Detecting and Evaluating Displacements of Paving Blocks Adjacent to Deep Excavation Sites Using Terrestrial Photogrammetry

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The terrestrial photogrammetry technique provides an efficient and accurate solution for evaluating ground deformations induced by construction activities.

Abstract

In urban areas, deep excavation-induced ground deformations may damage adjacent existing structures and are conventionally evaluated by levelling at installed settlement points. However, a small number of measurements cannot represent the total changes in ground deformations adjacent to excavation sites. Furthermore, significant local subsidences may occur in places where settlement points have not been installed and only noticed after an accident. For deep excavation sites located in urban areas, paved pedestrian sidewalks are often located adjacent to sites, and construction activities can cause these paving blocks to become displaced. This study introduces a method to detect paving block displacements adjacent to deep excavation sites using terrestrial photogrammetry. A digital camera creating point cloud data (PCD) and an acquisition method satisfying the frontal and side overlap requirements were demonstrated. To investigate the displacement detections and measurement capabilities by PCD analysis, an experimental program was conducted, including a PCD comparison containing the uplift, settlement, and horizontal paving block displacement and reference data. The cloud-to-cloud distance computation algorithm was adopted for PCD comparisons. Paving block displacements were detected for displacements of 5, 7.5, and 10 mm in the uplift, settlement, and horizontal directions; however, the horizontal displacements were less clear. PCD analysis enabled satisfactory measurements between 0.024 and 0.881 mm for the vertical-displacement cases, but significant errors were observed for the horizontal-displacement cases owing to the cloud-comparison algorithm. The measurement blind spot of limited settlement points was overcome by the proposed method that detected and measured paving block displacements adjacent to excavation sites.

1. Introduction

Recent emphasis on serviceability control in geotechnical engineering projects demands accurate measurements of the displacements of structures and the ground surface. Numerous studies have been conducted to analyze the factors affecting the ground deformation during deep excavation, whether in rock or soil [1,2,3,4,5,6,7]. Routine measurements of ground settlements adjacent to a deep excavation project are legally mandated, although only a minimum number of monitoring points are controlled in most projects with tight budgets. Unfortunately, such legal efforts have not successfully prevented a catastrophic collapse, mainly because the location initiating the collapse is often out of the range controlled by the measurement of the monitoring points. The adaptive management technique for ground deformation control including the inverse analysis is also limited because it relies on those monitoring points [8,9]. Settlement measurements are possible with synthetic-aperture radar (SAR), but images of the area of interest may be insufficient for frequent investigation [10]. Consequently, a technique for measuring the displacements induced by excavation work in the entire range or full field is crucial for ensuring construction safety [11].

Recent developments in computer performance and the increased use of digital photographs have stimulated advances in photogrammetric software. Photogrammetry is a technique for determining the three-dimensional geometry of physical objects by measuring and analyzing their two-dimensional photographs. Terrestrial photography provides detailed dimensional information about an object using images near or on the surface of the earth. In close-range terrestrial photography, the size of the object and the camera-to-object distance are both less than 100 m [12]. Several papers related to close-range photogrammetry have been dedicated to various application fields such as industrial engineering [13], cultural heritage documentation [14,15,16,17,18], and geomorphology [19,20,21,22,23]. Close-range terrestrial digital photogrammetry is widely applied in rock mass discontinuity characterization [24]. In civil engineering, close-range photogrammetry plays a vital role in engineering surveys, including as-built documentation of existing facilities and building information modeling. The bridge deformation and health monitoring were measured using the photogrammetry technique [12,25,26,27,28,29]. The deformation of concrete tanks and retaining walls under working conditions can be measured using high-precision photogrammetry with high-resolution cameras [30,31].

Various applications of the close-range terrestrial photogrammetry technique also reveal the possibility of full-field measurements of displacements induced by deep excavation work in urban areas. Pedestrian sidewalks paved with concrete pavement blocks are frequently located adjacent to deep excavation sites. Measuring the displacements of these pavement or paving blocks via close-range photogrammetry can resolve the practical difficulties in investigating the ground deformation induced by deep excavation works in urban areas. We opted to use Unmanned Ground Vehicles (UGVs) as an alternative to Unmanned Aerial Vehicles (UAVs), as the latter often lead to safety and regulatory concerns when operated in urban areas [32,33,34,35,36].

To the extent of our understanding, the methodology of monitoring the movements of paving blocks through close-range photogrammetry, carried out by cameras affixed to the UGV system, has not been systematically presented. Figure 1 displays the paving blocks adjacent to the excavation site. In Figure 1, the construction site is located behind the wall; moreover, various displacements of paving blocks can be observed.

