Application of particle image velocimetry (PIV) to measure the displacement of sandy soil in laboratory

Nội dung text: Application of particle image velocimetry (PIV) to measure the displacement of sandy soil in laboratory

1. earth Sciences | Geology Doi: 10.31276/VJSTE.63(3).70-77 Application of particle image velocimetry (PIV) to measure the displacement of sandy soil in laboratory Tan-Phong Ngo1, 2*, Thuy-Chung Kieu-Le1, 2 1Faculty of Geology and Petroleum Engineering, Ho Chi Minh city University of Technology 2Vietnam National University, Ho Chi Minh city Received 1 March 2021; accepted 14 June 2021 Abstract: Particle image velocimetry (PIV) has been heavily used to measure the displacement and flow velocity in fluid mechanics. However, applications of this method to determining soil displacement in geotechnical laboratory tests are rare. This paper aims to verify the applicability of this method in determining the displacement of sandy soil under different saturation conditions and soil grain sizes. The results showed that this method could effectively determine soil displacement with an accuracy of 0.13 mm. Furthermore, the degree of saturation of soil did not influence the PIV results whereas the homogeneity of soil, as indicated by grain size distribution, reduced the precision of the PIV method. Keywords: particle image velocimetry, sandy soil, soil displacement. Classification number: 4.2 Introduction using displacement data recorded by a strain gauge during the tests. In geotechnical engineering, it is important to measure soil displacement in soil specimens for all laboratory Materials and methods tests, in physical models or in the field. This data is Theory of the PIV method usually recorded using a strain gauge attached to the soil sample during the tests. With the availability of image PIV is an important technique used in fluid dynamics analysis software, soil displacement analysis can be (Fig. 1). It allows to obtain instantaneous velocity measurements and related properties at a specific carried out easily and inexpensively using various image- Theory of the PIV method Theory of the PIV method based techniques such as X-ray, stereo-photogrammetric area,PiV called is an important‘interrogation’ technique areas, used in in the fluid fluid dynamics [10]. (Fig.PIV 1). it allows to obtain PiVTheory is an of important the PIV method technique used in fluid dynamics (Fig. 1). it allows to obtain techniques, image processing, and PIV and each instantaneoustechniquePiV is an has velocity important its roots measurements technique from the usedlaser and in speckle relatedfluid dynamics velocimetryproperties (Fig. at 1)a .specific it allows area, to obtain called instantaneous velocity measurements and related properties at a specific area, called „interrogation‟instantaneoustechnique developed velocity areas, inmeasurements inthe the fluid late [10] 1970sand. PiVrelated [11, technique 12].properties In hasPIV, at its a specificroots from area, the called laser technique has its own advantages and limitations [1- „interrogation‟ areas, in the fluid [10]. PiV technique has its roots from the laser s„interrogation‟peckle velocimetry areas, techniquein the fluid developed [10]. PiV in technique the late 1970shas its [11,roots 12] from. in thePiV, laser the 4]. Among these techniques, PIV is an important non- specklethe displacement velocimetry techniqueof an interrogation developed inarea the of late a pair 1970s of [11, 12]. in PiV, the displacementspeckle velocimetry of an interrogation technique developedarea of a pair in of the digital late 1970simages [11, is calculated 12]. in PiV,with helpthe invasive method to quantify local displacements on a displacementdigital images of an is interrogation calculated with area helpof a pairof cross-correlation of digital images is calculated with help ofdisplacement cross-correlation of an interrogation or autocorrelation area of techniques. a pair of digital The imagescross-correlation is calculated functions with help are ofor cross autocorrelation-correlation or autocorrelationtechniques. Thetechniques. cross-correlation The cross-correlation functions are solids’ surface [5]. In this method, a series of successive presentedof cross-correlation in Equations or autocorrelation(1) to (3) below techniques The cross-correlation functions are presentedfunctions in areEquations presented (1) to in (3) Equations below. (1) to (3) below. images of an object are captured during the test without presented in Equations (1) to (3) belo w. (1) (1) using any strain gauge sensors. By comparing the spatial (1) (1) ∑ variations on the same patches in these images using ( ) ∑ ( ) (( )) (2) ( ) ∑ ( ) ( ) (2) (2) image analysis softwares, the displacement data can be (2) ∑ obtained [6, 7]. PIV has been evidenced to be an effective ( ) ∑ [ ( )) (( ))]] (( )) (3) ( ) ∑ [ ( ) ( )] ( ) (3) technique for observation of stresses and strains of the ( ) (3) ( ) (3) ( ) glass ballotini and soil deformation in creep movement wherewhere R( ( R(s )) s=) cross= cro( )-ss-correlationcorrelation matrix matrix,, N(s N() =s )normalisation = normalisation matrix , Rn(s) = normalized where R( (s )) = cross ( )-correlation matrix, N(s) = normalisation matrix, Rn(s) = normalized where R((s )) = cross ( )-correlation matrix, N(s) = normalisation matrix, Rn(s) = normalized on the slope [4, 6, 8, 9]. In the present study, the PIV crossmatrix,-correlation R (s) = matrixnormalized, M(U )cross-correlation = dummy mask matrix matrix,, I testM( (U)) = intensity matrix of test cross-correlationn matrix, M(U) = dummy mask matrix, Itest (U) = intensity matrix of test cross-correlation matrix, M(U) = dummy mask matrix, Itest (U) = intensity matrix of test technique was adopted to predict the deformation of patch,= dummy Isearch (U mask + s) =matrix, intensity I matrix(U) of= searchintensity patch, matrix U and of s = test pixel coordinate vector. patch, Isearch (U + s) = intensity testmatrix of search patch, U and s = pixel coordinate vector. patch, Isearch (U + s) = intensity matrix of search patch, U and s = pixel coordinate vector. sandy soil with different degrees of saturation and soil patch, Isearch (U + s) = intensity matrix of search patch, U grain size. The precision of the technique was verified and s = pixel coordinate vector. *Corresponding author: Email: ngotanphong@hcmut.edu.vn Vietnam Journal of Science, 70 Technology and Engineering September 2021 • Volume 63 Number 3 Fig. 1. Principles of image maninipulationpulation inin PIVPIV analysisanalysis [4][4] Fig. 1. Principles of image manipulation in PIV analysis [4]. Testing materials Testing materials The soil used in the test was yellow fine sand (Fig. 2A), which was air-dried The soil used in the test was yellow fine sand (Fi(Fig. 2A)),, which was airair drieddried until its water content of about 0.1%. According to the Unified soil classification until its water content of about 0.1%. According to the Unified ssoil cclassificationlassification system (USCS), the sand was classified as “SP” (i.e., poorly graded sand). The system (USCS), the sand was classified as “SP” (i.e.,, poorly graded sand). TheThe distribution of particle sizes was determined by the sieving method according to distribution of particle sizes was determined by thethe sieving methodmethod accordingaccording toto ASTM D422, and the grain size distribution curve is shown in Fig. 2B. ASTM D422, and the grain size distribution curve isis shownshown inin Fig.Fig. 2B
2. earth Sciences | Geology Fig. 1. Principles of image manipulation in PIV analysis [4]. Several physical and mechanical properties of the sand are presented in Table 1. Testing materials Fig. 2B. The specific gravity was 2.65. The maximum dry density and optimum water content (ASTMThe soil D698) used in werethe test 16.7was yellow kN/m fine3 and sand 14.0 (Fig. %, respectively.Several physical andThe mechanical internal properties friction of the angle sand 2A), which was air-dried until its water content of about  are presented in Table 1. The specific gravity was 2.65. and0.1%. cohesionAccording to the(ASTM Unified soil D3080 classification) were system 38 Theand maximum 0 kPa, dry respectively.density and optimum The water average content hydraulic(USCS), the conductivity sand was classified of saturated as “SP” (i.e.,sand atpoorly 29(ASTMC, i.e. D698), ambient were 16.7 laboratorykN/m3 and 14.0%, temperature, respectively. 3 forgraded dry sand). unit The weight distribution var yingof particle from sizes 14.2 was to The 16 internal.7 kN/m friction, anglewhich and determinedcohesion (ASTM by D3080) the consdeterminedtant by water the sieving head method method according ASTM to ASTM D2434, were 38 ° was and 0 kPa, 2.1x10 respectively.-4 m/s The and average inversely hydraulic proportionalD422, and the grain to the size drydistribution unit weight curve is (shownFig. 3in) . conductivity of saturated sand at 29°C, i.e., ambient 100 80 60 40 Percent % finer, Percent 20 0 0.1 1 Particle diameter, mm Fig. 2. Image of the poorly( gradedA) sand used in testing and its grain size distribution curve.(B) Fig. 2. Image of the poorly graded sand used in testing and its grain size distribution curve. Vietnam Journal of Science, September 2021 • Volume 63 Number 3 Technology and Engineering 71 Table 1. Physical and mechanical properties of the sand. Properties Value Unit Standard applied Grain size distribution: sand - 100-0-0 % ASTM D422 silt - clay D10, D30, D60 0.16-0.19-0.25 mm - Coefficient of uniformity, Cu 1.5 - - Coefficient of curvature, Cc 0.9 - - Classification SP - ASTM D2487 3 Dry unit weight, d 14.5 kN/m ASTM D7263 3 Maximum dry unit weight, dmax 16.7 kN/m ASTM D698 Optimum water content, Wopt 14.0 % ASTM D698 Specific gravity, Gs 2.65 - ASTM D854 Cohesion, c‟ 0 kPa ASTM D3080 Angle of internal friction,  38  ASTM D3080 -4 Hydraulic conductivity, ksat 2.1x10 m/s ASTM D2434
