Scholarly article on topic 'Slope excavation quality assessment and excavated volume calculation in hydraulic projects based on laser scanning technology'

Slope excavation quality assessment and excavated volume calculation in hydraulic projects based on laser scanning technology Academic research paper on "Materials engineering"

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Abstract of research paper on Materials engineering, author of scientific article — Chao Hu, Yi-hong Zhou, Chun-ju Zhao, Zhi-guo Pan

Abstract Slope excavation is one of the most crucial steps in the construction of a hydraulic project. Excavation project quality assessment and excavated volume calculation are critical in construction management. The positioning of excavation projects using traditional instruments is inefficient and may cause error. To improve the efficiency and precision of calculation and assessment, three-dimensional laser scanning technology was used for slope excavation quality assessment. An efficient data acquisition, processing, and management workflow was presented in this study. Based on the quality control indices, including the average gradient, slope toe elevation, and overbreak and underbreak, cross-sectional quality assessment and holistic quality assessment methods were proposed to assess the slope excavation quality with laser-scanned data. An algorithm was also presented to calculate the excavated volume with laser-scanned data. A field application and a laboratory experiment were carried out to verify the feasibility of these methods for excavation quality assessment and excavated volume calculation. The results show that the quality assessment indices can be obtained rapidly and accurately with design parameters and scanned data, and the results of holistic quality assessment are consistent with those of cross-sectional quality assessment. In addition, the time consumption in excavation quality assessment with the laser scanning technology can be reduced by 70%–90%, as compared with the traditional method. The excavated volume calculated with the scanned data only slightly differs from measured data, demonstrating the applicability of the excavated volume calculation method presented in this study.

Academic research paper on topic "Slope excavation quality assessment and excavated volume calculation in hydraulic projects based on laser scanning technology"

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Slope excavation quality assessment and excavated volume calculation in hydraulic projects based on laser scanning technology

Chao Hu a, Yi-hong Zhou a b c *, Chun-ju Zhao b,c, Zhi-guo Pan b,c

a School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan 430072, PR China b College of Hydraulic and Environmental Engineering, China Three Gorges University, Yichang 443002, PR China c Collaborative Innovation Center for Geo-Hazards and Eco-Environment in Three Gorges Area, Yichang 443002, PR China

Received 1 June 2014; accepted 4 March 2015 Available online 7 May 2015

Abstract

Slope excavation is one of the most crucial steps in the construction of a hydraulic project. Excavation project quality assessment and excavated volume calculation are critical in construction management. The positioning of excavation projects using traditional instruments is inefficient and may cause error. To improve the efficiency and precision of calculation and assessment, three-dimensional laser scanning technology was used for slope excavation quality assessment. An efficient data acquisition, processing, and management workflow was presented in this study. Based on the quality control indices, including the average gradient, slope toe elevation, and overbreak and underbreak, cross-sectional quality assessment and holistic quality assessment methods were proposed to assess the slope excavation quality with laser-scanned data. An algorithm was also presented to calculate the excavated volume with laser-scanned data. A field application and a laboratory experiment were carried out to verify the feasibility of these methods for excavation quality assessment and excavated volume calculation. The results show that the quality assessment indices can be obtained rapidly and accurately with design parameters and scanned data, and the results of holistic quality assessment are consistent with those of cross-sectional quality assessment. In addition, the time consumption in excavation quality assessment with the laser scanning technology can be reduced by 70%—90%, as compared with the traditional method. The excavated volume calculated with the scanned data only slightly differs from measured data, demonstrating the applicability of the excavated volume calculation method presented in this study.

© 2015 Hohai University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Slope excavation; Quality assessment; Volume calculation; Three-dimensional laser scanning technology

1. Introduction

In hydraulic engineering, slope excavation needs to be conducted before the pouring of concrete for dam foundations, dam abutments, water inlets, and so on. The quality of excavation projects directly affects the stability and safety of main structures. Highly efficient and precise control of excavation projects can not only reduce the workload and cost and shorten

This work was supported by the National Natural Science Foundation of China (Grant No. 51379109)

* Corresponding author. E-mail address: yhzhou_ctgu@qq.com (Yi-hong Zhou). Peer review under responsibility of Hohai University.

the time duration, but also diminish the disagreements between owners, contractors, and supervisors.

