Earth Pressures with Sloping Backfill · EARTH PRESSURES WITH SLOPING BACKFILL By Yung-ShowFang,l Associate Member, ASCE, Jiung-MingChen,z and Cheng-Yu Chen3 ABSTRACT: This paper

EARTH PRESSURES WITH SLOPING BACKFILL

By Yung-Show Fang,l Associate Member, ASCE, Jiung-Ming Chen,z and Cheng-Yu Chen3

ABSTRACT: This paper presents experimental data of earth pressure acting against a vertical rigid wall, whichmoved away from or toward a mass of dry sand with an inclined surface. The instrumented retaining-wallfacility at National Chiao Tung University (NCTU) Taiwan, was used to investigate the variation of earth pressureinduced by the translational wall movement. Based on experimental data, it has been found that the earthpressure distributions are essentially linear at each stage of wall movement. Both the wall movement requiredfor the backfill to reach an active state and the wall movement needed for the backfill to reach a passive stateincrease with an increasing backfill inclination. The experimental active and passive earth-pressure coefficientsfor various backfill sloping angles are in good agreement with the values calculated by Coulomb's theory. Itmay not be appropriate to adopt the Rankine theory to determine either active or passive earth pressure againsta rigid wall with sloping backfill.

INTRODUCTION

Retaining walls are frequently used to hold back the earthand maintain a difference in the elevation of the ground surface. In highway construction, they are used along cuts andfills where space is inadequate for the appropriate side slopes.Fig. 1 illustrates the retaining walls constructed on a slope.After cut and fill, a flat area is created for road constructionor housing. On the uphill side of the upper retaining wall,active earth pressure developed with a positive backfill inclination (+ i angle). On the downhill side of the lower wall,passive earth pressure developed with a negative backfill inclination (- i angle). For a safe design of the retaining structure previously mentioned, it is necessary to determine themagnitude and distribution of the active and passive stressesacting on the walls.

Traditionally, civil engineers calculate the active and passiveearth pressure against the wall following either Coulomb orRankine's theory. Another popular method to estimate theearth pressure is the logarithmic-spiral method proposed byTerzaghi (1943). It should be emphasized that, depending onthe backfill sloping angle, the active and passive thrusts calculated with these methods could be quite different. From anengineering point of view, it would be interesting to knowwhich method would be more appropriate to use for design.

Valuable experimental work associated with earth pressurehas been conducted by Terzaghi (1932), Schofield (1961),Rowe and Peaker (1965), Mackey and Kirk (1967), Narainet al. (1969), James and Bransby (1970), Matteotti (1970),Bros (1972), Sherif and Mackey (1977), Sherif et al. (1982),Sherif et al. (1984), Duncan and Seed (1986), Fang and Ishibashi (1986), Duncan et al. (1991), Fang et al. (1994), andother researchers. Unfortunately, most of the work is associated with a backfill with horizontal surface. In fact, little experimental justification has been reported in the literature regarding the development of active and passive earth pressuresagainst a wall with sloping backfill. As a result, how to evaluate the validity of the theoretical solutions remainedproblematic.

'Prof. and Dir.• Inst. of Civ. Engrg., Nat. Chiao Tung Univ.• Hsinchu,Taiwan, 30050, ROC.

2Grad. Student, Inst. of Civ. Engrg., Nat. Chiao Tung Univ., Hsinchu,Taiwan, 30050, ROC.

'Grad. Student, Inst. of Civ. Engrg.• Nat. Chiao Tung Univ.• Hsinchu.Taiwan, 30050. ROC.

Note. Discussion open until August I, 1997. To extend the closingdate one month, a written request must be filed with the ASCE Managerof Journals. The manuscript for this paper was submitted for review andpossible publication on August 7, 1995. This paper is part of the Journalof Geotechnical and Geoenvironmenllll Engineering. Vol. 123. No.3.March, 1997. cASCE. ISSN 1090-0241/97/0003-0250-0259/$4.00 +$.50 per page. Paper No. 11349.

This paper presents experimental data of earth pressureagainst a vertical rigid wall, which moved away from or toward a mass of dry sand with a stress-free inclined surface.The backfill sloping angles used for the tests ranged from-200 to +200 as shown in Fig. 2. All of the earth-pressureexperiments mentioned in this paper were conducted in theNational Chiao Tung University (NCTU) retaining-wall facility, which is described in the following section. Horizontalearth pressure against the wall is measured with the soil-pressure transducers mounted on the model wall. Due to the scaleeffect, it may not be appropriate to predict the behavior oflarger walls from the results obtained from small-scale models.However, the test findings should enhance a better understanding regarding the effect of backfill inclination on the development of earth pressure.

NATIONAL CHIAO TUNG UNIVERSITYRETAINING-WALL FACILITY

The entire facility consists of four components, namely, themodel retaining wall, soil bin, driving system, and data-acquisition system.