3. earth Sciences | Geology laboratory temperature, for dry unit weight varying from Experimental soil box 3 14.2 to 16.7 kN/m , which determined by the constant An experimental soil box made of acrylic was designed water head method ASTM D2434, was 2.1x10-4 m/s and and developed. This acrylic box consists of two parts: inversely proportional to the dry unit weight (Fig. 3). the upper box and the lower box. The upper box could slide easily while the lower box was attached firmly to Table 1. Physical and mechanical properties of the sand. the base. A bolt and a down gauge were used to move the upper box in the horizontal direction and the horizontal Standard Properties Value Unit displacement could be measured (Fig. 4). There was applied also a guide located on the surface of the lower box to Grain size ensure the upper box could be moved easily. In order to distribution: sand - 100-0-0 % ASTM D422 calculate the ‘scale factor’ for PIV analysis, a steel ruler silt - clay was attached to the lower box surface. The calibration D , D , D 0.16-0.19-0.25 mm - process was also carried out on the same sand at different 10 30 60 degrees of saturation from 0 to 90%. The camera Canon Coefficient of 1.5 - - EOS REBEL T4i/EOS 650 was used for capturing the uniformity, C u photos. The testing process was conducted carefully in a 3-m long, 2-m wide, and 2-m high ‘cell’ under the light Coefficient of 0.9 - - conditions induced by two LED spotlights. curvature, Cc Classification SP - ASTM D2487 3 Dry unit weight, γd 14.5 kN/m ASTM D7263 Maximum dry unit 16.7 kN/m3 ASTM D698 weight, γdmax Optimum water 14.0 % ASTM D698 content, Wopt Specific gravity, Gs 2.65 - ASTM D854 Cohesion, c’ 0 kPa ASTM D3080 Angle of internal 38 ° ASTM D3080 friction, φ Hydraulic 2.1x10-4 m/s ASTM D2434 conductivity, ksat Fig. 4. The acrylic testing soil box. Experimental set-up The initial soil sample mentioned above, soil group A, had a particle size distribution that varied in the range of 0.85-0.15 mm. In order to evaluate the effect of particle distribution on PIV imaging results, group A was divided into 3 groups: group B (size range: 0.85-0.425 mm), group C (size range: 0.425-0.3 mm), and group D (size range: 0.3-0.15 mm). In addition, the effect of moisture on the results of the PIV image analysis were also evaluated for all four soil groups by moistening the soils to achieve the desired degrees of saturation. A series of tests were carried out for each soil group by using the following experimental set-up: Fig. 3. Hydraulic conductivity variation with dry unit weight 1. Mix the soil with water to achieve the designed of saturated sand. degree of saturation (Sr=0, 20, 40, 60, 80, and 90%). Vietnam Journal of Science, 72 Technology and Engineering September 2021 • Volume 63 Number 3
4. earth Sciences | Geology 2. Put wet soil samples into the test box, compact the soil sizes (prototype). In other words, the effect of distortion until the designed dry weight was attained (14.5 kN/m3). is neglected. Moreover, according to White (2002) [13], 3. And then move the upper part of the soil box at the distortion effect causes a small error compared to different intervals: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, the random PIV error so it could be neglected when 1, 2, 3, 4, 5, 6, 7, and 8 mm and capture photos at every analysing the displacement measurement. The size of the moving step. interrogation area selected was 128 pixels × 128 pixels. Note that the distance from the camera to the test box It should be noted that the output data from the was fixed at 40 and 80 cm to obtain the images of each OpenPIV are horizontal and vertical velocities. condition with 2 different resolutions, 0.05 and 0.12 mm/ Therefore, the soil’s displacement from movement was pixel, respectively. In total, there were 48 experiments cumulatively calculated from both velocities multiplied conducted for the four groups of soil particles in 6 by the displacement time. different degrees of saturation with 2 image resolutions Results and discussion (Table 2). Horizontal displacement The images captured after the experiments were analysed using OpenPIV image analysis software, A series of successive images captured during developed by Taylor, et al. (2010) [2] in MATLAB, to the experiments were analysed using the OpenPIV obtain the displacement of the soil. OpenPIV is defaulted image analysis software to obtain the soil’s horizontal to use a given linear scaling factor, which is an input displacement at intervals of 0.1, 1, 2, 3, 4, and 5 mm parameter, to convert the output data in pixel to real as presented in Fig. 5. As described previously, only Table 2. Soil particle size, degree of saturation, and image scaling factor for the 48 experimental set-ups. Degree of saturation, S % Soil type Scaling factor (mm/pixel) r, 0 ~20 ~40 ~60 ~80 ~90 0.05       A (0.85-0.15 mm) 0.12       0.05       B (0.85-0.425 mm) 0.12       0.05       C (0.425-0.3 mm) 0.12       0.05       D (0.3-0.15 mm) 0.12       Fig. 5. Scheme of interpreting the horizontal displacement using PIV method. Vietnam Journal of Science, September 2021 • Volume 63 Number 3 Technology and Engineering 73
