TerraSAR-X and GNSS Data for Deformation Detection and Mechanism Analysis of a Deep Excavation Channel Section of the China South–North Water-Diversion Project

Abstract

Due to expansive soils and high slopes, the deep excavated channel section of the China South–North Water-Diversion Middle-Route Project has a certain risk of landslide disaster. Therefore, examining the deformation law and mechanism of the channel slope in the middle-route section of the project is an extreme necessity for safe operation. However, the outdated monitoring method limits research on the surface deformation law and mechanism of the entire deep excavation channel section. For these reasons, we introduced a novel approach that combines SBAS-InSAR and GNSS, enabling the surface domain monitoring of the study area at a regional scale as well as real-time monitoring of specific target regions. By using SBAS-InSAR technology and leveraging 11-view high-resolution TerraSAR-X data, we revealed the spatiotemporal evolution law of surface deformations in the channel slopes within the study area. The results demonstrate that the predominant deformation in the study area was uplifted, with limited evidence of subsidence deformation. Moreover, there is a distinct region of significant uplift deformation, with the highest annual uplift rate reaching 19 mm/y. Incorporating GNSS and soil-moisture-monitoring timeseries data, we conducted a study on the correlation between soil moisture and the three-dimensional deformation of the ground surface, revealing a positive correlation between the soil moisture content and vertical displacement of the channel slope. Furthermore, combining field investigations on surface uplift deformation characteristics, we identified that the main cause of surface deformation in the study area was attributed to the expansion of the soil due to water absorption in expansive soils. The research results not only revealed the spatiotemporal evolution law and mechanism of the channel slope deformation in the studied section of the deep excavation channel but also provide successful guidance for the prevention and control of channel slope-deformation disasters in the study area. Furthermore, they offer effective technical means for the safe monitoring of the entire South–North Water-Diversion Middle-Route Project and similar long-distance water-conveyance canal projects.

1. Introduction

Spanning a total length of 1432 km, the China South–North Water-Diversion Middle-Route Project stands as the largest water-diversion project globally. The project route traverses through a region characterized by complex and diverse geological conditions, including challenging geological engineering factors such as high side slopes, expansive soils, mining areas, and wet sink loess [1,2,3]. Particularly, in the elevated canal section near the Danjiangkou Reservoir, a deep excavation construction method was employed to facilitate the implementation of the “self-flow” water-transfer approach. Consequently, a deep excavation side slope was formed, which is susceptible to slippage. Additionally, our research has indicated that the slope soil in the canal section belonged to expansive soil, which is prone to swelling and deformation upon exposure to rainwater. Thus, the combination of swelling soil and deep excavation side slope poses a high risk of geological disasters on the channel’s side slope. Failure to promptly comprehend the relevant slope-deformation patterns and mechanisms may compromise the overall safety of the project operations [4,5].

Considering the prevailing soil conditions and construction methods, deformation of deep excavation channel slopes is an inevitable occurrence. The presence of cracks in the lining structure of the channel slope since the commencement of the project indicates an ongoing deformation. However, the current monitoring methods for channel slope deformation in the entire China South-North Water-Diversion Project primarily rely on traditional leveling measurements. These measurements can only detect point deformations at specific measurement points, thus failing to provide a comprehensive understanding of surface area deformations resulting from deep excavation. Furthermore, they do not facilitate the all-weather real-time monitoring of critical deformation areas, significantly limiting our ability to provide an early warning of channel slope-deformation hazards. Clearly, the utilization of traditional leveling measurements does not meet the current demands of channel slope-deformation monitoring. On the other hand, a review of the existing literature highlights a dearth of research regarding the influence of soil moisture content on the three-dimensional deformation of channel slopes in deep excavation sections. This knowledge gap hinders the comprehensive understanding of the slope-deformation mechanism.

In recent years, Interferometric Synthetic Aperture Radar (InSAR) interferometry has emerged as a valuable tool for monitoring ground subsidence [6,7], landslides [8], and other geohazards. With the increasing availability of SAR data, it is now possible to perform long-term monitoring of various targets using historical archives [9,10,11]. In particular, InSAR-based methods offer distinct advantages for large-area monitoring tasks such as deformation monitoring of long-distance water-transmission channels. These methods provide extensive spatial coverage and are unaffected by weather conditions such as clouds and rain, making them highly sensitive to ground deformation. Chaussard et al., Fernández-Torres et al., Figueroa-Miranda et al., and Du et al. investigated the long-term subsidence law in Mexico using the InSAR technique [12,13,14,15,16]. Kang et al. deduced the geometry and volume of creep-slide surfaces in the Jinsha River Basin based on InSAR [17]. Pu et al. performed detailed mapping and conducted a kinematic trend assessment of potential landslides associated with large-scale land construction projects using multitemporal InSAR [18]. Li et al. revealed the complex surface displacement of the Zhouqu Nanyu landslide using multiplatform InSAR observational data [19]. These studies have yielded promising monitoring results, introducing a new technical approach for detecting deformation law in the deep excavation channel section of the South–North Water-Diversion Middle-Route Project. However, the temporal resolution of InSAR monitoring methods for key monitoring areas is currently limited by data acquisition and processing constraints.

