基于灰色关联理论的红层软岩尺寸效应研究

为探究红层软岩岩体与小尺寸软岩试件实验强度的关系,对定西红层软岩的不同高径比试样进行单轴压缩试验,研究该类软岩的尺寸效应。考虑软岩力学性质复杂,弹性模量、泊松比、变形模量均为不确定值,引入灰色关联理论(比较了现有的4个灰色关联模型,表明相对关联模型更适合于软岩的尺寸效应研究)。计算和分析了软岩高径比、弹性模量、变形模量、泊松比与强度的相对关联度,结果表明:试样高径比≥1.2范围,泊松比对强度影响最大,高径比其次;试样高径比<1.2范围,高径比对强度影响最大,泊松比其次;变形模量对强度的影响大于弹性模量。对该类红层软岩进行尺寸效应研究,需要考虑高径比、泊松比、变形模量共同影响作用。定义了尺寸效应系数、变形模量兆帕像,采用简化维度的方法给出了尺寸效应系数的四维方程,拟合结果与试验结果具有良好的一致性。

Size Effect Study of Red Soft Rock Based on Grey Relating Analysis Theory

To investigate the size effect relationship between rock mass and small size sample on strength of red bed soft rock, a series of uniaxial compression tests of the red bed soft rock from Dingxi with different ratio of height to diameter were done. Elastic modulus, Poisson ratio and deformation modulus of soft rock are all uncertain values due to its complicated mechanical properties. The grey correlation analysis theory was introduced and four grey correlation analysis models were compared. Research results showed that grey correlation incidence model is more suitable for the red bed soft rock. By calculating correlation incidence degree of the sample’s height diameter ratio, elastic modulus, deformation modulus, Poisson ratio on strength, the analysis results show that when the height diameter ratio is greater than or equals to 1.2, the effect of Poisson ratio on strength is largest and the height diameter ratio is second, when the height diameter ratio is less than 1.2, the effect of height diameter ratio on strength is the largest, the Poisson ratio is second and the effect of deformation modulus on strength is greater than elastic modulus. Thus, research on size effect of the red bed soft rock needs to consider the joint effect of height diameter ratio, Poisson ratio and deformation modulus. By defining the size effect coefficient and deformation modulus megapascal image, the four-dimensional equation of size effect is fitted by using the method of simplifying dimension. The simulation results show good agreement with the test results.