5. earth Sciences | Geology horizontal deformation in the soil sample was allowed. Figure 7 presents the relationship between the Therefore, the total displacement is equal to the horizontal predicted displacement determined from PIV and displacement. Fig. 6 shows an image of the movement true displacement measured by the down gauge. Their vector of the soil after moving the upper box at a distance of 1 mm in the horizontal direction. correlation function was given by Equation (4) with the coefficient of determination2 R =1.0, which indicates that the predicted displacement from PIV was equivalent to the true displacement. Predicted displacement=0.97×True displacement (4) Accuracy The predicted horizontal displacements of the soil sample were also determined by OpenPIV software for interval values ranging from 0.1 to 5 mm corresponding to the four soil groups A, B, C, and D. The accuracy of the predicted displacement was calculated using the following equation: Accuracy=True displacement - Predicted displacement (5) For the four soil groups A, B, C, and D, there were no considerable differences in the accuracy of predicted Fig. 6. Horizontal displacement of sand. displacement (Fig. 8). The accuracy varied from 0.02 mm (soil A, Sr=74%) to 0.24 mm (soil B in dry condition, i.e. Sr=0) with an average accuracy of 0.13 mm. Considering the accuracy in the same soil group as the degree of saturation was increased, the variation of the accuracy did not show any clear pattern or trend. Therefore, the effect of saturation could be ignored when analysing PIV results. In all four soil groups A, B, C, and D, with the same test patch size of 128 pixels × 128 pixels used in the interpretation process, the image with the scaling factor of 0.12 mm/pixel gave a smaller accuracy value than the image with scaling factor of 0.05 mm/pixel. This can be explained by the fact that the area of the​​ test patch of the 0.12 mm/pixel image is larger than the 0.05 mm/pixel image, so the results of PIV interpretation Fig. 7. Correlation between predicted displacement and true displacement. are more accurate. Vietnam Journal of Science, 74 Technology and Engineering September 2021 • Volume 63 Number 3
6. earth Sciences | Geology Fig. 8. Change of accuracy with saturation degree for the four sample groups. from PIV was defined as the standard error of the predicted displacement. The precision values for all experimental setups for the four soil groups are shown in Fig. 10. Soil group A, which contained the larger particle grain sizes, presented quite low precision when compared to the other soil groups indicating that the more homogeneous the soil, the more scattered the predicted displacement. Considering the effect of the degree of saturation of soil for all soil groups, there did not appear to be much Fig. 9. Average accuracy in the measurement range of 0.1 difference in the precision as the degree of saturation of to 5 mm. soil changed. Therefore, the variation of soil’s degree The average accuracies of PIV for the measurement of saturation did not affect the scattering of the results intervals from 0.1 to 5 mm were also determined as the predicted from PIV. average value of all separate accuracy values. As shown In all four soil groups A, B, C, and D, with the same in Fig. 9, the average accuracy was 0.13 mm. test patch size of 128 pixels × 128 pixels used in the interpretation process, the image with scaling factors of Precision 0.05 and 0.12 mm/pixel gave precision values of 0.002 The precision of the predicted displacement obtained and 0.01 mm, respectively. Vietnam Journal of Science, September 2021 • Volume 63 Number 3 Technology and Engineering 75
7. earth Sciences | Geology Fig. 10. Change of precision with saturation degree for the four sample groups. 0.12 mm/pixel, the average values of accuracy and precision were 0.13 and 0.005 mm, respectively. This study also evidenced that PIV can be used to predict the displacement of sandy soil. The results also showed that while the degree of saturation of the soil did not influence the PIV results, and can therefore be ignored when analysing PIV results, the homogeneity of soil could reduce the precision of the PIV method. In order words, PIV works effectively for more heterogeneous soil when Fig. 11. Average precision in the measurement range of 0.1 to 5 mm. grain size distribution is concerned. ACKNOWLEDGEMENTS The average precision values of PIV for measurement intervals from 0.1 to 5 mm were also determined as the This research is funded by Ho Chi Minh city average value of all separate precision values. As shown University of Technology (HCMUT) under grant number in Fig. 11, the average precision was 0.005 mm. T-DCDK-2019-32. Conclusions COMPETING INTERESTS The results showed that in the measurement ranges The authors declare that there is no conflict of interest of 0.1 to 5 mm with image scaling factors of 0.05 and regarding the publication of this article. Vietnam Journal of Science, 76 Technology and Engineering September 2021 • Volume 63 Number 3
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