quantificationofthetransparencyofthetransparentsoilin...

Research ArticleQuantification of the Transparency of the Transparent Soil inGeotechnical Modeling

Li-Da Yi12 Hua-Bin Lv1 Tian Ye1 and Yi-Ping Zhang 1

1College of Civil Engineering and Architecture Zhejiang University 866 Yuhangtang Road Hangzhou Zhejiang China2Power China Huadong Engineering Co Ltd 201 Gaojiao Road Hangzhou Zhejiang China

Correspondence should be addressed to Yi-Ping Zhang zhangyipingzjueducn

Received 11 April 2018 Revised 2 July 2018 Accepted 15 July 2018 Published 9 September 2018

Academic Editor Yonggui Chen

Copyright copy 2018 Li-Da Yi et al+is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

An indispensable process of geotechnical modeling with transparent soils involves capturing and analyzing images in whichfavorable transparency is required for optical measurements +is paper proposes an objective framework for quantification oftransparency in transparent soil based on its transmittance Specifically transparent soil with fused quartz serves as the soil samplefor the detection of transmittance and transmittancersquos impact on imaging quality in geotechnical modeling with transparent soil isinvestigated through an evaluation function of image clarity According to the results of research about transparent soil with fusedquartz viewing depth and refractive index matching are the dominant factors that affect variations in transmittance of transparentsoil and the variations of transmittance are subjected to exponential decay regarding viewing depth or refractive index matchingbased on the theoretical modelingrsquos function of curve fitting Moreover experimental results indicate that imaging quality ofgeotechnical modeling with transparent soil is enhanced with increasing transmittance and imaging quality shows a remarkableimprovement when transmittance is greater than 90

1 Introduction

For geotechnical testing transparent soil is perceived asa model to visualize the internal geotechnical propertiessuch as deformation strain and flow [1] It is a porousmedium which consists of a transparent surrogate rep-resenting natural soil and fluids with a matched refractiveindex Transparent soil provides approaches for geotech-nical modeling of soil-structure interactions and multi-phase flow in soils [2] Pioneering researchers oftransparent soil introduced precipitated silica to investigatenon-Newtonian fluid flow [3] and conducted further re-search on the geotechnical properties of low-plasticity clay[4 5] Over time other families of transparent soils havebeen developed for geotechnical testing including silica gel[6] hydrogel [7] fused quartz [8] and laponite [9] Inaddition to investigation of soil-structure interactionmechanisms and hydraulic behavior notable work hasrecently extended geotechnical applications of transparentsoils to centrifuge tests [10] soil mechanics lessons in

elementary schools [11] and research involving geo-environmental models [12]

In addition to the ability of transparent soil to modelnatural soil visualization of the transparent soil is of equalimportance to application in geotechnical testing An in-dispensable process of modeling with transparent soil in-volves capturing and analyzing images By capturingcontinuous images in noninvasive measurements includingdigital image correlation (DIC) transparent soil techniquesrival apparatuses such as X-rays computerized tomography(CT) and magnetic resonance imaging (MRI) [13] DICserves as a methodology of image analysis for measurementof kinematics within transparent soils [14] in whichtransparency is required

To determine a favorable level of transparency for opticalmeasurements the transparency of transparent soil has beenevaluated in recent studies For example grid lines wereobserved through some viewing depth of transparent soil torank different levels of transparency for possible analysis[15] an adapted Snellen chart was utilized in an ldquoeye testrdquo

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 2915924 8 pageshttpsdoiorg10115520182915924

calibration for viewing decreasing font-sized letters throughtransparent soils to estimate the transparency that isavailable for visualization [16] However the conventionalmethodology of the above assessments is subjective andnonquantitative and infers variable levels of acceptabletransparency for visualization of transparent soils +usa comprehensive objective quantitative and robustframework of transparency assessment awaits developmentRecently the modulation transfer function (MTF) has beenproposed for quantitative assessment and comparison oftransparency [17]

However MTF is determined according to the fidelity oftransferred details from object to image which involves anoverall imaging capability of the whole optical system whichis characterized by not only transparency of transparent soilbut also the photographic apparatus Hence in order toprovide observations of how transparency affects the ac-curacy of imaging and measurement in transparent soil thepurpose of this research is to quantitatively evaluate thetransparency of transparent soil itself If such a framework ofevaluation is developed for the optical characteristics oftransparent soil it shall provide guidance for modelingexperiments of transparent soil to reduce limitations ongeometry and refractive index matching

Specifically in this paper an objective framework forquantification of transparency based on transmittance isestablished by combining geotechnical engineering andoptics First the calculationmethod of transmittance and theexperimental setup for detecting transmittance is proposedso that transmittance data of transparent soil are acquiredSecond it is suggested that variations of transmittance aresubjected to exponential decay which is well explained bythe principle of the Christiansen effect And such obser-vation of transmittance shall provide approaches to im-proving transparency quality of transparent soil +ird forexperiments of detecting transmittance for different trans-parent soil samples experimental results and digital imagesdemonstrate the relationship between transmittance andimaging quality of visualization in transparent soil +erelationship between transmittance and imaging clarity isinvestigated using an evaluation function of the digitalimage

