Statistical Approach And Numerical Simulation Of Strength Size Effect Of Quasi-brittle Materials

The average strength of quasi-brittle materials such as rock, concrete, etc., which are of very importance in engineering application, presents size effect due to the heterogeneity. In orther words, the strength decreases obviously with the increase in size of materials. The statistical approach and the numerical simulation are widely resorted to in the research of this problem.In theoretical analysis, the classical Weibull size effect theory is first introduced briefly in this thesis. Then a statistical model for the strength size effect is established based on the weakest link model and the Poisson distribution of defects during the failure process of materials. The general expressions of the failure probability and the strength size effect are derived for the uniaxial stress state. From these expressions we know that with respect to volume the failure probability monotonically increases and the strength monotonically decreases. The strength varies very slowly and thus may be regarded as constant when the volume becomes very big within usual limited scope. As for defect free ideal materials, the issue of size effect no longer exists. The Weibull distribution and the lognormal distribution are then, respectively, introduced into the general expressions. The applicability of these expressions is demonstrated with the results of some typical uniaxial compressive strength tests of eight kinds of rocks and some three point bending strength tests of three kinds of concretes. It can be found that the two distributions are able to describe the size effect of quasi-brittle materials, with less strength given by using Weibull distribution at the same volume. The difference between the strengths from these two distributions is somewhat slight when the specimen volume is near the reference volume. The expression using the lognormal distribution can give more accurate strengths throughout the volume range, which is valuable in the strength evaluation through indoor test with small specimens. It is also concluded that the lognormal distribution can be used in the research of strength size effect by statistical approach as a simple improvement of the classical Weibull size effect theory.In numerical simulation, numerical tests of rock specimens with different sizes under compression, tension and three point bending are carried out by the Realistic Failure Process Analysis (RFPA^2D) code, and the numerical results of strength size effect are analyzed. It can be found that the peak strength and the residual strength of rock specimens decrease with the increase in specimen size. The change of the specimen size does not obviously change the failure patterns. The results of numerical simulation also fit well with the Weibull strength size effect theroy. In the fitting results, the degree of homogeneity can describe the difference of strength size effect of rock materials in different loading states. It is not a static variable but a dynamic parameter varying with loading patterns. If the degree of homogeneity is larger, i.e. the rock specimen is more homogeneous, the strength size effect is less obvious. Compared with the numerical results, it can be seen that the strength size effect is remarkable under three point bending test and is not apparent under compression test with lateral pressure. Now that the theoretical research of strength size effect needs still further more development, the numerical simulation by RFPA^2D code is an effective and straightforward approach which can be used in the research of quasi-brittle materials.