Introduction Water Passage
Necessary components of the hydraulic turbines in a hydropower installation are specially
designed water passages and gates for controlling and directing the water as it flows to,
through, and from the turbines. The principal features to consider in engineering feasibility
and design studies are the flumes, penstocks, gates and valves, spiral cases, and draft tubes.
OPEN FLUMES
In very simple low-head installations the water can be conveyed in an open channel directly
to the runner. Open flume settings of turbines do require a protective entrance with a trash
rack. The principal problem to be solved is to provide inlet conditions to the turbine that are
relatively free from swirling and vortex flow as the water approaches the turbine runner. An
example of an open flume setting of a hydro installation is shown in Fig. 1. A usual upper
limit of the use of open flume settings for hydraulic turbines is that heads should not exceed
20 ft. Flumes and canals are also used to convey water to penstocks for turbine installations
with higher heads.
Figure 1 Diagram of open-flume, low-head turbine installation.
PENSTOCKS
A penstock is the conduit that is used to carry water from the supply sources to the turbine.
This conveyance is usually from canal or reservoir.
Penstocks can be classified as to operational type and as to the type of construction. Two
operational types are the pressure penstock and the siphon penstock. The pressure penstock
requires that the water discharging to the turbine always be under a positive pressure (greater
than atmospheric pressure). The siphon penstock is constructed in such a way that at points in
the penstock the pressure may be less than atmospheric pressure and sections of the conduit
act as a siphon. This requires that a vacuum pump or some other means for initiating the
siphon action must be used to fill the conduit with water and to evacuate air in the conduit.
Figure 2 shows a simple diagram of a siphon penstock that has been installed in Finland.
Penstocks may be classified according to type of construction, for example:
1. Concrete penstock
2. Fiber glass or plastic pipe
3. Steel penstock
4. Wood stave pipe
Figure 2 Diagram of siphon penstock type of hydropower installation (Kaarni Power Station,
Finland). SOURCE: Imatran Volrna OY.
Traditionally, steel penstocks have been considered as very high pressure conduits, usually of large
diameter, and operating with frequent surges during the normal condition. Penstocks may also be subject
to pulsations of varying frequency and amplitudes transmitted from the turbine or pump. When
penstocks are installed above ground, this can sometimes cause excessive vibration. These are the
perceived differences between a penstock and an ordinary pipeline. Based on these conditions,
penstocks have been designed to standards established in 1949 with minor revisions based on an
allowable design stress at normal conditions of 2/3 of yield or 1/3 of tensile strength.
Today there are many penstocks installed utilizing thousands of feet of pipe with operating
Pressures varying from no pressure at the inlet structure, to low or moderate pressures, or to very
high pressures at the power plants. Most of these penstocks are buried and many parallel the stream from
which the water was diverted. They are usually in remote locations. With certain types of turbines and
an adequate control valve system, sometimes involving a synchronous bypass system, transient pressures
can be limited. A buried penstock will not be subject to the problem of harmonic vibrations sometimes
associated with the traditional penstock.
Cast-in-place or precast reinforced concrete pipe can be used for penstocks. Very large diameters are
somewhat impractical. Cast-in-place concrete pipes are usually limited to heads of less than 100 ft.
According to Creager and Justin (1950), precast reinforced concrete penstocks can be used up to 12.5 ft in
diameter and under heads up to 600 ft by using a welded steel shell embedded in the reinforced concrete.
Fiberglass and polyvinyl chloride (PVC) plastic pipe have proven to be useful for penstocks. A penstock
at the Niagara Mohawk plant uses a fiber glass pipe of 10 ft (3 m) in diameter.
Wood stave pipes have been used in diameters ranging from 6 in. up to 20 ft and utilized at heads up to
600 ft with proper design. Useful information for the design of wood stave pipes is contained in the
handbook by Creager and Justin (1950).
Steel penstocks have become the most common type of installation in hydropower developments due to
simplicity in fabrication, strength, and assurance that they will perform in a wide variety of
circumstances. Normal practice is to use welded steel pipe sections. An excellent U.S. Department of the
Interior monograph (1967) treats the topic of steel penstocks. This covers the many details of making
selection of size and design considerations as to stresses and structural mounting.
