Analysis Of Surface Deformation Research Articles

Analysis of surface deformation and related factors over mining areas based on InSAR: A case study of Fengcheng mine

Abstract. Ground surface deformation in mines affects mining production, damages the ecological environment, and endangers human safety. Mastering the detailed time series deformation and related triggering factors can provide key information for the safety of the mining area. Therefore, the Fengcheng mining area, a large and ancient coal mine in Jiangxi Province, China, was selected as the study area in this work, and the following research was conducted: 1. The accuracy and applicability of the Stacking, Small-Baseline Subset InSAR (SBAS-InSAR), and Interferometric Point Target Analysis (IPTA) methods were preliminarily explored while monitoring the annual deformation rate based on Sentinel-1A data from October 2019 to November 2022. 2. The time-series deformation of the Fengcheng mining area was obtained with SBAS-InSAR technology, and the sedimentation was validated with leveling results. 3. The correlation factors of deformation, such as rainfall and land cover, were studied, and the relationship between the influencing factors, such as coal mining dip angle, digital elevation, coal mining elevation, and deformation, was quantitatively explored with the Grey correlation model and Pearson correlation analysis method. The following conclusions were drawn: The SBAS method has the best adaptability in the dense vegetation mining area, and the root-mean-square error of the difference between deformation results and leveling data does not exceed 4mm. The evolution process of deformation centers is mainly divided into the stages of initial deformation, constant velocity deformation, accelerated deformation, and stable condition. Compared with the natural factors, the settlement of the Fengcheng mining area is mainly affected by human-induced mining and construction of artificial facilities.

Quantitative Assessment and Impact Analysis of Land Surface Deformation in Wuxi Based on PS-InSAR and GARCH Model

Land surface deformation, including subsidence and uplift, has significant impacts on human life and the natural environment. In recent years, the city of Wuxi, China has experienced large-scale surface deformation following the implementation of a groundwater abstraction ban policy in 2005. To accurately measure the regional impacts and understand the underlying mechanisms, we investigated the spatiotemporal characteristics of surface deformation in Wuxi from 2015 to 2023 using 100 Sentinel-1A SAR images and the Persistent Scatterer InSAR (PS-InSAR) technique. The results revealed that surface deformation in Wuxi exhibited significant spatial and temporal variations, with some areas experiencing alternating trends of subsidence and uplift rather than consistent unidirectional change. To uncover the factors influencing this volatility, we conducted a comprehensive analysis focusing on groundwater, precipitation, and soil geology. This study found strong correlations between the groundwater level changes and surface deformation, with the soft soil geology of the area, characterized by alternating layers of sand and clay, further increasing the surface volatility. Moreover, we innovatively applied the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model, typically used in financial analyses, to analyze the subsidence displacement time series in Wuxi. Based on this model, we propose a new “Amplitude Factor” index to evaluate overall surface deformation volatility in the city. Our qualitative assessment of surface stability based on the Amplitude Factor was consistent with research findings, demonstrating the accuracy and effectiveness of the proposed model. These results provide valuable insights for urban planning, construction, and safety control, highlighting the importance of continuous monitoring and analysis of surface deformation volatility for the city’s future development and safety.

Mechanochemical modeling of morphogenesis in cell polarization for budding yeast

Cell polarization is a multiphysics problem resulting from coupling protein pathways and cell morphological evolution. The most common example is asexual reproduction in budding yeast through Cdc42 and septin signals. However, how the interaction between the Cdc42-septin systems and the mechanical deformation of the cell surface is not well understood. To explore the interaction, we build a three-dimensional mechanochemical coupling framework to investigate the Cdc42-septin systems and elucidate how morphogenesis at the cell scale enhances the robustness of cell polarization in budding yeast. We utilize the viscous active shell model to describe the moving boundary of the cell surface, and the mechanochemical coupling is achieved through the introduction of cell surface mean curvature and active contraction-growth effects. With a normal effect of septin, numerical results demonstrate the budding processes with different transition shapes of budding profiles. On the other hand, the mechanochemical coupling problem with a weak effect of septin drives the emergence of wrinkles on the cell surface. We also apply linear perturbation analysis of the cell surface deformation to show how cell shape evolution is subjected to active contraction-growth effects. Our results show that a 3D coupled mechanochemical model can reproduce the budding morphology in yeast. Such a model provides a more comprehensive portrait of cell polarity and can be used to characterize both wild-type and mutant phenotypes such as septin mutants.