The movable model retaining wall and its driving systemare illustrated in Fig. 3. The model wall is a 1,000 mm wide,550 mm high, and 120 mm thick solid plate, and is made ofsteel. For the test shown in Fig. 3, the effective wall height H(or height of backfill at the soil-wall interface above the wallbase) is only 300 mm. The retaining wall is vertically supported by two unidirectional rollers and is laterally supportedby four driving rods. The 1,000 mm wide, 337 mm high, and120 mm thick steel plate on top of the movable wall is designed to resist the uplift components of passive earth pressure.To investigate the distribution of earth pressure, soil-pressuretransducers (SPT) are attached to the model retaining wall asshown in Fig. 4. Ten strain-gauge-type earth-pressure transducers have been arranged within the central zone of the wall.Another three transducers (SPT 10, I I, and 12) have beenmounted between the central zone and sidewall to investigate

+i

FIG. 1. Retaining Walls on Slope

250/ JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / MARCH 1997

J. Geotech. Geoenviron. Eng. 1997.123:250-259.

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(a)

I Driving Rod •

Ml'M2,{tDIFr=TH~-~/-=-------=-'--=----=---~--rlWorm I' I~ "I ' ',' .!G QJ • g . I ~pacing

ear ~ ,:'::,' . Soil· j Frame

System I I W~I! '.,. tl~"I Base ~..J I ====2~OO~O::'::::=--==::::-=t

I ~ -,~--,

PlanUnit: mm

Ml,M2: Variable Speed Molors, Section Transparent.r-- Acrylic Wall

CohesionlessBackfill-r,= 15.5 kN/m

3

!p=30.9'0= 19.2'

~ RuptureSurface

Ideal\ Rankine

" Zone\\\

H

FIG. 3. National Chiao Tung University Retaining-Wail Facility

HStraight Line

Logarithmic Spiral

(b)

550

CLISPTO 50

100 SPTI •

• ISPT2100

100 SPT3 •

• ISPT4100

Model Retaining 100 SPT5 • 30

100 -I I-

Wall • I SPT6 SPT10 SPTII SPT12100 SPT7 • • • •

• ISPT8 100

100 SPT9 •

50 ·1 100

FIG. 4. Locations of Soli·Pressure Transducers

130 160 I

1000

Front -view

Unil : mm

450

I:

adequate friction between the soil and the base of the bin.According to the general wedge theory (Terzaghi 1941), thepassive failure surface developed in the backfill would extendbelow the base of the wall. As shown in Fig. 3, the fixed bedlocated below the wall serves to hold the bottom 113 mm ofsoil to accommodate the entire log-spiral failure surface. Foractive experiments it may not be necessary to fill the entire 2m long soil bin to develop the failure wedge. To save the timeand energy for soil placement, a spacing frame made of steelwas put into the soil bin. However, the frame was removedfor all passive experiments.

As illustrated in Fig. 3, the variable speed motors Ml andM2 (Electro, M4621AB) are used to compel the upper andlower driving rods, respectively. The shaft rotation compelsthe worm-gear linear actuators, and the actuator pushes orpulls the model wall. Since only the variation of earth pressurecaused by the translational wall movement is investigated,therefore the motor speeds at M1 and M2 were kept the samefor all experiments in this study.

Due to the considerable amount of data collected by SPTs,a data-acquisition system is used. The analog signals from thesensors are digitized by an analog-to-digital converter. Thedigital data are then stored and processed by a microcomputer.For more details regarding the NCTU retaining-wall facility,the reader is referred to Wu (1992) and Fang et al. (1994).

i=-20'

FailureWedge

(c)

H

FIG. 2. Active Wedge Calculated with Terzaghl's Log-SplralMethod

the sidewall effect. To eliminate the soil-arching effect, allearth-pressure transducers are quite stiff and are installed flushwith the face of the wall. For passive tests Kyowa BE-2KRS17(196 kN/m2 capacity) transducers are used. For active experiments, since the overburden pressure is very small, extremelysensitive Kyowa PGM-02KG (19.6 kN/m2 capacity) transducers are used.

The soil bin is fabricated of steel members with inside dimensions of 2,000 X 1,000 X 1,000 mm (see Fig. 3). Bothsidewalls of the soil bin are made of 30 mm thick transparentacrylic plates through which the behavior of backfill can beobserved. The bottom of the soil bin is covered with a layerof SAFETY WALK manufactured by 3M Company to provide

JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / MARCH 1997/251


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0.8

i = 0°H = 0.3 m

0.6

N('--.

0.4'-....Q

b

0.2

00000 SPT 500000 SPT 6t::.t::.t::.t::.t::. SPT 700000 SPT 8***** SPT 9

The frictional resistance developed between the sidewall andOttawa sand was evaluated by a special direct shear test. Inthe test, an acrylic plate (same material as the sidewall) wasplaced under the upper shear box. Following the testingmethod suggested by Tatsuoka and Haibara (1985), it is foundthat, if the normal stress is greater than 40 kN/m2

, the frictionangle can be successfully reduced to less than 1°. However, ifthe normal stress at the interface is less than 10 kN/m2

, thefriction angle becomes higher. Based on the results of modelwall experiments, Terzaghi (1932) found that, even withoutthe lubrication layers, the intensity of earth pressure is practically independent of the length of the wall (inside width ofthe soil bin), if the length of the wall exceeds twice the wallheight. For this study the width of the soil bin (W = 1.0 m) iskept to be at least twice the height of backfill.

