# Scanning Scheme for Underwater High-Rise Pile Cap Foundation Based on Imaging Sonar

^{*}

## Abstract

**:**

## 1. Introduction

- Analyzed the effect of scanning position on the accuracy of sonar imaging experimentally, which provides a basis for the placement of IS measurement points in Section 2;
- Designed a sonar-carried platform suitable for HRPCF scanning and field tested in Section 3;
- Tested the proposed scheme in the field at the Wulong River New Bridge, and verified the theoretical feasibility in Section 5.

## 2. Relationship between the Measuring Accuracy of IS and the Scan Distance, and the Pitch Angle

#### 2.1. Experiment Design and Operation

#### 2.2. Results and Discussion

_{m}) from each image. On the right side of Figure 2a, the yellow area similar in shape to the component shown in Figure 3a indicates the spalling in the concrete column. The bright lines on the leftmost side of the column and spalling are regarded as straight lines AB and CD in Figure 2b. Thus, the value of dm was directly and easily measured. Table 1 lists all values of d

_{m}for different values of l and ω.

_{m}and d first decreased and then increased, indicating the existence of a reasonable value range for both l and ω to reduce the measurement error. The fact that the maximum measuring distance increased to 3.5 m when the spalling depth increased to 20 mm indicates that the preset maximum value of l in a practical inspection is approximately 3.5 m. The preset minimum value of l can be 0.75 or 1.0 m, depending on the error variation trend. Furthermore, the allowable ω increased with a decrease in l, and vice versa. Third, the measured d

_{m}value was always greater than the actual spalling depth. This indicates that, compared with the defect identified from the sonar image, the real damage is less severe, and the sonar-image-based safety evaluation of a defective pile is conservative.

_{m}values are mostly above the blue line and below the red line, except for the case of ω ≤ 10°. Furthermore, it reveals that a distance l that is too close will result in an increased measurement error, whereas increasing l can reduce the measurement error. In addition, even if l remains constant, the measurement error will increase if ω ≥ 40°. When 1.0 m ≤ l ≤ 3.0 m, the measurement error of each case is less than the allowable error. In contrast, at l ≥ 3.5 m, most measurement errors reach or exceed the allowable error. Based on the above analysis, the appropriate preset value ranges of l and ω are set as 1.0 m ≤ l ≤ 3.0 m and 0° ≤ ω ≤ 50°, respectively.

## 3. Design and Manufacture of an Assembled Sonar-Carried Platform

#### 3.1. The Assembled Floating Island

#### 3.2. The Lifting Device to Carry the IS Device

#### 3.3. Onsite Testing of the Platform

#### 3.3.1. Overview of the Substructure of the Onsite Bridge

#### 3.3.2. Test Procedure and Results

## 4. Measuring Point Arrangement

#### 4.1. Absence of a Pile Cap

_{0}is the maximum horizontal beamwidth of IS, and it is also a predesigned value based on the IS performance. l

_{0}is the corresponding horizontal distance from the IS device to the pile edge. β

_{0}is equal to the supplementary angle of α

_{0}. Thus, β

_{0}/2 = π/2 − α

_{0}/2. Therefore, the relationship between l

_{0}and r is as follows:

_{0}is obtained as follows:

_{0}of the required measuring points is determined as follows:

_{0}) < 0.5, the total overlap area is relatively large, whereas for 0.5 ≤ mod(2π/β

_{0}) < 1, the total overlap is relatively small. Thus, n

_{0}must be increased to increase the range of the overlap area.

_{0}is significantly lower than the expected number determined from experience, both l and α need to be reduced. Figure 9b shows the relationship of α, r, and l for l ≤ l0 and α ≤ α

_{0}. By pre-determining the appropriate values of l and α, Equation (4) exists based on the law of sines.

