Passive Earth Pressure of Overconsolidated Cohesionless Backfill

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Passive Earth Pressure of OverconsolidatedCohesionless Backfill

Adel Hanna, F.ASCE,1 and Imad Al Khoury2

Abstract: An experimental investigation on the passive earth pressure of overconsolidated cohesionless soil on retainingconducted. A prototype model of a vertical rough wall, retaining horizontal backfill, was developed in the laboratory. The minstrumented to measure the total passive earth pressure acting on the wall, the passive earth pressure acting on selected locwall, and the overconsolidation ratio~OCR! of the sand in the testing tank. In order to develop the state of passive pressure, the wpushed horizontally toward the backfill without any rotation. Overconsolidated sand was produced in the testing tank by placinin thin layers; each was compacted mechanically for a period of time. Tests were performed on walls retaining homogeneousolidated sand, and overconsolidated sand backfill overlying the deep sand layer. The method of slices developed for precoefficient of passive earth pressure for normally consolidated soil was adopted for the conditions stated above. The theorecompared well with the experimental results of the present investigation. It is of interest to note that the OCR and the soil condithe founding level significantly affect the value of the coefficient of passive earth pressure on these walls. Design charts and fopresented for practical use.

DOI: 10.1061/~ASCE!1090-0241~2005!131:8~978!

CE Database subject headings: Earth pressure; Passive pressure; Overconsolidated soils; Cohesionless soils; Backfills.

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Introduction

Quite often retaining walls for bridge abutments or plate ancrest on natural soil deposits, while the backfill is made ucompacted granular material. The passive earth pressure onwalls is currently estimated based on the theories developehomogeneous normally consolidated backfill material. Comtion of cohesionless soil induces additional stresses in themass, which are locked in, causing the soil to consolidate~Poulos1988; Hanna and Saad 2001!. Stress level in the soil massusually represented by the overconsolidation ratio~OCR!, whichinfluences the behavior of the soil and its response to the foutions, accordingly. Research has been lagging in this subjecmarily because precise reconstruction of the field stress levlaboratory testing is difficult and almost impossible for cohesless soil.

In the literature, numerous reports can be found dealingthe problem of passive earth pressure on walls retaining coheless soil~Caquot and Kerisel 1948; Shields and Tolunay 19

1Professor, Dept. of Building, Civil, and Environmental EngineerConcordia Univ., 1455 DeMaisonneuve Blvd., W. Montreal, QueCanada H3G 1M8 ~corresponding author!. E-mail: [email protected]

2Research Associate, Dept. of Building, Civil, and EnvironmeEngineering, Concordia Univ., 1455 DeMaisonneuve Blvd., W. MontQuebec, Canada H3G 1M8.

Note. Discussion open until January 1, 2006. Separate discumust be submitted for individual papers. To extend the closing daone month, a written request must be filed with the ASCE ManaEditor. The manuscript for this paper was submitted for review andsible publication on March 13, 2003; approved on November 17, 2This paper is part of theJournal of Geotechnical and GeoenvironmentEngineering, Vol. 131, No. 8, August 1, 2005. ©ASCE, ISSN 109
0241/2005/8-978–986/$25.00.
978 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINE

J. Geotech. Geoenviron. Eng

e

Kumar and Subba Rao 1997; Soubra 2000; Zhu and Qian 2!.Most of these studies considered the angle of shearing resiof the soil and the angle of wall/soil friction as the only pareters governing the coefficient of passive earth pressure onwalls. With the exception of the coefficient of earth pressurrest ~Sherif and Mackey 1977; Hanna and Ghaly 1992!, no at-tempts were made to incorporate the effect of the stress histthe design theories for earth pressure. Furthermore, the contion of the soil below the founding level of the wall to the pasearth pressure has not been examined.

Experimental Investigation

The experimental setup consisting of a testing tank, loadingtem, and a retaining wall was designed to measure the paearth pressure acting on the wall and the OCR in the sandFig. 1 presents the layout of the experimental setup used ipresent investigation. The testing tank was 1,080, 197, andmm in length, width, and depth, respectively. The tank sidesmade of 10 mm Plexiglas plates to allow observation of thedeformation during testing. The tank was braced with a frmade of steel angles to prevent lateral bulging under maxiloading condition. The loading system consisted of a geacapable of producing a wide range of strain rates.

