Prediction model for sandstone strength based on Weibull distribution of micro-element strength and power-law distribution of crack length

考虑微元强度韦伯分布与裂纹长度幂律排布的砂岩强度预测模型

¹ Anhui Key Laboratory of Mining Construction Engineering, Anhui University of Science and Technology, Huainan 232001, China
² State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China
³ School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China
⁴ School of Civil Engineering and Architecture, Anhui University of Science and Technology, Huainan 232001, China
⁵ State Key Laboratory of Strata Intelligent Control and Green Mining Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China
⁶ China Coal Mine Construction Group Corporation LTD, Hefei 230000, China

Received: 5 January 2023

Abstract

It is of the great significance to construct the strength prediction model that considers the influence of the macro and micro defects in the rock in an overall manner to ensure the construction of smart mines and the safety of underground personnel and equipment. Based on the Weibull distribution of rock micro-element strength and the power-law distribution of crack length and the discrete element calculation model, the prediction model for strength of damaged rock specimens were established by numerical simulation and theoretical derivation respectively. Then the rationality of the model was verified by the calculated results. The results show that: 1) The weibull distribution of the micro-element strength and the power-law distribution of the crack length in the PFC2D calculation model are realized by programming, and the quantitative corresponding relationship between the macro, micro and micro damage in the rock and the corresponding distribution parameters is analyzed. 2) 400 sandstone specimens with macro, micro and micro damage are numerically established and loaded to achieve statistical analysis of the relationship between micro element strength, pre-crack information and rock strength. According to the simulation results, the four-dimensional space scatter points of uniaxial compressive strength of sandstone specimens are constructed, and the flow law of compressive strength of sandstone specimens under the influence of multiple damage parameters is obtained. 3) Combined with Mori Tanaka method and rock damage probability distribution theory, a 12 parameter rock strength prediction model is established. The model can both describe the influence of the micro-element strength and macroscopic crack information on the rock strength, and the model calculation results are highly consistent with the simulated results, with the correlation coefficient up to 0.991.

摘要

构建统筹考虑岩石内部宏细微观缺陷影响的强度预测模型对于保障智慧矿山的建设以及井下人员设备的安全都具有重要意义。综合考虑岩石微元强度的韦伯分布与裂纹长度的幂律排布规律, 采用数值模拟与理论推导方法分别建立损伤岩石试件的离散元计算模型与强度预测模型, 并利用数值计算结果对理论模型的合理性进行验证。结果表明: ①通过编程同时实现了PFC^2D计算模型中微元强度的韦伯分布与裂纹长度的幂律排布, 分析了岩石中的宏、细微观损伤与相应分布参数间的定量对应关系。②数值建立了400个同时考虑宏、细微观损伤的砂岩试件并对其进行了模拟加载, 实现了对微元强度、预制裂纹信息及岩石强度间关系的统计分析。根据模拟结果构建了砂岩试件单轴抗压强度四维空间散点, 得到了多损伤参量影响下的试件抗压强度流动规律。③联合Mori-Tanaka方法及岩石损伤概率分布理论, 推导建立了12参数的岩石强度预测模型。该模型能够同时描述细微观微元强度与宏观裂纹信息对岩石强度的影响, 并且理论模型计算结果与数值模拟结果高度吻合, 相关系数达0.991。