2 Objective Framework for Quantification ofTransparency in Transparent SoilBased on Transmittance

21 Transmittance Transmittance defines the property thata substance permits transmitted light to pass through whileincident light is partially absorbed or scattered It is themathematical description of transparency +e theory ofradiometry indicates that transmittance T is the luminousflux ratio of transmitted light φt to incident light φi [18]which is expressed as

T φt

φi (1)

+e luminous flux refers to the power of electromagneticradiation which is modified due to varied sensitivity of thehuman eye to different wavelengths of light It is calculatedby a luminosity function regarding the issue In the lumi-nosity function luminous efficacy is the weighting co-efficient that represents the ratio of the luminous flux to theradiant flux For a certain wavelength of light the luminousflux φ is expressed as

φ KλP (2)

where Kλ refers to the weighting coefficient at wavelength λand P refers to the radiant flux Based on (1) and (2)transmittance is denoted by the following equation

T Pt

Pi (3)

where Pt and Pi refer to the radiant flux of transmitted andincident light respectively Hence the calculation method iscapable of acquiring transmittance using optical measure-ments of a laser power meter in the experimental setup

22 Measurement Method for Transmittance

221 Material In the experimental setup fused quartzwhich is common in manufacturing is applied as the solidparticle of transparent soil During the manufacturingprocess fused quartz is highly purified by melting at ap-proximately 2000degC and is formed by crystalline silica witha purity level of 999 to 9995 [1] Specifically for theselected fused quartz in this research it is shown in Figure 1that the particle size ranges from 200 to 280mm At eachwavelength of visible light transmittance of fused quartz iswell beyond 90 +e refractive index of fused quartz isreported as 14585 [19]

Fused quartz aggregate is matched with a blend of twooils namely 15 PURITY FG WO white mineral oil pro-duced by Petro-Canada and EI solvent oil produced byTEACSOL Both oils are transparent as well as colorlesswith the physical properties that are listed in Table 1

As listed in Table 1 higher flashing points of flamma-bility indicate that the oils are safe to use under normallaboratory conditions at room temperature Since thedensity of mineral oil is similar to that of EI oil mixtures ofsuch two oils are well blended +e refractive index of well-blended oils changes with the specific blending ratio toachieve different levels of refractive index matching +erefractive index is then measured by implementation ofa 2WAJ refractometer with a precision of 00002 Howeverthere is considerable variation in the refractive index ofmatching liquids at different temperatures [20] To in-vestigate the variation of the refractive index due to changingtemperature configuration of the DK-S18 water bath andcirculating pump is connected to the refractometer formaintaining a constant temperature of the matching liquid[8 21] On the basis of the Arago-Biot function [22] therelationship between the resulting refractive index andblending ratio is expressed by the following equation

2 Advances in Civil Engineering

n12 λ θn1 +(1minus θ)n21113858 1113859 + g (4)

where n12 n1 and n2 refer to the refractive index of blendedliquids the first matching liquid and the second matchingliquid respectively θ refers to the volume fraction of the firstmatching liquid and λ or g refers to the coefficient de-termined by temperature Specificallyn12 represents therefractive index of blended oils and θ represents the volumefraction of the 15 white mineral oil For the followingexperiment the room temperature is strictly maintained as20degC using an air conditioner whereas λ and g are exper-imentally determined as 10159 and minus00232 based on thecalculation of the blending ratio

222 Experimental Apparatus For optical measurementsthe layout of the experimental setup is shown in Figure 2(a)which involves a laser transmitter that emits 532 nm laserlight a test chamber a detector of light power and a laserpower meter for detecting transmitter light power As alsoshown in Figures 2(b) and 2(c) the test chambers providedesirable ranges of viewing depth and a cuvette or acrylicglass box serves as the test chamber with identical wallthickness on each side When a light beam from a lasertransmitter passes through transparent soil in the testchamber the radiant flux of transmitted light Pt is measured+en the radiant flux of incident light Pi is measuredwithout transparent soil in the test chamber Pt and Pi aremeasured from multiple incident positions of light at oneside of the test chamber +e side of the test chamber forincident light was switched over for each measurement ofthe transparent soil sample Specifically the incident posi-tions of light are located roughly equidistant In this way 16pairs of Pt and Pi are acquired for eachmeasurement On thebasis of the 16 pairs of experimental results the averageresults of transmittance are calculated Moreover the con-fidence interval of the average transmittance is also denotedas the error bar in the figures

