The hydropower station is located downstream of the confluence of the Yalong and Xianshui Rivers, approximately 3 km from the confluence. The river’s elevation is about 2600 m during the dry season, with a width of 40–60 m. The valley slopes steeply, with heights ranging from 500 to 1,000 m. The stratum exposed in the dam’s river section belongs to the Maduo-Maerkang stratigraphic division, a shallow metamorphic rock series of the Upper Triassic Xinduqiao and Lianghekou Formations in the Yajiang stratigraphic area. The Xinduqiao and Lianghekou Formations can be divided into upper, middle, and lower sections. The study focuses on the upper section of the Xinduqiao Formation (T₃ xd ³) and the middle and lower sections of the Lianghekou Formation (T₃ lh ¹, T₃ lh ²). The dam site’s geological structure consists of monoclinic strata on a macro level, with a normal stratigraphic sequence and an overall occurrence of N60-80ºW/SW∠50º-80°. The fold classification at the dam site is below three levels, according to the surrounding regional structure. The main structure of the dam’s river section includes the Qingdahekou anticline with a steep dip to the southeast, the longitudinal reverse fault f1 in the northwest steep wing of the anticline, and fault f4 at the interface between T₃ lh ²⁽²⁾ and T₃ lh ²⁽³⁾. The Qingdahekou anticline axis is located at the intersection of the Qingda and Yalong Rivers. The basic structural outline and characteristics of the dam’s river section, and the distribution of rock strata, are influenced by these features.

The GNSS arrangement of the earth dam in a hydropower station in Southwest China is as follows (Figure 2).

In this study, a Riegl VZ-2000i instrument, which has a maximum range of 2000 m, a maximum angular resolution of 0.001°, a maximum pitch angle of 60°, a maximum scanning distance parameter of 1500 m and an angular resolution of 0.05°, was used for data acquisition. Two periods of data were collected on 10 January 2023 and October 25 of the same year (Figure 3).

TLS determines the distance from the surface of the target object to the laser scanner is then determined by calculating the time delay and optical path difference of the reflected beam. The horizontal and vertical angles of the scan are also recorded to calculate the relative coordinate difference between the scanning point and the scanning station (Xu et al., 2020). In this study, 11 TLS scanning points were deployed at suitable locations on the top and both sides of the dam. Each point was scanned multiple times by continuously changing the rotation direction and angle. The point spacing of the point cloud is approximately 0.4 m.

Scanners operating in field environments face complex challenges. These include the movement of construction machinery and personnel, as well as environmental factors such as trees, buildings and obstructions. Additionally, construction dust and the variable reflective properties of the scanned targets contribute to instability and noise in the point cloud data. To ensure quality, it is imperative to preprocess the 3D laser scanning data. This preprocessing involves verifying the data integrity and consistency, normalizing the data formats and filtering the point cloud. During the measurement of the earth dam, multistation scanning was employed to capture comprehensive surface details. However, this approach results in significant data overlap after registration, leading to large datasets with considerable redundancy. To enhance the efficiency and quality of surface reconstruction, it is crucial to selectively sparsify the data based on the smoothness of the dam surface. This process effectively reduces the overall data volume.