For purposes of engineering feasibility and preliminary design, there are three major considerations that
need engineering attention: (1) the head loss through the penstock, (2) the safe thickness of the penstock
shell, and (3), the economical size of the penstock. Another consideration might be the routing of the
penstock.
Hydraulic Losses
Hydraulic losses in a penstock reduce the effective head in proportion to the length and
approximately as the square of the water velocity. The mechanism of resistance in the flow of
fluids is complex and has not yet been fully evaluated. Several conventional flow formulas
have been developed and used in the past. Of these, the most notable and widely used in the
waterworks field are the exponential formulas of Hazen-Williams and Scobey. At present,
these conventional flow formulas are more widely used in the waterworks field than the
universal flow formulas. The latter are rationally founded formulas applicable to many fluids
having different viscosity, density, and fluidity characteristics which change with
temperature. The Hazen-Williams formula is widely used in the waterworks field. However,
Scobey’s formula is more widely used in the design of penstocks and is expressed as:
Values of Ks vary depending on the interior surface condition and range from 0.32 to 0.40.
The loss coefficient of 0.32 may be used for penstocks with a newly applied lining. To allow
for some deterioration of the lining a value of Ks = 0.34 is usually assumed in the design of
penstocks whose interior is readily accessible for periodic inspection and lining maintenance.
For penstocks too small to permit entering for inspection and lining maintenance, a value of
Ks = 0.40 is usually assumed. Friction losses for various flows and pipe diameters computed
from Scobey’s formula using Ks = 0.34 are shown in Figure 3.
Losses through intake trashracks vary according to the velocity of flow through the trashrack
and may be taken as 0.1, 0.3, and 0.5 foot, respectively, for velocities of 1.0, 1.5, and 2.0 feet
per second.
Entrance losses depend on the shape of the intake opening. A circular bellmouth entrance is
considered to be the most efficient form of intake if its shape is properly proportioned. It may
be formed in the concrete with or without a metal lining at the entrance. The most desirable
entrance curve was determined experimentally from the shape formed by the contraction of a
jet (vena contracta) flowing through a sharp-edged orifice. For a circular orifice, maximum
contraction downstream from the orifice occurs at a distance of approximately one-half its
diameter. Losses in circular bellmouth entrances are estimated to be 0.05 to 0.1 of the
velocity head. For square bellmouth entrances, the losses are estimated to be 0.2 of the
velocity head.
Bend losses vary according to the shape of the bend and the condition of the inside surface.
Mitered bends constructed from plate steel no doubt cause greater losses than smooth
curvature bends formed in castings or concrete.
The following formula is based on experiments using 1.7-inch-diameter smooth brass bends having
Reynolds numbers up to 225,000, and is expressed as:
........................................................................................................ (1)
Where:
Hg = bend loss in feet
C = experimental loss coefficient, for bend loss
V = velocity of flow in feet per second
g = acceleration due to gravity
The losses in figure 3 vary according to the R/D ratio and the deflection angle of the bend. An R/D
ratio of six results in the lowest head loss, although only a slight decrease is indicated for R/D ratios
greater than four. As the fabrication cost of a bend increases with increasing radius and length, there
appears to be no economic advantage in using R/D ratios greater than five.
Figure 3 Loss coefficients for pipe bends of smooth interior.
Head losses in gates and valves vary according to their design, being expressed as:
................................................................................................................. (2)
In which K is an experimental loss coefficient whose magnitude depends upon the type and size of
gate or valve and upon the percentage of opening. Because gates or valves placed in penstocks are not
throttled (this being accomplished by the wicket gates of the turbines), only the loss which occurs at
the full open condition needs to be considered.
For gate valves, an average value of K = 0.10 is recommended; for needle valves, K = 0.20; and for
butterfly valves with a ratio of leaf thickness to diameter of 0.2, a value of K = 0.26 may be used. For
sphere valves having the same opening as the pipe, there is no reduction in area and the head loss is
negligible.
