Error analysis of an inclinometer based on numerical analysis
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摘要:
测斜仪在边坡深部位移监测中应用比较广泛，但其监测结果存在一定误差。已有测斜仪监测误差研究多是针对系统误差进行，缺少针对测斜仪监测数据计算原理引起的误差进行的研究。基于测斜仪监测数据计算方法原理与数值分析中常微分方程Euler解法的一致性，讨论了造成测斜仪监测误差的原因。分析结果表明：测斜仪监测误差与测斜仪监测初始值、测量分段长度和位移变形曲线形状有关；测斜仪监测初始值变化将给监测带来误差；测斜仪测量段长与监测误差呈线性关系，误差随测量段长减小而变小；当位移变形曲线为直线时，误差为0；当位移变形曲线为单-凸曲线或凹曲线时，监测误差随曲线变形程度和孔口变形位移增大而变大；测斜仪位移变形监测误差为累积误差，孔口误差大于孔底误差。在使用测斜仪监测时，为了减少监测误差，建议将每次监测初始值设为固定值，并尽可能减少测量段长。
Abstract:Inclinometer is widely used in slope deep displacement monitoring, and the error of an inclinometer is an issue of concern. The existing research on the inclinometer error is based on the system error, and the error caused by the calculation principle of inclinometer monitoring data was seldom examined. Based on the consistency between the calculation principle of inclinometer monitoring data and the Euler solution of the ordinary differential equation in numerical analysis, this paper discusses the monitoring error of inclinometer according to the principle of numerical analysis method. The analysis results show that the monitoring error of an inclinometer is related to the initial value of the inclinometer, the length of the measurement section and the shape of the displacement deformation curve. Among them, the change of the initial value of inclinometer monitoring will bring errors to the monitoring. The length of the measuring section of the inclinometer has a linear relationship with the monitoring errors, and the errors decrease with the decrease of the measuring section length. When the displacement deformation curve is straight, the errors are zero; when the displacement deformation curve is a single convex curve or concave curve, the monitoring errors increase with the increase of the curve deformation degree and the orifice deformation displacement. The error of displacement deformation monitoring is the cumulative error, and the error of orifice is larger than that of the bottom. When using an inclinometer for monitoring, in order to reduce the monitoring error of the inclinometer, the initial value of each monitoring should be fixed, and the length of the measuring section should be reduced as much as possible.
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Key words:
- slope /
- deep displacement /
- monitoring /
- numerical analysis /
- Euler method /
- error analysis
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表 1 不同孔口水平位移下的计算误差
Table 1. Errors under different orifice displacement
孔口水平位移/m 0.5 0.4 0.3 0.2 0.1 误差/mm 二次曲线 5.0 4.0 3.0 2.0 1.0 三次曲线 15.0 12.0 9.0 6.0 3.0 
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表 2 不同测量分段长度下的计算误差
Table 2. Errors under different length of the measuring section with conic curve
测量段长/m 0.5 1.0 2.0 3.0 4.0 误差/mm 二次曲线 5 10 20 30 40 三次曲线 15 30 60 90 120
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[1] 马水山, 张保军, 汤平. 钻孔测斜仪在滑坡体深部变形监测中的应用[J]. 中国地质灾害与防治学报,1996,7(增刊):109 − 114. [MA Shuishan, ZHANG Baojun, TANG Ping. Application of borehole inclino-meter in monitoring deep deformation of slidebody[J]. The Chinese Journal of Geological Hazard and Control,1996,7(Sup):109 − 114. (in Chinese with English abstract)
