Thrust Block Design

AWWA MANUAL

Chapter

BURIED PIPE THRU ST RES TRAINTS

M45

7 Buried Pipe Thrust Restraints

7.1 UNBALANCED THRUST FORCES ________________________ Unbalanced thrust forces occur in pressure pipelines at changes in direction (i.e., elbows, wyes, tees, etc.), at changes in cross-sectional area (i.e., reducers), or at pipeline terminations (i.e., bulkheads). These forces, if not adequately restrained, may cause pipeline movement resulting in separated joints and/or pipe damage. Thrust forces are: (1) hydrostatic thrust due to internal pressure of the pipeline, and (2) hydrodynamic thrust due to changing momentum of flowing fluid. Since most pressure lines operate at relatively low velocities, the hydrodynamic force is very small and is usually ignored.

7.1.1 Hydrostatic Thrust Typical examples of hydrostatic thrust are shown in Figure 7-1. The thrust in dead ends, tees, 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 ∆ and is given by: T = 2PA sin (∆/2) Where: T = hydrostatic thrust, lb P = internal pressure, psi

91

Copyright (C) 1999 American Water Works Association All Rights Reserved

(7-1)

92

FIBERGLASS PIPE DESIGN

PA0

T = 2PA sin ∆ 2

D

∆

∆ 2

PA

PA

PA sin ∆ 2

Bend

Wye

PA

∆

T = PA0

PA2

PA

∆ 2

T = PA

PA1

T Dead End ∆ 2

T = 2 PA2 cos ∆ – PA1 2

PA0 PA2

Bifurcation

PA2

PA1 T = PA0

T

T = P (A1 – A2 ) Tee

Reducer

Figure 7-1 Thrust force definitions A = (π/4) Dj2 = cross-sectional area of pipe joint, in., where Dj is the pipe joint diameter, in. ∆ = deflection angle of bend, degrees

7.2 THRUST RESISTANCE For buried pipelines, unbalanced horizontal thrust forces have two inherent sources of resistance: (1) frictional drag from dead weight of the pipe, earth cover, and contained fluid, and (2) passive resistance of soil against the pipe or fitting in the direction of the thrust. If this resistance is not sufficient to resist the thrust, then it must be supplemented by increasing the supporting area on the bearing side of the fitting with a thrust block; increasing the frictional drag of the line by “tying” adjacent pipe to the fitting; or otherwise anchoring the fitting to limit or prevent movement. Unbalanced uplift thrust at a vertical deflection is resisted by the dead weight of the fitting, earth cover, and contained fluid. If this type of resistance is not sufficient to resist the thrust, then it must be supplemented by increasing the dead weight with a gravity-type thrust block; increasing the dead weight of the line by “tying” adjacent pipe to the fitting; or otherwise anchoring the fitting to limit or prevent movement.


BURIED PIPE THRUST RESTRAINTS

93

LB A

. . . . . . .. . . . .

. . . . . . ..

h

. . . .. . . . ... ... .

HB

Section A–A

A

Reinforcing Steel

. .. ... . . . .. .. .. . . . . . .. . . . . . ..

h

. .. .

HB

Alternate Section A–A

... .. ... . . . Piles

Alternate Section A–A

Figure 7-2 Typical thrust blocking of a horizontal bend

7.3 THRUST BLOCKS Concrete thrust blocks increase the ability of fittings to resist movement by increasing the bearing area and the dead weight of the fitting. Typical thrust blocking of a horizontal bend (elbow) is shown in Figure 7-2. Calculation of size. Ignoring the dead weight of the thrust block, the block size can be calculated based on the bearing capacity of the soil: Area of block = LB × HB = (T × FS)/σ

(7-2)

Where: LB × HB = area of bearingsurfac eo f thrust block, ft2 T = thrustforc e,lb σ = bearing valuefor soil, lb/ft2 FS = design factor, 1.5 Typical values for conservative horizontal bearing strengths of various soil types are listed in Table 7-1.


94


Table 7-1 Horizontal soil-bearing strengths Soil Muck Soft clay Silt Sandy silt Sand Sandy clay Hard clay

Bearing Strength σ (lb/ft2)* 0 1,000 1,500 3,000 4,000 6,000 9,000

*Although the bearing strength values have been used successfully in the design of thrust blocks and are considered to be conservative, their accuracy is dependent on accurate soil identification and evaluation. The design engineer must select the proper bearing strength of a particular soil type.

