Digital image-based measurement of degree of saturation on moving soil

1 Digital image-based measurement of degree of saturation on moving soil Gerardo Morales PhD candidate Department of Civil and Environmental Engineering Universitat Politècnica de Catalunya, Barcelona, Spain ORCID: 0000-0002-9548-3556 Núria M. Pinyol Associate Professor (corresponding author) Department of Civil and Environmental Engineering Universitat Politècnica de Catalunya, Barcelona, Spain Centre Internacional de Mètodes Numèrics a l'Enginyeria ORCID: 0000-0002-1878-1365 Address: Campus Nord UPC. Edificio D2. 08034 Barcelona Phone: 34 93 401 18 20 e-mail: [email protected] Mauricio Alvarado Post-Doctorate candidate Department of Civil and Environmental Engineering Universitat Politècnica de Catalunya, Barcelona, Spain ORCID: 0000-0001-6033-8327 Eduardo Alonso Pérez de Ágreda Full Professor Centre Internacional de Mètodes Numèrics a l'Enginyeria Universitat Politècnica de Catalunya, Barcelona, Spain ORCID: 0000-0003-2472-3951 2 ABSTRACT This paper presents a novel methodology that combines Particle Image Velocimetry - Numerical Particles (PIV-NP) and Short-Wave Infrared Spectral Imaging for the non-invasive measurement of displacements and degree of saturation on moving soils. This allows for continuous monitoring and visualization of soil behavior and provides valuable insight into the deformation patterns and moisture evolution. The method was applied to a small-scale dam failure experiment. The methodology offers an integrated, comprehensive, and non-invasive approach to investigating soil physical models by simultaneously measuring displacements, strains, velocities, and degree of saturation in soils in motion. Keywords: Digital image correlation, particle image velocimetry, SWIR image analysis, geotechnical physical modelling, unsaturated soils INTRODUCTION Image-based techniques are widely applied in laboratory tests. For instance, particle image velocimetry (PIV) technique (Adrian 1991) is used in the geotechnical field (Take et al. 2004; Wang et al. 2020). Pinyol and Alvarado (2017) presented a numerical tool (PIV-NP) for processing Eulerianbased PIV displacement measurements to provide large deformations and strains. Soil water content can be also measured from images because of the dependence of the soil surface reflectance with the water content (Leu 1977; Sadeghi et al. 2015). Parera et al. (2021) presented a procedure to measure the degree of saturation (Sr) from short-wave infrared (SWIR) digital images by correlating the light reflectance and Sr. This method allows measuring water content for specific configuration experiments and specific times. This Note proposes a methodology for continuously mapping the incremental and cumulative displacements, velocities, strains, and Sr over a soil domain in motion by means of combining the PIV-NP technique (Pinyol and Alvarado 2017) and SWIR image-based methodology presented in Parera et al. (2021). The measurements are plotted with the preand post-processing software GiD 3 (GiD 2020). An instrumented small-scale homogeneous dam failure is analysed comparing imagebased and sensor-based measurements. PIV-NP-Sr TECHNIQUE Figure 1 presents a schematic illustration of the method. Following Pinyol and Alvarado (2017), comparing successive images taken at an elapsed time interval, the Eulerian-based PIV analysis methodology provides the velocity of centres of material domain-filled subsets fixed in space which are taken as nodes of a support mesh in the PIV-NP methodology. The material domain is then discretized into numerical particles (NPs) that are initially distributed within the support mesh. The velocity values at the nodes are transferred into the NPs using mapping functions and their position are updated at the end of each time step. The Sr is measured at each time step at subset centres coinciding with the support mesh nodes of SWIR images after applying Gaussian smoothing over an area of interest surrounding each point of measure. The Sr is also transferred to the NPs. In this context, the necessary input data is: (i) time interval between consecutive frames; (ii) coordinates of subset centres; (iii) PIV Eulerian velocity results (Figure 1a; and (iv) SWIR-based