In the excavation process, the average gradient, overbreak and underbreak, and half cast factor (HCF) of each excavated surface should be inspected (Zhu and Sun, 2010). Quality assessment and testing methods are mainly based on profile analysis through assessment of characteristic point coordinates selected from excavated surfaces using the total station, theodolite, or other instruments (Li and Chen, 2004; Zheng et al., 2012; Fu, 2012). However, these instruments have some limitations: first, all these surveying methods are single-point surveying methods, the amount of data acquired is limited, and data processing is time-consuming and inefficient; second,

http://dx.doi.org/10.1016/j.wse.2015.03.001

1674-2370/© 2015 Hohai University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).

hydraulic engineering project sites are generally located on complex terrain, and complete data sets are difficult to obtain, especially on steep terrain and inaccessible locations; third, data accuracy depends greatly on external environmental factors. Therefore, a new approach for excavation quality assessment should be developed to meet the construction requirements.

The three-dimensional (3D) laser scanning technology can capture integrated, comprehensive, consecutive, and associated panoramic coordinate data with high precision and resolution at an extremely high speed. This method has been widely applied in Ordnance Survey and earthwork engineering, including surveying of landslide deformation (Strouth et al., 2006; Xu et al., 2010), building structures (Olsen et al., 2010), rock deformation (Kim, 2002), and shoreline evolution (Olsen et al., 2009). A landslide volume was precisely evaluated by Du and Teng (2007) using a 3D laser scanner and GPS in Taiwan. Dong (2007) developed a highly precise digital terrain model (DTM) for an engineering project based on 3D laser-scanned data. Zhang and Arditi (2013) proposed an automated progress control method using the scanning technology. However, literature and methods related to the application of the 3D laser scanning technology in hydraulic engineering are rare because of the limitations: first, there are no official standards or instructions regarding the application of this technology in hydraulic engineering; second, the data quantity acquired by the laser scanner is much higher than that acquired by other instruments, and it is difficult to process such massive data sets automatically; third, research needs to be conducted on quality assessment indices and calculation of the excavated volume with scanned data at a high efficiency.

This study aimed to demonstrate that the 3D laser scanning technology is capable of slope excavation quality assessment. Two different types of scanners were used in this study. A workflow of slope excavation data acquisition was developed, which is quite different from that of traditional methods, such as those involving the total station, GPS, or real time kinematic (RTK) technology. A ray casting algorithm was used for scanned data de-noising, a least-distance algorithm was used for data compression, and an effective scanned data management method using the SQL server was introduced. According to the Inspection and Assessment Standard for Separated Item Project Construction Quality of Water Conservancy and Hydroelectric Engineering-Earth-Rock Works (SL 631—2012), methods for slope excavation quality assessment using the average gradient, slope toe elevation, and overbreak and underbreak were established. An excavated volume calculation method was also presented in this study. To verify these methods, a field application and a laboratory experiment were carried out.

2. Methodology

2.1. Data acquisition and management

2.1.1. Data acquisition by 3D laser scanner

Two types of laser scanners were used in this study: the Leica ScanStation C10 and Leica HDS8800. Table 1 compares the main parameters of the two scanners.

In practice, these two scanners can handle different situations. The HDS8800 can scan a large area with a high-resolution camera of 70 million pixels, and capture a clear picture of the target from a far distance at a high speed, whereas the ScanStation C10 can scan a small area at a low speed from a short distance, but with a high precision. In this study, the HDS8800 was used to collect data at a hydropower construction site in southwestern China to verify the method of slope excavation quality assessment. To verify the excavated volume calculation, The ScanStation C10 was used in a laboratory experiment carried out at China Three Gorges University.

