Earth pressures

&Gravity RetainingWalls

Sean T. D. Mills

Theorists have developed different methods for predicting the amountof earth pressure exerted on the back of a retaining wall in order todesign against failure by sliding, overturning and bearing. Historictheories, such as those by Rankine (1857) and Coulomb (1776), set outthe principles for modern application, but are somewhat outdated anddo not necessarily err on the side of safety. Eurocode 7 gives a morecomprehensive modern method for predicting earth pressures, basedon a more realistic failure pattern and for a greater amount of wall andsoil variables. It also gives a bearing capacity equation based on theorydeveloped in part by Terzaghi (1943) and Brinch Hansen (1970). Thisequation is suitable for most common cases, but should be used withcaution for cases with ground sloping away from the foundation.

INTRODUCTION

Research shows that in many cases Rankine's theory is limited, by onlyconsidering a vertical back of wall and the strength only related to theangle of shearing resistance. Coulomb underestimated active earthpressures and overestimated passive, when back of wall friction isutilised. The project aims to investigate the effects of changing theparameters of how the modern analytical method in Annex C.2 and D,Eurocode 7 will effect to design of a retaining wall.

PROJECT AIMS

CONCLUSION

RESULTS

METHODOLOGYThe method used for this was to considera simple initial baseline wall to Rankineconditions (figure 1). Subsequent wallshad individual parameters changed tomeasure the effect in terms of sliding,bearing and overturning failure. For thisstudy, the soil was considered to begranular and drained. Some values havebeen normalised to make the resultsindependent of the wall height.

φ' = variesγret = 18kN/m3

δw = 0

B1

B

qret,n = 0.15B1 = B

γwall =24kN/m3

HF

h f

D = 0

δw = 2/3φ' and φ'

W

ew = 0

Figure 1: Baseline wall C1

The methods given by Eurocode 7 prove to be more adaptable in most situations forcalculating earth pressures and are based on more accurate modern theory.Changing the shape of a wall can help resist overturning forces and give a greater effectivefoundation area supporting bearing pressures.Ultimately, the minimum amount of mass required for a gravity retaining wall will be related tothe amount required to resist the sliding force. Leaning the wall back will reduce thehorizontal force and therefore will improve not only sliding resistance, but will provide agreater stability and improve bearing capacity.Leaning the wall away increase the soil wedge and in turn the sliding force, but it may bemore desirable to give a greater amount of usable space above the wall.Back of wall friction can be helpful for all failure modes, but the use and extent appears to bemore controversial. The current view on use and application of back of wall friction may meritfurther study.Bearing resistance can be improved by maximising the foundation base area and utilisingembedment, but retaining wall design will likely be limited by the effect of the load inclination.

φ' = variesγret = 18kN/m3

δw = 0

B1

B

qret,n = 0.15B1 = 0.75B

HF

h f

D = 0

δw = φ'

γwall (conc.)= 24kN/m3

W

ew < 0

Wal

l C2

HH HH = HF.cos θθ

h f

HF

φ' = variesγret = 18kN/m3

δw = 0θ = 8°

qret,n = 0.15B1 B1 = B

D = 0

γwall (conc.)= 24kN/m3

W

ew < 0

Bδw = 2/3φ' and φ'

Bδw = 2/3φ' and φ'

HH

θ

h f

HF

φ' = variesγret = 18kN/m3

δw = 0θ = 8°

qret,n = 0.15B1

HH = HF.cos θ

HV

HV = HF.sin θ

B1 < B

θ

γwall (conc.)= 24kN/m3

W

ew = 0

D = 0W

all C

4W

all C

5W

all C

6

Bearing capacity

φ' = variesγret = 18kN/m3

δw = 2/3φ'

B1

B

qret,n = 0.15B1 = B

γwall (conc.)= 24kN/m3

h f

D = 0

δw = 2/3φ' and φ'

W

ew = 0HH

δwHF

DhHH = H.cos δw

Dh = H.sin δw

Sliding failure relies on sufficient vertical force and base frictionto overcome the horizontal force, therefore in this case theweight of wall is unchanged from the baseline.

Inclining the front face of the wall or adding a toe shifts the masstoward the soil, providing a stabilising eccentricity andmaximises the foundation area of soil bearing the wall load.

The results below are given as a percentageof weight/height, based on the baseline wallin figure 1. They are calculated so that theresistance is exactly equal to thedestabilising action for each wall setup.

KEY

Slid

ing

failu

reB

earin

g fa

ilure

Ove

rtur

ning

failu

re

H ≤

Rd =

V ta

n δ d

V ≤

R d (A

nnex

D, E

C7)

e/6

≤ B

(bas

e w

idth

)

Leaning a wall back will reduce the size of the soil wedge beingsupported, reducing the horizontal force. As the force actsnormal to the back of the wall, the sliding force is furtherreduced to the horizontal component (HH), improving the slidingresistance.

This arrangement gives a greater stabilising moment, improvingthe overturning stability and increasing the base area the soil issupporting.

Leaning the back wall away from the retained soil increases thesize of the soil wedge being supported, increasing the horizontalforce. As the force acts normal to the back of the wall, thisreduces HH and introduces a vertical component (HV). Thisincreases the sliding force, but due to the increased base widthand HV, there is still a beneficial effect to bearing andoverturning resistance. Although reducing sliding resistance, abenefit could be providing more useable space above the wall.

Utilising back of wall friction reduces the horizontal force andadds a stabilising vertical down drag force, helping to reduce allfailure modes. The greater accuracy of the theory used, will givemore confidence to actual effect of the friction and provide bettersafety. The amount of friction gained will depend on a number offactors, including the soil particle size and consolidation of thesoil. Caution should be taken in situations near vibration sourcesor excessive downward wall movement may occur.

In retaining wall design, bearing capacity is mostly governed by theeccentricity of the load and the effective area of foundation beingsupported by the ground. Increasing the base size or stabilisingeccentricity with the wall shape will improve capacity. Additionally,utilising an embedded depth of the foundation will significantlyimprove the bearing, by giving additional supporting soil mass. Thecapacity is also limited by the inclination of the load, which isdependent on the ratio of H/V, as the ratio increases, the bearingstress field dramatically reduces

V

H

V

H

References:Brinch Hansen, J., 1970. A revised and extended formula for bearing capacity. The Danish geotechnical institute, Volume Buletin No. 28,pp. 5-11.Coulomb, C. A., 1776. Essai sur une application des r`egles de maximis et minimis a quelques probl`emes de statique, relatifs al'architectur. Paris: Memoirs Divers Savants, Acad`emie Sciences (in French).Rankine, W. J. M., 1857. II. On the stability of loose earth. Philosphical Transactions, The Royal Society, Volume 147, pp. 9-27.Terzaghi, K., 1943. Theoretical Soil Mechanics. London: John Wiley and sons, inc,.

NB. Wall C3 (adding a toe) has been omitted from this poster.