On the other hand, GNSS technology offers the advantage of continuous and all-weather monitoring without being affected by climate or other factors. The monitoring process, including data acquisition, processing, transmission, and analysis, can be easily automated and operated. Jiang et al. realized high-precision deformation monitoring by combining GNSS and ground-distance observation under harsh environmental conditions [20]. Shu et al. conducted real-time and high-precision monitoring of landslide displacement based on a GNSS CORS network [21]. Wang et al. carried out research on the evaluation of a real-time, high-precision detection algorithm for landslide displacement using GNSS virtual reference station technology [22]. Given these advantages of GNSS technology, this study proposes a collaborative monitoring approach using SBAS-InSAR and GNSS to investigate the deformation law in the deep excavation channels of the China South–North Water-Diversion Middle-Route Project. This approach aims to achieve surface domain deformation monitoring and the real-time online monitoring of key deformation areas in the study region, thereby enhancing the deformation disaster forecasting and early-warning capabilities. By considering the surface deformation law and geological engineering conditions in the study area, the mechanism of surface deformation was inferred. Additionally, the correlation between soil moisture and three-dimensional surface deformation was carried out by combining GNSS and soil-moisture online-monitoring data. The research results not only revealed the spatial and temporal evolution rules and mechanisms of surface deformation in the channel slope of this deep excavation channel section but also improved the deformation disaster-prevention capability in the study area. Furthermore, the results provided an effective technical means for the safety monitoring of the whole China South–North Water-Diversion Middle-Route Project and similar long-distance water-transmission channel projects.

2. Methods

2.1. Introduction to the Study Area

The head section of the South–North Water-Diversion Project in China spans a total length of 176.7 km, with the expansive-soil section covering 149.5 km, accounting for 84.5% of the total length of the channel. Expansive soil is a type of soft rock characterized by its strong hydrophilicity, expanding when exposed to water, and shrinking and collapsing when it dries out [23]. The stability of structures built on expansive soils is seriously threatened during wet–dry cycles [24]. Despite efforts to improve the expansion characteristics of the channel slope soil during construction, years of deformation monitoring and on-site investigations have revealed that the enhanced expansive soil still exhibits expansion characteristics, making it prone to deformation in the deep excavation expansive-soil channel slope under the combined influences of expansive soil and steep slopes. In addition, to facilitate the “self-flow” water-transmission mode, the channel passes through an elevated terrain, necessitating the implementation of the deep excavation project. The head section of the deep excavation spans a length of 58.4 km, with a maximum depth of 47 m and a maximum opening width of 373.2 km. Daily level measurements indicate the long-term existence of surface deformations in the channel slope of the deep excavation section, potentially influenced by the soil and steep slopes. However, there is a lack of monitoring and research on the deformation law of the surface area of this section. The deep excavation section is located between the dam at the head of the South–North Water-Diversion Project and the channel pile no. 52 + 100, as shown in Figure 1. (Figure 1a is the aerial view of the deep excavation section, Figure 1b is the field photo, and Figure 1c is the cross-section of the channel slope).

2.2. Monitoring Data Preparation

2.2.1. SAR Data

In this paper, we aimed to comprehensively analyze the deformation law of the slopes of the deep excavation channels of the South–North Water-Diversion Project in China. For this purpose, we acquired a set of 11 views of high-resolution, programmed TerraSAR-X uplink images. The selected StripMap mode offers a coverage width of 35 km and a spatial resolution of 3 m, rendering it suitable for fine deformation monitoring in key areas. The coverage of the programmed TerraSAR-X images is shown in Figure 2, and the related parameter information is shown in

Table 1. TerraSAR-x programming data.

No.	Data	Track Number	Strip	Orbital Direction
1	10 June 2020	51	009R	Ascending
2	2 July 2020	51	009R	Ascending
3	24 July 2020	51	009R	Ascending
4	26 August 2020	51	009R	Ascending
5	9 October 2020	51	009R	Ascending
6	31 October 2020	51	009R	Ascending
7	3 December 2020	51	009R	Ascending
8	25 December 2020	51	009R	Ascending
9	5 January 2021	51	009R	Ascending
10	16 January 2021	51	009R	Ascending
11	7 February 2021	51	009R	Ascending

. SRTM-DEM with a 30 m grid resolution was selected as the reference data for the topographic phase removal process.

2.2.2. GNSS and Soil Moisture Data

SBAS-InSAR is effective in capturing the surface deformation law in the study area, but it lacks real-time monitoring capabilities for key areas. To address this limitation and enable the real-time monitoring of severe deformation points, we installed a GNSS + soil moisture sensor-based monitoring system at a specific location in the study area, as depicted in Figure 3. This system was equipped with solar power supply and signal transmission capabilities allowing for an extended unattended operation. The deployment of this system serves the following primary objectives: first, to monitor the real-time three-dimensional deformation of the selected severe deformation point, providing reliable early-warning reference data for the deformation disaster prevention and control of deep excavation channel slopes; second, to investigate the law and mechanism underlying the influence of soil moisture on the three-dimensional deformation of channel slopes. In order to provide a benchmark for monitoring the surface deformation of channel slopes and minimize monitoring errors, another GNSS monitoring system was simultaneously deployed in the surface deformation stabilization area in the study area. The locations of the two monitoring systems are presented in Figure 3.