A metal plate was installed in the upper part of the tansimulate the retaining wall. The plate was 215 and 197 mheight and width, respectively. The plate was held verticthrough a rod that was supported by two sets of roller bearThe rod was connected to the loading system through a loato measure the horizontal component of the total passivepressure acting on the wall. In order to simulate the case of pstrain condition in the sand mass, the width of the wall was
sentially the same as the width of the testing tank. To minimize
ERING © ASCE / AUGUST 2005

. 2005.131:978-986.

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friction between the wall and the glass sides of the testing tacut of 4 mm was made at both sides in the wall materialreplaced with flexible foam. One side of the foam was gluethe wall, while the other side was covered with polyethylenshould be noted that the angle of friction between the sandthe glass sides was small enough to be ignored. In order tosure the distribution of the passive earth pressure acting owall, five pressure transducerssW1–W5d were installed at representative locations on the plate~see Fig. 2!.

In order to develop the state of passive pressure in the retsand mass, the wall was pushed horizontally toward the bawithout rotation. Four linear variable displacement transdu~LVDTs! were installed to measure the displacement of the pThe uniform readings of the LVDTs taken during testing supthe design requirement of the setup. In order to develop a rsurface, sandpaper was glued to the backfill side of the wallsandpaper sheets were fine to medium rough to simulate theof roughness of concrete walls. The produced angles of frictdwere within the following range:~1/2 f,d,2/3 f!.

The induced vertical stresses in the sand mass due to cotion were measured by means of nine pressure transducersb-1–b-9d placed in the sand mass at the three levels showFig. 1. Each unit was housed in a metal box connected to a hbar, through which the electrical wires pass to the data acquisystem~DAS!. The box was made of aluminum with dimensioof 40, 40, and 40 mm in height, width, and length respectiv~see Fig. 3!.

The pressure transducers used in this investigation wehigh stiffness, insensitive to temperature variations, and simpinstall. The transducers were individually calibrated in air ansand before testing. Each transducer was subjected to diflevels of air and sand pressures through plastic pipe conneca pressure gage~see Fig. 4!. The calibration factor was calculatfor each transducer, and entered into a computer program tovert the output signal registered by DAS to pressure. This pdure was in accordance with the manufacturer’s guidelines.installing all the transducers in the predetermined locationsconnections were checked with the characterized computer odata. The computer program was coded to allow the readinthe measuring devices to be registered in a manual mode adesired time or in an automatic mode at predetermined inte

Fig. 1. Layout
of experimental setup
The soil used in this study was well-graded sand~Unified soil

JOURNAL OF GEOTECHNICAL AND G


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Fig. 2. Location of transducers on retaining wall

EOENVIRONMENTAL ENGINEERING © ASCE / AUGUST 2005 / 979

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classification system!. Table 1 presents a summary of the physcharacteristics of the sand. The angles of shearing resistansfdof the sand and the angles of friction between the sandpapethe sand were determined from the results of a direct sheatest~Hanna and Nguyen 2003!. The unit weight of the sand in thtesting tank was measured by means of density cans, whichplaced in a staggered scheme in the vertical direction to aboundary effects. The cans measure 62 and 45 mm in diaand depth, respectively. At the end of each test, these canscarefully taken out and weighed. The unit weight of the sandtaken as the average unit weight of the sand in these canaccordingly the relative density was calculated~ASTM D-2049!.

The technique of placing the sand in the testing tank waveloped and calibrated so that the desired unit weight anoverconsolidation ratio could be achieved. The technique waried out by spreading the sand through a hose from a minheight to minimize particle segregation. The sand was placlayers 100 mm thick. A layer of 170 mm thick dead sandplaced at the bottom of the testing tank to reduce the effevibration reflection from the base. Compaction was applieeach layer using a hand air compactor with an end steelhaving dimensions of 110, 85, and 10 mm length, width,thickness, respectively. The air pressure of the compactorfixed to a value of 207 kPa and the range of the compaduration varied from 2 to 11 s. The relationship between the

Table 1. Summary of Physical Characteristics of Sand

Property Value

Classification Well graded~SW–SC!

