- 169 -

Particle Shape Quantities and Measurement Techniques–A Review

Juan M. Rodriguez

Ph.D. Student Department of Civil, Environmental and Natural resources engineering, Luleå

University of Technology, Tel: +46 920 491523, SE – 971 87, Luleå, Sweden e-mail: juan.rodriguez@ltu.se

Tommy Edeskär

Assistant Professor Department of Civil, Environmental and Natural resources engineering, Luleå

University of Technology, Tel: +46 920 493065, SE – 971 87, Luleå, Sweden e-mail: tommy.edeskar@ltu.se

Sven Knutsson

Professor Department of Civil, Environmental and Natural resources engineering, LuleåUniversity of Technology, Tel: +46 920 491332, SE – 971 87, Luleå, Sweden

e-mail: sven.knutsson@ltu.se

ABSTRACT It has been shown in the early 20th century that particle shape has an influence on geotechnical properties. Even if this is known, there has been only minor progress in explaining the processes behind its performance and has only partly implemented in practical geotechnical analysis. This literature review covers different methods and techniques used to determine the geometrical shape of the particles. Particle shape could be classifying in three categories; sphericity - the overall particle shape and similitude with a sphere, roundness - the description of the particle’s corners and roughness - the surface texture of the particle. The categories are scale dependent and the major scale is to sphericity while the minor belongs to roughness. The overview has shown that there is no agreement on the usage of the descriptors and is not clear which descriptor is the best. One problem has been in a large scale classify shape properties. Image analysis seems according to the review to be a promising tool, it has advantages as low time consumption or repeatability. But the resolution in the processed image needs to be considered since it influences descriptors such as e.g. the perimeter. Shape definitions and its potential role in soil mechanics are discussed.

KEYWORDS: Particle shape, Quantities, Image analysis.

Vol. 18 [2013], Bund. A 170

INTRODUCTION Effects on soil behavior from the constituent grain shape has been suggested since the earliest

1900’s when Wadell (1932), Riley (1941), Pentland (1927) and some other authors developed their own techniques to define the form and roundness of particles. Into the engineering field several research works conclude that particle shape influence technical properties of soil material and unbound aggregates (Santamarina and Cho, 2004; Mora and Kwan, 2000). Among documented properties affected by the particle shape are e.g. void ratio (porosity), internal friction angle, and hydraulic conductivity (permeability) (Rousé et al., 2008; Shinohara et al., 2000; Witt and Brauns, 1983). In geotechnical guidelines particle shape is incorporated in e.g. soil classification (Eurocode 7) and in national guidelines e.g. for evaluation of friction angle (Skredkommisionen, 1995). This classification is based on ocular inspection and quantitative judgment made by the individual practicing engineer, thus, it can result in not repeatable data. The lack of possibility to objectively describe the shape hinders the development of incorporating the effect of particle shape in geotechnical analysis.

The interest of particle shape was raised earlier in the field of geology compared to geotechnical engineering. Particle shape is considered to be the result of different agent’s transport of the rock from its original place to deposits, since the final pebble form is hardly influenced by these agents (rigor of the transport, exfoliation by temperature changes, moisture changes, etc.) in the diverse stages of their history. Furthermore, there are considerations regarding on the particle genesis itself (rock structure, mineralogy, hardness, etc.) (Wentworth 1922a). The combination of transport and mineralogy factors complicates any attempt to correlate length of transport and roundness due that soft rock result in rounded edges more rapidly than hard rock if both are transported equal distances. According to Barton & Kjaernsli (1981), rockfill materials could be classified based on origin into the following (1) quarried rock; (2) talus; (3) moraine; (4) glaci-fluvial deposits; and (5) fluvial deposits. Each of these sources produces a characteristic roundness and surface texture. Pellegrino (1965) conclude that origin of the rock have strong influence determining the shape.

To define the particle form (morphology), in order to classify and compare grains, many measures has been taken in consideration (axis lengths, perimeter, surface area, volume, etc.). Furthermore, corners also could be angular or rounded (roundness), thus, the authors also focus on develop techniques to describe them. Additionally corners can be rough or smooth (surface texture). Nowadays some authors (Mitchell & Soga, 2005; Arasan et al., 2010) are using these three sub-quantities, one and each describing the shape but a different scale (form, roundness, surface texture).

During the historical development of shape descriptors the terminology has been used differently among the published studies; terms as roundness (because the roundness could be apply in the different scales) or sphericity (how the particle approach to the shape of a sphere) were strong (Wadell, 1933; Wenworth, 1933; Teller, 1976; Barrett 1980; Hawkins, 1993), and it was necessary in order to define a common language on the particle shape field; unfortunately still today there is not agreement on the use of this terminology and sometimes it make difficult to understand the meaning of the authors, that’s why it is better to comprehend the author technique in order to misinterpret any word implication.

Several attempts to introduce methodology to measure the particle’s shape had been developed over the years. Manual measurement of the particles form is overwhelming, thus, visual charts were developed early to diminish the measuring time (Krumbein, 1941, Krumbein and Sloss, 1963; Ashenbrenner, 1956; Pye and Pye, 1943). Sieving was introduced to determine

Vol. 18 [2013], Bund. A 171 the flakiness/elongation index but it is confined only for a certain particle size due the practical considerations (Persson, 1988). More recently image analysis on computer base has been applied on sieving research (Andersson, 2010, Mora and Kwan, 2000, Persson, 1998) bringing to the industry new practical methods to determine the particle size with good results (Andersson, 2010). Particle shape with computer assisted methods are of great help reducing dramatically the measuring time (Fernlund, 2005; Kuo and Freeman 1998a; Kuo, et al., 1998b; Bowman, et al., 2001).

In the civil industry e.g. Hot Asphalt mixtures (Kuo and Freeman, 1998a; Pan, et al., 2006), Concrete (Mora et al., 1998; Quiroga and Fowle, 2003) and Ballast (Tutumluer et al., 2006) particle’s shape is of interest due the material’s performance, thus, standards had been developed (e.g. EN 933-4:2000 Tests for geometrical properties of aggregates; ASTM D 2488-90 (1996) Standard practice for description and identification of soils).

Sieving is probably the most used method to determine the particle size distribution. This traditional method, according to Andersson (2010) is time consuming and expensive. Investigations shows that the traditional sieving has deviations when particle shape is involve; the average volume of the particles retained on any sieve varies considerably with the shape (Lees, 1964b), thus, the passing of the particles depend upon the shape of the particles (Fernlund, 1998). In some industries the Image analysis is taking advantage over the traditional sieving technique regardless of the intrinsic error on image analysis due the overlapping or partial hiding of the rock particles (Andersson, 2010). In this case the weight factor is substitute by pixels (Fernlund et al., 2007). Sieving curve using image analysis is not standardized but after good results in the practice (Andersson, 2010) new methodology and soil descriptions could raise including its effects.

Describing the particle’s shape is the main objective, there are 42 different quantities in this document, and it is required to review the information about them to comprehend and interpret the implication of each quantity to determine them usability and practice.

DESCRIPTION OF SHAPE PROPERTIES Particle shape description can be classified as qualitative or quantitative. Qualitative describe

in terms of words the shape of the particle (e.g. elongated, spherical, flaky, etc.); and quantitative that relates the measured dimensions; in the engineering field the quantitative description of the particle is more important due the reproducibility.

Quantitative geometrical measures on particles may be used as basis for qualitative classification. There are few qualitative measures in contrast with several quantitative measures to describe the particle form. Despite the amount of qualitative descriptions none of them had been widely accepted; but there are some standards (e.g., ASTM D5821, EN 933-3 and BS 812) specifying mathematical definitions for industrial purposes.

Shape description of particles is also divided into two: -3D (3 dimensions): it could be obtained from a 3D scan or in a two orthogonal images and -2D (2 dimensions) or particle projection, where the particle outline is drawn.