2.3. Data Processing Method

The overall workflow of this research is shown in Figure 4.

2.3.1. SAR Data Processing Method

To acquire the deformation spatio-temporal evolution law of the slopes in the deep excavated expansive-soil canal section of the South–North Water-Diversion Middle-Line Project, we collected 11 TerraSAR images from ascending track 51. These images were collected between 10 June 2020 and 7 February 2021. Initially, we employed DInSAR technology to process all eligible interferometric pairs. Subsequently, the SBAS-InSAR method (as shown in Figure 5) was utilized to extract the timeseries deformation of the deep excavation expansive-soil channel slope.

During the utilization of DInSAR technology, Gamma software [25] was employed, and a multilook ratio of 10:2 in the range and azimuth directions was set to effectively mitigate noise to some extent. To ensure relatively high co-registration accuracy, a combination of methods accounting for scene topography and spectral diversity, considering the interferometric phase of the burst-overlap region, was adopted [26]. Precise orbits provided by the agency and a 30 m shuttle radar topography mission digital elevation model were utilized to compensate for topography effects [27]. A power spectrum filter was applied to reduce the impact of phase noise [28]. Subsequently, the interferograms were unwrapped using the branch cut method [29], followed by the WGS84 geographic coordinates.

Using the SBAS-InSAR technology, we used the open-source MintPy package to process the regional timeseries of the deformation by employing the small baseline method [30,31,32]. We selected the image taken on 10 June 2020 from all of the SAR images as the master image and registered the other images with the master image. Then, the M-amplitude interferograms that conformed to the spatiotemporal baseline threshold were selected using the freely combined differential interferometry pairs. The interference phase ($\psi$) of each interferogram is composed of a reference ellipsoid phase (${\phi }_{\mathrm{ref}}$), terrain phase (${\phi }_{\mathrm{top}}$), LOS surface deformation phase (${\phi }_{\mathrm{def}}$), atmospheric delay phase (${\phi }_{\mathrm{atm}}$), and random noise (${\phi }_{\mathrm{noi}}$), as shown in Equation (1):

$$\psi ={\phi }_{\mathrm{ref}}+{\phi }_{\mathrm{top}}+{\phi }_{\mathrm{def}}+{\phi }_{\mathrm{atm}}+{\phi }_{\mathrm{noi}}$$

(1)

After the reference ellipsoid phase removal, topographic phase removal, and minimum-cost flow phase unwinding, the interferogram phase can be expressed as Equation (2):

$$\Delta \phi =A\phi +\Delta {\phi }_{\epsilon }$$

(2)

where $\Delta \phi ={\left[\Delta {\phi }^1,\dots ,\Delta {\phi }^M\right]}^T$ is the interferometric phase of each interferogram; $\phi ={\left[{\phi }^2,\dots ,{\phi }^{N+1}\right]}^T$ is the temporal interferometric phase of other images relative to the reference image (assuming that the phase of the reference image is ${\phi }_1$); $\Delta {\phi }_{\epsilon }={\left[\Delta {{\phi }_{\epsilon }}^1,\dots ,\Delta {{\phi }_{\epsilon }}^M\right]}^T$ is the residual interferometric phase error; and A is an M × N design matrix, which represents the interferometric combination mode and consists of 1, 0, and −1, where −1 represents the master image, and 1 represents the slave image. The least-square norm method can be used to calculate the optimal estimation value of the timeseries of the interferometric phase:

$$\widehat{\phi }=\mathit{argmin}\Vert W^{1/2}(\Delta \phi -A\phi {)\Vert }_2={\left(A^{T}WA\right)}^{-1}{A}^{T}W\Delta \phi$$

(3)

where $\widehat{\phi }$ is the best estimation of the timeseries of the interferometric phase, W is an M × M diagonal weight matrix, and the weight matrix method adopted in this paper was the Fisher information matrix (FIM). The interferometric phase of each CT that conformed to the SC threshold can be obtained with DInSAR processing. Temporal coherence (TC) can be used to select the CTs with high quality, and by using WLS estimation of the small baseline network, high-quality and high-precision timeseries deformation results of CTs in the study area can be obtained. TC can be expressed by the following:

$${\gamma }_{\mathrm{tmp}}=\frac{1}{M}\left|{\displaystyle {\displaystyle \sum }_{i=1}^M}\mathit{exp}\left[j\left(\Delta {\phi }_i-A{\widehat{\phi }}_i\right)\right]\right|$$

(4)

In Equation (4), j is the imaginary unit. In addition, due to the heavy regional atmosphere present in the images of Nanyang city, Henan Province, atmospheric correction was required before using the SBAS-InSAR method.

