Coop,M.R.,Sorenn,K.K.,Bodas Freitas,T.&Georgoutsos,G.(2004).Ge
´otechnique 54,No.3,157–163157
Particle breakage during shearing of a carbonate sand
M.R.COOP Ã
,K.K.SORENSEN y ,T.BODAS FREITAS
Ã
and G.GEORGOUTSOS {
A ries of ring shear tests was conducted to investigate
the development of particle breakage with shear strain for a carbonate sand.It was found that at very large displacements the soil reached a stable grading,but that the final grading was dependent on both the applied normal stress and the initial grading.The particle break-age caud a volumetric compression,which again cead only when the stable grading had been attained,empha-sising that
critical states as obrved at much smaller strains in triaxial tests are not rigorously defined.Despite the vere degradation of the soil particles the mobilid angle of shearing resistance was found not to change significantly.
KEYWORDS:calcareous soils;sands;shear strength
Nous avons mene
´une ´rie d’essais de cisaillement annu-laire afin d’enque
ˆter sur le de ´veloppement des cassures de particules avec une de
´formation de cisaillement pour un sable carbonate.Nous avons trouve
´qu’avec de tre `s importants de
´placements,le sol parvenait a `une granulo-me
´trie stable mais que la granulome ´trie finale de ´pendait de la contrainte normale applique
´e et de la granulome ´-trie initiale.La cassure des particules provoque une
compression volume
´trique qui,encore une fois,ne ces que lorsque la stabilite
´granulome ´trique est atteinte,soulignant le fait que les e
´tats critiques tels que ceux qui sont obrve
´s avec des de ´formations bien plus petites dans les essais triaxiaux ne sont pas rigoureument de ´finis.Nous avons trouve ´que malgre ´la de ´gradation
´ve `re des particules de sol,l’angle mobili ´de re ´sistance au cisaillement ne changeait pas de manie
`re significative.INTRODUCTION
By means of triaxial testing over an extended range of pressures,Coop &Lee (1993)concluded that for a variety of sands of different mineralogies there was a unique relation-ship between the amount of particle breakage that occurred on shearing to a critical state and the value of the mean normal effective stress.The identification of a unique critical state line was then ud as the basis for a critic
al state framework for sands at both large strains and small (Jovicic &Coop,1997)and for the analysis of the behaviour of geotechnical structures in sands,such as driven piles (Klotz &Coop,2001).The approach had much in common with the state parameter framework of Been &Jefferies (1985).
The implied assumption in the framework was that at the critical state a sand would reach a stable grading at which the particle contact stress would not be sufficient to cau further breakage.An alternative assumption,bad on the work by Chandler (1985)for material with deformable grains and implemented by Baharom &Stallebrass (1998)for soils with breakable grains,is that a critical state reached in the triaxial apparatus reprents a balance between volu-metric compression arising from particle breakage and volu-metric dilation from particle rearrangement.
Luzzani &Coop (2002)identified that there was some doubt,particularly at higher stress levels,as to whether samples did reach a true constant-volume state in triaxial tests and therefore whether the particle breakage had com-pletely cead.To investigate this further they carried out ring shear tests on two sands,one with a quartz and one a carbonate mineralogy.In both cas particle breakage was found to continue to strains very much higher than tho reached in the triaxial apparatus,so confirming the hypoth-esis that any constant-volume state obrved in a triaxial test
must be the result of counteracting components of volu-metric strain and not becau a stable grading has been reached.However,the displacements or strains that were achievable in their tests were insufficient to e whether the soil would eventually reach a stable grading or not.For tests on the carbonate sand at one stress level a constant ratio was found between volumetric strain and the amount of particle breakage as quantified with relative breakage,B r ,defined by Hardin (1985),suggesting that the volumetric strain would cea only when particle breakage stopped and a stable grading was reached.
Through improved testing techniques it has proved possi-ble to reach higher displacements in the ring shear appara-tus,allowing an investigation to be made of the evolution of grading at even larger strains,so identifying whether or not a stable grading is ever reached.As for most of the tests prented by Luzzani &Coop,a carbonate sand has been ud for this study,to maximi the breakage and so minimi the strains that would be required to reach a constant grading,should it exist.However,the patterns of behaviour are likely to be applicable to sands of other mineralogies,although it is still not possible to reach the even higher strains that would be required to confirm the conclusions prented here for a quartz sand.Luzzani &Coop also restricted their investigation to one initial grading and loo samples at higher stress levels,so that the carbonate sa
nd was starting from an initial state that was on its normal compression line,or limiting compression curve (Pestana &Whittle,1995).Here a variety of gradings,densities and stress levels has been investigated.