2.1.2. Data de-noising

The outline of each excavated surface can be considered a polygon, and the polygon vertexes refer to the control points of the excavated surface. The scanned area must cover the entire surface to ensure data integrity. During the scanning process, some noise points, meaning useless points, may be generated. These noise points can be divided into two categories: peripheral points and isolated points. Peripheral points are points outside the surface area, whereas isolated points are points that have an abnormal distance from the scanned surface. Isolated points are often caused by dust and ground vibration during the scanning process. To delete peripheral points, a ray casting algorithm was used in this study. The algorithm is appropriate for both convex and concave polygons. The workflow for the ray casting algorithm is shown in Fig. 1. The isolated points were removed in the data compression process.

2.1.3. Data compression

The scanned data contain millions of points. Thus, processing those data with high precision requires large amounts of computer memory. The computational efficiency will decrease, and some errors may be generated. According to the Code for Water Resources and Hydropower Engineering Surveying (SL 197—2013), the average point number in a specified area should be 8—15 per 100 cm2, which means that the maximum distance between two points should be 0.035 m. However, the point density acquired by a highly accurate scanner is much higher than the standard. Therefore, a data

Table 1

Comparison of parameters of two scanners.

Scanner

Scan distance (m)

Reflectivity (%)

Scan angle (°)

Speed (points/s)

Vertical

Horizontal

Accuracy (mm)

HDS8800

ScanStation C10

1 400 500 300

80 10 90 18

80 270

360 360

8 800 50 000

10-200 000 50-2 000 000 4—50 000

Fig. 1. Workflow for ray casting algorithm.

compression function is needed to reduce the point density. In this study, a least-distance algorithm was introduced to compress point data layer by layer. According to the algorithm, the distance between any two points in a layer was calculated. If the distance between two points was less than a criterion value, the second point would be deleted. The operation was repeated until the distance between any two points was not less than the criterion value. The criterion value was determined according to the engineering or specific accuracy requirements, but could not be greater than 0.035 m. By judging the distance between two points layer by layer, the point density was reduced.

2.1.4. Data management

Scanning of each excavated surface will generate a large data file containing millions of points. The total file capacity will dramatically increase after several scanning processes. Therefore, an effective data management method is needed. One feasible way of dealing with such massive data sets is to use a database management system (DBMS) to store all the data in a database along with several data tables. Another approach is to use a file management system (FMS) to store data in an external storage memory, and to establish a data index file containing the file path, which can be read directly as needed. The DBMS is more convenient than the FMS because it can ensure data integrity, safety, and reliability. Currently, the most common DBMSs are the Oracle database server, Microsoft SQL server, and MySQL database. Point cloud data management using the Oracle server (Li and Li, 2000; Schon et al., 2013) and SQL server (Zhang, 2012) has been studied. Both databases have their own data structures. The SQL server was adopted in this study because its spatial function was based on a B+ tree data structure, and it could easily import and process scanned data.

2.2. Excavation quality assessment

Excavation quality is mainly determined by assessment of the dominant item and general item. The dominant item includes three indices: the protective layer quality, the average gradient, and the slope stability. However, only the average gradient can be measured exactly, whereas the other two are subjective. The general item also contains three indices: the slope toe elevation, overbreak and underbreak, and HCF. The HCF is considered when an explosion occurs.

2.2.1. Average gradient and slope toe elevation

Slope excavation in hydraulic construction should meet the design requirements of a certain gradient. In the traditional method of assessing the average gradient, a set of specific coordinates on several cross-sections are measured using a total station. This method is inefficient and inaccurate. With 3D laser-scanned data, the gradient of any cross-section can be measured accurately through extraction of data of the corresponding cross-section from the scanned data. Then, the average gradient can be calculated by averaging several cross-sections' gradients.

The slope toe elevation is the bottom elevation of an excavated slope, which must be strictly controlled during the construction. By extracting the lowest elevation from the scanned data, the slope toe elevation can be obtained.

2.2.2. Concept of overbreak and underbreak

In excavation projects, overbreak means that the excavated surface is beyond the design surface, and underbreak means that the excavated surface does not reach the design surface. According to construction specifications, underbreak should be prevented, and overbreak should be strictly controlled. Overbreak and underbreak are measured by the perpendicular distance from a point on the actual excavated surface to the design surface.

