Testing of Structural Integrity of U-Shaped Sheet Pile in Canal Engineering Using Ground Penetrating Radar

Abstract

Compared with other piles with the same cross-sectional area, “U-shaped” structural section sheet pile can increase the moment of inertia of the structure’s section. Due to the large excavation depth of the open section of the “Yin Jiang Ji Huai” river canal project in Anhui province, China, the unprotected excavated inclined canal slope covers a large land area, which results in the current situation of high housing demolition costs and a shortage of land resources in densely populated areas. In this study, the non-destructive testing of a U-shaped sheet-pile wall to protect the vertical slope of the underwater expansive soil in the canal project is studied, which is of great significance in reducing the construction area and minimizing the cost of construction. It is necessary to test the structural integrity of the U-shaped sheet pile, which is also vital to ensuring the whole project quality. Ground penetrating radar (GPR) is used to detect the structural integrity of the U-shaped sheet pile in expansive soil. On the basis of identification and conversion of the original GPR data format, the processing methods based on the time-varying automatic gain and wavelet analysis are implemented. This case study proves that the GPR testing method is effective to estimate the quality of the U-shaped sheet pile.

1. Introduction

GPR is shallow geophysical detection equipment based on the transmission and reception of high-frequency electromagnetic pulse waves. Because of the difference in the electrical parameters of the subsurface medium, we can analyze and infer the structural and physical property characteristics of the medium [1,2,3,4]. GPR is also a non-destructive testing method for pile foundation, which has the advantages of high detection efficiency and accuracy [5,6]. It is difficult to detect some potential damage hidden in the pile foundation using a low strain testing method. GPR can be used to retest and provide an accurate analysis to ensure the engineering quality of pile foundation.

At present, research on GPR mainly focuses on the following directions: Bradford applied the method of reverse-time prestack depth migration to amplitude reconstruction in complex environments [7]. Chen and Jeng used GPR to detect a near-surface geothermal river valley using contemporary data decomposition techniques [8]. Montiel-Zafra et al. proposed a novel method to remove GPR background noise based on the similarity of non-neighboring regions [9]. Rodriguez et al. proposed a prediction algorithm for data analysis in GPR-based surveys [10]. Santos and Teixeira used time-reversal-based processing techniques to enhance GPR’s detection ability of targets [11]. Terrasse et al. applied the curvelet transform for clutter and noise removal in GPR data [12]. Tosti et al. investigated the dielectric properties of a railway ballast using different GPR antennas and frequency systems [13]. Wang and Liu studied the shearlet transform to remove noise suppression and direct wave arrivals in GPR data [14]. In some special places, three-dimensional GPR images can provide a more intuitive interpretation [15]. Zhao and Al-Qadi developed an analytic approach to estimate asphalt pavement thickness using 3-D ground-penetrating radar [16]. Zhou and Zhu researched the application of GPR in detecting deeply embedded reinforcing bars in pile foundation [17].

The literature review above shows that the applications of GPR mainly include geological engineering investigations, disaster geology surveys, foundation detection, military applications, archaeological and environmental pollution investigations, highway and tunnel engineering detection, as well as other fields. However, there are limited studies on its application in non-destructive testing of U-shaped pile foundation. The integrity of the pile is a very important part of the whole project quality. According to the theory of electromagnetic wave propagation of GPR, this georadar can be used to investigate the pile quality within a certain range of pile length. When the pile length is not more than 30 m, the receiving antenna can receive the effective radar echo signal.

2. Materials and Methods

2.1. Project Overview

U-shaped sheet pile is derived from traditional flat sheet pile by folding it into a “U-shaped” plate section (see Figure 1). The length is 1200 mm and height 800 mm. While maintaining the U-shaped structure, it enhances the rigidity of the section, improves the moment of inertia and bending resistance of the section, and achieves the comprehensive advantage of being thin, having high mechanical performance while saving on materials.

The Xiaohe section is located in Feixi county, Anhui province, China. The U-shaped sheet-pile wall segment of the Xiaohe dividing line is a hilly area. This is a test section project. The east-west length of the bottom of the canal deep excavation is 13.75 m and the south-north length of the bottom of the canal deep excavation is 11 m. The sheet-pile wall has an elevation of 9.5 m on the west and 8.5 m on the east. This project location is shown in Figure 2. The canal is dug deeply into the existing ground without the need for levees on both sides. A continuous wall of vertical U-shaped prestressed reinforced concrete slab pile is used on both sides of the canal (see Figure 3).

