Compression of Granular Soils_T08-123

Compression of granular materials

Gholamreza Mesri and Barames Vardhanabhuti

Abstract: Compression data on over 100 sands were examined to clarify the role of particle rearrangement through inter-particle slip and rotation and particle damage on primary compression, including the yield stress, secondary compression,and coefficient of lateral pressure at rest. During the increase in effective vertical stress, mechanisms such as tighter pack-ing that promote particle locking and interparticle slip and particle damage that promote particle unlocking together deter-mine the relationship between void ratio and effective vertical stress. Three levels of particle damage together withinterparticle slip and rotation determine three types of compression behavior and a yield stress at the abrupt onset of par-ticle fracturing and splitting. The ratio of secondary compression index to compression index is independent of whethercompression results from overcoming interparticle friction through interparticle slip, from overcoming particle strengththrough particle damage, or both; and therefore it is a constant independent of the effective stress range. The coefficient oflateral pressure at rest of an initially dense sand starts with a value defined by the Jaky equation and the maximum frictionangle and remains constant up to the abrupt onset of particle fracturing and splitting, at which point it begins to increasewith an increase in effective vertical stress.

Key words: sand, compression, yield stress, secondary compression, coefficient of earth pressure at rest.

Resume : Des donnees de compression de plus de 100 sables ont ete examines afin d’eclaircir le role du rearrangementdes particules par glissement et rotation inter-particulaire et du dommage sur les particules lors de la compression primaire,incluant la limite d’ecoulement, la compression secondaire, et le coefficient de pression laterale au repos. Pendant l’aug-mentation de la contrainte verticale effective, les mecanismes tels que le serrage qui entraıne le blocage des particules, etle glissement inter-particules et le dommage qui entraınent le deblocage des particules, determinent ensemble la relationentre l’indice des vides et la contrainte verticale effective. Trois niveaux de dommage aux particules, en plus du glisse-ment et de la rotation inter-particules, determinent trois types de comportement en compression ainsi que la limite d’ecou-lement au moment ou il y a fracture et separation des particules. Le ratio entre l’indice de compression secondaire etl’indice de compression est independant de l’origine de la compression, que ce soit le surpassement de la friction entre lesparticules par glissement inter-particulaire ou le surpassement de la resistance des particules par du dommage, ou les deux,alors ce ratio est une constante independante de l’intervalle des contraintes effectives. Le coefficient de pression lateraleau repos d’un sable initialement dense est premierement definit par l’equation de Jaky avec l’angle de friction maximal, etdemeure constant jusqu’au moment ou les particules commencent soudainement a fracturer et a se separer; a partir de cepoint le coefficient de pression laterale commence a augmenter avec l’augmentation de la contrainte verticale effective.

Mots-cles : sable, compression, limite d’ecoulement, compression secondaire, coefficient de la pression des terres au re-pos.

[Traduit par la Redaction]

IntroductionIn all soils, one-dimensional compression and isotropic

compression are achieved through particle rearrangementinto a tighter packing. In some soils, particle rearrangementis accompanied by particle deformation, such as bendingand particle compression, as in fibrous peats. In all soils,particle rearrangement into a more compact configuration isachieved by overcoming interparticle friction through inter-

particle slip and rotation. In some soils, particle rearrange-ment is also facilitated by overcoming particle strengththrough particle damage as in granular soils. Particle dam-age may be quantified as level I damage (abrasion or grind-ing of particle surface asperities), level II damage (breakingor crushing of particle surface protrusions and sharp particlecorners and edges), and level III damage (fracturing, split-ting, or shattering of particles) (Roberts and de Souza 1958;Hendron 1963; Marsal 1967; Hardin 1985; Rahim 1989;Coop 1990; Pestana and Whittle 1995; Nakata et al. 2001a,2001b; Chuhan et al. 2002, 2003).

Compression, i.e., more intimate packing of particles, pro-motes locking, including engaging surface roughness, amongsoil particles and increases the stiffness of a granular aggre-gate (Vesic and Clough 1968; Lambe and Whitman 1969).However, interparticle slip and especially particle damageare unlocking mechanisms that decrease the stiffness of agranular mass. During compression of granular materials,both unlocking and locking mechanisms operate simultane-ously. The net effect determines the shape of the void ratio

Received 13 March 2008. Accepted 5 December 2008.Published on the NRC Research Press Web site at cgj.nrc.ca on3 April 2009.

G. Mesri.1 Department of Civil and Environmental Engineering,University of Illinois at Urbana-Champaign, 205 North MathewsAvenue, Urbana, IL 61801, USA.B. Vardhanabhuti. Department of Civil Engineering, KasetsartUniversity, 50 Phahonyotin St., Ladyao Jatujak, Bangkok 10900,Thailand.

1Corresponding author (e-mail: [email protected]).

369

Can. Geotech. J. 46: 369–392 (2009) doi:10.1139/T08-123 Published by NRC Research Press

Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

or volumetric strain versus effective stress relationship and,in the case of one-dimensional compression, the behavior ofthe tangent-constrained modulus (M ¼ Ds 0v=D3v) versus ef-fective vertical stress (s 0v) relationship, where 3v is the verti-cal strain. When the locking effect of more intimate packingdominates over the unlocking effect of interparticle slippageand particle damage, a net locking behavior develops and Mincreases with an increase in s 0v (Chuhan et al. 2002, 2003).A net unlocking behavior results when the unlocking effectsof particle damage and interparticle slip exceed the effect of

improved locking through denser particle packing and M de-creases with an increase in s 0v. An equal balance behavior isalso possible when unlocking and locking effects are equaland M remains constant with s 0v.

One-dimensional and isotropic compression of all soilscan be interpreted in terms of primary compression that oc-curs during the increase in effective stress and secondarycompression that follows at constant effective stress. One-dimensional compression is observed in a laterally con-strained condition in response to an increase in s 0v, and

Fig. 1. Scanning electron micrographs of the surface of three particles of Ottawa sand (a–c) and three particles of Lake Michigan sand (d–f).a, �1401; b, �21552; c, �5000; d, �560; e, �1647; f, �835.

370 Can. Geotech. J. Vol. 46, 2009

Published by NRC Research Press

Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

isotropic compression is observed under an equal all-aroundpressure (p’) in response to an increase in p’. The mecha-nisms that facilitate compression during an increase in effec-tive stress continue with time during secondary compression.

An inherent manifestation of internal friction is the frac-tion of the vertical force that is transmitted to the verticalplanes under the laterally constrained deformation condition.The angle of friction that is mobilized in one-dimensionalcompression, and therefore the behavior of the coefficientof lateral pressure at rest Ko ¼ s 0h=s

0v, where s 0h is the effec-

tive horizontal stress, is determined by the nature of par-ticles, nature and history of particle packing, and particledamage.

In this paper, we utilized data from 182 oedometer testson 98 sands and 17 isotropic loading tests on six sands re-ported in the literature (Vardhanabhuti 2005) to examineand clarify the role of particle rearrangement through inter-particle slip and rotation and particle damage on primarycompression including the yield stress, secondary compres-sion, and coefficient of lateral pressure at rest. This paper

Fig. 1. (continued). Scanning electron micrographs of the surface of three particles of Niigata sand (g–i) and three particles of Toyoura sand(j–l). g, �2364; h, �1674; i, �3700; j, �40000; k, �7500; l, �1200.

Mesri and Vardhanabhuti 371


Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

does not consider compression resulting from vibration ofgranular materials (Mesri and Vardhanabhuti 2007).