This study introduces a workflow for detecting the displacements of paving blocks adjacent to deep excavation sites. This workflow mainly relies on close-range terrestrial photogrammetry and structure-from-motion (SfM) photogrammetric techniques. The requirements for establishing reliable point cloud data (PCD) for paving blocks including ground sampling distance, image network geometry, and parameters of the camera mounted on an unmanned ground vehicle (UGV) are presented. The applicability of the cloud-to-cloud (C2C) distance computation algorithm is discussed to trace temporal changes in the uplift, settlement, and horizontal movement of paving blocks.

2. Materials and Methods

Figure 2 illustrates a flowchart of the proposed methodology. It shows the flow of the digital image acquisition method, PCD creation using digital images, and displacement detection and measurement through PCD comparison. The details of individual items in the flowchart are presented in the following sections.

2.1. Digital Image Acquisition

A camera was selected to move the UGV in a paving block adjacent to the excavation site. The camera must be lightweight, capable of continuous shooting for photogrammetry, and able to obtain stable images without shaking. An action camera (GoPro HERO7 Black) was used to obtain digital images for terrestrial photogrammetry. Action cameras specialize in recording smooth videos while moving. It may not need a gimbal, but using a gimbal makes it easy to adjust the angle of viewing and can also provide auxiliary stabilization. The GoPro HERO 7 Black weighs 116 g, and the Feiyu WG2X gimbal used weighs 238 g. If a digital single-lens reflex camera was employed for image acquisition, the total weight would be greater than 3 kg. This is approximately ten times heavier than that of the action camera system, and therefore, the UGV would be inefficient as more energy is used to move.

To obtain digital images for terrestrial photogrammetry, it is necessary to evaluate the ground sample distance (GSD), which is the distance between the pixel centers measured on the ground and the field of view (FOV) according to the camera shooting height. For the employed camera, the width of the charge-coupled device was 6.17 mm with 4096 pixels, and the horizontal FOV was 86°. As shown in Figure 3a, the GSD increased with the camera shooting height, and was less than 0.911 mm when the shooting height was lower than 2.0 m. The GSD value appeared to be sufficient to evaluate the paving block displacements adjacent to the excavation sites. The maximum shooting height was set to be 2.0 m.

Figure 3b demonstrates the ground distances depicted in an image with a pitch angle (α) while the camera is positioned at a height of 2.0 m. In this scenario, the camera is mounted in a manner where it faces downwards, and the top of the image corresponds to the front direction. Half of the vertical FOV of the camera was 35°. When α is greater than 0°, the image becomes oblique, so it shows more of the ground in the travel direction. The ground distance PB shown in Figure 3b increases rapidly with increasing α, increasing the ground distance AB. However, the distance AP decreases. As a result, information far from the camera’s position can be included in the image with a large α, making it difficult to properly create PCD. Consequently, a low-oblique image closer to a vertical image or vertical image was adopted to create PCD, rather than the high-oblique images. This is consistent with the recommendations of the SfM software manual that the camera should be kept as constant as possible over the terrain to ensure the desired GSD. The Pix4D mapper version 4.8.1 was used for the SfM software in this study.

To create a PCD, the recommended frontal overlap between the images should be at least 75%. The camera employs two methods to obtain digital images: capturing a snapshot with time lapse and extracting a frame from a video. The minimum interval between images is 0.5 s for time lapse. For frame extraction from a video at 30 fps, 30 images can be obtained in 1 s; therefore, the time interval between two consecutive images is 0.033 to 1 s. Note that digital images are obtained while moving on the sidewalk; therefore, moving at a high speed is dangerous for pedestrians. Accordingly, the practical moving speed range for image acquisition is 2.0 m/s or less, which is a typical jogging speed. As can be seen in Figure 4, the frontal overlap is affected by the movement speeds and α. If the moving speed is fast, it may not be possible to obtain a sufficient number of images that satisfy the 75% minimum frontal overlap recommended for photogrammetry [37]. When the moving speed was 1.0 m/s, frontal overlap could be satisfied with both image acquisition methods, as shown in Figure 4a. However, when the moving speed was 2.0 m/s, as indicated in Figure 4b, only the frame extraction whose interval was shorter than 0.33 s could satisfy the required frontal overlap, regardless of α. The method of capturing a snapshot with time lapse cannot satisfy the requirement when α is smaller than or equal to 25°; only the case of α = 30° can satisfy the requirement. Consequently, a method of extracting frames from videos was selected to obtain sufficient images for PCD creation.

