Calculation Model And Experimental Investigation Of Modulus Of Elasticity In Ultra-high Performance Concrete

As the critical mechanical property in concrete engineering,elastic modulus is a measure for the elastic deformation resistance.With the required concrete strength but low elastic modulus,member stiffness decreases and its deformation under load increases,finally cannot be used as normal.Elastic modulus of concrete usually increases with the increased compressive strength.As a new cementitious material,ultra-high performance concrete(UHPC)is famous for its ultra-high strength,high toughness,and excellent durability.The compressive strength exceeds 120 MPa,which is 1.5 times higher than that of plain concrete and high strength concrete.However,its elastic modulus is 40-55 GPa,only about 20%higher than that of plain concrete and high performance concrete,whose increment is significantly lower than that of compressive strength,making UHPC application more difficult.Improving the elastic modulus of UHPC can strength the stiffness of concrete member,and reduce its production cost and energy consumption,which is of great significance to the sustainable development of UHPC.For the purpose of UHPC elastic modulus regulation,this paper mainly focuses on the microstructure and macro properties,and investigates the component design,mechanical properties,and constitutive relationship of UHPC with high elastic modulus.In the first section of this study,an analytical model of elastic modulus in UHPC was proposed based on composition to analyze its key factors and corresponding increments.This model combines a multi-scale model and homogenization method,and takes the volume fractions and elastic moduli of composed phases at various scales as inputs,finally estimates the elastic moduli of UHPC at micro-,meso-,and macro-scales.The model was first verified using measured elastic moduli of cement paste,mortar,and UHPC in literature.The effects of water-to-binder ratio,coarse aggregate content,and steel fiber content on compressive strength and elastic modulus were then experimentally evaluated to verify the applicability of the proposed model.Experimental results were in good agreement with the calculated results from the proposed model.Quantitative analyses of the effects of key factors on the elastic modulus of UHPC using the proposed model indicated that water-to-binder ratio was the most important factor,followed by coarse aggregate content,sand content,cement content,steel fiber volume,slag and silica fume content.Then selective dissolution,thermogravimetric analysis,and X-ray diffraction were utilized.The degrees of reaction of cementitious components in UHPC paste and their interactions were investigated,and their influences on elastic modulus of UHPC were discussed.The statistical model for the elastic modulus of UHPC with degree of reaction of cementitious components was established,which provides a theoretical basis for the preparation of UHPC with high elastic modulus.Results showed that improving the degrees of reaction of silica fume and slag can make cement fully consumed and bring out their optimal performance.However,the cementitious components affect each other in the reaction process,which affects their degree of reaction.The reaction degrees of both silica fume and slag in the binary paste were higher than those in ternary paste;the addition of silica fume or slag delayed the reaction process.In addition,the degree of reaction of different cementitious materials had different influences on the elastic modulus of UHPC.Increasing the degree of reaction of cement had a positive effect on improving the elastic modulus,and the significant level was the highest,followed by those of silica fume and slag.Compared with the cement,the degree of reaction of slag had less influence.In the third section,the effects of coarse aggregate content on UHPC compressive behavior were investigated.Based on the effects of fiber and aggregate content,the prediction equations of key parameters of UHPC compressive behavior were proposed.The constitutive relationship of UHPC compression performance incorporating coarse aggregate with high elastic modulus was established.It was found that with the increase of coarse aggregate content,the compressive strength of UHPC gradually increased and decreased after reaching the maximum value,while the elastic modulus increased and elastic modulus of the sample containing 1200 kg/m~3 coarse aggregate was 61 GPa.The peak strain of UHPC reduced continuously,while the compressive toughness increased first and then decreased.Meanwhile,the synergic effect of fiber and coarse aggregate is related to aggregate contents.When its content increases to the optimum value,the optimal packing density is obtained,and steel fibers are uniformly distributed in the rigid skeleton.However,the fiber dispersion and direction are affected and crack restraint from fiber is limited in UHPC with excessive aggregate content,resulting in UHPC compressive performance reduction.Finally,this paper investigates the effects of different types of coarse aggregate with high elastic modulus on the mechanical properties of UHPC.Based on the factorial design method,the influences of three types of coarse aggregate,basalt,limestone,and brown corundum,on the properties and microstructure of UHPC were explored,and the correlations between coarse aggregate type and content and UHPC properties were discussed.The compression and flexural constitutive relationships of UHPC with three types of coarse aggregate with high elastic modulus were established.Results showed that UHPC workabilities were decreased with the increased brown corundum and basalt,while improved with the increased limestone.The addition of a certain volume of basalt or brown corundum can effectively improve the elastic modulus and compressive strength of UHPC;UHPC elastic modulus was higher than64 GPa when brown corundum volume was 100%.Mixing limestone reduces the compressive strength and elastic modulus,and was less effective in improving UHPC compressive behavior,but the compressive stress-strain curve and flexural load-displacement curve of UHPC containing limestone had great ductility.Afterwards,based on scanning electron microscopy and energy spectrum analysis(SEM-EDS),results indicated that the enhancement mechanism of UHPC made with coarse aggregates with high elastic modulus and their ITZ microstructures were related to the chemical composition of coarse aggregate,and then affected the mechanical properties of UHPC.