Primary compression

Laboratory information on the compressibility of granular

soils comes from oedometer tests in which a soil specimenis subjected to laterally constrained vertical loading andfrom triaxial tests in which a soil specimen is subjected toequal all-around pressure. Most laboratory tests on granularsoils have been conducted on dry (and less frequently on sa-turated), reconstituted specimens using incremental or con-

Fig. 2. Type A compression behavior of a loose Ottawa sand (data from Roberts and de Souza 1958). CU, uniformity coefficient; Dr, rela-tive density; D50, mean grain size; Mmax, tangent constrained modulus at the first inflection point; Mmin, tangent constrained modulus at thesecond inflection point; ðs 0vÞMmax

, effective vertical stress at the yield point defined at the first inflection point; ðs0vÞMmin, effective vertical

stress at the yield point defined at the second inflection point; ðs0vÞMC, effective vertical stress at the yield point defined at the point ofmaximum curvature.

Fig. 3. Type A compression behavior of a dense Ottawa sand (data from Roberts and de Souza 1958). eo, initial void ratio.



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

tinuous loading. Because of the dry condition or high per-meability of saturated granular soils, primary consolidationof a laboratory specimen essentially is completed as soon asthe load is applied, and the end-of-primary (EOP) void ratioor volumetric strain for incremental loading is defined atseveral seconds or minutes past the application of the loadincrement. The EOP void ratio or volumetric strain some-times corresponds to a relatively fast constant rate of load-ing (e.g., 0.01 MPa/s in oedometer tests conducted byChuhan et al. 2002, 2003) or constant rate of compression

(e.g., 0.01 mm/min in oedometer tests by Nakata et al.2001b). The compression data are interpreted either in termsof EOP void ratio versus effective vertical stress or EOPvoid ratio versus the logarithm of effective vertical stress(log s 0v). Most of the existing data on primary compressionof granular soils can be summarized in terms of type A, B,or C void ratio versus effective stress relationships.

Type A void ratio e versus s 0v behavior (such as thatshown in Fig. 2) displays three distinct stages of compres-sion (Chuhan et al. 2003). During the first stage, small par-

Fig. 4. Type A compression behavior of Toyoura sand (data from Nakata et al. 2001a).

Fig. 5. Type A compression behavior of Ottawa sand (data from Pestana and Whittle 1995).



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

ticle movements further engage particle surface roughnessand enhance interparticle locking. There is minor to smalllevel I and level II particle damage (e.g., Vaid et al. 1985;Yudhbir and Rahim 1987; Rahim 1989); however, improvedlocking dominates over unlocking effects, and M increaseswith an increase in s 0v. The second compression stage beginswith level III particle damage, i.e., fracturing of the heavilyloaded particles and collapse of the load-bearing aggregateframework (Cundall and Strack 1979; McDowell 2002;McDowell and Harireche 2002). Particle fracturing unlocks

the aggregate framework, allowing larger interparticle move-ments, and M begins to decrease with an increase in s 0v. Thefirst inflection point in the e versus s0v relationship marksthe beginning of the second stage at an effective verticalstress ðs 0vÞMmax

, and a second inflection point at ðs 0vÞMmin

marks the end at which major particle fracturing and split-ting are substantially complete (Nakata et al. 2001a,2001b). Figure 1 shows examples of sand particle surfaceroughness that is further engaged during small interparticlemovements of the first stage of compression and is disen-

Fig. 6. Type A compression behavior of mono-quartz sand (data from Chuhan et al. 2003).

Fig. 7. Type A compression behavior of a quartz sand (data from Nakata et al. 2001b).



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

gaged during large interparticle movements of the secondstage of compression. During the third compression stage,the stiffness gain from improved particle packing exceedsthe unlocking effect of level I, level II, and some level IIIparticle damage (to both original particles and new angularfragments) and interparticle slip, and M continuously in-creases with an increase in s 0v. During this stage, particledamage may decrease with an increase in the uniformity co-efficient as a result of particle fragmentation and particle

concentration and a decrease in the void ratio, and the asso-ciated relative movement among grains is small (DeBeer1963, 1965; Hagerty et al. 1993; Lade et al. 1996; Boppand Lade 1997; Nakata et al. 2001a, 2001b; Chuhan et al.2002, 2003). Examples of type A e versus s 0v behavior areshown in Figs. 2–7. Type A compression behavior is mostcommonly, but not exclusively, observed for clean well-rounded, strong (high degree of hardness) coarse particles(Nakata et al. 2001b; Chuhan et al. 2002).

Fig. 8. Type B compression behavior of Ganga sand (data from Rahim 1989).

Fig. 9. Type B compression behavior of Wabash River sand (data from Hendron 1963).



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

Type B e versus s 0v behavior (such as that shown inFig. 8) represents a transition between type A and type Ccompression behavior. It is similar to type A compressionbehavior, as it displays three stages of compression; and totype C compression behavior, as M never decreases with anincrease in s 0v throughout the compression. During the firstcompression stage, starting at low stresses, there is level Iand level II particle damage, but improved locking domi-

nates and M gradually increases with an increase in s 0v. Dur-ing the second stage, improved packing just balances theunlocking produced by level III particle damage, and M re-mains constant with s 0v. During the third stage, improvedpacking dominates over the effects of particle damage andinterparticle slip, and M gradually increases with an increasein s 0v (Nakata et al. 2001a, 2001b; Chuhan et al. 2003). Ex-amples of type B e versus s 0v behavior, which is less com-

Fig. 10. Type B compression behavior of Mol sand (data from DeBeer 1963).

Fig. 11. Type B compression behavior of Feldspar sand (data from Pestana and Whittle 1995).



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

mon than type A and type C behavior, are shown in Figs. 8–11 where vertical line segments mark the effective verticalstress range where M remains constant.

In type C, e versus s 0v behavior of granular soils (such asthat shown in Fig. 12) significant level I and level II particledamage begins early at low effective stresses and continueswith or without gradual level III particle damage at highereffective stresses (Coop 1990; Coop and Lee 1993; Chuhan

et al. 2003). The locking effect of improved gradation andpacking dominates over unlocking effects of gradual particledamage and interparticle slippage, and M continuously in-creases with an increase in s 0v (e.g., Pestana and Whittle1995). Examples of type C e versus s 0v behavior are shownin Figs. 12–17. Type C compression behavior is especiallyobserved for angular weak (low degree of hardness) par-ticles such as carbonate sands, in the presence of platy par-

Fig. 12. Type C compression behavior of Quiou sand (data from Pestana and Whittle 1995).

Fig. 13. Type C compression behavior of carbonate sand (data from Chuhan et al. 2003). D60, grain size at which 60% of the sample isfiner.



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

ticles of mica or clay minerals, or for very fine granular ma-terials for which particle damage is a minor factor (Hardin1985; Chuhan et al. 2002, 2003).

Yield stressYield stress traditionally has been considered to mark the

abrupt onset of increased deformability or increased com-pressibility as in the present case. For soils where particle

damage is not a factor, the yield stress in oedometer loading,called preconsolidation pressure (s 0p or s 0pI for isotropicloading; Terzaghi et al. 1996), defines the boundary betweenthe recompression range where compressibility is small andthe compression range where compressibility is much larger.Recompression results from particle deformation and minorinterparticle slip; and therefore the preconsolidation pressuremarks the onset of major interparticle slip, which is quite

Fig. 14. Type C compression behavior of silty sand (data from Huang et al. 1999). FC, fines content passing number 200 US standard sieve.

Fig. 15. Type C compression behavior of mono-quartz sand (data from Chuhan et al. 2003).