23 Variation in Transmittance

231 Principle of the Christiansen Effect To investigate thevariation in transmittance of transparent soil and to analyzethe qualitative relationship between the factors (that affectthe variation in transmittance) and the transmittance theprinciple of Christiansen effect is proposed for the curvefitting of experimental results of transmittance of trans-parent soil Preparation of transparent soil should ensurethat the transparent substance is immersed in the refractiveindex matching liquid which is also involved in the processof producing transparent media in the experiment of theChristiansen effect [23] Numerous solid-liquid interfacesexist within such transparent media For incident light witha specific wavelength on the solid-liquid interface theprinciple of the Christiansen effect indicates that whendispersion curves of solid and liquid coincide at specificwavelength incident light in Christiansen experiment ismostly transmitted [24] Either the optical interference orthe scattering results in attenuation of transmitted light inthe Christiansen effect +e theory of the Christiansen ex-periment is concluded from optical interference [24] and itstates that the transmittance of transparent media undergoesexponential decay Particularly within transparent soil in-cident light is scattered and refracted consecutively onmultiple solid-liquid interfaces while transmitted light isattenuated Assuming that inhomogeneity of randompacking in solid particles has a Gaussian distribution in therefractive index [25] a modified equation of the RamanVarshneya [26] method is derived as follows

T exp minusk12π2 ns minus nl 1113857

2+ k21113960 1113961d

λ2m

⎧⎨

⎩

⎫⎬

⎭ (5)

where ns and nl refer to the refractive index of the solid andliquid respectively k1 refers to the coefficient that ismodified by the size shape and distribution of the solidparticle k2 refers to the coefficient that is modified by theshape and volume fraction of the solid particle d refers to thetransmitted thickness or viewing depth and λm refers to thematching wavelength at which the solid and liquid refractiveindexes are matched

+e principle of the Christiansen effect is the theoreticalbasis of this research that explains the factors that affecttransmittance in optical measurements of transparent soilWith a consistent combination of grain size gradation andcompactness within transparent soil the subsequent impactsof size shape and distribution of solid particles are neglectedin the following analysis Besides themodified equation of theRaman Varshneya method shall be utilized to provide ob-servations into the function of curve fitting of the factors andto provide explanations on statistical parameterrsquos physicalmeaning +erefore coefficients k1 and k2 remain constantfor the same transparent soil sample For the experimentalsetup in this study the wavelength of transmitted light ismaintained constant as 532 nm +erefore the viewing depthd and the refractive index matching (ns minus nl) are the mainfactors that affect transmittance and they are analyzed infollowing verification experiments For transparent soil with

Table 1 Physical properties of the pore fluid

Matching liquid Flashingpoint (degC)

Density(kgL)

Refractiveindex (at 20degC)

15 white mineral oil 180 0847 14662EI solvent oil 83 0796 14380

Figure 1 Selected particle of fused quartz

Advances in Civil Engineering 3

fused quartz and mineral oil the experiments are set up tovalidate that the transmittance of transparent soil is subjectedto exponential decay due to viewing depth d and refractiveindex matching (ns minus nl)

232 Impact of Viewing Depth Assuming that viewingdepth d is the single variable in (5) expression of trans-mittance T is simplied as

T eminusKd (6)

where K refers to the attenuation coecient In practice (6)is also deduced from the BeerndashLambert law [27] Accordingto the BeerndashLambert law the light that is absorbed bya substance is proportional to its transmitted thickness Inparticular transmitted thickness is identied as the viewingdepth in this research Figure 3 reveals the relationshipbetween transmittance T and viewing depth d For in-vestigated transparent soil with fused quartz the attenuationcoecient K is calculated to be 00021mmminus1 based onverication of experimental data However deviation rangesexist in the transmittance results and the condence intervalof mean transmittance is denoted as the error bar in Figure 3

233 Impact of Refractive Index Matching A refractiveindex matching technique has been applied in various eldsof study including granular media and riverbeds [28]Further research has also sought to establish a methodologyof assessment for allowable refractive index mismatch [22]In this analysis to investigate the impact of refractive indexmatching on transmittance the matching liquid is preparedwith various oil mix ratios to achieve dierent levels of

refractive index matching (ns minus nl) However consideringthat a refractive index of fused quartz ns remains consistentat room temperature of 20degC changes in the resulting re-fractive index of matching liquid nl represent refractiveindex matching Assuming that the refractive index ofmatching liquid nl is the single variable in (5) expression oftransmittance T is simplied as

T eK1n2l +K2nl+K3 (7)

where K1 K2 and K3 refer to the coecients that are de-termined by the tted curve In Figure 4 the curve tting

CuvetteAcrylic glass boxT=endashKd

20 40 60 80 100 120 140 160 180 2000Distance d (mm)

30

40

50

60

70

80

90

100

Tran

smiss

ion

rate

T (

)