By replacing the acrylic plate with a steel plate (same material as the model retaining wall) and removing the lubrication

FIG. 5. Relationship between (J'h1oyzand SIH

0.0050.0040.003

.-.------ Coulomb- - Rankine. - - - Terzaghi00000 H = 0.5 mt::.6666 H = 0.4 m00000 H = 0.3 m00000 H = 0.2 m

siB0.002

0.8

0.70°

0.6

0.5

.Q

::.:::: 0.4

0.3

0.2

0.1

0.00.000 0.001

SiB0.0 +----,-------,----,----,--------1

0.000 0.001 0.002 0.003 0.004 0.005

FIG. 7. Variation of Kh with Active Wall Movement for VariousBackfill Heights

FIG. 8. Comparison of Earth Pressures Measured at DifferentDistances from Sidewall

5.0

H = 0.5 m

4.0

00000 SPT 600000 SPT 10

,--..Lo.Lo.Lo.6t::. SPT 11'"S 3.0 00000 SPT 12

..........Z~'--'

..c:: 2.0b

1.0

0.005

Jaky--.------ Coulomb

m - - Rankine. - - - TerzaghiGBeB0 S/H = 0GBf3B-EJ S!H = 2.0x10-4

~ S!H = 5.0x10-4

~ S!H = 2.0x10-3

--trlrlrlrll S!H = 3.0x10-3

~ S!H 4.8x10-3

0.0 +----r-----.------.-----,---------10.000 0.001 0.002 0.003 0.004-

siR

0.20

0.25

0.05

Horizontal Earth Pressure, CTh (kN/m2)

0.0 0.5 1.0 1.5 2.0 2.50.00 tt_----'-----------'-------'-------"-----j

0.30 ..1..- --"-_-'- ---'_--'

FIG. 6. Distributions of Lateral Earth Pressure for HorizontalBackfill

,..q..;..> 0.15p..Q)

Q

BACKFILL AND INTERFACE CHARACTERISTICS

Air-dry Ottawa sand (ASTM C-I09) was used throughoutthis investigation. Physical properties of the soil include G, =2.65, em.. = 0.76, emin = 0.50, D60 = 0.36 mm, and D IO = 0.23mm. For this study, the backfill was deposited by air pluviationfrom the slit of a hopper into the soil bin. The drop distancewas kept to be approximately 600 mm to the soil surfacethrough the placement process. The soil unit weight "y

achieved with the pluviation method was 15.5 kN/m3• The

corresponding internal friction angle <l> determined from directshear tests with normal stresses less than 40 kPa was found tobe 30.9°. To limit the scope of this study, only one densitywas used throughout all experiments.

To reduce the friction between sidewall and backfill, a lubrication layer was furnished for the earth-pressure experiments. The layer consists of a 0.2 mm thick latex rubber membrane and a thin layer of silicone grease (Shin-Etsu KS-63G).

S 0.10



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Horizontal Earth Pressure, Uh (kN/m2)

0.000...0,-_---=IC1:.0__---=2C1:.0__---=3.:.:.0__----'-'I4 .O

....._... Coulomb- - Rankine. - - - Terzaghi

GeeE>€l S!B = 0eeeee SjB = 3.0xlO::---. SjB = 2.0xlO~ SjB = 5.0xlO-:***** SjB = 2.0xlO-•...- S/H = 4.4xlO-

""\


0.0 1.0 2.0 3.0 4.00.00

0.25

0.05

0.20

.J::+' 0.15P.1Il

Q

1°·10-

.......... Coulomb- - Rankine. - - - Terzaghi~S!H = 0........., SjB = 3.0xlO::""""'""" SjB = 2.0xlO~ SjH = 5.0xlO=:***** SjH = 2.0xlO •...- S/H = 4.4xlO-

i = +200

\.0.25

0.20

0.05

.J::+' 0.150-1IlA

1°·10-

0.30 -'--------'-----------'0.30 l- ....l.I.. ----l

(al (b)

0.30.L-----.LI.----------'

.......... Coulomb- - Rankine. - - - Terzaghi

GeeE>€l S!B = 0eeeee SjB = 3.0xlO-o

---. SiB = 2.0xlO-·~ SiB = 5.0xlO-:***** SiB = 2.0xlO=•...- SiB = 4.6xlO

0.30 l- ---1-'- ---'

Horizontal Earth Pressure. Uh (kN/m2

)

0.0 1.0 2.0 3.0 4.00.00

0.25

0.05

0.20

.J::+' 0.15P.1Il

Q

]: 0.10

i


GeeE>€l S!B = 0 _0

eeeee SjB = 3.0xlO •""""'""" SjH = 2.0xlO=.~ SjH = 5.0xlO_.***** SjH = 2.0xlO....- siB = 4.BxlO-

]: 0.10

.J::+' 0.150-1Il

Q

0.05

0.25

0.20

Horizontal Earth Pressure. Uh (kN/m2

)

0.0 1.0 2.0 3.0 4.00.00

(el (d)

FIG. 9. Distributions of Horizontal Earth Pressure for Positive Backfill Inclinations

layer, the friction angle 8 between Ottawa sand (-y = 15.5 kNlm3

) and the steel plate is found to be 19.2°. The <I> and 8 anglesdetermined from the tests are assumed for the calculation ofearth pressure for Coulomb, Rankine, and Terzaghi's theoriesin the following sections. Figs. 2(a)-2(c) show the failurewedges for i = +20°, 0°, and -20° calculated with Terzaghi'slog-spiral method. The figures will be used to interpret theexperimental results in the present study.