Description 99% silica

Shape of particles Angular

Coefficient of uniformitysCud 10.93

Coefficient of curvaturesCcd 1.30

Specific gravitysGsd 2.62

Maximum unit weightsgmaxd 19.92 kN/m

Minimum unit weightsgmind 17.45 kN/m

Maximum void ratiosemaxd 0.52 ~ASTM!

Minimum void rationsemind 0.33 ~ASTM!

of individual transducers

Fig. 3. Transducers box unit used to measure vertical stresses inmass

Fig. 4. Layout of calibration


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paction duration and the mechanical properties of the sand
established in the laboratory before testing~Hanna and Saa2001!.

Tests were performed on walls retaining homogeneousconsolidated dense, medium, or loose sands, overconsoldense sand backfill overlying medium sand deposit, and ovesolidated medium sand backfill overlying dense sand depTable 2 presents a summary of the testing program togethethe physical and mechanical properties of the sand tested.

In each test, the initial readings of the measuring devicesregistered by DAS using the manual mode. The OCR of thein the testing tank was then calculated as follows:

OCR =sc

ghs1d

wheresc5vertical pressure at a given level as recorded byrespective transducer; andgh5overburden pressure at the salevel.

The wall was then pushed toward the sand mass, and thein DAS was switched to an automatic mode to record the reaof the measuring devices at 1 min intervals during loading.wall movement continued until failure was reached, at whichsand mass behind the wall became loose and separated frorest of the sand in the testing tank through a failure surfacesand movement was observed from the glass sides of the ttank until the failure mechanism was fully developed behindwall. In this investigation, each test was repeated twice to areproducibility of the test data.

Results

Typical test results of the horizontal component of the pasearth pressure, as measured by the load cell and the indivtransducers mounted on the wall, are presented in Figs. 5respectively, in the form of load–displacement curves. It shbe noted from these figures that the horizontal component oearth pressure acting on the wall increases due to an increthe wall displacement up to the failure point. In this investigathe failure point was determined, where a significant increathe rate of change of displacement accompanies an increaload.

The horizontal component of the maximum passive earthsure acting on the wallsPhd was determined at the failure pointthe load–settlement curve, directly from the load cell read~Fig. 5! or indirectly by integrating the pressure diagram pduced by the individual transducers readings~Fig. 6!. Fig. 7 pre-sents typical plots of the individual transducers readings vedepth for the cases of loose, medium, and dense sands. It s

Table 2. Summary of Testing Program

Testnumber

Sandcondition

RelativedensityDr

s%d

Unit weigg

skN/m3d

1 Dense 75 19.25

2 Medium 52 18.65

3 Loose 21 17.75

4 Dense/medium 75/52 19.25/1

5 Medium/dense 52/75 18.65/1

be reported here that both experimental techniques for measuring



e

f

the values ofPh revealed the same results, indicating thatfriction between the wall and the sides of the testing tankencountered during the wall displacement.

In this investigation, values ofsPhd measured by the load cwere used to calculate the coefficient of passive earth pressuKp

as follows:

Pp = Ph/cosd s2d

i.e.,

Pp = 1/2gh2dKp s3d

i.e.,

Kp =2Pp

gh2ds4d

where Ph5horizontal component of the passive earth presacting on the wall;Pp5total passive earth pressure acting aangled with the horizontal;g5unit weight of the sand; andd andh5width and the height of the wall, respectively.

Angle of shearingresistance,f

~degrees!