Figure 3 Relationship of transmittance T to viewing depth d

(a) (b)

(c)

Figure 2 Layout of the experimental apparatus and test chambers


results demonstrate that the transmittance reaches a peakvalue with the best match of the refractive index matchingwhereas there are dips of transmittance as a result of therefractive index mismatch In general the impact of re-fractive index matching is well described by the exponentialdecay of principle of the Christiansen eect

3 Relationship between Transmittance andImaging Quality

31 Evaluation Function of Image Clarity Transmittancedescribes transparency mathematically and it is the delityin optical measurement of transparent soil that quanti-cation of transparency counts for us it is necessary toestablish the relationship between transmittance and eval-uation function of image clarity For digital image processingof transparent soil image clarity is the primary concern ofDIC precision [29] because captured images within trans-parent soil consist of dierent intensities at dierent pixelpositions which allow for identication Improved imageclarity of image texture is associated with a greater degree ofvariation in pixel intensity For example image intensitychanges with the degree of saturation of transparent soil[30ndash32] with unsaturated transparent soil yielding degradedoptical clarity

Accordingly the variation in pixel intensity is estimatedby the intensity gradient in this research e intensitygradient is calculated by the Sobel operator which isprevalently adopted in the image processing technique ofedge detection It calculates the norm of the vector at eachpixel of the digital image By computing the approximatednorm of the image gradient at the pixel position (x y) in thehorizontal and vertical directions the Sobel operator isusually less computationally expensive with an isotropic3times 3 kernel However approximations of the derivatives canbe dened at higher or lower degrees of accuracy by dierentkernels In this paper the experimental data demonstrate

that the approximated results of the isotropic 3times 3 gradientSobel operator are sucient for distinguishing betweendierent levels of the evaluation function which corre-sponds to delity in the optical measurements

As a gradient-based sharpness function in digital pho-tography the evaluation function E of image clarity oftransparent soil is adapted from the Sobel operator A digitalimage withW timesH pixels is shown in Figure 5 and the pixelposition (x y) is determined in the following calculations

Initially the image intensity of pixel position (x y) isdenoted as f(x y) A(x y) is the 3times 3 matrix that describesimage intensity around pixel position (x y) in a 3times 3 pixelregion en 3times 3 kernels are utilized in the Sobel operatorto convolve with the image intensity A(x y) As a result theimage gradient vectors at pixel position (x y) in the hori-zontal and vertical directions are acquired as Gx(x y) andGy(x y) in (8) and (9) resp

Gx(x y) minus1 0 1

minus2 0 2

minus1 0 1

lowastA(x y) (8)

Gy(x y) minus1 minus2 minus10 0 01 2 1

lowastA(x y) (9)

where lowast represents a 2-dimensional signal that computesconvolution In other words nablaf(x y) is calculated as

nablaf(x y) Gx(x y) Gy(x y)( ) (10)

Meanwhile |nablaf(x y)| refers to an approximatedmodulus of the image gradient vector at pixel position (x y)in a 3times 3 pixel region us |nablaf(x y)| is calculated by animage intensity vector from a convolution of the Sobeloperator in both the horizontal and vertical directions asfollows

|nablaf(x y)| Gx(x y)

2 + Gy(x y)2

radic (11)

where Gx(x y) and Gy(x y) refer to the result of thediscrete dierentiation operator at pixel position (x y) inthe horizontal and vertical directions respectively

e approximated modulus of the image gradient|nablaA(x y)| lays the foundation of evaluation function EEvaluation function E is designated to establish dierentlevels of image clarity Considering that the mean intensitygradient is proposed to evaluate speckle pattern quality inDIC [33] the evaluation function E is dened as the meansquare of the norm of the image gradient at all pixels in thecaptured image denoted as follows

E sumW

x1sumH

y1

|nablaf(x y)|2

N (12)

where N refers to the sum of pixels in the digital image Inaddition it is noted that the evaluation function given in (12)is sensitive to changes of intensity Consequently forcomparison between dierent levels of image clarity the

d=50 mmd=100 mm

d=150 mmd=200 mm

00

01

02

03

04

05

06

07

08

09

10

Tran

smiss

ion

rate

T (

)

1445 1450 1455 1460 1465 14701440nh

Figure 4 Relationship of transmittance T to refractive indexmatching


evaluation function E is normalized as EN in unit-basednormalization expressed as follows

EN E

Emax (13)

where EN refers to the normalized evaluation function andEmax is determined by the evaluation function of imageclarity with no degradation in transparent soil Image clarityof transparent soil is quantitatively evaluated using thenormalized evaluation function EN