_{0}is significantly higher than the expected number determined from experience, l must be increased. Figure 9c shows the diagram of assuming l ≥ l

_{0}. If l is preset, β is obtained as follows:

_{0}–P

_{n−1}are (ρ

_{0}, θ

_{0}) − (ρ

_{n−1}, θ

_{n−1}). The center angle of each overlapping part is named φ. These parameters are derived as follows:

_{0}generally for a monopile without a cap because the scan accuracy decreases with an increase in l.

#### 4.2. Existence of a Pile Cap

#### 4.2.1. A Monopile

_{0}to P

_{n−1}must be moved outward from the original positions determined by the method proposed in Section 4.1 owing to the existence of the pile cap. For example, Point O was assumed to be the center of the horizontal cross section of the pile. Along the straight line OP

_{0}, P

_{0}is moved outward to P’

_{0}just outside the cap edge. Accordingly, the distance between the point and pile edge increases from l to l′. The other points can then similarly be moved outward to their appropriate positions. Replacing l with l′ in Equations (5) and (10) can produce β′ and φ′.

#### 4.2.2. Four Piles (2 × 2) in a Pile Cap

_{0}, P

_{5}, P

_{6}, and P

_{7}must be moved outward to P′

_{0}, P′

_{5}, P′

_{6,}and P′

_{7}, respectively, which are located immediately outside the pile cap edge. Both P′

_{0}and P′

_{5}showed the same movement, whereas the other two points showed different movements.

_{0}and P′

_{5}

_{0}is given as (p/sinθ

_{0}, θ

_{0}) in the polar coordinate system. Point Q is assumed to be the center of the horizontal cross section of Pile 2. Points A and B represent the two ends of the overlapping range φ covered by two beams emitting from P′

_{0}and P′

_{7}, respectively. Point C is the intersection of the straight-line BP’

_{7}and the line perpendicular to BP′

_{7}through point Q, and point D is the intersection of the straight-line AP’

_{0}and the line perpendicular to AP′

_{0}through point Q. Point M is the intersection of the straight lines OQ and AP′

_{0}.

_{0}A.

_{0}A is derived as follows:

_{0}M, Equation (13) is built similarly based on the law of sines.

_{0}, the obstruction should not reduce φ. This requirement can be expressed using Equation (15).

_{0}. By applying symmetry, analogous deductions can be made to derive the conditions that ensure that the pile cap and Pile 4 will not affect the IS device placed at P′

_{5.}

_{7}B, Equation (16) is valid based on the law of sines.

_{7}M is derived as follows.

_{7}M, Equation (18) is built similarly based on the law of sines.

_{6}and P′

_{5}can also be derived through an analogous deduction.

#### 4.2.3. N Piles Arranged in a Row in a Pile Cap

#### 4.2.4. Six Piles (2 × 3) in a Pile Cap

_{3}and P

_{4}are symmetrical to those of P

_{0}and P

_{7}, respectively. The applicable conditions for these movements are the same as those in Equations (11)–(20).

#### 4.3. Replacement of Unmovable Measuring Point

_{4}), and Figure 15b shows three unmovable points (P

_{0}, P

_{7}, and P

_{6}). In these cases, a feasible solution is to replace the obstructed points with adjacent free points or additional points to guarantee that the scanning range remains unchanged.

#### 4.3.1. Feasibility of Replacing One Point

_{4}is obstructed by Pile 4. Thus, the feasibility of placing an IS device at P′

_{5}to scan Pile 4 is given as follows: Points O and R represent the centers of the cross sections of Pile 1 and Pile 3, respectively. P

_{5}is moved outward to P′

_{5}, located at the edge of the cap. The distance p from the center of the cross section to the edge of the cap is uniform for each pile, ranging from Pile 1 to Pile 4. F is the intersection of OP

_{4}and the pile surface, and G is the intersection between OR and FP′

_{5}. S is the intersection of FP′

_{5,}and the line perpendicular to FP′

_{5}through R. A polar coordinate system can be constructed for Pile 1, assuming the center O of Pile 1 is the original point, and the horizontal line is the polar axis. δ is the angle between OR and the polar axis. θ

_{4}and θ

_{5}represent the angular coordinates of P

_{4}and P

_{5}, respectively. According to symmetry, the replacement is valid if the signal emitted from P′

_{5}can reach F without hindrance.

