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# Craig's Soil Mechanics 7th Edition

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```between values
of the factors Fs and Fp over the practical ranges of wall geometry and shear
strength parameters, particularly in the case of clays. Burland et al. proposed that
the factor of safety should be based on net passive resistance on the basis of an
analogy with the ultimate bearing capacity of a foundation.

Guidance on the selection of suitable factors of safety for use in the above methods
is given by Padfield and Mair [15]. Values of �m andM are given in EC7 and BS 8002,
respectively. Either gross or net water pressures can be used in design (because, unlike
earth pressures, no coefficient is involved), the latter being more convenient. To allow
for over-excavation or dredging, the soil level in front of the wall should be reduced by
10% of the depth below the lowest tie or prop, subject to a maximum of 0.5m. Again,
a minimum surcharge pressure of 10 kN/m2 should be assumed to act on the soil
surface behind the wall.
It should be realized that full passive resistance is only developed under conditions

of limiting equilibrium, i.e. when the safety or mobilization factor is unity. Under
working conditions, with a factor greater than unity, analytical and experimental work
has indicated that the distribution of lateral pressure is likely to be of the form shown
in Figure 6.24, with passive resistance being fully mobilized close to the lower surface.
The extra depth of embedment required to provide adequate safety (whether measured
by lumped or partial factors) results in a partial fixing moment at the lower end of the
wall and, consequently, a lower maximum bending moment than the value under
limiting equilibrium or collapse conditions. In view of the uncertainty regarding the
pressure distributions under working conditions it is recommended that bending
moments and tie or prop force under limiting equilibrium conditions (i.e. F ¼ 1)

Figure 6.24 Anchored sheet pile wall: pressure distribution under working conditions.

198 Lateral earth pressure

should be used in the structural design of the wall. The tie or prop force thus calculated
should be increased by 25% to allow for possible redistribution of pressure due to
arching (see below). Bending moments should be calculated on the same basis in the
case of cantilever walls. In limit state design, Case B applies to the determination of
maximum bending moment.

Effect of flexibility and K0

The behaviour of an anchored wall is also influenced by its degree of flexibility or
stiffness. In the case of flexible sheet pile walls, experimental and analytical results
indicate that redistributions of lateral pressure take place. The pressures on the most
yielding parts of the wall (between the tie and excavation level) are reduced and those
on the relatively unyielding parts (in the vicinity of the tie and below excavation level)
are increased with respect to the theoretical values, as illustrated in Figure 6.25.
These redistributions of lateral pressure are the result of the phenomenon known as
arching. No such redistributions take place in the case of stiff walls, such as concrete
diaphragm walls.
Arching was defined by Terzaghi [25] in the following way. ‘If one part of the

support of a soil mass yields while the remainder stays in place, the soil adjoining
the yielding part moves out of its original position between adjacent stationary soil
masses. The relative movement within the soil is opposed by shearing resistance within
the zone of contact between the yielding and stationary masses. Since the shearing
resistance tends to keep the yielding mass in its original position, the pressure on the
yielding part of the support is reduced and the pressure on the stationary parts is
increased. This transfer of pressure from a yielding part to adjacent non-yielding parts
of a soil mass is called the arching effect. Arching also occurs when one part of a
support yields more than the adjacent parts.’
The conditions for arching are present in anchored sheet pile walls when they

deflect. If yield of the anchor takes place, arching effects are reduced to an extent
depending on the amount of yielding. On the passive side of the wall, the pressure is
increased just below excavation level as a result of larger deflections into the soil. In the
case of backfilled walls, arching is only partly effective until the fill is above tie level.

Figure 6.25 Arching effects.

Embedded walls 199

Arching effects are much greater in sands than in silts or clays and are greater in dense
sands than in loose sands.
Redistributions of earth pressure result in lower bending moments than those

obtained from the free earth support method of analysis; the greater the flexibility of
the wall, the greater the moment reduction. Rowe [21, 22] proposed the use of moment
reduction coefficients, to be applied to the results of free earth support analyses, based
on the flexibility of the wall. Wall flexibility is represented by the parameter � ¼ H4/EI
(units m2/kN per m), where H is the overall height of the wall and EI the flexural
rigidity. The tie force is also influenced by earth pressure redistribution and factors are
also given for the adjustment of the free earth support value of this force. Details of
Rowe’s procedure are given by Barden [2].
Rowe’s moment reduction factors should only be used if a factored passive resist-

ance (F > 1) has been used for the calculation of bending moments. If bending
moments have been calculated for the limiting equilibrium condition (F ¼ 1), Rowe’s
factors should not be used.
Potts and Fourie [18, 19] analysed a propped cantilever wall in clay by means of the

finite element method, incorporating an elastic–perfectly plastic stress–strain relation-
ship. The results indicated that the required depth of embedment was in agreement
with the value obtained by the free earth support method. However, the results also
showed that in general the behaviour of the wall depended on the wall stiffness
(confirming Rowe’s earlier findings), the initial value of K0 (the coefficient of earth
pressure at-rest) for the soil and the method of construction (i.e. backfilling or
excavation).
In particular, maximum bending moment and prop force increased as wall stiffness

increased. For backfilled walls and for excavated walls in soils having a low K0 value
(of the order of 0.5), both maximum bending moment and prop force were lower than
those obtained using the free earth support method. However, for stiff walls, such as
diaphragmwalls, formed by excavation in soils having a high K0 value (in the range 1–2),
such as overconsolidated clays, both maximum bending moment and prop force
were significantly higher than those obtained using the free earth support method.
For the particular (excavated) wall and material properties considered by Potts and
Fourie, the patterns of variation shown in Figure 6.26 were obtained for a factor of

Figure 6.26 Analysis of propped cantilever wall in clay by the finite element method. (Repro-
duced from D.M. Potts and A.B. Fourie (1985) Geotechnique, 35, No. 3, by
permission of Thomas Telford Ltd.)

200 Lateral earth pressure

safety (Fr) of 2.0. In this figure,Mfe and Tfe denote the maximum bending moment and
prop force, respectively, obtained from the finite element analysis, and Mle and Tle
denote the corresponding values obtained from a limiting equilibrium (free earth
support) analysis.

Pore water pressure distribution

Sheet pile and diaphragm walls are normally analysed in terms of effective stress. Care
is therefore required in deciding on the appropriate distribution of pore water pres-
sure. Several different situations are illustrated in Figure 6.27.

Figure 6.27 Various pore water pressure distributions.

Embedded walls 201

If the water table levels are the same on both sides of the wall, the pore water
pressure distributions will be hydrostatic and will balance (Figure```