MATERIAL TESTED AND PROCEDURES
The soil tested was Dog’s Bay sand,a biogenic carbonate sand that was tested extensively in the triaxial apparatus by Coop (1990)and Coop &Lee (1993).The particles are predominantly foraminifera and mollusc shells and shell fragments,and so are angular with frequent intra-particle voids.They are also delicate,and break easily under load.As has been obrved by others and is confirmed here,particle breakage is greater for uniformly graded than for well-graded sands,and so to maximi the breakage most of Manuscript received 12June 2003;revid manuscript accepted 12December 2003.
Discussion on this paper clos 1October 2004,for further details e p.ii.Ã
Department of Civil and Environmental Engineering,Imperial College,London.y
University College London,formerly Imperial College,London.{
Formerly Imperial College,London.
the tests were conducted on soil from the sieve interval 300–425ìm.To investigate the effects of particle size a test (RS7)was also carried out on a cond uniform grading defined between the212ìm and300ìm sieve sizes.An-other test(RS8)investigated the influence of the uniformity of the initial grading,for which a well-graded sample was created with25%of the particles from each of the four sieve intervals63–150ìm,150–212ìm,212–300ìm and 300–425ìm.In each ca the initial particle size was defined carefully by wet-sieving the soil into its constituent particle sizes before lecting the grading to be ud or reconstituting a sample in the chon proportions.
Ring shear tests were conducted in the Bishop type of apparatus(Bishop et al.,1971),which allows the shearing to occur at the mid-height of the sample by means of split confining rings.This system also allows the friction lost on the side walls to be quantified by measuring the resistance to raising the upper rings,so creating a gap between the two ts of rings.During the‘gap open’stages,the shear stress applied to the sample may also be measured,whereas when the gap is clod the shear stress is unknown owing to the friction between the two pairs of rings.However,the gap-open stages were reduced to a minimum as the displacement that could be reached during a test was determined by the amount of soil lost through the gap between the rings,which accelerated for t
he gap-open stages.All tests were stopped before the sample became so thin that thefins attached to the top platen would enter the central part of the sample, which is that principally ud for the particle size analysis as described below.It is the loss of soil through the gap, which occurs even when the gap is clod,that prevents a similar investigation being carried out for a quartz sand,as the displacements required to reach a constant grading would be very much larger.
A summary of the tests undertaken is given in Table1. Tests denoted LC are tho that were previously prented by Luzzani&Coop(2002).The net vertical effective stress (ó9v)quoted for each test includes the deduction made for the side friction.The nominal vertical stress applied were 1MPa(LC1-4&RS1-8),400kPa(RS9-14)or100kPa (RS15-19),and it is the side friction that accounts for the variation inó9v.Whereas for the tests that were stopped at smaller displacements the side friction was fairly constant, that for the tests taken to very large displacements varied significantly,largely becau of the changing sample thick-ness,and so a range is given for the net vertical stress.
The uniformly graded samples were created by water pluviation,but moist tamping had to be ud for the well-graded sample to avoid gregation,after which the water bath wasflooded to saturate the samples.Denr samples were created infive layers using gentle hand-tamping of each layer afte
r pluviation.Shearing was conducted at a rate of about1.9mm/min for consistency with previous work. The data are prented in this paper in terms of shear and vertical strains rather than displacements,so that:
ª¼
äh
H0
(1)åv¼
äv
H0
(2)
whereäh andäv are the horizontal and vertical displace-ments and H0is the initial sample height.Although the particle size data do indicate some non-uniformity of strains, albeit not excessive,
prenting the data in terms of strains has the advantage that qualitative comparisons are more easily made with data from other apparatus.One objective of this rearch is also to emphasi the very large strains that are required to reach a stable grading,and this is better achieved by plotting strains rather than displacements.How-ever,it should be stresd that the values of strain are purely notional,and that both vertical and shear strains are likely to be similarly affected by strain localisation.