measurements of Sr (Figure 1b). When using different cameras for PIV-NP analysis, in visual range, and Sr measurement, in SWIR range, the images have different perspectives to capture the same scene. Merging the two images is required. It was made through the homographic technique (Hartley and Zisserman 2003). More details of the procedure are available in the Supplementary Material. APPLICATION The soil selected for the experiment was the same one used in Parera et al. (2021), but in this case, the sand was dyed (15 % of the grains). The visual range images were taken with a Canon EOS 600D camera with a CMOS image sensor and 1920x1080 pixel resolution at 30 frames per second. For SWIR images, the same camera described in Parera et al. (2021) was used. Figure 2 shows two similar calibration curves derived from SWIR images of samples prepared at two void ratios (e) (0.9 and 1.0). To capture the effect of the soil density, Parera et al. (2021) investigated what moisture-related variable, either water content or Sr, determines the light reflectance of 4 saturated soil. This is a key aspect especially when dealing with experiments of deformable soils. The authors, after testing samples at different e (ranging from 0.7 to 1.08) and water content, concluded that Sr is, instead of the water content, the variable that can be properly correlated with the variation of the pixel intensity. The experiment involves the wetting-induced failure of a small-scale dam placed in a transparent Perspex tank 400mm high, 1000mm long, and 200mm deep (Figure 3a). The dam was prepared by moist tamping seven layers at 5.2% of initial water and 1.39g/cm3 of dry density (e=0.93), in average. It was instrumented with six conventional soil moisture sensors emplaced at the rear wall of the tank. Two different stages are noticed: (a) An initial wetting collapse; and (b) a subsequent rapid motion after failure. Since two processes have different time scales, two frame speeds (1fps and 30fps) were selected. Figure 3 shows some visual frames of the model and the cracks developed. The experiment is interpreted with the proposed technique (Figure 4). Displacements and deviatoric strains increased abruptly when the toe of the downstream slope reached complete saturation, at around 723s, and crack#1 develops exhibiting positive volumetric strain, clearly affected by the location of the moisture sensor E2. The upper part remains stable, which may have an effect on the failure mechanism. Further saturation induces the second failure phase (773s). Crack#2 conditioned by the position of sensor E1, mobilizes the upper unsaturated region. The failure delimited by crack#2 did not exhibit a sliding surface mechanism. The soil experienced a toppling forward instead of a sliding shearing. These observations underline the influence of sensors in the nature and geometry of failure. This limitation is not present in image-based monitoring. The interpretation of continuous PIV-NP-Sr maps enables the assessment of profile variations of Sr at specific locations and times within the model (Figure 5). Image-based measurements fit well with sensor readings. Figure 6 shows a comparison between Sr values interpreted through PIV-NP-Sr technique and sensor data. The correspondence is good below the time of soil saturation. The drop in the sensor values after maximum saturation may be explained by a decay in the permittivity associated with wetting with a liquid with high electrical conductivity (water from the general network instead of the initially deionized water used for moist tamping of the layers) as observed by Schwartz et al. (2013). 