Title Particle Shape Quantities and Influence On

TITLE

PARTICLE SHAPE QUANTITIES AND INFLUENCE ON GEOTECHNICAL PROPERTIES – A REVIEW

Juan Manuel Rodriguez Zavala

Division of Mining and Geotechnical Engineering

Department of Civil, Environmental and Natural Resources

Luleå University of Technology

PREFACE

The work in this report has been carried out at the Division of Mining and Geotechnical Engineering at Luleå University of Technology.

In this new journey, now as a Ph.D. student I have face new questions and challenges that have improved myself not only as a student but also as a person. It has been not easy but the fellowship environment with professors, students, technicians, etc., all in general friends benefits the daily discussion and the interchange of ideas.

The intention of the report is to build up a starting point from where the research on particle shape developed by the author will take place. It is also the intention to present the general overview on particle shape research and make it understandable for all readers. Particle shape research is a wide area and the author focus the report in Geotechnical Engineering. The report has been split in chapters with the intention to describe first how the measurements were developed in time and according with authors follow by the techniques used to measure the particle’s dimensions. It is also included those properties found in literature affected by the particle’s shape. Finally findings are discussed with the proper conclusion.

I appreciate the time taken by my supervisors Sven Knutsson and Tommy Edeskär to address me in the right direction, the support they always gave me and they for sure will give me in the near future, I also must be grateful to my colleague Jens Johansson who previous work, experience on the image analysis and discussions has been of great value and help.

I would like to thank my family by the support they gave me this last two years in the work and the joy they provide me during our spare time, I understand it has not been easy for them ether and I appreciate them effort.

Juan Rodriguez Luleå 2012

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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 as well as reported effects of shape on granular material behaviour.

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.

Empirical relations and standards had been developed to relate soil properties, e.g. internal friction angle, minimum and maximum void ratio, density, permeability, strain, with the particle shape. The use of the relations and standards enhance the bulk material performance e.g. asphalt mixtures and rail road ballast.

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 many advantages. But the resolution in the processed image needs to be considered since it influence descriptors such as e.g. the perimeter.

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1 INTRODUCTION ...... 1 2 AIM AND GOAL ...... 3 3 DESCRIPTION OF SHAPE PROPERTIES ...... 3 3.1 INTRODUCCTION ...... 3 3.2 SCALE DEPENDENCE ...... 4 3.3 FORM (3D)...... 5 3.4 FORM (2D)...... 9 3.5 ROUNDNESS OR ANGULARITY ...... 11 3.6 ROUGHNESS OR SURFACE TEXTURE ...... 18 4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE SHAPE ...... 20 4.1 HAND MEASUREMENT ...... 20 4.2 SIEVE ANALYSIS ...... 21 4.3 CHART COMPARISON ...... 21 4.4 IMAGE ANALYSIS ...... 23 5 EFFECT OF SHAPE ON SOIL PROPERTIES ...... 25 5.1 INTRODUCTION ...... 25 5.2 INFLUENCE OF SIZE AND SHAPE ...... 28 5.3 VOID RATIO AND POROSITY ...... 29 5.4 ANGLE OF REPOSE...... 32 5.5 SHEAR STRENGTH...... 33 5.6 SEDIMENTATION PROPERTIES ...... 36 5.7 HYDRAULIC CONDUCTIVITY, PERMEABILITY...... 37 5.8 LIQUEFACTION ...... 39 5.9 GROUNDWATER AND SEEPAGE MODELLING ...... 40 6 DISCUSSION ...... 40 6.1 TERMS, QUANTITIES AND DEFINITIONS...... 40 6.2 PROPERTIES ...... 41 6.3 IMAGE ANALYSIS ...... 42 6.4 APPLICATIONS ...... 43 7 CONCLUSIONS ...... 43 8 FURTHER WORK ...... 44 9 ACKNOWLEDGMENT ...... 44 10 REFERENCES ...... 44

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ABBREVIATIONS Symbol Description Units A Area of the projected particle, area of the particle outline (2D) m2 A1 Area of the projected particle after “n” dilatation-erosion cycles m2 2 AC Area of the smallest circumscribed circle m 2 AC2 Area of circle with diameter equal to longest length of outline m 2 ACON Convex area m AF Sukumara angularity factor - ANGCON Angles subtending convex parts of the outline degree (º) ANGPLA Angles subtending plane parts of the outline degree (º) a Longest axes diameters of the particle m B Greatest breadth perpendicular to L m b Medium axes diameters of the particle m C Circularity - CR Convexity ratio - c Shorter axes diameters of the particle m

Co Cohesion Pa CPER Convex perimeter m DA Diameter of a circle equal on area to that of the particle outline m DAVG Mean average diameter m DC Diameter of the smallest circumscribed circle in the particle outline m DCIR Diameter of circumscribed sphere m DI Diameter of the largest inscribed circle m DS Diameter of circle fitting sharpest corner (two sharper corners, DS1, DS2) m DSV Diameter of a sphere of the same volume as particle m DX Diameter of a pebble particle through the sharpest corner DS m d Grain diameter (average) m dN Nominal diameter, diameter of a sphere of the same volume as the natural m particle e Void ratio % F Angularity factor - FR Fullness ratio - g Gravitational acceleration m/s2 I Intermediate axis m k Hydraulic conductivity m/s L Longest axis of the outline m N Number of corners (items counted) or number of divisions - n Porosity - P Perimeter of the projected particle, perimeter of outline (2D) m PC Perimeter of a circle of same area as particle outline m PCON Sum of perimeter of all convex parts m PCD Perimeter of circle of same area as drainage basin m PD Perimeter of a drainage basin m PI Particle index - R Roundness - RAVG Mean average radio of the pebble m RCON Radius of curvature of the most convex part m Re Reynolds number - Rmax-in Radius of the maximum inscribed circle. m Rmin-cir Radius of the minimum circumscribed circle m RO Roughness or surface texture - Re Equivalent roughness of particle - R1 Equation for predicting the settling velocity of sphere - R3 Equation for predicting the ratio of the settling velocity of an angular - particle to that of a well-rounded particle. ri Radius of curvature of the corner “i”. m S Actual surface area of the particle. m2

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Symbol Description Units Se Equivalent strength of particle - Ss Specific surface area - SF Sukumara shape factor - Sm Short axis “c” in minimum projection plane m s Surface area of a sphere of the same volume as the particle. m2 sD Specific gravity of the sediment given by the relation density of - sediment/fluid R2 Equation for predicting the ratio of the settling velocity of a non-spherical, - well-rounded particle to be settling velocity of a sphere with the same dimensionless nominal diameter S* Dimensionless fluid-sediment parameter - V Total volume of soil m3 3 VCIR Volume of circumscribed sphere m Ve Velocity m/s 3 VP Volume of particle m Vs Volume of voids m3 Vv Volume of solid m3 V10 % voids in the aggregate compacted with 10 blows per layer - V50 % voids in the aggregate compacted with 50 blows per layer - W Weight of the particle ton WS Settling velocity m/s W* Dimensionless settling velocity - Y Constant to obtain by fitting to experimental data for certain ranges of S* - Z Constant to obtain by fitting to experimental data for certain ranges of S* - x Distance of the tip of the corner from the center of the maximum inscribed mm circle α Measured angle degree (º) αi Sakamura angles used to describe shape degree (º) βi Sakamura angles used to describe angularity degree (º) Σ Summation - Ψ Sphericity - ν Kinematics viscosity m2/s φb Basic friction angle degree (º) φcs Friction angle critical state degree (º) φmc Friction angle maximum contraction degree (º) φrep Angle of repose degree (º) φ' Peak friction angle Pa τ Shear strength Pa σc Compressive strength Pa σn Normal stress Pa  Angle of internal friction degree (º) μ Viscosity Pa·s μF Friction coefficient - p Pressure drop - 3 ρ Density of water ton/m 3 ρp Density of the particle ton/m υ Specific discharge m/s

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1 INTRODUCTION

Effects on soil behaviour 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 judgement made by the individual practicing engineer, thus, it can result in not repeatable data. In evaluation of e.g. standard penetration test Holubec and D’Appolonia (1973) are suggesting the inclusion of the particle shape in the evaluation of the data. According with Folk (1955) the form error is negligible but it is not in the second sub-quantity related with the corners (roundness). These systems are not coherent in definitions. 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) glacifluvial 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.). Probably when authors had developed the form descriptors realize that they hadn’t provide enough information about the corners, they could be angular or rounded (roundness), thus, the authors also focus on develop techniques to describe them. Furthermore, the corners or the general surface 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).