The vertical strains have been corrected for the soil lost through the gap between the rings during shearing,and are bad on the weight of soil recovered from outside the rings after the test.As discusd above,the rings were kept clod for most of the test to minimi the loss.Although the soil loss accelerated during the gap-open stages,it is not known by how much,and as for the tests the gap-open stages
Table1.Details of the tests conducted
Test Notes Initial grading:
ìm e prior to
shearing
Netó9v during
shearing:kPa
Finalª:
%
LC1300–4251.58%805207
LC2300–4251.61%805730
LC3300–4251.57%805104
LC4300–4251.56%805251
LCSB1Shear box test300–4251.4693052
RS1300–4251.51%670171
RS2300–4251.46%6702860
RS3300–4251.55650–66011100
RS4300–4251.52%6701430
RS5300–4251.46740–86011030
RS6300–4251.43750–8202780
RS7Finer grading212–3001.41750–8502910
RS8Well graded63–4250.96725–82511710
RS9300–4251.50250–28010920
RS10300–4251.47248–3463350
RS11300–4251.46283–37513280
RS12300–4251.45296–3681180
RS13300–4251.59288–38626650
RS14300–4251.60290–343285
RS15300–4251.5060–77147000
RS16300–4251.7962–709040
RS17300–4251.7266–8031700
RS18300–4251.6878–9423900
RS19300–4251.6968–9737500
LC,test conducted by Luzzani&Coop(2002).
158COOP,SORENSEN,BODAS FREITAS AND GEORGOUTSOS
were few,most of the soil loss actually occurred during gap clod stages.The simple assumption has therefore been made that the correction to the vertical strain is proportional to the displacement,regardless of whether the gap was open or clod,although this does mean that for the gap-open stages there is a jump in vertical strain,which reprents the acceleration of soil loss.A det
ailed comparison between uncorrected and corrected data was made by Luzzani &Coop (2002).For the test at the higher stress level that reached the largest strain (RS8)the correction reprented a reduction of the volumetric strain by 5.4%on a total meas-ured value of about 26%,but the corrections for most of the other tests were much smaller.
Following each test the soil was carefully retrieved from the apparatus in three layers.The central layer,Zone 2,was that within Æ2.5mm of the split in the rings;Zone 1was that soil above and Zone 3the soil below.Luzzani &Coop found that the particle breakage in Zones 1and 3was always similar,but that there was significantly higher break-age in Zone 2,confirming some non-uniformity of strains.For some of the tests taken to the largest strains at the highest stress levels a well-defined band of shearing could be identified after the test,with a cohesive central zone of soil that parated easily from the remainder of the sample,in which ca the soil in this band was taken as Zone 2.An example is shown in Fig.1.However,it was found that the thickness of the shear band was in any ca generally around 5mm.
Following the tests the final particle size distribution was determined by wet-sieving by hand,which was complemen-ted by dimentation tests using the hydrometer method in some cas.For some tests the particle size distribution of only Zone 2was determined,whereas in other cas all three zon
es were examined.The amount of particle breakage was quantified by means of Hardin’s (1985)relative breakage,B r ,the definition of which is given in Fig.2.This is partly for consistency with previous work.However,there are many
means of quantifying breakage that have been chon by different authors.In particular,the total surface area of the particles,as ud for example by Miura &Y amanouchi (1977)and Miura &O-Hara (1979),has many advantages,but the general assumption made in calculating the surface area is that the particles are spherical.Dog’s Bay sand was chon for this study as it highlights particle breakage,and—as will be en later—many of the conclusions reached might not have been possible for sands with stronger,solid and spherical particles.However,one disadvantage is that the delicate,open and angular particles that promote break-age also mean that an assumption of a spherical shape would be unjustifiable.For simplicity,and again for consistency with previous work,rather than defining B r from the baline of the US standard 74ìm sieve,the British Standard 63ìm sieve size has been ud,but this makes only a small difference to the values calculated.