_{5}F.

_{5}= θ

_{5}− θ

_{4}, OP’

_{5}= (a − p)/cos(2π − θ

_{5}) into Equation (21), ∠FOP′

_{5}is shown as follows:

_{5}G, Equation (23) is built similarly based on the law of sines.

_{5}GO = π − ∠OP’

_{5}F − (θ

_{5}− δ) into Equation (23), the length of OG is obtained as follows:

#### 4.3.2. Feasibility of Replacing More Than One Point

_{0}. ∠BOQ = θ

_{0}+ β/2. P′

_{70}is the intersection of the bisector line of ∠P

_{7}OP

_{0}and the pile cap edge. P′

_{67}is the intersection of the bisector line of ∠P

_{6}OP

_{7}and the pile cap edge. C is the intersection of BP’

_{70}and the line perpendicular to BP′

_{70}through Q. E is the intersection of OP

_{7}and the edge of P

_{1}. S is the intersection of EP′

_{70}and the line perpendicular to EP′

_{70}through R. M is the intersection of BP′

_{70}and OQ. θ

_{0}and θ

_{7}are the angular coordinates of P

_{0}and P

_{7}, respectively.

_{0}, P

_{6}, and P

_{7}with P′

_{67}and P′

_{70}. First, the scanning ranges of the IS device placed at P′

_{67}and P′

_{70}can cover those of the IS device placed at P

_{6}and P

_{0}. Second, the scanning ranges of the IS device placed at P’

_{67}and P′

_{70}can cover those of the IS device placed at P

_{7}. Because of symmetry, the above conditions are simplified as follows: (a) the scanning range of the IS device placed at P′

_{70}can cover the scanning range of the IS device placed at P

_{0}, and (b) the scanning range of the IS device placed at P′

_{70}can cover the half-scanning range of the IS device placed at P

_{7}.

- Feasibility of replacing P0 with P′
_{70}

_{70}B.

_{70}B is derived by substituting ∠BOP′

_{70}= β/2 + (θ

_{0}+ 2π − θ

_{7})/2 and OP′

_{70}= (a − p)/cos[(θ

_{0}+ 2π − θ

_{7})/2] into Equation (26).

_{70}M, Equation (28) is built similarly based on the law of sines.

_{70}MO = π − ∠OP’

_{70}B − (θ

_{0}+ 2π − θ

_{7})/2 into Equation (28), OM is obtained as follows:

_{70}to propagate its signal unaffected by the pile cap and pile 2.

- 2.
- Feasibility of replacing P
_{7}with P′_{70}

_{70}E.

_{70}= (θ

_{0}+ 2π − θ

_{7})/2 and OP’

_{70}= (a − p)/cos[(θ

_{0}+ 2π − θ

_{7})/2] into Equation (31), ∠OP′

_{70}E is obtained as follows:

_{7}can be covered by that at P′

_{70}. Thus, Pile 3 does not affect the replacement scan.

_{6}can be replaced by P′

_{67}are similarly deduced.

#### 4.4. Layout of the Vertical Position of the Measuring Point

## 5. Onsite Test for the Proposed Arrangement of Measuring Points

#### 5.1. Overview of the Substructure of an Onsite Bridge

#### 5.2. Arrangement of the Measuring Points

_{0}= 3.92 m and n

_{0}= 3. The scan accuracy decreased due to insufficient measurement points. Thus, based on experience, n was increased to six. The maximum value of l was calculated as 2 + (2 − 1.25) = 2.75 m. Substituting l = 2.75 m into Equations (5), (6), and (10) gave β = 73.43°, n = 6, and φ = 13.43°. Six points, P