Manifold or fittings should be designed with as smooth and streamlined interiors as practicable, since
this results in the least loss in head. Data available on losses in large fittings are meager. For smaller
fittings, as used in municipal water systems, the American Water Works Association recommends the
following values for loss coefficients, K: for reducers, 0.25 (using velocity at smaller end); for
increasers, 0.25 of the change in velocity head; for right angle tees, 1.25; and for wyes, 1.00. These
coefficients are average values and are subject to wide variation for different ratios between flow in
main line and branch outlet. They also vary with different tapers, deflection angles, and streamlining.
Model tests made on small tees and branch outlets at the Munich Hydraulic Institute show that for
fittings with tapered outlets and deflection angles smaller than 90° with rounded corners, losses are
less than in fittings having cylindrical outlets, 90° deflections, and sharp corners. (See Figure 1.1.3.)
These tests have served as a basis for the design of the branch connections for many penstock
installations.
Figure 4 Loss coefficients for divided flow through branch connections.
Economic Diameter
A penstock is designed to carry water to a turbine with the least loss of head, consistent with the
overall economy of the installation. An economic study to determine the penstock size generally
requires that the annual penstock cost plus the value of power lost in friction be minimal. The annual
penstock cost includes amortization of all related construction costs, operation and maintenance costs,
and replacement reserve. A precise analytical evaluation, taking all factors into account, may be
neither justified nor practical, since all variables entering into the problem are subject to varying
degrees of uncertainty. Several formulas or procedures have been found convenient and practical to
use in estimating economic penstock diameters. After an economic diameter has been tentatively
selected, based on monetary considerations, this diameter must be compatible with all existent design
considerations. An example would be an installation where the economic diameter would require the
installation of a surge tank for regulation, but an overall more economical installation would be to
install a considerably larger penstock in lieu of the surge tank.
Figure 5 was derived from the method presented by Voetsch and Fresen and Figure 6 is an example of
its use. Special attention must be given to the “load factor,” Figure 5 as this item materially affects the
calculations.
The “step-by-step” method should be considered for the final design of long penstocks, in which case
it is frequently economical to construct a penstock of varying diameters.
Water Hammer
“Water Hammer” is a term applied to the phenomenon produced when the rate of flow in a conduit is
rapidly changed. It consists of the development of a series of positive and negative pressure waves,
the intensity of which is proportional to the spread of the propagation and the rate at which the
velocity of flow is decelerated or accelerated. Joukovsky’s fundamental equation, which is based on
the elastic water column theory, gives the maximum increase in head for closure times of less than
2L/a seconds:
𝑎𝑎𝑎𝑎
∆𝐻𝐻 = 𝑔𝑔
.............................................................................................................................................. (3)
In which: DH = maximum increase in head - feet
a = velocity of pressure wave – ft/sec
v = velocity of flow destroyed – ft/sec
g = acceleration due to gravity – ft/sec2
L = length of penstock from forebay to turbine gate – feet
From this formula, Allievi, Gibson, Durand, Quick, and others developed independent equations for
the solution of water hammer problems.
A comprehensive account of methods used for the analysis of water hammer phenomena occurring in
water conduits, including graphical methods, was published by Parmakian. In this reference, the
graphical method of analysis provides a method for determining the head changes at various points in
a pipeline for any type of gate movement. When the effective gate opening varies uniformly with
respect to time, the gate motion is called “uniform gate closure.” Figure 7 shows R.S. Quick’s chart
for uniform gate closure to zero gate and a chart showing velocity of pressure wave in elastic water
column. To determine maximum pressure rise at gate it is necessary to calculate time constant, N =
aT/2L, and pipeline constant, K = aVo/29Ho. Then the value of pressure rise, P, as a proportion of hmax
is read from the chart. From the relation, 2KP = h/Ho, the pressure rise, h, is calculated.
NOTATION
a = Cost of pipe per lb, installed, dollars.
H = Weighted overage head including water hammer, feet.
B = Diameter multiplier from Graph B.
b = Value of lost power in dollars per kwh.
Ks = Friction coefficient in Scobey’s formula.
D = Economic diameter in feet.
n = Ratio of overweight to wt. of pipe shell.
e = Overall plant efficiency.
Q - Flow in cubic feet per second.
ej = Joint efficiency.
r = Ratio of annual cost to a.
f = Loss factor from Graph A.
Sg : Allowable tension, p.s.i.