2.2.3. Vertical cross-section overbreak and underbreak

Slope excavation projects can be divided into several

separate projects. Each separate project contains one vertical cross-section. Based on the design parameters and scanned data of the excavated cross-section, quality assessment can be conducted for each separate project:

(1) The position parameters, including the starting position, ending position, interval between two cross-sections, and height of each vertical cross-section to be excavated, are determined.

(2) The design cross-section to be excavated is generated according to the design parameters, including the cross-sectional position, slope ratio, and control point coordinates. The design excavation line of the cross-section to be excavated is denoted by la in Fig. 2.

(3) The excavated cross-section is obtained based on scanned data, and the actual excavation line is generated, as denoted by lb in Fig. 2.

The formulas above can be transformed into the following matrix:

Fig. 2. Comparison of design and excavated cross-sections.

(4) The profiles denoted by la and lb are intercepted by a series of horizontal lines, with a certain interval along the vertical direction, as shown in Fig. 2. The horizontal distance dh is calculated with the coordinates of the intersection points at the same elevation. With the design value of the slope ratio, the perpendicular distance d from an excavated cross-section to its design cross-section is calculated. The excavation quality at point P, which is on the excavated cross-section, is assessed according to the value of d.

2.2.4. Holistic overbreak and underbreak

The section above describes the excavation quality assessment from a cross-sectional perspective. Considering that the scanned data cover the whole surface, and the surface points are evenly distributed, the excavation quality assessment from a holistic perspective can be performed by calculating the standard deviation of the perpendicular distance from all points on the excavated surface to its design surface.

Most design surfaces are considered a plane, which can be expressed as Ax+By+Cz+D=0, where A, B, C, and D are coefficients, and CS0. By assuming that a0 = —A/C, a1 = —B/C, and a2 = —D/C, the formula can be converted to z=a0x+a1y+a2. Using a series of outline control points to fit the plane formula, we set

S = Yh (a0xi + a1yi + a2 — zi) , where xi, yi, and zi are the

coordinates of control point i, and n is the number of control points, with n > 3.

A small value of S indicates high precision in the fitting results. Thus,

— = 0 k = 0; 1; 2 (1) vak

Therefore, we can derive the following formulas:

J2 2(aoXi + ai yi + a2-Zi)xi = 0 i=i n

J2 2(aoXi + ai yi + a2 - Zi )y = 0 (2)

J2 2(a0Xi + ai yi + a2 - Zi ) = 0

n Ex2 i=i n xiyi i=i n xi i=i

n xiyi i=i n Ey2 i=i n yi i=i

n xi i=i n yi i=i n

To satisfy the excavation standard, S should also meet the following requirement:

0 < S < min(nDl, nDl)

where Du and Do are the underbreak and overbreak thresholds, respectively, with Du > 0 and Do < 0.

After solving Eq. (3), we can obtain the values of a0, ai, and a2, followed by the values of A, B, C, and D. According to the plane formula, the distance from point Q on the excavated surface to the design plane can be calculated by

AXq + ByQ + CZQ + D ' VaAl2 ^ 2 + C2

where xq, yQ, and zq are the coordinates of point Q. Thus, when dq > Du, point Q does not reach the design surface, and the excavation quality can be assessed as underbreak. When Do < dQ < Du, the excavation quality is qualified. When dQ < Do, point Q is beyond the design surface, and the excavation quality is overbreak. Three data sets, designated the overbreak set, qualified set, and underbreak set, are established to store scanned points with different distances.

The standard deviation s

d2 /N is used for holistic

excavation quality assessment, where N is the number of points on the excavated surface extracted from scanned data, and di is the distance from point i on the excavated surface to the design surface. The smaller the value of s is, the higher the excavation quality of the project will be.

