Research on deformation monitoring of tunnel engineering based on 3D laser scanning

3D laser scanning technology records the 3D coordinates, reflectivity and other information of the scanned object at the rate of tens of thousands or even millions of points per second. In the data processing of the office, the high-precision data processing system is used to efficiently model the measured object, and the practical engineering problems are solved by analysing the point cloud model [7]. There are many kinds of scanners that differ in structure, but all 3D laser scanners are mainly composed of laser transmitter, receiver, camera, timer, power control system and other components [8]. The laser transmitter actively emits the laser in front of the rotating lens, and the laser will be reflected back once it touches the surface of the measured object. Due to the fast propagation rate of light, the reflected laser is collected by the laser receiver along almost the same path. Then the timer calculates the distance by calculating the corresponding changes of laser before and after transmission and reception. At the same time, the encoder simultaneously measures the current attitude of the lens, namely the horizontal rotation angle and vertical rotation angle [9]. In this way, the X, Y and Z coordinates of the illuminated point can be obtained based on the coordinate system. After the number of scanning points per second is set before scanning, automatic and adaptive transmission devices can be set inside the scanner to ensure that the all-round and high-precision 3D position of the target object can be captured at different distances [10,11,12,13,14,15]. The 3D laser scanner is based on the instrument coordinate system to save the spatial position information of scanning points. The principle of the coordinate system is that the coordinate origin is in the centre of the instrument, that is, the location of laser beam emission, where the Z-axis is vertically upward in the vertical scanning plane, while the X-axis and the Z-axis are vertically in the horizontal scanning plane. The Y-axis is the scanning direction of laser pulse and it represents the right-hand rectangular coordinate system with X-axis and Z-axis. Figure 1 is a schematic diagram of a common scanner, where the instrument scans the surface of an object to capture the oblique distance S between the target point P and the laser beam emission place, the transverse scanning angle α and the longitudinal scanning angle β, thus obtaining the 3D coordinates of any point as follows: (1) {XP=S⋅cosβ⋅cosαYP=S⋅cosβ⋅sinαZP=S⋅cosβ \left\{ {\matrix{ {{X_P} = S \cdot \cos \beta \cdot \cos \alpha } \hfill \cr {{Y_P} = S \cdot \cos \beta \cdot \sin \alpha } \hfill \cr {{Z_P} = S \cdot \cos \beta } \hfill \cr } } \right.

Fig. 1

The traditional measurement means that it obtains the 3D position information of the target point by using a single point. The 3D laser scanning technology has the advantages of rapidity, continuity and automation when collecting the surface of the target object. In the protection of cultural relics, the on-site records can be quickly completed, and the real restoration can be carried out in the computer through 3D information. 3D laser scanning is a way to obtain information pertaining to the surfaces of objects at a certain resolution, and it has the following characteristics:

High precision. Due to the influence of scanning distance and scanning angle, the single-point accuracy of the instrument may not reach the accuracy of the total station when acquiring the scanning point position in the middle and long distance, but modelling by the point cloud data has great advantages over the total station data single-point modelling [16].

According to the principle of 3D laser scanning technology and point cloud registration, the workflow of applying 3D laser scanning technology in tunnels can be divided into four stages: pre-preparation, point cloud data collection, point cloud data processing and deformation analysis.

Using a 3D laser scanner to carry out measurement can improve the efficiency of measurement, but the amount of data collected is large. Compared with traditional measurement methods, the point cloud data processing scanned by 3D laser scanner is a complicated process, in which point cloud data pre-processing is the first and most important step. The result of pre-processing directly affects the difficulty of later data application and the accuracy of application results. Each 3D laser scanner uses special pre-processing software, and there are also many commercial software, which can be used to pre-process point cloud data, or the corresponding point cloud pre-processing algorithm can be compiled to fulfil the purpose of data processing. Point cloud data pre-processing mainly includes point cloud registration, point cloud denoising, point cloud compression and so on.

The purpose of fitting the tunnel axis is to accurately intercept the tunnel section and to draw the longitudinal deformation curve of the tunnel according to the axis.