Use of chart: Obtain loss factor f from Graph A Compute K and obtain B from Graph B. Take D1 from
Graph C. The economic dia. is D = B x D1.
Figure 5 Economic diameters for steel penstocks and pump lines
Figure 6 Sample calculation of economic diameter of penstocks
Figure 7 Water hammer charts
Various experience curves and empirical equations have been developed for determining the
economical size of penstocks. Some of these equations use very few parameters to make initial size
determinations for reconnaissance or feasibility studies. Other more sophisticated equations use many
variables to obtain more precise results which may be necessary for final design as the previous case.
Economical size varies with type of installation and materials, as well as whether used above ground
or buried, Gordon and Penman (1979) give a very simple equation for determining steel penstock
diameter for small hydropower installations:
.................................................................................................................... (3)
Where Dp = penstock diameter, m
Q = water flow, m3/sec.
Sarkaria (1979) developed an empirical approach for determining steel penstock diameter by using
data from large hydro projects with heads varying from 187 ft (57 m) to 1025 ft (313 m) and power
capacities ranging from 206,000 hp (154 MW) to 978,000 hp (730 MW). He reported that the
economical diameter of the penstock is given by the equation
................................................................................................................ (4)
Where D = economical penstock diameter, ft
p = rated turbine capacity, hp
h = rated net head, ft
The study verified his earlier study reported in 1958. The two empirical studies giving eqs. (3) and (4)
were for periods before present energy crunch conditions and did not take into account penstock
length or the cost of lost power in penstock flow. Therefore, the equations should be used with
caution.
Materials and Allowable Stresses
For the AWWA (American water works association) M-11 design, an allowable design stress of 50%
of yield at (1) working pressure and 75% of yield at (2) transient pressure is suggested. These values
are given in Table 2.
For the AWWA design (1) “working pressure” is defined as the vertical distance between the
penstock centerline and the hydraulic grade line or the static head, whichever is greater, times .434 to
convert feet of head to pressure in pounds per square inch. (2) “Transient pressure” is defined as the
static head plus the water hammer and surge for a plant load rejection when all units are operating,
with normal governor closure time. Field test pressures shall not exceed this pressure.
For the traditional design, an allowable design stress of 2/3 of yield or 1/3 of tensile at (1) normal
operating condition is suggested. At (2) intermittent condition an allowable design stress of .8 of yield
or .44 of tensile is suggested. These values are given in Table 2.
For the Traditional design (l), “normal operating condition” is defined as the maximum static head
plus the water hammer and surge for a plant load rejection when all units are operating with normal
governor closure time. (2) “Intermittent condition” is defined as condition during filling and draining
and earthquake during normal operation.
Design is based on circumferential (hoop) stress or combined equivalent stress, circumferential and
longitudinal, calculated in accordance with Hencky-Mises Theory, whichever is greater.
TABLE 1 BASIC CONDITION FOR INCLUDING THE EFFECTS OF WATER HAMMER IN
THE DESIGN OF STEEL PENSTOCKS
The basic conditions for including the effects of water hammer in the design of turbine penstock
installations are divided into normal and intermittent conditions with suitable factors of safety
assigned to each type of operation.
TABLE 2 MATERIALS & ALLOWABLE STRESSES
Internal Pressure
With pressure determined, the wall thickness is found using the equation:
Where: t = wall thickness (in.)
p = pressure (psi)
d = outside diameter of pipe (in.) steel cylinder (not including coatings)
s = allowable stress (psi), for design condition.
Minimum Thickness for Handling
Two well-known formulas, in existence some 40 years, have been adopted by many specifying
agencies. They are:
........................ (5)
The Pacific Gas and Electric formula is more liberal in diameters below 54” and the Bureau of
Reclamation formula more liberal in diameters above 54”.