3D and 2D image analysis present challenges itself. 3D analysis requires a sophisticated equipment to scan the particle surface and create the 3D model or the use of orthogonal images and combine them to represent the 3 dimensions. The orthogonal method could present new challenges as the minimum particle size or the placing in orthogonal way of the particles (Fernlund, 2005). 2D image analysis is easy to perform due the non-sophisticated equipment

V requir2D imintermor ran1941;

Indefiniusing morphdefine

Adescridescrishapedescricornethe paFigurRegarthe sasmalleanton

Wthe p

Vol. 18 [20

red to take pimage analysimediate axis lndom, some ; Hawkins, 19

n order to desitions used inthree sub-qu

hology/form, ed.

Figur

At large scaleibing terms aiption at large

e is marked iption of the rs and edges article’s boune 1. A generding the smaame kind of aner scale. Surf

nyms are summ

Table 1:

Wentworth in particle dime

13], Bund.

ictures (e.g. rs the particlelie more or leauthors publi

993).

scribe the parn the literatureantities; one aroundness an

re 1: Shape d

the particle’as spherical, pe scale is sphwith the daspresence of of different s

ndary, deviatierally accepteallest scale, tenalysis as theface texture imarized in tab

Sub-quantitScale Large scalIntermediaSmall scale

1922 (Blott aensions, this

. A

regular camere is assumedess parallel toish their own

SCALE Drticle shape ie. Some authand each descnd surface te

describing su

’s diameters platy, elonga

hericity (antonshed line in

f irregularitiessizes are idenions are founed quantity erms like roue one describeis often used ble 1.

ties describin

e ate scale e

FOand Pye, 200

consisted o

ra or the use d to lay overo the surface n preferences

DEPENDEin detail, therhors (Mitchellcribing the shexture. In Fig

ub quantities

in different dated etc., are nym: elongat

Figure 1. As. Depending

ntified. By dond and valuatefor this scalgh or smooth

ed above, but to name the

ng the particQuantity Sphericity Roundness Roughness

RM (3D)8), was proba

on the obtain

of microscopr its more stawhile the sho

s about this i

ENCE re are a numbl & Soga, 200

hape but at difgure 1 is show

s (Mitchell &

directions areused. An oft

tion). GraphicAt intermediag on at what oing analysis ied. The mentle is roundnh are used. This applied wiactual quant

cle’s morphoAntonymElongatioAngulariSmoothn

) ably one of thning of the

pe for smalleable axis (e.gortest axis is issue (Wadell

ber of terms, 05; Arasan etfferent scales.wn how the s

& Soga, 200

e considered.ten seen quancally the consate scale it scale an ana

inside circlestioned circles

ness (antonymhe descriptor ithin smaller ctity. The sub-

ology and itsm on ity ness

the first autholength of

17

er particles). Ig. longest anperpendiculal, 1935; Riley

quantities ant al., 2010) ar. The terms arscale terms ar

5)

At this scalntity for shapsidered type ois focused oalysis is dons defined alons are shown im: angularity

is considerincircles, i.e. at-quantities an

antonym

ors on measurthe tree axe

72

In nd ar) y,

nd re re re

le, pe of on e;

ng in

y). ng t a nd

re es

V perpespheri

Figu

Kthis iparticc/b arhe cal

Figu

Wschemsame

Vol. 18 [20

ndicular amoicity (Equatio

ure 2: Measu

Krumbein (194s done by m

cle, it can be sre located in tlled (See Figu

ure 3: Detail

Wadell (1932)matic represen

volume.

13], Bund.

ong each otheron 1).

urement of th

41) develop ameasuring theseen in Figurthe chart deveure 3). This ch

ed chart to d

) defined the ntation of the

. A

r (see Figure

he 3 axes pe

a rapid methoe longest (a), re 2 (Always eloped by his hart is an easy

determining

sphericity as sphere surfac

Ψ

2) on the tree

erpendicular

od for shape mmedium (b)

perpendicularown where it

y graphical w

Krumbein in

the specific ce and particl

c2

ba

+=Ψ

e dimensions

among each

measurement ) and shorterar among eacht can be foun

way to relate th

ntercept sphe

surface ratio e surface, bot

(where a≥b≥c

h other (Krum

to determine r (c) axes diah other). The

nd the Intercephe dimension

ericity (Krum

(Equation 2)th particle an

17

c) to obtain th

(

mbein, 1941

the sphericityameters of thradios b/a an

pt sphericity ans.

mbein 1941)

). Figure 4 is d sphere of th

73

he

1)

)

y; he nd as

).

a he

V

F

Tdeclar

WEquat

WEquat

Vol. 18 [20

Figure 4: Sam

This way to res, due the d

Wadell (1934)tion 3 (see Fig

Figure 5:

Wadell (1934tion 4).

13], Bund.

me volume s

obtain the sdifficulty to ge

) also definedgure 5):

Relation betcircumsc

4) used a new

. A

sphere surfacJohansson

phericity is et the surface

d the spheric

tween the vocribed sphere

w formula sim

ce (s) and pan and Vall, 2

almost impoarea on irreg

city based up

olume of the e (Johansson

mple to manag

3

CIR

P

V

V =Ψ

CIR

SV

D

D=Ψ

article surfac2011).

ossible to acgular solids.

pon the partic

particle andn and Vall, 2

ge using the d

ce (S). (mod

hieve, as Ha

cle and spher

d the volume2011).

diameters (se

17

(2

dified after

awkins (1993

re volumes, a

(3

e of the

e Figure 6 an

(4

74

2)

3)

as

3)

nd

4)

V

Figu

Zeasy tsummthe Fi

Inseen,

Vol. 18 [20

ure 6: The reof a spher

Zingg (Krumbto find out th

marized on Figigure 3.

Figure 7:

n Figure 8 thit is an easy w

13], Bund.

elation betwre of the sam

ein, 1941) dehe main formgure 7. Zingg

Zingg’s cla

e Figures 3 away to unders

. A

een the diamme volume as

evelop a classm of the particg’s classificat

ssification o(Krum

and 7 are comstand the mor

meter of a cirs the particle

ification basecles as a disktion is related

of pebble shambein 1941)

mbined, the rrphology rega

rcumscribede (Johansson

ed on the 3 axks, spherical, d with Krumb

ape based on).

elation in thearding on the

d sphere and n and Vall, 2

xes relation, iblades and r

bein intercept

n ratios b/a a

e two classifia, b and c dim

17

the diameter2011).

in this way it rod-like; this

sphericity an

and c/b

ications can bmensions

75

r

is is

nd

be

V

Pycompspheriby Krwith eFolk Projec

InSpher

FpublisDobk

Vol. 18 [20

Figure 8:

ye and Pye (are the Wadicity” based orumbein (194exception of in (1958) d

ction Spheric

n a similar waricity”

orm or shapeshed on 1949

kins & Folk (o

=Ψ

13], Bund.

Classificati

(1943), in thdell’s sphericon an ellipse,41). Axis meaEquation 8 w

describes a rity” (Equation

ay Ashenbren

e factor name, Williams (sh

oblate-prolate

(c/b)(11+=

. A

ion made by (Krumbein

e article “sphcity develope, this last Equasurement is where the origrelation betwn 6).

nner (1956) sh

s are used byhape factor, e index, eq. 11

6))a/b(

( 12,8 3

++

∗

Zingg’s andn and Sloss,

hericity detered in 1934 (uation (numbdone as Figuginal docume

ween the tree

howed his Eq

y authors like eq. 9) in 19651) in 1970 (Bl

b/c(16

/b()b/c( 2

+∗

∗

d chart to det1963)

rminations of(based on th

ber 5) appearsure 1 denotesent was not pe dimensiona

quation (7) at

Corey (shap5, Janke (formlott and Pye,

a/b((1)b

)a2 +

termine sphe

f pebbles andhe diameter) s two years es for Equationpossible to obal axes calle

t that time nam

pe factor, eq. m factor, eq. 1

2008).

