Study On The Boundary And Size Effects Of Concrete And Rock Fracture Characteristics

Accurate determination of the material's true parameters and reasonable assessment of the actual structure's true characteristics have been the scientific and engineering community's unflagging goal.The fracture toughness and tensile strength are important material parameters for concrete and rock.However,under laboratory conditions,the material parameters determined by small-sized specimens have obvious size effects.In order to obtain the fracture parameters without size effect,large three-point bending?3-p-b?and wedge split?WS?are generally used,but this will cause defects such as large specimens weight,deviation of external force position,and complicated loading equipment and test methods.The main research contents and conclusions of this article on concrete and rock materials are as follows:?1?This paper presents a theoretical model and an associate specific application method for the fracture toughness and tensile strength of concrete can simultaneously be determined by using four-point-bending?4-p-b?specimens.The influence of different fictitious crack growth length on the determination of the fracture and strength parameters has been in-depth analyzed.The validity of the proposed model and associate method were confirmed by different experimental results.The results of this study gave a new ideal to determine the true material parameters of concrete.?2?Based on the theoretical model of boundary effect and size effect model,the fracture toughness and tensile strength without size effect can simultaneously be determined through the curve-fitting method,but the constraints of curve fitting have not been broken.In this paper,the boundary effect model is developed to a mathematical level,and a normal distribution fracture model and method are proposed.Through mathematical statistical analysis of a large number of experimental data,it is concluded that:for concrete materials,the characteristic crack length can be taken as 1.5 times the maximum aggregate size,and the normal distribution of the fracture toughness and tensile strength has the smallest dispersion;for rock materials,the characteristic crack length can be taken as 3.0 times the average grain size.The normal distribution of fracture toughness and tensile strength has the smallest dispersion.The determined fracture toughness and tensile strength using the normal distribution methodology are almost identical to those determined by curve-fitting method.Based on the fracture toughness and tensile strength obtained from the normal distribution fracture model,the fracture failure curve of concrete and rock can be established,and the obtained fracture failure curve is close to or even better than the curve fitting method.When the normal distribution fracture model adopts a 95%guarantee rate,the corresponding upper and lower limits??±2??can basically cover all the test data.The formula between the peak load Pmax and the equivalent area is derived based on the Characteristic crack length value and the fictitious crack growth length value obtained from the normal distribution fracture model.The predicted peak load P_maxax of the fracture toughness and tensile strength obtained from the normal distribution fracture model is almost the same as that obtained from the fitted test data.And when the normal distribution fracture model adopts a 95%guarantee rate,the corresponding upper and lower limits??±2??can basically cover all the test data.?3?This paper proposes a Weibull distribution fault model and method.According to the Weibull distribution of the virtual crack expansion at the crack tip,the quasi-brittle fracture process of concrete is studied.The fracture toughness and tensile strength law of concrete obtained by the Weibull distribution fracture model is the same as that of the normal distribution fracture model,which not only proves that the Weibull distribution is also applicable to the fracture analysis of concrete,but also verifies that the normal distribution fracture model is correct.