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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 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 (see appendix A). On asphalt mixtures limits of flat and elongated particles or the amount of natural sands typically are incorporated into specifications; flat and elongated particles tend to cause problems with compaction, particle breakage, loss of strength and segregation in pavement (Kuo and Freeman, 1998a). Rutting resistance of asphalt concrete under traffic and environmental loads depend on the stability of aggregates structure in the asphalt mix (Pan et., al., 2006). According with the American Railway Engineering and Maintenance of Way Association (AREMA), ballast aggregate should be open graded with hard, angular shaped particles providing sharp corners and cubical fragments with a minimum of flat and elongated pieces (Tutumluer et. al., 2006). The American standard ASTM D 3398 (test method for index of aggregate particle shape and texture) is an example of an indirect method to determine particle shape (see appendix A). Aggregate characteristics of shape, texture, and grading influence workability, finishability, bleeding, pumpability, and segregation of fresh concrete and affect strength, stiffness, shrinkage, creep, density, permeability, and durability of hardened concrete. In fact, flaky, elongated, angular, and unfavorably graded particles lead to higher voids content than, cubical, rounded, and, well-graded particles. (Quiroga and Fowle, 2003).

Sieving is probably the most used method to determine the particle size distribution, it consist of plotting the cumulative weight of the weighted material retained by each mesh (European standard EN 933-1, 1992). 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

2 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.

2 AIM AND GOAL

The aim of this report is to review the state of the art on how to describe particle shape of individual grains of geotechnical material and knowledge on the influence of shape in geotechnical properties.

The goals in this study are to:  Describe, discuss and compare particle shape and definitions.  Review the known effect of particle shape on soil mechanics parameters  Discuss the potential of the role of particle shape in soil mechanics

Focus in this study has been on 2 dimensional shape definitions. The content of the report is based upon published and peer reviewed papers in English.

3 DESCRIPTION OF SHAPE PROPERTIES

3.1 INTRODUCCTION

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 in: o 3D (3 dimensions): it could be obtained from a 3D scan or in a two orthogonal images and o 2D (2 dimensions) or particle projection, where the particle outline is drawn.

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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 required to take pictures (e.g. regular camera or the use of microscope for smaller particles). In 2D image analysis the particle is assumed to lay over its more stable axis (e.g. longest and intermediate axis lie more or less parallel to the surface while the shortest axis is perpendicular) or random, some authors publish their own preferences about this issue (Wadell, 1935; Riley, 1941; Hawkins, 1993).

3.2 SCALE DEPENDENCE

In order to describe the particle shape in detail, there are a number of terms, quantities and definitions used in the literature. Some authors (Mitchell & Soga, 2005; Arasan et al., 2010) are using three sub-quantities; one and each describing the shape but at different scales. The terms are morphology/form, roundness and surface texture. In figure 1 is shown how the scale terms are defined.

Figure 1. Shape describing sub quantities (Mitchell & Soga, 2005)

At large scale the particle’s diameters in different directions are considered. At this scale, describing terms as spherical, platy, elongated etc., are used. An often seen quantity for shape description at large scale is sphericity (antonym: elongation). Graphically the considered type of shape is marked with the dashed line in Figure 1.

At intermediate scale it is focused on description of the presence of irregularities. Depending on at what scale an analysis is done; corners and edges of different sizes are identified. By doing analysis inside circles defined along the particle’s boundary, deviations are found and valuated. The mentioned circles are shown in Figure 1. A generally accepted quantity for this scale is roundness (antonym: angularity).

Regarding the smallest scale, terms like rough or smooth are used. The descriptor is considering the same kind of analysis as the one described above, but is applied

4 within smaller circles, i.e. at a smaller scale. Surface texture is often used to name the actual quantity. The sub-quantities and antonyms are summarized in table 1.

Table 1 Sub-quantities describing the particle’s morphology and its antonym. Scale Quantity Antonym Large scale Sphericity Elongation Intermediate scale Roundness Angularity Small scale Roughness Smoothness

3.3 FORM (3D) Wentworth in 1922 (Blott and Pye, 2008), was probably one of the first authors on measure the particle dimensions, this consisted on the obtaining of the length of the tree axes perpendicular among each other (see figure 2) on the tree dimensions (where a≥b≥c) to obtain the sphericity (equation 1).

a  b   (1) 2c

Figure 2. Measurement of the 3 axes perpendicular among each other (Krumbein, 1941)

Krumbein (1941) develop a rapid method for shape measurement to determine the sphericity; this is done by measuring the longest (a), medium (b) and shorter (c) axes diameters of the particle, it can be seen in figure 2 (Always perpendicular among each other). The radios b/a and c/b are located in the chart developed by his own where it can be found the Intercept sphericity as he called (See figure 3). This chart is an easy graphical way to relate the dimensions.

Figure 3. Detailed chart to determining Krumbein intercept sphericity (Krumbein 1941)

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Wadell (1932) defined the sphericity as the specific surface ratio (equation 2). Figure 4 is a schematic representation of the sphere surface and particle surface, both particle and sphere of the same volume.

s   (2) S

Figure 4 Same volume sphere surface (s) and particle surface (S). (modified after Johansson and Vall, 2011).

This way to obtain the sphericity is almost impossible to achieve, as Hawkins (1993) declares, due the difficulty to get the surface area on irregular solids.

Wadell (1934) also defined the sphericity based upon the particle and sphere volumes, as equation 3 (see figure 5):

VP (3)   3 V CIR

Figure 5 Relation between the volume of the particle and the volume of the circumscribed sphere (Johansson and Vall, 2011).

Wadell (1934) used a new formula simple to manage using the diameters (see figure 6 and equation 4).

D (4)   SV DCIR

Figure 6 Figure is showing the relation between the diameter of a circumscribed sphere and the diameter of a sphere of the same volume as the particle (Johansson and Vall ,2011).

Zingg (Krumbein, 1941) develop a classification based on the 3 axes relation, in this way it is easy to find out the main form of the particles as a disks, spherical, blades

6 and rod-like; this is summarized on figure 7. Zingg’s classification is related with Krumbein intercept sphericity and the figure 3.

Figure 7 Zingg’s classification of pebble shape based on ratios b/a and c/b (Krumbein 1941).

In figure 8 the figures 3 and 7 are combined, the relation in the two classifications can be seen, it is an easy way to understand the morphology regarding on the a, b and c dimensions

Figure 8 Classification made by Zingg’s and chart to determine sphericity (Krumbein and Sloss, 1963)

Pye and Pye (1943), in the article “sphericity determinations of pebbles and sand grains” compare the Wadell’s sphericity developed in 1934 (based on the diameter) with “Pebble sphericity” based on an ellipse, this last equation (number 5) appears two years early published by Krumbein (1941). Axis measurement is done as figure 1 denotes for equations 5 trough 12 with exception of equation 8 where the original document was not possible to obtain.

b  c   3 (5) a 2

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Sneed & Folk in (1958) found a relation between the tree dimensional axes called “Maximum Projection Sphericity”.

2 (6) c   3 a  b

In a similar way Ashenbrenner (1956) showed his equation at that time named “Working Sphericity”

12,8  3 (c / b)2 (b / a)   (7) 2 2 1 (c/b)(1  (b / a))  6 1 (c / b) (1 (b / a) )

Form or shape factor names are used by authors like Corey (shape factor, eq. 8) in the paper published on 1949, Williams (shape factor, eq. 9) in 1965, Janke (form factor, eq. 10) in 1966 and Dobkins & Folk (oblate-prolate index, eq. 11) in 1970 (Blott and Pye, 2008).

c   (8) ab

ac b2 (9)   1- when b2  ac, 1 when b2  ac b2 ac

c   2 2 2 a  b  c (10) 3

 a - b  10  0.5 a - c (11)     c a

Aschenbrenner (1956) develop the shape factor by using the relation of the tree axis but the square of the middle one.

ac   (12) b 2

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Table 2 General overview over different particle shape definitions for 3D sphericity has been compiled and arranged chronologically Aspect Name Author Year Based on Sphericity (3D) Flatness index Wentworth 1922a 3-axes True Sphericity Wadell 1932 Surface Operational sphericity Wadell 1932 Volume Sphericity Wadell 1934 Sphere diameter Zingg’s clasification Zingg’s1 1935 3-axes Intercept sphericity chart Krumbein 1941 3-axes Pebble sphericity Pye and Pye 1943 3-axes Corey shape factor Corey2 1949 3-axes Working sphericity Ashenbrenner 1956 3-axes shape factor Ashenbrenner 1956 3-axes Maximum projection sphericity Sneed & Folk 1958 3-axes Williams shape factor Williams2 1965 3-axes Janke form factor Janke2 1966 3-axes

Oblate-prolate index Dobkins & Folk 1970 3-axes 1) Krumbein and Sloss, 1963 2) Blott and Pye, 2008

3.4 FORM (2D)

The technique to measure the sphericity is based in tree dimensions, it can be found in literature some ways to measure the “two dimensions sphericity” which is simply the perimeter of the particle projection, some authors named “particle outline” or “circularity”.

Wadell in 1935 (Hawkins, 1993) adopt a conversion of his 1934 3D sphericity formula (equation 4) to a 2D outline. He defined an orientation on the particles and they were based on the maximum cross sectional area (outline of the particle projecting the maximum area). The equations show the relation between diameters of a circle of same area and smallest circumscribed circle.