_{1,0}–P

_{1,5}, around Pile 1, were placed as shown in Figure 17a. P

_{1,0}, P

_{1,1}, and P

_{1,2}coincided with P′

_{1,0}, P′

_{1,1}, and P′

_{1,2}, respectively. However, because P

_{1,3}, P

_{1,4}, and P

_{1,5}were just under the pile cap, they had to be replaced by P′

_{1,3}and P′

_{1,5}. The feasibility of this replacement will be discussed in the following section. Because of the symmetry, the proof was simplified as follows: (a) the scanning range of the IS device placed at P′

_{1,5}covered the scanning range of the IS device placed at P

_{1,5,}and (b) the scanning range of the IS device placed at P′

_{1,5}covering half the scanning range of the IS device placed at P

_{1,4}. A polar coordinate system for Pile 1 was constructed; the center O of Pile 1 was assumed to be the original point, and the horizontal line was considered the polar axis. Thus, the coordinates of P

_{1,4}and P

_{1,5}were (4, 270°) and (4, 330°), respectively. The definitions of points B, M, C, F, G, S, and R in Figure 20a are the same as those in Figure 16 and Figure 17 (δ = 312.88° and OR = 9.55 m).

_{1,5}B is calculated as follows:

_{1,5}could cover the scanning range of the IS device placed at P

_{1,5}. Equation (33) is proven to be valid by the following calculation.

_{1,5}F is calculated as follows:

_{1,5}covered half the scanning range of the IS device placed at P

_{1,4}. Equation (41) is proven to be valid by the following calculation.

#### 5.3. Analysis of the Obtained Images

_{1,0}–P′

_{1,5}. Scan distance l in Figure 22(a3,a4) was longer than that in the other images, which was consistent with the proportion of the scan distance corresponding to the different positions shown in Figure 21. A similar characteristic can be observed in the sonar images in Figure 22(b1–b5,c1–c5). In addition, two features of the sonar images obtained from the onsite experiment demonstrated the applicability of the proposed measuring point arrangement for underwater HRPCF inspection. First, no echo signals, except for the echo signal from the tested pile within the scanning range of every image, were detected. Second, the echo signal from the outer surface of the tested pile in each image was intact. These features indicate that the adjacent piles are far from the scanning range of the sonar placed at any preset measuring point. The signal and echo signals were unobstructed during emission and reflection. Thus, the proposed IS measuring point placement is verified to be effective in the current case.

## 6. Conclusions

- The appropriate preset value ranges of two key parameters for the design of measuring point placement, including the horizontal measuring distance l and the pitch angle ω, are experimentally summarized as 1.0 m ≤ l ≤ 3.0 m and 0° ≤ ω ≤ 50°.
- The proposed assembled sonar-carried platform can provide a 13 m deep stable scan in a strong current with a flow speed close to 2.0 m/s. This provides a feasible alternative for solving the problem of unstable scans by AUVs in strong currents.
- Theoretical derivations and onsite tests show that the obstruction of the sonar signal by adjacent piles can be avoided by moving outward, adding, and replacing the obstructed measuring points. The obtained measuring point arrangement is helpful for the IS to scan the entire surface of each pile in the pile group without obstruction.

## 7. Scope for Future Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic diagram of HRPCF and scanning: (

**a**) pile group; (

**b**) layout of measurement points placement.

**Figure 2.**Experiment design and operation: (

**a**) design and manufacture of columns with spalling; (

**b**) locations of IS device and columns.

**Figure 3.**Measured depth (d

_{m}) of spalling from the obtained sonar image: (

**a**) d

_{m}= 51 mm (d = 50 mm, l = 1.5 m, ω = 10°); (

**b**) d

_{m}is not measurable (d = 10 mm, l = 0.75 m, ω = 20°).

