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研究岩石区间非定值强度问题以期适应实验室试验有限性、随机性的特点,以此反映岩石强度参数取值的区间性特征及可能性分布。首先,提出了岩石的抗压区间强度、抗拉区间强度的概念;其次,基于区间分析、未确知数学理论,结合实验室实际,给出了区间强度的求解方法,并提出了区间内不同强度代表值的可信度确定方法,有利于工程计算时强度参数的选取。最后,通过小样本和大样本的分析比较,对本文方法的合理性进行了验证。小样本研究表明,取可信度为95%时,岩石抗压、抗拉强度代表值小于常规均值计算得到的值,且常规均值计算求取的岩石抗压、抗拉强度代表值可信度在65%左右,可见通过常规均值计算的结果是偏危险的;将某矿山砂岩的320个试样(大样本)随机分成64组,每组5个试样(小样本),研究发现,320个岩样强度呈正态分布,把平均值238.17 MPa作为该区域砂岩的名义值,64个传统均值有32个的取值的大于名义值,证明小样本下(5个样本),用传统均值代表岩石强度其保证率为50%;64个区间强度有55个包含名义值,准确率为86%,且另外6个区间强度上限值均小于名义值,可见用区间强度代表岩石强度的保证率为95%。区间强度较传统均值更充分地表达了岩石强度的信息,完善了岩石强度参数确定方法,为实际工程设计施工、强度校核及可靠性研究中岩石强度参数的取值提供一条新途径。
This paper studies the problem of non-fixed strength in the interval of rock so as to adapt to the limited and random characteristics of the laboratory test, so as to reflect the interval characteristics and probability distribution of rock strength parameters. Firstly, the concepts of compressive strength and tensile strength of rock are put forward. Secondly, based on the interval analysis, unascertained mathematical theory and the laboratory practice, the method of solving the interval strength is given, The method of determining the reliability of the representative value of strength is in favor of the selection of the strength parameters in engineering calculation. Finally, the rationality of this method is verified through the analysis and comparison of small samples and large samples. The small sample study shows that the representative value of compressive strength and tensile strength of rock is less than the value calculated by conventional mean when the reliability is 95%, and the reliability of representative value of rock compressive strength and tensile strength calculated by conventional mean calculation At about 65%, the results calculated by conventional means are risky; 320 samples (large samples) of a mine sandstone were randomly divided into 64 groups of 5 samples (small sample), the study found that 320 The intensity of the samples was normal distribution. The average value of 238.17 MPa was used as the nominal value of the sandstone in the area, and the value of 32 of 64 traditional means was greater than the nominal value. It was proved that the small sample (5 samples) Representing the rock strength of the guarantee rate of 50%; 64 interval strength of 55, including the nominal value, the accuracy rate of 86%, and the other six upper bounds are less than the nominal value of strength, showing the use of interval strength on behalf of rock strength guarantee The rate is 95%. The interval strength expresses the information of rock strength more fully than the traditional average value, and improves the determination method of rock strength parameters. This provides a new way for the value of rock strength parameters in practical engineering design and construction, strength check and reliability study.