DA C  (13) DC

He also used the term “degree of circularity” as the ratio of the perimeter of a circle of same area and the actual particle perimeter:

P C  C (14) P

Tickell in 1931 (Hawkins, 1993) used his empirical relation. The particle orientation proposed was a random one. It is described by the ratio between the area outline and the area of smallest circumscribed circle.

A C  (15) AC

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Some other authors has been working with the “circularity” concept and had develop them own equations as Pentland (1927) relating the area outline and area of a circle with diameter equal to longest length outline, and Cox (Riley, 1941) with the ratio area and perimeter time a constant, equations 16 and 17 respectively. Both authors did not define any definite orientation of the grains.

A C  (16) A C2

4A (17) C  2 P

Riley (1941), realize the problems that an area, perimeter and some other measurements proposed by the above authors can carry as the time consuming and tedious work (at that time were not computer, all was made by hand), and that’s why he develop this equation easy to handle called “inscribed circle sphericity”. He used the same particle orientation proposed by Wadell and the relation of diameters of inscribed and circumscribed circles.

D C  I (18) D C

Horton 1932 (Hawkins, 1993) use the relation of the drainage basing perimeter and the perimeter of a circle of the same area as drainage basin

P C  D (19) P CD

Janoo in 1998 (Blott and Pye, 2008) develop his general ratio of perimeter to area.

P 2 C  (20) A

Sukumaran and Ashmawy (2001) develop his own shape factor (SF) defined as the deviation of the global particle outline from a circle. Figure 9 can be used as a reference to determine the items used in the equation 21. N

∑ αiParticle (21 ) SF = i=1 N x 45º

N, is referred to the number of sampling intervals o radial divisions.

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Figure 9 Description of the Sukumaran factors to determine the shape and angularity (Sukumaran and Ashmawy, 2001)

Table 3 General chronological overview of the particle shape definitions for 2D sphericity Aspect Name Author Year Based on Circularity (2D) roundness Pentland 1927 area roundness Cox1 1927 area-perimeter roundness Tickell2 1931 area Circularity Horton2 1932 drainage basin outline circularity Wadell 1935 Circle diameter degree of circularity Wadell 1935 Perimeter inscribed circle sphericity Riley 1941 Circle diameter Circularity Krumbein and Sloss 1963 chart

Janoo 1998 area-perimeter Segmentation of particle and Shape factor Sukumaran 2001 angles 1) Riley, 1941 2) Hawkins, 1993

3.5 ROUNDNESS OR ANGULARITY

Roundness as described in section 3.2 is the second order shape descriptor. Sphericity lefts beside the corners and how they are, this was notice by most of the authors sited before and they suggested many ways to describe this second order particle property.

Roundness is clearly understandable using the figure 10. Particle shape or form is the overall configuration and denotes the similarities with a sphere (3D) or a circle (2D). Roundness is concerning about the sharpness or the smoothness of the perimeter (2D). Surface texture (Barret, 1980), is describe as the third order subject (form is the first and roundness the second), and it is superimposed in the corners, and it is also a property of particles surfaces between corners.

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Figure 10 Form (shape), Roundness and Texture graphical description (Bowman et., al., 2001)

Wadell (1935) describes his methodology, calling it total degree or roundness to obtain the roundness of a particle using the average radius of the corners in relation with the inscribed circle diameter (see figure 11) on the equation:

 r     R  (22) R   max in  N

In the same study Wadell (1935) has used the equation

N R   R   max in  (23)  r 

This two last equation shows slightly differences on the results (Wadell, 1935)

Figure 11 Wadell’s method to estimate the roundness, corners radius and inscribed circle (Hawkins, 1993)

Powers (1953) also published a graphic scale to illustrate the qualitative measure (figure 12). It is important to highlight that any comparing chart to describe particle properties has a high degree of subjectivity. Folk (1955) concludes that when charts are used for classification, the risk of getting errors is negligible for sphericity but large for roundness.

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Figure 12 A Roundness qualitative scale (Powers, 1953)

Some authors as Russel & Taylor in 1937, Pettijohn in 1957 and Powers in 1953 developed a classification based on five and six classes (Hawkins, 1993) each one with its own class limits; it is important to denote that the way they measure the roundness is the developed by Wadell (1935). This classification and class limits are showed in the table 4.

Table 4 Degrees of roundness: Wadell Values. (Hawkins, 1993), N/A = no-applicable Grade terms Russell & Taylor (1937) Pettijohn (1957) Powers (1953) Class Arithmetic Class limits Arithmetic midpoint Class Arithmetic limits (R) midpoint (R) limits (R) midpoint

Very angular N/A N/A N/A N/A 0.12-0.17 0.14

Angular 0.00-0.15 0.075 0.00-0.15 0.125 0.17-0.25 0.21

Subangular 0.15-0.30 0.225 0.15-0.25 0.200 0.25-0.35 0.30

Subrounded 0.30-0.50 0.400 0.25-0.40 0.315 0.35-0.49 0.41 0.59 Rounded 0.50-0.70 0.600 0.40-0.60 0.500 0.49-0.70

Well rounded 0.70-1.00 0.800 0.60-1.00 0.800 0.70-1.00 0.84

Krumbein and Sloss (1963) published a graphical chart easy to determine the sphericity and roundness parameters using comparison. See figure 13. (Cho, et. al. 2006).

Figure 13 Sphericity and roundness chart. (Cho et., al., 2006). The roundness equation that appears here in the chart is the wadell’s equation number 22

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Fischer in 1933 (Hawkins, 1993) used a straightforward method to quantify roundness using a central point in the outline and dividing the outline in angles around this point that were subtended by the straight or non curved parts of the profile were measured. This is illustrated in figure 14.

Figure 14 Fischer’s methods of angularity computation (Hawkins, 1993) A=inscribed circle; B=circumscribed circle

To express the angularity value Fischer used the ratio of angles standing linear parts on the outlines and concave respectively:

∑ANG PLA (24) R= 360°

ANG R   CON (25) ANGPLA

Figure 14 left (A) and right (B), gives a similar angularity of approximately 0.42 using the above equations. (Hawkins, 1993).

Wentworth in 1922 used the maximum projection to define the position of the particle to obtain the outline or contour (Barret, 1980). The equation reflects the relation of the diameter of a circle fitting the sharpest corner and the longest axis plus the shortest axis c (minimum projection).

D R  S (26) (L S ) / 2 M Wentworth (Hawkins, 1993) expressed the roundness as the ratio of the radius of curvature of the most convex part and the longest axis plus short axis:

R (27) R  CON (L  B)/4

Actually these last two equations are the same, just expressed in different terms, when the particle is in its maximum projection.

Dimensions can be seen on figure 15, L and B represents the mayor axis a and intermediate axis b. The intention is to make difference between the 2 and 3 dimensions (L and B are for 2D as a, b and c are for 3D)

14

Figure 15 Description of L and B axes (Hawkins, 1993)

Wentworth 1919 has a second way to express the roundness called Shape index (Barrett, 1980) and it relates the sharpest corner and the diameter of a pebble trough the sharpest corner. D s R  (28) D x Wentworth (1922b), used define the roundness as the ratio of the sharpest corner and the average radius of the pebble:

R CON R  (29) R AVG

2*R  D  3 a *b*c AVG AVG (30)

Cailleux (Barrett, 1980) relates the radius of the most convex part and the longest axis:

R R  CON (31) L/2

Kuenen in 1956 show his roundness index (Barrett, 1980) between the sharpest corner and the breath axis: D R  s (32) B

Dobkins & Folk (1970) used a modified Wentworth roundness with the relation of sharpest corner and inscribed circle diameters:

D R  s (33) D i

15

Swan in 1974 shows his equation (Barrett, 1980) relating the sharpest (or the two sharpest) corner(s) and inscribed circle diameter:

D  D / 2 R  s1 s2 (34) Di

Szadeczsky-Kardoss has his Average roundness of outline (Krumbein and Pettijohn, 1938) relating the concave parts perimeter and the actual perimeter:

P R  CON *100 (35) P

Lees (1964a) developed an opposite definition to roundness, it means that he measures the angularity instead of the roundness, and he calls it Degree of angularity. Figure 16 shows the items considered when equation 36 applies as the angles (α), inscribed circle (Rmax-in) and the distance (x). The main formula is:

x R  (180  ) (36) R max in

Figure 16 Degree of angularity measurement technique (Blot and Pye, 2008)

In order to apply the last equation corners needs to be entered in the formula, and each individual result will add to each other to obtain the final degree of angularity.

A roundness index appears on Janoo (1998), Kuo and Freeman (1998a) and Kuo, et., al. (1998b) it is described as:

4A R  (17) P 2

The last equation is on section 3.4 also because there is not a general agreement on the definition furthermore some authors had used to define the roughness, this is not the only equation that has been used trying to define different aspects (sphericity, roundness or roughness) but it is a good example of the misuse of the quantities and definitions.