))a 2

17

ericity

d sand grainswith “Pebb

early publishens 5 trough 1btain. Sneed &ed “Maximum

(5

(6

med “Workin

(7

8) in the pape0) in 1966 an

(8

76

s” le ed 12 & m

5)

6)

ng

7)

er nd

8)

V

A

square

T

Tliteratthe pa

Vol. 18 [20

Aschenbrennere of the midd

Table 2: Gen

Aspect Sphericity (3D)

The techniqueture some wayarticle project

13], Bund.

r (1956) devedle one.

neral overviehas been

Name

FlatnessTrue SpOperati

Spheric

Zingg’sIntercepPebble Corey sWorkinshape faMaximusphericiWilliamJanke fo

Oblate-p

e to measure ys to measuretion, some aut

. A

eloped the sha

ew over diffn compiled a

s index phericity onal sphericity

city

s classificationpt sphericity chsphericity

shape factor ng sphericity actor um projection ity

ms shape factororm factor

prolate index

FOthe sphericit

e the “two dimthors named “

ape factor by

ferent particland arranged

Author

WentwoWadell

y Wadell

Wadell

Zingg’s1

hart KrumbePye and Corey2

AshenbrAshenbr

Sneed &r William

Janke2

Dobkins

RM (2D)ty is based inmensions sph“particle outli

using the rela

le shape defid chronologic

orth

1

ein d Pye

renner renner

& Folk ms2

s & Folk 1) K2) B

) n three dime

hericity” whicine” or “circu

ation of the tr

initions for 3cally

Year Base

1922a 3-axe1932 Surfa1932 Volu

1934 Sphediam

1935 3-axe1941 3-axe1943 3-axe1949 3-axe1956 3-axe1956 3-axe

1958 3-axe1965 3-axe1966 3-axe

1970 3-axeKrumbein and SlosBlott and Pye, 2008

ensions, it cach is simply thularity”.

17

(9

(10

(1

ree axis but th

(12

3D sphericity

ed on

es ace ume ere

meter

es es es es es es

es es es

es ss, 1963 8

an be found ihe perimeter o

77

9)

0)

1)

he

2)

y

in of

V

W(Equathe mEquatcircumof the

Torientand th

Sown Eequal (P) timorient

Rpropowere handlWade18). Hperim

JaEquatdeviatdetermradial

Vol. 18 [20

Wadell in 193ation 4) to a 2

maximum crotions (13) shomscribed circe perimeter of

Tickell in 193tation proposehe area of sma

ome other auEquations as to longest len

me a constantation of the g

Riley (1941), osed by the ab

not computee called “ins

ell and the relHorton 1932 (

meter of a circl

anoo in 1998tion 20. Sukution of the gmine the iteml divisions).

13], Bund.

35 (Hawkins2D outline. Hss sectional aow the relatiole (DC). He a

f a circle of sa

31 (Hawkins,ed was a randallest circums

uthors has bePentland (192ngth outline (

nt, Equations grains.

realize the pbove authors

er, all was mscribed circlelation of diam(Hawkins, 19le of the same

(Blott and Pumaran and Aglobal particlems used in the

. A

, 1993) adopHe defined anarea (outline on between dlso used the t

ame area (PC)

, 1993) useddom one. It iscribed circle

en working w27) relating th(AC2), and Co16 and 17 re

problems that can carry as

made by hand sphericity”.

meters of insc993) use the re area as drain

Pye, 2008) deAshmawy (200e outline frome Equation 2

pt a conversin orientation o

of the particdiameters of aterm “degree and the actua

d his empirics described b(AC).

with the “cirche area (A) oox (Riley, 194espectively. B

t an area, pes the time con

d), and that’s He used the

cribed (DI) anrelation of thenage basin (P

evelop his ge01) develop hm a circle. F1 (N, referred

ion of his 19on the particlcle projectinga circle of saof circularityal particle per

cal relation (Eby the ratio be

cularity” concoutline and ar41) with the rBoth authors

erimeter and nsuming andwhy he dev

e same particnd circumscre drainage baPCD), see Equa

eneral ratio ofhis own shapFigure 9 can d to the num

934 3D spheles and they g the maximuame area (DA

y” (Equation rimeter (P).

Equation 15)etween the ar

cept and hadrea of a circleratio area (A)did not defin

some other d tedious worvelop this Eqcle orientationribed (DC) cirasing perimeteation 19.

f perimeter (Pe factor (SF) be used as

mber of sampl

17

ericity formuwere based oum area). Th

A) and smalle14) as the rati

). The particrea outline (A

(13

(14

(15

d develop theme with diamete) and perimetene any defini

(16

(17

measuremenrk (at that timquation easy tn proposed brcles (Equatioer (PD) and th

(18)

(19)

P) to area (Adefined as tha reference t

les intervals o

78

la on he est io

le A)

3)

4)

5)

m er er te

6)

7)

nts me to by on he

)

)

A), he to or

V

F

Rbesidesugge

Rconfigconce1980)superi

Wroundcircleused Eon the

Vol. 18 [20

Figure 9: De

Roundness as e the corners ested many w

Roundness is cguration and erning about t), is describe imposed in th

Wadell (1935)dness of a par diameter (RmEquation 23 (e results (Wad

13], Bund.

escription of (S

ROUdescribed pand how theyays to describ

clearly underdenotes the

the sharpnessas the third o

he corners, an

) describes hirticle using thmax-in), see (N, is the numdell, 1935).

. A

the SukumaSukumaran a

UNDNESSreviously is y are, this wabe this second

standable usisimilarities w

or the smootorder subject nd it is also a p

is methodologhe average raFigure 11 an

mber of corne

aran factors tand Ashmaw

S OR ANGthe second o

as notice by md order particl

ing the Figurewith a spherthness of the (form is the fproperty of pa

gy, calling it adius of the cnd Equation 2ers). This two

to determinewy, 2001).

GULARITorder shape most of the aule property.

e 1. Particle sre (3D) or a perimeter (2D

first and rounarticles surfac

total degree corners (r) in 22. In the sam last Equation

e the shape a

TY descriptor. Suthors sited b

shape or formcircle (2D).

D). Surface tndness the secces between c

or roundnesn relation withme study Wadn shows sligh

17

and angularit

(20

(2

Sphericity lefbefore and the

m is the overaRoundness

texture (Barrecond), and it corners.

s to obtain thh the inscribedell (1935) hahtly difference

79

ty

0)

1)

fts ey

all is

et, is

he ed as es

V

ACi

PIt is idegreof get

Fi

Vol. 18 [20

Table 3:

Aspect ircularity

(2D)

d

owers (1953)important to e of subjectivtting errors is

igure 11: W

13], Bund.

General chr

Name

roundness

roundness

roundness

Circularity

outline circuladegree of circul

inscribed circsphericity

Circularity

Shape facto

) also publishhighlight tha

vity. Folk (19negligible fo

adell’s meth

. A

ronological o for 2

y

arity larity cle

y Kru

or S

ed a graphic at any compa955) concludeor sphericity b

hod to estimacircle (H

(22)

overview of 2D sphericity

Author

Pentland

Cox1

Tickell2

Horton2

Wadell Wadell

Riley

umbein and Sloss

Janoo

ukumaran

scale to illustaring chart toes that when cbut large for ro

ate the roundHawkins, 19

f the particle y.

Year

1927

1927

1931

1932

1935 1935

1941

1963

1998

2001 Seg

1) R2) H

trate the qualio describe parcharts are useoundness.

dness, corner993).

shape defini

Based o

area

area-perim

area

drainage b

Circle diamPerimet

Circle diam

chart

area-perim

gmentation of angles

Riley, 1941 Hawkins, 1993

itative measurticle propert

ed for classific

rs radius and

18

itions

on

meter

basin

meter ter

meter

t

meter

particle and s

ure (Figure 12ties has a higcation, the ris

d inscribed

(23)

80

2). gh sk

)

V

Sclassiis imp(1935

TabG

VeAn

Sub

Sub

Ro

We

Kround

Fa censubtenFigur

T(ANG

Vol. 18 [20

F

ome authors fication basedportant to de

5). This classi

ble 4: Degrerade terms

liery angular ngular 0

bangular 0

brounded 0

ounded 0

ell rounded 0

Krumbein anddness paramet

ischer in 193ntral point in nded by the se 14.

To express thGPLA) on the o

13], Bund.