32 Relevance of Transmittance to the Normalized EvaluationFunction for Transparent Soil with Fused Quartz As shownin Figure 6 the relevance of transmittance to image clarity isrevealed by the relationship between transmittance T andthe normalized evaluation function EN Such relevance isinvestigated for transparent soil with fused quartz In detailgrid lines are uniformly printed on paper but are viewedthrough transparent soil with varied depth Dierent sizes ofthe acrylic glass box are utilized for the test chamber con-taining the transparent soil to determine the viewing depthFor various viewing depths images of grid lines are capturedby a Nikon D7000 digital camera with a 50mm f18D lensSuch photographic equipment produces images with

a resolution of 4928times 3264 pixels by an aperture of f22 anexposure time of 5 s and ISO100 For digital image pro-cessing the digital images are cut to the same size for cal-culation of the evaluation function EN that denes the imageclarity To capture digital images ①sim⑤ in Figure 6 con-guration of the photographic equipment and alignment ofthe optical system are made consistent in eachmeasurementwhile transmittance of the transparent soil sample variesfrom case to case Meanwhile transmittance T of trans-parent soil is measured in each case As a result the cor-relation of transmittance to image clarity is revealed by therelevance of transmittance T to the evaluation function ofEN in Figure 6 Figure 6 includes representative results oftransmittance for varied image clarity of transparent soil atthe viewing depths of 50mm (⑤) 100mm (④) 150mm(③) and 200mm (②) In addition when no transparent soilis in the test chamber digital image ① is captured and thetransmittance of the test chamber without transparent soil isdetected

For transparent soil with fused quartz and mineral oilthe experimental data show a signicant increase in imageclarity with transmittance higher than 90 (digital image②with a transmittance of 9009 plusmn 222) In addition basedon previous research of portraying the level of transparency[15] the viewing depth of transparent soil in the test was

W pixels

H pixels

f (xy)Y

X0

Figure 5 A digital image with W timesH pixels (x isin [1W] y isin [1 H])

00

02

04

06

08

10

Nor

mal

ized

eval

uatio

n fu

nctio

n va

lue E N

50 60 70 80 90 10040Transmission rate T ()

1 2 3

4

51

2

3

4

5

Figure 6 Relevance of transmittance T to the normalized evaluation function of image clarity EN


typically 50mm +us the digital image ③ deliversa transmittance of 6729 plusmn 259 which corresponds toa viewing depth of 50 mm To draw a conclusion for somecategories of transparent soil such as the soil sample withfused quartz there is a certain calibration curve as shown inFigure 6 that indicates the relationship between trans-mittance and imaging quality And such relationship shall beof great value in further research into accuracy of digitalimage analysis

4 Conclusions

+e fundamental purpose of this paper is to propose anobjective framework for quantification of transparency intransparent soil based on transmittance In this frameworkexperimental apparatuses including laser transmitter andpower meter are introduced in the measurement method fortransmittance Additionally analysis of transparent soilproperty and the principle of the Christiansen effect areintegrated in this paper +e principle of the Christianseneffect is proposed to govern the variation in transmittanceand to investigate the impact factors that affect trans-mittance Furthermore the relationship between trans-mittance and imaging quality is also investigated

On a basis of experimental results exponential decay oftransmittance is validated and the dominant factors thataffect variation in transmittance are viewing depth andrefractive index matching Besides according to the rele-vance of transmittance to the evaluation function of theintensity variation imaging quality of geotechnical model-ing with transparent soil is enhanced with increasingtransmittance and imaging quality shows a remarkableimprovement when transmittance is greater than 90

Above all the principle of the Christiansen effect pro-vides guidance for increasing the viewing depth of trans-parent soil and refining the refractive index matchingtechnique to improve transparency in transparent soil ingeotechnical modeling Meanwhile the relationship betweentransmittance and image clarity is established Such re-lationship lays a foundation of further research regarding theaccuracy of digital image analysis in transparent soil withdifferent transmittance

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the National Natural ScienceFoundation of China (no 51579219)

References

[1] M IskanderModeling with Transparent Soils Visualizing SoilStructure Interaction and Multi Phase Flow Non-IntrusivelySpringer New York NY USA 2010

[2] P Kelly Soil structure interaction and group mechanics ofvibrated stone column foundations PhD+esis University ofSheffield Sheffield UK 2013

[3] R Mannheimer Slurries You Can See rough TechnologyToday Southwest Research Institute San Antonio TX USA1990

[4] M Iskander J Lai C Oswald and R Mannheimer ldquoDe-velopment of a transparent material to model the geotechnicalproperties of soilrdquo Geotechnical Testing Journal vol 17 no 4pp 425ndash433 1994

[5] R J Mannheimer and C J Oswald ldquoDevelopment oftransparent porous media with permeabilities of soils andreservoir materialsrdquo Ground Water vol 31 no 5 pp 781ndash788 1993

[6] M Iskander S Sadek and J Liu ldquoOptical measurement ofdeformation using transparent silica gel to model sandrdquoInternational Journal of Physical Modelling in Geotechnicsvol 2 no 4 pp 13ndash26 2003

