SYSTEM DESIGN:
3.5 PIPELINE DESIGN
3.5.3 Thrust Restraint
Thrust forces are unbalanced forces in pressure pipelines that occur at changes in direction (such as in bends, wyes, and tees), at changes in cross-sectional area (such as in reducers), or at pipeline terminations (such as at bulkheads). If not adequately restrained, these forces tend to disengage nonrestrained joints. Two types of thrust forces are (1) hydrostatic thrust due to internal pressure of the pipeline and (2) hydrodynamic thrust due to the 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 thrast. For example, the dynamic force created by water flowing at 2.4 m/s (8 ft/s) is less than the static force created by 6.9 kPa (1 psi).
Typical examples of hydrostatic thrust are shown in Fig. 3.11. The thrust in dead ends, outlets, laterals, and reducers is a function of the internal pressure P and the cross-sectional area A at the pipe joint. The resultant thrast at a bend is also a function of the deflection angle ⌬ and is given by the following:
(3.6) where T=hydrostatic thrust, in pounds, P=internal pressure, in pounds per square inch, A=cross-sectional area of the pipe joint, in square inches, and ⌬=deflection angle of bend, in degrees.
For buried pipelines, thrust resulting from small 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 not usually needed. Thrust at in-line fittings, such as valves and reducers, is usually restrained by frictional drag on the longitudinally compressed downstream pipe. Other fittings subjected to unbalanced horizontal thrust have the following two inherent sources of resistance: (1) frictional drag from the dead weight of the fitting, earth cover, and contained water and (2)
Unbalanced uplift thrust at a vertical deflection is resisted by the dead weight of the fitting, earth cover, and contained water. If that is not adequate to resist the thrust involved, then it must be supplemented either by increasing the dead weight with a gravity-type thrust block or by increasing the dead weight of the line by “tying” adjacent pipe to the fitting.
TABLE 3.20 Average Values of Modulus of Soil Reaction, E (for Initial Flexible Pipe Deflection)*
†ASTM Designation D 2487, USBR Designation E-3.
‡Or any borderline soil beginning with one of these symbols (i.e. GM-GC, GCOSC).
*For ±1% accuracy and predicted deflection of 3%, actual deflection would be between 2% and 4%.
Note: Values applicable only for fills less than 50 ft (15 m). Table does not include any safety factor.
For use in predicting initial deflections only; appropriate deflection lag factor must be applied for long-term deflections. If bedding falls on the borderline between two compaction categories, select lower E value or average the two values. Percentage Proctor based on laboratory maximum dry density from test standards using about 12,500 ft-lb/ft3 (598,000 J/m3) American Society for Testing of Material (ASTM D698, AASHTO T-99, USBR Designation E-1 11). 1 psi=6.9 kPa.
Source: Howard, A.K., Soil Reaction for Buried Flexible Pipe, U.S. Bureau of Reclamation, Denver, CO. Reprinted with permission from American Society of Civil Engineers.
Abbreviations: CH, CH-MH, CL, GC, GM, GP, GW, LL, liquid limit; MH, SC, SM, SP, SW.
When a high water table or submerged conditions are encountered, the effects of buoyancy on all materials should be considered.
3.5.3.1 Thrust blocks. Thrust blocks increase the ability of fittings to resist movement by increasing the bearing area. Typical thrust blocking is shown in Fig. 3.12. Thrust block size can be calculated based on the bearing capacity of the soil as follows:
(3.7) where
LB×HB = area of bearing surface of thrust block (ft2) T = thrust force (lb)
σ = safe bearing value for soil (lb/ft2)
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.
FIGURE 3.11 Hydrostatic thrust for typical fittings (AWWA M9, 1995).
FIGURE 3.12 Typical thrast block details (Sanks, et al., 1989).
Determining the safe bearing value is the key to “sizing” a thrust block. Values can vary from less than 1000 lb/ft2 (49.7 kN/m2) for very soft soils to several tons per square foot (kN/m2) for solid rock. Determining the safe bearing value of soil is beyond the scope of this text. It is recommended that a qualified geotechnical expert, knowledgeable of local conditions, be consulted whenever the safe bearing value of a soil is in question.
Most thrust block failures can be attributed to improper construction. Even a correctly sized block can fail if it is not properly constructed. The thrast 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. Many people involved in construction do not realize the magnitude of the thrusts involved. As an example, a thrust block behind a 36 in (900 mm), 90° 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 about four times the thrust produced by an 18-in (450-mm) pipe operating at the same internal pressure.
Even a properly designed and constructed thrust block can fail if the soil behind it is disturbed. Thrast blocks of proper size have been poured against undisturbed soil only to fail because another excavation immediately behind the block collapsed when the line was pressurized. The problems of later excavation behind thrust blocks and simply having
“chunks” of buried concrete in the pipeline right-of-way have led some engineers to use tied joints only.
