准脆性材料的破坏概率与强度尺寸效应

基于最弱链模型和缺陷的Poisson分布假设,综合体积和材质因素,建立准脆性材料破坏概率和强度尺寸效应的统计模型和一般表达式。由此可知物体的破坏概率随体积单调增加,强度随体积单调减小,在通常有限的尺度范围内,当体积很大时,强度变化很小可视作常值;无缺陷材料则没有尺寸效应。通过分别采用Weibull分布和对数正态分布,得到材料破坏概率和强度尺寸效应的具体形式并进行对比分析,最后利用典型岩石强度试验结果验证其适用性。分析结果发现,这2种分布都能描述材料的尺寸效应,而且体积相同时Weibull分布给出的强度值较低。当试样体积与参考体积接近时,2种分布给出的强度结果差别很小,而对数正态分布在整个体积范围都能给出更接近工程实际的强度值。在准脆性材料强度尺寸效应的统计途径研究中,采用对数正态分布可作为Weibull尺寸效应理论的简单改进。

FAILURE PROBABILITY AND STRENGTH SIZE EFFECT OF QUASI-BRITTLE MATERIALS

The failure probability and the average strength of quasi-brittle materials such as rock，concrete，etc.，have size effect due to the heterogeneity，and the statistical approach is of importance in the research of this problem. A statistical model for the strength size effect is established based on the weakest link model and the Poisson¢s 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 case of uniaxial compression. From these expressions，it is known that，with respect to volume，the failure probability is monotonically increasing and the strength is monotonically decreasing. The strength varies very slowly and thus may be regarded as constant when the volume becomes very large within usual limited scope. As for defect-free perfect materials，the issue of size effect does not longer exist. The Weibull distribution and the lognormal distribution are then introduced into the general expressions，respectively. The applicability of these expressions is demonstrated with the results of some typical uniaxial compressive strength tests of eight kinds of rocks. 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.