Multitemporal analysis of land subsidence induced by open-pit mining activity using improved combined scatterer interferometry with deep learning algorithm optimization

Mine operational safety is an important aspect of maintaining the operational continuity of a mining area. In this study, we used the InSAR time series to analyze land surface changes using the ICOPS (improved combined scatterers with optimized point scatters) method. This ICOPS method combines persistent scatterers (PS) with distributed scatterers (DS) to increase surface deformation analysis’s spatial coverage and quality. One of the improvements of this study is the use of machine learning in postprocessing, based on convolutional neural networks, to increase the reliability of results. This study used data from the Sentinel-1 SAR C-band satellite during the 2016–2022 observation period at the Musan mine, North Korea. In the InSAR surface deformation time analysis, the maximum average rate of land subsidence was approximately > 15.00 cm per year, with total surface deformation of 170 cm and 70 cm for the eastern dumping area and the western dumping area, respectively. Analyzing the mechanism of land surface changes also involved evaluating the geological conditions in the Musan mining area. Our research findings show that combining machine learning and statistical methods has great potential to enhance the understanding of mine surface deformation.

Extract and analysis of surface deformation caused by Mengyuan earthquake in Qinghai using ascending and descending tracks D-InSAR technology

Precision in uncovering the seismic source mechanism and conducting a thorough monitoring of deformation characteristics resulting from surface rupture is of paramount importance for geological comprehension, disaster management, and emergency response. This study employs both ascending and descending orbit Sentinel-1 data to capture the horizontal and vertical deformation traits of the Ms6.9 earthquake in Menyuan, Qinghai, on January 8, 2022, consequently exposing its seismogenic structure. The research outcomes suggest: the Menyuan earthquake generated an elliptical deformation zone measuring 30 × 20 km, with the maximum line-of-sight seismic displacement reaching 6.8 cm. And then, the vertical deformation field exhibited a range between -0.28 m and 0.42 m, while the horizontal deformation field ranged from -0.89 m to 0.94 m. This indicates that the earthquake's deformation is primarily oriented in the east-west direction. The left plate exhibited an upward trend with a NWW orientation, while the right plate displayed a downward trend with a SEE orientation, suggesting that the Menyuan earthquake can be classified as a "NWW-SEE" type. Furthermore, the seismic epicenter of this earthquake was predominantly concentrated in the western segment of the Lenglongling Fault. Two powerful earthquakes sequentially struck along this fault zone, intensifying the imperative for seismic geological research in the region. Additionally, this instance can serve as a benchmark for monitoring deformations and elucidating the seismic source mechanism in earthquakes with comparable seismogenic structures.

The Utility of LiCSBAS to Carry out InSAR Time Series to Analyze Surface Deformation: An Overview

Surface deformation analysis plays a crucial role in understanding geodetic phenomena and their implications for hazard assessment, infrastructure management, and environmental studies. In recent years, the incorporation of synthetic aperture radar (InSAR) and advanced processing techniques have been used to monitor surface deformation. One such technique, LiCSBAS, has shown great promise in analyzing InSAR time series data to accurately detect and quantify surface displacements. It has been successfully employed in various geodetic monitoring scenarios such as landslide monitoring, infrastructure stability assessment, and volcanic deformation analysis. In this study, studies were reviewed in which performance evaluation and comparison of LiCSBAS with other technologies were discussed as well as future developments and challenges in this field. The results of a review of previous studies show the effectiveness of LiCSBAS in detecting and analyzing surface deformation, allowing for a better understanding of geodetic processes. This overview will provide a set of ideas that will assist stakeholders involved in surface deformation analysis and geodetic monitoring and contribute to decision-making to achieve sustainable development.

