114 CIVIL WORKS GUIDELINES FOR MICRO-HYDROPOWER IN NEPAL
gland and smoothness of sliding surfaces. If there is not a
change in the pipe direction (α=β) upstream and downstream
of the anchor block, the forces (from upstream and downstream
expansion joints) cancel out.
F7 - F7 is the hydrostatic force on exposed ends of pipe in
expansion joints. The two sections of penstock pipe entering
an expansion joint terminate inside the joint; therefore, their ends
are exposed to hydrostatic pressure, resulting in a force “F ”
7
which pushes against the anchors upstream and downstream
of the joint. This force usually contributes minimally to the
total forces on an anchor since the ratio of pipe thickness to
the diameter is low. However, this force can be significant at
mild steel-HDPE joint section (since HDPE pipes are thicker).
Note that h is the total head at the expansion joint.
total
F8 - F8 is the dynamic force at the pipe bend. At the bend, the
water changes the direction of its velocity and therefore the
direction of its momentum. This requires that the bend exert
a force on the water. Consequently, an equal but opposite
reaction force “F8 “ acts on the bend; it acts in the direction
which bisects the exterior angle of the bend (same as F3).
Since velocities in penstocks are relatively low (< 5 m/s), the
magnitude of this force is usually insignificant.
F9 - F9 is the force exerted due to the reduction of pipe
diameter. If there is a change in the diameter of the penstock,
the hydro-static pressure acting on the exposed area creates a
force “F” which acts in the direction of the smaller diameter
pipe. If the penstock length is long (as in the case of Jhankre
mini-hydro), then the pipe thickness is increased with
increasing head. However, the effect of changing the diameter
by a few mm does not contribute significant forces and can be
ignored.
F10 - F10 is the force on the anchor blocks or support piers due
to the soil pressure acting on the upstream face. If there is a
significant difference between the upstream and downstream
buried depth (h1 - h2 > 1 m) of the block then a force will be
exerted on the anchor block due to soil pressure. In such cases,
this force should be considered since it has a destabilising
effect. Note that the resultant of this force acts at 1/3 h1.
7.4.3 DESIGN PROCEDURE
Once all of the above relevant forces have been calculated the
design procedure for anchor blocks and support piers requires
checking the three conditions of stability as follows:
Safety against overturning
The forces acting on the structure should not overturn the
block. For structures that have rectangular bases, this condition
is met if the resultant acts within the middle third of the
base. This is checked as follows:
First take moments about one point of the block along the
face parallel to the penstock alignment.
Find the resultant distance at which the sum of vertical
forces act using the following equation:
( )d = ΣM
ΣV
where:
d is the distance at which the resultant acts.
ΣM is the sum of moments about the chosen point of the block.
ΣV is the sum of vertical forces on the block.
Now calculate the eccentricity of the block using the
following equation:
e = (Lbase / 2) - d
For the resultant to be in the middle third of the block, the
eccentricity must be less than 1/6 of the base length as
follows:
eallowable = Lbase / 6
Finally check that e<eallowable
Safety on bearing
The load transmitted to the foundation must be within the
safe bearing capacity limit of the foundation material. If the
transmitted load exceeds the bearing capacity limit of the
foundation, the structure will sink. The bearing pressure at
the base is checked using the following equations:
( )where:
Pbase
=
Σv
Abase
1+
6e
Lbase
Pbase = maximum pressure transmitted to the foundation.
ΣVbase= the sum of vertical forces acting on the block.
Lbase = length of the base.
Abase = the base area of the block eccentricity calculated
earlier.
e = eccentricity calculated earlier.
The calculated Pbase must be less than the allowable bearing
pressure (Pallowable) for the type of soil at the foundation level.
Allowable bearing pressure for different types of soil is shown
in Table 7.3.