2.3.2. GNSS Monitoring Technology

In this study, the real-time monitoring of three-dimensional deformation of the channel surface was conducted using the GNSS relative positioning method. GNSS relative positioning involves collecting GNSS observational data simultaneously from multiple receivers. Through differential processing of the observation values, errors such as satellite clock difference, receiver clock difference, and atmospheric delay can be eliminated or weakened, thus realizing high-precision GNSS positioning. Typically, least-squares (LS) or Kalman filtering methods are employed in GNSS relative positioning solutions. These methods necessitate the appropriate determination of the functional model and stochastic model within the solution framework. The functional model describes the mathematical relationship between the unknown parameters and the GNSS observations, while the stochastic model describes the statistical properties of the observations themselves and their interdependencies, usually represented by a suitable variance–covariance matrix. To obtain highly accurate and reliable positioning results, it is crucial to accurately and appropriately determine both the functional model and the stochastic model [33].

Function Model

The functional model relative positioning establishes the mathematical relationship between the unknown parameters and the double-difference observations. Developing an accurate functional model requires a comprehensive understanding of the various physical phenomena occurring during signal transmission from GNSS satellites and on the receiver’s side. GPS and BDS navigation systems utilize code division multiple access (CDMA) to distinguish satellites. The original observation equation for the carrier and pseudo-range of the observation data corresponding to any satellite’s ephemeris can be expressed [34] (unit: meter):

$$\left\{\begin{array}{c}{P}_{k,i}^j={\rho }_{k,i}^j+I_{k,i}^j+T_{k,i}^j+M_{k,ip}^j+c\left({\epsilon }_t-\epsilon t^j\right)+{\epsilon }_p^j\\ {\lambda }_i{\phi }_{k,i}^j={\rho }_{k,i}^j+{\lambda }_i{N}_{k,i}^j-I_{k,i}^j+T_{k,i}^j+M_{k,i\phi }^j+c\left(\epsilon t_i-{\epsilon }^j\right)+{\epsilon }_{\phi }^j\end{array}\right.$$

(5)

where $k$ is the ground receiver number, $j$ is the satellite number, $i$ is the frequency of the observed data, $P$ is the pseudo-distance observation, $\rho$ is the distance from the satellite to the receiver, $I$ is ionospheric delay, $T$ is the tropospheric delay, $M$ is the multipath error, $c$ is the speed of light, $\epsilon t^j$ is the clock difference of the receiver $i$, $\epsilon t_i$ is the satellite clock difference, ${\epsilon }_p$ is the chance error of the pseudo-distance observation, ${\epsilon }_{\phi }$ is the chance error of the carrier observation, $\lambda$ is the corresponding carrier wavelength, $\phi$ is the carrier phase observation, and $N$ is the nondifferential raw ambiguity of the corresponding satellite for this receiver. After processing the original observation equation for inter-station and inter-star differences, we obtained the following:

$$\left\{\begin{array}{c}\Delta \nabla P_{kr,i}^{jh}=\Delta \nabla {\rho }_{kr,i}^{jh}+\Delta \nabla I_{kr,i}^{jh}+\Delta \nabla T_{kr,i}^{jh}+\Delta \nabla {\epsilon }_{kr,ip}^{jh}\\ {\lambda }_i\Delta \nabla {\phi }_{kr,i}^{jh}=\Delta \nabla {\rho }_{kr,i}^{jh}+{\lambda }_i\Delta \nabla N_{kr,i}^{jh}-\Delta \nabla I_{kr,i}^{jh}+\Delta \nabla T_{kr,i}^{jh}+\Delta \nabla {\epsilon }_{kr,i\phi }^{jh}\end{array}\right.$$

(6)

where $\Delta \nabla$ is the double difference operator, $h$ is the reference satellite number, and $r$ is the reference station receiver number.

Inter-station differencing is effective in mitigating satellite orbit errors and satellite clock differences. On the other hand, inter-satellite differencing helps eliminate receiver-side errors and partially attenuates the effects of ionospheric and tropospheric delays. When the baseline between stations is short, double-difference processing can significantly reduce the impact of atmospheric delay. However, for longer baselines, residual errors are typically compensated for by employing empirical models or introducing additional parameters. Through double-difference processing, common error terms in relative positioning are eliminated or mitigated, making this method a preferred choice for high-precision positioning purposes.

In relative positioning, the coordinates of the reference point (assumed to be A) are generally precisely determined. Thus, the vector of unknown parameters contains mainly the coordinates of the flow station (assumed to be B) and the double-difference ambiguity:

$$x={(X_B,Y_B,Z_B,N_{AB,f}^i)}^T,i=1,\cdots ,m_{sp}$$

(7)

where $m_{sp}$ refers to the number of double-differential satellite pairs ($m_{sp}$ should be ≥4 in relative positioning). Since least squares is used in the solution, it is necessary to linearize the observation equation, which is the expansion of the observation equation to the first-order Taylor series at the approximation of the unknown parameters:

$$B={[\frac{\partial F\left(x\right)}{\partial X_B},\frac{\partial F\left(x\right)}{\partial Y_B},\frac{\partial F\left(x\right)}{\partial Z_B},\frac{\partial F\left(x\right)}{\partial N_{AB,f}^i}]}_{i=1,\cdots ,m_{sp}}^{x=x_0}$$