2.3. Excavated volume calculation

The excavated volume directly affects the project's cost and schedule. To calculate the total excavated volume of a project, the entire project is divided into several horizontal layers. The area of a typical excavated cross-section in a horizontal layer is calculated and multiplied by the thickness of the layer. Thus, the excavated volume of this layer is obtained. The total excavated volume can be obtained by summing the excavated volume of each layer. However, if the thickness of a horizontal layer is too large, the results will not be accurate. If the thickness is too small, data collection and processing will take a long time. In recent years, some scholars have researched calculation of the excavated volume with scanned data in tunnels (Argiielles-Fraga et al., 2013), building foundations (Bosche, 2010), and landslides (Du and Teng, 2007; Chen et al., 20i3). However, all the calculations were based on

commercial software that lacked applicability in hydraulic engineering. This paper presents a method to calculate the excavated volume based on calculating the outlined area formed by scanned points before and after excavation.

By importing the two groups of scanned data of the same layer before and after excavation, a polygon in the layer is formed with the scanned points. In Fig. 3, orange points denote the original border, whereas the blue points denote the border after excavation.

The polygon is the excavated area of this horizontal layer. All the points (xj, yi) are arranged in a clockwise or anticlockwise direction. The excavated area is calculated by

Ak = 2E - x,+iy,)

Fig. 3. Polygon formed by point cloud data.

where Ak is the excavated area of the layer k, and m is the number of scanned points in the layer k. The total excavated volume V is obtained by

V =J2 Ak Dh

where Dh is the thickness of each layer, and K is the number of layers.

3. Case study

3.1. Field application

A field application was conducted in a hydraulic engineering slope excavation project in southwestern China using the HDS8800, with an accuracy of 50 mm-2 000 m. As shown in Fig. 4, the excavated surface was 15 m high and 88 m long. The design value of the slope ratio was 1:0.75.

3.1.1. Scanned data processing

The scanned area of the excavated surface is shown in Fig. 5(a). The design surface was determined by four control

(b) Actual scene Fig. 4. Scanned area.

(c) Final data after de-noising Fig. 5. Scanned data processing.

m— 1

points, which formed a polygon (Fig. 5(b)). It was evident that the scanned area was larger than the design area to be excavated. Thus, the points located outside the design area were removed by the ray casting algorithm. The final data after de-noising are shown in Fig. 5(c).

3.1.2. Cross-sectional quality assessment

According to the Inspection and Assessment Standard for Separated Item Project Construction Quality of Water Conservancy and Hydroelectric Engineering-Earth-Rock Works (SL 631—2012), the overbreak threshold is —20 cm, and underbreak threshold is 10 cm. The slope excavation project was divided into 10 separate projects, with one vertical cross-section included in a separate project. The scanned data from a vertical cross-section at y = 3 013.125 km in the world geodetic system (WGS) are shown in Fig. 6, and the assessment results are listed in Table 2, demonstrating that the excavated cross-section is overbreak in the lower part and qualified in the upper part. By running the program, results of each cross-section were obtained.

3.1.3. Holistic assessment of slope excavation quality

Four surface control points were obtained from the design parameters (Table 3). The design plane was calculated with control point coordinates in the WGS using Eq. (3). The coefficients of the design plane were A = —1.359 349 66, B = —0.052 761 05, C = 1.0, and D = 959 644.828. The fitting error Dz was quite small, as shown in Table 3.

The distance di from each scanned point on the excavated surface to the design surface was obtained. The values of the distance were classified into the overbreak set Po, qualified set Pq, and underbreak set Pu. The overbreak point number was 187 437, underbreak point number was 78, and qualified point

1 160 -1 158 -1 156 -1 154 -^ 1 152 -

1 150 -1 148 -1 146 -1 144 -

589.850 589.854 589.858 589.862

x (km)

Fig. 6. Comparison of design and excavated cross-sections at y = 3 013.125 km.