Alarming a tailings dam failure with a joint analysis of InSAR-derived surface deformation and SAR-derived moisture content

A tailings dam failure can be catastrophic. One constantly dumps or removes ore-related materials behind or within a dam before its closure, creating substantial surface change or deformation. The deformation can be assessed with multiple temporal synthetic aperture radar (SAR) observations and interferometric SAR (InSAR) techniques. The surface deformation is one prerequisite causing the failure. The water content increase is another primary factor that can reduce the surface friction among piled materials and induce further surface deformation. Intuitively, large deformation and high water content behind the tailings dam are concerns of a possible dam failure. Thus, we propose a new joint analysis of the InSAR-derived surface deformation and SAR-derived moisture content to achieve the objectives, delineating the stable/unstable status of a tailings dam and capturing a possible pre-failure signal of the dam. We study three types of tailing dams to verify the proposed analysis. The first is the Majiatian tailings dam in China, closed safely at the end of 2020. Our analysis determines that the dam status is stable. The second is the collapsed Córrego de Feijão Tailings Dam I in Brazil. The analysis identified a turning point from stable to unstable near December 2018, and the dam failure occurred in January 2019. In case three, an unstable status first at the Maanshan tailings dam was delineated. The findings were conveyed to parties interested in dam safety, and they carried out mitigation activities afterward. The analysis continued until February 2023, indicating a stable status of the tailings dam. The analysis is also robust to slight variations of moving window size around the proposed value. Thus, a valid joint analysis has been studied and is transferable to locations since the analysis and multitemporal SAR observations are available.

Optimizing feature based image alignment for surface deformation measurements

A novel method for efficient and reliable detection of surface features on weakly structured surfaces is presented. This method enables the analysis of surface deformations without the need for extensive sample preparation. Our simplified workflow, which eliminates the need for preparation, focuses on feature filtering to produce reliable transformations between different surface configurations. The versatility and robustness of this approach is demonstrated by a series of surface tests under different loads that provide consistent results. This method shows promise for a wide range of applications in surface feature detection and comprehensive deformation analysis, and provides a practical tool for the precise investigation of weakly textured surfaces.

Analysis of Surface and Building Deformation by Shield Tunneling through Geology

The research in this paper relies on the Baochang shield construction section of Jinan Metro Line R2 and uses MIDAS GTS and MIDAS GEN to construct a three-dimensional calculation model to numerically simulate the process of shield tunneling through abrupt geology. The main research focuses on surface settlement and building deformation during excavation, as well as monitoring of building deformation and surface settlement after adopting settlement control measures. The research results are as follows: The maximum settlement of tunnel excavation from hard rock to soft rock and from soft rock to hard rock occurs at the longitudinal center of the tunnel, with values of 1.66 mm and 4.82 mm. The excavation direction has a significant impact on surface deformation. The tunnel is excavated from hard rock to soft rock and the maximum deformation values in the vertical and horizontal directions of the building are 2.04 mm and 1.92 mm. After adopting settlement control measures, surface settlement and deformation of buildings were monitored. The monitoring results showed that the deformation monitoring values of the surface and buildings, after adopting engineering measurements, were lower than the values of numerical simulation. This indicates that the engineering control measures adopted can effectively constrain surface settlement and the deformation of buildings.

Monitoring and Analysis of Surface Deformation in Songyuan City, Jilin Province Based on Time Series InSAR

Monitoring and Analysis of Surface Deformation in Songyuan City, Jilin Province Based on Time Series InSAR

Dam Surface Deformation Monitoring and Analysis Based on PS-InSAR Technology: A Case Study of Xiaolangdi Reservoir Dam in China