Figure 12: A

as Russel & Td on five andenote that thefication and c

es of roundnRussell & Tayl

Class imits (R)

Am

N/A 0.00-0.15

0.15-0.30

0.30-0.50

0.50-0.70

0.70-1.00

d Sloss (1963)ters using com

3 (Hawkins, the outline

straight or no

he angularityoutlines and co

. A

A Roundness

Taylor in 193d six classes (e way they mclass limits ar

ness: Wadelllor (1937)

Arithmetic midpoint l

N/A 0.075 0

0.225 0

0.400 0

0.600 0

0.800 0

) published amparison. See

1993) used aand dividing

on-curved par

y value Fischoncave (ANG

s qualitative

37, Pettijohn iHawkins, 199measure the re showed in t

l Values. (HaPettijohn

Class limits (R)

N/A 0.00-0.15

0.15-0.25

0.25-0.40

0.40-0.60

0.60-1.00

a graphical che Figure 13. (C

a straightforwg the outline ts of the prof

her used theGCON) Equatio

scale (Powe

in 1957 and P93) each one roundness isthe Table 4.

awkins, 199n (1957)

Arithmetic midpoint

N/A 0.125

0.200

0.315

0.500

0.800

hart easy to dCho, et al. 20

ward method tin angles ar

file were mea

e ratio of anons 24 and 25

ers, 1953)

Powers in 195with its own

s the develop

3), N/A = noPowers

Class limits (R) 0.12-0.17 0.17-0.25

0.25-0.35

0.35-0.49

0.49-0.70

0.70-1.00

determine the 006).

to quantify roround this pasured. This i

ngles standin5 respectively

18

53 developed class limits;

ped by Wade

o-applicables (1953)

Arithmetic midpoint

0.14 0.21

0.30

0.41

0.59

0.84

sphericity an

oundness usinoint that weris illustrated i

ng linear par.

81

d a it

ell

e

nd

ng re in

rts

V

Figu

Fabove

Wparticdiamein miratio oaxis (

Vol. 18 [20

ure 13: Sphethat

Figure 1

igure 14 left e Equations. (

Wentworth in cle to obtain teter of a circlenimum projeof the radius B), see Equat

13], Bund.

ericity and rappears here

4: Fischer’s A=ins

(A) and righ(Hawkins, 199

1922 (Equatithe outline ore fitting the shection (SM). Wof curvature tion 27.

. A

oundness che in the chart

methods of scribed circl

ht (B), gives 93).

ion 26) used tr contour (Baharpest corneWentworth (Hof the most c

(24)

(26

hart. (Cho et,t is the wade

f angularity ce; B=circum

a similar ang

the maximumarret, 1980). Ter (DS) and theHawkins, 199convex part (R

)

, al., 2006). Tell’s Equatio

computation mscribed circ

gularity of ap

m projection tThe Equatione longest axis

93) also exprRCON) and the

The roundneon number 22

(Hawkins, 1cle

pproximately

to define the n reflects the s (L) plus the ressed the roue longest axis

18

ess Equation2

1993)

0.42 using th

position of threlation of thshortest axis

undness as ths (L) plus sho

(25)

(27)

82

n

he

he he c he ort

V

Apartic

Daxis ba, b an

W1980)the sh

Wthe av

C(EquacorneWentwEquat

Swcornehis Aperim

Langul

Vol. 18 [20

Actually thesecle is in its ma

Dimensions cab. The intentiond c are for 3

F

Wentworth 19) and it relateharpest corner

Wentworth (19verage radius

Cailleux (Barration 31). Kur (DS) and tworth roundntion 33.

wan in 1974 r(s) (DS1 and

Average roundmeter (PCON) an

Lees (1964a) darity instead

13], Bund.

e last two Equaximum proje

an be seen onon is to make D).

Figure 15: D

919 has a seces the diameter (DX).

922b), used dof the pebble

rett, 1980) reuenen in 1956the breath axness with the

shows his EqDS2) and ins

dness of outlnd the actual

developed anof the round

(31

. A

(

uations are thection.

n Figure 15, Ldifference be

Description o

cond way to er of the shar

define the roue (RAVG):

elates the rad6 show his roxis (B), Equarelation of sh

quation (Barrcribed circle line (Krumbeperimeter (P)

n opposite dedness, and he

(29)

)

(34)

he same, just

L and B repreetween the 2

of L and B a

express the rpest corner (D

undness as the

dius of the moundness indeation 32. Doharpest corner

rett, 1980) rediameter (DI

ein and Petti), Equation 35

finition to roe calls it Deg

t expressed in

esents the maand 3 dimens

axes (Hawkin

roundness caDS) and the d

e ratio of the

most convex ex (Barrett, 1

obkins & Folr (DS) and ins

lating the shaI), Equation 3ijohn, 1938) 5.

oundness, it mgree of angul

(32)

n different te

ayor axis a ansions (L and B

ns, 1993)

alled Shape idiameter of a

sharpest corn

part and th1980) betweelk (1970) usescribed circle

arpest (or the34. Szadeczsk

relating the

means that helarity. Figure

18

(35)

erms, when th

nd intermediaB are for 2D a

index (Barreta pebble troug

ner (RCON) an

he longest axen the sharpeed a modifie diameter (DI

e two sharpesky-Kardoss ha

concave par

e measures th 16 shows th

(28)

(30)

(33)

83

he

te as

tt, gh

nd

xis est ed I),

st) as rts

he he

V requirthe di

Inindivi

A(1998

Tthe deEquatbut it

Vol. 18 [20

rements consiistance (x). Se

n order to apidual result w

Figure 16

A roundness i8b) it is descri

The last Equatefinition furthtion that has bis a good exa

13], Bund.

idered when Eee Equation 3

pply the Equwill add to eac

6: Degree of

index appearibed as:

tion appears ahermore sombeen used tryiample of the m

. A

Equation 36 a36.

uation 36 corh other to obt

f angularity m

rs on Janoo (

also as a 2D dme authors ha

ing to define misuse of the

applies as the

rners needs ttain the final

measuremen

(1998), Kuo

descriptor becad used to dedifferent aspequantities an

e angles (α), i

to be entereddegree of ang

nt technique

and Freeman

cause there is efine the rougects (spherici

nd definitions.

inscribed circ

d in the formgularity.

(Blot and P

n (1998a) an

not a generalghness, this iity, roundness.

18

cle (Rmax-in) an

mula, and eac

(36

ye, 2008)

nd Kuo, et, a

l agreement ois not the onls or roughnes

(

(17)

84

nd

ch

6)

al.

on ly s)

V

Sunumbshown

Subecaube use

Asp

Round

Vol. 18 [20

Table

ukumaran anber of sharpnen in Figure 9:

ukumaran anuse it is the cued to describe

pect

dness shape in

shape in

roundne

Averagoutline

roundne

roundne

roundne

roundne

roundne

roundne

roundne

degree

Angula

13], Bund.

e 5: General

nd Ashmawyess corners (E:

nd Ashmawyut off betweene the roughne

Name

ndex

ndex

ess

e roundness of

ess

ess

ess

ess

ess

ess

ess

of angularity

rity factor

. A

chronologic

y (2001) presEquation 37).

y (2001) also n angularity fass.

