完整岩石单轴抗压强度确定方法研究

薛东杰

摘 要

完整岩石单轴抗压强度是传统和普适Hoek-Brown（HB）强度准则中的关键参数，其与岩石软硬程度和岩石破碎程度具有强关联性，而理想的或理论值严格意义上并不等同于单轴测试值。真值的唯一性确定直接影响HB强度准则的准确性，由此提出一种新的思路解决这一难题。首先明确了岩石软硬程度和岩石破碎程度的确定应基于分布特征而非单一样品，这可使完整岩石单轴抗压强度、岩石软硬程度和岩石破碎程度三参数力学意义上自洽。进而证实了传统HB强度准则表达式的不确定性，本质原因是三参数无法从单一曲线中唯一确定，明确问题的关键核心是完整岩石单轴抗压强度值的唯一性。由此提出了确定HB强度准则新的线性解决方案，将三参数改为两参数，可简单快速唯一地确定HB强度准则曲线。最后为了提高精度，引入四种误差评判方式：绝对误差绝对值和、绝对误差平方和、相对误差绝对值和与相对误差平方和，可显著缩小预测值与实验值的偏离误差。新的线性方案匹配任意一种误差形式可确保完整岩石单轴抗压强度的唯一性，研究工作为深入理解HB强度准则提供了新思路。

关键词

完整岩石单轴抗压强度；Hoek-Brown破坏准则；唯一性；线性；误差

Determination of uniaxial compressive strength of intact rock

XUE Dongjie

Abstract

The parameter of uniaxial compressive strength of intact rock is a key concept in the traditional and universal Hoek-Brown (HB) failure criterion. It has a strong correlation with the parameters of rock hardness and rock fragmentation. The determination of the uniqueness of the uniaxial compressive strength is still facing challenges. Indeed, its true value is not the same as the measured result. So according to the HB failure criterion, the necessity and rationality of determining the uniaxial compressive strength are discussed. Firstly, it is pointed out that the determination of rock hardness and rock fragmentation should be based on the distribution characteristics rather than a single sample. It will make the uniaxial compressive strength, rock hardness and rock fragmentation of intact rock to be self-consistent in the mechanical sense. Furthermore, the uncertainty of the traditional HB failure criterion expression is confirmed, the essential reason is that the three parameters cannot be uniquely determined from a single curve, and it is clear that the key is the uniqueness of determining the uniaxial compressive strength of intact rock. Therefore, a new linear solution to determine HB failure criterion is proposed. By changing three parameters into two parameters, HB failure criterion can be determined simply, quickly and uniquely. Finally, in order to improve the accuracy, four error evaluation methods are introduced by the sum of absolute value of absolute error, the sum of squares of absolute error, the sum of absolute value of relative error, the sum of squares of relative error, which can significantly reduce the deviation error between the predicted value and the experimental value. The new linear solution matching one of the error forms can ensure the uniqueness of uniaxial compressive strength of intact rock. The research provides a new idea for further investigation of HB failure criterion.

Key words

uniaxial compressive strength of intact rock; HB failure criterion; uniqueness; linear solution; error

引用格式：

薛东杰. 完整岩石单轴抗压强度确定方法研究[J].山东科技大学学报-自然科学版, 2020, 39(04):28-36. (Xue Dongjie. Determination of uniaxial compressive strength of intact rock[J], Journal of Shandong University of Science and Technology (Natural Science), 2020, 39(04):28-36.)

创新点：

1. 证实了传统Hoek-Brown（HB）强度准则表达式的不确定性

2. 提出了确定HB强度准则新的线性解决方案。

3. 提出了完整岩石单轴抗压强度确定的建议方案。

(a)线性拟合

(b)非线性拟合

σ₁～ σ₃非线性关系的线性确定（图片版权所有，侵权必究）

定拟合参数 和 的循环算法（图片版权所有，侵权必究）