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考虑取样间隔的Barton标准JRC表征公式推导研究

王刚1,2, 陈明瑞1, 刘廷方1,2,3, 王长盛2, 吴学震3, 管辉4, 陈慧源5, 管尚尚6

1.福建理工大学 地下工程福建省高校重点实验室，福建 福州  350118；2.山东科技大学 山东省土木工程防灾减灾重点实验室，山东 青岛  266590；3.福州大学 土木工程学院，福建 福州  350108；4.青岛市勘察测绘研究院，山东 青岛  266033；5.莒县公路事业发展中心，山东 日照  276599；6.中建八局检测科技有限公司，北京  102488

摘要: 目的 为实现结构面粗糙度（JRC）的精确表征，本文选用粗糙度统计参数中的一阶导数均方根Z₂表征二维节理轮廓线粗糙度JRC^2D。 方法 首先，使用Photoshop对10条Barton标准轮廓线分别开展修补断点、去除杂点、增强像素等图像优化工作，并将轮廓线图像导入Matlab中，提取各轮廓线在不同取样间隔SI下的坐标数据，计算各条Barton标准JRC轮廓线在不同SI下的Z₂值；然后分析SI对Z₂的影响，基于Z₂随SI的增大而减小的规律，对各组数据的Z₂值、SI值进行指数函数拟合推导，调整拟合式参数后与JRC值进行回归拟合。 结果 获取了适用于SI∈［0.1 mm， 2.0 mm］的JRC^2D表征新公式，并引入参数JRC_P对新公式的精确性进行验证，通过对比本文JRC-Z₂与前人JRC表征公式的计算结果，分析各条轮廓线的JRC_P值变化规律。  结论 本文提出的考虑取样间隔的JRC-Z₂表征公式在其适用范围SI∈［0.1 mm， 2.0 mm］内精确性更高，新公式更真实地表征了Barton标准JRC轮廓线的粗糙特性，研究成果可为准确评估结构面粗糙度提供理论参考。

关键词:Barton标准轮廓线;结构面粗糙度;取样间隔;一阶导数均方根;指数拟合

DOI:10.16186/j.cnki.1673-9787.2024030005

基金项目:国家自然科学基金资助项目（52079077）；福建理工大学高层次人才引进科研启动基金资助项目（GY-Z23005）

收稿日期:2024/03/02

修回日期:2024/05/30

出版日期:2025/07/23

Derivation of a Barton standard JRC characterization formula considering sampling interval

Wang Gang1,2, Chen Mingrui1, Liu Tingfang1,2,3, Wang Changsheng2, Wu Xuezhen3, Guan Hui4, Chen Huiyuan5, Guan Shangshang6

1.Key Laboratory of Underground Engineering， Fujian University of Technology， Fuzhou  350118， Fujian， China；2.Key Laboratory of Civil Engineering Disaster Prevention and Mitigation， Shandong University of Science and Technology， Qingdao  266590， Shandong， China；3.College of Civil Engineering， Fuzhou University， Fuzhou  350108， Fujian， China；4.Qingdao Surveying ＆ Mapping Institute， Qingdao  266033， Shandong， China；5.Juxian Highway Development Center， Rizhao  276599，  Shandong， China；6.China Construction Eighth Bureau Testing Technology Co.， Ltd.， Beijing  102488， China

Abstract: Objectives To achieve accurate characterization of the joint roughness coefficient （JRC）， this study employs the root mean square of the first derivative （Z₂）， a statistical roughness parameter， to quantify the two-dimensional joint profile roughness （JRC^2D）. Methods Ten Barton standard profiles were processed using Photoshop to repair breakpoints， remove noise， and enhance pixel quality. The images were then imported into MATLAB to extract coordinate data at different sampling intervals （SI）， and Z₂ values were computed accordingly. The influence of SI on Z₂ was analyzed， revealing that Z₂ decreases with increasing SI. An exponential function was fitted to the Z₂- SI data， and the resulting expression was then regressed against JRC values.  Results A new JRC^2D characterization formula applicable for SI ∈ ［0.1 mm， 2.0 mm］ was proposed. The parameter JRC was introduced to validate the accuracy of the formula. A comparative analysis was conducted between the proposed JRC-Z₂ formula and previous JRC characterization models， with the JRC variation trends across profiles examined.  Conclusions The proposed JRC-Z₂ formula， which accounts for sampling interval effects， demonstrates improved accuracy within its applicable range and more realistically reflects the roughness characteristics of the Barton standard profiles. These findings provide a theoretical reference for the precise evaluation of structural surface roughness.

Key words:Barton standard profile;structural surface roughness;sampling interval;root mean square of first derivative;exponential fitting