16

Sukumaran and Ashmawy (2001) present an angularity factor (AF) calculated from the number of sharpness corners. Angles βi required to obtain the angularity factor are shown in figure 9:

N N 2 2

∑(βiParticle- 180º) - ∑(βicircle-180º) AF = i=1 i=1 (37) N 2 2 3 x (180º) - ∑(β circle- 180º) i i=1

Sukumaran and Ashmawy (2001) also suggested use not bigger sampling interval of N=40 because it is the cut off between angularity factor and surface roughness. If so this equation could be used to describe the roughness.

Table 5 General chronological overview of the particle roundness Aspect Name Author Year Based on

Roundness shape index Wentworth 19191 diameter of sharper corner shape index Wentworth 1922b sharpest corner and axis roundness Wentworth 1933 convex parts Fischer 19332 noncurved parts outline Fischer 19332 noncurved-streigth parts outline

Average roundness of Szadeczsky-Kardoss 19333 convex parts-perimeter outline roundness Wadell 1935 diameter of corners roundness Wadell 1935 diameter of corners roundness Russel & Taylor 19372 class limit table roundness Krumbein 1941 chart Cailleux 19471 convex parts roundness Pettijohn 19494 class limit table roundness Powers 1953 chart and class limit table Kuenen 19561 axis-convex corner roundness Krumbein and Sloss 1963 chart degree of angularity Lees 1964a corners angles and inscribed circle Dobkins & Folk 1970 diameter of sharper corner

Swan 19741 diameter of sharper corners

Angularity factor Sukumaran and 2001 Segmentation of particles and Ashmawy angles 1) Barret, 1980 2) Hawkins, 1993 3) Krumbein and Pettijohn, 1938 4) Powers, 1953

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3.6 ROUGHNESS OR SURFACE TEXTURE

A third property called texture appears early in the literature with the sphericity and roundness properties, since then, texture property was longed described but it was in accordance with the authors, at that time, not measurable.

Wright in 1955 developed a method to quantify the surface texture or roughness of concrete aggregate using studies done on 19 mm stones. The test aggregates were first embedded in a synthetic resin. The stones were cut in thin sections. The sections projection was magnified 125 times. The unevenness of the surface was traced and the total length of the trace was measured. The length was then compared with an uneven line drawn as a series of chords (see figure 17). The difference between these two lines was defined as the roughness factor. (Janoo 1998).

Figure 17 Measurement method for characterizing the surface texture of an aggregate (Janoo, 1998)

However, with the advance of technology it has become easier measure the roughness and here is presented some researcher’s ideas how this property should be calculated.

One technique used by Janoo (1988) to define the roughness can be seen in figure 18a and is defined as the ratio between perimeter and convex perimeter:

P R  (38) O C PER

b) a)

Figure 18 a) Convex perimetera) Convex (C perimeterPER), b) F eret(C PER measurement), b) Feret measurement (modified after Janoo, 1998)

The convex perimeter is obtained using the Feret’s box (or diameter) tending a line in between the touching points that the Feret’s box describes each time it is turn (figure 18b).

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Kuo and Freeman (1998a) and Kuo et. al., (1998b) use the roughness definition as the ratio perimeter and average diameter:

P (39) R O  *DAVG Erosion and dilatation image processing techniques are used to obtain the surface texture. Erosion is a morphological process by which boundary image pixels are removed from an object surface, which leaves the object less dense along the perimeter or outer boundary. Dilatation is the reverse process of erosion and a single dilatation cycle increases the particle shape or image dimension by adding pixels around its boundary. (Pan et.al., 2006).

A  A1 R  *100 (40) O A

The “n” erosion and dilatation cycles are not standardized.

Mora and Kwan (2000) used the “convexity ratio, CR” (equation 41) and the “fullness ratio, FR” (equation 42) in their investigation, they are:

A R = (41) o A CON

A (42) R = o A CON

The convex area is the area of the minimum convex boundaries circumscribing the particle. This is illustrated in the figure 19. The convex area is obtained in a similar way as the convex perimeter but in this case the area between the original outline and the convex perimeter is our convex area.

Figure 19 Evaluation of area and convex area (Mora and Kuan, 2000)

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4 TECHNIQUES IN ORDER TO DETERMINE PARTICLE SHAPE

4.1 HAND MEASUREMENT

Hand measurement technique was the first used by obvious reasons, in order to improve the accuracy special devices developed as the “sliding rod caliper” used by Krumbein (1941), it works placing the sample on the sliding road calliper as show figure 20b the length in different positions can be obtain by using the scale provided in the handle; the “convexity gage” that was actually used by opticians to measure the curvature of lenses but easily applicable to the particle shape analysis (Wentworth, 1922b) works measuring the movement of the central pivot as figure 20a shows (the two adjacent pivots are invariable) as many the central pivot moves more is the curvature; or the “Szadeczky-Kardoss’s apparatus” develop in 1933 that traces the profile of the rock fragment, so, the outline traced is then analyzed (Krumbein and Pettijohn, 1938) figure 20c show equipment.

b) c)

a)

Figure 20 a) convexity gage, used to determine the curvature in particle corners (Wenworth, 1922b) b)sliding rod caliper, device to measure the particle axis length (Krumbein, 1941) and c)Szadeczky- Kardoss (1933) apparatus, it was utilized to obtain the particle outline.

Another helpful tool to determine the particle dimensions was the “camera lucida” to project the particle’s contour over a circle scale appearing in Figure 21, thus it is possible to measure the particle’s diameter.

Figure 21 Circle scale used by Wadell (1935) to determine particle’s diameter and roundness

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4.2 SIEVE ANALYSIS

Bar sieving, e.g. according to EN 933-3:1997, can be used to determine simple large scale properties. By combining mesh geometries the obtained results can be used to quantify flakiness and elongation index, ASTM D4791 (Flat and elongated particles are defined as those coarse aggregate particles that have a ratio of length to thickness equal to or greater than a specified value such as 5:1. The index represents the percentage on weight of these particles). The method is not suitable for fine materials. This due to the difficulty to get the fine grains passed through the sieve, and the great amount of particles in relation to the area of the sieve (Persson, 1998) e.g. EN 933- 3:1997 related to flakiness index. The test is performed on aggregates with grain size from 4 mm and up to 63 mm. two sieving operations are necessary, the first separates on size fraction and the second use a bar sieve, after the first sieving the average maximum diameter of the particles is obtain and with the second sieving (bar sieving) the shortest axis diameter is found, finally with this two parameters the flakiness index is determined.

There are more standards related with the particle shape (see appendix A) but, this above presented are probably the most known using sieve analysis to determine particle’s geometrical properties.

Sieve analysis is facing the computers age and image analysis sieving research is taking place (Andersson, 2010; Mora and Kwan, 2000; Persson, 1998). Industry is also applying the image analysis sieving with decrees on the testing time compare with the traditional sieving method. An inconvenient of image analysis is the error due the overlapping or hiding of the particles during the capture process but the advantages are more compare with disadvantages (Anderson, 2010).

4.3 CHART COMPARISON

Charts developed over the necessity of faster results because the long time consuming required when measuring each particle.

Krumbein (1941) present a comparison roundness chart for pebbles which were measured by Wadell’s method because this property was the most difficult to measure due to the second order scale that roundness represents. (See figure 22).

Figure 22 Krumbein (1941) comparision chart for roundness

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A qualitative chart by Powers (1953) try to include both (sphericity and roundness) particle’s characteristics, it was divided on six roundness ranges (very angular, angular, sub-angular, sub-rounded, rounded and well rounded) and two sphericity series (high and low sphericity). This chart was prepared with photographs to enhance the reader perspective. (See figure 23)

Figure 23 Powers (1953) qualitative shpericity-roundness chart.

A new chart including sphericity and roundness appear, this time it was easier to handle the two mean properties of particle’s shape, furthermore, there was included the numerical values that eliminated the subjectivity of qualitative description. The chart is based on Wadell’s definitions. (Krumbein and Sloss, 1963). (See figure 24)

Figure 24 Sphericity-roundness comparison chart (Krumbein and sloss 1963).

Folk (1955) worried about the person’s error on the chart’s comparison studied the determination of sphericity and angularity (he used the Powers 1953 comparison chart), he found that the sphericity determination by chart comparison has a negligible error while the roundness, he concluded, it was necessary to carry out a more wide research due the high variability show by his study.

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4.4 IMAGE ANALYSIS

Image analysis is a practical method to use for shape classification since it is fast and can be automated. Different techniques appear to process these images, among them are:

o Feret Diameter: the Feret diameter is the longitude between two parallel lines, this lines can rotate around one particle, or outline, to define dimensions, as it is shown in figure 25 these method is not a fine descriptor, but as it was say above it is a helpful tool to determine diameters (Janoo, 1988)

Figure 25 Feret measurement technique is defined by two parallel lines turning around the particle to define the shortest and longest Feret diameter. (Janoo, 1988)

o Fourier Mathematical Technique: It produces mathematical relations that characterize the profile of individual particles. This method favours the analysis of roughness and textural features for granular soils. The problem in the methodology remains in the re-entrant angles in order to complete the revolution (Bowman et. al., 2001), see figure 26.