ACTIVE TESTS RESULTS

Wall with Horizontal Backfill

At the beginning, the earth pressure behind a wall with a0.3 m high (H = 0.3 m) and horizontal (i = 0°) backfill isinvestigated. After the backfill has been placed into the soilbin, the model wall slowly moves away as a solid block (translation mode) from the soil mass at a constant speed of 0.02mmls.

The variation of earth pressure Uh measured at differentdepths as a function of horizontal wall displacement S isshown in Fig. 5. The Uh and S have been normalized withvertical stress -yz and the height of backfill H, respectively. Asthe wall started to move, the earth pressure decreased rapidlyand eventually a limiting active pressure was reached. An active state was reached at different depths nearly simultaneously. The distribution of earth pressure at different stages ofwall movement (SIH) are indicated in Fig. 6. The pressuredistributions are essentially linear at each stage of deformationup to failure.

To investigate the effect of H on earth-pressure develop-

ment, experiments with backfill heights of 0.2, 0.3, 0.4, and0.5 m are conducted. In Fig. 7, the horizontal earth-pressurecoefficient Kh decreases with increasing wall movement, andfinally a constant total thrust is reached. It is clear that, withinthe range tested, the backfill height has limited influence onthe development of the Kh curve. The coefficient Kh is definedas the ratio of the horizontal component of total thrust to-yH2/2. The horizontal soil thrust is calculated by summing thepressure diagram shown in Fig. 6. The ultimate value of Kh isdefined as the horizontal active earth pressure K aJlo Due topractical difficulties, no SPT had been fixed at the bottom edgeof the retaining wall. The earth pressure assumed for integration at depth H was approximated by linear extrapolation ofthe valid data points. However, it should be emphasized thatsome theoretical calculations indicate that the stress at the bottom of the wall may be much more complicated than what hasbeen assumed.

The active condition is reached at approximately SIH =0.0015. It should be mentioned that to locate the active pointon the curve may not be an easy task. It also may be observedfrom Fig. 7 that both Coulomb and Terzaghi's theories wouldprovide a good evaluation of the active thrust. However, Rankines' theory tends to overestimate the active earth pressure.

To evaluate the effect of sidewall friction, SPTs SPT6, 10,11, and 12 are installed on the model wall at the same elevation across the wall face. Experimental data plotted in Fig.8 indicates that, with the lubrication layer, earth pressures measured at different distances from the sidewall are in fairly goodagreement. However, since the monitored stress level is verylow, data fluctuation becomes apparent.



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0.30 -'------'-----'----- -1

(a)

Horizontal Earth Pressure, Uh (kN/m2 )

0.000.0 1.0 2.0 3.0 4.0

.......... Coulomb- - Rankine. - - - Terzaghi<>eeee SiR = 0G<H>l*l S!R = 3.0xlO-o

............... S!B 2.0%10-'~ S!B 5.0%10-4***** S!B 2.0xlO-·-- S!H 3.4%10-'

0.05

0.20

0.25i

\0.30 -'-----,'----'- ---.J

(b)

..c::

..., 0.15P.II)

A

"S0.10

----


0.000.0 1.0 2.0 3.0 4.0


<>eeee SIH = 0G<H>l*l S!H = 3.0xlO-o

............... S!H 2.0xlO-·~ S!H 5.0xlO-·***** S!H 2.0xlO-·-- S!H 4.2xlO-·

0.05

0.20

0.25

..c::

..., 0.15P.II)

A

SO.10

----

i

--.------. Coulomb- - Rankine. - - - Terzaghi<>eeee S/H = 0Ga-EH3-€J S!H = 3.0xlO-:............... S!H 2.0%10-~ S!H 5.0xlO-:***** S!H 2.0%10--- s/H 4.8xlO-·


1.0 2.0 3.0 4.0

\\,~0.30 -'-----"------"-----------'

0.20

0.05

0.25

..c::

..., 0.15P.cu

A

S 0.10

----

i


<>eeee SIH = 0B<>aefJ S!H = 3.0xlO-o

............... S!H 2.0xlO-·~ S!H 5.0xlO-·***** S!H 2.0xlO-·-- S!H 4.6xlO-·


0.0 1.0 2.0 3.0 4.00.00 ._---'----------'-------'-----"'1

,,~~

0.30 -'------"------'-----------'

0.25

0.05

0.20

..c::

..., 0.15P.II)

A

1:0.10

(e) (d)

FIG. 10. Distributions of Horizontal Earth Pressure for Negative Backfill Inclinations

SiR

00000 i=+20°00000 i=+15°f!"f!"f!"f!"f!" i=+10°00000 i=+ 5°'{:rtrtrtrt{ i = 0°***** i=- 5°••••• i=-10°••••• i=-15°............... i=-20° 00000 i=+20°

00000 i=+15°f!"f!"f!"f!"f!" i=+10°00000 i=+ 5°***** i= 0°***** i=- 5°

i=-10°••••• i=-15°................ i=-20°

0.3 mH

0.1

0.0 +----,-----,----r-------,-------j0.000 0.001 0.002 0.003 0.004 0.005

siR

0.4,--------------------,

-~0.3

0.0050.0040.0030.002

0.3 m

0.001

H

1.0

0.9

0.8

0.7

0.6.Q

~ 0.5

0.4

0.3

0.2

0.1

0.00.000

FIG. 11. Variation of Kh with Active Wall Movement for VariousBackfill Inclinations

