Comparison of measuring accuracies of tunnel displacements with RDM method and 3D measurement method based on total station
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摘要: 根据测量学原理和误差传播定律, 分析了全站仪自由设站对边量测(RDM) 法和三维坐标(3D) 量测法, 建立了2种量测法的隧道变形精度分析模型, 利用中误差评价隧道变形量测精度, 推导了2种方法量测隧道变形的中误差计算公式, 并以某三车道公路隧道为例, 对2种方法的量测精度进行了对比和验证; RDM法通过三角高程测量原理和三角余弦定理得出任意点之间的水平距离、高差和斜距, 根据任意测点之间的三角几何关系得到隧道变形; 3D量测法从任意观测点观测若干已知点的方向和距离, 通过坐标变换计算各测点坐标, 根据各测点坐标得到隧道变形。分析结果表明: 采用RDM法和3D量测法量测隧道拱顶下沉的精度评价公式相同, 而量测隧道水平收敛的精度评价公式不同, RDM法的精度优于3D量测法, 且随着全站仪到量测断面距离的增加, 差值逐渐增大, 当距离为100 m时, 两者精度差值已增大至0.43 mm; 在三车道公路隧道中, 当距离为40~60m时, 2种方法量测隧道水平收敛的精度均为最高, RDM法可达0.61~0.68mm, 3D量测法可达0.78~0.84mm; RDM法和3D量测法量测的隧道拱顶下沉曲线平滑、圆顺, 拟合度都大于0.95, 而在量测隧道净空收敛方面, RDM法的曲线拟合度大于0.9, 3D量测法的曲线拟合度小于0.9, 因此, RDM法量测精度优于3D量测法。Abstract: Based on geodesy principles and error propagation laws, the remote distance measurement (RDM) method and 3Dcoordinate measurement method of based on free stationing of total station were analyzed, the accuracy analysis models of tunnel displacement based on the two measuring methods were established, and the mean square error was used to evaluate the measuring accuracy. The formulas of mean square error on the two methods were deduced. Athree-lane highway tunnel was taken as an example to compare and verify the measuring accuracies of the two methods. In RDM method, through gaining the horizontal distance, the elevation difference and slant distance of two random measurement points were gained by the triangulate height measurement principle and the cosine theorem, and the tunnel displacement was obtained according to the trigonometric and geometric relationship between two random measurement points. In 3D measurement method, the directions and distances of several known points were observed from the random observation point, the coordinates of random measurement points were calculated by using the coordinate conversion, and the tunnel displacement was obtained according to the coordinates of random measurement points. Analysis result shows that the accuracy evaluating formulas of RDM method and 3D measurement method computing tunnel vault settlement are same, however, the formulas computing tunnel horizontal convergence are different, and the accuracy of RDM method is higher than 3D measurement method. When the distance of total station and measured profile increases, the measuring accuracy difference of two methods increases. When the distance is 100 m, the accuracy difference increases to 0.43 mm. In three-lane highway tunnel, when the distance is 40-60 m, the measuring accuracies of tunnel horizontal convergences for the two methods are highest, the accuracy of RDM method can reach 0.61-0.68 mm, and the accuracy of 3D measurement method can reach 0.78-0.84 mm. The curves of tunnel vault settlement measured by using RDM method and 3D measurement method are smooth, and the fitting degrees of the curves are greater than 0.95. However, in the aspect of measuring tunnel horizontal convergence, the curve's fitting degree for RDM method is greater than 0.9, and the degree is less than 0.9 for 3D measurement method. So, the measuring accuracy of RDM method is higher than 3D measurement method.
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Key words:
- tunnel engineering /
- tunnel displacement /
- measurement accuracy /
- total station /
- RDM method /
- 3D measurement method
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图 3 3D量测法量测隧道变形模型
Figure 3. Measurement model of tunnel displacement with 3D measurement method
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