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 concrete thrust block size, and reinforcement if necessary, based on the bearing capacity of soil, the shear resistance of the passive soil wedge behind the thrust block should be checked because 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 bearing capacity of the soil. However, if the height of the block, HB, 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 bearing and shear resistance of the soil and thrust block reinforcement is beyond the scope of this manual. Consulting a qualified geotechnical professional is recommended. Typical configurations. Determining the bearing value, σ, is the key to “sizing” a thrust block. Values can vary from less than 1,000 lb/ft2 (48 kN/m2) for very soft soils to several tons per square foot (kN/m2) for solid rock. Knowledge of local soil conditions is necessary for proper sizing of thrust blocks. Figure 7-2 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 7-3 illustrates typical thrust blocking of vertical bends. Design of the block for a bottom bend is the same as for 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. Proper construction is essential. 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 because of 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 in. (900 mm), 90 degree bend operating at 100 psi (689 kPa) must resist a thrust force in excess of 150,000 lb (667 kN). Another factor frequently overlooked is that thrust increases in proportion to the square of pipe diameter. A 36 in. (900 mm) pipe produces approximately four times the thrust produced by an 18 in. (450 mm) pipe operating at the same internal pressure.


95


Finished Grade

Concrete Collar

. . . . . . . . . . . . .. .

. . . . . . .. .

Figure 7-3 Typical profile of vertical bend thrust blocking

Adjacent excavation. Even a properly designed and constructed thrust block can fail if the soil behind the block is disturbed. Properly sized thrust blocks 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. If the risk of future nearby excavation is high, the use of restrained (tied) joints may be appropriate.

7.4 JOINTS WITH SMALL DEFLECTIONS The thrust at pipe joints installed with angular deflection is usually so small that supplemental restraint is not required. Small horizontal deflections. Thrust T at horizontal deflected joints is resisted by friction on the top and bottom of the pipe as shown in Figure 7-4. Additional restraint is not required when: T ≤ fLp (Wp + Ww + 2We)

(7-3)

Where: T = 2PA sin (θ /2) = result and thrust force, lb where θ is the deflection angle created by the deflected joint, degrees f = coefficient of friction Lp = length of pipe, ft Wp = weight of pipe, lb/lin ft


96


θ T = 2PA sin 2

T

T

Lp

Lp Lp 2

Lp 2

A

θ θ

A

Lp

θ

F= T

Plan View

We f Lp We

Wp Ww

F

T

f Lp (Wp + Ww + We ) Section A–A

Figure 7-4 Restraint of thrust at def lected joints on long-radius horizontal curves

Ww = weight of fluid in pipe, lb/lin ft We = earth cover load, lb/lin ft The passive soil resistance of the trench backfill against the pipe is ignored in the previous analysis. Depending on the installation and field conditions, the passive soil resistance of the backfill may be included to resist thrust. The selection of a value for the coefficient of friction f is dependent upon the type of soil and the roughness of pipe exterior. Design values for the coefficient of friction generally vary from 0.25 to 0.50. 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 lb/ft3 to 130 lb/ft3 (14 kN/m3 to 20 kN/m3), depending on the degree of capaction. We may be conservatively determined using the Marston equation for loads imparted to a flexible pipe, as follows: We = (Cd) (W) (Bd) (Bc) Where: We = earth load, lb/lin ft Cd = a coefficient based on type of backfill soil and on the ratio of H (depth of fill to top if pipe, ft) Bd (see Figure 7-5)


(7-4)


1.5 E D C B A 1.0

Computation Diagram for Earth Loads on Trench Conduits (conduits buried in trenches)

0.9 0.8 0.7 0.6

Coefficient Cd

0.5

0.4

0.3 0.25

0.2

A = Cd K µ and K µ' = 0.1924 for granular materials without cohesion B = Cd K µ and K µ' = 0.165 maximum for sand and gravel C = Cd K µ and K µ' = 0.150 maximum for saturated topsoil D = Cd K µ and K µ' = 0.130 ordinary maximum for clay E = Cd K µ and K µ' = 0.110 maximum for saturated clay

0.15

0.1 0.1

0.15

0.2

0.3

0.4

0.5

0.6

0.7

0.8 0.9 1.0

1.5

Values of H/Bd 5 E 4 D C B

Coefficient Cd

3

A 2 Expanded Scale of Computation Diagram for Earth Loads on Trench Conduits

1.5

1 1

1.5

2

3

4

5

6

7

8

9 10

15

20

25

30

Values of H/Bd

Figure 7-5 Computation diagram for earth loads on trench conduits


40

97

98


A

T T = 2PA sin

θ 2

Lp T

Lp

Lp 2

Lp 2

θ θ

ϕ

( ϕ– θ ) 2 F=T

A Horizontal Plane

Lp θ

Profile View

We

Wp Ww Wt = (Wp + Ww + We ) Section A–A

Figure 7-6 Restraint of uplift thrust at deflected joints on long-radius vertical curves

W = unit weight of soil, lb/ft3 Bd = ditch width at top of pipe, ft Bc = outside diameter of pipe, ft Small vertical deflections with joints free to rotate. Uplift thrust at deflected joints on long-radius vertical curves is resisted by the combined dead weight, Wt, as shown in Figure 7-6. Additional restraint is not required when: T ≤ Lp (Wp + Ww + We) COS (ϕ – θ/2) Where: T = 2PA sin (θ/2) Lp = length of standard or beveled pipe, ft