(8)

where

$$\left\{\begin{array}{c}\frac{\partial F\left(x\right)}{\partial X_B}=\frac{X_B-X^k}{{\rho }_B^k}-\frac{X_B-X^j}{{\rho }_B^j}\\ \frac{\partial F\left(x\right)}{\partial Y_B}=\frac{Y_B-Y^k}{{\rho }_B^k}-\frac{Y_B-Y^j}{{\rho }_B^j}\\ \frac{\partial F\left(x\right)}{\partial Z_B}=\frac{Z_B-Z^k}{{\rho }_B^k}-\frac{Z_B-Z^j}{{\rho }_B^j}\\ \frac{\partial F\left(x\right)}{{\partial N}_{B,f}^i}=0or{\lambda }_f\end{array}\right.$$

(9)

The corresponding linearized matrix of the unknown parameters is given:

$$\Delta x=x-x_0={(\Delta X_B,\Delta Y_B,\Delta Z_B,N_{AB,f}^i)}^T,i=1,\cdots ,m_{sp}$$

(10)

The corresponding constant term is as follows:

$$f={\left[\Delta \nabla P^1,\dots ,\Delta \nabla P^i,\lambda \Delta \nabla {\phi }^1,\dots ,\lambda \Delta \nabla {\phi }^i\right]}^T-F(x_0)$$

(11)

The linearization of the two-difference observation equation for the relative localization can be simplified and expressed:

$$B\Delta x-f=v$$

(12)

Once the design matrix $B$, the constant term in the functional model, is determined, a suitable stochastic model can be found based on the corresponding functional model.

Stochastic Model

In a GNSS positioning solution, along with the functional model describing the mathematical relationship between the unknown parameters and GNSS observations, a stochastic model is also required to describe the statistical properties of the observations. The stochastic model is usually described by a variance–covariance matrix [35]. The variance component primarily reflects the accuracy information of the observations themselves, while the covariance component describes the correlation between the observations. The stochastic model affects not only the estimation of the unknown parameters but also the estimation of the ambiguity and tropospheric parameters. Hence, an accurate and appropriate stochastic model plays an important role in the quality control of the GNSS solution, solution accuracy, and other aspects.

In the stochastic model, ${\sigma }^2$ mainly represents the statistical accuracy of the observed quantity itself, while the variance element is mainly determined by various empirical models. The appropriate variance element should satisfy the following: more precise observations have less variance and larger weights and contribute more to the parameter estimates. However, in the actual GNSS solution, the satellite signal is affected by the hardware characteristics of the receiver’s antenna, multipath effect, atmospheric effect, and other factors. Accurate power fixing is a difficult, complex task. The commonly used empirical models are the equal-weight model and height-angle-based and signal-to-noise ratio-based stochastic models.

Due to the disparity between the equal-weighting model assumption, which assumes that observation data from all GNSS satellites in each constellation and orientation have the same level of accuracy, and the actual scenario, this model finds limited application in practical algorithms. Instead, the altitude angle model is commonly employed in practical solutions because of its simplicity and reliability. The main errors in the double-difference post-GNSS observations include tropospheric, ionospheric, and multipath errors. As the altitude angle increases, the tropospheric and ionospheric error decreases, and the likelihood of multipath errors diminishes, leading to a higher accuracy in the corresponding observations. The height angle stochastic model used in this system is as follows:

$${\sigma }^2=a^2+b^2/\left(\mathrm{s}\mathrm{i}\mathrm{n}\right(Elev){)}^2$$

(13)

where $Elev$ denotes the altitude angle of the satellite, and $a$ and $b$ are empirical values, generally chosen as $a=4 \mathrm{m}\mathrm{m} \mathrm{a}\mathrm{n}\mathrm{d} b=3 \mathrm{m}\mathrm{m}$.

Conversion of XYZ to NEU

The above model directly obtains the three-dimensional coordinates $(X, Y, Z)$ of the monitoring points in a specific spatial Cartesian coordinate system. Deformation monitoring is concerned with the change in the displacement of the monitoring point in the horizontal and elevation directions. Therefore, it is necessary to convert the coordinates $(X_{t_i}, Y_{t_i}, Z_{t_i})$ at any moment, $t_i$, into coordinates $({{\rm N}}_{t_i},{{\rm E}}_{t_i},U_{t_i})$ in the station-centered horizon coordinate system with the initial coordinate point $(X_0, Y_0, Z_0)$ as the origin. The conversion equation is as follows:

$$\left\{\begin{array}{c}\Delta X_{t_i}=X_{t_i}-X_0\\ \Delta Y_{t_i}=Y_{t_i}-Y_0\\ \Delta Z_{t_i}=Z_{t_i}-Z_0\end{array}\right.$$

(14)

$$(X_{t_0},Y_{t_0},Z_{t_0})\to (B_{t_0},L_{t_0},H_{t_0})$$

(15)

$$\left[\begin{array}{c}{N}_{t_i}\\ E_{t_i}\\ U_{t_i}\end{array}\right]=\left[\begin{array}{ccc}-\sin B_{t_0}\cos L_{t_0}& -\sin B_{t_0}\sin L_{t_0}& \cos B_{t_0}\\ -\sin L_{t_0}& \cos L_{t_0}& 0\\ \cos B_{t_0}\cos L_{t_0}& \cos B_{t_0}\sin L_{t_0}& \sin B_{t_0}\end{array}\right]$$