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

abrupt for the ‘‘bonded’’ clays such as those from easternCanada (Terzaghi et al. 1996).

The yield stress for granular materials has been assumedto signal the abrupt onset of particle fracturing and splittingand associated particle rearrangement (e.g., Coop and Lee1993; McDowell and Bolton 1998; Nakata et al. 2001a).Therefore, ðs 0vÞMmax

defined at the first inflection point ofthe EOP e versus s 0v relationship best conforms to the phe-

nomenological definition of the yield stress, as it corre-sponds to the abrupt onset of level III particle damage. Thevalues of ðs 0vÞMmax

for 61 oedometer tests on 57 sands inFig. 18 show that the yield stress may range from less than0.3 MPa for an angular biogenic carbonate sand to near30 MPa for a well-rounded quartz sand. (The ‘‘other’’ sandscategory corresponds to the mixtures of quartz, carbonate,and other minerals.) Figure 18 also shows that the net un-

Fig. 16. Type C compression behavior of Ganga sand (data from Rahim 1989).

Fig. 17. Type C compression behavior of silica-2 sand (data from Nakata et al. 2001b).



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

locking effect of major fracturing and splitting for differentsands is substantially complete at about 2–5 times the effec-tive vertical stress at which level III particle damage begins.

The yield stress for compression of granular soils hasbeen previously determined at the point of maximum curva-ture in the e versus log s 0v relationship, ðs 0vÞMC (Hagerty etal. 1993; McDowell et al. 1996; Nakata et al. 2001a,2001b; McDowell 2002; Chuhan et al. 2003). Figures 19and 20 compare ðs 0vÞMC with ðs 0vÞMmax

and ðs0vÞMmin, respec-

tively. The values of ðs 0vÞMC=ðs0vÞMmaxand ðs 0vÞMC=ðs 0vÞMmin

are in the range of 0.7–2.5 and 0.3–0.8, respectively. Most

of the data in Figs. 18–20 correspond to type A e versus s 0vbehavior. For type B behavior, the values for ðs 0vÞMmax

andðs 0vÞMmin

were taken as the beginning and end, respectively,of the s 0v range where M remains constant. However, asthere is no abrupt onset of compressibility change (no inflec-tion point) for type C e versus s 0v compression behavior, a‘‘yield stress’’ determined at ðs 0vÞMC is only an artifice of asemilogarithmic plot (e.g., Figs. 12, 16).

The values of tangent compression indexCc ¼ De=Dlog s 0v as a function of effective vertical stressare summarized in Fig. 21 for three groups of sands, namelyquartz sands, quartz sands with 10%–20% fines content, andcarbonate sands. In the effective vertical stress range of0.001–1000 MPa, the values of Cc are in the range of0.002–1.0. However, the values of the compression index ofsands at an effective vertical stress range beyond ðs0vÞMC arein the range of 0.1–1.0. In addition to sand particle mineral-ogy and aggregate relative density, the value of Cc at thelow effective stress range is determined by sand particleshape and surface characteristics.

The degree of abruptness of the onset of level III particledamage may be characterized in terms of the magnitude ofMmax/Mmin (e.g., Figs. 2, 3). The highest values are observedfor well-rounded coarse uniform strong particles. The transi-tion from the first stage to the second stage is most suddenin uniformly graded sands when yielding is a manifestationof the fracturing of the largest particles that form the aggre-gate framework. The transition is not as sudden in well-graded sands because of the higher particle concentrationand because fracturing begins with smaller particles thatdoes not cause as dramatic an unlocking of the aggregatestructure (McDowell and Bolton 1998; Nakata et al. 2001b).

The onset of level III particle damage takes place athigher effective stresses in isotropic compression than inone-dimensional compression, as illustrated by a comparison

Fig. 18. Data on ðs0vÞMmaxand ðs0vÞMmin

for 42 sands.

Fig. 19. Comparison of ðs 0vÞMC and ðs 0vÞMmax.

Fig. 20. Comparison of ðs0vÞMC and ðs0vÞMmin.



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

of Toyoura sand data in Figs. 4 and 22 (Kwag et al. 1999;Nakata et al. 2001a). This is because shear stresses in one-dimensional compression contribute to particle damage(DeBeer 1963; Bishop 1966; Lee and Farhoomand 1967;Coop and Lee 1993; Pestana and Whittle 1995). Compres-sion data in Figs. 4, 5, 6, and 22 show that, in general, levelIII particle damage occurs at higher ðs 0vÞMmax

or ðp0ÞMmaxas

initial relative density increases, where ðp0ÞMmaxis the all-

around pressure at the yield point defined at the point ofmaximum curvature of e vesus p’. This behavior is a resultof a larger number of interparticle contacts, and thereforelower contact stresses at a higher relative density (Robertsand de Souza 1958; DeBeer 1963; Hendron 1963; Coop andLee 1993; Hagerty et al. 1993; Lade et al. 1996; Nakata etal. 2001a). For the same reason, at a given initial relative

density and particle characteristics, a well-graded sand is ex-pected to display a higher ðs0vÞMmax

than a uniformly gradedsand (Hall and Gordon 1964; Lade and Yamamuro 1996;Nakata et al. 2001b). An increase in particle angularity pro-motes level I and level II particle damage during the firststage of compression, leads to higher normal and shearstresses at interparticle contacts, and results in lower valuesof Mmax/Mmin and ðs 0vÞMmax

(Kjaernsli and Sande 1963; Hag-erty et al. 1993; Lade and Yamamuro 1996; McDowell andBolton 1998).

Secondary compression

Secondary compression is a continuation of the processesthat begin during an increase in effective stress. All mecha-

Fig. 21. Data on Cc for three groups of sands.



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

nisms of compression (including particle rearrangementthrough interparticle slip and rotation and through particledamage) and particle deformation (including bending andcompression) that operate during primary compression con-tinue into the secondary compression. In other words, allphenomena playing a role in compression are time-dependent (e.g., Terzaghi and Peck 1948; Roberts and de

Souza 1958; Lee and Farhoomand 1967; Mesri and Godlew-ski 1977; Mejia et al. 1988; Lade et al. 1997; Mesri 2001).The term creep should not be used to refer to secondarycompression observed under drained, laterally constrained,one-dimensional loading or drained, equal all-around load-ing. The term creep should be reserved for time-dependentdeformation that may develop under both drained and un-drained conditions when a soil is subjected to external shearstresses (e.g., Mesri et al. 1981; Murayama 1983; Murayamaet al. 1984). A major distinction is that time-dependent de-formation due to creep may lead to global failure, whereassecondary compression does not.

Fig. 22. Type A compression behavior of Toyoura sand in isotropic compression (data from Kwag et al. 1999). ðp0ÞMC, equal all-aroundpressure at the yield point defined at the point of maximum curvature of e versus log p’; ðp0ÞMmax

, equal all-around pressure at the yield pointdefined at the first inflection point of e versus p’; ðp0ÞMmin

, equal all-around pressure at the second inflection point of e versus p’ defining theend of the second stage of compression.

Fig. 23. Data on Ca versus Cc for 17 granular materials (from Mesriet al. 1990).

Fig. 24. Data on the ratio Ca/Cc for Antelope Valley sand in one-dimensional and isotropic compression (data from Lade and Liu1998).



