a different approach and result to the measurement of ko of granular soils

8/9/2019 A Different Approach and Result to the Measurement of Ko of Granular Soils

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Talesnick, M. L. (2012). Ge otechnique 62, No. 00, 1–5 [http://dx.doi.org/10.1680/geot.11.P.009]

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P R O O F

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TECHNICAL NOTE

A different approach and result to the measurement of K o of granular soils

M . L . T A L E S N I C K

An in-soil version of the null soil pressure measurementsystem has been used in the measurement of lateral earthpressures of granular soils for at-rest K o conditions. Fouruniformly graded soils were tested, from particle dia-meter 0.15 mm through to 15 mm. Two significant obser-vations were made based upon the data presented. Forinitial loading, the coefficient of lateral earth pressure, K o, was found to be higher for soil placed in a densepacking arrangement in comparison to that measured forthe same soil placed in a loose packing arrangement. Thedevelopment of horizontal pressure during unloading andreloading was found to be very similar to that of initial

loading.

KEYWORDS:

On a utilise une version dans le sol du systeme de mesurede pression nulle du sol dans la mesure de pousseeslaterales de la terre pour des sols granulaires dans desconditions K o au repos. On a soumis a des essais quatresols a granulometrie uniforme, de 0,15 mm a 15 mm. Oneffectue deux observations significatives sur la base desdonnees presentees. Pour les charges initiales, on releveque le coefficient de poussee laterale des terres est super-ieur pour des sols places dans une configuration a com-pactage dense par rapport au coefficient mesure pour lememe sol soumis a un compactage lache. Le developpe-ment de la pression horizontale au cours du decharge-

ment et du rechargement s’est avere fort similaire a celuide la charge initiale.

INTRODUCTIONThe coefficient of lateral earth pressure at rest, K o, is defined in equation (1).

K o ¼ 9h= 9 z (1)

K o represents the effective horizontal pressure in relationto effective vertical pressure under conditions of zero lateral

strain (h¼

0). It is obviously not a shear failure condition,and should not be described in terms of limiting equilibrium.Despite this, K o is often estimated according to equation (2).

K o ¼ 1 sin 9 (2)

Equation (2) was suggested in a slightly different form for normally consolidated soils by Jaky (1944). Note that someresearchers (e.g. Michalowski, 2005) have criticised the useof this equation.

The objective of this article is to present experimentaldata which provide reliable measurement of the coefficientof lateral earth pressure at rest. Attention has been aimed,specifically, at the effects of particle size, density and stresshistory on the magnitude of K o of granular soils.

BACKGROUNDThe coefficient of lateral earth pressure at rest is a

parameter which cannot be determined theoretically, for thisreason, empirical models have been developed for its estima-tion. Most models (e.g. Alpan, 1967; Schmidt, 1967; Dar-amola, 1980; Mayne & Kulhawy, 1982) are founded onequation (2) and have been extended, based on availableexperimental data and statistical analysis, to estimate K oduring unloading and reloading.

In the case of granular soils, and in view of the fact that9 is an increasing function of the relative density ( Dr ), K ois expected to be higher for a loose sand than for a densesand. Over the years, researchers (e.g. Brooker & Ireland,1965; Mesri & Vardhanabhuti, 2007) have plotted measured values of K o as a function of 9: This is problematic, since9 is dependent upon density, testing apparatus, specimen preparation and compaction method. From a search of the

literature, the author has not found reliable data demonstrat-ing the reduction of K o with increasing density.

Consider two packing arrangements of spheres, one looseand one dense, within infinitely rigid, frictionless containersof equal volumes, as shown in Fig. 1. Intuitively, in order for the denser material to deform vertically, a greater horizontal pressure would develop on the cylinder sides thanin the case of the loose arrangement. This possibility can beattributed to its dilatant nature in comparison with thecontractive nature of the loose material.

Alternatively, if K o is determined according to isotropic,linear elastic theory, K o would be written as

K o ¼ 9h

9v

¼

1

(3)

where is the Poisson ratio, which is greater for densesands than for loose sands (e.g. Itasca, 2008; Budhu, 2000)and consequently K o would be greater for a denser sand than

Article Number: 11p009

Manuscript received 16 January 2011; revised manuscript accepted 21February 2012. Published online ahead of print XX XXXXXXXXXX.