External Loads
EARTH LOAD DETERMINATION
Determine the load on the pipe by the “Soil Prism” theory, as follows
............................................................................................................................................ (6)
Where: We = vertical soil load, pounds per inch
w = weight of earth per unit volume, lbs/(ft)3
H = height of fill over pipe (feet)
D = outside diameter of pipe (feet)
LIVE LOAD DETERMINATION
Determine the appropriate live load on the pipe using Table 3
EXTREME EXTERNAL LOADING CONDITIONS
Allowable deflection for various lining and coating systems that are often accepted are:
Mortar-lined and coated = 2 percent of pipe diameter
Mortar-lined and flexible coated = 3 percent of pipe diameter
Flexible lining and coated = 5 percent of pipe diameter
TABLE 3
Thrust Restraint
Thrust forces are unbalanced forces which occur in pressure pipelines at changes in direction (such as
in bends, wyes, tees, etc.), at changes in cross-sectional area (such as in reducers), or at pipeline
terminations (such as at bulkheads). These forces, if not adequately restrained, tend to disengage
joints, as illustrated in Figure 8. Thrust forces of primary importance are: (1) hydrostatic thrust due to
internal pressure of the pipeline, and (2) hydrodynamic thrust due to changing momentum of flowing
water. Since most water lines operate at relatively low velocities, the dynamic force is insignificant
and is usually ignored when computing thrust. For example, the dynamic force created by water
flowing at 8 fps is less than the static force created by 1 psi.
Hydrostatic Thrust
Typical examples of hydrostatic thrust are shown in Figure 9. The thrust in dead ends, outlets, laterals,
and reducers is a function of internal pressure, P, and cross-sectional area, A, at the pipe joint. The
resultant thrust at a bend is also a function of the deflection angle, Δ, and is given by:
...................................................................................................... (7)
Where: T = hydrostatic thrust, lbs.
P = internal pressure, psi
𝜋𝜋𝐷𝐷 2
𝐴𝐴 = 4 = cross-sectional area of pipe O.D., sq. in.
∆ = deflection angle of bend, deg.
Figure 8 Unbalanced thrusts and movements in pipeline
Figure 9 Hydrostatic thrust, T, for typical fittings
Thrust Resistance
For buried pipelines, thrust resulting from angular deflections at standard and beveled pipe with
rubber gasket joints is resisted by dead weight or frictional drag of the pipe, and additional restraint is
usually not needed. Other fittings subjected to unbalanced horizontal thrust have two inherent sources
of resistance: (1) frictional drag from dead weight of the fitting, earth cover, and contained water, and
(2) passive resistance of soil against the back of the fitting. If this type of resistance is not adequate to
resist the thrust involved, then it must be supplemented either by increasing frictional drag of the line
by “tying” adjacent pipe to the fitting or by increasing the supporting area on the bearing side of the
fitting with a thrust block. Unbalanced uplift thrust at a vertical deflection is resisted by the dead
weight of the fitting, earth, cover, and contained water. If this type of resistance is not adequate to
resist the thrust involved, then it must be supplemented either by increasing the dead weight of the
line by “tying” adjacent pipe to the fitting or by increasing the dead weight with gravity type thrust
block.
Joints with Small Deflections
The thrust at beveled pipe or standard pipe installed with angular deflection is usually so small that
supplemental restraint is not required.
Small Horizontal Deflections
Thrust, T, at deflected joints on long-radius horizontal curves is resisted by friction on the top and
bottom of the pipe as shown in Figure 10. The total friction developed is equal to the thrust and acts
in the opposite direction. Additional restraint is not required when:
T ≤ fL (Wp + Ww + 2 We)
Where: T = 2 P A sin(θ/2) = resultant thrust force, lbs.,
Where θ is the deflection angle created by the deflected joint, deg.
f = coefficient of friction
L = length of standard or beveled pipe, ft.
Wp = weight of pipe, lbs/lin ft.
Ww = weight of water in pipe, lbs/lin ft.
We = earth cover load, lbs/lin ft.
Figure 10 Restraint of thrust at deflected joints on long radius horizontal curves
The passive soil resistance of the trench backfill against the pipe was ignored in the above analysis.
Depending on installation and field conditions, the passive soil resistance of the backfill may be
included to resist thrust.
Tests and experience indicate that the value of f is not only a function of the type of soil, it is also
greatly affected by the degree of compaction and moisture content of the backfill. Therefore, care
must be exercised in the selection of f. Coefficients of friction are generally in the range of 0.30-0.40.