For a side overlap, the spacing between moving tracks is important to satisfy the requirement of at least 60% [37]. As shown in Figure 5, when the spacing was shorter than approximately 1.5 m, the required overlap was satisfied. Accordingly, the spacing was set shorter than 1.5 m when obtaining the images. Note that the camera was maintained at a constant shooting height of 2.0 m.

2.2. Testing Program

In urban areas, existing buildings are often demolished and new buildings are constructed. In this case, the sidewalk adjacent to the excavation site used before construction continues to be used. Accordingly, ground movement adjacent to the excavation site causes displacements of the paving blocks. In this study, three cases of paving block movements that can be found in Figure 1 were evaluated: uplift, settlement, and horizontal displacement. Evaluations were performed at 5 mm, 7.5 mm, and 10 mm in each case.

Figure 6 shows the reference without displacement setup to detect and measure the movements of the paving blocks measuring 1380 cm × 1380 cm. Seventy-two paving blocks with dimensions of 230 mm × 115 mm × 60 mm were used. The four corner markers were ground control points (GCPs), where the coordinates were measured using a global navigation satellite system rover, Trimble R10. These GCPs were utilized for the georeferencing of the PCD. By adding geographic information to the image, it is easy to detect and calculate changes in the PCD. The uplift and horizontal displacement of the paving block were induced by installing spacers in the reference paving block setup. Settlement was created by lowering the level of the floor where the paving block was placed.

For each test setup, two round-trip videos were recorded using GoPro 7 Hero Black, and the frames extracted from the videos were used for PCD creation. In a single round trip, videos were recorded along the same track at a height of 2 m. The distance between the tracks was within 1.5 m to satisfy the side-overlap requirement. The PCD was created using a Pix4D mapper.

2.3. Data Interpretation

PCD with various displacements, PCDd, were compared with the reference PCD, PCDr. The open-source software CloudCompare version 2.12.4 was used for point cloud processing. Since identical GCPs were used for the creation of the PCD, the PCD were well aligned during the comparison. For better results, PCDd was slightly rotated and translated to fit PCDr using the iterative closest point (ICP) algorithm. Note that the ICP algorithm can minimize the difference between two PCD and is often used to construct a single PCD from different scans in several engineering fields. The displaced paving blocks were excluded while the ICP algorithm optimized the transformation matrix to determine the best fit, because the displaced paving blocks would influence matrix optimization. After obtaining the optimized transformation matrix, it was applied to the paving blocks with displacements. By conducting this process, it was possible to precisely align the PCD.

The C2C algorithm was used to compare PCDd with PCDr. It calculates the distance between two PCD by simply determining the nearest neighbor distance between points. After calculation using the C2C algorithm, the points in the zones where the displacement occurrence was detected were subset. For this subset, the mean and standard deviation of the displacements were calculated, and the distribution was analyzed using a histogram.

3. Results and Discussion

3.1. Vertical Displacements

For the investigation of uplift cases, eight paving blocks were lifted by 5, 7.5, and 10 mm. As shown in Figure 7, Figure 8 and Figure 9, it was possible to detect every tested uplift case. Note that blue indicates no displacement and green indicates displacement. The number of subset points where displacements occurred was approximately between 25,000 and 30,000. As indicated in the subfigures (d) of Figure 7, Figure 8 and Figure 9, it can be seen that the distribution of displacements appears close to the normal distribution. When the accuracy was evaluated by subtracting the actual uplift value from the mean value (μ) measured by the PCD, the tested cases of 5, 7.5, and 10 mm were 0.241, 0.074, and 0.080 mm, respectively. Herein, the standard deviation (σ) of the PCD measurements was regarded as precision. The precisions for the tested cases of 5, 7.5, and 10 mm were 0.930, 0.939, and 1.003 mm, respectively.

To investigate the settlement of the paving blocks, eight paving blocks were set to 5, 7.5, and 10 mm. As displayed in Figure 10, Figure 11 and Figure 12, it is possible to detect every tested case. Since the C2C algorithm calculates the distance to the nearest point between PCD, information about directionality, such as settlement and uplift, is unknown. Similar to the investigated uplift cases, blue indicates no displacement, and green indicates displacement. The number of subset points where displacements occurred was approximately between 25,000 and 30,000. As shown in the histogram of each case, the distribution was close to the normal distribution like the uplift cases. The mean values of the PCD measurements for the three cases were 5.881, 7.468, and 9.876 mm, respectively. When the accuracies were evaluated as in the uplift cases, the accuracies of the 5, 7.5, and 10 mm cases were 0.881, 0.032, and 0.024 mm, respectively. In addition, the standard deviations of three cases were 1.672, 1.231, and 1.445 mm for cases of 5, 7.5, and 10 mm, respectively.