Discussion on this paper closed on XX XXXXXX XXXX, for further details see p. ii. Faculty of Civil and Environmental Engineering, Technion – IIT,Haifa, Israel.

60 particles45 particles

Fig. 1. Schematic idealisation of loose and dense packingarrangements

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for its looser counterpart. However, soil is not an elasticsolid, therefore this approach is not applicable.

The difficulty in substantiating this hypothesis lies in thefact that reliable measurement of soil pressure is not trivial.Many researchers have reported upon the aspects whichhamper the measurement of soil pressure (e.g. Taylor, 1944;Selig, 1980; Weiler & Kulhawy, 1982). Because of the particulate nature of soil, the measurement of pressure must

be done without allowing any deflection of the measurementdevice. Minute deflection of the sensor induces redistributionof soil pressure in the vicinity, and error in the response of the transducer (Tory & Sparrow, 1967).

To highlight this difficulty a set of experiments using acommercially available soil pressure sensor (Kulite 0234)embedded in a fine-grained dune sand was performed. TheKulite sensor has an active sensing diameter of 36 mm, anoverall diameter of 55 mm and a thickness of 15 .5 mm. Thetests were carried out in a soil pressure vessel 550 mm indiameter and 300 mm high. The sides of the pressure vesselwere covered with a friction-reducing tarp comprising twothin layers of graphite grease, sandwiched within three layersof thin polyethylene sheeting (Tognon et al., 1999). Meas-urement of soil pressure on the vessel base has illustrated that side wall friction has no effect on the vertical pressureat the centre of the test vessel. Soil was placed in the testingvessel using a funnel according to testing procedures used inthe determination of minimum unit weight (ASTM 4254,ASTM (2006)). The transducer was placed horizontally or vertically on the soil at the mid-height of the vessel. Thevessel was then topped up with soil using the funnel and sealed with a latex membrane and vessel top. Under suchconditions the transducer was tested in soil placed at arelative density of 12%. Controlled air pressure was thenapplied to the latex membrane, which in turn applied pressure to the soil below.

Figure 2 presents the response of the Kulite 0234 tovertical pressure in one case, and to horizontal pressure

under K o conditions in a second case. When the sensor isoriented horizontally it responds directly to a known vertical pressure and should result in a set of points which fall alonga unique straight line both in loading and unloading. As isseen from the plot, the signal output during initial loading islinear. However, the signal output over the unloading portion

is highly hysteretic and does not return to the origin. Thishysteretic response is obviously erroneous. Despite the highstiffness of the Kulite 0234, the hysteretic response seen inthe figure is inherent to the sensor and is in reaction to theminute deflection of the sensing membrane, which inducesinteraction between the sensor and the surrounding particles.The same sensor was then placed in the same soil, under thesame conditions, in the vertical orientation. In this case it

responds to unknown horizontal pressure that develops inresponse to K o conditions. The output signal in response toinitial loading is linear, and to unloading is also highlyhysteretic. Determination of the horizontal pressure duringunloading is unrealistic since it is impossible to differentiate between the real response and the inherent hysteresis intro-duced by the sensing technique. It should not be assumed that the soil response to unloading is hysteretic.

EXPERIMENTAL TOOLS: SOIL PRESSUREMEASUREMENT WITH THE IN-SOIL NULL GAUGE

Talesnick (2005, 2010) described a soil pressure measure-ment system based on the null concept in which the sensingmembrane is constantly forced to remain in an undeflected state. The internal pressure required to maintain the membrane in the undeflected state is equal in magnitude to thesoil pressure applied to the outer face of the sensor.

In a series of control tests Talesnick (2005) illustrated that, when installed at a soil structure boundary, the responseof the sensor is unaffected by soil type, stiffness, particlesize or the stress history. The concept implies that calibra-tion of the sensing system is not required.