2.2. GPR Data Acquisition and Processing

The field data acquisition adopted the SIR-3000 GPR with a ground coupling system, shielded antenna with a central frequency of 400 MHz and 100 MHz, center control unit, and host computer (for data acquisition). The main testing equipment are shown in Figure 4, and the parameter settings for field data collection are shown in

Table 1. Parameter settings for field data collection.

Antenna Type	400 MHz	100 MHz
Collection mode	Point collection	Point collection
Distance of points (m)	0.2	0.5
Time window (ns)	240	380
Sampling points	1024	1024
Gain points	5	5
Band-pass filtering (MHz)	100~800	25~300
Transmit ratio (KHz)	100	50
Data bits	16	16
Stack	64	64
Scan number/meter	64	64

.

The testing line was arranged in a series of U-shapes along the U-shaped sheet-pile wall, as shown in Figure 5, with the testing line indicated by the red line. The starting point of the measurement was at the southern endpoint of pile #1, and the ending point was at the northern endpoint of pile #6. The length of the test line was about 11.7 m, of which the length of the measuring line of pile #1 was 1.7 m, while that of the other piles was 2 m each. The starting point of the measuring line is displayed in Figure 5. A 400 MHz antenna and 100 MHz antenna were used for the non-destructive testing. Due to the limitation of site conditions, the measuring wheel could not be used, and the GPR data was collected by point detection.

The GPR data storage format is binary or hexadecimal in domestic and international systems. Additionally, each GPR data file has a file header. In this study, we adopted Yang’s method to process the GPR data because of the flexibility [18]. In the meanwhile, the converted data can be reconverted to the original data format, and the build-in processing software can be used for display and processing.

During propagation in an electric medium, radar signals rapidly attenuate and the amplitude decreases, especially for deep information. In the radar detection of U-shaped sheet piles, deep information is often weak, which is not conducive to the recognition of deep abnormal signals. Therefore, it is very important to develop new GPR data processing methods. Based on the conventional processing (zero correction, bad trace elimination, and background filtering), two kinds of data processing methods to improve deep reflection information recognition are studied, namely, time-varying automatic gain and wavelet transform processing.

Through the gain processing of the radar signal, the amplitude of deep information can be improved, which is helpful for radar signal comparison and waveform tracking. The commonly used gain processing methods in build-in software are mainly linear gain and exponential gain. In this study, the time-varying automatic gain was studied, and the gain weight was automatically adjusted according to the strength of signals at different moments, to achieve the purpose of automatic gain. The calculation equation is as follows:

$$x^{\prime }\left(t\right)=x\left(t\right)w\left(t\right)$$

(1)

where $w\left(t\right)$ is the gain weight at $t$ time, $x\left(t\right)$ is the original signal, and $x^{\prime }\left(t\right)$ is the signal after time-varying automatic gain.

By multiplying the stronger signal by a smaller weight and the weaker signal by a larger weight, the purpose of energy balance is achieved and the gain weight changes slowly with time. The calculation process is as follows:

(1)

The signal is divided into $M$ time-windows, with half of each time-window overlapping, to reduce the drastic fluctuation of gain weight.

(2)

The average amplitude of each time-window $A\left(i\right)$ is calculated.

$$A\left(i\right)=\frac{{{\displaystyle \sum }}_{t=t_1}^{t_2}\left|x\left(t\right)\right|}{N}$$

(2)

where $i\in M$, $t_1$, $t_2$ are the start and end time of the time-window, and $N$ is the number of sampling points in the time-window.

(3)

Calculation of the weight $w\left(i\right)$ of the time-varying automatic gain, which is the weight of the center of the time-window.

$$w\left(i\right)=\frac{1}{A\left(i\right)}$$

(3)

(4)

The weight of the center point of the adjacent time-window is linearly interpolated to obtain the gain weight of other points. The flowchart for the calculation program is shown in Figure 6.

Wavelet transform has been widely applied in signal processing, image processing, radar, seismic exploration, CT imaging and other fields in the past 30 years [19]. The wavelet transform is a time-frequency analysis method in which the time-frequency window has a fixed size but its shape can be changed. The main characteristics of the wavelet transform are a high-frequency resolution and low-time resolution in the low-frequency range, and a high-time resolution and low-frequency resolution in the high-frequency range. So it’s highly adaptive, and also known as a mathematical microscope.