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

The Ca/Cc law of compressibility (where Ca is the secon-dary compression index and Cc is the compression index) in-dicates that Ca/Cc is a constant at all instances duringsecondary compression. At any instant (e, s0v, t, where t isthe time) during secondary compression, Cc ¼ De=Dlog s 0vis the slope of the e versus log s 0v relationship, and Ca =

De/Dlog t is the slope of the e versus log t relationship(Mesri and Godlewski 1977; Mesri 1987, 2001; Mesri andCastro 1987; Mesri et al. 1994, 1997). Mesri et al. (1990)previously summarized data on Ca versus Cc for granularsoils, as shown in Fig. 23. These data, which suggest a Ca/Cc range of 0.01–0.03 for granular soils, were obtained inthe s 0v range of 0.05–3 MPa. In fact, most of the data wereobserved in the s 0v range of less than 1 MPa on sands withstrong particles. In this stress range, particle rearrangementduring both primary and secondary compression mainly oc-curs by interparticle slip and rotation. In addition to thereferences cited in Fig. 23, secondary compression of granu-lar soils, including rock fill, has been reported by Robertsand de Souza (1958), Holestol et al. (1965), Sowers et al.

Fig. 25. Compression behavior of silica sand used to study secondary compression (data from Yet 1998).

Fig. 26. The Ca/(1+eo) and Cc/(1+eo) data for silica sand (data fromLeung et al. 1996 and Yet 1998).

Table 1. Computed and measured s0pI for test IC-8-1 of Lade and

Liu (1998).

Preconsolidation pressure inisotropic compression, p0pI (kPa)

PressureNo.

Equal all-aroundpressure, p’ (kPa) Measured Computed

1 50 70 612 100 121 1203 197 246 2504 393 500 5005 785 — 1004



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

(1965), Lee and Farhoomand (1967), Leung et al. (1996),Lade and Liu (1998), Yet (1998), and Takei et al. (2001).

Terzaghi and Peck (1948, p. 59) observed that compres-sion of a sand is not instantaneous but continues over a con-siderable period of time: ‘‘if the process of loading isinterrupted, the void ratio decreases at constant load. . .’’Terzaghi and Peck (1948) illustrated the time-dependent be-havior by secondary compression of a loose silica sand at aneffective vertical stress 60% of the pressure at which ‘‘. . .the grains begin to crush. . .’’ Incidentally, the Terzaghi andPeck (1948) data suggest Ca/Cc = 0.028 for their silica sand.

Takei et al. (2001) reported secondary compression at s 0vequal to 1.11, 2.34, 4.82, 9.95, and 20 MPa for a granularsoil consisting of 2.00–4.75 mm angular quartz particles.The values of Cc/(1+eo) from an EOP e versus log s 0v rela-tionship defined at 10 s, where eo is the initial void ratio,and reported values of Ca/(1+eo) lead to Ca/Cc = 0.012 ±0.002 for this granular material.

Figure 24 shows the compressibility data interpreted fromlaboratory measurements reported by Lade and Liu (1998)for a subangular 0.075–0.250 mm micaceous Antelope Val-ley sand, with eo = 0.96, void ratio in the loosest state emax =1.24, and void ratio in the densest state emin = 0.98. Both

isotropic and one-dimensional compression tests were car-ried out on saturated, reconstituted specimens in a triaxialcell in the pressure range of 0.05–1.5 MPa. The laterallyconstrained condition for one-dimensional compression wasrealized through ‘‘proportional loading’’ (i.e., axial strain =volumetric strain). Consistent with secondary compressionbehavior observed for soft clay and silt deposits (e.g., Mesri1987), Ca/Cc has the same value for both isotropic and one-dimensional compression despite the fact that EOP e versusthe logarithm of effective stress relations for isotropic andone-dimensional compression are different. Lade and Liu(1998) reported that 20% of the particles passed the number200 US standard sieve after a compression test, whereasnone of the sand passed this sieve before testing.

A comprehensive series of one-dimensional compressiontests with secondary compression measurements have beenreported by Leung et al. (1996) and Yet (1998) on a uni-form, subangular, fine (D50 = 0.2 mm) silica sand withCU = 2.4, emax = 0.9820, and emin = 0.5904. Reconstitutedspecimens were prepared in a relative density range of37%–77% and tested in a s 0v range of 0.05–37 MPa. A ser-ies of EOP compression curves are shown in Fig. 25. Allthree initial relative densities display type A compression

Fig. 27. Behavior of Ko for normally consolidated young loose Wabash River sand with Dr = 5% (data from Hendron 1963). K�

, slope of s0hversus s0v ¼ Ds0h=Ds 0v; Kop, coefficient of earth pressure at rest in normally consolidated young loose sands.



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

behavior with ðs 0vÞMmaxvalues of 13.5, 18.0, and 20.0 MPa

for Dr of 37%, 52%, and 77%, respectively. The end of thesecond stage of compression for the specimen with Dr =37% was reached at ðs 0vÞMmin

= 26.5 MPa; however, ðs 0vÞMmin

was beyond the s 0v range used for the Dr = 52% and 77%specimens. In the one-dimensional compression tests on thissilica sand, particle rearrangement at very low stress levelswas facilitated by interparticle slip and rotation; however,level I and level II particle damage started at relatively lowstress levels (*1 MPa), as suggested in Fig. 25b by thegradual transition from the first to the second compressionstage (e.g., Mmax/Mmin = 1.22 for Dr = 37%). Therefore, thecompression that started at low stress levels with interpar-ticle slip and rotation was facilitated through level I, levelII, and subsequently level III particle damage in the s 0vrange that was utilized in these tests.

The Cc/(1+eo) values at each value of s 0v were evaluatedfrom the EOP e versus log s0v curves and together with cor-responding values of Ca/(1+eo) from Fig. 16 of Leung et al.(1996) are shown in Fig. 26. It is apparent that for any onesand of grain mineralogy, grain size, grain shape, and grada-tion, Ca/Cc is a constant, independent of initial relative den-sity and the effective stress level. The latter factor suggests

that Ca/Cc for a given sand is a constant, independent ofwhether compression is facilitated mainly through interpar-ticle slip or predominantly through particle damage (in-cluding levels I, II, and III).

Lade and Liu (1998, p. 912) concluded that (i) the amountof secondary compression ‘‘increases with confining pres-sure, particularly after crushing becomes important at highstresses’’; and (ii) loose sands and sands consisting of weakparticles generally exhibit more time-dependent deformationthan dense sands or sands with strong particles. These con-clusions are correct to the extent that, for any one sand, Ca/Cc is a constant and Ca is directly related to Cc, which doestake the highest values when particle damage becomes im-portant and for loose sands with weak particles. However,for both initially loose and initially dense conditions insome sands, Cc takes the same value at a certain range ofpressure, and both particle damage and Cc begin to decreaseat very high pressures, as is shown by the data in Fig. 21.

The Ca/Cc law of compressibility predicts not only themagnitude of Ca but also the behavior of Ca with time interms of the shape of the EOP e versus log s 0v relationship.The magnitude of Ca is expected to increase, remain con-stant or decrease with time, respectively, in the range of s 0v

Fig. 28. Behavior of Ko for normally consolidated young dense Wabash River sand with Dr = 71% (data from Hendron 1963).



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

at which Cc increases, remains constant, or decreases withan increase in s 0v. The shape of most EOP e versus log s 0vrelationships for granular soils includes increasing Cc, con-stant Cc, and at very high pressures (e.g., Yamamuro et al.1996) decreasing Cc with an increase in s 0v.

