红砂岩抗压强度概率分布尺寸效应的试验研究

doi:10.13722/j.cnki.jrme.2021.0588

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摘要岩石抗压强度概率分布是否存在尺寸效应，对能否准确确定其概率分布以及得到正确的可靠度计算结果至关重要。对边长分别为80，120和160 mm的红砂岩立方体岩块进行压缩试验，研究结果表明：(1) 岩石峰值抗压强度的概率分布类型服从正态分布，且分布类型不会随着尺寸的变化而变化。(2) 岩石抗压强度平均值和标准差的点估计值、区间估计值和反证法表明平均值和标准差均存在明显的尺寸效应，当尺寸从80 mm增加到160 mm时，平均值从56.64 MPa减小至51.14 MPa，标准差则从14.33 MPa减小至3.96 MPa，其中标准差的降幅更为显著。 (3) 以尺寸为160 mm的柱础为例进行可靠度分析，不同尺寸下的概率分布对可靠度计算结果影响很大，80 mm尺寸下概率分布得到的失效概率为11.00%，160 mm尺寸下概率分布得到的失效概率为0.12%，前者结果是后者的91.67倍，此外，如果仅考虑平均值的尺寸效应而忽略标准差的尺寸效应则会得到与实际情况相反的结论。因此，在实际工程中应重视岩石抗压强度概率分布的尺寸效应问题。

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	翟友成

关键词 ：岩石力学, 概率分布, 尺寸效应, 可靠度, 峰值抗压强度, 标准差, 平均值

Abstract：The size effect on the probability distribution of rock compressive strength is very important for accurately determining its probability distribution and obtaining the correct reliability calculation results. The compressive tests were carried out on cubic red sandstone blocks with side lengths of 80，120 and 160 mm respectively. The results show that：(1) the probability distribution type of peak compressive strength of rock obeys normal distribution and will not change with the change of size. (2) The point estimation，interval estimation and disproof method show that both average and standard deviation of rock compressive strength have obvious size effect. When the size increases from 80 to 160 mm，the average decreases from 56.64 to 51.14 MPa，the standard deviation decreases from 14.33 to 3.96 MPa. The standard deviation decreases more significantly. (3) Taking the plinth with size of 160 mm as an example，the reliability calculation results are greatly influenced by the probability distribution under different sizes. The failure probability obtained by the probability distribution under 80 mm size is 11.00%，and the failure probability obtained by the probability distribution under 160 mm size is 0.12%. The former result is 91.67 times that of the latter. In addition，if only the size effect of the average value is considered and the size effect of the standard deviation is ignored，it will be realistic Therefore，The size effect of probability distribution of rock compressive strength in practical engineering should be paid attention.

Key words： rock mechanics probability distribution size effect reliability peak compressive strength standard deviation average value

引用本文:

翟友成. 红砂岩抗压强度概率分布尺寸效应的试验研究[J]. 岩石力学与工程学报, 2022, 41(S1): 2649-2657.
ZHAI Youcheng. Experimental study on size effect of probability distribution of compressive strength of red sandstone#br#. , 2022, 41(S1): 2649-2657.

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http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2021.0588 或 http://rockmech.whrsm.ac.cn/CN/Y2022/V41/IS1/2649

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