Continuous wavelet transform (CWT) is defined:

$$\left(CW{T}_{\psi }f\right)\left(a,b\right)=\frac{1}{\sqrt{\left|a\right|}}{{\displaystyle \int }}_{-\infty }^{+\infty }f\left(t\right)\overline{\psi \left(\frac{t-b}{a}\right)}dt$$

(4)

where

$${\psi }_{a,b}\left(t\right)=\frac{1}{\sqrt{\left|a\right|}}\psi \left(\frac{t-b}{a}\right)$$

(5)

$a$ = coefficient of time scale dilation; $b$ = coefficient of time translation; $f\left(t\right)$ = original radar signal.

The above series of functions is called the wavelet function, or wavelet for short, which is obtained by different time scale dilation and different time translation. Thus, $\psi \left(t\right)$ is the wavelet prototype, which is called the mother wavelet or basic wavelet.

In the radar signal, the useful signal is usually manifested as a low-frequency signal or some relatively stable signal, and the noise signal is usually manifested as a high-frequency signal. Therefore, after wavelet decomposition, the noise part is usually included in the high frequency, and the amplitude of the high-frequency coefficient of the noise is rapidly attenuated with the increase in scale and decomposition levels. Additionally, the performance of noise on different scales is also unrelated. Thus, the high-frequency wavelet coefficients are processed in the form of threshold values and then the processed signals are reconstructed to achieve the purpose of denoising.

Liu’s research showed that Daubechies wavelet was more suitable for radar signal processing, and through the study of various wavelet bases of Daubechies, it was found that the “db4” wavelet had the best effect in denoising and maintaining the original signal characteristics [20]. In this experiment, the decomposed layer $N$ is equal to 3.

3. Results and Discussions

In order to determine the relative dielectric constant value, two undriven piles were selected on the ground surface, and 100 MHz antennas were used for the radar test, respectively. Since the test pile length is known (11.5 m), the top-bottom interface was determined according to the reflection characteristics of radar images at the top and bottom of the sheet pile, and the depth h (m) corresponding to the bottom interface was set as 11.5 m. The electromagnetic wave propagation time t (ns) can be directly read by the ordinate of the radar image, the electromagnetic wave propagation speed v (m/ns) can be obtained by the formula v = 2 h/t, and then the relative dielectric constant $\epsilon ={\left(C/v\right)}^2$ can be obtained by the formula v = C/$\sqrt{\epsilon }$. Where C is the velocity of light (C = 0.3 m/ns). The average relative permittivity $\overline{\epsilon }=\left({\epsilon }_1+{\epsilon }_2\right)/2$ can be acquired from the two piles. Where ${\epsilon }_1$ and ${\epsilon }_2$ are the relative dielectric constant values of the two piles, respectively.

Taking into account the fact that reinforced concrete U-shaped sheet piles were used, through the radar measurement of undriven piles on the ground, the average relative permittivity was set at 5.5 to obtain depth information when GPR was used with its own software. The non-destructive testing results of 400 and 100 MHz antennas are shown in Figure 7 and Figure 8, respectively. The abscissa of all the radar images is the measurement line length and the vertical coordinates are the testing depth. These black vertical lines are the connection between piles. The black oval frames are the middle damaged position in Figure 7. The black horizontal line indicates the position of the pile bottom in Figure 8.

As can be seen from the two figures, the high frequency components of the radar signal are not well suppressed and there are many burrs, which cause certain interference to the normal reflected signals. There is serious crushing in the middle and the pile bottom reflection is invisible in Figure 7. While the pile bottom interface is visible in Figure 8, and the bottom is seriously broken. These results indicate that the detection depth of the 400 MHz antenna is limited and the situation of pile bottom cannot be seen, but the detection depth of the 100 MHz antenna is deeper and can better reflect the situation of the pile bottom.

As can be seen from the following figures (Figure 9 and Figure 10), the interference signal of the left image is relatively obvious, while the right image is smooth. The interference is filtered out, and the location of the pile foundation damage is easier to determine. For the non-destructive testing image of the 400 MHz antenna, the damage is mainly in the upper and middle parts; the damage location of the pile foundation processed by wavelet transform is relatively clear. It is shown in the white curve box in Figure 9. For detecting the image of the 100 MHz antenna, the white curve box shows the areas of severe damage. After the wavelet transform processed, the damage location and status are clearly visible, interference filtered, which is on the right side of the image in Figure 10. The bottom of Pile#1, Pile#2 and Pile#5 are the most damaged.