The increases in Ca/(1+eo) with an increase in time areplotted in Fig. 26, based on secondary settlement observa-tions for about 100 h by Yet (1998) on silica sand speci-mens with an initial Dr = 75% at effective vertical stressesof 15.4 and 37.4 MPa at which Cc/(1+eo) increases with anincrease in s0v (Fig. 25). The increase in Ca/(1+eo) with anincrease in time at 15.4 MPa is shown by points a and band that at 37.4 MPa it is shown by points c, d, and e. Thevalues of Cc/(1+eo) at points a and c were determined fromthe EOP e versus log s 0v curve at 15.4 and 37.4 MPa, re-spectively. The Cc/(1+eo) values corresponding to points b,d, and e, which show the observed increase in Ca/(1+eo)with an increase in time, were computed using Ca/Cc =0.018 for the silica sand.

Secondary compression is an important aging mechanismfor granular soils (Mesri et al. 1990). The preconsolidationpressures resulting from secondary compression can be com-puted using the following equation (Mesri 1987; Mesri andCastro 1987):

½1�s 0ps 0v¼ t

tp

� � Ca =Cc1�Cr =Cc

where s 0p is the preconsolidation pressure resulting fromsecondary compression, s 0v is the effective vertical stress atwhich secondary compression takes place, Cr is the recom-pression index, t is the age of the sand, and tp is the durationof primary compression. As an example, Table 1 comparesvalues of preconsolidation pressure observed by Lade andLiu (1998) after secondary compression under equal all-around pressure with values computed according to eq. [1],with Ca/Cc = 0.026 and Cr/Cc = 0.1. The s 0pI values pre-dicted using eq. [1] agree well with the measured values.

Coefficient of lateral pressure at rest

The coefficient of lateral pressure at rest, Ko ¼ s 0h=s0v, of a

normally consolidated, young, loose sand starts at

½2� Kop ¼ 1� sin f0cv

where f0cv is the constant-volume friction angle. Kop is thecoefficient of earth pressure at rest in normally consolidatedyoung loose sands and remains constant with s 0v (Jaky 1944,1948; Mesri and Hayat 1993; Vardhanabhuti and Mesri

Fig. 29. Behavior of Ko for normally consolidated young dense Pennsylvania sand with Dr = 63% (data from Hendron 1963).



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

2007). This is illustrated by the oedometer test result inFig. 27 for Wabash River sand with Dr = 5%. During type Be versus s 0v compression behavior, the slope K

�¼ Ds 0h=Ds 0v

remains constant and equal to Kop = 0.44. On the other hand,the coefficient of lateral pressure of an initially dense sandstarts at (Mesri and Hayat 1993)

½3� K�¼ 1� sin f0

where f0 is the maximum friction angle. The value of K�

,which is less than Kop, remains constant until the onset oflevel III particle damage, at which point it begins to in-crease. Level III particle damage disengages particle inter-locks, leading to an increase in s 0h=s

0v. This type of behavior

is observed in Fig. 28 for a Wabash River sand with Dr =71% and in Figs. 29 and 30 for Pennsylvania sand withDr = 63% and 74%, respectively. In all of these cases, K

�is

initially less than Kop, however, K�

begins to increase atðs 0vÞMmax

. There is some evidence to suggest that, even for anormally consolidated young loose sand with K

�¼ Kop dur-

ing the first stage of compression, which displays dramatictype A e versus s 0v behavior with high Mmax/Mmin (i.e.,abruptly destructured by level III particle damage), startingat ðs 0vÞMmax

, K�

may temporarily increase, returning to

K�¼ Kop by the end of the second stage of compression.

For the Minnesota sand (a well-rounded quartz sand) withDr = 89% in Fig. 31, K

�starts at a value significantly less

than Kop = 0.41 and remains constant in the entire range ofs 0v up to 23 MPa of the oedometer test, during which no in-flection point is observed. In other words ðs 0vÞMmax

is greaterthan 23 MPa for this sand specimen.

In summary, these data suggest that, for initially loose,young, and normally consolidated granular materials, Kostarts at Kop and remains constant with s0v. On the otherhand, for initially dense granular materials, Ko starts at a K

�,

which is less than Kop, remains constant until ðs0vÞMmax, and

then begins to increase with an increase in s 0v toward Kop.Laterally constrained compression tests in the triaxial cell

were conducted by Coop (1990) on Dogs Bay biogenic car-bonate sand (D50 = 0.29 mm, CU = 2.07, relatively unbrokenangular shells) by keeping the measured volumetric strainequal to the axial strain (Bishop 1958). An initially loosespecimen of Dogs Bay sand displayed a type A e versus s 0vcompression behavior; however, both ðs 0vÞMmax

¼ 0:04 MPaand ðs 0vÞMmin

¼ 0:25 MPa were small. For this carbonatesand, level I, II, and III particle damage began at low effec-tive stresses and gradually continued with s 0v. The laterally

Fig. 30. Behavior of Ko for normally consolidated young dense Pennsylvania sand with Dr = 74% (data from Hendron 1963).



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

constrained compression stress paths reported by Coop(1990) suggest that, beyond about s 0v = 0.3 MPa,Ko ¼ s 0h=s

0v remained constant in the entire stress range of

the test up to 5 MPa. The measured value of Ko = 0.51,however, was significantly higher than Kop = 0.36, accordingto eq. [2] with f0cv = 408, which was independent of effec-tive stress level. Coop (1990) observed an increase in Koduring secondary compression, concluding that Ko valuesobtained from triaxial tests are likely affected by the speedof testing. Because the Bishop (1958) method previouslyhas been used successfully to measure Kop corresponding tothe end of primary compression, the high value of Ko deter-mined by Coop (1990) for a sand consisting largely of skel-etal bodies apparently included the increase in coefficient oflateral pressure resulting from secondary compression. Mesriand Hayat (1993) have suggested an equation to estimate theincrease in Ko during secondary compression. For a nor-mally consolidated, initially loose granular material

½4� Ko ¼ Kop

t

tp

� �Ca=Cc

Incidentally, for Mexico City clay, which contains a sig-nificant proportion of siliceous skeletal fragments (Mesri et

al. 1975) and displays f0cv = 438, a Kop = 0.31 was directlymeasured (Diaz-Rodriguez et al. 1992) and is very close tothe value according to eq. [2] (Mesri and Hayat 1993). It ap-pears from the following that the constant-volume frictionangle of granular materials is independent of the level ofparticle damage, ranging from none to level III: (i) the be-havior of f0cv of Dogs Bay carbonate sand, which was inde-pendent of effective stress level; (ii) the observed behaviorof Kop of initially young loose sands, in which Kop remainsconstant with s0v (e.g., Fig. 27); and (iii) constanta ¼ sin f0cv, independent of initial relative density in theSchmidt (1966) equation for the Ko of overconsolidatedsands unloaded from a stress level greater than ðs 0vÞMmin

(Mesri and Hayat 1993) (for a further examination of thisissue, reference is made to Yamamuro and Lade (1996) andLade and Yamamuro (1996)).

Yamamuro et al. (1996) inferred the lateral pressures dur-ing one-dimensional compression from measurements of ra-dial strain of a thick-walled oedometer confining ring. For auniform angular quartz sand and a uniform rounded Cambriasand of intermediate hardness, they inferred values of Ko &0.4, which remained constant in the s 0v range from 50 to850 MPa. For a soft uniform gypsum sand, the inferred Koincreased at a decreasing rate to values in the range of 0.7–

Fig. 31. Behavior of Ko for normally consolidated young dense Minnesota sand with Dr = 89% (data from Hendron 1963).



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

0.9 at s 0v = 850 MPa. Yamamuro et al. (1996) attributed theincrease in Ko with an increase in time to plastic deforma-tion of the soft gypsum sand particles. Yamamuro et al.(1996) reported an increase in Ko during secondary compres-sion for both the Cambria and gypsum sands. However, themeasurements, which extended over a period of only30 min, suggest a rate of increase in Ko with an increase intime, which is less than that predicted by eq. [4] with Ca/Ccin the range of 0.01–0.03.