N (43) R()  a0  (a n cos n  bn sin n) n1

Figure 26 Fourier technique with two radiuses at one angle. (Bowman et. al., 2001)

o Fractal Dimension: Irregular line at any level of scrutiny is by definition fractal (Hyslip and Vallejo, 1997), Figure 27 shows fractal analysis by the dividing method. The length of the fractal line can be defined as:

P()  n1DR (44)

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Figure 27 Fractal analysis by the dividing method at different scrutiny scale (Hyslip and Vallejo, 1997)

o Orthogonal image analysis: This technique is basically the use of two images orthogonal between them to acquire the three particle dimensions (Fernlund, 2005), any of the above techniques can be used in this orthogonal way.

o Laser Scanning Technique: this kind of laser scanning 3D is one of the most advanced techniques. In figures 28a) we have the laser head scanning the rock particles, the particles have control points in order to keep a reference point when move them to scan the lower part, in figure 28b) we can see the laser path followed. (Lanaro and Tolppanen, 2002)

a) b)

Figure 28 a) Scanning head, b) scanning path (Lanaro and Tolppanen, 2002)

Another technique is the Laser-Aided Tomography (LAT), in this case a laser sheet is used to obtain the particles surveying (see figure 29). This technique is different and has special requirements as to use liquid with same refractive index as the particles, particles must let the laser or certain percent of light go through. (Matsushima et. al., 2003)

Figure 29 LAT scaning particles Figure 30 3D scan completed ready to (Matsushima et. al., 2003) use for any further measure. (Matsushima et. al., 2003)

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Both 3D techniques obtain the particle shape that is later used to achieve measures as we can see in figure 30.

All these previous techniques are easily written in codes or scripts to be interpreted in a digital way obtaining the desired measurement, but there are some interesting points in the image analysis regarding on the errors involve, among them are image resolution and orientation of the particles; orientation is not relevant when it is random and large number of particles are involve; resolution have an influence on the accuracy. (Zeidan et. al., 2007)

When resolution is increase more accuracy is obtain and the object representation match better with the real form, in the other hand, more resolution means more spending on memory and time; thus, resolution needs to be according with the goal and precision needed in any work. (Schäfer, 2002).

Schäfer (2002) conclude that attributes like length when measuring digital images present relative high errors. It can be vanish or at least diminish using high resolution just for diameter but not for perimeter that keep the error as big as initially. Johansson and Vall (2011) obtain similar results when 3 different resolutions were used in the same particle obtaining an unstable output for those terms/quantities that involve the perimeter. Thus all quantities relating the perimeter should be treated with care.

5 EFFECT OF SHAPE ON SOIL PROPERTIES

5.1 INTRODUCTION

In laboratory test on the effect on particle size on basic properties has been investigated in several studies, this relation has been discussed and various mechanisms had been proposed to explain the behaviour of the soil in dependency, also, with the shape. Basically there are two mechanisms proposed: The arrangement of particles and the inter-particle contact (Santamarina and Cho, 2004) and subsequence breakage.

The arrangement of particles: Arrangement of the particles can be presented in three different forms, loose, dense and critical; this arrangement determines the soil properties (e.g. density increase with more dense arrangement). Loose and dense states are easy understandable when figure 31 is explained, while in the upper part of the figure the particles are arranged using the minimum space needed in the lower part a span is created using the flaky particle as a bridge, this phenomena is known as “bridging”. Bridging can produce different geotechnical results when just the shape of the particle is changed, e.g. void ratio (Santamarina and Cho, 2004). Particles are able to rearrange, this could be done applying pressure (energy) to the soil, the pressure (energy) will create such forces that soil particles will rotate and move (see figure 34) finishing in a more dense state.

25

Figure 31. Bridging effect when flaky particles are combined in the bulk material (Santamarina and Cho 2004)

A loose soil will contract in volume on shearing, and may not develop any peak strength (figure 32, left). In this case the shear strength will increase gradually until the residual shear strength is revealed, once the soil has ceased contracting in volume. A dense soil may contract slightly (figure 32, right) before granular interlock prevents further contraction (granular interlock is dependent on the shape of the grains and their initial packing arrangement). In order to continue shearing once granular interlock has occurred, the soil must dilate (expand in volume). As additional shear force is required to dilate the soil, a peak shear strength occurs (figure 32, left). Once this peak shear strength caused by dilation has been overcome through continued shearing, the resistance provided by the soil to the applied shear stress reduces (termed strain softening). Strain softening will continue until no further changes in volume of the soil occur on continued shearing. Peak shear strengths are also observed in overconsolidated clays where the natural fabric of the soil must be destroyed prior to reaching constant volume shearing. Other effects that result in peak strengths include cementation and bonding of particles. The distinctive shear strength, called the critical state, is identified where the soil undergoing shear does so at a constant volume. (Schofield and Wroth, 1968).

Figure 32 The left part of the figure show a typical behaviour. of loose and dense material over shear stress, while at the right the figures illustrate the typical volume changes.

The inter-particle contact: For frictional soil, i.e. coarse grained soil, the friction between particles is the dominating factor for strength. Materials usually consisting of coarse grains (diameter 26

> 0.06mm) behave as a frictional soil; it means that the strength of coarse soils (silt, sand, gravel, etc.) comes from an inter-particle mechanical friction, thus, ideally they do not have traction strength. In figure 33 the inter-particle contact is illustrated, here the pressure (P) is applied and two more components are found, the normal load (N) and the tangential load (T) described as the friction coefficient (μF). The forces stand in equilibrium. (Johansson and Vall, 2011).

Figure 33 Inter-particle contact and forces acting (Axelsson, 1998)

When particles equilibrium is disturbed (friction coefficient is not enough to keep particles unmoved) the rotation is imminent, and it is necessary in order to compact the soil, in figure 34 can be seen that the arrangement is a fact that inhibit or allow this rotation, and the shape in the 3 different scales are also factors because the more spherical and/or more rounded and/or less roughness more easy is the rotation. (Santamarina and Cho, 2004).

Figure 34 Rotation inhibition by the particles compaction or low void ratio (Santamarina and Cho, 2004)

Breakage: Breakage is a side effect of the inter-particle contact and rotation when pressure exceed the rock strength, it can happened when the particles are tight together and there is not enough space to rotate, it is more obvious in angular particles (mesh form) or as in figure 31 where the flaky particle “bridging” is not able to rotate but it can brake by the pressure increase. Yoginder et. al., (1985) notice that the angular particle break during his experiments and they turn more rounded changing the original size and form configuration at the same time there was a soil properties loosening.

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5.2 INFLUENCE OF SIZE AND SHAPE

Wenworth (1922a) and Pellegrino (1965) among others suggest that agent transport of the rocks (rigor of transport, temperature and moisture changes, etc.) determine its shape but also the particle genesis itself (rock structure, mineralogy, hardness, etc.). It is not possible to determine the shape of the particles based on the agent transport or genesis but generally a shape behaviour is expected according to Mitchell and Soga (2005) specially when the particle size is in the clay size (>2μm). The shapes of the most common clay minerals are platy (figure 35), with some exceptions (e.g. halloysite, occurs as tubes, kaolinite are large, thick, and stiff, Smectites are composed of small, very thin, and filmy particles, Illites are intermediate between kaolinite and smectite and attapulgite occurs in lathlike particle shapes). Some clay minerals photographs are presented in figure 35.

a) b) c)

d) e)

Figure 35 Clay mineral shape, a) hallosite, b) Kaoline, c) Smactites, d) Illites and e) attapulgite. (Modified from Mitchell and Soga, 2005)

Figure 36 Particle size range in soils. Generally the particles of clay size are plate shaped. (Mitchell and Soga, 2005).

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5.3 VOID RATIO AND POROSITY

The void ratio (e) is the ratio of the volume of voids to the volume of solid; it is defined by the equation: V V e = (45) VS

Porosity (n) is the ratio of the volume of voids to the total volume of the soil; it is represented by the equation: VV n= (46) V

Holubec and D’Appolonia (1973), found a relation between the void ratio and sphericity (referred in the paper as coefficient of angularity, ratio of particle surface and equivalent sphere surface), their results show that the maximum and the minimum void ratio increases as the shpericity decreases. In this study the surface was obtained for an indirect method based on the permeability developed by Hoffman in 1959, described in the same document. Rousé et., al., (2008) defined the roundness as Wadell (1935) and he found it as an important factor controlling the minimum and maximum void ratios. Some other authors as Youd (1973) and Cho et. al., (2006) conclude the same, minimum and maximum void ratios increase when sphericity and roundness decrease. Another interesting result (all above authors) was the bigger influence of the form (sphericity, circularity) and roundness on the maximum void ratio. The change of the maximum void ratio is more pronounced than the change of the minimum void ratio when the form and roundness changes. (See figure 39)

Particles arrangement and interlocking are probably the factor that controls the void ratio; bridge effect permit the existence of void among the particles while interlocking allowed the particles to form arches avoiding the possibility to rotate and stay in a more stable configuration e.g. as it happens with marbles.