(16)

Equation (14) is used to find the cumulative displacements $\Delta X_{t_i}$, $\Delta Y_{t_i}$, and $\Delta Z_{t_i}$ of the monitoring point in the spatial three-dimensional direction at moment $t_i$. Equation (15) is the transformation of the spatial three-dimensional coordinates $(X_{t_0}, Y_{t_0}, Z_{t_0})$ of the monitoring point at the initial ($t_0$) moments into geodesic coordinates $({{\rm B}}_{t_0}, L_{t_0}, H_{t_0})$. Equation (16) is used to obtain the coordinates of the monitoring station in the station-centered horizon coordinate system at any moment ($t_i$), where $N_{t_i}$ denotes the cumulative displacement of the monitoring point in the north–south direction relative to the moment ($t=0$) and positive to the north; $E_{t_i}$ indicates the cumulative displacement in the east–west direction, positive to the east; and $U_{t_i}$ indicates the accumulated displacement in the elevation direction, where upward is positive. The monitoring point displacement is obtained from the coordinate difference of two consecutive GNSS measurements.

3. Results

3.1. Deformation Law Analysis of the Deep Excavation Channel Slope Based on TerraSAR-X Data

To comprehensively examine the surface deformation patterns across the entire channel slope area in the study region, we conducted a relevant investigation utilizing SBAS-InSAR technology and 11-view high-resolution TerraSAR-X uplink data. The deformation outcomes, pertaining to the rail lifting baseline and channel slope, are presented in Figure 6 and Figure 7, respectively.

According to processing results of the TerraSAR-X data (Figure 7), the surface deformation characteristics of the deep-dug expansive-soil channel section in the middle route of the South–North Water-Diversion Project could be classified into two main types: uplift and settlement. The uplift deformation area was mainly located in the middle and downstream of the channel in the study area and the settlement deformation area in the middle and upstream of the channel in this section. Notably, the uplift deformation area was not only larger in scope than the settlement area but also more serious in the degree of deformation. Furthermore, the uplift deformation was more severe on the right bank of the channel than on the left bank.

The spatial distribution of the deformation could be classified into four distinct regions (as shown in Figure 7). There was almost no deformation of the channel slopes within the range of region A, with an annual deformation rate of −5 mm/y to +5 mm/y. In area B, the channel slopes were mainly subsided, with an annual settlement rate ranging from −15 mm/y to +5 mm/y. In the range of area C, the channel slope deformation was dominated by an uplift. The maximum uplift deformation of the channel slope accumulated more than 19 mm per year; in fact, in the range of the region, the uplift deformation caused serious damage to the channel slope (Figure 8). Consequently, based on these findings, channel management personnel have undertaken necessary reinforcement measures in the severely deformed areas. Additionally, a GNSS monitoring station has been installed at a representative deformation point to enable the real-time monitoring of surface deformation, facilitating a scientific assessment of the channel slope’s safety. In region D, the channel slope deformation was also predominantly uplifted, with a maximum uplift deformation of approximately 12 mm per year. However, compared to region C, the lifting deformation in this area was relatively minor. Through on-site investigations, no evidence of damage to the channel slope was observed.

To further reveal the temporal deformation characteristics of the channel slope, we randomly selected two points, P1 and P2, in the severe uplift deformation region C and a point, P3, in the settlement region B. Taking these three points as examples, relevant temporal deformation values were extracted to carry out research, as shown in Figure 9. The timeseries deformation values of the three monitoring points revealed a certain periodicity in both the uplift deformation and settlement deformation processes. All three points experienced a deformation pattern of “lifting→settling→lifting” during the time period, as shown in

Table 2. Deformation process characteristics of the three monitoring sites.

Number	Date	Deformation Characteristic	Deformation Value (mm)
P1	10 June 2020–29 August 2020	Uplift	0→12
	29 August 2020–28 October 2020	Settlement	12→4.3
	28 October 2020–5 February 2021	Uplift	4.3→10
P2	10 June 2020–29 August 2020	Uplift	0→9.8
	29 August 2020–28 October 2020	Settlement	9.8→3
	28 October 2020–5 February 2021	Uplift	3→10
P3	10 June 2020–29 August 2020	Uplift	0→3
	29 August 2020–27 December 2020	Settlement	3→−1.7
	27 December 2020–5 February 2021	Uplift	−1.7→1.5

. Since P1 and P2 are both in zone C, where severe uplift and deformation occurred, their deformation rules were basically the same. From 10 June 2020, both points have sustained uplift and deformation, and they reached the maximum value on 29 August 2020. Subsequently, the uplift and deformation fell back somewhat and stopped falling on 28 October 2020 and then occurred again. From this trend, the re-uplifting deformation value may exceed the previous peak value. On the other hand, point P3 is located in zone B, which is characterized by an overall weak settlement deformation. It experienced continuous uplifting deformation from 10 June 2020, reaching its maximum value on 29 August 2020, before transitioning into subsidence deformation. The subsidence process halted on 27 December 2020, and then, uplifting deformation occurred again, but the uplifting deformation value did not exceed the previous peak value.

