| Accidents caused by tensile failure of brittle materials such as rock and concrete are common in geotechnical engineering.At present,the test method of the tensile strength of brittle materials generally adopts the splitting test.The commonly used splitting tensile specimens are cylindrical and cubic specimens.The theoretical analysis and experimental research on the splitting tensile strength of disc-shaped specimens are relatively complete,while the splitting tensile strength of the cubic specimen is directly calculated by the theoretical formula based on the disc specimen,which lacks theoretical basis.And numerical simulation research on the splitting test of the cubic specimens often only considers the elastic properties of the material,the influence of the plastic change of the material and the load distribution on the loading surface on the results of the splitting test is ignored.Combined with the standard,the analytical solution of the stress components inside the cubic specimens under the symmetrical load is deduced;The finite element method is used to simulate the splitting tensile strength characteristics of the cubic specimens under the elastic model and the plastic damage model.It is founded that the splitting tensile strength of the specimen calculated by the standard formula is small.The main conclusions can be given as follows:(1)Based on the theory of complex variable,the analytical solutions of the stress components inside the cubic specimens are deduced under the concentrated load,uniform load and complex load.Combined with the results of the analytical solution of the stress components,the differences in the calculation of the splitting tensile strength of the four tensile strength criteria are compared and analyzed,and the change of the location of the specimen’s crack initiation is summarized.The results show that with the increase of the width ratio of the loading surface,the tensile stress at the center of the specimen gradually decreases,and the error caused by the standard formula to calculate the splitting tensile strength of the specimen becomes larger.(2)Two-dimensional and three-dimensional numerical method were carried out under elastic conditions for the wooden strip loading mode and uniform displacement loading mode.The analysis focuses on the influence of the ratio of the width of the loading surface on the plane and spatial stress distribution of the specimen,as well as the maximum equivalent stress and the initial crack initiation on the splitting surface of the specimen under the two loading modes.The correction formula of splitting tensile strength considering the width of the loading surface is proposed.It is found that as the width of the loading surface increases,the maximum equivalent stress on the specimen surface gradually decreases,and the position of the crack initiation gradually moves to the center of the specimen’s end surface.Compared with the wooden strip loading mode,the specimens under the uniform displacement loading mode are easier to meet the requirements of cracking from the center.In the wooden strip loading mode,when the width of the wooden strip changes within the range of 15mm～20mm,the result using the standard formula is 18.6%～4.7% smaller.(3)Based on the numerical simulation results of concrete splitting test considering plastic damage,comparing the results obtained by different methods,it is found that the result of the correction formula proposed in this paper is closer to the uniaxial tensile strength.For the splitting test using cubic specimen,it is recommended that the width ratio of the loading surface should be about 16.7% under the wooden strip loading mode,and the width ratio of the loading surface should be about 23.3% under the uniform displacement loading mode. |
