Experimental Study And Theoretical Analysis Of Multiple Hooked-end Steel Fiber Reinforced Concrete Subjected To Uni-axial Tensile And Flexural Properties

Steel fiber reinforced concrete（SFRC）has excellent physical and mechanical properties,which has been widely used in civil engineering and other fields at home and abroad.So far,the research on straight and single hooked-end（3D）steel fiber reinforced concrete has made great progress,while the research on multiple hooked-end（4D and 5D）steel fibers reinforced concrete is still in the primary stage.Therefore,based on the National Natural Science Foundation of China-Henan Joint Foundation Key Project（U1704254）,this paper carried out the tests on the bonding behavior of multiple hooked-end steel fiber and cement mortar,the uni-axial tensile stress-strain constitutive relationship,the uni-axial tensile stress-crack width constitutive relationship and the flexural properties of beams with multiple hooked-end steel fiber reinforced concrete.The effects of the steel fiber hook number,steel fiber volume fraction,steel fiber aspect ratio and concrete strength were systematically analyzed.The main contents are as follows:（1）A pullout model for straight steel fiber in cement mortar was established according to the right-and left-sided anchorages.To reflect the mechanical anchoring force of fiber hooked part,the residual friction of fiber hook straightening part and the friction of fiber straight part,the calculation method for changing rate of curvature（R）was proposed by considering the curvature reduction of the fiber plastic hinge;the analytical equations of elastic-plastic responses of the fiber beam with circular section were modified using the regression method,and the area conversion rule（ACR）for the original and normalized curves was presented and proved;based on the law of energy conservation,the modified elastic-plastic responses of the fiber beam,the ACR and the modified frictional pulley model,the fiber cold drawing force generated by one plastic hinge(F_PH)and the total mechanical anchoring force of fiber with n plastic hinges were obtained;the fiber hook straightening and straight parts were further considered,and the pullout models of multiple hooked-end steel fiber were finally proposed.（2）Based on the bonding mechanism of the fiber-matrix interface,the calculation formula of tensile strength（including splitting tensile strength and uni-axial tensile strength）and the four-segment uni-axial tensile stress-strain constitutive relationship of SFRC were proposed,in which the influences of different parameters were considered.（3）By considering the effects of fiber embedded angle,fiber embedded length and concrete crack width,the diverse angle-length-width model（DAM）reflecting theσ-w relationship was proposed.A test method forσ-w relationship of SFRC was also proposed.（4）Based on the non-linear hinge model,the polylinearσ-w constitutive relationship and the modified integration by substitution,the closed-form solutions of the full process analysis of SFRC notched beams subjected to bending was established,and the polylinearσ-w relationship of SFRC was obtained by using the inverse analysis method;by considering the effects of the fiber hook number,fiber volume fraction,fiber aspect ratio,fiber yield strength and concrete strength,theσ-w relationship expressed by the polylinear form was transformed into the polynomial form;based on the established polylinear and polynomial stress-crack width constitutive relationships of SFRC,the theoretical and semi-theoretical calculation methods for the residual flexural strengths of SFRC were proposed.