Talesnick (2010) illustrated that the same concept can beused successfully in the measurement of soil pressure withina soil mass. Under such conditions the sensor responds asan infinitely stiff inclusion in a deforming medium. Testingof the system illustrated that the small over-registrationassociated with the stiffness mismatch between the transdu-

cer and the surrounding soil was in agreement with calcula-tions made by Tory & Sparrow (1967). It was further shownthat the sensor exhibited no hysteresis and was unaffected by stress history. Talesnick (2010) described a rather largesensor 105 mm in diameter (9.8 mm thick) which allowed for the measurement of soil pressure in particulate mediawith particle dimensions of up to 15 mm.

In the present study this sensor and one of smaller dimensions have been used. The smaller sensor is 44 mm indiameter and 5.7 mm thick, with a sensing diaphragm23 mm in diameter. The response of the sensors was eval-uated in the same pressure vessel described earlier. Thesensors were placed in the horizontal orientation such thatthey responded directly to the applied vertical pressure. The

response of the two sensors when embedded in loose dunesand is shown in Fig. 3. As may be seen, there is nohysteretic response noted in the load–unload cycle, nor wasthere any hysteresis in subsequent load–unload cycles.

This outcome makes the null sensor ideal for the meas-urement of lateral pressure under K o conditions; it inherently prohibits deflection, therefore its output is unaffected by parasitic hysteresis, which plagues the response of deflectingdiaphragm sensors (Fig. 2).

TESTING SET-UP, PROGRAMME AND MATERIALSTESTED

In this study, testing has been performed on four uni-

formly graded soils of particle size varying from 0.15 mmthrough 12 mm, placed at different densities. All the testinghas been performed in the vat described earlier, according tothe same protocols.

0

0·01

0·02

0·03

0·04

0 40 80 120

Signaloutput: V d

c

Applied surface pressure: kPa

Vertically oriented

Horizontally oriented

Kulite 0234, calibrated – loose dune sand

Unloading path

Loading path

Fig. 2. Response of the Kulite soil pressure sensor when placed indune sand in the horizontal and vertical orientations

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SEach material was tested in two particle arrangements:

loose and dense. The loose condition was achieved by either funnelling the materials into the test vat, or, in the case of the gravel-sized materials, by spooning the particles into thevat. The dense arrangement was achieved by tapping theouter side of the pressure vat with a hammer, not by directcompaction or tamping. Direct compaction and tampinginduce compaction stresses and pre-compression pressureswhich are to be avoided in this type of experiment. Thevibrations caused by the hammer blows to the cell sides donot induce pre-compression pressures.

Vertical deformation of the soil was monitored duringtesting in order to consider the form of the vertical stress– strain response during the load–unload cycles. Table 1supplies data relevant to particle size and testing configura-tions. In each test, at least two full load–unload cycles were performed.

TEST RESULTSFigure 4 shows typical results obtained when using the in-

soil null gauge for the measurement of horizontal soil pressure in loosely placed dune sand. The lower section of the figure illustrates almost no hysteresis in horizontal pressure during unloading or subsequent reloading. The ini-

tial loading portions of the plots are near to linear, thereforethe slope represents the coefficient of lateral earth pressure

at rest, K o: The slope has been determined based on a least-

squares regression and was found to be 0.45.The upper portion of the figure depicts the stress–strain

response of the loose sand in the vertical direction. Aswould be expected, the plot illustrates very non-linear re-sponse and low stiffness of the sand upon initial, virginloading. On unloading, almost all of the vertical strain isseen to be irrecoverable. During the second load– unload cycle the response is far less non-linear and displays asignificant increase in stiffness.

Figure 5 presents plots similar to those shown in Fig. 4, but for the case of dense dune sand. The lower plot showsthe same outcome as found for the case of the loosely placed dune sand. The development of horizontal pressureon initial loading is linear. Slight hysteresis upon unloading

is noted in comparison to that noted for the loose sand;however, it is minimal. The slope of the initial loadingsegments is 0.54.

This outcome is significant, it implies that K o for theloosely placed sand, ,0.45, is less than that of the densely placed sand, ,0.54. This result is contrary to the K o ¼ 1 sin 9 relation.