Van Gosligaf fitted the tunnel cylinder by the least square method, and defined the shortest distance between any measured point in the point cloud and the axis of the cylinder to be determined as follows: (9) ei=‖(pi−c)×a→‖ {e_i} = \left\| {\left( {{p_i} - c} \right) \times \vec a} \right\| where p_i = (x_i, y_i, z_i) is the coordinate of any measured point in the original point cloud; c = (x₀, y₀, z₀) is a fixed point on the axis of the cylindrical surface; and a→=(cosλcosϕ,sinλcosϕ,sinϕ)T \vec a = (\cos \lambda \cos \phi ,\sin \lambda \cos \phi ,\sin \phi {)^T} is the unit vector of the axis direction of the cylindrical surface.

The tunnel axis fitting problem can be transformed into an optimisation problem: (10) minimizef(u)=∑i=1n(ei−R)2 minimizef(u) = \mathop {\sum\limits_{i = 1}^n }\limits_ {\left( {{e_i} - R} \right)^2} where R is the tunnel radius obtained by scanning.

During the construction, the structural shape of the tunnel only satisfies the horizontal symmetry, and the preprocessed original point cloud data of the tunnel is irregularly distributed in spatial coordinates. The longitudinal slope of the tunnel is usually between 0.3% and 3%, and thus the tunnel axis is not a completely horizontal curve in space. In this paper, based on the projection method, a fitting method for the central axis of point cloud data is proposed.

The projection equation of the central axis on the XOY and XOZ planes can be calculated by the projection boundary of point cloud data. Along the axial direction, the left and right boundaries of the XOY plane projection are parallel curves. Therefore, the boundaries of the XOY plane projection with polynomials are fitted as follows: (11) y=h1(x)y=h2(x)} \left. {\matrix{ {y = {h_1}(x)} \hfill \cr {y = {h_2}(x)} \hfill \cr } } \right\} For any point (x₀, y₀) on one of the boundaries, the tangent equation is: (12) y−h1(x0)=h1'(x)(x−x0) y - {h_1}\left( {{x_0}} \right) = h_1^\prime (x)\left( {x - {x_0}} \right) Then the intersection point of the tangent perpendicular with another boundary and the midpoint of the line connecting the point (x₀, y₀) exist on the central axis, and the curve with quadratic function can be fitted to obtain the projection of the central axis of the tunnel on the XOY plane: (13) y=f(x)=C1x2+C2x+C3 y = f(x) = {C_1}{x^2} + {C_2}x + {C_3} For the XOZ plane, due to the complex terrain during tunnel construction, the equation of the central axis on this plane cannot be calculated by the same method. In addition, because of the longitudinal slope of the tunnel, the central axis of the tunnel is not a horizontal curve. For simple calculation, the vault curve equation of the tunnel is taken as the basic curve equation of the central axis, which is: (14) z=h3(x) z = {h_3}(x) Shifting the curve downward along the Z-axis by d, the projection equation of the central axis in the XOZ plane can be obtained as: (15) z=g(x)=h3(x)−d z = g(x) = {h_3}(x) - d The axis of a mountain tunnel with a large cross-section often has a small curvature. In the intercepted unit tunnel area, the axis can be considered as a straight line. The direction of axis coincides with the X-axis through two coordinate transformations, namely: (16) {XYZ}i=R(α,β){xyz}i+{x0y0z0} {\left\{ {\matrix{ X \cr Y \cr Z \cr } } \right\}_i} = {\bf R}(\alpha ,\beta ){\left\{ {\matrix{ x \cr y \cr z \cr } } \right\}_i} + \left\{ {\matrix{ {{x_0}} \cr {{y_0}} \cr {{z_0}} \cr } } \right\} where α and β are the angles between the XOY and XOZ planes and the X-axis, respectively, in the normal direction of the tunnel.

Based on a cross-section coordinate system, for any cross-section plane x = x₀, setting the intercept thickness as δ, through the plane of x=x0δ2 x = {x_0}{\delta \over 2} , the point cloud data is intercepted near the section: (17) Q={pi∈P||xi−x0≤δ2} Q = \left\{ {{p_i} \in P||{x_i} - {x_0} \le {\delta \over 2}} \right\} Section convergence usually represents radial convergence, which cannot be directly calculated in rectangular coordinates. Based on the section coordinate system, a polar coordinate system can be built to calculate the radial convergence value of the tunnel in any direction.