[7] K Tabe ldquoTransparent aquabeads to model LNAPL Gangliamigration through surfactant flushingrdquo Geotechnical TestingJournal vol 38 no 5 pp 787ndash804 2015

[8] F M Ezzein and R J Bathurst ldquoA transparent sand forgeotechnical laboratory modelingrdquo Geotechnical TestingJournal vol 34 no 6 pp 590ndash601 2011

[9] J Wallace and C Rutherford ldquoGeotechnical properties ofLaponite RDrdquo Geotechnical Testing Journal vol 38 no 5pp 574ndash587 2015

[10] Z Song Y Hu C OrsquoLoughlin and M F Randolph ldquoLoss inanchor embedment during plate anchor keying in clayrdquoJournal of Geotechnical amp Geoenvironmental Engineeringvol 135 no 10 pp 1475ndash1485 2009

[11] E Suescun-Florez M Iskander V Kapila and R CainldquoGeotechnical engineering in US elementary schoolsrdquo Eu-ropean Journal of Engineering Education vol 38 no 3pp 300ndash315 2013

[12] S Kashuk R Mercurio and M Iskander ldquoVisualization ofdyed NAPL concentration in transparent porous media usingcolor space componentsrdquo Journal of Contaminant Hydrologyvol 162 pp 1ndash16 2014

[13] M Iskander R Bathurst andM Omidvar ldquoPast present andfuture of transparent soilsrdquo Geotechnical Testing Journalvol 38 no 5 pp 557ndash573 2015

[14] S Sadek M Iskander and J Liu ldquoAccuracy of digital imagecorrelation for measuring deformations in transparent me-diardquo Journal of Computing in Civil Engineering vol 17 no 2pp 88ndash96 2003

[15] J Liu and M G Iskander ldquoModelling capacity of transparentSoilrdquo Canadian Geotechnical Journal vol 47 no 4pp 451ndash460 2010

[16] S A StanierModelling the behaviour of helical screw piles PhD +esis University of Sheffield Sheffield UK 2011

[17] J A Black andW A Take ldquoQuantification of optical clarity oftransparent soil using the modulation transfer functionrdquoGeotechnical Testing Journal vol 38 no 5 pp 588ndash602 2015

[18] J M Palmer and B G Grant e Art of Radiometry SPIEPress Bellingham WA USA 2010

[19] I H Malitson ldquoInterspecimen comparison of the refractiveindex of fused silicardquo Journal of the Optical Society of Americavol 55 pp 1205ndash1208 1965

[20] I Guzman M Iskander E Suescun and M Omidvar ldquoAtransparent aqueous-saturated sand-surrogate for use inphysical modelingrdquo Acta Geotechnica vol 9 no 2 pp 187ndash206 2014

[21] Y P Zhang L Li and S Z Wang ldquoExperimental study onpore fluid for forming transparent soilrdquo Journal of ZhejiangUniversity (Engineering Science) vol 48 no 10 pp 1828ndash1834 2014


[22] J A Dijksman F Rietz K A Lorincz M Van Hecke andW Losert ldquoRefractive index matched scanning of densegranular materialsrdquo Review of Scientific Instrument vol 83article 011301 2012

[23] J W Gooch Encyclopedic Dictionary of Polymers SpringerNew York NY USA 2011

[24] C V Raman and K S Viswanathan ldquoA generalised theory ofthe Christiansen experimentrdquo Proceedings of the IndianAcademy of Science vol 41 no 2 pp 55ndash60 1955

[25] S Kang D E Day and J O Stoffer ldquoMeasurement of therefractive index of glass fibers by the Christiansen-Shelyubskiimethodrdquo Journal of Non-Crystalline Solids vol 220 no 2pp 299ndash308 1997

[26] A K Varshneya M C Loo and T F Soules ldquoGlass in-homogeneity measurement using the Shelyubskii methodrdquoJournal of the American Ceramic Society vol 68 no 7pp 380ndash385 2010

[27] A Sassaroli and S Fantini ldquoComment on the modified Beer-Lambert law for scattering mediardquo Physics in Medicine andBiology vol 49 no 14 pp 255ndash257 2004

[28] A E Lobkovsky A V Orpe R Molloy A Kudrolli andD H Rothman ldquoErosion of a granular bed driven by laminarfluid flowrdquo Journal of Fluid Mechanics vol 605 pp 47ndash582008

[29] W A Take ldquo+irty-Sixth Canadian Geotechnical Collo-quium advances in visualization of geotechnical processesthrough digital image correlationrdquo Canadian GeotechnicalJournal vol 52 no 9 pp 1199ndash1220 2015

[30] S B Peters G A Siemens W A Take and F Ezzein ldquoAtransparent medium to provide a visual interpretation ofsaturatedunsaturated hydraulic behaviorrdquo in Proceedings ofGeoHalifax pp 59ndash66 Halifax Nova Scotia Canada 2009