A

Wentwort

Wentwort

Wentwort

Fischer

Fischer

Szadeczsk

Wadell

Wadell

Russel &

Krumbein

Cailleux

Pettijohn

Powers

Kuenen

Krumbein

Lees

Dobkins &

Swan

SukumaraAshmawy

cal overview

sent an anguAngles βi req

suggested usfactor and surf

Author

th

th

th

ky-Kardoss

Taylor

n

n and Sloss

& Folk

an and y

w of the parti

1) B2) H3) K4) P

ularity factor quired to obta

se not bigger face roughnes

Year

19191 diam

1922b shar

1933 conv

19332 nonc

19332 nonc

19333 conv

1935 diam

1935 diam

19372 clas

1941 char

19471 conv

19494 clas

1953 char

19561 axis

1963 char

1964a corncircl

1970 diam

19741 diam

2001 Segmangl

icle roundne

Barret, 1980 Hawkins, 1993 Krumbein and PettiPowers, 1953

(AF) calculain the angula

sampling intss. If so this E

Based on

meter of sharper

rpest corner and

vex parts

curved parts out

curved-straight p

vex parts-perime

meter of corners

meter of corners

s limit table

rt

vex parts

s limit table

rt and class limit

s-convex corner

rt ners angles and ile

meter of sharper

meter of sharper

mentation of parles

18

ss

ijohn, 1938

lated from tharity factor ar

terval of N=4Equation coul

n

corner

axis

tline

parts outline

eter

t table

inscribed

corner

corners

rticles and

(37)

85

he re

40 ld

V

Aroundwith t

WaggresynthtimesThe leThe d

Fig

Hhere i

Odefine

Tbetwe

Vol. 18 [20

A third propedness propertithe authors, at

Wright in 195gate using stetic resin. Th. The unevenength was the

difference betw

ure 17: Mea

However, withis presented so

One techniqueed as the ratio

The convex peen the touchi

Figu

13], Bund.

ROUGHerty called ties, since thent that time, no

5 developed tudies done ohe stones wernness of the sen compared ween these tw

asurement m

h the advanceome research

e used by Janoo between per

perimeter is oing points tha

ure 18: (a) C

. A

HNESS ORexture appean, texture proot measurable

a method to qon 19 mm stre cut in thin urface was trwith an unev

wo lines was d

method for ch(Ja

e of technoloher’s ideas how

oo (1988) to drimeter (P) an

obtained usinat the Feret’s b

Convex perim(modified

R SURFAars early in operty was lone.

quantify the stones. The tesections. The

raced and theven line drawdefined as the

haracterizinganoo, 1998)

ogy it has becw this propert

define the round convex per

ng the Feret’box describes

meter (CPER)after Janoo,

ACE TEXTthe literaturnged describe

surface texturst aggregatese sections proe total length wn as a seriese roughness fa

g the surface

come easier mty should be c

ughness can brimeter (CPER)

’s box (or ds each time it

), (b) Feret m, 1998)

TURE e with the sed but it was

re or roughnes were first eojection was of the trace w

s of chords (sfactor. (Janoo

e texture of a

measure the calculated.

be seen in Fig).

diameter) tendis turn (Figur

measurement

18

sphericity an in accordanc

ess of concretembedded in magnified 12was measuredsee Figure 171998).

an aggregate

roughness an

gure 18a and

ding a line ire 18b).

t

(38)

86

nd ce

te a

25 d.

7).

nd

is

in

V

Kratio p

EErosiosurfacthe redimencycleserosio

Mratio, invest

TThis iperimconve

Haccuraworks

Vol. 18 [20

Kuo and Freemperimeter (P)

Erosion and don is a morphce, which leaeverse processnsion by addis are not stanon-dilatation (

Mora and CR” (Equati

tigation, they

Figur

The convex aris illustrated

meter but in thex area

TECHN

Hand measureacy special ds placing the

13], Bund.

man (1998a) and average

dilatation imahological procaves the objecs of erosion ang pixels arou

ndardized. A (Equation 40)

ion 41) and tare:

re 19: Evalu

rea is the areain the Figure

his case the a

NIQUES

ment techniqdevices develsample on th

. A

and Kuo et adiameter (DA

age processincess by whichct less dense and a single dund its boundrepresents the).

Kwan the “fullness

ation of area

a of the minie 19. The conarea between

S TO DE

HAND Mque was the filoped as the he sliding roa

(39)

(41)

al., (1998b) uAVG), Equation

g techniques h boundary imalong the pe

dilatation cycdary (Pan et ae original are

(2000) uratio, FR” (E

a and convex

mum convexnvex area is othe original

ETERMIN

MEASUREirst used by o“sliding rod

ad calliper as

)

)

use the roughn 39.

are used to mage pixels a

erimeter or oucle increases al., 2006). Thea and A1 is

used the Equation 42)

x area (Mora

x boundaries cobtained in a outline and t

NE PART

EMENT obvious reasod caliper” use

show Figure

hness (RO) de

obtain the suare removed uter boundarythe particle s

he “n” erosionthe area after

“conin

a and Kuan,

circumscribina similar way the convex pe

TICLE S

ons, in order ted by Krumbe 20b the leng

18

efinition as th

urface texturfrom an objey. Dilatation shape or imagn and dilatatior “n” cycles o

nvexity the

2000)

ng the particlas the conve

erimeter is ou

SHAPE

to improve thbein (1941), gth in differen

(40)

(42)

87

he

re. ct is

ge on of

eir

le. ex ur

he it nt

V positiactualshape20a shcurvarock fshow

F(W

(Kru

Athe papartic

Fi

Spropeand eaggrevalue

Vol. 18 [20

ons can be oblly used by op

e analysis (Wehows (the tw

ature; or the “fragment, so, equipment.

Figure 20: (aWenworth, 19

umbein, 194

Another helpfuarticle’s contocle’s diameter

igure 21: Ci

ieving, e.g. aerties. By comelongation indgate particlessuch as 5:1.

13], Bund.

btain by usinpticians to mentworth, 192

wo adjacent pi“Szadeczky-K

the outline tr

a) convexity922b), (b) sli41) and c) Sz

ul tool to deteour over a cirr.

ircle scale us

according to mbining meshdex, ASTM Ds that have aThe index re

. A

ng the scale prmeasure the cu22b) works mivots are inva

Kardoss’s appraced is then

y gage, used iding rod calzadeczky-Ka

the pa

ermine the parcle scale app

sed by Wader

SIEVEEN 933-3:1

h geometries tD4791 (Flat

a ratio of lengepresents the p

rovided in thurvature of len

measuring the ariable) as maparatus” devel

analyzed (Kr

to determineliper, deviceardoss (1933article outlin

article dimensearing in Figu

ell (1935) to oundness

E ANALYS1997, can bethe obtained rand elongate

gth to thicknpercentage on

he handle; thenses but easimovement ofany the centrlop in 1933 trumbein and P

e the curvatue to measure 3) apparatus,ne.

sions was thegure 21, thus i

determine p

SIS e used to detresults can beed particles a

ness equal to n weight of th

e “convexity gly applicable f the central pral pivot movthat traces thePettijohn, 193

ure in particlthe particle it was utiliz

e “camera lucit is possible

particle’s dia

termine simpe used to quaare defined aor greater th

hese particles

18

gage” that wa to the particpivot as Figurves more is the profile of th38) Figure 20

le corners axis length

zed to obtain

cida” to projeto measure th

ameter and

ple large scaantify flakinesas those coarshan a specifies). The metho

88

as le re he he 0c

n

ct he

le ss se ed od

V is notthe sieEN 9from fractiothe pafoundstandausing compKwanthe teis theadvan

Crequirfor pdifficu

Acharacroundchart

Atwo mthat edefini

Fdetermthat thhe conhis stu

Vol. 18 [20

t suitable for eve, and the g33-3:1997 re4 mm and uon and the searticles is ob

d, finally witards related wsieve analys

uters age andn, 2000; Perssesting time coe error due thntages are mo

Charts develored when meebbles whichult to measur

Fig

A qualitative ccteristics, it w

ded, rounded was prepared

A new chart inmean propertieliminated thitions. (Krum

olk (1955) wmination of sphe sphericity ncluded, it waudy.