Figures 36, 37 and 38 shows proposed empirical relationships between void ratio and shape from tables 5 and 6 (graphically, the scale goes from 0 to 1 when cero mean high angularity, shpericity or circularity and one means low angularity, circularity or sphericity). Holubec and D’Appolonia (1973) data was taken to obtain a power curve and describe a tendency. Santamarina and Cho (2004) show Youd equations; in the original paper Youd (1973) never presented the equation but it is easy to use the information to draw a trend.

The graphics presented in this document (figures 36, 37 and 38) must be used with certain reserves due the fact that the original data was modified in order to fit all information in one graphic, what the figures shows is just the general trend of the behaviour’s material regarding on the shape. If more accurate description and information is required the author recommends consulting the reference data. In the same way equations from Holubec and D’Apollonia (1973) and Youd (1973) were not presented by the authors but the use of the information was taken in order to build up those equations on tables 6 and 7.

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Table 6 Minimum void ratio equations regarding on the quantity (Ψ for sphericity, C for circularity, R for roundness, SF for Sukumaran shape factor and AF for Sukumaran angularity factor) EQUATION NUMBER REFERENCE Figure 34 (left) 0.434 47 Holubec & D’Appolonia, 1973 (Ψ e =0.4549Ψ min was obtained using equation 2) 0.0634SF 48 Sukumaran & Ashmawy, 2001 (SF e =0.318+0.0219e min obtained using equation 21) e =1─0.051C 49 Cho et.al., 2006 (C obtained using min figure 12) Figure 34 (right) ─1 50 Youd, 1973 (R obtained from figure e =0.359+0.082R min 11 and table 3) e =0.8─0.34R 51 Cho, et. al., 2006 (R obtained using min figure 12) ─1 52 Rousé et. al., 2008 (R obtained by e =0.433+0.051R min equation 21) 0.0233AF 53 Sukumaran & Ashmawy, 2001 (AF e =0.0416+0.372e min obtained using equation 37)

Table 7 Maximum void ratio equations regarding on the quantity (Ψ for sphericity, C for circularity, R for roundness, SF for Sukumaran shape factor and AF for Sukumaran angularity factor) EQUATION NUMBER REFERENCE Figure 35 (left) 0.5152 54 Holubec and D’Appolonia, 1973 (Ψ emax =0.6112Ψ was obtained using equation 2) 0.119SF 55 Sukumaran & Ashmawy, 2001 (SF emax =0.718+0.00169e obtained using equation 21) e =1.6─0.86C 56 Cho et.al., 2006 (C obtained using max figure 12) Figure 35 (right) ─1 57 Youd, 1973 (R obtained from figure emax =0.554+0.15R 11 and table 3) e =1.3─0.62R 58 Cho, et. al., 2006 (R obtained using max figure 12) ─1 59 Rousé et. al., 2008 (R obtained by emax =0.615+0.1071R equation 21) 0.053AF 60 Sukumaran & Ashmawy, 2001 (AF emax =0.609+0.125e obtained using equation 37)

Comparing figures 37 and 38 (minimum and maximum void ratio) it can be seen on the right scheme of both figures 37 and 38 (when the factor is roundness/angularity) that all the empirical relations has a common initial point close to 1 (it means that particles are well rounded) while this common agreement disappear when the roundness factor decreases (when the particles become more angular). Same figures (37 and 38) on the left graphs (when the factor is sphericity/circularity/shape) do not present the same behaviour in fact there is more disperse initial point, close to 1(when the particles tend to be more spherical/circular).

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2 1.3 Holubec 1973 sphericity

1.2 1.8 Youd 1973 roundness Cho 2006 circularity 1.1 1.6 Rouse 2008 roundness 1 Sukumara 2001 SF 1.4 Cho 2006 roundness 0.9 Sukumaran 2001 AF 0.8 1.2 0.7

1 minimumvoid ratio 0.6 minimumvoid ratio 0.8 0.5 0.4 0.6 0.3 0.4

0.5 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 Factor (sphericity, circularity. shape) Factor (roundness, angularity) Figure 37 Minimum void ratio based upon the relation of shape factor proposed by the authors indicated in the figure

In Figure 39 the Δe (emax-emin) has been plotted to show how the maximum void ratio and the minimum void ratio has different rate change when the particle shape changes. Maximum void ratio increases more than minimum void ratio when the particle shape becomes less spherical and/or more angular. Comparing figure 39, left and right graphics, it can be seen that right present a common initial point when the quantity (roundness/angularity) is close to one while, in the left graphic the initial point is more disperse. Both ending points in both graphics (close to zero) are dispersed.

Figures 37, 38 and 39 present the same behaviour, right graphics (when the factor is roundness, angularity) in each figure have an initial common point while the left graphics do not (when the factor is sphericity, circularity, shape).

2.1 Youd 1973 roundness Holubec 1973 sphericity 3.5 1.9 Rouse 2008 roundness Cho 2006 circularity 1.7 3 Cho 2006 roundness 1.5 Sukumara 2001 SF 2.5 Sukumaran 2001 AF 1.3 2

1.1 Maximumvoid ratio Maximumvoid ratio 1.5 0.9 1 0.7

0.5 0.5 0 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 Factor (sphericity, circularity, shape) Factor (roundness, angularity) Figure 38 Maximum void ratio based upon the relation of shape factor proposed by the authors indicated in the figure

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1 Holubec 1973 sphericity 1.8 Youd 1973 roundness 0.9 1.6 Rouse 2008 roundness Cho 2006 circularity 0.8 1.4 Cho 2006 roundness 0.7 Sukumara 2001 SF 1.2 0.6 Sukumaran 2001 AF 1 0.5

0.8 0.4 0.3 0.6

Maximum- Minimum ratio Void 0.2 0.4 Maximum- Minimum Void ratio

0.1 0.2

0 0

0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 Factor (sphericity, circularity, shape) 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 Factor (roundness, angularity) Figure 39 Maximum minus minimum void ratio based upon the relation of shape factor proposed by the authors indicated in the figure

5.4 ANGLE OF REPOSE.

The angle of repose of a granular material is the steepest angle of descent or dip of the slope relative to the horizontal plane when material on the slope face is on the verge of sliding as show in figure 40.

According to Qazi (1975) there are five types of forces which may act between the particles in soils: 1. Force of friction between the particles 2. Force due to presence of absorbed gas and/or moisture of particle 3. Mechanical forces, caused by interlocking of particles of irregular shape 4. Electrostatic forces arising from friction between the particles themselves and the surface with which they come in contact 5. Cohesion forces operating between neighbouring particles

Rousé et. al., (2008) found a decrease of angle of repose with increase roundness based upon ASTM C1444 test (Standard Test Method for Measuring the Angle of Repose of Free-Flowing Mold Powders). The method consist in pouring sand on a surface cover by paper trough a funnel of specific dimensions (the nozzle diameter depend on the sand’s particle size) from an altitude of 1.5 inches (38.1 mm). The sand is release from the funnel until the peak of the cone formed by the sand stops the flow. The repose angle is obtained with the equation:

1 2H φ =tan (61) rep D d

H, represent the 1.5 inches, D and d represent the diameter of the cone formed by the sand and the diameter of the funnel respectively.

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Rousé (2008) shows an empirical relation to obtain the angle of repose based on the roundness of the particles.

(62)

Figure 40 Representation of the angle of repose

5.5 SHEAR STRENGTH.

The Mohr–Coulomb failure criterion represents the linear envelope that is obtained from a plot of the shear strength of a material versus the applied normal stress. This relation is expressed as:

  c  tan() (63) o n where τ is the shear strength, σn is the normal stress, co is the intercept of the failure envelope with the τ axis, and  is the slope of the failure envelope. The quantity c is often called the cohesion and the angle  is called the angle of internal friction

Studies show that the internal friction angle (under drained triaxial tests) increases more rapidly on those materials having higher angularity increasing the relative density. The internal friction angle is a function of the relative density and the particle shape (Holubec and D’Appolonia, 1973).

Chan and Page (1997) found in a study made with dry copper (using different shapes and sizes ranging from 180 to 106 μm) using a direct shear test (ring share test) that the internal friction angle increases as the angularity increases.

Shinohara et. al. (2000) did some experiments with steel powder different shapes using a triaxial cell, in the test Shinohara never used the roundness or angularity on the work but apply the shape factor (relation long axis/short axis) and the results were that as this relation deviate from factor 1 the internal friction angle increases.