ConclusionsThe following conclusions are based on a review and in-

terpretation of data from 182 oedometer tests on 98 sandsand 17 isotropic loading tests on six sands.

(1) In granular soils, subjected to static loading, particlerearrangement into a more compact configuration isachieved by overcoming interparticle friction throughinterparticle slip and rotation, by overcoming particlestrength through particle damage, or both.

(2) Particle damage may be level I damage (abrasion orgrinding of particle surface asperities), level II damage(breaking or crushing of particle surface protrusionsand sharp particle corners and edges), and level III da-mage (fracturing, splitting, or shattering).

(3) Particle rearrangement into more intimate packing pro-motes locking, whereas interparticle slip and espe-cially particle damage are unlocking mechanisms thatdecrease the stiffness of the granular mass.

(4) During compression, both unlocking and locking me-chanisms operate simultaneously, and the net effectdetermines the shape of the void ratio or vertical strainversus effective vertical stress relationship and the be-havior of the tangent constrained modulus with effec-tive vertical stress, M ¼ Ds 0v=D3v.

(5) When locking through tighter particle packing domi-nates over the unlocking effect of interparticle slipand particle damage, the constrained modulus in-creases with an increase in effective vertical stress,whereas when unlocking produced by level III particledamage and interparticle slip exceeds the locking ef-fect of denser packing, the constrained modulus de-creases with an increase in effective vertical stress.

(6) Three types of end-of-primary (EOP) void ratio versuseffective vertical stress relationship have been ob-served. Type A compression behavior, which is mostcommon for clean well-rounded strong medium tocoarse sands, consists of three stages of compression.A net locking first stage during which M increaseswith an increase in s 0v is followed by a net unlockingsecond stage as a result of an abrupt onset of level IIIparticle damage with M decreasing with an increase ins 0v. This is followed by a locking third stage. Type Bcompression behavior also consists of three stages ofcompression. Net locking behavior during the firstand third stages, respectively, precedes and follows anequal balance second stage compression behavior dur-ing which unlocking and locking effects are equal andM remains constant with s 0v. Type C compression be-havior, which is especially observed for angular weakparticles such as carbonate sands, for which significant

level I and level II particle damage begins at low ef-fective stress and continues with or without gradual le-vel III particle damage, displays a net locking effectthroughout the effective stress range.

(7) A yield stress for type A and type B compression be-havior is defined at ðs0vÞMmax

, which marks the abruptonset of particle fracturing and splitting. The valuesof ðs0vÞMmax

range from less than 0.3 MPa for an angu-lar biogenic carbonate sand to near 30 MPa for a well-rounded quartz sand.

(8) The effective stress that marks the end of the secondstage of compression, ðs 0vÞMmin

, is two to five timesthe value of ðs 0vÞMmax

.(9) The yield stress commonly defined at the point of

maximum curvature of void ratio against the logarithmof effective vertical stress, ðs 0vÞMC, is 0.7–2.5 times thevalue of ðs 0vÞMmax

and 0.3–0.8 times the value ofðs 0vÞMmin

.(10) All mechanisms of compression, including particle re-

arrangement through interparticle slip and rotation andparticle damage, that operate during primary compres-sion continue into secondary compression.

(11) Secondary compression of granular materials followsthe Ca/Cc law of compressibility, with Ca/Cc in therange of 0.01–0.03.

(12) The Ca/Cc for any one granular material is indepen-dent of the mechanism that facilitates particle rearran-gement. Therefore, Ca/Cc is a constant independent ofeffective vertical stress range. For any one sand, Ca/Cchas the same value for both one-dimensional compres-sion and isotropic compression.

(13) The Ca/Cc law of compressibility also correctly pre-dicts the behavior of Ca with time: when Cc increaseswith an increase in s 0v, Ca increases with an increasein time; and when Cc is constant with s 0v, Ca remainsconstant with time.

(14) The coefficient of lateral pressure at rest of a normallyconsolidated young loose sand starts atKop ¼ 1� sin f0cv and remains constant with an in-crease in effective vertical stress.

(15) The coefficient of earth pressure at rest of an initially

dense sand starts with K�¼ 1� sin f0, which is less

than Kop, and remains constant up to ðs 0vÞMmax, at

which point the onset of level III particle damage de-structures the aggregate framework and K

�begins to

increase, however, returning to K�

= Kop by the end ofthe second stage of compression.

(16) In summary, it is possible to provide a rational expla-nation of the observed primary compression, includingyielding of the aggregate framework, secondary com-pression, and lateral pressure in constrained compres-sion, of granular materials in terms of particlerearrangement facilitated through interparticle slip androtation and particle damage.

ReferencesBishop, A.W. 1958. Test requirements for measuring the coefficient

of earth pressure at rest. In Proceedings of the Conference onEarth Pressure Problems, Brussels, Belgium, Vol. 1, pp. 2–14.

Bishop, A.W. 1966. The strength of soils as engineering materials.Geotechnique, 162: 89–130.



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

Blumel, W., and Lackner, F. 1981. Performance of foundations formasts on sand. In Proceedings of the 10th International Confer-ence on Soil Mechanics and Foundation Engineering, Stock-holm, Sweden, 15–19 June 1981. A.A. Balkema, Rotterdam, theNetherlands. Vol. 2, pp. 49–52.

Bopp, P.A., and Lade, P.V. 1997. Effect of initial density on soilinstability at high pressures. Journal of Geotechnical and Geoen-vironmental Engineering, ASCE, 123: 671–677. doi:10.1061/(ASCE)1090-0241(1997)123:7(671).

Castro, G. 1969. Liquefaction of sands. Harvard University, Cam-bridge, Mass. Harvard Soil Mechanics, Series 81.

Chuhan, F.A., Kjeldstad, A., Bjorlykke, K., and Hoeg, K. 2002.Porosity loss in sand by grain crushing — experimental evi-dence and relevance to reservoir quality. Marine and PetroleumGeology, 19: 39–53. doi:10.1016/S0264-8172(01)00049-6.

Chuhan, F.A., Kjeldstad, A., Bjorlykke, K., and Hoeg, K. 2003.Experimental compression of loose sands: relevance to porosityreduction during burial in sedimentary basins. Canadian Geo-technical Journal, 40(5): 995–1011. doi:10.1139/t03-050.

Coop, M.R. 1990. The mechanics of uncemented carbonate sands.Geotechnique, 40: 607–626.

Coop, M.R., and Lee, I.K. 1993. The behavior of granular soils athigh stresses. In Predictive soil mechanics. Edited by G.T. Hous-bly and A.N. Schofield. Thomas Telford, London, U.K. pp. 186–198.

Cundall, P.A., and Strack, O.D.L. 1979. A discrete element modelfor granular assemblies. Geotechnique, 29: 47–65.

Davisson, M.T., and Salley, J.R. 1972. Settlement histories of fourlarge tanks on sand. In Proceedings of the Specialty Conferenceon Performance of Earth and Earth Supported Structures, Lafay-ette, Ind., 11–14 June 1972. ASCE, New York. Vol. 1, Part 2,pp. 981–996.

DeBeer, E.E. 1963. The scale effect in the transposition of the re-sults of deep sounding tests on the ultimate bearing capacity ofpiles and caisson foundations. Geotechnique, 13: 39–75.