Angle ofwall friction, d

~degrees!Overcons

olidation ratio

45 20 2.5

40 18 2.0

33 15 1.3

45/40 20 2.2

40/45 18 2.3

Fig. 5. Typical load–displacement curve for dense sand~load cellreading!

ht

8.65

9.25


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Wall Retaining Homogeneous OverconsolidatedSand

The method of slices developed by Shields and Tolunay~1973!for predicting the total passive earth pressures on rough vewalls retaining normally consolidated soil was adopted forcase of overconsolidated cohesionless soil. In developing thelytical model, Shields and Tolunay proposed a failure mechaconsisting of two parts: logarithmic spiral and plane portions~see

Fig. 6. Load–displacement curves for dense sand~individualtransducers readings!

Fig. 7. Horizontal pressure on wall at failure



Fig. 8!. The logarithmic spiral portionsBCd is bounding the deformable zonesABCEd and the plane portionsCDd is boundingthe Rankine’s passive zonesCDEd. Furthermore, they stated ththe center of the logarithmic spiral portion is located on thesCAd, and the plane portion is making an angle ofs45° -f /2dwith the horizontal. The interface between these two zonessCEdis subjected to a passive forcesPrd calculated according to Ranine’s theory ~Rankine 1857!. Then the equilibrium of the indvidual slices in the deformed zone was considered. ShieldTolunay proposed the following formula to predict the angleaw atwhich the logarithmic spiral curve, at failure, will depart frombottom of the wall

aw = S1

2DHarccosFcossf − dd −

sinsf − ddtanf

G − f − dJ s5d

where f5angle of shearing resistance of the backfill;d5angle of friction between the wall~sandpaper! and the backfilmaterial.

Based on this analysis, Shields and Tolunay presented thlowing formula to predict the minimum passive earth pressPpd acting on a rough wall retaining horizontal homogenenormally consolidated soil:

Pp =Pr + o w tansa + fd

1 − tand tansaw + fds6d

Furthermore

Pr =1

2g ·H2 tan2S45 +

f

2D

or

Pr =1

2g ·H2Kp s7d

where Pr5total passive earth pressure acting on the planeCE;Kp5Rankine coefficient of passive earth pressure;w5weight of agiven slice;a5slope of the base of a given slice; andH5heightof CE ~Fig. 8!.

In order to adopt Shields and Tolunay’s method of slicesthe case of overconsolidated cohesionless soil, the followingcedure was followed:1. The observed failure plane from the present experim

study was idealized by two parts, namely, logarithmic sand plane portions, similar to the one proposed by Shand Tolunay~Fig. 8!.

2. In order to determine the total passive earth pressuresPrd

Fig. 8. Method of slices~after Shield and Tolunay 1973!

acting on the interface planeCE ~Rankine condition!, tests


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were performed on smooth wallssd>0d retaining overconsolidated sand. Table 3 presents the results of this serismooth wall was developed in the laboratory by applyinthin layer of rubber membrane grease directly on the mplate ~wall! facing the sand. Based on these results, thelowing empirical formula is proposed to predict the coecient of passive earth pressure on smooth walls retahorizontal backfill made of overconsolidated sand:

Kpsocd = bÎOCRKpsncd s8d

whereKpsocd5coefficient of passive earth pressure for ovconsolidated sandsd=0d; Kpsncd5coefficient of passive earpressure for normally consolidated sand~Rankine’s values!;OCR 5 overconsolidation ratio; andb5constant, given iTable 3.It should be noted that in Eq.~8!, for the case of OCR=~Rankine condition! the constantb=1, while for the cases oOCR.1 the constantb is constantly higher than 2 aslightly increases with the increase of OCR. An avervalue of 2.5 was assumed to cover the rage of OCR upwhich represents a practical range for a backfill subjectelight compaction.The total passive earth pressuresPrd acting on the interfacplanesCEd was then replaced byPrm given by the followingequation:

Prm = 2.5ÎOCRPr s9d

3. Trial calculations on walls retaining overconsolidated susing different logarithmic spiral curves revealed thatvalue of the angleaw given by Shields and Tolunay for nomally consolidated sand@Eq. ~5!# provides the minimum pasive earth pressure for the case of overconsolidated sa

4. Eq.~6! given above was rewritten to predict the total pasearth pressure on rough vertical walls retaining overcondated sand

Table 3. Test Results of Earth Pressure on Smooth Walls

f Over consolidation ratio Kpsocd measured b

33 1.3 8.15 2.10

40 2.0 14.92 2.29

45 2.5 22.45 2.44

47 2.9 27.91 2.53

Table 4. Comparison between Experimental and Theoretical Vaof Kp

Experimental results Theoretical resultsKp

Testnumber

Total earthpressurePp

skNd

Coefficient ofearth pressure

Kp

ModifiedShields

and Tolunay~1973!