After data preprocessing, segmentation, classification, and registration of point cloud data are imperative for enhancing accuracy. Given the scanner’s operation from multiple locations, each dataset inherits a unique coordinate system. This necessitates registration of point cloud to enable a comprehensive view of the dam’s facade through data integration. Herein, the ICP algorithm plays a pivotal role in the registration processes, beginning with the identification of two point cloud models that share substantial overlap. These models are then merged and aligned within a singular coordinate system, forming a consolidated point cloud model via the ICP algorithm. To enhance the efficiency and accuracy of the ICP algorithm, manual selection of the dam’s point cloud data precedes the sequential registration of data from other sites into the model via the ICP algorithm. To verify registration accuracy, an initial examination of the point cloud uses a co-linear monitoring station along the y-axis as a reference for the profile line, extending from the upstream monitoring station to the downstream base, traversing the entire structure. This procedure was replicated four times based on the distribution of the monitoring stations across the dam surface. The intercepted point clouds, lying within the overlapping scan areas of different stations, should ideally fully overlap. Consequently, distinct layering within the intercepted point cloud may suggest the need for reregistration. A preliminary inspection followed by a quantitative accuracy analysis indicated that the majority of paired points clustered around a zero error margin, suggesting a minimal registration error (Figure 4). Positive values represent the relative vertical uplift values, and negative values represent the subsidence values. The horizontal coordinate represents the amount of error, and the vertical coordinate corresponds to the number of paired points. As the error increases from −0.278 m to 0.265 m, the number of paired points first increases and then decreases. When the error is approximately 0.015 m, the corresponding paired points peak at approximately 32,500. When the error approaches −0.278 m and 0.265 m, the number of paired points is only a few hundred. It was concluded that there was no significant delamination within the point cloud’s overlapping region after stitching and registration, allowing progression to subsequent stages.

The following figure shows the point cloud data of the earth dam in a hydropower station obtained on 25 October 2023, which were sequentially subjected to noise reduction and stitching registration to obtain a three-dimensional point cloud model of the dam (Figure 5).

The ICP algorithm serves as a method for change detection by matching point clouds, utilizing the coordinates of two point clouds to create a cost function that looks for a rigid transformation to minimize its residual error (Feng et al., 2019; An et al., 2024). The accurate calculation between points in 3D space is accomplished by calculating the rotations and translations generated during the matching of point clouds. With the ICP algorithm, the spatial rotation matrix M, and the spatial translation vector t → from the point cloud P, to be matched to the reference point cloud Q, can be derived. Q = M P + t → (1) M = r 11 r 12 r 13 r 21 r 22 r 23 r 31 r 32 r 33 , t → = t x t y t z (2)

The basic principle of the ICP algorithm is to separate the point cloud to be matched in the P and the reference point cloud Q . The basic principle of the ICP algorithm is to find the nearest neighboring points ( p i , q i ), calculate the distance between the corresponding pairs of points, iterate the rotation matrix and translation vector by minimizing this distance, and stop iterating if the convergence condition is met.

Each iteration of the process yields a spatial rotation matrix M n and a spatial translation vector t → . To obtain the original matched point cloud to the nth iteration, the transformation of the original matching point cloud to the nth iteration can be obtained by replacing M n , and t → n is unified into a 4 × 4 chi-square matrix R n and T n : T n = 1 0 0 t x n 0 1 0 t y n 0 0 1 t z n 0 0 0 1 , R n = r 11 n r 12 n r 13 n 0 r 21 n r 22 n r 23 n 0 r 31 n r 32 n r 33 n 0 0 0 0 1 (3)

Then, the spatial rotation matrix and the spatial translation vector for each iteration can be combined into the same spatial transformation matrix M R T n : M R T n = r 11 n r 12 n r 13 n t x n r 21 n r 22 n r 23 n t y n r 31 n r 32 n r 33 n t z n 0 0 0 1 (4)

Multiply each iteration M R T n to obtain the original matching point cloud to the nth iteration of the spatial transformation matrix: M R T = ∑ i = 1 n M R T i (5)

In this study, an error analysis method based on the ICP algorithm is proposed to analyze dam deformations by using TLS to collect data and to compensate for the lack of accuracy of algorithms such as the DoD method, the SD method and the M3C2 method.

The deformation values calculated by the ICP algorithm were geometrically compared with the 3D surface model obtained using the SD method. Although the SD method can quickly calculate the surface deformation, it will also lead to a slight measurement error. Since the SD method selects the nearest point on the reference plane, the measurement error will increase as the point cloud data become sparser. Since the point cloud data downstream of the dam were acquired at a longer distance, and the point density obtained was sparse, the ICP algorithm was used for the monitoring points on the downstream dam face. The ICP algorithm is a change detection method in which point clouds are matched, which is accomplished by calculating the rotational translations generated during the matching process of the point clouds. Compared to the SD method, which can only calculate the shortest distance between point clouds, the ICP algorithm can be aligned according to the terrain surface characteristics, and can accurately derive the amount of change on the slope surface even in complex situations.