(7-5)


99

Wp = weight of pipe, lb/lin ft Ww = weight of water in pipe, lb/lin ft We = earth cover load, lb/lin ft ϕ = slope angle, degrees θ = deflection angle, degrees, created by angular deflection of joint

7.5 RESTRAINED (TIED) JOINTS ____________________________ Unbalanced thrust forces at fittings or deflected joints may be resisted by using restrained joint(s) across the deflected joint or by tying adjacent pipes to the fitting. 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. Since thrust diminishes from a maximum value at a fitting to zero at distance L from the fitting, requirements for longitudinal strength to resist thrust can be calculated for the pipe length immediately adjacent to the fitting and prorated on a straight line basis for the remainder of the pipe within the tied distance L. Frictional resistance on the tied pipe acts in the opposite direction of resultant thrust T. Section A–A in Figure 7-4 shows a diagram of the external vertical forces acting on a buried pipe with horizontal thrust and the corresponding frictional resistance. Uplift thrust restraint provided by gravity-type thrust blocks, shown for the top bend in Figure 7-3, 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 7-6 shows a diagram of the vertical forces acting on a buried vertical (uplift) bend used in determining the thrust resistance by dead weight.

∆ T = 2PA sin __ 2

L

∆

L

F = 2Lf(Wp+Ww+2 We) = T Joint Not Tied

Figure 7-7 Thrust restraint with tied joints at bends


100


As previously stated, both of these analyses ignore the passive soil resistance of the backfill against the pipe. Depending on the installation and field conditions, the passive soil resistance of the backfill may be included to resist thrust. Horizontal bends and bulkheads. As illustrated in Figure 7-7, the frictional resistance F needed along each leg of a horizontal bend is PA sin (∆/2). Frictional resistance per lin ft of pipe against soil is equal to: Frictional resistance/ft of pipe = f (2We + Wp + Ww)

(7-6)

Where: f = coefficient of friction between pipe and soil We = overburden load, lb/lin ft Wp = weight of pipe, lb/lin ft Ww = weight of water in pipe, lb/lin ft F = frictional resistance Therefore, the length of pipe L to be tied to each leg of a bend is calculated as: L =

PA sin (∆/2) f (2We + Wp + Ww)

(7-7)

Where: L = length of pipe tied to each bend leg, ft P = internal pressure, psi A = cross-sectional area, in.2 ∆ = deflection angle of bend, degrees f = coefficient of friction between pipe and soil We = overburden load, lb/lin ft Wp = weight of pipe, lb/lin ft Ww = weight of fluid in pipe, lb/lin ft The length of pipe to be tied to a bulkhead or tee leg is: L =

PA f (2We + Wp + Ww)

Where: L = length of pipe tied to bulkhead to tee leg, ft with all other variables as defined previously.


(7-8)


T = 2PA sin

101

∆ 2

L1

L2

∆

ϕ1

2

ϕ

Horizontal Plane PA PA

Figure 7-8 Length of tied pipe on each leg of vertical (uplift) bend

Vertical (uplift) bends. As illustrated in Figure 7-8, the dead weight resistance needed along each leg of a vertical bend is 2PA sin (∆/2). Dead weight resistance per lin ft of pipe in a direction opposite to thrust is: Dead weight resistance/ft of pipe = (We + Wp + Ww) COS (ϕ–∆/2)

(7-9)

Where: We = overburden load, lb/lin ft Wp = weight of pipe, lb/lin ft Ww = weight of fluid in pipe, lb/lin ft ϕ = slope angle, degrees (see Figure 7-8) ∆ = deflection angle of bend, degrees (see Figure 7-8) Length of pipe L to be tied to leg of a vertical (uplift) bend is calculated as: L =

PA [ sin (∆/2) ] (We + Wp + Ww) COS [ ϕ − (∆/2) ]

(7-10)

with variables as defined previously. L1 =

PA sin ∆/2 (We + Wp + Ww) COS ( ϕ1 − ∆/2)


(7-11)

102


L2 =

PA sin ∆/2 (We + Wp + Ww) COS (ϕ2 − ∆/2)

(7-12)

Vertical downward bends are resisted by bearing of the trench against the bottom of the pipe. Properly bedded pipe should not have to be investigated for this condition. Transmission of thrust force through pipe. In addition to calculating pipe length to be tied to a fitting, designers must be sure that tied pipe lengths have sufficient strength in the longitudinal direction to transmit thrust forces. The maximum thrust force for which the pipe adjacent to a bend must be designed is equal to:  5.43∆ + 0.063 ∆2  Fy =   PA for 0 < ∆ ≤ 90° 1,000  

(7-13)

Fy = PA

(7-14)

for ∆ > 90°

Where: Fy = maximum axial thrust force for which the pipe adjacent a bend must be designed, lb P = internal pressure, psi A = cross-sectional area, in.2 ∆ = bend deflection angle, degrees


Thrust Block Design

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