FIG. 12. Variation of hlH with Wall Movement for VariousBackfill Inclinations

Wall with Sloping Backfill

The effects of backfill inclination on the development ofactive stress are discussed. Figs. 9 and 10 show the earthpressure distributions at different stages of wall movement for

positive and negative backfill inclinations, respectively. It canbe seen that, for H = 0.3 m and i varying from -20° to +20°,the experimental earth-pressure distributions are approximately linear at each stage of the wall movement. This implies



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Fig. 13(a) shows that the wall movement required for thebackfill to reach an active state (S/H)a increases with increasing backfill inclination. For the sloping angle i = - 20°, theactive wall movement required is about 0.0009. Nevertheless,for i = +20° the (S/H)a needed is about 0.0025. The experimental findings reported by Mackey and Kirk (1967), Bros(1972), Sherif et al. (1982), Fang and Ishibashi (1986), Bowles(1988), and Das (1990) are also plotted in Fig. 13. It shouldbe mentioned that the data point reported by Fang and Ishibashi (1986) was obtained for a backfill that had been densi-fied with the sinusoidal horizontal acceleration of 0.35g for 10s. It is apparent that soil density plays an important role regarding the determination of (S/H)a'

Fig. 14 shows the relationship between the active earth-pressure coefficient Ka.h and the backfill sloping angle i. It is clearfrom this figure that the experimental Ka,h increases with increasing backfill inclination. The Ka•h values calculated with

0.6 ....-----------------------,

.......... Coulomb0.5 - - Rankine

. - - - Terzaghi00000 NCTU Data

0.4

0.4.<loJ 0.3

0.3

0.2

0.1

..... Rowe·& Peaker (1965)Gaeae Mackey & Kirk (1967)***** Narain et al. (1969)_NCTurata

0.2

0.1

0.0 +--.,..--r----r--,----.---,-,..--..,...--.------i-25 -15 -5 5 15 25

i, (Degree)

20.0 ...----------------------,

0.500.400.30

S/HO. 00.10

0.0 +----,--,--.----,--.....------,r----.--..,...----,--,----l0.00

5.0

15.0

.<l

~10.0

FIG. 14. Active Earth-Pressure Coefficient K.,h versus BackfillInclination

FIG. 15. Variation of Kh with Passive Wall Movement for Various Backfill Inclinations

FIG. 13. (SfH). and (SfH)p versus Backfill Inclination

0.0 +--...-----.---..-----,----.-----,r----.----io -10 10 20

that the points of application of total thrusts would act at aboutH/3 above the wall base. It is also clear in these figures thatthe experimental active stress distributions are in fairly goodagreement with Coulomb and Terzaghi's solutions.

The variations of Kh with wall movement for various backfill inclinations are summarized in Fig. 11. It is clear from thefigure that Kh decreases with increasing wall movement beforereaching a stable value. It may be observed in Fig. 11 that,for the backfill with a negative sloping angle (e.g., i = -20°),an active state is reached at a relatively small wall movement.However, a larger wall movement is needed for a backfill witha positive sloping angle (e.g., i = +20°) to reach an activestate. The finding is logical in view of the fact that the rupturesurface illustrated in Fig. 2(c) is apparently shorter than thatshown in Fig. 2(a). Fig. 12 shows that, irrespective of thebackfill inclination, the points of application of the total thrustsare located at about 0.29H to 0.33H above the wall base. Notethat h is defined as the distance between the point of application of total thrust and the wall base.

i, (Degree)

(b)

JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING I MARCH 1997/255


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15.0

'oJ.10.0

20.0 -,---- ----,

a d900000 H=O.5m oa:r:P°oOb<P66666 H=O.4m «:>00000 H=O.3m Q:}900000 H=O.2~

/'5.0

/

6

20.0 -,------ ----,

i = +10a

00000 H=O.5m15.0 66666 H=O.4m

00000 H=O.3m00000 H=O.2m

0.0 0.00.00 0.10 0.20 0.30 0.40 0.50 0.00 0.10 0.20 0.30 0.40 0.50S/H S/H(a) (b)

20.0 20.0

i = -100i = -200

00000 H=O.5m 00000 H=O.5m15.0 66666 H=O.4m 15.0 66666 H=O.4m

00000 H=O.3m 00000 H=O.3m00000 H=O.2m 00000 H=O.2m

'oJ 10.0 'oJ 10.0

5.0 6.0

0.0~0.10 0.20 0.00 0.10 0.20 0.30 0••0 0.50

S/H S/H

(el (d)

FIG. 16. Variation of Kh with Passive Wall Movement for Various I and H

(1)

Coulomb, Rankine, and Terzaghi's theories are also indicatedin Fig. 14. It is obvious that the test data are in good agreementwith the values determined with Coulomb and Terzaghi's theories. Rankine's solution tends to overestimate the activethrust, especially for the backfill with a negative sloping angle.The Rankine active earth-pressure coefficient Ka is given bythe following relationship:

. cos i - y'cos2i - cos2<l>Ka =cos I

cos i + V cos2i - cos2<l>

Referring to Fig. 2(a) and 2(c), whether the backfill inclinationis +20° or -20°, we will get the same Ka from (1). Since theRankine active thrust Pa is always parallel to the surface ofbackfill, therefore for i = +20° and i = -20° the only difference is that the shearing components of Pa have opposite directions. However, for i = +20° and i = -20° the normalcomponents of the Rankine active thrusts are exactly the same.Based on the experimental data shown in Fig. 14, it is obviousthat it may not be appropriate to adopt Rankine's theory todetermine the active earth pressure behind a rigid wall withsloping backfill.