However, the results of the ICP algorithm calculation cannot be directly used for change detection. The ICP algorithm obtains a transformation matrix after registration, deriving the amount of translation and rotation in the process of registering the matched point cloud to the target point cloud. However, if the ICP algorithm uses the origin of the coordinates as the rotation center for the point cloud to be matched, it will cause a translation in the center of mass of the point cloud. At this point, the final translation amount of the matched point cloud derived from the transformation matrix is not equal to the true translation amount from the center of mass of the matched point cloud to the center of mass of the point cloud after registration (Figure 6A). Therefore, it is unreliable to use the transformation matrix obtained by the ICP algorithm directly for change detection.

To avoid translations in the centre of mass, when using the ICP algorithm to register each point cloud block, the center of mass of the point cloud block should be set as the center of rotation. In this case, the rotations and translations of the point cloud do not interfere with each other, and eventually, a transformation matrix is derived during the ICP registration process. The translations and rotations obtained from this transformation matrix can be regarded as the exact displacement values of the point cloud blocks during the registration process (Figure 6B), which can be used for change detection.

In addition, at least three planes with different normal vectors are required in the ICP algorithm computational object. Otherwise, misregistration of the planes along one of the faces may occur during the stitching process, a phenomenon known as in-plane movements (Figure 7). Since the GNSS monitoring sites are distributed on the surface of the earth dam in the form of houses, each monitoring house provides three planes with different normal vectors for the ICP algorithm (Figure 8). The houses have a regular shape and configuration, which facilitates the ICP algorithm calculations based on these houses. Therefore, when manually intercepting point cloud data from a dam prior to calculating the ICP algorithm, it was necessary to ensure that each point cloud block had a monitoring house.

The terrain occluded the monitoring houses at sites TPDB-49, TPDB-54, TPDB-58 and TPDB-61, precluding a TLS and the ICP algorithm analysis. Hence, these sites are omitted from the figures. In the x-direction, positive and negative values indicate deformation toward the left and right banks, respectively. Similarly, in the y-direction, a positive value indicates that the deformation direction of the dam is pointing upstream, and a negative value indicates that the deformation direction of the dam is pointing downstream. In the z-direction, positive and negative values correspond to vertical uplift and subsidence, respectively.

Analysis of the dam deformation trends reveals a predominant movement toward the right bank in the x-direction (Figure 9A), downstream in the y-direction (Figure 9B)—with some upstream exceptions—and an overall subsidence trend in the z-direction (Figure 9C), with some areas exhibiting uplift. In other words, the dam as a whole, while settling, also deforms toward the right bank and slides downstream on the riverbed. The dam’s settlement is primarily attributed to continuous water pressure on its upstream side and its own weight. The rightward movement is influenced by the topography, with the dam sliding downstream due to horizontal water pressure, creating a larger contact area with the right bank. At this point, this contact surface intersects the trend line of the overall downstream sliding of the dam surface, which takes up some of the force generated by the sliding of the dam. According to the analysis of the data from each site, in the x-direction, the absolute value of the deformation decreases with the increasing site number and is negative. This indicates that the downstream dam surface rotates toward the right bank with the bottom of the dam at the center of the circle. In the y-direction, the larger downstream-oriented deformation is distributed in the connection between the dam face and the right bank. The middle part of the dam appears to have an upstream-oriented deformation trend parallel to that of the right bank, which further confirms that the downstream dam face underwent a “rotational” deformation. In addition, the top of the dam is slightly compressed from the midpoint to the left bank. In the z-direction, the dam settles downward, and the subsidence of the dam face decreases with decreasing elevation. The whole process resulted in a partial uplift of the dam face downstream of the dam base due to extrusion, with a tendency for the dam face to be inserted below the right bank. This asymmetric pressure distribution necessitates focused maintenance on the areas of the downstream dam face near the right bank and the left bank to prevent damage in these stress concentration areas.