The Xiaolangdi Dam is a key project for the control and development of the Yellow River. It bears the functions of flood control, controlling water and sediment in the lower reaches, ice prevention, industrial and agricultural water supply, power generation, and so on. Its safety is related to people’s life and property safety and local economic and social development. It is of great significance to carry out comprehensive and regular deformation monitoring for dams since the deformation is an important evaluation index for dam safety. Interferometric Synthetic Aperture Radar (InSAR) technology has been a rapidly evolving technology in the field of space geodesy in recent years. It offers advantages such as high monitoring precision, extensive coverage, and high monitoring point density, making it a powerful tool for monitoring deformations in hydraulic engineering projects. Based on Sentinel-1 data covering the Xiaolangdi Dam from September 2020 to November 2022, the PS-InSAR technique was used to obtain the surface deformation of the Xiaolangdi Dam, and reservoir water level data on image acquisition dates were obtained for joint analysis. The results show that there is a large deformation in the center of the dam crest of the Xiaolangdi Dam, while both sides of the slope and downstream dam foot are relatively stable. The time series deformation of the dam body is closely related to the reservoir water level change. When the water level increases, the dam body tends to deform downstream; when the water level decreases, the dam body tends to deform upstream. The deformation and water level of the Xiaolangdi Dam exhibit a clear negative correlation. There is no significant cumulative deformation on the dam slopes or at the base of the dam. However, cumulative deformation occurs over time in the central area of the dam’s crest. The deformation process at the central area of the dam’s crest follows a continuous and non-disruptive pattern, which is consistent with the typical deformation behavior of the Xiaolangdi earth–rock dam structure. Therefore, it is judged that the current deformation of the Xiaolangdi Dam does not impact the safe operation of the dam. InSAR technology enables the rapid acquisition of high-precision, high-density deformation information on the surfaces of reservoir dams. With an increasing number of radar satellites in various frequency bands, such as Sentinel-1 and TerraSAR-X, there is now an ample supply of available data sources for InSAR applications. Consequently, InSAR technology can be extended to routine monitoring applications for reservoir dam deformations, especially for small and medium-sized reservoirs that may not be equipped with ground measurement tools like GNSS. This holds significant importance and potential for enhancing the safety monitoring of such reservoirs.

Monitoring and analysis of surface deformation in alpine valley areas based on multidimensional InSAR technology

Joshimath has received much attention for its massive ground subsidence at the beginning of the year. Rapid urbanization and its unique geographical location may have been one of the factors contributing to the occurrence of this geological disaster. In high mountain valley areas, the complex occurrence mechanism and diverse disaster patterns of geological hazards highlight the inadequacy of manual monitoring. To address this problem, the inversion of deformation of the Joshimath surface in multiple directions can be achieved by multidimensional InSAR techniques. Therefore, in this paper, the multidimensional SBAS-InSAR technique was used to process the lift-track Sentinel-1 data from 2020 to 2023 to obtain the two-dimensional vertical and horizontal deformation rates and time series characteristics of the Joshimath ground surface. To discover the causes of deformation and its correlation with anthropogenic activities and natural disasters by analyzing the spatial and temporal evolution of surface deformation. The results show that the area with the largest cumulative deformation is located in the northeastern part of the town, with a maximum cumulative subsidence of 271.2 mm and a cumulative horizontal movement of 336.5 mm. The spatial distribution of surface deformation is based on the lower part of the hill and develops towards the upper part of the hill, showing a trend of expansion from the bottom to the top. The temporal evolution is divided into two phases: gentle to rapid, and it is tentatively concluded that the decisive factor that caused the significant change in the rate of surface deformation and the early onset of the geological subsidence hazard was triggered by the 4.7 magnitude earthquake that struck near the town on 11 September 2021.