3.5.3.2 Restrained joints. Many engineers choose to restrain thrust from fittings by tying adjacent pipe joints. This method fastens a number of pipe joints on each side of the fitting to increase the frictional drag of the connected pipe and resist the fitting thrust.
Much has been written about the length of pipe that is necessary to resist hydrostatic thrust. Different formulas are recommended in various references, particularly with respect to the length of pipe needed at each leg of a horizontal bend. AWWA M9 (AWWA, 1995) provides the following:
(3.8)
where L=length of pipe tied to each bend leg (ft), P=internal pressure (lb/in2), A=cross-sectional area of first unrestrained pipe joint (in2), ⌬=deflection angle of bend (°), f=
coefficient of friction between pipe and soil, We=weight of soil prism above pipe (lb/Lft), Wp=weight of pipe (lb/Lft), and Ww=weight of water in pipe (lb/Lft).
This formula assumes that the thrust is resolved by a frictional force acting directly opposite to the hydrostatic thrust. It also assumes that the weight of the earth on top of the pipe can be included in the frictional calculation no matter what the installation depth. The factor 2We appearing in the denominator indicates that the weight of the earth is acting both on the top and the bottom of the pipe.
AWWA M11 (AWWA, 1989) presents the following alternative formula:
(3.9)
This formula assumes that the thrust is resolved by frictional forces acting along the length of the pipe and does not assume that the weight of the earth acts both on the top and bottom of the pipe.
The resolution of hydrostatic thrust, acting on a bend of angle A, by a length of restrained-joint pipe on each side of the bend is governed by the following:
• Restraint of the pipe is accomplished by a combination of indeterminate forces, includ-ing friction between the pipe and soil along the pipe and passive soil pressure perpen-dicular to the pipe.
• When the pipe is pressurized, the thrust T is not counteracted until the elbow (and length of restrained pipe) moves an amount sufficient (albeit very small) to mobilize friction and passive pressures.
• To develop the frictional resistance at the top of the pipe, it is necessary that the prism of earth above the pipe be restrained from movement.
Given the above statements, the reader is directed to Fig. 3.13. The following should be noted:
• The method proposed in AWWA M9 (AWWA, 1995) does not directly relate the resolu-tion of thrust to a fricresolu-tional force acting along a length of pipe.
• The method proposed in AWWA M1 1 (AWWA, 1989) relates the resolution of thrust to a frictional force acting along one leg of the pipe to be restrained. In practice, both legs on each side of the bend are restrained.
• The resolved forces method presents a rational distribution of forces acting to resolve the thrust.
According to Fig. 3.13, the resolution of thrust T by frictional forces acting along the pipe is given by the following equation:
(3.10)
where
Rf=frictional forces acting along each leg of pipe from bend of angle ⌬ Inspection of Fig. 3.13 also indicates the following:
• The PA sin ⌬/2 cos ⌬/2 force is a shearing force acting across the pipe joint. These forces can be significant, even for small ⌬s and should be considered in the design.
• The length of pipe to be restrained, using AWWA M9 (AWWA, 1995) or AWWA M11 (AWWA, 1989) formulas, is always greater than the lengths using the resolved forces method, PA sin2⌬/2, so either AWWA method can be used as a conservative analysis.
As stated above, to develop the frictional resistance at the top of the pipe, it is necessary that the prism of earth above the pipe be restrained from movement. This can be assumed to be true and the frictional resistance at the top of the pipe included in the calculation if the following can be shown:
(3.11) Po is further defined as:
where Po=force available from earth prism to provide frictional resistance (lb), W=weight of soil prism above pipe (lb), f=coefficient of friction between pipe and soil, H=height of cover over top of pipe (ft), ko=coefficient of soil at rest: 0.4 for crushed rock, 0.6 for saturated silty sands, and ϕ=soil internal angle of friction (varies with soil type) consult geotechnical expert.
FIGURE 3.13 Frictional thrust restraint.
Therefore, if the soil prism above the pipe is restrained from movement and can be included in the restraint calculation, the formula for the length of pipe with restrained joints, in accordance with Fig. 3.13, becomes:
(3.12)
If the soil prism above the pipe is not restrained from movement and cannot be included in the restraint calculation, the formula for the length of pipe with restrained joints, in accordance with Figure 3.13, becomes:
(3.13)
In all the above equations, the value of the coefficient of friction/between the pipe and soil affects the length of pipe that will be required to be restrained. Tests and experience indicate that the value of f is not only a function of the type of soil, but it is also greatly affected by the degree of compaction and moisture content of the backfill, the pipe exterior, and even the pipe joint configuration. Therefore, care should be exercised in the selection of f. Coefficients of friction are generally in the range of 0.2 for PVC or a polyethylene bag to 0.35–0.4 for a cement mortar coating.