DeBeer, E.E. 1965. The scale effect on the phenomenon of pro-gressive rupture in cohesionless soils. In Proceedings of the 6thInternational Conference on Soil Mechanics and Foundation En-gineering, Montreal, Que. University of Toronto Press, Toronto,Ont. Vol. 2, pp. 13–17.

Diaz-Rodriguez, J.A., Leroueil, S., and Aleman, J.D. 1992. Yield-ing of Mexico City and other natural clays. Journal of Geotech-nical and Geoenvironmental Engineering, ASCE, 118: 981–995.

Hagerty, M.M., Hite, D.R., Ullrich, C.R., and Hagerty, D.J. 1993.One-dimensional high pressure compression of granular mate-rial. Journal of Geotechnical and Geoenvironmental Engineer-ing, ASCE, 119: 1–18.

Hall, E.B., and Gordon, B.B. 1964. Triaxial testing with large-scalehigh pressure equipment. In Laboratory Shear Testing of Soils.American Society for Testing and Materials, Philadelphia, Penn.Special Technical Publication STP-361, pp. 315–328.

Hansen, B. 1961. The bearing capacity of sand, tested by loadingcircular plates. In Proceedings of the 5th International Confer-ence on Soil Mechanics and Foundation Engineering, Paris,France, 17–22 July 1961. Dunod, Paris. Vol. 1, pp. 659–664.

Hardin, B.O. 1985. Crushing of soil particles. Journal of Geotech-nical and Geoenvironmental Engineering, ASCE, 10: 1177–1192.

Hendron, A.J. 1963. The behavior of sand in one-dimensional com-pression. Ph.D. thesis, Department of Civil and EnvironmentalEngineering, University of Illinois at Urbana-Champaign, Ur-bana, Ill.

Holestol, K., Kjaernsli, B., and Torblaa, I. 1965. Compression oftunnel spoil at Venemo Dam. In Proceedings of the 6th Interna-

tional Conference on Soil Mechanics and Foundation Engineer-ing, Montreal, Que., 8–15 September 1965. University ofToronto Press, Toronto, Ont. Vol. 2, pp. 490–494.

Huang, A.-B., Hsu, H.-H., and Chang, J.-W. 1999. The behavior ofa compressible silty fine sand. Canadian Geotechnical Journal,36(1): 88–101. doi:10.1139/cgj-36-1-88.

Jaky, J. 1944. A nyugalmi nyomas tenyezoje — The coefficient ofearth pressure at rest. Magyar Mernok es Espitesz-Egylet Kozlo-nye. pp. 355–358.

Jaky, J. 1948. Pressure in silos. In Proceedings of the 2nd Interna-tional Conference on Soil Mechanics and Foundation Engineer-ing, Rotterdam, the Netherlands, June 1948. Vol. 1, pp. 103–107.

Kjaernsli, B., and Sande, A. 1963. Compressibility of some coarse-grained materials. In Proceedings of the 1st European Confer-ence on Soil Mechanics and Foundation Engineering, Weisba-den, Germany. pp. 245–251.

Kwag, J.M., Ochiai, H., and Yasufuku, N. 1999. Yielding stresscharacteristics of carbonate sand in relation to individual particlefragmentation strength. In Engineering for calcareous sediments.Edited by K.A. Al-Shafei. A.A. Balkema, Rotterdam, the Neth-erlands. pp. 79–87.

Lade, P.V., and Liu, C.T. 1998. Experimental study of drainedcreep behavior of sand. Journal of Engineering Mechanics,ASCE, 124: 912–920. doi:10.1061/(ASCE)0733-9399(1998)124:8(912).

Lade, P.V., and Yamamuro, J.A. 1996. Undrained sand behavior inaxisymmetric tests at high pressures. Journal of Geotechnicaland Geoenvironmental Engineering, ASCE, 122: 120–129.

Lade, P.V., Yamamuro, J.A., and Bopp, P.A. 1996. Significance ofparticle crushing in granular materials. Journal of Geotechnicaland Geoenvironmental Engineering, ASCE, 122: 309–316.

Lade, P.V., Yamamuro, J.A., and Bopp, P.A. 1997. Influence oftime effects on instability of granular materials. Computers andGeotechnics, 20: 179–193. doi:10.1016/S0266-352X(97)00002-5.

Lambe, T.W., and Whitman, R.V. 1969. Soil mechanics. John Wi-ley & Sons, New York.

Lee, K.L., and Farhoomand, I. 1967. Compressibility and crushingof granular soil in anisotropic triaxial compression. CanadianGeotechnical Journal, 4: 68–99. doi:10.1139/t67-012.

Leung, C.F., Lee, F.H., and Yet, N.S. 1996. The role of particlebreakage in pile creep in sand. Canadian Geotechnical Journal,33(6): 888–898. doi:10.1139/t96-119.

Marsal, R.J. 1967. Large scale testing of rockfill materials. Journalof the Soil Mechanics and Foundations Division, ASCE, 93: 27–43.

McDowell, G.R. 2002. On the yielding and plastic compression ofsand. Soils and Foundations, 42: 139–145.

McDowell, G.R., and Bolton, M.D. 1998. On the micromechanicsof crushable aggregates. Geotechnique, 48: 667–679.

McDowell, G.R., and Harireche, O. 2002. Discrete element model-ing of yielding and normal compression of sand. Geotechnique,52: 299–304. doi:10.1680/geot.52.4.299.41018.

McDowell, G.R., Bolton, M.D., and Robertson, D. 1996. The frac-tal crushing of granular materials. Journal of the Mechanics andPhysics of Solids, 44: 2079–2102. doi:10.1016/S0022-5096(96)00058-0.

Mejia, C.A., Vaid, Y.P., and Negussey, D. 1988. Time dependentbehavior of sand. In Proceedings of the International Conferenceon Rheology and Soil Mechanics, Coventry, UK, 12–16 Septem-ber 1988. Edited by M.J. Keedwell. Elsevier Applied Science,London. pp. 312–326.

Mesri, G. 1987. Fourth law of soil mechanics: a law of compressi-bility. In Proceedings of the International Symposium on Geo-



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

technical Engineering of Soft Soils, Mexico City, Mexico, 13–14 August 1987. Mexican Society for Soil Mechanics, MexicoCity, Mexico. Vol. 2, pp. 179–187.

Mesri, G. 2001. Primary compression and secondary compression.In Soil behavior and soft ground construction. Edited by J.J.Germaine, T.C. Sheahan, and R.V. Whitman. ASCE Geotechni-cal Special Publication 119, pp. 122–166.

Mesri, G., and Castro, A. 1987. The Ca/Cc concept and Ko duringsecondary compression. Journal of Geotechnical and Geoenvir-onmental Engineering, ASCE, 113: 230–247.

Mesri, G., and Godlewski, P.M. 1977. Time- and stress-compressi-bility interrelationship. Journal of Geotechnical and Geoenviron-mental Engineering, ASCE, 103: 417–430.

Mesri, G., and Hayat, T.M. 1993. The coefficient of earth pressureat rest. Canadian Geotechnical Journal, 30(4): 647–666. doi:10.1139/t93-056.

Mesri, G., and Vardhanabhuti, B. 2007. Coefficient of earth pres-sure at rest for sands subjected to vibration. Canadian Geotech-nical Journal, 44(10): 1242–1263. doi:10.1139/T07-032.

Mesri, G., Rokhsar, A., and Bohor, B.F. 1975. Composition andcompressibility of typical samples of Mexico City clay. Geo-technique, 25: 527–554.

Mesri, G., Febres-Cordero, E., Shields, D.R., and Castro, A. 1981.Shear stress – strain – time behavior of clays. Geotechnique, 31:537–552.