Empiricalformulae

1 2.013 23.00 22.63@Eq. ~10!# 22.95@Eq. ~11!#

2 1.314 15.49 14.41@Eq. ~10!# 14.93@Eq. ~11!#

3 0.686 8.49 7.94@Eq. ~10!# 8.41 @Eq. ~11!#

4 1.692 19.30 18.30@Eq. ~13!# 19.55@Eq. ~14!#

5 1.586 18.70 17.50@Eq. ~10!# 17.44@Eq. ~11!#



Ppsocd =Prm + o w tansa + fd

1 − tand tansaw + fds10d

Furthermore

Ppsocd = 1/2gh2d Kpsocd

A computer program was coded to perform the analysescribed above. The input data are the angle of shearing resisfd, the angle of wall frictionsdd, the OCR, and the height athe width of the wall. The program was first used to predicttheoretical values of the coefficient of passive earth pressuthe conditions stipulated in the present experimental studyresults are given in Table 4, where good agreement can be fThe program was then used to calculate the coefficient of paearth pressureKpsocd for a wide range of the parameters mentioabove. These values are given in Figs. 9–12 in the form of dcharts for OCR values of 1–4, respectively. Based on the the

Fig. 9. Design charts: coefficient of passive earth pressure



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ical values ofKpsocd produced in this investigation, the followinempirical formula was developed to predict the coefficient ofsive earth pressure for overconsolidated cohesionless soilKpsocdfor rough wallss1/2 f,d,2/3 fd;

Kpsocd = KpsncdH1.5 −Sd − 25

100DJhOCRjsin d s11d

where Kpsncd5coefficient of passive earth pressure for normconsolidated soil, under the same wall/soil conditions, whichbe determined from the results of the conventional methodnormally consolidated soil or from the design charts presentthis paper for the case of OCR=1~Fig. 9!. The predicted valueusing Eq.~11! are also given in Table 4, where reasonable agment can be found.

In order to validate the design charts presented hereinresults reported by Diab~1994! were compared with the theorical values given in the present design charts~Table 5!, wheregood agreement can be found.





Overconsolidated Sand Overlying Natural Deposit

The case of vertical rough walls retaining horizontal bacmade of overconsolidated cohesionless material overlyingnatural deposit can be classified as follows.

Strong Overconsolidated Cohesionless BackfillOverlying Weak Deposit

The observed failure surface for the case of overconsolidbackfill made of dense sand overlying medium sand depogiven in Fig. 13. It can be noted from this figure that in this cthe failure mechanism extends to the lower weak deposit.confirms that the presence of the weak deposit below the foing level contributes to the value of the passive earth preacting on this wall~see Table 4!.

The procedure described above for the case of walls retaoverconsolidated homogeneous cohesionless soil was mofurther for this case. In this analysis, the logarithmic spiral csBCd of the failure plane was assumed to be located entirely ilower layer, with pointC ~see Fig. 8! located on the interfacethe backfill and the deposit. Thus, the shear strength on therithmic spiral curve was calculated according to the anglef2 ofthe deposit and the passive earth pressure on the planesCEd,Prm , was calculated according to the anglef1 of the backfill.Thus, Eqs.~5! and~10! can be rewritten, respectively, as follow

aw = S1

2DHarccosFcossf2 − dd −

sinsf2 − ddtanf2

G − f2 − dJs12d

Ppsocd =Prm + o w tansa + f2d

1 − tand tansaw + f2ds13d

The computer program, developed earlier in this study,adjusted to incorporate the changes mentioned above. Theparameters are: the angles of shearing resistancesf1d andsf2d ofthe backfill material and the lower deposit, respectively, the aof wall/backfill friction sdd, and the OCR. Once again, the pgram was used first to predict the theoretical value of the cocient of the passive earth pressure for the case of overcodated dense sand backfill overlying medium sand deposit~TestNo. 4!. This result is also given in Table 4 where good agreemcan be found.