Conventionally, the vertical displacement is evaluated by the level instrument at the installed settlement point; therefore, information about only that point can be obtained. However, the advantage of the level instrument is that it can measure a vertical displacement of 5 mm or less, which has not been tested here. Note that the standard deviation for the 1 km double-run levelling of these instruments is approximately 1 or 2 mm, as evaluated by ISO 17123-2 [38]. Based on the cases investigated using terrestrial photogrammetry, it can be inferred that it was possible to detect a vertical displacement of more than 5 mm. Vertical displacement evaluation using PCD is a measurement of a surface, and not a single point. Accordingly, it has the advantage of being able to determine displacements that would not have been known if there were no settlement points for the level instrument. From this point of view, PCD measurements seem to be sufficiently valuable for evaluating the vertical displacements adjacent to a deep excavation site. If the vertical displacement of the ground adjacent to the construction site is measured at the levelling error level, it is also possible to perform displacement detection using PCD and apply the level measurement to the area where displacements occur.

3.2. Horizontal Displacements

To investigate the horizontal displacements of the paving blocks, six blocks were horizontally displaced by 5, 7.5, and 10 mm, respectively. As demonstrated in Figure 13, it was possible to detect all the investigated cases, but the horizontal displacement of 5 mm was not clear, compared with the other cases. Overall, the horizontal displacement cases were not clearly visible compared with the vertical displacement. Note that blue indicates no displacement and green indicates displacement. Since the displacement zone is narrow, the number of subset points is approximately 1000, which is only 4% of that of the vertical cases. If the number of detected displaced points is small, the visibility may be poor.

As shown in Figure 14, the histogram of each case was close to the normal distribution, but the histogram bars were jagged compared with the vertical cases. The mean values of the PCD measurements for the 5, 7.5, and 10 mm displacement cases were 2.260, 3.614, and 6.225 mm, respectively. Clearly, the differences between the actual displacement value and mean were large, and the counts were very small at the actual displacements. Although horizontal displacements can be detected, the measurement errors are significant.

To determine why the measurement errors in the horizontal displacements were large compared with the vertical cases, further investigation was performed on the horizontal displacement cases. Figure 15 shows the PCD of the reference and investigated cases of a 10 mm horizontal displacement. Note that only a portion was extracted from the PCD for better presentation. The small dent shown in Figure 15a represents the chamfers of two closely adjoining paving blocks. Figure 15b indicates the PCD when one of the two adjacent paving blocks is horizontally separated by 10 mm, and the two PCD are plotted together in Figure 15c. In Figure 15d, the color of PCDd is expressed using the calculated distance from PCDr instead of actual color information obtained from the digital image, and the distance scale is shown in the color bar. As previously noted, the algorithm used to compare PCDd with PCDr was C2C, which calculates the distance between two PCD. Since the algorithm simply computes the distance between the nearest neighbor points, the calculated distance does not represent the horizontal displacement; rather, it is closer to the vertical distance. Thus, it only provides scalar information and not vectors. Additionally, it cannot be concluded whether the vertical displacement is a rise or subsidence based on the computation results alone. When a displacement is detected, it is necessary to compare the PCD in the corresponding area.

Figure 16 shows an enlarged view of the area where the 10 mm horizontal displacement occurred. As can be seen in Figure 16, a 10 mm displacement could be found from the PCDd with the actual color. In addition, it was not easy to determine the difference from Figure 16b. However, it was shown that the green lines parallel to the slit were found to the right of the 10 mm displacement in Figure 16c, and the PCD was expressed using the calculated distance from PCDr. This is because the paving blocks on the right side of the slit moved to the right when the spacing was 10 mm. When paving blocks are horizontally displaced, this pattern is expected to be found in the field.

4. Conclusions

The close-range terrestrial photogrammetry technique was applied to measure the displacements of paving blocks, indicating the ground movement caused by deep excavation works. Sequential sets of PCD were generated using Pix4D software version 4.8.1 with SfM photogrammetry. The workflow for measuring temporal changes in the displacements of the paving blocks by computing the PCD sets is provided. The requirements of the photogrammetric technique, such as ground sampling distance, image network geometry, and camera parameters, were presented to obtain reliable point-cloud data.

Vertical displacements of the paving blocks exceeding 5 mm could be detected through the workflow using the C2C algorithm. However, the detection of the horizontal displacements was less successful than that of the vertical displacements, possibly because of the theoretical limit of the adopted C2C algorithm. The measurement accuracy of the proposed workflow can be improved by introducing a vector-based algorithm to compare PCD sets.