A Theoretical Method To Determine The Tensile Strength Of Concrete Based On The Fracture Tests

The mesoscopic heterogeneity of the internal structure of the concrete greatly affects the macroscopic mechanical properties,resulting in the material being easily cracked under the tensile stress.As a basic mechanical parameter,tensile strength can be used to evaluate the tensile properties of materials,to predict the generation and propagation of cracks,to solve the cracking problem of concrete structures in practical engineering,and to provide safety assessment for concrete structural members.The direct tension test is commonly used to determine the value of tensile strength.However,it is widely accepted that the direct tension test is difficult to implement and is easily affected by the local stress concentration and the eccentricity.Therefore,a convenient and accurate method to determine the tensile strength of concrete is imperative for research and practical engineering.In this paper,a theoretical method for determining the tensile strength of concrete based on fracture test is presented.The proposed method is verified and analyzed.The results are listed as follows:（1）The method proposed in this paper is based on the fracture extreme theory.The tensile strength f_t of concrete is calculated by using the initial crack load P_ini and the peak load P_max measured in the fracture test.This method requires fracture test with only one specimen and avoids complex numerical integration and finite element modeling processes.In this paper,the method to determine the tensile strength of concrete is respectively established for the three-point bending notched beams,the wedge splitting test and the compact tension test.Through the comparison and analysis between the experiments and the results calculated by proposed method,it shows that the theoretical method proposed in this paper has good applicability and high accuracy to the above three commonly used fracture tests and can be applied to institutions and engineering practice.（2）The theoretical method proposed in this paper can determine the critical effective crack length to the specimen depth a_c/D and critical fracture parameters such as critical crack tip opening displacement CTOD_c of the specimen while determining the tensile strength.The comparison between the calculated results and the existing experimental results shows that the calculated values of a_c/D and CTOD_c are accurate and even more stable than traditional methods.In addition,the paper also analyzes the influence of various factors including initial effective crack length to the specimen depth a₀/D,specimen size and gradation on the calculation results.The analysis indicates that the calculation results are not sensitive to the above factors.It should be noted that in the comparison of the results of different gradations,the fracture of high-strength concrete with low water-cement will tend to brittle failure,which makes the material unable to fully exert the ability of crack-resistance and crack-resistance,resulting in error in calculation results of several specimens.（3）The tensile strength calculated by the method proposed in this paper is taken as a known parameter to verify the proposed method by the numerical simulation.Using the non-linear hinge model based on the toughness criterion and the finite element simulation method based on the cohesive element,the P～CMOD curves of the whole fracture process are determined.The accuracy of the proposed method is verified by comparing with the experimental data.The results show that the proposed method is not affected by the initial effective crack length to the specimen depth a₀/D of the specimen size,and is suitable for determining the tensile strength of normal concrete and aligned steel fiber reinforced concrete specimens.