3.2. Analysis of the Surface Deformation Mechanism of the Channel Slope

Based on Figure 7 and previous analysis, it is evident that the surface deformation of the slope of the channel section in the study area was mainly uplifted. Among the areas studied, the most severe uplift deformation was observed in area C, while a certain degree of uplift deformation was also produced in area D. These deformations can be attributed to the long-term impact of expansive soil on the channel slope in the study area. Expansive soil has the characteristics of high water absorption, high plasticity, fissure, and intense expansion and contraction because its composition contains strong hydrophilic minerals. During the early stages of deposition, when the consolidation characteristics are prominent, the surface plasticity of expansive soil was not significant. However, during the construction of the channel project, the excavation of the slope disrupted the soil consolidation, leading to the release of internal expansion forces and subsequent expansion deformation. Moreover, due to rainfall, the expansive soil underwent repeated expansion and contraction deformation, leading to expansive-soil channel landslide deformation with gradual and long-term characteristics. In area B, slight settlement deformation was observed. Considering the geographical environment of area B, which is characterized by numerous residential buildings and a major traffic road traversed by large trucks, it can be inferred that this type of deformation is likely caused by the combined effect of static loads from buildings and dynamic loads generated by the substantial number of trucks exceeding the capacity of the expansive soils in the area to accommodate expansion.

In order to further analyze the influence of the soil moisture content on the deformation of expansive-soil channel slopes, we examined the relationship between surface deformation and soil moisture content by combining the real-time monitoring data of GNSS and soil moisture content in the area of uplift deformation (Figure 10). The monitoring data revealed that both uplift and subsidence deformations occurred vertically at the monitoring site due to changes in the soil water content, although the overall trend was the occurrence of an uplift. From 31 December 2020 to 26 February 2021, the soil moisture content remained relatively stable, at approximately 26.5%, and no significant lifting or settling deformation was observed on the surface during this period. From 27 February to 30 April, the soil water content increased to about 28.5%, and the surface was slightly lifted, with a maximum lift of 5 mm. From 1 May 2021 to 16 May 2021, the soil water content first decreased from 28% to 25.5% and then increased to 28%, and the surface was first deformed by subsidence and then by lift; from May 17 to July 3, the soil water content decreased from 28% to 22.5%, with fluctuations near the lowest point, and surface deformation also occurred as well as obvious fluctuations; from July 4 to July 8, the soil moisture content rose from 22.5% to 33%, and the surface also showed an obvious lifting deformation; from July 8 to September 17, the soil moisture content fluctuated in the range of 30 to 36%, and the surface lifting deformation basically moved up and down around a 5 mm axis, with a maximum lifting value of 14 mm and a minimum of 0 mm.

In the horizontal plane, notable displacements occurred in north and west directions. Both the northward and westward displacements exhibited an increasing trend in absolute values. It is worth noting that the northward displacement was toward the interior of the channel, reaching a maximum horizontal displacement of 17 mm. Consequently, the channel management department has implemented necessary restoration measures. On the other hand, the westward displacement was relatively small, measuring at only 7 mm, and it aligned with the channel direction. Therefore, the horizontal displacement in this direction had a lesser impact on the safety of the channel. Furthermore, the study highlighted the significant influence of soil moisture on vertical displacements at the surface. It was observed that smaller soil moisture levels correspond to smaller vertical displacements, while higher soil moisture levels are associated with larger vertical displacements. A strong positive correlation between the magnitude of the surface vertical displacement and soil moisture content was evident. Moreover, the influence of soil moisture on horizontal displacement was more pronounced toward the interior of the channel slope, while its impact on westward horizontal displacement along the channel slope was comparatively smaller. These research results provide valuable guidance for the prevention and control of channel slope-deformation hazards in the study area.

4. Discussion

4.1. Reliability Analysis of the Detection Results

To assess the reliability of the research results, we conducted a comparative analysis between the SBAS-InSAR and GNSS methods, focusing on surface subsidence at the GNSS observation point as an example. By adopting the mutually corroborating method, we quantitatively examined the monitoring results of both methods. From 31 December 2020 to 7 February 2021, as depicted in Figure 10, the cumulative surface settlement measured using GNSS was 1.2 mm, while Figure 7 illustrates that the cumulative surface settlement detected using SBAS-InSAR was 2 mm. The difference between the two measurements was less than 1 mm, indicating a high level of reliability within our detection results. Furthermore, we also conducted a field survey in the area experiencing significant deformation. Through discussions with the channel manager, we verified the severity of the left bank uplift in area C, as shown in Figure 7. It was confirmed that repair work had indeed been carried out on the channel slope in this area, as depicted in Figure 11. This alignment between our research findings and the actual site conditions provides further evidence of the reliability of our results. It underscores the valuable support our scientific data can offer in ensuring the safety and protection of the channel slope.

In addition, to validate the accuracy of the measurement results obtained using the SBAS-InSAR technology in this study, we conducted a comparative analysis between the 10-phase SBAS-InSAR measurements and leveling measurements at three points within the severely uplifted deformation area (Figure 11). The results are statistically presented and compared in

Table 3. Comparison of level measuring vs. SBAS-InSAR.