PASSIVE TEST RESULTS

Wall with Sloping Backfill

The effect of backfill inclination on the development of passive stress are discussed. After the backfill has been placedinto the soil bin, the model wall slowly moves toward the soilmass in translation mode at a constant speed of 0.27 mm/s.

The variation of coefficient Kh for various backfill inclinationsis summarized in Fig. 15. It is clear that Kh increases with wallmovement before reaching an ultimate value; then Kh remainsapproximately a constant. This ultimate value is defined as thehorizontal passive earth-pressure coefficient Kp•h ' For the backfill with a negative sloping angle (e.g., i = -20°), a passivestate is reached at a relatively small wall movement. On theother hand, larger wall movements are needed for the backfillwith a positive sloping angle (e.g., i = +20°) to reach its passive state.

To study the effects of backfill height H on passive pressure,experiments with backfill heights of 0.2, 0.3, 0.4, and 0.5 mhave been conducted. Figs. 16(a)-16(d) show the variation ofKh as a function of wall movement for various backfill heightsfor i = +20°, + 10°, -10°, and -20°, respectively. It may beseen that most data are concentrated in a narrow band. It appears that, within the range tested, the backfill height has littleinfluence on the development of passive stress. Due to thelimitation of the experimental facility, the maximum wallmovement allowed for the 120 mm thick model wall is only110 mm. To ensure that a passive state would occur duringtesting, the H = 0.2 m condition is adopted in the followingdiscussion. It should be mentioned that as the height of backfillH reduces from 0.5 to 0.2 m, the valid earth-pressure measurements on the retaining wall decreases from 10 to 4.

Figs. 17(a)-17(d) illustrate the distributions of earth pressures at various stages of wall movement for i = +20°, + 10°,-10°, and -20°, respectively. From these data it may be seenthat the experimental earth pressures are nearly linear at eachstage of wall movement. This implies that the points of ap-



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.--.------ Coulomb- - Rankine. - -- -- TerzaghiGeGe9 S!H = aaaeae S!H = 0.01..-S!H = 0.05~S!H = 0.1***** S!H = 0.15+++++ S!H = 0.25_S!H = 0.42

\\

\

\\

\

Horizontal Earth Pressure, Uh (kN/m2

)

a w ~ ~ 400.00

0.05,......

!:S 0.10p..

Q)

i=I

0.15

\

\

0.20\

....-... Coulomb- - Rankine- - -- Tenachi

ooeeEl S/H = 0ooeeEl S!.H = 0.01~S!.H = 0.05~S!.H = 0.1***** S!.B = 0.15

'.+++++ S!.H = 0.25~S/H = 0.46

1"'= +20·-.......................

0.15 ,,,,,,,0.20 ..L..._--L --.:.' --'


)

a 10 20 30 400.00

0.05

!:S 0.10p..Q)

i=I

(aJ (b)

..-------. Coulomb- - Rankine. -- - - TerzaghiGe69€l S!H = aGaee£l S!H = 0.01..-S!H = 0.05~S!H = 0.1***** sjH = 0.15-S!H = 0.24

\\


)

10 20 30 400.00 ....-~--=':.--~-.;:.::..-~--'---~---j

0.20 -"-------'------------~

0.15

0.05

:S 0.10p..Q)

i=I

.--------- Coulomb- - Rankine. -- -- -- Terzaghi'****' S!H = aGaee£l S!H = 0.01~S!H = 0.05~S!H = 0.1***** S!H = 0.15_S!H = 0.28

0.05


)

0.00 ....._~~10::....-~_ _=2:.::.0_~--'3::L0_~____j40

0.20 -'----__~.lL_ __"

0.15

..c:+' 0.10p..Q)

i=I

,......S'-'

(cJ (d)

FIG. 17. Distributions of Horizontal Earth Pressure for Various Backfill Inclinations

0.50 ,--------------------,

0.500.40

00000 i=+20·66666 i= +10°***** i= 0°••••• i=-lO°........ i=-20°

0.20 0.30

siR0.10

0.20

0.10

0.40

H = 0.2 m

0.00 +---.--,----,,---,--.---,-.-----,--....,-----,--10.00

~ 0.30

..........Q

FIG. 18. Variation of hlHwlth Passive Wall Movement for Various Backfill Inclinations

O.04H). Similar findings were also reported by Mackey andKirk (1967) and Narain et al. (1969). In this study, the soildensity obtained was quite loose. The unusually high passivewall movement needed (0.46H) is most probably due to the

plication of total thrust would act at about H/3 above the wallbase. Passive earth-pressure distribution calculated with Coulomb, Rankine, and Terzaghi's theories are also indicated inFig. 17. It should be stressed that, for i = +20°, the discrepancy among the theoretical solutions is quite significant. Itmay be observed in Fig. 17 that the experimental passiveearth-pressure distributions are in relatively good agreementwith Coulomb's solution for various backfill inclinations. Fig.18 shows that, irrespective of the backfill sloping angle, thepoints of application of total thrusts varied between 0.33H and0.41H above the wall base.