The polar coordinate system is constructed as follows:

Import a point cloud matrix in 3D coordinates P = (X, Y, Z);

The underground utility tunnel of Tianhe Smart City has a total length of about 19.39 km, and the main routes are arranged along the existing Keyun Road, Kexiang Road, Huaguan Road, Gaotang Road, Ruan Road, Gaopu Road, Daguan Road, Guangcan Road, Kemulang South Road and Mubei West Road, Lingcen Road. The section of shield construction is 7.6 km, and the pipe gallery section is circular; further, it is mainly divided into Keyun Road and Huaguan Road. The open cut construction section is 10.8 km, and the section of the pipe gallery is rectangular. The road section studied in this paper is the sum of Huaguan Road and the pipe gallery. In order to get the deformation of the pipe section, a comparative analysis of the same section of the pipe section is made by three periods.

In this paper, the total station measured data is used to measure the control points, the geodetic coordinates of two fixed points outside the tunnel are measured by the total station and the coordinates of the fixed points are discussed in the forthcoming content. This coordinate of fixed point is the common point of scanning data. Through these two fixed points, the multi-phase scanning data can be transformed in the same coordinate system to analyse the segment deformation.

As an ultra-long linear structure, the scanning interval is 1.6 km in total. In this paper, a scheme is made before scanning, which is divided into 15 stations for scanning and splicing. The stations are named as Station 1 to Station 11. The station is arranged in the middle of the tunnel, which is scanned in all directions using 360° scanning.

By measuring the geodetic coordinates of three stations, a complete control network system can be formed. Among them, the geodetic coordinates of Station 1, Station 5 and Station 11 are measured by the total station. The layout scheme and geodetic coordinate values are shown in Table 2.

After the scheme of 3D laser scanning is made, the first part of deformation analysis needs to be conducted, and the same is described in the previous section. The application of Leica P50, a ground 3D laser scanning instrument, and cyclone, its supporting software, is used to collect and splice point cloud data to complete the preliminary work of the model. In this section, we need to fit and transform the spliced point cloud data that is transformed into a curved surface model for overall section analysis, which includes three parts: the unification of point cloud coordinates, the transformation of point cloud data, the establishment of fitting surface and the extraction of cross-section.

4.3.2

Transformation of point cloud data

Based on the unified point cloud data in the previous section, the output is imported into 3DReshaper (3D point cloud data modelling) software to extract the central axis and create the cross-section along the central axis.

The content of this paper is the length range of segment from 500 ring to 670 ring, the width of segment is 1.5 m, and the total length of research area is 255 m. A part of the tunnel section is selected, and cross-sectional interception is carried out with every 10 m as a truncated surface, which is formed into 25 truncated surfaces, as shown in Figure 5.

Fig. 5

4.3.3

Extraction of cross-section

As shown in Figure 6, there are four models near the same position; one is the basic circle model, and the other three are the cubic measurement models. By extracting the cross-section information, a comparison chart of 25 cross-sections is obtained, as shown in Figure 7.

Fig. 6

Fig. 7

In order to study the distribution law of each characteristic monitoring point with time, the changes of arch crown, arch bottom and arch waist of lining segment measured by scanning in three periods are sorted out. It can be seen that the four monitoring points of vault, arch bottom and arch waist on both sides have similar changes with time. Mainly, as time goes by, the deformation of each monitoring point becomes larger [32].

The speed of deformation from ring 500 (section 0) to ring 670 (section 24) is also gradually increasing, which is due to the fact that ring 670 (section 24) is closer to the excavated face than ring 500 (section 0). In the first scanning survey in the early stage, the lining segment was installed soon, and with the continuous excavation of shield, the surrounding rock around the lining segment changed more. The lining segment is deformed by the secondary stress of surrounding rock. In addition, ring 500 (section 0) is farther away from the excavated face, and the disturbance of surrounding rock at this section is small. The surrounding rock is supported by the lining segment and stable grouting effect, and the deformation is small and tends to converge. For the multi-stage monitoring of a large number of sections, the whole deformation monitoring of shield tunnel is formed, which can search the deformation law and the deformation characteristic points that need to be controlled. Compared with the limited number of monitoring points in traditional methods, the ground 3D laser scanning monitoring method can monitor the whole section. It can also extract the deformation monitoring feature points of the whole section, with a larger amount of data, which has a greater guiding role for the safety and stability of the lining tunnel.

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