摘要
最小二乘法是在岩石三轴压缩试验条件下估计抗剪强度参数的常规方法,该方法存在无法对相对误差和莫尔圆进行有效约束的局限性。为此,本文在摩尔应力空间中指出了岩石抗剪强度参数估计的目标,以莫尔圆半径相对误差的平方和构造目标函数,提出了岩石抗剪强度参数相对误差最小二乘估计方法;定义了莫尔圆贴近度的概念,用于检验岩石抗剪强度参数估计值的合理性;同时提出以单轴抗压强度的相对误差作为间接指标来表征抗剪强度参数估计值与理论值的一致性,并用多种岩石的三轴试验数据进行适用性验证。结果表明:相对误差最小二乘法计算的莫尔圆贴近度均方根和单轴抗压强度相对误差均小于传统最小二乘法,该方法提升了对莫尔圆的修正性能,提高了对岩石抗剪强度参数的估计精度。
The least square method is a conventional method for estimating shear strength parameters under the condition of rock triaxial compression test.This method has the limitation that it cannot effectively constrain the relative error and Mohr circle.Therefore,in this paper,the target of rock shear strength parameter estimation was pointed out in the Mohr stress space.The objective function was constructed by the square sum of the relative error of Mohr circle radius,and the least square estimation method of relative error of rock shear strength parameters was proposed.The concept of Mohr circle closeness was defined to test the rationality of the estimated value of rock shear strength parameters.At the same time,the relative error of uniaxial compressive strength was proposed as an indirect index to characterize the consistency between the estimated value of shear strength parameters and the theoretical value.The applicability verification was carried out by using the triaxial test data of various rocks.The results show that the root mean square of Mohr circle closeness and the relative error of uniaxial compressive strength calculated by the relative error least square method are lower than those calculated by the traditional least square method,indicating that the relative error least square method improves the correction performance of Mohr circle and improves the estimation accuracy of rock shear strength parameters.
作者
李斌
苟淦昊
张敏
顾鑫
高尚
毛龙敏
LI Bin;GOU Ganhao;ZHANG Min;GU Xin;GAO Shang;MAO Longmin(School of Environment and Resource,Southwest University of Science and Technology,Mianyang Sichuan 621010,China)
出处
《化工矿物与加工》
2025年第10期66-73,共8页
Industrial Minerals & Processing
基金
国家自然科学基金项目(51904248)
四川省自然科学基金项目(2024NSFSC0975)。
关键词
抗剪强度
最小二乘法
相对误差
莫尔圆
三轴压缩试验
参数估计
shear strength
least square method
relative error
Mohr circle
triaxial compression test
parameter estimation