[31] G A Siemens S B Peters and W A Take ldquoComparison ofconfined and unconfined infiltration in transparent porousmediardquoWater Resources Research vol 49 no 2 pp 851ndash8632013

[32] G A Siemens W A Take and S B Peters ldquoPhysical andnumerical modeling of infiltration including consideration ofthe pore air phaserdquo Canadian Geotechnical Journal vol 51no 12 pp 1475ndash1487 2014

[33] B Pan Z Lu and H Xie ldquoMean intensity gradient an ef-fective global parameter for quality assessment of the specklepatterns used in digital image correlationrdquo Optics amp Lasers inEngineering vol 48 no 4 pp 469ndash477 2010


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calibration for viewing decreasing font-sized letters throughtransparent soils to estimate the transparency that isavailable for visualization [16] However the conventionalmethodology of the above assessments is subjective andnonquantitative and infers variable levels of acceptabletransparency for visualization of transparent soils +usa comprehensive objective quantitative and robustframework of transparency assessment awaits developmentRecently the modulation transfer function (MTF) has beenproposed for quantitative assessment and comparison oftransparency [17]

However MTF is determined according to the fidelity oftransferred details from object to image which involves anoverall imaging capability of the whole optical system whichis characterized by not only transparency of transparent soilbut also the photographic apparatus Hence in order toprovide observations of how transparency affects the ac-curacy of imaging and measurement in transparent soil thepurpose of this research is to quantitatively evaluate thetransparency of transparent soil itself If such a framework ofevaluation is developed for the optical characteristics oftransparent soil it shall provide guidance for modelingexperiments of transparent soil to reduce limitations ongeometry and refractive index matching

Specifically in this paper an objective framework forquantification of transparency based on transmittance isestablished by combining geotechnical engineering andoptics First the calculationmethod of transmittance and theexperimental setup for detecting transmittance is proposedso that transmittance data of transparent soil are acquiredSecond it is suggested that variations of transmittance aresubjected to exponential decay which is well explained bythe principle of the Christiansen effect And such obser-vation of transmittance shall provide approaches to im-proving transparency quality of transparent soil +ird forexperiments of detecting transmittance for different trans-parent soil samples experimental results and digital imagesdemonstrate the relationship between transmittance andimaging quality of visualization in transparent soil +erelationship between transmittance and imaging clarity isinvestigated using an evaluation function of the digitalimage

2 Objective Framework for Quantification ofTransparency in Transparent SoilBased on Transmittance

21 Transmittance Transmittance defines the property thata substance permits transmitted light to pass through whileincident light is partially absorbed or scattered It is themathematical description of transparency +e theory ofradiometry indicates that transmittance T is the luminousflux ratio of transmitted light φt to incident light φi [18]which is expressed as

T φt

φi (1)

+e luminous flux refers to the power of electromagneticradiation which is modified due to varied sensitivity of thehuman eye to different wavelengths of light It is calculatedby a luminosity function regarding the issue In the lumi-nosity function luminous efficacy is the weighting co-efficient that represents the ratio of the luminous flux to theradiant flux For a certain wavelength of light the luminousflux φ is expressed as

φ KλP (2)

where Kλ refers to the weighting coefficient at wavelength λand P refers to the radiant flux Based on (1) and (2)transmittance is denoted by the following equation

T Pt

Pi (3)

where Pt and Pi refer to the radiant flux of transmitted andincident light respectively Hence the calculation method iscapable of acquiring transmittance using optical measure-ments of a laser power meter in the experimental setup

22 Measurement Method for Transmittance

221 Material In the experimental setup fused quartzwhich is common in manufacturing is applied as the solidparticle of transparent soil During the manufacturingprocess fused quartz is highly purified by melting at ap-proximately 2000degC and is formed by crystalline silica witha purity level of 999 to 9995 [1] Specifically for theselected fused quartz in this research it is shown in Figure 1that the particle size ranges from 200 to 280mm At eachwavelength of visible light transmittance of fused quartz iswell beyond 90 +e refractive index of fused quartz isreported as 14585 [19]

Fused quartz aggregate is matched with a blend of twooils namely 15 PURITY FG WO white mineral oil pro-duced by Petro-Canada and EI solvent oil produced byTEACSOL Both oils are transparent as well as colorlesswith the physical properties that are listed in Table 1