Determination of earth cover load should be based on a backfill density and height of cover consistent
with what can be expected when the line is pressurized. Values of soil density vary from 90 to 130
pounds per cubic foot, depending on the degree of compaction. Earth cover load should be taken as
the prism of soil on top of the pipe:
We = wBcH
Where: We = earth cover load, lbs/lin ft.
w = unit weight of backfill, pcf
Bc = pipe outside diameter, ft.
H = height of earth cover, ft.
Small Vertical Deflections
Uplift thrust at deflected joints on long-radius vertical curves is resisted by the combined dead weight,
Wt, as shown in Figure 11. Additional restraint is not required when:
T≤ fL (Wp + Ww + 2 We) cos (α – θ/2)
Where: T = 2 P A sin(θ/2);
L = length of standard or beveled pipe, ft.
Wp = weight of pipe, lbs/lin ft.
Ww = weight of water in pipe, lbs/lin ft.
We = earth cover load, lbs/lin ft.
α = slope angle, deg.
θ = deflection angle, deg., created by angular deflection of joint
Figure 11 Restraint of uplift thrust at deflected joints on long radius vertical curves
Tied Joints
Many engineers choose to restrain thrust from fittings by tying adjacent pipe joints. This method
fastens a number of pipe on each side of the fitting to increase the frictional drag of the connected
pipe to resist the fitting thrust. Frictional resistance on the tied pipe is assumed to act in the opposite
direction of resultant thrust, T. Section A-A in Figure 11 shows a diagram of the external vertical
forces acting on a buried pipe and the corresponding frictional resistance.
TYPES OF TIED JOINTS
Generally, there are two types of tied joints: (1) welded and (2) harnessed.
WELDED JOINTS
Figure 12 shows two typical details of a welded joint. Figure 12 (A) shows a lap welded joint.
Normally, for pipe sizes larger than 30 inches, this joint is welded on the inside of the pipe. Figure 12
(B) shows a butt welded joint. This joint is usually specified for areas of high internal working
pressures (above 400 psi).
Figure 12(A) Welded Lap Joint (B) Welded Butt Joint
HARNESSED JOINTS
An alternate approach is to use harnessed joints, which provide a mechanical means of transmitting
longitudinal thrust across the joints.
Other Uses for Restraints
Tied joints have other uses that are not related to thrust caused by internal pressure. If it is necessary
to install a pipeline on a steep slope, it may be desirable to use anchor blocks, harnessed joints, or
welded joints to keep the pipe from separating due to downhill sliding. Although the pipe may be
capable of resisting downhill movement because of its own frictional resistance with the soil, the
backfilling operation can sometimes provide enough additional downhill force to open the joint.
Horizontal Bends and Bulkheads
As illustrated in Figure 13, the frictional resistance, F, needed along each leg of a horizontal bend is
PAsin(∆/2). Frictional resistance per linear foot of pipe against soil is equal to:
F = f(2 We + Wp + Ww)
Where: F = frictional resistance, lbs/lin ft.
f = coefficient of friction between pipe and soil
We = earth cover load, lbs/lin ft.
Wp = weight of pipe, lbs/lin ft.
Ww = weight of water in pipe, lbs/lin ft.
Determination of the earth load is similar to the previous section. Tests conducted on buried pipe have
shown that resistance to pipe movement approximately doubles after rainfall or if jetting of the trench
consolidates the soil around the pipe. The length of pipe L to be tied to each leg of a bend is calculated
as:
.......................................................................................... (8)
Where: L = length of pipe tied to each bend leg, ft.
P = internal pressure, psi
A = cross-sectional area of pipe joint, sq. in.
∆ = deflection angle of bend, deg.
f = coefficient of friction between pipe and soil
We = earth cover load, lbs/lin ft.
Wp = weight of pipe, lbs/lin ft.
Ww = weight of water in pipe, lbs/lin ft.
The length of pipe to be tied to a bulkhead is:
......................................................................................................... (9)
Where: L = length of pipe tied to bulkhead, ft.
and all other variables are as defined above.
Figure 13 Thrust restraint with tied joints at bends
Vertical Bends
The dead weight resistance needed along each leg of a vertical bend is PA sin(∆/2). Dead weight
resistance per linear foot of pipe in a direction opposite to thrust is:
D = (We + Wp + Ww ) cos (α – ∆/2)
Where: D = dead weight resistance, lbs/lin ft.