Integration of DInSAR-PS-Stacking and SBAS-PS-InSAR Methods to Monitor Mining-Related Surface Subsidence

Over-exploitation of coal mines leads to surface subsidence, surface cracks, collapses, landslides, and other geological disasters. Taking a mining area in Nalintaohai Town, Ejin Horo Banner, Ordos City, Inner Mongolia Autonomous Region, as an example, Sentinel-1A data from January 2018 to October 2019 were used as the data source in this study. Based on the high interference coherence of the permanent scatterer (PS) over a long period of time, the problem of the manual selection of ground control points (GCPs) affecting the monitoring results during refinement and re-flattening is solved. A DInSAR-PS-Stacking method combining the PS three-threshold method (the coherence coefficient threshold, amplitude dispersion index threshold, and deformation velocity interval) is proposed as a means to select ground control points for refinement and re-flattening, as well as a means to obtain time-series deformation by weighted stacking processing. A SBAS-PS-InSAR method combining the PS three-threshold method to select PS points as GCPs for refinement and re-flattening is also proposed. The surface deformation results monitored by the DInSAR-PS-Stacking and SBAS-PS-InSAR methods are analyzed and verified. The results show that the subsidence location, range, distribution, and space–time subsidence law of surface deformation results obtained by DInSAR-PS-Stacking, SBAS-PS-InSAR, and GPS methods are basically the same. The deformation results obtained by these two InSAR methods have a good correlation with the GPS monitoring results, and the MAE and RMSE are within the acceptable range. The error showed that the edge of the subsidence basin was small and that the center was large. Both methods were found to be able to effectively monitor the coal mine, but there were also shortcomings. DInSAR-PS-Stacking has a strong ability to monitor the settlement center. SBAS-PS-InSAR performed well in monitoring slow and small deformations, but its monitoring of the settlement center was insufficient. Considering the advantages of these two InSAR methods, we proposed fusing the time-series deformation results obtained using these two InSAR methods to allow for more reliable deformation results and to carry out settlement analysis. The results showed that the automatic two-threshold (deformation threshold and average coherence threshold) fusion was effective for monitoring and analysis, and the deformation monitoring results are in good agreement with the actual situation. The deformation information obtained by the comparison, and fusion of multiple methods can allow for better monitoring and analysis of the mining area surface deformation, and can also provide a scientific reference for mining subsidence control and early disaster warning.

DinSAR coseismic deformation measurements of the Mw 8.3 Illapel earthquake (Chile)

Abstract The beginning of radars goes back to the 1930s where its main boost was related to the second world war. Nowadays, the techniques associated with radars are focused around a vast variety of civil, geodetic, and military applications. The development of the synthetic aperture principle, in the 1950s and 1960s, gave birth to a lot of new applications, and together with the technological progress of the last decades, the technique of interferometry with synthetic aperture radar (SAR) data became one of the most powerful ones for sensing remotely, with high quality and a vast spatial coverage. We used Sentinel-1 data and the differential interferometry SAR (DinSAR) technique to map and measure the surface deformation related to the 2015 Mw 8.3 Illapel earthquake (Chile). We also validated the results, by analysing the temporal variation of coordinates acquired from global navigation satellite system observations and projecting them in the geometry of the SAR system. Using this application we prove the DinSAR technique to be useful and powerful for the observation and analysis of surface deformation caused by the release of stress during the Mw 8.3 Illapel earthquake. It proved to be an efficient tool to detect and map the surface deformation with high spatial resolution in an approximate area of 20,000 km2.

Landslide surface horizontal displacement monitoring based on image recognition technology and computer vision

The deformation and displacement of landslides has always been the priority of landslide monitoring and early warning. With the development of image processing technology in recent years, the analysis of landslide surface deformation through image data has become a popular method and different methods of image analysis are rapidly increasing. However, the current method of analyzing landslide deformation and displacement using a single image processing method tends to analyze the displacement of the local deformation area of the landslide, which lacks overall monitoring of the slope and is difficult to use for pre-disaster monitoring of landslide hazards, easily leading to missed detection of landslide potential hazard points. Therefore, this paper combines image recognition technology and computer vision (IR-CV) to propose a method for monitoring and identifying the deformation displacement of landslide surfaces, which has been validated by indoor landslide model tests and unmanned aerial vehicle field simulation displacement recognition tests. In the model tests, the IR-CV method successfully identified the displacements generated during the deformation and damage of the landslide model while using the model deformation time series image data recorded by the camera to analyze the overall deformation of the surface of the landslide model. Further, in this paper, a field simulation displacement identification test was conducted using an unmanned aerial vehicle (UAV), and the orthophoto data obtained by the UAV verified that the IR-CV method can be used for overall deformation displacement identification of landslides in the field. The results of indoor model tests and field UAV simulation tests show that the monitoring method of IR-CV can effectively identify the deformation and displacement of landslide surfaces, which has good application prospects in pre-disaster monitoring and displacement identification of landslides, thus providing a cost-effective and feasible solution for monitoring the deformation and displacement of landslide surfaces.

