Civil Engineering Reference
In-Depth Information
grouting, while resin grouted anchors may be
installed in up-holes. It should be noted that bolts
installed at an angle steeper than the normal to the
sliding plane (i.e.
(ψ
p
+
to each other. The shear resistance of the
doweled joint comprises the shear strength
due to friction on the joint, and the elastic
response of the steel dowel, grout and rock.
(b)
Yield stage
—At displacements of less than
about 1 mm in installations where the rock
is deformable and the grout thickness is at
least equal to the dowel radius, the steel is
deformed in order to mobilize shear resist-
ance. As a result of the deformation, the yield
strengths of the steel and grout are reached
in bending and compression respectively.
(c)
Plastic stage
—All the materials in the grouted
dowel installation yield at an early stage
of shear displacement and at low shear
forces. Therefore, the shear resistance of the
doweled joint depends on the shear force-
displacement relationship of the plasticized
materials. The contribution of the dowel to
the total shear strength of the joint is a func-
tion of the friction angle
(φ)
and roughness
(i)
of the joint, the dowel inclination
(α)
,
the compressive strength of the rock and
grout
(σ
ci
)
and the tensile strength of the steel
bar
(σ
t
(
s
)
)
. In general, the shear resistance is
enhanced where the joint has a high friction
angle and is rough so there is some dilation
during shearing, the inclination angle
α
is
between about 30
◦
and 45
◦
, and the rock
is deformable but not so soft that the dowel
cuts into the rock.
ψ
T
)>
90
◦
) can be detri-
mental to stability because the shear component
of the tension, acting down the plane, increases
the magnitude of the displacing force.
Since the stability analysis of plane failures is
carried out on a 1 m thick slice of the slope, the
calculated value of
T
for a specified factor of
safety has the units kN/m. The procedure for
designing a bolting pattern using the calculated
value of
T
is as follows. For example, if the ten-
sion in the each anchor is
T
B
, and a pattern of
bolts is installed so that there are
n
bolts in each
vertical row, then the total bolting force in each
vertical row is
(T
B
·
n)
. Since the required bolting
force is
T
, then the horizontal spacing
S
between
each vertical row is given by
T
B
n
T
kN
kN
/
m
S
=
(6.24)
This design method is illustrated in the worked
example at the end of this chapter.
6.4.2 Reinforcement with fully grouted
untensioned dowels
Fully grouted, untensioned dowels comprise steel
bars installed in holes drilled across the poten-
tial sliding plane, which are then encapsulated in
cement or resin grout. The steel acts as a rigid
shear pin across any plane of weakness in the
rock. A method of calculating the reinforcement
provided by dowels, developed by Spang and
Egger (1990), is discussed here.
Figure 6.9 shows the results of a finite element
analysis of a steel bar grouted into a drill hole
in a rock containing a joint surface; the angle
α
between the axis of the bolt and the normal to
the joint is 30
◦
. Shear displacement on the joint
causes deformation of the bolt that takes place in
three stages as follows:
Based on the tests conducted by Spang and
Egger, the shear resistance
R
b
(kN) of a dowelled
joint is given by
0.011
σ
1.07
ci
sin
2
(α
R
b
=
σ
t
(
s
)
[
1.55
+
+
i)
]
×
σ
−
0.14
ci
(
0.85
+
0.45 tan
φ)
(6.25)
where the units of
σ
ci
are MPa and of
σ
t
(
s
)
are kN.
The corresponding displacement
δ
s
of a dowelled
joint is given by
55.2
σ
−
0.14
ci
56.2
σ
−
0.28
ci
δ
s
=
(
15.2
−
+
)
tan
α(
70
/σ
c
)
0.125
(
cos
α)
−
0.5
)
(6.26)
×
(
1
−
(a)
Elastic stage
—After overcoming the cohesion
of the joint, the blocks begin to slide relative