The program was then used to predict the coefficient ofsive earth pressure for a wide range of the above-mentioneddata. Based on the results produced in this stage, it was noteboth the backfill and the lower deposit contribute almost eqto the coefficient of the passive earth pressure of the soil syAccordingly, the following empirical formula is proposed to pdict the coefficient of passive earth pressures for the case

Fig. 13. Experimental results—observed failure planes

strong backfill overlying weak deposit:


. 2005.131:978-986.

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KpSbackfill
depositD = FKp sbackfilld + Kp sdepositd

2G s14d

where Kp ~backfill! 5 coefficient of passive earth pressurehomogeneous backfill material; andKp ~deposit! 5 coefficient ofpassive earth pressure of homogeneous lower deposit.

Kp ~backfill! andKp ~deposit! can be directly determined froEq. ~10! or from the design charts given in Figs. 9–12, or by uthe empirical formula given in Eq.~11!. It should be admittehere that due to lack of experimental and or field data onsubject matter, the empirical formula presented in Eq.~14! wasonly validated by the test data of the present investigation.ertheless, Eq.~14! presents a reasonable solution to the probstated in which the contribution of the lower layer was recognand considered, while currently, the coefficient of the pasearth pressure is calculated based on the shear strength of bmaterial, ignoring the effect of the lower layer, leading tooverestimation of the passive earth pressure on the wall.

Weak Overconsolidated Cohesionless BackfillOverlying Strong Deposit

The observed failure surface for the case of overconsolidbackfill made of medium sand overlying dense sand depoalso given in Fig. 13. It should be noted from this figure thatfailure mechanism remained confined in the upper backfill laand further, the lower strong deposit does not contribute sigcantly to the passive earth pressure produced on the wall.

The deduced value ofKp from the present experimental stufor the case of backfill made of overconsolidated mediumoverlying dense sand deposit~Test No. 5! is also given in Table 4It should be noted from this table that the experimental valuthe coefficient of passive earth pressure for this case is reasoclose to the value of the coefficient of passive earth pressuthe case of overconsolidated homogeneous medium sand~TestNo. 2!. Accordingly, these values may be predicted directly fthe design charts given in Figs. 9–12, or by using the empformula given in Eq.~11!, utilizing the input data for the homgeneous backfill material.

Conclusions

An experimental investigation into the coefficient of passive epressure of overconsolidated homogeneous sand and overcdated sand backfill overlying deep cohesionless deposit wasducted. The following can be concluded:1. Compaction of backfill made of cohesionless materia

duces additional stresses in the backfill, which is lockedcausing the backfill material to become overconsolidaand accordingly, increases the overconsolidation ratio

Table 5. Comparison between Experimental Result and Theoretica

Over consolidation ratiosOCRd=2

f d Experimental values Design charts~Fig. 10! Experimental

30 20.0 8.8 8.5 10.2

35 22.5 12.1 11.95 13.9

40 24.0 17.4 17.1 20.7

45 28.0 27.1 26.65 31.3

further the passive earth pressure on the retaining wall.



l

-

2. The method of slices developed by Shields and Tol~1973! to predict the passive earth pressure of normallysolidated cohesionless soil was adopted for the cases omogeneous overconsolidated sand and overconsolibackfill overlying deep deposit.

3. For the case of a strong overconsolidated cohesionlessfill overlying a weak deposit, the failure mechanism exteto the weak deposit, resulting in a significant reduction opassive earth pressure acting on these walls.

4. For the case of a weak overconsolidated cohesionless boverlying a strong deposit, the failure mechanism doesextend to the strong deposit and remained confined inbackfill layer. Accordingly, the passive earth pressurethese walls can be calculated based on the condition obackfill material, as the lower deposit does not influencefailure mechanism.