**Figure 4.**Values of d

_{m}for different values of l and ω: (

**a1**) d = 50 mm, l = 0.5 m and 0.75 m; (

**a2**) d = 50 mm, l = 1.0 m to 3.0 m; (

**a3**) d = 50 mm, l = 3.5 m to 5.0 m; (

**b1**) d = 40 mm, l = 0.5 m and 0.75 m; (

**b2**) d = 40 mm, l = 1.0 m to 3.0 m; (

**b3**) d = 40 mm, l = 3.5 m to 5.0 m; (

**c1**) d = 30 mm, l = 0.5 m and 0.75 m; (

**c2**) d = 30 mm, l = 1.0 m to 3.0 m; (

**c3**) d = 30 mm, l = 3.5 m and 4.0 m; (

**d1**) d = 20 mm, l = 0.5 m and 0.75 m; (

**d2**) d = 20 mm, l = 1.0 m to 3.0 m; and (

**d3**) d = 20 mm, l = 3.5 m.

**Figure 5.**Trial-produced prototype of the assembled floating island: (

**a**) 3D sketch of the design; (

**b**) photo of the trial-produced prototype.

**Figure 6.**Trial-produced prototype of the lifting device: (

**a**) 3D sketch of the design; (

**b**) photo of a trial-produced prototype.

**Figure 8.**Photo of step III to step VII of the test: (

**a**) step III; (

**b**) step IV; (

**c**) step V; and (

**d**) step VI.

**Figure 9.**Relationships between α, r, and l: (

**a**) l = l

_{0}; (

**b**) l ≤ l

_{0}and α ≤ α

_{0}; and (

**c**) l > l

_{0}and α ≤ α

_{0}.

**Figure 15.**Few points that cannot be moved outward: (

**a**) one unmovable point; (

**b**) three unmovable points.

**Figure 19.**Details of the substructure of the Wulong River New Bridge: (

**a**) photo of the bridge; (

**b**) sizes and arrangement of the piles in the No. 2 pile cap (unit: cm).

**Figure 22.**Obtained images: (

**a1**) P′

_{1,1}; (

**a2**) P′

_{1,2}; (

**a3**) P′

_{1,3}; (

**a4**) P′

_{1,5}; (

**a5**) P′

_{1,0}; (

**b1**) P′

_{2,1}; (

**b2**) P′

_{2,2}; (

**b3**) P′

_{2,34}; (

**b4**) P′

_{2,5}; (

**b5**) P′

_{2,0}; (

**c1**) P′

_{6,1}; (

**c2**) P′

_{6,2}; (

**c3**) P′

_{6,3}; (

**c4**) P′

_{6,45}; and (

**c5**) P′

_{6,0}.

d/mm | l/m | ω | d/mm | l/m | ω | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

0° | 10° | 20° | 30° | 40° | 50° | 60° | 0° | 10° | 20° | 30° | 40° | 50° | 60° | ||||

50 | 0.5 | 59 | 55 | 51 | 51 | 51 | 51 | 53 | 40 | 0.5 | 46 | 44 | 42 | 42 | 40 | 40 | 41 |

0.75 | 57 | 54 | 51 | 51 | 51 | 54 | - | 0.75 | 44 | 42 | 41 | 41 | 41 | 41 | - | ||

1.0 | 53 | 51 | 51 | 51 | 51 | 54 | - | 1.0 | 41 | 41 | 40 | 41 | 41 | 42 | - | ||