Table 2

Results of cross-sectional quality assessment.

z (m) d (m) Assessment result

1 145.0 -0.616 Overbreak

1 145.5 -0.586 Overbreak

1 146.0 -0.583 Overbreak

1 146.5 -0.488 Overbreak

1 147.0 -0.323 Overbreak

1 147.5 -0.272 Overbreak

1 148.0 -0.294 Overbreak

1 148.5 -0.294 Overbreak

1 149.0 -0.384 Overbreak

1 149.5 -0.393 Overbreak

1 150.0 -0.231 Overbreak

1 150.5 -0.183 Qualified

1 151.0 -0.211 Overbreak

1 151.5 -0.214 Overbreak

1 152.0 -0.166 Qualified

1 152.5 -0.170 Qualified

1 153.0 -0.108 Qualified

1 153.5 -0.194 Qualified

1 154.0 -0.199 Qualified

1 154.5 -0.083 Qualified

1 155.0 -0.092 Qualified

1 155.5 -0.102 Qualified

1 156.0 -0.100 Qualified

1 156.5 - 0.043 Qualified

1 157.0 -0.089 Qualified

1 157.5 -0.133 Qualified

1 158.0 -0.118 Qualified

1 158.5 -0.013 Qualified

1 159.0 -0.004 Qualified

1 159.5 -0.003 Qualified

1 160.0 -0.002 Qualified

number was 38 145. The standard deviation (s) was 0.522 m, much higher than the overbreak or underbreak thresholds. The result of the holistic excavation quality assessment was not qualified because of the presence of a serious overbreak problem. Based on the analytical data, a quality assessment distribution diagram was generated, as shown in Fig. 7. It is clear that the excavation is qualified in upper part, and over-break in the lower part, which is consistent with the results of cross-sectional quality assessment.

To measure the average gradient, 10 vertical cross-sections were extracted from the scanned data. The average slope ratio of this project was 1:0.726, which was steeper than the design value. The design slope toe elevation was 1 144.7 m, and the measured result was 1 144.647 m, indicating that the slope toe was overbreak.

Table 3

Control points and fitting error of design plane.

Control point x (km) У (km) z (m) Dz (mm)

1 589.848 8 3 013.184 5 1 144.7 -7.381

2 589.851 7 3 013.1100 1 144.7 -9.203

3 589.8625 3 013.121 8 1 160.0 -9.198

4 589.8600 3 013.1864 1 160.0 -7.173

Fig. 7. Results of holistic excavation quality assessment

In addition, the traditional way to assess an excavation project takes about 10-15 h. However, using the present method, the total time consumption was only 2—3 h, including the time for modeling and data scanning and processing. Thus, the total time consumption can be reduced by 70%-90%.

3.2. Laboratory experiment

3.2.1. Model setting and scanning

A laboratory experiment was carried out at China Three Gorges University to verify the excavated volume calculation method. The experimental process and models are shown in Fig. 8. The model was about 0.5 m long, 0.6 m wide, and 0.25 m high. Fig. 8(a) shows the original model before excavation. In the experiment, silver sand was used as the excavated material. A small amount of water was mixed with the filling material to obtain its plasticity and stability without altering the density during the experiment. The excavation process was divided into five steps from the top to bottom, with a height of 0.05 m at each step.

(c) After excavation Fig. 8. Laboratory experimental process.

Fig. 9. Six groups of point cloud data and total point numbers.

We used the ScanStation C10, with an accuracy of 4 mm-50 m, in this study. The scanner was combined with a four million-pixel camera to record the excavation process. The scanner was placed in front of and above the model to cover the entire target, as shown in Fig. 8(b). Following the excavation process, six groups of scanned data were obtained before and after each excavation step. Each group of scanned data contained about 0.5 million points. Photos taken by the camera, with scanned data superimposed, are shown in Fig. 9. Data are numbered from X1 to X6.

3.2.2. Excavated volume calculation

During the experiment, when a layer was excavated, the excavated sand volume was measured with a wooden box of 37 cm long, 31.2 cm wide, and 9 cm deep. The box was put on horizontal ground, and the depth of the excavated volume was measured with a micrometer. The total volume of the filling material used in the experiment was 23 667.01 cm3. The measured data are listed in Table 4.

The excavated volume was calculated with the scanned data. As mentioned before, each group of scanned data contained approximately 0.5 million points. The model was only 25 cm in height. Thus, nearly 2 000 points were distributed in one millimeter on average. The density was much higher than the standard. The huge number of points would reduce the computational efficiency. Thus, the least-distance algorithm was applied to data compression.