VOLUME CHANGE AND EVOLUTION OF GRADING Figure 3shows the volumetric strains measured for a lection of the tests.The jumps in the data,for example at around 500%shear strain for test RS8,result from the gap-open stages,for which there was an acceleration of soil loss through
the gap that is evident even after the data have been corrected,becau the correction has assumed that the loss is proportional to the displacement irrespective of whether the gap is open or not,which,as discusd above,is inaccurate.Tests often ended with a gap-open stage to check the final stress,and so jumps in the data of this kind are sometimes evident at the end of the data.Nevertheless,the volumetric strain data do indicate that for most of the tests,which were carried out at vertical stress levels in the range 650–860kPa,a constant volumetric strain is reached at a shear strain of around 2000%.It had been intended that each of the tests (RS3,RS5and RS7)should have had similar vertical stress.For the tests by Luzzani &Coop
~5 mm
RS8 (63–425 µm), γfinal ϭ 11707%
Fig.1.Cross-ction of a shear band retrieved from test
RS8
100806040
2000·01
0·101·0010·00
P e r c e n t a g e p a s s i n g
Particle size: mm
Total breakage, B t ϭ area BCDB Breakage potential, B p ϭ area BCAB Relative breakage, B r ϭ B t /B p
Fig.2.Definition of relative breakage,B r (Hardin,
1985)
Shear strain: %
20
40
V o l u m e t r i c s t r a i n : %
(a)
20
40
V o l u m e t r i c s t r a i n : %
(b)
Shear strain: %
Fig.3.Influence of stress level and grading on volumetric strains
PARTICLE BREAKAGE DURING SHEARING OF A CARBONATE SAND
159
(2002)the vertical stress could be controlled with reasonable accuracy,but here greater difficulty was experienced in achieving a particular vertical stress,particularly at the high-er stress levels.This wasfirst becau the side friction was found to be much more variable in the ring shear apparatus ud,and cond becau at the very large strains reached the side friction was found to vary significantly during the test.
In Fig.3(b)it can be en that the tests at lower stress levels(RS8,RS13,RS15)take much larger strains for the volumetric strain to stabili,with about20000%required for test RS13at288–386kPa.F
or test RS15at60–77kPa the volumetric strain initially shows the dilation that would be en at smaller strain levels in triaxial tests,but then the volume change becomes compressive,although very slow, and it had just about stabilid when the test was terminated at147000%.At low shear strains the volume change is highly dependent on the confining stress,with,as expected, low stress level tests dilating and tho at higher stress compressing.However,the large volumetric compression that appears at very large shear strains for all stress levels as a result of particle breakage ems to be much less dependent on stress level.
Tests RS3,RS5and RS7all have similarfinal volumetric strains.Test RS3was at a slightly lower stress level,but on a slightly loor sample than test RS5,factors that may have counteracted each other.However,test RS7,which is on a sample with a grading that is again uniform,but in this ca finer,reaches a similarfinalåv.Test RS8,which is on a well-graded sample,also reaches a constantåv at a similar shear strain to the other tests,but the ultimate value is lower.
In Fig.4the particle size distributions are shown with both the usual linear and logarithmic percentage passing axes for all tests conducted with a vertical stress in the range650–930kPa.The variation in vertical stress undoubt-edly adds to the data scatter,but this range reprents the extreme stress,and most tests have an average stress in the range750–850kPa.Despite the variation of ver
tical stress a number of interesting features can be obrved.Data
are also repeated here from the tests at smaller shear strains by Luzzani&Coop(2002)for completeness,one of which (LCSB1)at the smallest strains was conducted in a shear box rather than a ring shear apparatus.The‘no shearing’curve reprents the particle grading of the soil subjected to one-dimensional loading to a vertical stress of800kPa in the oedometer.
Comparing tests RS2,RS3and RS4with the particle size distributions from tests that reached smaller shear strains,it is evident that,just asåv stabilid at around2000–4000% shear strain,so does the grading.Initially the grading changes rapidly with increasing shear strain,but the change from test RS2(2860%)to test RS3(11100%)is very small. Using a linear percentage passing axis gives a gradings curve that rotates around the largest particle size,but remains concave upwards.The rotation around the maximum particle size is similar to obrvations that McDowell& Bolton(1998)made for the compression of sands.With a logarithmic axis it is clear that the gradings curve evolves towards a linear distribution.McDowell&Bolton also identified that the particle size distribution of sands under-going one-dimensional compression evolves with a fractal distribution,which results in a linear particle size distribu-tion on the double logarithmic graph.They found that in compression the gradient was generally around0.5,corre-sponding to a fractal dimensio
n of2.5.Here there again appears to be a tendency towards a fractal distribution,but with a slightly lowerfinal gradient of0.43for test RS3and so a fractal dimension of2.57.
From the tests at lower stress(Figs5and6)it is clear that again there is a tendency at the largest strains towards a uniquefinal gradings curve.However,thefinal gradings curves are different for each stress level,so that not only does thefinal amount of breakage reduce with stress level, but also thefinal gradings curve tends to become more curved even when double logarithmic axes are ud.
Figure7shows thefinal gradings curves for the two tests investigating the influence of initial grading.From Fig.7(a) it can be en that for the initially well-graded sample the final gradings curve for test RS8,which reached11710% shear strain,is slightly higher than that of the initially poorly graded samples.The difference is small,but significant when compared with the scatter of data from tests RS3and RS5, which are tho tests on the original0.3–0.425mm grading that are at the same stress level and are considered to have reached a stablefinal grading.