The calculation results were statistically analyzed. The ICP algorithm demonstrates high accuracy, with mean error values of 2.2 mm, 2.5 mm, and 3.1 mm in the x, y, and z directions, respectively, and standard deviations of 23.3 mm, 3.7 mm, and 23.5 mm. The minimum and maximum errors of the algorithm’s three-dimensional calculated values were 0 mm and 4.2 mm, respectively, with an average error of 2.3 mm and a median of 2.6 mm (Table 1). These results indicate a tight clustering of errors around the mean, especially in the y-direction. The algorithm’s maximum error is 7.6 mm, with some measurements achieving zero error and an average error maintained at 2.6 mm, suggesting strong agreement with GNSS data and confirming the suitability of the ICP algorithm for millimeter-level dam monitoring. In summary, 3D deformation analysis based on TLS and the ICP algorithm can indeed be used to effectively identify the deformation vectors of dam surfaces. For the areas where houses are not scanned, although the displacement vectors of the dam face points cannot be accurately calculated using the ICP algorithm, it is still possible to estimate them based on the general trend.

The SD method was utilized to generate a 3D deformation cloud map (Figure 10). In this graph, red represents uplift, and blue represents subsidence. The color gradation from red to blue signifies the deformation magnitude, with deeper hues indicating more substantial deformations. The upstream and central portions of the dam, which experience direct reservoir pressure and minimal lateral restraint, are the most deformed and at greatest risk, necessitating prioritized protection. The entire downstream face of the dam has less stress in contrast to the upstream section and crest. Such discrepancies in deformation distribution are likely due to uneven stresses within the dam structure, drawing attention to the necessity of monitoring the more deformed areas. In the mountainous and alpine canyon regions, TLS scanning stations are often restricted to river valleys, with steep terrain on either side causing significant occlusions and a marked reduction in data completeness. Dense vegetation further exacerbates this challenge. Consequently, the isolated 50 mm bulges on the dam face can be attributed to modeling inaccuracies caused by the sparse density of the point cloud in January and shading by vegetation, highlighting the need for thorough downstream face scans in future surveillance.

By annotating ten points surrounding the monitoring station in three-dimensional space, the average value is taken as the deformation calculation result of the SD method and compared with the GNSS data. The precision of the SD method was inconsistent, with a maximum error of 110.8 mm and a minimum of 0.4 mm. The substantial overall calculation error indicates that the SD method is unsuitable for analyses requiring fine-scale deformation monitoring.

To determine the most appropriate algorithm for analyzing deformations in earth dams, a comparative error assessment of the SD method and the ICP algorithm is performed. Consistent with earlier findings, the data from stations TPDB-49, TPDB-54, TPDB-58 and TPDB-61 were excluded. The maximum errors for the SD method in the x (Figure 9D), y (Figure 9E) and z (Figure 9F) directions were 79.6 mm, 109.4 mm and 100.2 mm, with average errors of 32.1 mm, 25.4 mm and 32.9 mm, respectively. This is because the limitations of the SD method stem from its inability to accurately determine the displacement vector direction, which relies instead on calculating the shortest distance between point clouds. Furthermore, identifying identical points within two distinct scans becomes increasingly challenging as the point cloud density diminishes, leading to greater deviations in the displacement vector direction from reality and the associated reference points from their true locations. As a result, the error magnitude escalates. In addition, with increasing monitoring station serial number, the error tends to decrease, especially in the x-direction. Notably, the error tends to decrease with increasing monitoring station number, particularly in the x-direction, where the error of the ICP algorithm distribution tends to decrease. This could suggest a correlation between the actual deformation magnitudes and calculated error values, indicating that the errors tend to decrease as the actual deformation decreases.

