2120
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
The same mechanism of a non-linear load and bond
distribution was confirmed by laboratory full-scale test
accomplished by Weerasinghe (1993). It is also important to
mention investigation done by Coates and Yu (1970), which
studied stress distribution around a cylindrical anchorage in
triaxial stress field using finite element methods. The results
emphasize the non-uniform bond stress distribution for the ratio
of the elastic modulus of the anchor material (E
A
) and the rock
(E
R
) less than 10 (E
A
/E
R
<10) , which is very common for wide
range of rocks and soils in which anchors are usually
constructed.
2.3
Efficiency factor
There have been a number of attempts to quantify the non-
uniform load distribution and to introduce effects of progressive
debonding into Formula 1. Casanovas (1989) recommended
design based on definition of apparent fixed length (L
ve
) over
which the ultimate bond stress can be mobilized:
0
) ·1.0 log(
1
0
ve
·
) (
L
0
L
L
L
ult
fix
(2)
(2)
where: L
ve
= apparent fixed length over which τ
ult
(kN/m
2
)
operates, L
0
= reference length of 1 m, τ
0
= reference value of 1
kN/m
2
.
To understand better efficiency factor concept it is possible
to analyze Figure 1 and to compare area A, that corresponds to
the final and maximum load stage, with the total area below τ
ult
.
ult
eff
below Area
A Area
f
.
.
.
(3)
Then, ultimate anchor capacity can be expressed as follows:
eff
fix
fix
ult
f
Ld
T
· ·
· ·
(4)
Research based on over 60 full scale tests performed on
different anchor fixed lengths, installed in wide range of soil
(clays, silty clays, sandy clays, boulder clay and glacial till),
permitted development of the concept of the efficiency factor
(Barley 1995 and 1997, Barley and Windsor 2000). Figure 2
presents the distribution of the values of the efficiency factor
(f
eff
) against anchor fixed length, and the best fit curve can be
expressed by following expression:
57,0
0
6,1
L
L
f
fix
eff
(5)
It is important to emphasize that Barley´s efficiency factor is
quite consistent with Ostermayer (1974) diagrammatic
presentation of the ultimate medium skin friction against fixed
length for similar soil characteristics and anchor construction
process, as it can be seen in Figure 2.
Figure 2. Ostermayer´s (1974) boundary lines vs. Barley´s (1995)
efficiency factor.
Barley (1995) also suggested the efficiency factor for sands,
correlating efficiency with the fixed length and the friction
angle:
·tan
L
L
eff
0
fix
0,91)
(
f
(6)
One of the most extensive attempts to model construction
technique, characteristics and behaviour of anchors have been
accomplished by Mecsi (1995), based on analysis of results
from numerous installed and monitored anchors.
Analytical solution and simple graphical method based on
the theory of expanded cylindrical cavity provide the possibility
to define the approximate pull-out capacity. The Analysis of
load distribution for the known anchor geometry and rigidity
permits determination of the specific pull-out resistance of a 1
m anchor length (t
ult
) and the length of the fully mobilised bond
stress (L
b
). Considering that only reduced percentage of
maximum bond stress can be mobilised over the remaining
fixed anchor length (L
fix
– L
b
), the ultimate anchor capacity can
be expressed by the following expression:
)L k·(L ·th
k
1 L· τ T
0
fix
0
ult
ult
(7)
ult
steel
steel
ult
A E
k
·
·
(8)
where: k = rigidity index, E
steel
= steel deformation modulus,
A
steel
= steel tendon area, ∆
ult
= elongation of the shear strength
length (L
fix
– L
0
).
Based on data from Ostermayer and Scheele (1997), Woods
and Barkhordari (1997) proposed efficiency factor for its
incorporation in the expression for ultimate capacity of low-
pressured anchors in sand (Formula 10), recommended in BS
8081 (1989), which is a function both of fixed anchor length
and friction angle:
)
·tan
·05.0 exp(
0
L
L
f
fix
eff
(9)
where: L
0
= reference length of 1 m.
)
·tan(
·
·
nL f
T
fix
eff
ult
(10)
2.4
Single Bore Multiple Anchors - SBMA
This system involves the installation of a multiple unit anchors
into a single borehole, with enough short unit lengths to reduce
or even to avoid the progressive debonding. Each unit is formed
by individual tendon and is loaded with the corresponding unit
stressing jack, mobilizing its own capacity independently of
other unit anchors.
Application of this system permits the unlimited theoretical
total fixed length, while conventional anchors formed by only
one unit do not provide beneficial effects in load capacity for
fixed length superior to 10 m as is stated by numerous authors
and design guidelines or codes.
Figure 3. Development of bond stress along a four unit single bore
multiple anchor (Barley, 1997).
Total fixed lengths of 10 to 20 m are frequently used in all
types of soils, achieving high anchor capacities (2000 to 5000
kN) that are almost three times greater than the normal
conventional anchors capacity values (Barley 1997, Barley and
Windsor 2000). A comparison of load distribution between
conventional and SBMA anchor is presented in Figure 3.