5. Design charts are presented for predicting the coefficiepassive earth pressure for rough walls retaining overcondated homogeneous sand and overconsolidated sand boverlying deep cohesionless deposit. Empirical formwere also developed and tested in the rage of OCR=1–4 and1/2 f,d,2/3 f.

Acknowledgments

The financial support received from the Natural Science andgineering Research Council of Canada~NSERC! and ConcordiUniversity are acknowledged.

Notation

The following symbols are used in this paper:b 5 constant;

Cc 5 coefficient of curvature;Cu 5 coefficient of uniformity;Dr 5 relative density;d 5 width;

Gs 5 specific gravity;H 5 height;h 5 depth;

Kp 5 coefficient of passive earth pressure;Kpsncd 5 coefficient of passive earth pressure for normally

consolidated sand;Kpsocd 5 coefficient of passive earth pressure for

overconsolidated consolidated sand;OCR 5 overconsolidated ratio;

Pp 5 total passive earth pressure;Pr 5 total earth pressure according to Rankine’s theory

s ofp Given in Design Charts

CR=3 OCR=4

s Design charts~Fig. 11! Experimental values Design charts~Fig. 12!

10.0 11.3 11.2

13.5 15.6 15.2

19.50 22.9 21.95

30.95 35.4 34.75

l ValueK

O

value

for normally consolidated sand;


. 2005.131:978-986.

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Prm 5 modified total earth pressure for overconsolidatedsandsd=0d;

w 5 weight of given slice;a 5 slope of slice;

aw 5 angle at which logarithmic spiral curve will departfrom bottom of wall;

g 5 unit weight of sand;d 5 angle of friction between wall and backfill material

sc 5 vertical pressure;f 5 Angle of shearing resistance;

f1 5 angle of shearing resistance of backfill material; af2 5 angle of shearing resistance of soil below foundin

level.

References

Caquot, A., and Kerisel, L.~1948!. Tables de poussee et butee, Gauthier-Villars, Paris.

Diab, R. ~1994!. “Numerical modeling of passive earth pressure formally and overconsolidated sands.” MASc thesis, Concordia UMontréal.

Hanna, A. M., and Ghaly, A. M.~1992!. “Effects of K and overconsol
o


dation on uplift capacity.”J. Geotech. Eng., 118~9!, 1449–1469.Hanna, A. M., and Nguyen, T. Q.~2003!. “Shaft resistance of sing

vertical and batter piles in sand subjected to axial compressioning.” J. Geotech. Geoenviron. Eng.,, 129~7!, 601–607.

Hanna, A. M., and Saad, N.~2001!. “Effect of compaction duration othe induced stress levels in a laboratory prepared sand bed.”GeotechEng., 24~4!, 430–438.

Kumar, J., and Subba Rao, K. S.~1997!. “Passive pressure coefficiencritical failure surface and its kinematics admissibility.”Geotechnique, 47~1!, 185–192.

Poulos, S. J.~1988!. “Compaction control and the index unit weighGeotech. Test. J., 11~2!, 100–108.

Rankine, W. J. M.~1857!. On the stability of loose earth, Trains RoyaSociety, London, 147–147.

Sherif, A M., and Mackey, R D.~1977!. “Pressures on retaining wawith repeated loading.”J. Geotech. Eng. Div., Am. Soc. Civ. En,103~11!, 1341–1345.

Shields, D. H., and Tolunay, A. Z.~1973!. “Passive pressure coefficieby method of slices.”J. Soil Mech. Found. Div., 99~12!, 1043–1053

Soubra, A. H.~2000!. “Static and seismic passive earth pressure cocients on rigid retaining structures.”Can. Geotech. J.,, 37, 463–478

Zhu, D. Y., and Qian, Q.~2000!. “Determination of passive earth presscoefficients by the method of triangular slices.”Can. Geotech. J.,, 37,485–491.


. 2005.131:978-986.

Documents

Passive Earth Pressure of Overconsolidated Cohesionless Backfill