The following empirical relations were found in the literature showing the behaviour of the friction angle (obtained under different conditions)

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Cho et. al. (2006):

(64)

(R is obtain by comparing the Krumbein chart, figure 13)

Rousé (2008):

(65)

(66)

(R is defined using Wadell equation 22)

In figure 41, the suggested empirical relations above and lines constructed using author data from Holubec and D’Appolonia (1973) and Sukumara and Ashmawy (2001) are plotted together to display the general trend on the particle shape and friction angle relation. Sukumaran reports two lines, one based on the shape factor (SF) and the second referring the angularity factor (AF). Sukumaran performed the tests at constant volume.

Figure 41. The changes on the internal friction angle shows a general increase when the particle roundness becomes angular or in the case of Sakamuran less spheric (Shape factor, SF)

The scale used for Holubec and D’Appolonia (1973) have lower and upper limits of 1 and 2 respectively (angularity form), and a scale change was applied to be able to presented in the actual figure 41. As in the previous section (5.2) the author recommend to use the original data from the references due that the figure just follows the general trend of the behaviour’s particle regarding on the shape.

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Barton and Kjaernsli (1981) suggested a model (equation 67) to predict the peak friction angle (φ’) based upon numerous trixial and direct shear data tests.

 Se   '  R e  Log     b (67)    n  where Se, equivalent strength of particle Re, equivalent roughness of particle φb, basic friction angle (obtained from basic tilting test) σn, normal load

The information required for the model is: (1) the uniaxial compressive strength of the rock; (2) the d50 particle size (mesh size where 50% of the particles pass through) required to define Se (figure 42); (3) the degree of particle roundness and (4) the porosity following compaction. All data can be estimated by simple index tests. Barton and Kjaernsli (1981) suggest that particle size and sample scale has an effect on the friction angle and includes them to obtain the equivalent strength (Se), figure 42 shows the method to obtain this value. Compressive strength (σc) was chosen to be the factor affecting the scale because micro fractures influence this property while samples are bigger more micro fractures contain and its compressive strength reduces.

Figure 42 Method of estimating Equivalent Strength (Se) of rockfill based on uniaxial compressive strength (σc ) and d50 particle size (Barton & Kjaernsli, 1981)

The equivalent roughness is obtain using figure 43 where is required to know the porosity (n) and the origin of the particles (a small chart is provided in the same figure to compare the particles profile).

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Figure 43 Method of estimating Equivalent Roughness (Roe) based on porosity of rockfill, origin material, degree of roundedness and smoothness of particle (Barton & Kjaernsli, 1981).

5.6 SEDIMENTATION PROPERTIES

A particle released in a less dense Newtonian fluid initially accelerate trough the fluid due to the gravity. Resistances to deformation of the fluid, transmitted to the particle surface drag, generate forces that act to resist the particle motion. The force due to the weight (Fw) can be written as:

(68) FW  (ρP ρ)gVP

Where ρp, ρ are density of the particle and fluid (water) respectively; g, is the gravitational force and Vp, is the volume of the particle.

And the resistance force (FD) is:

W2 F  C ρ A (69) D D 2

Where CD, is the dimensionless drag coefficient; W, is the weight of the particle and A is the cross section area.

Particle’s shape has been assumed to be spherical when equations are applied on the settling velocity. Correlation deviates when particle shape departs from spherical form

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(Dietrich, 1982) and it is known that natural particles depart from spherical form, thus, it is evident that this departure would have consequences.

The below equation is proposed to account the shape (in this case the Corey shape factor, equation 8) in the settling velocity. (Jimenez and Madsen, 2003).

1 W  Z  W  S  Y   *   (70) sD 1gd N  S* 

d S  N (s 1)gd (71) * 4 D N

Jimenez and Madsen (2003), Dietrich (1982), Briggs and McCulloch (1962), and others were working in the hydraulic shape of particles to solve problems as sediment transport. It is obvious that the equation presented and the researcher’s investigation works under certain conditions (e.g. grain size between 0.063-1 mm).

Dietrich (1982) suggests an empirical relation that accounts settling velocity, size, density, shape and roundness of a particle:

R1R2 (72) W*  R310

R1, R2 and R3 are fitted equations for size and density, shape, and roundness respectively.

5.7 HYDRAULIC CONDUCTIVITY, PERMEABILITY.

Darcy’s Law. Permeability is one component of Darcy’s law. Darcy's law is a simple proportional relationship between the instantaneous discharge rate through a porous medium, the viscosity of the fluid and the pressure drop.

k Ve   p (73) 

The total velocity, Ve is equal to the product of the permeability of the medium (porous media), k , the pressure drop, ∆p, all divided by the viscosity, μ (Muskat, 1937).

Darcy's law is only valid for slow, viscous flow; most groundwater flow cases fall in this category. Typically Darcy’s law is valid at any flow with laminar flow (see figure 44).

Reynold’s number (Laminar and turbulent Flow). Typically any laminar flow is considered to have a Reynold’s number less than one, and it would be valid to apply Darcy's law. Experimental tests have shown that flow regimes with Reynolds numbers

37 up to 10 may still be Darcian (laminar flow), as in the case of groundwater flow. The Reynolds number (a dimensionless parameter) for porous media flow is typically expressed as:

d (74) Re   where ρ is the density of water (units of mass per volume), υ is the specific discharge (with units of length per time), d is a representative average grain diameter for the porous media (often taken as the 30% passing size from a grain size analysis using sieves - with units of length), and μ is the viscosity of the fluid (Muskat, 1937).

Shape effects. Permeability, as Head and Epps (2011) suggested, is affected by the shape and texture of soil grains. Elongated or irregular particles create flow paths which are more tortuous than those spherical particles. Particles with a rough surface texture provide more frictional resistance to flow. Both effects tend to reduce the water flow through the soil.

Kozeny-Carman empirical relation accounts for the dependency of permeability on void ratio in uniformly graded sands; serious discrepancies are found when it is applied to clays due the lack of uniform pores (Mitchell and Soga, 2005).

There are various formulations of the Kozeny-Carman equation; one published by Head and Epps (2011) takes the void ratio e; the specific surface area Ss and an angularity factor F into account of permeability, k:

2  e3  k    (75) 2   FSs 1 e 

The angularity factor F considers the shape of the particles and ranges from 1,1 for rounded grains; 1.25 for sub rounded to 1,4 for angular particles. The specific surface Ss is defined as: 6 Ss  (76) d1d2 d1 and d2 represent the maximum and minimum size particle in mm.

Kane & Sternheim (1988) suggest that the inclusion of the shape factor (F) has probably the background on the Reynolds number due this factor is dependent significantly on the shape of the obstacles and Reynolds number determines the presence of laminar or turbulent flow. Figure 44 show how the laminar flow has low energy dissipation while turbulent flow (e.g. the roughness and path tortuosity) has high energy dissipation.

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Figure 44 The figure show the extremes of flow behaviour. First turbulent conditions where the flow is essentially random and unpredictable and second the well defined Laminar flow conditions.

According to Nearing and Parker (1994) the amount of soil detached during laminar and turbulent flow is dependent on each soil and also greater on turbulent flow due the greater shear strength generated during this kind of flow, this could suggest the greater erosion when turbulent flow is present.

5.8 LIQUEFACTION

Soil liquefaction is a phenomenon in which soil loses much of its strength or stiffness for a generally short time by earthquake shaking or other rapid loading. Static and dynamic liquefactions occur been the second one the most regular known. Liquefaction often occurs in saturated soils, that is, soils in which the space between individual particles is completely filled with water. This water exerts a pressure on the soil particles that influences how tightly the particles themselves are pressed together. Shaking or other rapid loading can cause the water pressure to increase to the point where the soil particles can readily move with respect to each other (Jefferies and Been, 2000).

Jefferies and Been (2000) state that it is clear that minor variation in intrinsic properties of sand have major influence on the critical state. These might be variations on grain shape, mineralogy, grain size distribution, surface roughness of grains, etc.

Yoginder et. al., (1985) found that substantial decrease on liquefaction resistance occur with increase in confining pressure for rounded and angular sands (1600 kPa); also rounded sands show an rapidly build up of resistance against liquefaction with increasing density while angular tailing sand , in contrast, show such rapid increase only at low confining pressures. At low confining pressure angular material is more resistant to liquefaction. Probably the breakage of the corners on the angular particles in tailings is ruling the lost in resistance at high confining pressures (sieve analysis

39 after test identify the breakage of angular particles while on rounded particles the sieve analysis was practically the same).

5.9 GROUNDWATER AND SEEPAGE MODELLING

In groundwater flow the particle’s shape affects the soil’s pore size distribution, hence, the flow characteristics (Sperry and Peirce, 1995). Tortuosity and permeability (also see section 5.7) are two significant macroscopic parameters of granular medium that affect the passing flow (Hayati, et. al., 2012). Current models incorporating the effects of particle shape have failed to consider irregular particles such as those that would prevail in a natural porous medium (Sperry and Peirce, 1995).

Hayati, et. al. (2012) suggested based on his results that tortuosity effect converge when the porosity increases indicating that the shape have dominance at low and mid porosity ranges.