Ground Surface Deformation Analysis Integrating InSAR and GPS Data in the Karstic Terrain of Cheria Basin, Algeria

Karstic terrains are usually dominated by aquifer systems and/or underground cavities. Overexploitation of groundwater in such areas often induces land subsidence and sometimes causes sinkholes. The Cheria basin in Algeria suffers from severe land subsidence issues, and this phenomenon has been increasing in recent years due to population expansion and uncontrolled groundwater exploitation. This work uses GPS data and persistent scatterer interferometry synthetic aperture radar (PS-InSAR) techniques to monitor the land subsidence rate by employing Sentinel-1 satellite data for the period from 2016 to 2022. Our results demonstrate that the Cheria basin experiences both uplift and subsidence in places, with an overall substantial change in the land surface. The total cumulative subsidence over 6 years reached a maximum of 500 mm. Comparison of land deformation between PSI and GPS showed root mean square error (RMSE) values of about 2.83 mm/year, indicating that our analyzed results are satisfactorily reproducing the actual changes. Nonetheless, these results can be used to extract the susceptible zones for vertical ground displacement and evaluate the surface deformation inventory map of the region for reducing damages (e.g., human losses, economic impact, and environmental degradation) that may occur in the future (e.g., sinkholes) and can be further utilized in perspective for a sinkhole early warning system.

Combined analysis of PS-InSAR and hypsometry integral (HI) for comparing seismic vulnerability and assessment of various regions of Pakistan

InSAR-based deformation analysis and the geomorphic hypsometric integral (HI) technique are powerful tools for assessing the susceptibility and comparison of seismic sites to earthquakes. Therefore, this paper mainly focuses on surface deformation analysis associated with the Mw 5.0 earthquake (2019) in Mach and Quetta, Balochistan, Pakistan. Sentinel-1 IW data was used to perform PS-InSAR time series analysis. SRTM DEM of 30 m spatial resolution was utilized for the geomorphic Hypsometry Integral (HI) method. The obtained results of the Interferogram indicate the changes in velocity and vertical displacement during pre-seismic, co-seismic, and post-seismic activity. Integral values were calculated using Hypsometry curves delineating the future probability and comparison of vulnerable seismological sites in Mach, Quetta, Ghazaband, Chamman and surroundings of Balochistan region. The combined results of HI and PS-InSAR revealed that Mach and Quetta regions are in between two lines known as the mature stages. Class 1_moderate (0.35 ≤ HI ≤ 0.52); with an integral value of HIMach = 0.398 and HIQuetta = 0.435 with a modest seismic forthcoming rate in future and susceptible to both erosion/uplifting with a vertical displacement rate more than existing ± 55 mm/year. Class 2_high (HI ˃ 0.53) with the younger and more tectonically active region surrounded by Chaman fault, which possesses a future susceptible tendency towards subsidence more than an existing velocity rate ~ 8 mm/year and Ghazaband fault towards uplifting more than 5–6 mm/year. No region of the study area was found at Monadnock: class 3_Low (HI ˂ 0.35) stabilized condition, all sites are unstable and tectonically active. Therefore, obtained results through combined PS-InSAR and HI techniques can be used for the identification of most vulnerable seismic sites and can ascertain future safe metropolitan planning.