Thefiner but uniformly graded sample(RS7,Fig.7(b)) reached afinal gradings curve that was again above that of the other samples at this stress level.In compression, McDowell&Bolton(1998)showed that the gradings curves at a given stress level for samples with similar initial uniformity of grading,bu
t different absolute particle sizes, were all parallel.In Fig.7(b)a reference line has been drawn that is approximately parallel to an average of the final gradings for tests RS3and RS5,but passing through the maximum initial particle size of0.3mm for test RS7.It can be en that thefinal gradings curve lies quite clo to
this.
Initial grading
No shearing
LCSB1 52%
LC3 104%
RS1 171%
LC4 251%
LC2 730%
RS4 1430%
RS2 2860%
RS3 11100%
RS5 11030%
RS6 2780%
Initial grading
No shearing
LCSB1 52%
LC3 104%
RS1 171%
LC4 251%
LC2 730%
RS4 1430%
RS6 2780%
RS2 2860%
RS5 11030%
RS3 11100% 100
80
60
40
20
Particle size: mm
(a)
P
e
r
c
e
n
t
a
g
e
p
a
s
s
i
n
g
100
10
1
0·0010·0100·1001·000
Particle size: mm
(b)
P
e
r
c
e
n
t
a
g
e
p
a
s
s
i
n
g
Fig.4.Evolution of particle size distribution for Zone2for tests withó9v in range650–930kPa(LC,test by Luzzani& Coop(2002);SB,shear box test):(a)mi-logarithmic axes;(b) double logarithmic axes
160COOP,SORENSEN,BODAS FREITAS AND GEORGOUTSOS
QUANTIFICATION OF PARTICLE BREAKAGE
For some of the tests on 0.3–0.425mm samples in the stress range 650–930kPa,the relative breakage has been quantified for all three zones,and the data from the tests are shown in Fig.8.The initial value of B r of 0.057at zero shear strain is that caud by a vertical stress alone of a
bout 800kPa,from an oedometer test.There is significantly greater breakage in Zone 2than in either Zone 1or Zone 3,and the breakage in Zones 1and 3is similar.However,the breakage in all three zones stabilis at around 2000–4000%,which is similar to the strains required for the volumetric strain to stabili at this stress level.
In Fig.9the ratio of the volumetric strain to the relative breakage has been calculated,and,as Luzzani &Coop had obrved for lower strain levels,the ratio remains constant,confirming that the compressive volumetric strain is directly related to the particle breakage.The ratio is not much affected by either the uniformity of the initial grading (RS8)or the absolute particle size (RS7).
The evolution of the percentage passing within each particle size interval is illustrated in Fig.10.The data points shown at 1%are tho from the oedometer test,but as a logarithmic strain scale has been ud for clarity,the points have had to be plotted at a finite strain,thereby making the assumption,for the sake of the plot,that there is no breakage in the first 1%of shearing.None of the tests investigated breakage in the medium strain range,so the trends shown up to 100%shear strain are uncertain.How-ever,the data for larger strains from the ring shear tests illustrate some interesting features.The percentage passing for the coarst interval (0.3–0.425mm)reduces rapidly,whereas that for the particles passing 0.063mm sieve in-creas from almost zero at the start of the test,so th
at
the
10010
1
Particle size: mm
P e r c e n t a g e p a s s i n g
Initial grading RS14 285%RS12 1180%RS10 3350%RS9 10920%
RS11 13280%RS13 26650%
Fig.5.Evolution of particle size distribution for Zone 2for tests with ó9v in range 248–386
kPa
100
10
1
Particle size: mm
P e r c e n t a g e p a s s i n g
Initial grading
RS16 9040%RS18 23900%
RS17 31700%RS19 37500%RS15 147000%
Fig.6.Evolution of particle size distribution for Zone 2for tests with ó9v in range 60–97
kPa
100
10
1Particle size: mm
(a)
P e r c e n t a g e p a s s i n g
100
10
1Particle size: mm
(b)
P e r c e n t a g e p a s s i n g
Fig.7.The influence of initial grading:(a)effect of range of initial particle sizes;(b)effect of absolute value of particle
size
1·00·80·60·40·20
B r
γ: %
Zone 1
Fig.8.Particle breakage in the three zones for tests in stress range 650–930kPa
PARTICLE BREAKAGE DURING SHEARING OF A CARBONATE SAND
161