[2] 尧林, 彭小平, 罗大国. 深部位移监测技术在滑坡勘察中的应用[J]. 西部探矿工程,2011,23(12):32 − 34. [YAO Lin, PENG Xiaoping, LUO Daguo. Application of deep displacement monitoring technology in landslide investigation[J]. West-China Exploration Engineering,2011,23(12):32 − 34. (in Chinese) doi: 10.3969/j.issn.1004-5716.2011.12.012
[3] 陈开圣, 彭小平. 测斜仪在滑坡变形监测中的应用[J]. 岩土工程技术,2006,20(1):39 − 41. [CHEN Kaisheng, PENG Xiaoping. Application of inclinometer in monitoring deformations of landslide[J]. Geotechnical Engineering Technique,2006,20(1):39 − 41. (in Chinese with English abstract) doi: 10.3969/j.issn.1007-2993.2006.01.010
[4] 彭纪超, 王松林, 张运勋, 等. 钻孔测斜仪在滑坡变 形监测中的应用研究[J]. 西安科技大学学报,2014,34(4):440 − 444. [PENG Jichao, WANG Songlin, ZHANG Yunxun, et al. Application of borehole inclinometer in landslide deformation monitoring[J]. Journal of Xi'an University of Science and Technology,2014,34(4):440 − 444. (in Chinese with English abstract)
[5] 黄飞澜, 肖红. 测斜仪在高填方地基侧向水平位移监测中的应用[J]. 公路工程,2010,35(5):112 − 115. [HUANG Feilan, XIAO Hong. Inclinometer in high embankment lateral horizontal displacement monitoring[J]. Highway Engineering,2010,35(5):112 − 115. (in Chinese) doi: 10.3969/j.issn.1674-0610.2010.05.025
[6] 方大勇. 边坡长期监测中测斜仪测量数据的修正[J]. 水电自动化与大坝监测,2006,30(4):56 − 58. [FANG Dayong. Inclinometer data correction in long-term slope monitoring[J]. Hydropower Automation and Dam Monitoring,2006,30(4):56 − 58. (in Chinese with English abstract)
[7] 李国维, 胡龙生, 王润, 等. 滑动式测斜仪测试与误差处理方法[J]. 河海大学学报 (自然科学版),2013,41(6):511 − 517. [LI Guowei, HU Longsheng, WANG Run, et al. Testing of slip inclinometer and error treatment methods[J]. Journal of Hohai University(Natural Sciences),2013,41(6):511 − 517. (in Chinese with English abstract)
[8] 王永卫, 陈从新, 宋鑫颖, 等. 自然三次样条法处理边坡变形数据的应用研究[J]. 水文地质工程地质,2013,40(2):88 − 91. [WANG Yongwei, CHEN Congxin, SONG Xinying, et al. A study of deformation data of landslide using natural cubicspline[J]. Hydrogeology & Engineering Geology,2013,40(2):88 − 91. (in Chinese with English abstract)
[9] 孙虹虹, 邓兴升. 边坡监测中测斜误差与精度分析[J]. 水电自动化与大坝监测,2015,39(1):26 − 28. [SUN Honghong, DENG Xingsheng. Accuracy analysis of inclinometer in slope monitoring[J]. Hydropower Automation and Dam Monitoring,2015,39(1):26 − 28. (in Chinese with English abstract)
[10] 乔美英, 王波, 肖学军, 等. 煤矿井下随钻测斜仪误差联合校正方法[J]. 煤田地质与勘探,2020,48(2):202 − 208. [QIAO Meiying, WANG Bo, XIAO Xuejun, et al. Research on joint correction method of errors in coal mine while drilling inclinometer[J]. Coal Geology & Exploration,2020,48(2):202 − 208. (in Chinese with English abstract) doi: 10.3969/j.issn.1001-1986.2020.02.030
[11] 徐胜强, 张旭东, 张保平, 等. 测斜仪监测技术在地热井压裂中的应用研究及实践[J]. 钻探工程,2021,48(2):42 − 48. [XU Shengqiang, ZHANG Xudong, ZHANG Baoping, et al. Application and practice of Tiltmeter monitoring technology in geothermal well fracturing[J]. Drilling Engineering,2021,48(2):42 − 48. (in Chinese with English abstract) doi: 10.12143/j.ztgc.2021.02.006
[12] 张军. 钻孔随钻三维轨迹测量技术研究[J]. 探矿工程(岩土钻掘工程),2019,46(12):7 − 12. [ZHANG Jun. Borehole trajectory 3-D survey while drilling[J]. Exploration Engineering (Rock & Soil Drilling and Tunneling),2019,46(12):7 − 12. (in Chinese with English abstract)
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