Date	Level Measuring/mm			SBAS-InSAR/mm			Errors/mm
	A1	A2	A3	A1	A2	A3	A1	A2	A3
2 July 2020	3	4	4	4	5	5	−1	−1	−1
24 July 2020	4	5	5	6	7	7	−2	−2	−2
26 August 2020	12	13	13	14	15	15	−2	−2	−2
9 October 2020	7	8	8	8	9	9	−1	−1	−1
31 October 2020	4	5	5	5	6	6	−1	−1	−1
3 December 2020	6	7	7	7	8	8	−1	−1	−1
25 December 2020	5	6	7	6	8	8	−1	−2	−1
5 January 2021	6	7	7	7	8	8	−1	−1	−1
16 January 2021	10	11	11	11	12	12	−1	−1	−1
7 February 2021	10	11	11	11	11	12	−1	0	−1

. From the table, it can be seen that (1) the maximum subsidence value observed at the monitoring point was 15 mm, which is within the range of 19 mm. This can be attributed to the location of the three leveling monitoring points on the cemented surface of the channel walkway, which is hardened by the cement material, and due to the influence of the hardened surface, the uplift deformation of the walkway is obviously not the largest. (2) The SBAS-InSAR monitoring results consistently show larger values compared to the leveling results. This can be attributed to the fact that the SBAS-InSAR monitoring results average multiple nearby SBAS-InSAR points around the leveling points. The surface of these surrounding points was not hardened, making them more prone to expansion compared to the hardened surface. (3) The comparison of the two monitoring methods revealed that the maximum error between them was merely 2 mm in absolute value. This further confirms the high reliability of the findings obtained in this study.

4.2. Shortcomings and Future Research Plans

In this study, SBAS-InSAR technology was employed to investigate the slope-deformation law of the deep excavation channel section in the China South–North Water-Diversion Middle-Route Project. The spatial distribution and temporal evolution of uplift and subsidence deformations were analyzed in the study area. By considering the geological engineering conditions, the deformation mechanism of the study area was revealed. Additionally, the relationship between three-dimensional surface deformation and the soil water content change was analyzed. The research results provide valuable scientific and technological support for the prevention and control of channel slope-deformation disasters in the study area. However, the research results also have some limitations: (1) the analysis was based on a limited dataset of only 11 periods, which restricts a comprehensive understanding of the temporal deformation characteristics in the study area; and (2) the study did not specifically investigate the physical properties of soil expansion, which hinders a thorough understanding of the surface deformation mechanism of the channel slope in the study area. In future research, we plan to use additional freely available SAR data sources to further study the temporal deformation law of the study area. Moreover, we aim to focus on studying the physical characteristics of soil expansion to gain deeper insights into the deformation mechanism of the channel slope.

5. Conclusions

(1)

Aiming at the limitations of current deformation monitoring means in the study area, the cooperative monitoring technology of SBAS-InSAR and GNSS was proposed. By employing SBAS-InSAR technology and high-resolution TerraSAR-X data, this study unveils the distribution and temporal sequence characteristics of deformations within the slope domain of the deep-dug expansive-soil channel section in the South–North Water-Diversion Middle-Route Project in China. The results exhibited two distinct deformation types: uplift and subsidence. Uplifted deformation was primarily concentrated downstream, while subsidence was predominantly observed in the middle and upstream regions of the section. The uplifted deformation areas surpassed the subsidence areas in both the extent and magnitude of occurrence, emphasizing their greater severity. Analysis of the temporal deformation characteristics at the measurement points within the deformation area revealed a cyclic pattern of “uplift→partial fallback→uplift again”. Moreover, horizontal displacement demonstrated a continuous accumulation trend, with larger displacements occurring toward the inner part of the channel;

(2)

Combined with the geological engineering conditions of the study area, the deformation mechanism of the channel slope was elucidated. The study pointed out that the primary cause of the uplift deformation was the expansion of expansive soil upon contact with water. Conversely, the slight settlement was attributed to the combined effects of static loads from buildings, dynamic loads from large trucks, and the expansion of expansive soil in contact with water. Through the analysis of the soil moisture content and GNSS measurements, it was concluded that soil humidity exerted significant influence on vertical displacement at the surface. A lower soil moisture content corresponds to smaller vertical displacement, whereas higher soil moisture content results in larger vertical displacement. Moreover, there exists a strong positive correlation between surface vertical displacement and soil moisture;

(3)

Based on the study results and field research, it was observed that the surface of the channel slopes within the severely uplifted deformation area suffered varying degrees of damage, which was estimated to be further aggravated during the subsequent evolution of the soil in many dry–wet alternations. To comprehensively elucidate the deformation pattern and mechanism of the channel, we advocate for an extended duration of surface deformation monitoring in this area. This will facilitate a thorough understanding of the deformation process and enable appropriate repair measures to be recommended to ensure the safe operation of the channel. Furthermore, the proposed SBAS-InSAR and GNSS collaborative monitoring technology provides a safety guarantee for the high-quality development of China’s South–North Water-Diversion Follow-up Project as well as an effective technical means for accurately carrying out the deformation monitoring of large-scale banded water-conservancy projects.