Analysis of Surface Deformation Induced by Backfill Mining Considering the Compression Behavior of Gangue Backfill Materials

Coal gangue, as a solid waste produced in the coal mining process, can be disposed by being prepared into backfill materials and then filled in underground goafs, thus controlling strata movement and surface subsidence. However, gangue backfill materials are non-continuous; therefore, research into the surface deformation induced by backfill mining should consider the creep compression behavior of gangue backfill materials. The research took a backfill panel in Tangshan Coal Mine (Tangshan City, Hebei Province, China) as the background. In addition, broken coal gangue was collected in the field to prepare specimens of gangue backfill materials, and their creep compression properties were measured. The corresponding constitutive equation of creep compression was then established and embedded in the numerical software, FLAC3D. By building the numerical model for surface deformation induced by backfill mining, the surface deformation above the backfill panel under conditions of different creep durations of backfill materials was simulated and evaluated. In addition, two measuring lines were arranged on the surface to monitor changes in surface subsidence. After surface subsidence stabilized, the maximum surface subsidence was 163.4 mm, which satisfied the fortification criterion of surface buildings. This means the backfill mining did not affect nearby buildings. The results provide a theoretical basis for predicting surface deformation induced by backfill mining and its effective control.

Viscoelastic analysis of surface deformation above salt caverns for gas storage based on semi-infinite space

The construction of salt caverns for energy storage is of strategic significance, but the operation of underground gas storages in salt formations will cause surface deformation. The research and analysis of surface deformation is an important part of the stability evaluation of salt caverns for gas storage. From the perspective of classical mechanics theory, the analytical solution of surface deformation above salt caverns for gas storage is deduced. The surface displacement caused by the contraction of a salt cavern is regarded as the boundary displacement caused by the surface force acting on a spherical cavern in a semi-infinite space. The equivalent conversion of load form is carried out based on the mirror principle. The vertical subsidence and horizontal displacement of the surface of the elastic semi-infinite space is obtained. According to the elastic-viscoelastic correspondence principle, the viscoelastic solution of the surface displacement of the semi-infinite body, regarded as Maxwell body, can be obtained. A numerical model of a salt cavern for gas storage is established based on the engineering practice. The results of the analytical solution and the numerical simulation are compared and analyzed to verify the accuracy of the analytical solution. The analytical solution was applied to predict the surface displacement above a group of caverns, and the influence of the layout of salt caverns and cavern center spacing on the surface displacement is analyzed. The research results show that the regular triangular layout is slightly better than the square layout. The larger the cavern center spacing, the smaller the maximum surface subsidence. The proposed theoretical prediction model can provide a theoretical basis for controlling surface deformation for the construction of gas storage caverns.

Analysis of liquid surface deformation and breakups using three-dimensional high-speed data recorded with a single camera

Analyzing the deformation of liquid surfaces to better understand, for example, wave generation in oceanology or the formation of industrial spray systems, requires a series of three-dimensional snapshots that temporally resolve such events. This requirement is challenging, especially when applied to transient liquid surfaces that deform rapidly. A technique called Fringe Projection-Laser Induced Fluorescence (FP-LIF), developed by the authors, generates three-dimensional surface reconstructions of irregular liquid structures using snapshots recorded via a single camera only. In this article, FP-LIF is associated, for the first time, with a high-speed detection system, allowing the three-dimensional visualization of liquid surface deformation and breakups at a kHz frame rate. The technique is applied here at 20 kHz for imaging the complete development of a wide hollow-cone water spray and analyzing, in detail, the transition from early injection to stabilization. The three-dimensional image series covered a total time window of 300 ms (6000 frames). It is observed during the first 100 ms that the initial liquid jet deforms into a stable tulip shaped sheet. Then, between 100 and 180 ms, the tulip shape gradually grows until its stabilization corresponds to the final conical shaped sheet. Once the stabilization is reached, the fluctuation of the final spray-angle—ranging from 40° to 50°—is extracted by post-processing 1000 consecutive three-dimensional images, providing a detailed analysis of the radial symmetry of the spray over time and three-dimensional space. The results provided in this article are relevant for the validation of Computational Fluid Dynamics spray models.