Sperry and Peirce (1995) research conclusions suggest that particle size and porosity are more important predictors for hydraulic conductivity explaining the 69% of the variability but particle shape appears to be the next most important. This however apparently comprises particles larger than 295-351 μm. Differences for particle size 295-351 μm and smaller are not detectable. Another interesting result in the research was the interaction effect of the particle size and particle shape. It suggests a different packing configuration for particles of the same shape but different size (scale dependent).

6 DISCUSSION

6.1 TERMS, QUANTITIES AND DEFINITIONS.

In order to describe the particle shape in detail, there are a number of terms, quantities and definitions (qualitative and quantitative) used in the literature (e.g. Wadell, 1932, 1934; Krumbein, 1941; Sneed & Folk, 1958). All mathematical definitions (quantitatives) are models used to simplify the complexity of shape description. Some authors (Mitchell & Soga, 2005; Arasan et al., 2010) are using three sub-quantities; one and each describing the shape but at different scales. The terms are morphology/form, roundness and surface texture (figure. 1). The three sub-quantities are probably the best way to classify and describe a particle because not a single definition can interpret the whole morphology. Common language is needed when descriptors are explained, and these three scales represent an option. It is evident in the reviewed literature that many of the shape descriptors are presented with the same name but also that there is not a clear meaning on what this descriptor defines. e.g. when there is no upper limit in the roundness, does it means that the angularity never ends? Could they be more and more angular? Probably they could be on theory but not in reality.

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6.2 PROPERTIES

Trough various article’s review done in the present investigation it is recognized that the particle’s shape has an effect on the material properties, among these are:

1. Porosity (Tickell, 1938; Fraser, 1935; Kolbuszewski, 1948) and void ratio (Cho et. al., 2006; Shergold, 1953; Rousé et. al., 2008; Santamarina and Cho, 2004) 2. Permeability (Witt and Brauns, 1983) 3. Internal friction angle (Shinohara et. al., 2000; Chan and Page, 1997; Cheshomi et. al., 2009) 4. Density (Youd, 1973; Holubec and D’Appolonia, 1973) 5. Drag coefficient Hydraulics (Briggs and McCulloch, 1962)

In Table 5 is a short resume of the properties and shape effect found in peer review articles trough different journals. Most of the reviewed articles based its research on uniform graded sands.

Table 8 Compilation of properties influenced by particle shape

Repose Friction Porosity and Settling velocity angle angle Void ratio Density Permeability Drag coefficient Deformation Sphericity (3D)/shape NI x x x x x x factor Circularity (2D) NI x x x x NI NI

Roundness x x x x NI NI x x, influence NI, no information available

Shape of particles has an effect on the arrangement producing bridging or avoiding the rotation of the particles and the resulting geotechnical property is affected; e.g. including flaky particles can result in a higher void ratio due the bridging effect (Santamarina and Cho, 2004) and depending on the loads even the size distribution is changed due the breakage (Yoginder et. al., 1985) in similar way angular particles produce higher void ratio due the avoided possibility of the particles to rotate and compact.

The influence of the chosen shape descriptor appears, in this review, to have minor influence on the soil properties in the reviewed studies except on the void ratio and the friction angle. Influence of particle shape in some cases is hider by other factors (e.g. size distribution); also the particle shape probably does not have influence when particle size is in the clay order (e.g. hydraulic conductivity), the reason could be due to forces as electrostatic or capillarity become more important at this level.

Among the shape descriptors, some are chosen more often in literature (e.g. aspect ratio) there is no apparent scientific basis to use it (probably due to the simplicity of the measurement it becomes one of the most use) but there are still some other descriptors that may or may not show better correlation with the soil properties. Instead empirical relations had been developed regarding roundness or shape to describe the soil behaviour it is clear that the mechanism behind the results is still not completely understood.

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There is necessity to define the best(s) shape descriptor(s) to be used for particular geotechnical properties.

6.3 IMAGE ANALYSIS

Many image analysis techniques had been used to describe the particle shape, e.g. Fourier analysis, fractal dimension, tomography, etc., (Hyslip and Vallejo, 1997) but there is not agreement on the usage or conclusion to ensure the best particle descriptor for geotechnical applications.

There are several shape descriptors and also various techniques to capture the particles profile (3-dimensions, 3-dimension orthogonal and 2-dimensions). Each technique presents advantages 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.

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6.4 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 information in a short period of time with a similar result, at least enough from the practical point of view, as the traditional sieving.

7 CONCLUSIONS

The conclusions of this literature review are:

 It has been shown that particle shape has influence on the soil behaviour despite of partial knowledge of the mechanism behind. Understanding of the particle shape and its influence needs to be accomplished.

 A common language needs to be built up to standardize the meaning on geotechnical field that involve the particle shape. General relationships between shape and properties should be developed.

 Based on this review it is not clear which is the best descriptor to use in geotechnical engineering affecting he related shape to properties. Instead of a couple of standards there is no shape descriptor in geotechnical field fully accepted.

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

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 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.

8 FURTHER WORK

Three main issues have been identified in this review that will be further investigated; the limits of shape descriptors, 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 and the relation with the soil properties it is convenient to determine the descriptor’s correlation with the soil properties.

9 ACKNOWLEDGMENT

I would like to thanks to Luleå University of Technology (LTU), the time I had spent in its facilities and the kind environment it offers, and University of Sonora (UNISON) that has been providing me the financial support and the time to conclude this journey.

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APENDIX A

List of standards related to particle shape based on geological origin materials.

BS812: Section 105.1:1989. Determination of aggregate particle shape (flakiness index).

BS812: Section 105.2:1990. Determination of aggregate particle shape (elongation index)

ASTM D 4791 (2005). Standard test method for flat particles, elongated particles or flat and elongated particles in coarse aggregate. Flat or elongated particles of aggregates, for some construction uses, may interfere with consolidation and result in harsh, difficult to place materials. This test method provides a means for checking compliance with specifications that limit such particles or to determine the relative shape characteristics of coarse aggregates. (ASTM, 2011)

ASTM D 3398 (2006). Standard test method for index of aggregate particle shape and texture. This test method provides an index value to the relative particle shape and texture characteristics of aggregates. This value is a quantitative measure of the aggregate shape and texture characteristics that may affect the performance of road and paving mixtures. This test method has been successfully used to indicate the effects of these characteristics on the compaction and strength characteristics of soil-aggregate and asphalt concrete mixtures

ASTM D5821 - 01(2006) Standard Test Method for Determining the Percentage of Fractured Particles in Coarse Aggregate. Some specifications contain requirements relating to percentage of fractured particles in coarse aggregates. One purpose of such requirements is to maximize shear strength by increasing inter-particle friction in either bound or unbound aggregate mixtures. Another purpose is to provide stability for surface treatment aggregates and to provide increased friction and texture for aggregates used in pavement surface courses. This test method provides a standard procedure for determining the acceptability of coarse aggregate with respect to such requirements. Specifications differ as to the number of fractured faces required on a fractured particle, and they also differ as to whether percentage by mass or percentage by particle count shall be used. If the specification does not specify, use the criterion of at least one fractured face and calculate percentage by mass.

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ASTM C1252 - 06 Standard Test Methods for Uncompacted Void Content of Fine Aggregate (as Influenced by Particle Shape, Surface Texture, and Grading).These test methods cover the determination of the loose uncompacted void content of a sample of fine aggregate. When measured on any aggregate of a known grading, void content provides an indication of that aggregate's angularity, sphericity, and surface texture compared with other fine aggregates tested in the same grading. When void content is measured on an as-received fine-aggregate grading, it can be an indicator of the effect of the fine aggregate on the workability of a mixture in which it may be used.

EN 933-3:1997. Tests for geometrical properties of aggregates. Determination of particle shape. Flakiness index. This European Standard specifies the procedure for the determination of the flakiness index of aggregates. It applies to aggregates of natural or artificial origin, including lightweight aggregates. (Replaces BS 812- 105.1:1989 which remains current.)

EN 933-4:2000. Tests for geometrical properties of aggregates. Determination of particle shape. Shape index. This European Standard specifies a method for the determination of the shape index of coarse aggregates. It applies to aggregates of natural or artificial origin, including lightweight aggregates.

EN 933-5:1998. Tests for geometrical properties of aggregates. Determination of percentage of crushed and broken surfaces in coarse aggregate particles

ASTM D 2488-90 (1996). Standard practice for description and identification of soils (visual-manual procedure) describes the shape of aggregates as either flat or elongated, or flat and elongated using the criteria in tables. This same standard describes the angularity of coarse grained materials on angular, sub-angular, sub- rounded or rounded (Janoo 1998). New standard ASTM D2488-09a.

Swedish national testing research method to determine size distribution of aggregates by computer assisted image analysis (suitable for concrete or mortar) (Persson, 1998)

AASHTO TP 56: Standard Method of Test for Uncompacted Void Content of Coarse Aggregate (As Influenced by Particle Shape, Surface Texture, and Grading).

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