As listed in Table 1 higher flashing points of flamma-bility indicate that the oils are safe to use under normallaboratory conditions at room temperature Since thedensity of mineral oil is similar to that of EI oil mixtures ofsuch two oils are well blended +e refractive index of well-blended oils changes with the specific blending ratio toachieve different levels of refractive index matching +erefractive index is then measured by implementation ofa 2WAJ refractometer with a precision of 00002 Howeverthere is considerable variation in the refractive index ofmatching liquids at different temperatures [20] To in-vestigate the variation of the refractive index due to changingtemperature configuration of the DK-S18 water bath andcirculating pump is connected to the refractometer formaintaining a constant temperature of the matching liquid[8 21] On the basis of the Arago-Biot function [22] therelationship between the resulting refractive index andblending ratio is expressed by the following equation


n12 λ θn1 +(1minus θ)n21113858 1113859 + g (4)






2+ k21113960 1113961d

λ2m

⎧⎨

⎩

⎫⎬

⎭ (5)





Density(kgL)







T eminusKd (6)







20 40 60 80 100 120 140 160 180 2000Distance d (mm)

30

40

50

60

70

80

90

100

Tran

smiss

ion

rate

T (

)


(a) (b)

(c)










Gx(x y) minus1 0 1

minus2 0 2

minus1 0 1

lowastA(x y) (8)


lowastA(x y) (9)





2 + Gy(x y)2

radic (11)



E sumW

x1sumH

y1

|nablaf(x y)|2

N (12)


d=50 mmd=100 mm

d=150 mmd=200 mm

00

01

02

03

04

05

06

07

08

09

10

Tran

smiss

ion

rate

T (

)

1445 1450 1455 1460 1465 14701440nh




EN E

Emax (13)





W pixels

H pixels

f (xy)Y

X0


00

02

04

06

08

10

Nor

mal

ized

eval

uatio

n fu

nctio

n va

lue E N


1 2 3

4

51

2

3

4

5




4 Conclusions






Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


n12 λ θn1 +(1minus θ)n21113858 1113859 + g (4)






2+ k21113960 1113961d

λ2m

⎧⎨

⎩

⎫⎬

⎭ (5)





Density(kgL)







T eminusKd (6)







20 40 60 80 100 120 140 160 180 2000Distance d (mm)

30

40

50

60

70

80

90

100

Tran

smiss

ion

rate

T (

)


(a) (b)

(c)










Gx(x y) minus1 0 1

minus2 0 2

minus1 0 1

lowastA(x y) (8)


lowastA(x y) (9)





2 + Gy(x y)2

radic (11)



E sumW

x1sumH

y1

|nablaf(x y)|2

N (12)


d=50 mmd=100 mm

d=150 mmd=200 mm

00

01

02

03

04

05

06

07

08

09

10

Tran

smiss

ion

rate

T (

)

1445 1450 1455 1460 1465 14701440nh




EN E

Emax (13)





W pixels

H pixels

f (xy)Y

X0


00

02

04

06

08

10

Nor

mal

ized

eval

uatio

n fu

nctio

n va

lue E N


1 2 3

4

51

2

3

4

5




4 Conclusions






Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




T eminusKd (6)







20 40 60 80 100 120 140 160 180 2000Distance d (mm)

30

40

50

60

70

80

90

100

Tran

smiss

ion

rate

T (

)


(a) (b)

(c)










Gx(x y) minus1 0 1

minus2 0 2

minus1 0 1

lowastA(x y) (8)


lowastA(x y) (9)





2 + Gy(x y)2

radic (11)



E sumW

x1sumH

y1

|nablaf(x y)|2

N (12)


d=50 mmd=100 mm

d=150 mmd=200 mm

00

01

02

03

04

05

06

07

08

09

10

Tran

smiss

ion

rate

T (

)

1445 1450 1455 1460 1465 14701440nh




EN E

Emax (13)





W pixels

H pixels

f (xy)Y

X0


00

02

04

06

08

10

Nor

mal

ized

eval

uatio

n fu

nctio

n va

lue E N


1 2 3

4

51

2

3

4

5




4 Conclusions






Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









Gx(x y) minus1 0 1

minus2 0 2

minus1 0 1

lowastA(x y) (8)


lowastA(x y) (9)





2 + Gy(x y)2

radic (11)



E sumW

x1sumH

y1

|nablaf(x y)|2

N (12)


d=50 mmd=100 mm

d=150 mmd=200 mm

00

01

02

03

04

05

06

07

08

09

10

Tran

smiss

ion

rate

T (

)

1445 1450 1455 1460 1465 14701440nh




EN E

Emax (13)





W pixels

H pixels

f (xy)Y

X0


00

02

04

06

08

10

Nor

mal

ized

eval

uatio

n fu

nctio

n va

lue E N


1 2 3

4

51

2

3

4

5




4 Conclusions






Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



EN E

Emax (13)





W pixels

H pixels

f (xy)Y

X0


00

02

04

06

08

10

Nor

mal

ized

eval

uatio

n fu

nctio

n va

lue E N


1 2 3

4

51

2

3

4

5




4 Conclusions






Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



4 Conclusions






Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia

















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


quantificationofthetransparencyofthetransparentsoilin...

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