Compared with those of the SD method, the accuracies of the ICP algorithm in determining the deformation values at x (Figure 9D), y (Figure 9E) and z (Figure 9F) are significantly improved by 93.1%, 90.0%, and 90.5%, respectively, showing substantial consistency with the field measurement data. This is because the ICP algorithm correctly identifies the direction of displacement, resulting in a displacement vector calculated with minimal error. It can be indicated that the computational errors of the ICP algorithm are lower than those of the SD method, and fall within an acceptable error margin. These findings demonstrate the superiority of the ICP algorithm over the SD method, making the results of the ICP algorithm a reliable foundation for dynamic deformation analysis of dams.

In this study, when point cloud deformation analysis is carried out, the artificial segmentation method is used to divide the point cloud, which introduces subjectivity. The shape, dimensions and positioning of the point cloud segments partially influence the calculation accuracy. Consequently, employing artificial intelligence algorithms is essential for dividing point clouds to eliminate subjective human factors, thereby minimizing subjective bias and registering error estimates more closely to the actual values. The algorithm designates each monitoring station as a circular subunit’s center, divides the point cloud into circular subunits and determines the radius of the circular point cloud subunits. The search radius is incrementally increased to expand the point cloud blocks, and the displacement of the same measurement point is calculated after the registration of different block sizes of the point cloud. The computational results are then compared against GNSS data, and the computation errors of different block sizes are obtained.

The dimensions of the monitoring houses are approximately 6.6 m on the downstream-facing side and 4 m on the riparian-facing side. To satisfy the ICP algorithm calculation conditions, each block must encompass the monitoring house. Therefore, the initial search radius for each site was set to 20 m, and the radius was increased by 1 m for each calculation. Figures 11A–C show the block sizes of 20 m, 30 m, and 40 m, respectively. However, excessively large segments might encompass multiple monitoring sites. Since the deformation of the dam surface is inhomogeneous, the deformation around different monitoring stations is not consistent, precluding their collective analysis. Consequently, the calculation ceases when the radius expands to 100 m. Given the substantial data volume from the results, the error values in three-dimensional space are sorted out by mathematical statistics, and the error value corresponding to each search radius is the average of the errors of the 54 stations, underscoring its statistical relevance (Figure 12).

The results show that the computational accuracy of the ICP algorithm is high, and the errors are all approximately 10 mm, which meets the accuracy requirements of a small deformation analysis. Meanwhile, the error values in three-dimensional space show an obvious V-shape with the gradual increase in the search radius, the average error corresponding to the valley of the V-shape is the smallest error searched for in this study, and the corresponding search radius is the optimal search radius.

Point cloud registration involves adjusting one point cloud y i to another point cloud x i passed through a spatial rotation matrix M with a spatial translation vector t → by calculating the computational error of the ICP algorithm E M , t → . E M , t → = 1 N i ∑ i = 1 N M y i + t − x i 2 (6)

Where N i represents the number of point clouds. The matrices y i and x i are the point sets of the two point clouds.

The ICP algorithm seeks to optimize by minimizing E M , t → , which requires that the number of points in each piece of the point cloud block be appropriate. Significant errors are observed in the point cloud blocks when the search radius is smaller than the optimal radius due to the relatively limited number of point cloud features within the included range. When the search radius is larger than the optimal radius, the point cloud block is too large, and one point cloud covers at least two monitoring houses. Due to the uneven deformation of the dam surface, the deformation of the two monitoring houses is different. If they are calculated as a whole, the calculation error will increase with the increasing radius. This shows that the “V-shaped” relationship between the search radius and the computational error is generally consistent with reality, and can be widely applied in other studies.

From the scanning results, the shortest distance between two neighboring monitoring houses is approximately 66 m, and the farthest distance is approximately 109 m. To minimize the computational error of the point cloud block covering as many points as possible with only one monitoring house, the optimal radius should be less than 66 m. As shown in the figures, the optimal search radii in the x, y and z directions are 40 m, 45 m, and 44 m, respectively, and the computational error is minimized, and the computational results are most reliable when the corresponding optimal search radius is obtained in each direction. Therefore, in subsequent deformation analyses, the optimal search radius can be determined according to the method described in this study as the basis of the point cloud block size to improve the accuracy and credibility of the calculation results.