1.5 | 51 | 51 | 51 | 52 | 54 | - | - | 1.5 | 40 | 42 | 42 | 44 | 45 | - | - | ||

2.0 | 50 | 50 | 51 | 53 | - | - | - | 2.0 | 40 | 42 | 42 | 43 | - | - | - | ||

2.5 | 50 | 51 | 51 | 54 | - | - | - | 2.5 | 40 | 41 | 42 | 44 | - | - | - | ||

3.0 | 51 | 51 | 52 | - | - | - | - | 3.0 | 41 | 43 | 45 | - | - | - | - | ||

3.5 | 51 | 52 | 54 | - | - | - | - | 3.5 | 41 | 43 | 45 | - | - | - | - | ||

4.0 | 52 | 55 | - | - | - | - | - | 4.0 | 42 | 44 | - | - | - | - | - | ||

4.5 | 54 | 56 | - | - | - | - | - | 4.5 | 43 | 46 | - | - | - | - | - | ||

5.0 | 59 | 60 | - | - | - | - | - | 5.0 | 46 | 47 | - | - | - | - | - | ||

d/mm | l/m | ω | d/mm | l/m | ω | ||||||||||||

0° | 10° | 20° | 30° | 40° | 50° | 60° | 0° | 10° | 20° | 30° | 40° | 50° | 60° | ||||

30 | 0.5 | 35 | 33 | 32 | 31 | 31 | 31 | 33 | 20 | 0.5 | 27 | 24 | 23 | 21 | 20 | 21 | 22 |

0.75 | 34 | 33 | 31 | 31 | 30 | 33 | - | 0.75 | 25 | 24 | 22 | 20 | 21 | 21 | - | ||

1.0 | 32 | 32 | 31 | 30 | 30 | 31 | - | 1.0 | 23 | 23 | 22 | 21 | 21 | 20 | - | ||

1.5 | 32 | 31 | 30 | 32 | - | - | - | 1.5 | 21 | 21 | 21 | 21 | 21 | - | - | ||

2.0 | 31 | 31 | 30 | 32 | - | - | - | 2.0 | 21 | 20 | 21 | 22 | - | - | - | ||

2.5 | 30 | 32 | 33 | 34 | - | - | - | 2.5 | 21 | 21 | 22 | 24 | - | - | - | ||

3.0 | 32 | 33 | 35 | - | - | - | - | 3.0 | 21 | 21 | 23 | - | - | - | - | ||

3.5 | 33 | 33 | 38 | - | - | - | - | 3.5 | 23 | 25 | 26 | - | - | - | - | ||

4.0 | 36 | 44 | - | - | - | - | - | 4.0 | * | * | - | - | - | - | - | ||

4.5 | * | * | - | - | - | - | - | 4.5 | * | * | - | - | - | - | - | ||

5.0 | * | * | - | - | - | - | - | 5.0 | * | * | - | - | - | - | - | ||

d/mm | l/m | ω | |||||||||||||||

0° | 10° | 20° | 30° | 40° | 50° | 60° | |||||||||||

10 | 0.5 | * | * | * | * | * | * | * | |||||||||

0.75 | * | * | * | * | * | * | - | ||||||||||

1.0 | * | * | * | * | * | * | - | ||||||||||

1.5 | * | * | * | * | * | - | - | ||||||||||

2.0 | * | * | * | * | - | - | - | ||||||||||

2.5 | * | * | * | * | - | - | - | ||||||||||

3.0 | * | * | * | - | - | - | - | ||||||||||

3.5 | * | * | * | - | - | - | - | ||||||||||

4.0 | * | * | - | - | - | - | - | ||||||||||

4.5 | * | * | - | - | - | - | - | ||||||||||

5.0 | * | * | - | - | - | - | - |

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## Share and Cite

**MDPI and ACS Style**

Shen, S.; Cao, Z.; Lai, C.
Scanning Scheme for Underwater High-Rise Pile Cap Foundation Based on Imaging Sonar. *Sustainability* **2023**, *15*, 6402.
https://doi.org/10.3390/su15086402

**AMA Style**

Shen S, Cao Z, Lai C.
Scanning Scheme for Underwater High-Rise Pile Cap Foundation Based on Imaging Sonar. *Sustainability*. 2023; 15(8):6402.
https://doi.org/10.3390/su15086402

**Chicago/Turabian Style**

Shen, Sheng, Zheng Cao, and Changqin Lai.
2023. "Scanning Scheme for Underwater High-Rise Pile Cap Foundation Based on Imaging Sonar" *Sustainability* 15, no. 8: 6402.
https://doi.org/10.3390/su15086402