Fig. 13(b) shows that the wall movement required for thebackfill to reach a passive state (S/H)p obviously increaseswith increasing backfill inclination. In the figure, for i = +20°,the passive wall movement needed is 0.46H. The physicalmeaning of the preceding finding is that, for a retaining structure backfilled with 1.0 m of loose sand, the wall displacementrequired for the soil to reach a passive state would be as muchas 0.46 m. From a practical point of view, even a portion ofsuch a large lateral displacement could damage the functionof the wall and nearby facilities. Under such a circumstance,when evaluating the adequacy of a retaining structure, exceptassessing the factors of safety associated with sliding, overturning, and bearing capacity, it might be necessary to establish a displacement criterion for the designers.

Based on his experimental results using a rotating modelwall, Schofield (1961) reported that the wall movement required for a loose horizontal backfill to reach a passive stateis approximately 0.2H. However, the passive wall movement needed for a dense backfill would be much less (only



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300.0 -r------------------,passive earth-pressure coefficient Kp is given by the followingrelationship:

25

200.0

GBae£l Mackey & Kirk (1967)GeeeEl NCTU Data

100.0

I0.0 +::--,-----,-----r--.---.-------,r----r--.---..,....------1

-25 -20 -15 -10 -5 0 5 10 15 20

i, (Degree)

FIG. 19. (SlH)"J(SlH). versus Backfill Inclination

K. cos i + vicos2i - cos2<j>

p=C~1 (~

cos i - vicos2i - cos2<j>

Whether the backfill inclination is +20° or -20°, the K coeffici~nt calculated with (2) would be the same. Although thesheanng component of the passive thrust for i = +20° and-20° have opposite directions, however, the normal components of Rankine's passive thrust are identical. That is there~on why R~nkine's Kh versus i relationship shown in Fig.2~ IS symmetrIcal with the i = 0 vertical axis. In Fig. 20, thedIscrepancy between test data and Rankine's solution increaseswith increasing backfill sloping angle. For example, for i =+ 15° Rankines' passive thrust is only 18% of the experimentalvalue. It should be mentioned that the Kp •h values would occurat a large wall displacement as indicated in Fig. 13(b). Forpr~tical purposes the variation of Kh as a function of i angleat dIfferent stages of wall movement are also indicated in Fig.20. It may be seen that, if SIH = 0.20 is arbitrarily assumedto be the displacement criterion for passive failure, then testdata would be in fairly good agreement with the curve obtained with the log-spiral method proposed by Terzaghi.

25.0 -r-----------------~ CONCLUSIONS

ACKNOWLEDGMENTS

Based on the experimental data obtained during the investigations, the following conclusions can be drawn about theeffects of backfill inclination on the development of active andpassive earth pressures.

For a wall moving away from the backfill, the experimentalearth-pressure distributions are essentially linear at each stageof wall movement up to failure. The points of application ofthe total thrust are located at about 0.29H to 0.33H above thewall base for various backfill inclinations. An active state isreached at different depths nearly simultaneously. The wallmovement required for the backfill to reach an active stateincreases with increasing backfill inclination. The experimental active earth-pressure coefficient Ka•h is in good agreement with the values determined with Coulomb and Terzaghi'stheories. Rankine's solution tends to overestimate the activethrust, especially for the backfill with a negative sloping angle.It may not be appropriate to adopt Rankine's theory to determine the active earth pressure against a rigid wall with slopingbackfill.

For a wall moving toward the backfill, the experimentalearth-pressure distributions are nearly linear at each state ofwall movement. Irrespective of the backfill sloping angle, thepoints of application of total thrusts varied between 0.33H andOAIH above the wall base. The experimental passive earthpressure distributions are in relatively good agreement withthat determined with the approach originally developed byCoulomb in 1776. The wall movement required for the backfillto reach a passive state increases with increasing backfill inclination. For the same wall the passive wall displacement required to reach a passive state is approximately 230 times thedisplacement required to reach an active state. Rankine's theory tends to underestimate the passive thrust. The discrepancybetween test data and Rankine's solution increases with increasing backfill sloping angle. For a backfill inclination of+ 15°, the passive thrust calculated with Rankine's theory isonly 18% of the experimental value. It may not be appropriateto adopt Rankine's theory to determine the passive earth pressure against the rigid wall with sloping backfill.

The writers wish to acknowledge the National Science Council of theRepublic of China government (NSC 83-0410-E-0009-032) for the finan-

** 0

*0

a~v •

••

t:>. t:>.

__ Coulomb.......... Rankine_____ Terzaghi

00000 Kp h

***** S7H=O.3000000 S!H=O.20••••• S!H=O.10t:>.t:>.t:>.t:>.t:>. S!H=O.05••••• S!H=O.0200000 S!H=O.OO

5.0

20.0

15.0

10.0

combined effect of the soil density and the +20° backfillinclination.

The ratio of (SIH)p to (SIH)a as a function of backfill inclination is indicated in Fig. 19. On the average, the passive walldisplacement required to reach a passive state is about 230times the displacement required to reach an active state for thesame wall. The low ratio reported by Mackey and Kirk (1967)is mainly due to the fact that their (SIH)a value is located atthe high end of all data reported by different researchers shownin Fig. 13(a).

