八种岩石三轴压缩强度经验函数计算研究 |
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八种岩石三轴压缩强度经验函数计算研究 Caculation study on triaxial compression strength empirical function for eigtht different rocks 发布时间：2011-06-27 浏览量：125 收藏数：0 评论数：0 总览 评价 刘光连1*， 牛杰2 （ 1、中南大学机电工程学院； 2、中南大学机电工程学院，湖南长沙 410083； ）
摘要： 本文提出了岩石三轴压缩破坏强度经验函数，将最大主应力用显函数表示为最小主应力和中间主应力多项式，用数值计算方法确定多项式系数，提出了岩石三种强度经验函数：最小主应力和中间主应力二元线性强度函数和双抛物线强度函数，及最小主应力直线和中间主应力抛物线即直线抛物线强度函数。对普遍引用的8种岩石三轴压缩强度数据，应用数值计算方法求出了岩石强度三种经验函数的系数，并用最大主应力相对误差、最大主应力相关系数、最大主应力计算方差等方法对计算结果与实验结果进行了分析。计算的相对误差绝大多数在10%以内，三种强度经验函数计算的相关系数都大于0.94且平均值大于0.97。岩石强度三种经验函数计算岩石强度的方差与Hoek-Brown(MN)准则相当，优于Mohr-Coulomb准则、Hoek- Brown准则、Mogi（1971）线性函数、修正Lade-Duncan准则、修正Wiebols-Cook准则等五个岩石强度准则。双抛物线强度函数计算效果最好、直线抛物线强度函数次之，岩石强度三种经验函数的系数分析表明，中间主应力对岩石强度的影响可用有最大值的二次抛物线描述，与中间主应力对岩石强度影响的实验结果相符，也与混凝土三轴压缩强度中间主应力的影响一致。岩石三轴压缩强度经验函数为岩石强度计算提供了一种新方法，具有较大的实用价值。
关键词： 岩石；三轴压缩；强度；经验函数；极限应变能强度理论 LIU Guanglian1*， NIU Jie2 （ 1、School of Mechanical and Electrical Engineering,Central South University； 2、School of Mechanical and Electrical Engineering,Central South University,Changsha 410083； ）
Abstract： In this paper, triaxial compression strength empirical functions of rock is proposed. The maximum principal stress is represented with an explicit function of the minimum principal stress and the intermediate principal stress polynomial, and the coefficients of the polynomial are determined by numerical approaches.Three kinds of strength empirical functions for rock can be expressed as followings: binary linear strength function and dual-parabola strength function of the minimum principal stress and the intermediate principal stress, the minimum principal stress line and the intermediate principal stress parabola which is linear parabolic strength function. Triaxial compression strength data of eight rocks,which has been universally cited,was used to determine the coefficients of the three empirical functions for rock strength by numerical approaches.And approaches such as the maximum principal stress relative error 、the maximum principal stress correlation coefficient、the maximum principal stress calculation variance .etc.are used to analyze the calculated results and the experimental results. The vast majority of thecaculated relative errors are less than 10%,what is more,the correlation coefficients according to the three kinds of strength empirical functions are all greater than 0.94 and the average is higher than 0.97. The calculation variances according to the proposed three empirical functions are equal to that by Hoek-Brown(MN) criterion,but better than the following five rock strength criterion: Mohr-Coulomb criterion, Hoek-Brown criterion,Mogi（1971）linear function,modified Lade-Duncan criterion, modified Wiebols-Cook criterion. Dual-parabola strength function has the highest accuracy , followed by the linear parabolic strength function. Coefficients analysis of three empirical functions of rock strength shows that the influence of the intermediate principal stress on rock strength could be described with a parabola that has peak value,which corresponds with the experimental results that the effect of the intermediate principal stress on rock strength and is consistent with that of the intermediate principal stress on triaxial compression strength of concrete.The new method is provided for the calculation of rock strength by strength empirical function for rock under triaxial compression, having great practical value,compression, having great practical value.
Keywords： rock; triaxial compression; strength; empirical function; limiting strain energy
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