Similar outcomes were noted for the other three materialstested. The values for K o are given in Table 2 and illustratethat in each case K o of the dense material is greater thanthat of the loose material. In all cases hysteresis was small, but not exactly the same for each material. In the case of the coarse quartz sand the hysteresis was the greatest, butfar below that predicted according to models such as those

of Mayne & Kulhawy (1982) or Schmidt (1967).The upper graph of Fig. 5 illustrates the typical non-linear

response expected during initial, virgin loading. In this casethe stiffness is significantly higher in comparison to the

0

40

80

120

160

200

240

0 40 80 120 160 200 240

Nullpressure:kPa

Applied vertical pressure: kPa

Large, first load

Large, first unload

Small, first load

Small, first unload

Fig. 3. Response of the in-soil null gauge when placed in dune

sand in the horizontal orientation

Table 1. Soil particle sizes andplacement densities (givenin kg/m3)

Material D50: mm Density Null gauge

Small Large

Dune sand 0.15 Loose 1410 1415Dense 1630 1650

Coarse sand 1.5 Loose 1580 1570Dense 1710 1720

SumSum 5 Loose 1430Dense 1610

Adas 12–15 Loose 1455Dense 1555

0

0·5

1·0

1·5

2·0

2·5

Verticalstrain,

:%

ε z

Loose dune sand

First load

First unload

Second load

Second unload

0 40 80 120 160

Applied pressure: kPa

80

60

40

20

0

Horizontalpressure:kPa

Fig. 4. Typical results of horizontal pressure measured in loosedune sand using the in-soil null gauge

MEASUREMENT OF K o OF GRANULAR SOILS 3



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loose sand considered in Fig. 4. The unloading segment of the first cycle illustrates that almost all of the verticaldeformation is irrecoverable.

SUMMARY, CONCLUSIONS AND DISCUSSIONThe null soil pressure gauge has been used in the meas-

urement of horizontal pressure in granular materials of uni-form grain sizes ranging from 0.15 to 15 mm. The aim of the measurements was to quantify the magnitude of thecoefficient of lateral earth pressure, K o, at different densities;

and to consider qualitatively the development of horizontal pressure during unloading and reloading.

The data presented have led to two significant observa-tions.

(a) It has been experimentally observed that, for at-restconditions, K o for any specific granular soil is greater when in a dense arrangement in comparison with looser one.

(b) The development of hysteresis in horizontal pressureupon unloading and subsequent reloading of applied vertical pressure is small, and in general insignificant.

The first observation is contrary to our usual notions of soil mechanics and to accepted practice; however, it doesmake sense. A soil which is denser is more prone to dilatein order to accommodate the vertical deformations. Whenthese vertical deformations must be accommodated under K oconditions, the horizontal pressure will be greater in a denser packing arrangement than in a looser one.

Furthermore, there is no reason that K o should be asso-ciated with 9: It is more likely to be associated with, for example, some intrinsic material friction and angle of dila-tion.

The second observation is significant since it illustrates atype of reversibility in the development of the horizontal pressures during initial, virgin loading and unloading, in the

case of granular soils. This outcome is evidenced despite thefact that the vertical deformations over the same segmentsare mostly irreversible.

Models for the estimation of K o in the over-consolidated state are purely empirical and are based on experimentaldata and statistical approaches. The experimental resultsshown here indicate that granular soils exhibit minimalhysteresis in horizontal pressure in comparison to thatsuggested by the empirical models.

ACKNOWLEDGEMENTSThe author would like to acknowledge the guidance of,

and discussions with, Professor Sam Frydman during the

preparation of this submission.

NOTATION Dr relative density K o coefficient of lateral earth pressure at resth lateral strain Poisson ratio

9h 9v 9 z

9

REFERENCESAlpan, I. (1967). The empirical evaluation of the coefficient K o and

K oR : Soils Found . 7, No. 1, ???–???.ASTM (2006). ASTM D4254: Standard test methods for minimum

index density and unit weight of soils and calculation of relativedensity. West Conshohocken, PA, USA: American Society for Testing and Materials.

Brooker, E. W. & Ireland, H. O. (1965). Earth pressure at restrelated to stress history. Can. Geotech. J . 2 , No. 1, 1–15.