Mesri, G., Feng, T.W., and Benak, J.M. 1990. Postdensification pe-netration resistance of clean sands. Journal of Geotechnical andGeoenvironmental Engineering, ASCE, 116: 1095–1115.

Mesri, G., Lo, D.O.K., and Feng, T.W. 1994. Settlement of em-bankments on soft clays. In Vertical and horizontal deformationsof foundations and embankments. Edited by A.T. Yeung andG.Y. Feaalio. ASCE Geotechnical Special Publication 40,pp. 8–56.

Mesri, G., Stark, T.D., Ajlouni, M.A., and Chen, C.S. 1997. Sec-ondary compression of peat with or without surcharging. Journalof Geotechnical and Geoenvironmental Engineering, ASCE,123: 411–421. doi:10.1061/(ASCE)1090-0241(1997)123:5(411).

Murayama, S. 1983. Formulation of stress–strain–time behavior ofsoils under deviatoric stress condition. Soils and Foundations,23: 41–57.

Murayama, S., Michihiro, K., and Sakagami, T. 1984. Creep char-acteristics of sands. Soils and Foundations, 24: 1–15.

Nakata, Y., Kato, Y., Hyodo, M., Hyde, A.F.L., and Murata, M.2001a. One-dimensional compression behavior of uniformlygraded sand related to single particle crushing strength. Soilsand Foundations, 41: 39–51.

Nakata, Y., Hyodo, M., Hyde, A.F.L., Kato, Y., and Murata, H.2001b. Microscopic particle crushing of sand subjected to highpressure one-dimensional compression. Soils and Foundations,41: 69–82.

Nonveiler, E. 1963. Settlement of a grain silo on fine sand. In Pro-ceedings of the 3rd European Conference on Soil Mechanics andFoundation Engineering, Weisbaden, Germany. Vol. 1, pp. 285–294.

Parkin, A.K. 1977. The compression of rockfill. Australian Geome-chanics Journal, 7: 33–39.

Pestana, J.M., and Whittle, A.J. 1995. Compression model for co-hesionless soils. Geotechnique, 45: 611–631.

Rahim, A. 1989. Effect of morphology and mineralogy on com-pressibility of sands. Ph.D. thesis, Indian Institute of TechnologyKanpur, Kanpur, India.

Roberts, J.E., and de Souza, J.M. 1958. The compressibility ofsands. Proceedings of the American Society for Testing and Ma-terials, 58: 1269–1272.

Schmidt, B. 1966. Earth pressure at rest related to stress history:discussion. Canadian Geotechnical Journal, 3: 239–242. doi:10.1139/t66-028.

Sowers, G.F., Willams, R.C., and Willace, T.S. 1965. Compressi-bility of broken rock and the settlement of rockfills. In Proceed-ings of the 6th International Conference on Soil Mechanics andFoundation Engineering, Montreal, Que., 8–15 September 1965.University of Toronto Press, Toronto, Ont. Vol. 2, pp. 561–565.

Swiger, W.F. 1975. Evaluation of soil moduli. In Proceedings ofthe Conference on Analysis and Design in Geotechnical Engi-neering, Austin, Tex., 9–12 June 1974. ASCE, New York.Vol 2, pp. 79–92.

Takei, M., Kusakabe, O., and Hayashi, T. 2001. Time-dependentbehavior of crushable materials in one-dimensional compressiontests. Soils and Foundations, 41: 97–121.

Terzaghi, K., and Peck, R.B. 1948. Soil mechanics in engineeringpractice. John Wiley & Sons, New York.

Terzaghi, K., Peck, R.B., and Mesri, G. 1996. Soil mechanics inengineering practice. 3rd ed. John Wiley & Sons, New York.

Vaid, Y.P., Chern, J.C., and Tumi, H. 1985. Confining pressure,grain angularity and liquefaction. Journal of Geotechnical andGeoenvironmental Engineering, ASCE, 10: 1229–1235.

Vardhanabhuti, B. 2005. Vibration of sands. Ph.D. thesis, Depart-ment of Civil and Environmental Engineering, University of Illi-nois at Urbana-Champaign, Urbana, Ill.

Vesic, A.S., and Clough, G.W. 1968. Behavior of granular materi-als under high stresses. Journal of the Soil Mechanics and Foun-dations Division, ASCE, 94: 661–688.

Whitman, R.V., Miller, E.T., and Moore, P.J. 1964. Yielding andlocking of confined sand. Journal of the Soil Mechanics andFoundations Division, ASCE, 90: 57–84.

Yamamuro, J.A., and Lade, P.V. 1996. Drained sand behavior inaxisymmetric test at high pressures. Journal of Geotechnicaland Geoenvironmental Engineering, ASCE, 122: 109–119.

Yamamuro, J.A., Bopp, P.A., and Lade, P.V. 1996. One-dimensional compression of sands at high pressure. Journal ofGeotechnical and Geoenvironmental Engineering, ASCE, 112:147–154.

Yet, N.S. 1998. Time-dependent behavior of piles in sand. Ph.D.thesis, National University of Singapore, Singapore.

Yudhbir, and Rahim, A. 1987. Compressibility characteristics ofsands. In Proceedings of the 9th Southeast Asian GeotechnicalConference, Bangkok, Thailand. A.A. Balkema, Rotterdam, theNetherlands. Vol. 1, pp. 483–494.

List of symbols

Cc compression index (¼ De=Dlog s0v)Cr recompression index (¼ De=Dlog s0v)

CU uniformity coefficient (= D60/D10)Ca secondary compression index (= De/Dlog t)

D10 grain size at which 10% of the sample is finerD50 mean grain sizeD60 grain size at which 60% of the sample is finer

Dr relative densitye void ratio

eo initial void ratioemax void ratio in loosest stateemin void ratio in densest state

Ko coefficient of earth pressure at restKop coefficient of earth pressure at rest in normally con-

solidated young loose sandsK�

slope of s 0h versus s0v ¼ Ds0h=Ds0vM tangent constrained modulus (Ds0v=D3v)



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

Mmax tangent constrained modulus at the first inflectionpoint of s 0v versus 3v or p’ versus 3v

Mmin tangent constrained modulus at the second inflec-tion point of s 0v versus 3v or p’ versus 3v

p’ equal all-around pressure(p’)MC equal all-around pressure at the yield point defined

at the point of maximum curvature of e versus logp’

ðp0ÞMmaxequal all-around pressure at the yield point definedat the first inflection point of e versus p’

ðp0ÞMminequal all-around pressure at the second inflectionpoint of e versus p’ defining the end of the secondstage of compression

t timetp duration of primary consolidation3v vertical strain; volumetric strain

f0 maximum friction anglef0cv constant-volume friction angles 0h effective horizontal stresss 0p preconsolidation pressures 0pI preconsolidation pressure in isotropic compressions 0v effective vertical stress

ðs0vÞMC effective vertical stress at the yield point defined atthe point of maximum curvature of e versus log s 0v

ðs0vÞMmaxeffective vertical stress at the yield point defined atthe first inflection point of e versus s 0v

ðs0vÞMmineffective vertical stress at the second inflectionpoint of e versus s 0v defining the end of the secondstage of compression



Can

. Geo

tech

. J. D

ownl

oade

d fr

om w

ww

.nrc

rese

arch

pres

s.co

m b

y K

ing'

s C

olle

ge L

ondo

n -

CH

AN

Jou

rnal

s on

05/

05/1

1Fo

r pe

rson

al u

se o

nly.

Compression of Granular Soils_T08-123

Documents

Transcript of Compression of Granular Soils_T08-123