STABILITY OF EARTH-RETAINING STRUCTURES - Introduction to Soft Soil Geotechnique: Content, Context and Application - page 182

The behaviour of a reinforced earth wall, constructed by subsequent layers of
compacted soil of equal thickness in between reinforcement elements, shows, that
tension T in the ties increases from the face (wall) to a maximum and then
decreases with distance from the face. The loci of these maxima form a curved
surface that separates the front part, called the active zone ABC, from the backside,
which is considered stable and referred to as the resisting zone BCDE (Fig 11.9b).
The tensile force T in a tie can be estimated (Schlosser) by stating that it must be
able to resist the lateral pressure

v ' in the active zone and that this force
can be provided by the shear resistance (pulling out) of the tie in the resisting zone.
If ties are interspaced by

h ' = K a

h horizontally and by v vertically, then stability factors

can be defined, according to

yield F yield = f S tie /( K a v '

h v ) (11.11a)

pullout F pullout = f A tie L r tan ? /( K a v ' h v ) (11.11b)

Here, f is the yield strength, S and A are the cross-section and perimeter of the
tie, the angle of friction between the tie and the soil, and L r the length of the tie in

the resisting zone. Typical values for the safety factor are

?

pullout =
2.0. Using ribbed strips and/or grout can raise the friction significantly. In addition,
for stiff rods the bending moment and the shear force in the failure zone should be
considered (Fig 11.9c). The saturation degree may influence the soil-tie friction. In
practice, standard codes (NEN 3650 pipelines) are applied for designing stiff rods.
For the vertical stress one usually applies

yield = 1.5 and

z . This is on the safe side, as a
higher stress ( R : trapezoidal stress at the base) may be acting because of the
overturning moment due to the earth pressures P 1 = ½ K a

v ' =

H 2 and P 2 = K a qH
against the backside of the wall structure. Groundwater pressures have to be dealt
with separately; their effect can be reduced by proper drainage facilities.

application 11.1
Consider the case of a vertical rough earth retaining wall (Fig 11.10), which
supports an undrained cohesive soil mass (

max = c u ). The value of the
horizontal thrust P a is required. A plane failure surface is assumed ending at the tip
D of a tension crack CD at depth z 0 , filled with water. The equilibrium of the
wedge ABDC includes the following forces: weight W = ½

= 0,

( H 2 - z 0 2 )cot , normal

force N s on the slip plane, shear force at the slip plane T s = ( H - z 0 ) c u / sin , active

thrust on the wall P a , friction force along the wall T f = c f ( H - z 0 ), and the hydraulic
thrust in the crack P w = ½ w z 0 2 . The coefficient c f represents the soil-wall adhesion,

which may vary depending on the soil stiffness. The equilibrium of the wedge
ABDC is expressed by

N s cos = W - T s sin - T f and P a - P w = N s sin - T s cos

and so P a - P w = W tan - T s (sin

tan

+ cos ) - T f tan

Inserting the values of the forces yields