Budhu, M. (2000). Soil mechanics and foundations. ????????, ????:John Wiley.

Daramola, O. (1980). On estimating K o for overconsolidated gran-ular soils. Ge otechnique 30, No. 3, 310–314.

Itasca (2008). FLAC user manual . Minneapolis, USA: Itasca Con-sulting Group.

Jaky, J. (1944). A nyugalmi nyomas tenyezoje (The coefficient

of earth pressure at rest). Magyar Mernok es Epitesz-Eglyet Kozlonye (J. Soc. Hung. Eng. Arch.), 355–358 (in Hungarian).

Mayne, P. W. & Kulhawy, F. H. (1982). Ko–OCR relationships insoil. ASCE J. Geotech. Div. 108, No. GT6, 851–872.

0

0·2

0·4

0·6

0·8

1·0

Vertic

alstrain,

:%

ε z

Dense dune sand

First load

First unload

Second load

Second unload

150

100

50

0

Horizontal

pressure:kPa

0 50 100 150 200 250 300

Applied pressure: kPa

Fig. 5. Typical results of horizontal pressure measured in densedune sand using the in-soil null gauge

Table 2. Magnitude of K o for the different materials, densities,null gauges

Density K o

Small Large

Dune sand Loose 0.45 0.47Dense 0.54 0.52

Coarse sand Loose 0.54 0.53Dense 0.59 0.58

SumSum Loose 0.50Dense 0.57

Adas Loose 0.41Dense 0.49

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Mesri, G. & Vardhanabhuti, B. (2007). Coefficient of earth pressureat rest for sands subjected to vibration. Can. Geotech. J . 44 , No.??, 1242–1263.

Michalowski, R. L. (2005). Coefficient of earth pressure at rest. J. Geotech. Geoenviron. Engng 131, No. 11, 1429–1433.

Schmidt, B. (1967). Lateral stresses in uniaxial strain, Bulletin No.23, pp. 5– 11. Denmark: Geoteknisk Institut (The Danish Geo-technical Institute).

Selig, E. T. (1980). Soil stress gage calibration. Geotech. Testing J.

ASTM 3, No. 4, 153-158.Talesnick, M. (2005). Measuring soil contact pressure on a solid

boundary and quantifying soil arching. Geotech. Testing J. ASTM 28, No. 2, 171–179.

Talesnick, M. (2010). Discussion on experimental arrangements for investigation of soil stresses developed around a displacement

pile, and the use of miniature soil stress measuring cells inlaboratory applications involving stress reversals. Soils Found .50, No. 3, 447–448.

Taylor, D. W. (1947). Pressure distribution theories, earth pressurecell investigations and pressure distribution data. Vicksburg,USA: US Army Engineer Waterways Experiment Station.

Tognon, A. R., Rowe, R. K. & Brachman, R. W. I. (1999).Evaluation of side wall friction for a buried pipe testing facility.Geotextiles and Geomembranes 17, No. ?, 193–212.

Tory, A. C. & Sparrow, R. W. (1967). The influence of diaphragmflexibility on the performance of an earth pressure cell. J. Sci.

Instruments 44, No. ??, 781–785.Weiler, W. A. & Kulhawy, F. H. (1982). Factors affecting stress cell

measurements in soil. J. Geotech. Found. Div. ASCE 108, No.GT12, 1529–1548.

1: Please provide keyword terms from ICE approved list at http://www.icevirtuallibrary.com/upload/geotechniquekeywords.pdf 2: Taylor 1944 cited in text, 1947 listed in refs - please check year 3: ASTM 4254 - year has been completed as 2006 - OK?4: Please provide definitions for notation list5: Please give page nos. for Alpan (1967)6: ASTM ref - details have been added to complete reference. Pleasecheck.7: Budhu (2000) Location of publisher?

8: Itasca - details have been added to complete reference, please check 9: Mesri and Vardhanabhuti - please give issue no.10: Tognon et al. - please give issue no.11: Tory and Sparrow, please give issue no.

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MEASUREMENT OF K o OF GRANULAR SOILS 5

a different approach and result to the measurement of ko of granular soils

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