13], Bund.

fine materialgreat amount lated to flaki

up to 63 mm. econd use a bbtain and witth this two pwith the partisis to determid image analyson, 1998). Inompare with the overlappinre compare w

ped over theasuring each h were mease due to the s

gure 21: Kru

chart by Powewas divided oand well rou

d with photogr

ncluding spheies of particlhe subjectivit

mbein and Slos

worried abouphericity anddeterminatioas necessary t

. A

ls. This due tof particles i

iness index. two sieving

bar sieve, afteth the secondparameters thicle shape butine particle’sysis sieving rndustry is alsothe traditionang or hiding

with disadvant

CHART Ce necessity oparticle. Kru

sured by Waecond order s

umbein (194

ers (1953) tryon six roundnunded) and twraphs to enha

ericity and roe’s shape, futy of qualitass, 1963). (Se

ut the persoangularity (h

n by chart coto carry out a

to the difficuln relation to tThe test is poperations a

er the first sied sieving (bahe flakiness t, this above geometrical

research is tako applying thl sieving metof the partic

tages (Anders

COMPARof faster resuumbein (1941adell’s methoscale that roun

41) comparis

y to include bness ranges (vwo sphericityance the reade

oundness appeurthermore, thative descriptee Figure 13).

on’s error onhe used the Poomparison hasa more wide r

lty to get the the area of th

performed on are necessary,eving the avear sieving) th

index is depresented areproperties. S

king place (Ae image analythod. An incocles during thson, 2010).

RISON ults because 1) present a cod because thndness repres

son chart for

both (sphericitvery angular,y series (higher perspective

ear, this timehere was incltion. The ch

n the chart’owers 1953 cs a negligibleresearch due t

fine grains phe sieve (Persn aggregates w, the first sep

erage maximuhe shortest axetermined. The probably thSieve analysiAndersson, 20ysis sieving wonvenient of ithe capture p

the long timcomparison rohis property sents. (See Fi

r roundness

ty and roundn, angular, subh and low spe. (See Figure

e it was easierluded the numhart is based

s comparisocomparison che error while the high varia

18

passed througson, 1998) e.with grain sizparates on sizum diameter oxis diameter here are morhe most knows is facing th010; Mora anwith decrees oimage analys

process but th

me consuminoundness chawas the mogure 22).

ness) particleb-angular, subphericity). The 12)

r to handle thmerical value

d on Wadell

on studied thhart), he founthe roundnes

ability show b

89

gh g. ze ze of is re

wn he nd on sis he

ng art ost

’s b-

his

he es ’s

he nd ss, by

V

Imautom

-

-

-

Fth

Vol. 18 [20

mage analysismated. Differe

Feret Diamcan rotate 22 (left) tto determin

Fourier Teindividual textural feentrant ang(right).

Fractal Dimand Vallejof the fract

Figure 22: (lehe particle to

te

13], Bund.

s is a practicaent techniques

meter: the Feraround one phese method ne diameters

echnique: It particles (Eq

eatures for grgles in order

mension: Irreo, 1997), Figtal line can be

eft) Feret meadefine the shoechnique with

. A

IMAGEal method to us appear to pr

ret diameter iparticle, or ouis not a fine (Janoo, 1988

produces maquation 43). anular soils. to complete

egular line at gure 23 showse defined as E

asurement techortest and lonh two radiuses

E ANALYSuse for shaperocess these im

is the longituutline, to defidescriptor, bu)

athematical reThis methodThe problemthe revolutio

any level of s fractal analyEquation 44.

hnique is defingest Feret dias at one angle

YSIS e classificatiomages, among

ude between tfine dimensionut as it was s

elations that d favours the m in the methon (Bowman

f scrutiny is bysis by the d

ined by two pameter (Janooe (Bowman et

n since it is fg them are:

two parallel lns, as it is shay above it is

characterize analysis of

hodology remet al., 2001),

by definition dividing meth

parallel lines to, 1988), (right al., 2001)

19

fast and can b

lines, this linehown in Figurs a helpful too

the profile oroughness an

mains in the re see Figure 2

fractal (Hysliod. The lengt

turning arounht) Fourier

(43)

(44)

90

be

es re ol

of nd e-22

ip th

nd

V

-

-

-

Lcan se

Adigitaanalyparticresolu

Wbetter

Vol. 18 [20

Figure 2

Orthogonabetween thtechniques

Laser Scantechniquesparticles hthe lower Tolppanen

Laser-Aidesurveying as to use lcertain per

Figure 2

Last two 3D teee in Figure 2

All these preval way obtainisis regarding

cles; orientatioution have an

When resolutir with the real

13], Bund.

23: Fractal an

al image analyhem to acquirs can be used

nning Technis. In Figures have control p

part, in Fign, 2002).

ed Tomograp(see Figure 2iquid with sarcent of light

4: a) Scanni

echniques obt25 (right).

vious techniqing the desireon the errors

on is not releinfluence on

ion is increasl form, in the

. A

nalysis by th(Hyslip a

ysis: This tecre the three pain this orthog

ique: this kin24a) is show

points in ordegure 24b) it

phy (LAT), in25, left)). Thiame refractivego through. (M

ing head, b)

tain the partic

ques are easiled measuremes involve, amvant when it the accuracy

se more accuother hand, m

he dividing mnd Vallejo,

chnique is basarticle dimensgonal way.

nd of laser scwed the laserer to keep a r

can be see

n this case a lis technique ie index as theMatsushima e

scanning pat

cle shape that

ly written in ent, but there

mong them areis random an. (Zeidan et a

uracy is obtamore resolutio

method at dif1997)

sically the usesions (Fernlu

canning 3D isr head scann

reference pointhe laser pa

laser sheet is is different ane particles, paet al., 2003).

th (Lanaro a

t is later used

codes or scrare some inte

e image resolnd large numbal., 2007)

ain and the oon means mor

fferent scrut

e of two imagund, 2005), an

s one of the mning the rocknt when moveath followed

used to obtaind has speciaarticles must

and Tolppane

d to achieve m

ripts to be ineresting pointlution and oriber of particl

object represere spending o

19

tiny scale

ges orthogonny of the abov

most advancek particles, the them to sca. (Lanaro an

in the particleal requiremenlet the laser o

en, 2002)

measures as w

nterpreted in ts in the imagientation of thes are involv

entation matcon memory an

91

al ve

ed he an nd

es nts or

we

a ge he e;

ch nd

V time; (Schä

Srelativbut nsimilaoutpuperim

IndefiniKrumused Arasadifferthree singledescriliteratis notroundProbato rec

Manalyagreemother

T(3-dim

Vol. 18 [20

thus, resolutäfer, 2002).

Figure 25: c

chäfer (2002ve high errorot for perimear results wheut for those tmeter should b

Tn order to desitions (qualit

mbein, 1941; Sto simplify t

an et al., 201rent scales. Thsub-quantitie

e definition iptors are expture that manyt a clear meadness, does it ably they coulcognize in mo

Many image asis, fractal dment on the applications.

There are sevemensions, 3-d

13], Bund.

tion needs to

(left) LAT scompleted an

) conclude ths. It can be veter that keepen 3 differentterms/quantit

be treated with

TERMS, Qscribe the partative and qSneed & Folkthe complexit10) are usinghe terms are es are probabcan interpret

plained, and ty of the shap

aning on whameans that th

ld be on theorost of the case

analysis techndimension, tousage or con

eral shape desdimension ort

. A

o be accordin

scaning partind mesh gen

hat attributes vanish or at lp the error ast resolutions ties that invoh care.

DIS

QUANTITrticle shape i

quantitative) k, 1958). Allty of shape d

g three sub-qumorphology/

bly the best wt the whole these three sce descriptors t this descriphe angularityry but not in s.