The relationship between the passive earth-pressure coefficient Kp •h and backfill inclination is demonstrated in Fig. 20.It may be seen that Kp •h increases with increasing sloping angle. It is clear that experimental Kp •h values are in fairly goodagreement with the results determined with the concept originally developed by Coulomb in 1776. Note that Rankine'stheory tends to underestimate the passive thrust. The Rankine

0.0 +-----s,1---¥-_.Jt-~!....-+-¥_____Jf0-~0!....--0:;:..____j-25 -15 -10 -5 0 5 10 15 20 25

i, (Degree)

FIG. 20. Variation of Kh with I at Different Passive Wall Movements



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cial assistance that made this investigation possible. Special thanks areextended to Yih-Chung Tsai for his assistance.

APPENDIX I. REFERENCES

Bowles, J. E. (1988). Foundation analysis and design, 4th Ed., McGrawHill Book Co., Inc., New York, N.Y.

Bros, B. (1972). "The influence of model retaining wall displacementson active and passive earth pressure in sand." Proc., 5th Eur. Con! onSoil Mech., Vol. I, Madrid, 241-249.

Das, B. M. (1990). Principles ofgeotechnical engineering, 3rd Ed., PWSPublishing Co., Boston, Mass.

Duncan, J. M., and Seed, R. B. (1986). "Compaction-induced earth pressures under Ko conditions." J. Geotech. Engrg., ASCE, 112(1), 1-22.

Duncan, J. M., Williams, G. W., Sehn, A. L., and Seed, R. B. (1991)."Estimation earth pressures due to compaction." J. Geotech. Engrg.,ASCE, 117(2), 1833- 1847.

Fang, Y. S., and Ishibashi, I. (1986). "Static earth pressures with variouswall movements." J. Geotech. Engrg., ASCE, 112(3),317-333.

Fang, Y. S., Chen, T. J., and Wu, B. F. (1994). "Passive earth pressureswith various wall movements." J. Geotech. Engrg., ASCE, 120(8),1307-1323.

James, R. G., and Bransby, P. L. (1970). "Experimental and theoreticalinvestigations of a passive pressure problem." Geotechnique, London,England, 20(1), 17-37.

Mackey, R. D., and Kirk, D. P. (1967). "At rest, active and passive earthpressures." Proc., South East Asian Conf. on Soil Mech. and FoundEngrg., Bangkok, 187-199.

Maneotti, G. (1970). "Some results of quay-wall model tests on earthpressure." Proc., Inst. of Civ. Engrs., London, England, 47, 185-204.

Narain, J., Saran, S., and Nandakumaran, P. (1969). "Model study ofpassive pressure in sand." J. Soil Mech. and Found Engrg. Div., ASCE,95(4), 969-983.

Rowe, P., and Peaker, K. (1965). "Passive earth pressure measurements."Geotechnique, London, England, 15(1),57-78.

Schofield, A. N. (1961). "The development of lateral force of sandagainst the vertical face of a rotating model foundation." Proc., 5thInt. Con! Soil Mech. and Found Engrg., Paris, Vol. 2,479-484.

Sherif, M. M., and Mackey, R. D. (1977). "Pressure on retaining wallwith repeated loading." J. Geotech. Engrg. Div., ASCE, 103(11),1341-1345.

Sherif, M. A., Ishibashi, I., and Lee, C. D. (1982). "Earth pressure againstrigid retaining walls." J. Geotech. Engrg., ASCE, 108(5),679-695.

Sherif, M. A., Fang, Y. S., and Sherif, R. I. (1984). "K. and Ko behind

rotating and non-yielding walls." J. Geotech. Engrg., ASCE, 110(1),41-56.

Tatsuoka, F., and Haibara, O. (1985). "Shear resistance between sand andsmooth or lubricated surface." Soils and Found., 25(1), 89-98.

Terzaghi, K. (1932). "Record earth pressure testing machine." ENR,109(Sept. 29), 365-369.

Terzaghi, K. (1941). "General wedge theory of earth pressure." ASCETrans., 68-80.

Terzaghi, K. (1943). Theoretical soil mechanics. John Wiley & Sons, Inc.,New York, N.Y.

Wu, B. F. (1992). "Design and construction of National Chiao TungUniversity model retaining wall," MS thesis, Nat. Chiao Tung Univ.,Hsinchu, Taiwan.

APPENDIX II. NOTATIONThe following symbols are used in this paper:

D IO, D60 = grain size for which 10 and 60% of soil by weightare finer;

emu, emiR = maximum and minimum void ratios of soil;Os = specific gravity of soil;H =height of backfill at soil-wall interface above wall

base;h =distance between point of application of total resul

tant force and wall base;i = angle of backfill slope with horizontal;

K. = active earth-pressure coefficient;K•.h = coefficient of active horizontal soil thrust;Kh = coefficient of horizontal soil thrust;Kp = passive earth-pressure coefficient;

Kp•h = coefficient of passive horizontal soil thrust;p. = resultant of active earth pressure;Pp = resultant of passive earth pressure;S = lateral wall displacement;

(SIH). = wall movement required for backfill to reach activestate;

(SIH)p = wall movement required for backfill to reach passivestate;

z = depth measured from soil surface;'Y = unit weight of soil;8 = friction angle at soil-wall interface;

(fh = horizontal earth pressure; and<l> = internal friction angle of soil.



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Documents

Earth Pressures with Sloping Backfill · EARTH PRESSURES WITH SLOPING BACKFILL By Yung-ShowFang,l Associate Member, ASCE, Jiung-MingChen,z and Cheng-Yu Chen3 ABSTRACT: This paper