5 Moreover, the errors in sensor’s values near the failure of the dam model may be explained by observed cracks and air gaps of the model. Note that the image-based measurements at the numerical particle, initially located at the position of the sensor, can only be consistently compared with the fixed sensor-based measurements while the numerical particle remains at its initial position. CONCLUSIONS The paper presents the combination of the PIV-NP and SWIR-Sr image analysis techniques for measuring the surface Sr of soils during motion. The methodology was successfully applied to the analysis of soil motion and saturation variations during an instrumented small-scale dam failure experiment. The results show the capabilities of this non-invasive approach in providing comprehensive visualization and analysis of deformation patterns, moisture changes and failure mechanisms in soils. Some advantages are observed when compared with fixed physical sensors in case of large displacements. The water content measured around the sensor becomes unreliable and inaccurate when the surrounding soil goes into motion. The application of the technique to other types of soils remains to be done. ACKNOWLEDGEMENTS The first author acknowledges the financial support of SENACYT (Panama). The second author thanks the financial support received from Serra Húnter Program (Department of Enterprise and Knowledge of the Secretariat for Universities and Research of the Generalitat de Catalunya). FUNDING STATEMENT Project PDC2022-133222-I00 and PID2022-141429OB-I00 funded by MCIN/AEI/10.13039/501100011033/FEDER, UE. DATA AVAILABILITY STATEMENT Data generated or analyzed during this study are available from the corresponding author upon reasonable request. 6 REFERENCES Adrian, R.J. (1991) Particle-imaging techniques for experimental fluid mechanics. Annual Review of Fluid Mechanics, 23(1):261–304. doi:10.1146/annurev.fl.23.010191.001401. GiD (2020) The personal preand post-processor. Barcelona (Spain): CIMNE. www.gidsimulation.com. Hartley, R., and Zisserman, A. (2003). Multiple View Geometry in Computer Vision. Cambridge University Press. Leu, D.J. (1977). Visible and near - infrared reflectance of beach sands: a study on the spectral reflectance/grain size relationship. Remote Sensing of Environment, 6(3):169–182. Parera, F., Pinyol, N.M., and Alonso, E.E. (2021). Massive, continuous, and non-invasive surface measurement of degree of saturation by shortwave infrared images. Canadian Geotechnical Journal, 58(6):749-762. doi:10.1139/cgj-2019-0051. Pinyol, N.M., and Alvarado, M. (2017). Novel analysis for large strains based on particle image velocimetry. Canadian Geotechnical Journal, 54(7):933–944. doi: 10.1139/cgj-2016-0327. Sadeghi, M., Jones, S. B., and Philpot, W. D. (2015). A linear physically-based model for remote sensing of soil moisture using short wave infrared bands. Remote Sensing of Environment, 164:66-76. doi: 10.1016/j.rse.2015.04.007. Schwartz, R.C., Casanova, J.J., Pelletier, M.G., Evett, S.R., and Baumhardt, R.L. (2013). Soil permittivity response to bulk electrical conductivity for selected soil water sensors. Vadose Zone Journal, 12(2): 1-13. doi: 10.2136/vzj2012.0133. Take, W.A., Bolton, M.D., Wong, P.C.P., and Yeung, F.J. (2004). Evaluation of landslide triggering mechanisms in model fill slopes. Landslides,1(3):173–184. doi:10.1007/s10346-004-0025-1. Wang, Y., Hu, Y., and Hossain, M.S. (2020). Soil flow mechanisms of full-flow penetrometers in layered clays through particle image velocimetry analysis in centrifuge test. Canadian Geotechnical Journal, 57(11):1719–1732. doi:10.1139/cgj-2018-0094. FIGURE CAPTIONS Figure 1. Schematic representation for the Sr measurement of soils during motion, using PIV-NP discretization (one NP per element). Figure 2. SWIR-Sr calibration curve of used material (85% natural sand + 15% dyed sand). 7 Figure 3. Visual frames of the small-scale dam model at different times, t, in seconds including initial and deformed geometry sensors’ location, water level (Hw), and cracks and developed failure mechanism. Figure 4. PIV-NP-Sr plots of Sr, accumulated displacement, deviatoric strains and volumetric strains: (a) at triggering, t=723s; (b) at failure, t=724s; (c) at post-failure, t=773s; and (d) at the end of the test, t=810s. The deviatoric strains are defined as �2 3 ⁄𝑒𝑒𝑖𝑖𝑖𝑖𝑒𝑒𝑖𝑖𝑖𝑖, where 𝑒𝑒𝑖𝑖𝑖𝑖 is the deviatoric part of the strain tensor. Figure 5. PIV-NP-Sr based measurements of Sr distribution and vertical profiles compared with punctual sensor-based measurements (a) Hw/Hdam = 0.20, t = 240s; (b) Hw/Hdam = 0.40, t = 435s; and (c) Hw/Hdam = 0.60, t = 645s. (Hw/Hdam is the ratio of the water height to the height of the dam). Figure 6. Validation of the SWIR image-based measurement of Sr against SEN0193 capacitive soil moisture sensors (S1, S2, and S3) and EC-5 capacitive soil moisture sensors (E1, E2, and E3).