We = earth cover load, lbs/lin ft.
Wp = weight of pipe, lbs/lin ft.
Ww = weight of water in pipe, lbs/lin ft.
α = slope angle, deg.
∆ = deflection angle of bend, deg.
Length of pipe L to be tied to each leg of a vertical (uplift) bend is calculated as:
................................................................... (10)
With variables as defined above. Slopes above 20 degrees should have all the joints restrained. Use
eq. 10 only when solving for lengths of restrained joints on slopes less than 20 degrees.
Thrust Blocks
Thrust blocks increase the ability of fittings to resist movement by increasing the bearing area.
Typical thrust blocking of a horizontal bend is shown in Figure 14.
Figure 14 Typical thrust blocking of a horizontal bend
CALCULATION OF SIZE
Thrust block size can be calculated based on the bearing capacity of the soil:
Area of Block = Lb x Hb = (T/𝛿𝛿)
Where: Lb x Hb = area of bearing surface of thrust block, sq. ft.
T = thrust force, lbs.
𝛿𝛿 = safe bearing value for soil, psf
If it is impractical to design the block for the thrust force to pass through the geometric center of the
soil bearing area, then the design should be evaluated for stability.
After calculating the thrust block size based on the safe bearing capacity of soil, the shear resistance
of the passive soil wedge behind the thrust block should be checked since it may govern the design.
For a thrust block having its height, Hb less than one-half the distance from the ground surface to base
of block, h, the design of the block is generally governed by the safe bearing capacity of the soil.
However, if the height of the block exceeds one-half h, then the design of the block is generally
governed by shear resistance of the soil wedge behind the thrust block. Determining the value of the
safe bearing and shear resistance of the soil is beyond the scope of this course. Consulting a qualified
geotechnical consultant is recommended.
Typical Configurations
Determining the safe bearing value, s, is the key to “sizing” a thrust block. Values can vary from less
than 1000 pounds per square foot for very soft soils to several tons per square foot for solid rock.
Knowledge of local soil conditions is necessary for proper sizing of thrust blocks. Figure 14 shows
several details for distributing thrust at a horizontal bend. Section A-A is the more common detail, but
the other methods shown in the alternate sections may be necessary in weaker soils. Figure 15 shows
typical thrust blocking of vertical bends. Design of the block for a bottom bend is the same as for a
horizontal bend, but the block for a top bend must be sized to adequately resist the vertical component
of thrust with dead weight of the block, bend, water in the bend, and overburden.
Uplift thrust restraint provided by gravity type thrust blocks shown for the top bend in Figure 15 may
also be provided by the alternate method of increasing the dead weight of the line by tying adjacent
pipe to the vertical bend. Section A-A in Figure 11 shows a diagram of the vertical forces acting on a
buried vertical (uplift) bend used in determining the thrust resistance by dead weight.
Figure 15 Typical profile of vertical bend thrust blocking
Proper Construction
Most thrust block failures can be attributed to improper construction. Even a correctly sized block can
fail if it is not properly constructed. A block must be placed against undisturbed soil and the face of
the block must be perpendicular to the direction of and centered on the line of action of the thrust. A
surprising number of thrust blocks fail due to inadequate design or improper construction. Many
people involved in construction and design do not realize the magnitude of the thrusts involved. As an
example, a thrust block behind a 36-inch, 90-degree bend operating at 100 psi must resist a thrust
force in excess of 100,000 pounds. Another factor frequently overlooked is that thrust increases in
proportion to the square of pipe diameter. A 36-inch pipe produces approximately four times the
thrust produced by an l8-inch pipe.
ADJACENT EXCAVATION
Even a properly designed and constructed thrust block can fail if the soil behind it is disturbed. Thrust
blocks of proper size have been poured against undisturbed soil only to fail because another utility or
an excavation immediately behind the block collapsed when the line was pressurized. The problem of
later excavation behind thrust blocks has led many engineers to use tied joints.
ANCHOR RINGS
Anchor Rings for use in concrete anchor blocks or concrete walls are often required. These are usually
specified when the pipe goes through a structure (such as a valve vault) or to anchor the pipe at the
top and bottom of a steep slope.
