was verified that the above PL division method is reasonable.（2）The rationality of the drift limits of SRC components was evaluated,and the problems were pointed out,by comparing the drift limits of SRC components with those of RC members provided in DBJ/T 15-151-2019（named the Performance Code hereafter）.The results show some phenomena contrary to the structural concept:1)the drift limits of flexural-controlled SRC columns would be smaller than those of RC columns with the same parameters when bearing the equal axial force;2)under the same axial force,the drift limits of shear-controlled SRC shear walls are smaller than those of RC shear walls with the same parameters.In some cases,the drift limits of SRC shear walls are less than 50%of the drift limits of RC shear walls with the same parameters.It indicates that the drift limits of SRC columns and shear walls given by the Performance Code are unreasonable.（3）The experimental study on the seismic behavior of 30 SRC（RC）columns and 21rectangular SRC shear wall specimens was carried out.And the rationality of the above drift limits was further analyzed.The variation parameters of SRC columns were axial load ratio,steel ratio and shear-span ratio,and one RC reference specimen was set for each shear-span ratio group.The test parameters of SRC shear walls were axial load ratio,steel ratio,shear-span ratio,boundary stirrup ratio and horizontal reinforcement ratio.The hysteretic curve,skeleton curve,lateral strength,ductility,stiffness degradation,energy dissipation capacity as well as deformation capacity of both SRC columns and shear walls were analyzed.The results show that:1)under the same axial force,the drift limit of the SRC column is significantly larger than that of the RC column,and brittleness was not recorded in SRC columns that failed in shear.The shear-span ratio and failure mode have no obvious effect on the drift limit and ductility of the SRC columns.2)the average ratios of the calculated values according to the Performance Code and the test values are only 0.41,0.43 and 0.46,respectively,for the three key drift limits（θ₁,θ₅ andθ₆,）of shear-controlled SRC columns.3)the average ratios of the calculated values according to the Performance Code and the test values are only 0.74,0.39 and 0.41,respectively,for the three key drift limits of shear-controlled SRC walls.It can be concluded that the drift limits of shear-controlled SRC columns and shear walls in the Performance Code are too conservative and should be modified.（4）An experimental database containing 287 SRC columns and 104 SRC shear walls was established,and the drift limits for SRC columns and SRC shear walls were modified.Through parameter selection and parameter quantity optimization,control parameters for the three key drift limits of SRC columns and shear walls were determined.Then,regression formulas were established for the three key drift limits.The probabilities of exceedance for the key drift limits of SRC columns and shear walls were determined.Based on the regression formulas and the exceedance probabilities,drift limit tables for SRC columns and SRC shear walls were established.Then,the drift limit tables were evaluated using the tests performed in the study.The results showed that the average calculated-to-test values increased to 0.76,0.68,and 0.73,respectively for the three key drift limits of the shear-controlled SRC columns.And the values increased to 0.97,0.81,and 0.83,respectively,for SRC shear walls.So,the drift limits established in this paper are more accurate and reasonable.（5）The prediction accuracy of key drift limits of SRC columns and SRC shear walls was significantly improved by using the random forest（RF）algorithm.The model comparison results show that except for theθ₆ of SRC shear walls,the R² of the RF models is significantly higher than that of the linear regression models.The R² of the RF models is between 0.765 and0.944,the average prediction-to-test ratios are between 1.032 and 1.108.while the R² of the linear regression models ranges between 0.429 and 0.784,and the average prediction-to-test ratios are between 1.025 and 1.166.The modified drift limit tables in this paper have a certain degree of conservatism due to the adjustment according to the exceedance probability,with R²of 0.322～0.518,and average prediction-to-test ratios of 0.826～1.125.While the accuracy of the models proposed by other scholars based on finite element analysis is generally poor,with mostly negative R² and average prediction-to-test ratios of 0.521～1.852.（6）The flexural and shear strength formulas for SRC columns and shear walls were evaluated using the collected database,and some modification was made.The evaluation results show that the formulas given in the current code can provide accurate flexural capacity for SRC columns and shear walls,with average prediction-to-test ratios of 0.98 and 0.95,respectively.The formulas provided by the codes and other scholars cannot accurately calculate the shear strength of SRC components.And most of them generated conservative calculated results.The shear strength formulas proposed in this paper can generate more accurate results.The average calculated-to-test ratios are 1.01 and 1.00,for the shear strength of SRC columns and shear walls,respectively.（7）Restoring force models of SRC columns and shear walls considering the degradation effect of cyclic loading were proposed respectively.Using the fitting results of the test database and the drift limits established in this paper,the skeleton curve of the restoring force model is calculated to consider the influence of the component parameters on the skeleton curve.Based on the database,the relationship between unloading stiffness,reloading stiffness and damage index of components was established,so that the restoring force models proposed in this paper can consider the strength degradation caused by the cyclic loading process.The restoring force models proposed in this paper fit well with the hysteretic curve of the test.The research results of this paper can be used for the fast and accurate elastic-plastic analysis of SRC structures,and provide reliable judgment criteria for the performance evaluation of SRC columns and shear wall components,which will greatly promote the development of the performance-based seismic design and evaluation of SRC structures.