IMAGEniques had beomography, nclusion to en

criptors and athogonal and

ng with the g

icles (Matsunerated. (Mat

like length east diminishs big as initiwere used in

olve the peri

SCUSSI

TIES ANDin detail, therused in the

l mathematicadescription. Suantities; one/form, roundnway to classif

morphologyales represenare presented

ptor defines, ey never ends?

reality. Physi

E ANALYeen used to detc., (Hyslipnsure the bes

also various td 2-dimension

goal and prec

ushima et al.,tsushima et a

when measurh using high rially. Johanss

n the same paimeter. Thus

ON

D DEFINIre are a numb literature (al definitionsSome authore and each dness and surfafy and describy. Common nt an option. Id with the same.g. when the Could they bical meaning

SIS describe the

p and Vallejost particle des

techniques to ns). Each tech

cision needed

, 2003), (righal., 2003)

ring digital iresolution jusson and Vall article obtainin

all quantitie

ITIONS ber of terms, (e.g. Wadell,s (quantitatives (Mitchell &

describing theace texture (Fbe a particle language is

It is evident inme name but ere is no uppbe more and of the quanti

particle shapo, 1997) butscriptor for g

capture the phnique presen

19

d in any work

ht) 3D scan

images presenst for diamete(2011) obtai

ng an unstabes relating th

quantities an, 1932, 1934es) are mode& Soga, 2005e shape but Figure. 1). Th

because not needed whe

n the reviewealso that ther

per limit in thmore angular

ities is difficu

pe, e.g. Fouriet there is no

geotechnical o

particles profints advantage

92

k.

nt er in le he

nd 4;

els 5; at he a

en ed re he r?

ult

er ot or

le es

Vol. 18 [2013], Bund. A 193 and disadvantages. 3-dimensions is probably the technique that provide more information about the particle shape but the precision also lies in the resolution; the equipment required to perform such capture could be more or less sophisticated (scanning particles laying down in one position and later move to complete the scanning or just falling down particles to scan it in one step). 3-dimensions orthogonal, this technique use less sophisticated equipment (compare with the previous technique) but its use is limited to particles over 1cm, also, information between the orthogonal pictures is not capture. 2-dimensions require non sophisticated equipment but at the same time the shape information diminish compare with the previous due the fact that it is possible to determine only the outline; as the particle measurements are performed in 2-dimensions it is presumed that they will lie with its shortest axis perpendicular to the laying surface when they are flat, but when the particle tends to have more or less similar axis the laying could be random.

Advantages on the use of image analysis are clear; there is not subjectivity because it is possible to obtain same result over the same images. Electronic files do not loose resolution and it is important when collaboration among distant work places is done, files can be send with the entire confidence and knowing that file properties has not been changed. Technology evolutions allowed to work with more information and it also applies to the image processing area were the time consumed has been shortened (more images processed in less time).

One important aspect in image analysis is the used resolution in the analysis due the fact that there are measurements dependent and independent on resolution. Thus, those dependent measurements should be avoided due the error included when they are applied, or avoid low resolution to increase the reliability. Among these parameters length is the principal parameter that is influences by resolution (e.g. perimeter, diameter, axis, etc.). Resolution also has another aspect with two faces, quality versus capacity, more resolution (quality) means more storage space, a minimum resolution to obtain reasonable and reliable data must be known but it depend on each particular application.

APPLICATIONS Quantify changes in particles, in the author’s thought, is one of the future applications due the

non-invasive methods of taking photographs in the surface of the dam’s slope, rail road ballast or roads. Sampling of the material and comparing with previous results could show volume (3D analysis) or area (2D analysis) loss of the particles as well as the form, roundness and roughness. This is important when it has been suggested that a soil or rock embankment decrees their stability properties (e.g. internal friction angle) with the loss of sphericity, roundness or roughness.

Seepage, stock piling, groundwater, etc., should try to include the particle shape while modelling; seepage requires grading material to not allow particles move due the water pressure but in angular materials, as it is known, the void ratio is great than the rounded soil, it means the space and the possibilities for the small particles to move are greater; stock piling could be modelled incorporating the particle shape to determine the bin’s capacity when particle shape changes (void ratio changes when particle shape changes) Modelling requires all information available and the understanding of the principles that apply.

Industry is actually using the particle shape to understand the soil behaviour and transform processes into practical and economic, image analysis has been included in the quality control to determine particle shape and size because the advantages it brings, e.g. the acquisition of the sieving curve for pellets using digital images taken from conveyor, this allows to have the

Vol. 18 [2013], Bund. A 194 information in a short period of time with a similar result, at least enough from the practical point of view, as the traditional sieving.

CONCLUSIONS • A common language needs to be built up to standardize the meaning on geotechnical field

that involve the particle shape.

• Based on this review it is not clear which one is the best descriptor.

• Image analysis tool is objective, make the results repeatable, obtain fast results and work with more amount of information.

• Resolution needs to be taken in consideration when image analysis is been carried out because the effects could be considerable. Resolution must be set according to the necessities. Parameters as perimeter can be affected by resolution.

• There are examples where particle shape has been incorporated in industries related to geotechnical engineering, e.g. in the ballast and asphalt industry for quality control.

FURTHER WORK Three main issues have been identified in this review that will be further investigated; the

limits of shape descriptors (quantities) influence of grading and choice of descriptor for relation to geotechnical properties.

Shape descriptors have low and high limits, frequently the limits are not the same and the ability to describe the particle’s shape is relative. The sensitivity of each descriptor should be compare to apply the most suitable descriptor in each situation.

Sieving curve determine the particle size in a granular soil, particle shape could differ in each sieve size. There is the necessity to describe the particle shape on each sieve portion (due to practical issues) and included in the sieve curve. Obtain an average shape in determined sieve size is complicated (due to the possible presence of several shapes) and to obtain the particle shape on the overall particle’s size is challenging, how the particle shape should be included?

Since several descriptors have been used to determine the shape of the particles but how is the shape related with the soil properties? It is convenient to determine the descriptor’s correlation with the soil properties.

REFERENCES 1. Andersson T. (2010) “Estimating particle size distributions based on machine vision”.

Doctoral Thesis. Department of Computer Science and Electrical Engineering. Luleå University of Technology. ISSN: 1402-1544. ISBN 978-91-7439-186-2

2. Arasan, Seracettin; Hasiloglu, A. Samet; Akbulut, Suat (2010) “Shape particle of natural and crished aggregate using image analysis”. International Journal of Civil and Structural Engineering. Vol. 1, No. 2, pp. 221-233. ISSN 0970-4399

Vol. 18 [2013], Bund. A 195

3. Aschenbrenner, B.C. (1956) “A new method of expressing particle sphericity”. Journal of Sedimentary Petrology. Vol., 26, No., 1, pp. 15-31.

4. Barton, Nick & Kjaernsli, Bjorn (1981) “Shear strength of rockfill”. Journal of the Geotechnical Engineering Division, Proceedings of the American Society of Civil Engineers (ASCE) Vol. 107, No. GT7.

5. Barrett, P. J. (1980) “The shape of rock particles, a critical review”. Sedimentology. Vol. 27, pp. 291-303.

6. Blott, S. J. and Pye, K., (2008) “Particle shape: a review and new methods of characterization and classification”. Sedimentology. Vol. 55, pp. 31-63

7. Bowman, E. T.; Soga, K. and Drummond, W. (2001) “Particle shape characterization using Fourier descriptor analysis”. Geotechnique. Vol. 51, No. 6, pp. 545-554

8. Cho G., Dodds, J. and Santamarina, J. C., (2006) “Particle shape effects on packing density, stiffness and strength: Natural and crushed sands”. Journal of Geotechnical and Geoenvironmental Engineering. May 2006, pp. 591-602.

9. Dobkins, J. E. and Folk, R. L. (1970) “Shape development on Tahiti-nui”. Journal of Sedimentary Petrology. Vol. 40, No. 2, pp. 1167-1203.

10. Folk, R. L. (1955) “Student operator error in determining of roundness, sphericity and grain size”. Journal of Sedimentary Petrology. Vol. 25, pp. 297-301.

11. Fernlund, J. M. R. (1998) “The effect of particle form on sieve analysis: A test by image analysis”. Engineering Geology. Vol. 50, No. 1-2, pp. 111-124.

12. Fernlund, J. M. R. (2005)” Image analysis method for determining 3-D shape of coarse aggregate”. Cement and Concrete Research. Vol. 35, Issue 8, pp. 1629-1637.

13. Fernlund, J. M. R.; Zimmerman, Robert and Kragic, Danica (2007) “Influence of volume/mass on grain-size curves and conversion of image-analysis size to sieve size”. Engineering Geology. Vol. 90, No. 3-4, pp. 124-137.

14. Hawkins, A. E. (1993) “The Shape of Powder-Particle Outlines”. Wiley, New York.

15. Hyslip, James P.; Vallejo, Luis E. (1997) “Fractal analysis of the roughness and size distribution of granular materials”. Engineering Geology. Vol. 48, pp. 231-244.