A set of scanned data for a horizontal cross-section at the height of 0.1 m was chosen to validate the data compression method. The results of data compression are shown in Fig. 10, where s is the criterion value, and m is the number of point cloud data in the horizontal cross-section after compression. The coordinate origin was located at the scanner center. It was demonstrated that when the criterion value increased from 0 to 0.02 m, the number of points decreased by 81.38% from 317 to 59, while the outline of the excavated cross-section was maintained the same as the original one.

Table 4

Comparison of excavated volumes at each excavation step measured with wooden box and calculated with 3D entity models and scanned data.

Step Excavated volume (cm3) Relative error (%)

Measured Calculated with 3D entity model Calculated with scanned data Calculated with 3D entity model Calculated with scanned data

Dh = 0.05 m Dh = 0.01 m Dh = 0.05 m Dh = 0.01 m

1 3 878.26 3 890.328 4 032.84 3 691.19 0.311 3.97 -4.823

2 3 765.33 3 774.888 4 714.60 3 815.27 0.254 25.21 1.326

3 4 558.46 4 571.424 5 120.50 4 670.97 0.284 12.33 2.468

4 6 588.82 6 614.712 6 180.38 6 551.60 0.393 -5.77 -0.565

5 4 876.14 4 894.656 2 534.25 4 787.17 0.380 -48.03 -1.824

Total 23 667.01 23 746.008 22 582.57 23 516.20 0.334 -4.46 -0.637

Fig. 10. Compressed point cloud data.

The excavation project was divided into five steps, and the thickness of each layer was 0.05 m. The excavated cross-sectional areas at different heights were calculated using Eq. (6) with the compressed data by setting s = 0.02 m. The excavated volumes of different steps are given in Table 4. It is clear that there are significant differences between the calculated values and measured data. The error in calculation was mainly caused by the variation of the cross-sectional area at different heights, especially in areas with a gentle gradient. To avoid the error, we set Dh = 0.01 m. The calculated results are also shown in Table 4. Thus, by selection of a relatively small thickness for each layer, the error could be significantly decreased. What's more, the calculated total excavated volume was 23 516.20 cm3 for Dh = 0.01 m, while the actual volume measured with the wooden box was 23 667.01 cm3. The error of the calculated result of the total excavated volume was —0.637% as compared with the measured volume, demonstrating that the present method was reliable.

For further verifying the excavated volume calculation method with the scanned data, we introduced 3D entity models. With the point cloud data, 3D entity models for different excavation steps were established using a triangulated irregular network in AutoCAD with a second development program. The models are shown in Fig. 11, corresponding to the six groups of point cloud data in Fig. 9. The calculated results obtained by 3D entity models are also listed in Table 4.

It can be inferred from Table 4 that the excavated volumes calculated with 3D entity models slightly differ from the measured results with the wooden box. The relative error of the total excavated volume calculation was only 0.334% as compared with the measured data. Although 3D entity models

(a) XI (b)X2

(c) X3 (d) X4

(e) X5 (f) X6

Fig. 11. Entity models.

provide results with a higher precision than the calculation method using only the scanned data, the time consumption of 3D entity models and file storage space are significantly higher.

4. Conclusions

(1) In the slope excavation quality assessment with the 3D laser scanning technology, laser-scanned data are more abundant and precise than the measured data obtained by the total station, GPS, or RTK technology, and the quality assessment indices, including the average gradient, slope toe elevation, and overbreak and underbreak, can be obtained directly from the scanned data. The holistic quality assessment results are consistent with the results of cross-sectional quality assessment, and the time consumption in excavation quality assessment with the laser scanning technology is reduced by 70%—90% relative to that of the traditional method.

(2) The excavated volume calculation method with the scanned data has high precision, with an error of the total excavated volume of only —0.637% as compared with the measured data in the laboratory experiment, demonstrating its applicability in excavated volume calculation. The error can be reduced by decreasing the thickness of the horizontal layers.

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