As shown in Figure 7 and Figure 8, the high frequency radar signal is not well suppressed, and there are many burrs, which cause certain interference to the normal reflected signal. Wavelet transform was applied to the GPR data in Figure 7 and Figure 8, and the processing results are shown in Figure 9 and Figure 10.

After the wavelet transform processing, the processed data is converted into the format of the original radar data file so that the processed data can be displayed by means of the build-in software of the radar system. The comparison of the left and right images in Figure 9 and Figure 10 show that the wavelet transform can well filter out the high frequency interference components (burr phenomena) of the original radar signal and the useful signals have been reinforced.

As the difference is small between the dielectric parameters of piles and soil, the reflected wave signal is weak, and not easy to distinguish at the interface. Sometimes the anomaly reflection of expansive soil is understood as the anomalous reflection of a pile, and the interference of the reflected signal is bigger. These factors finally affect the accurate interpretation. Time-varying automatic gain and wavelet processing methods enhance the effective reflection wave signal and improve the accuracy of GPR data interpretation.

The water injection test was carried out by excavating the bottom of the foundation ditch to the elevation of the riverbed to evaluate the water injection effect of the sheet-pile wall. The results of the excavation can be used to further check the effect of the radar test before water injection. The surface of the U-shaped sheet pile after excavation is shown in Figure 11. The damages to the U-shaped sheet pile also verify the correctness of the radar test results.

All the U-shaped sheet piles are cracked to varying degrees in Figure 11. The maximum length of the cracks is more than 70 cm in Pile#2, and the minimum length of the cracks is also more than 10 cm in Pile#4. The crack lengths of Pile#1, Pile#3, Pile#5 and Pile#6 are, respectively, about 30, 35, 30 and 13 cm. The excavation results also prove that the damage of Pile#4 is minimal. Most cracks are slant. In the process of hammering, the piles are subjected to significant vertical soil resistance, which results in the piles cracking and breaking. Through the expansive soil and hard texture, the pile is difficult to drive down.

Expansive soil generally has high strength and low compressibility in the natural state. In the process of driving the U-shaped sheet pile, it is subjected to great resistance and requires many hammerings (up to hundreds of times) to drive, which inevitably has a high impact on the pile structure.

From the analysis of GPR images and cracks causes, some conclusions can be drawn:

(1)

The 400 MHz antenna radar image within the range of the white lines shows the highly abnormal area, which may be crushed, isolated, cracked or broken. The distortion is serious at the depth range of 4.5 to 8 m.

(2)

The pile length can be judged from the reflection of the pile bottom, which can be seen in the 100 MHz antenna image. The image shows that the deep distortion of the pile is serious, and the response to the shallow part and middle part is weak.

(3)

The 400 MHz antenna image shows that the distortion at the middle position of pile #1, #2, #3, #5, and #6 is more serious compared with pile #4.

(4)

The accuracy of the 400 MHz antenna is higher than that of the 100 MHz antenna, but the non-destructive testing depth is relatively shallow, and there is basically no response to deep distortion, which is also related to the attenuation of energy.

(5)

The non-destructive testing results of the GPR are consistent with those of field excavations, and the case study proves GPR is suitable for detection of the U-shaped-sheet pile.

4. Conclusions

The U-shaped sheet-pile wall is used for the protection of the vertical slope of the river canal. Most of the pile body after driving it down is hidden below the construction surface. The structural integrity of the pile body is an important factor that controls the bearing capacity and durability of the pile foundation. The method of adopting a U-shaped sheet-pile wall to protect expansive soil vertical slopes includes the mechanism of protection and method of testing the effectiveness of protection measures. Under the condition of natural expansive soil deposit, the U-shaped sheet pile must be strong enough to overcome the high stresses from the natural expansive soil layer. The damage degree of the pile structure is the key factor to determine the pile-driving technology.

A method of filtering the reflected radar wave of the U-shaped sheet pile in expansive soil was studied. The effective reflection information of abnormal parts of the U-shaped sheet pile was obtained, and the approach of discrimination of the defective radar wave was established. The integrality of the testing method of the U-shaped sheet-pile wall in expansive soil presented in this study can also be applied to other types of pile foundations, which has strong practicability.