16. Janoo, Vincent C. (1998) “Quantification of shape, angularity, and surface texture of base course materials”. US Army Corps of Engineers. Cold Region Research and Engineering Laboratory. Special report 98-1.

17. Johansson, Jens and Vall, Jakob (2011) “Jordmaterials kornform”. Inverkan på Geotekniska Egenskaper, Beskrivande storheter, bestämningsmetoder. Examensarbete. Avdelningen för Geoteknologi, Institutionen för Samhällsbyggnad och naturresurser. Luleå Tekniska Universitet, Luleå. (In Swedish)

18. Krumbein, W. C. and Pettijohn, F.J. (1938) “Manual of sedimentary petrography”. Appleton-Century Crofts, Inc., New York.

19. Krumbein, W. C. (1941) “Measurement and geological significance of shape and roundness of sedimentary particles”. Journal of Sedimentary Petrology. Vol. 11, No. 2, pp. 64-72.

Vol. 18 [2013], Bund. A 196

20. Krumbein, W. C. and Sloss, L. L. (1963) “Stratigraphy and Sedimentation”, 2nd ed., W.H. Freeman, San Francisco.

21. Kuo, Chun-Yi and Freeman, Reed B. (1998a) “Image analysis evaluation of aggregates for asphalt concrete mixtures”. Transportation Research Record. Vol. 1615, pp. 65-71.

22. Kuo, Chun-Yi; Rollings, Raymond and Lynch, Larry N. (1998b) “Morphological study of coarse aggregates using image analysis”. Journal of Materials in Civil Engineering. Vol. 10, No. 3, pp. 135-142.

23. Lanaro, F.; Tolppanen, P. (2002) “3D characterization of coarse aggregates”. Engineering Geology. Vol. 65, pp. 17-30.

24. Lees, G. (1964a) “A new method for determining the angularity of particles”. Sedimentology. Vol., 3, pp. 2-21

25. Lees, G. (1964b) “The measurement of particle shape and its influence in engineering materials”. British Granite Whinstone Federation. Vol., 4, No. 2, pp. 17-38

26. Matsushima, Takashi; Saomoto, Hidetaka; Matsumoto, Masaaki; Toda, Kengo; Yamada, Yasuo (2003) “Discrete element simulation of an assembly of irregular-shaped grains: Quantitative comparison with experiments”. 16th ASCE Engineering Mechanics Conference. University of Washington, Seattle. July 16-18.

27. Mitchell, James K. and Soga, Kenichi (2005) “Fundamentals of soil behavior”. Third edition. WILEY.

28. Mora, C. F.; Kwan, A. K. H.; Chan H. C. (1998) “Particle size distribution analysis of coarse aggregate using digital image processing”. Cement and Concrete Research. Vol. 28, pp. 921-932.

29. Mora, C. F. and Kwan, A. K. H. (2000) “Sphericity, shape factor, and convexity measurement of coarse aggregate for concrete using digital image processing”. Cement and Concrete Research. Vol. 30, No. 3, pp. 351-358.

30. Pan, Tongyan; Tutumluer, Erol; Carpenter, Samuel H. (2006) “Effect of coarse aggregate morphology on permanent deformation behavior of hot mix asphalt”. Journal of Transportation Engineering. Vol. 132, No. 7, pp. 580-589.

31. Pellegrino, A. (1965) “Geotechnical properties of coarse-grained soils”. Proceedings. International Conference of Soil Mechanics and Foundation Engineering. Vol. 1, pp. 97-91.

32. Pentland, A. (1927) “A method of measuring the angularity of sands”. MAG. MN. A.L. Acta Eng. Dom. Transaction of the Royal Society of Canada. Vol. 21. Ser.3:xciii.

33. Persson, Anna-Lena (1998) “Image analysis of shape and size of fine aggregates”. Engineering Geology. Vol. 50, pp. 177-186.

34. Powers, M. C. (1953) “A new roundness scale for sedimentary particles”. Journal of Sedimentary Petrology. Vol. 23, No. 2, pp. 117-119.

35. Pye, W. and Pye, M. (1943) “Sphericity determination of pebbles and grains”. Journal of Sedimentary Petrology. Vol. 13, No. 1, pp. 28-34.

36. Quiroga, Pedro Nel and Fowle, David W. (2003) “The effects of aggregate characteristics on the performance of portland cement concrete”. Report ICAR 104-1F. Project number 104. International Center for Aggregates Research. University of Texas.

Vol. 18 [2013], Bund. A 197

37. Riley, N. A. (1941) “Projection sphericity”. Journal of Sedimentary Petrology. Vol. 11, No. 2, pp. 94-97.

38. Rousé, P. C.; Fennin, R. J. and Shuttle, D. A. (2008) “Influence of roundness on the void ratio and strength of uniform sand”. Geotechnique. Vol. 58, No. 3, 227-231

39. Santamarina, J. C. and Cho, G. C. (2004) “Soil behaviour: The role of particle shape”. Proceedings. Skempton Conf. London.

40. Schäfer, Michael (2002) “Digital optics: Some remarks on the accuracy of particle image analysis”. Particle & Particle Systems Characterization. Vol. 19, No. 3, pp. 158-168.

41. Shinohara, Kunio; Oida, Mikihiro; Golman, Boris (2000) “Effect of particle shape on angle of internal friction by triaxial compression test”. Powder Technology. Vol. 107, pp.131-136.

42. Skredkommisionen (1995) ”Ingenjörsvetenskapsakademinen”, rapport 3:95, Linköping 1995.

43. Sneed, E. D. and Folk, R. L. (1958) “Pebbles in the Colorado river, Texas: A study in particle morphogenesis”. Journal of Geology. Vol. 66, pp. 114-150.

44. Sukumaran, B. and Ashmawy, A. K. (2001) “Quantitative characterisation of the geometry of discrete particles”. Geotechnique. Vol. 51, No. 7, pp. 619-627.

45. Szádeczy-Kardoss, E. Von (1933) “Die bistimmung der abrollungsgrades”. Geologie und paläontologie. Vol. 34B, pp. 389-401. (in German)

46. Teller, J. T. (1976) ”Equantcy versus sphericity”. Sedimentology. Vol. 23. pp. 427-428.

47. Tickell, F. G. (1938)” Effect of the angularity of grain on porosity and permeability”. bulletin of the American Association of Petroleum Geologist. Vol. 22, pp. 1272-1274.

48. Tutumluer, E.; Huang, H.; Hashash, Y.; Ghaboussi, J. (2006) “Aggregate shape effects on ballast tamping and railroad track lateral stability”. AREMA 2006 Annual Conference, Louisville, KY.

49. Wadell, H. (1932) “Volume, Shape, and roundness of rock particles”. Journal of Geology. Vol. 40, pp. 443-451.

50. Wadell, H. (1933) “Sphericity and roundness of rock Particles”. Journal of Geology. Vol. 41, No. 3, pp. 310–331.

51. Wadell, H. (1934) “Shape determination of large sedimental rock fragments”. The Pan-American Geologist. Vol. 61, pp. 187-220.

52. Wadell, H. (1935) “Volume, shape, and roundness of quartz particles”. Journal of Geology. Vol. 43, pp. 250-279.

53. Wentworth, W. C. (1922a) “The shape of beach pebbles”. Washington, U.S. Geological Survey Bulletin. Vol. 131C, pp. 75-83.

54. Wentworth, W. C. (1922b) “A method of measuring and plotting the shape of pebbles”. Washington, U.S. Geological Survey Bulletin. Vol. 730C, pp. 91-114.

55. Wentworth, W. C. (1933) “The shape of rock particle: A discussion”. Journal of Geology. Vol. 41, pp. 306-309.

Vol. 18 [2013], Bund. A 198

56. Witt, K. J.; Brauns, J. (1983) “Permeability-Anisotropy due to particle shape”. Journal of Geotechnical Engineering. Vol. 109, No. 9, pp. 1181-1187.

57. Zeidan, Michael; Jia, X. and Williams, R. A. (2007) “Errors implicit in digital particle characterization”. Chemical Engineering Science. Vol. 62, pp. 1905-1914.

© 2013 EJGE