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Rock, concrete, etc., as widely used in the construction of quasi-brittle materials, as heterogeneity, the average intensity of destruction when there is an obvious size effect that, as the material size increases, its strength will be significantly lower than a constant. In this regard, the statistical approach and numerical simulation of quasi-brittle material strength size effect is an important research method. In the theoretical analysis, this paper first Weibull statistical size effect of the classical theory for a brief introduction, as a basis, this paper based on the weakest chain model and assuming a Poisson distribution of defects, comprehensive volume and material factors, established in uniaxial stress situations , the quasi-brittle material failure probability and strength size effect on the statistical model and the general form of expression. It can be seen as the volume increases, the intensity decreases, in the usual limited range of scales, when the volume is large, small changes may be regarded as constant intensity, defect material is not the size effect. Respectively, the Weibull distribution and lognormal distribution, strength size effect was specific forms and perform a comparative analysis, the use of typical rock and concrete compressive strength test point bending strength test results verify its applicability. Analysis found that both intensity distribution can describe the size effect, and the intensity of the Weibull distribution gives lower values. When the specimen volume and reference volume approaches, given the strength of the results of two distributions little difference, while the lognormal distribution in the entire volume range can be given closer to the actual intensity value engineering. In the quasi-brittle material strength size effect of statistical research approach, using a lognormal distribution can be used as a simple Weibull size effect theory improvements. In the numerical simulation, this paper with a real failure process analysis RFPA 2D , on rock compression test, tensile test and three-point bending test carried out numerical experiments, rock strength size effect obtained numerical results. Be seen in the different loading conditions, the rocks and the residual strength of the peak intensity increases with the size reduced, but their destructive patterns do not change significantly, and different sizes of rock specimen strength numerical results are available on Weibull size effect formula better fit. Rock material under different loading conditions strength size effect differences can be destroyed through its homogeneous degree to reflect the different loading conditions have different homogeneity, the greater its value, which means that the rock destroyed more uniform size effect, the less obvious. Tests also show that the three-point bending test strength size effect is most obvious, uniaxial tension and compression testing, followed by a lateral pressure of the compression test the most obvious. In the present theoretical study on the size effect is still unsatisfactory in the case, after all, a numerical simulation of rock, concrete and other quasi-brittle material strength size effect and effective way.
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