PD Thrust Restraint Design Equations and Tables

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Thrust Restraint Design Equations and Tables PD-6 5-95 These equations and tables are an effort to provide the piping system designer with conservative techniques and parameters for the design of

1 Thrust Restraint Design Equations and Tables PD These equations and tables are an effort to provide the piping system designer with conservative techniques and parameters for the design of underground restrained joint piping systems. They utilize recognized design equations and conservative soil parameters. The design equations in this handbook have proven useful in a wide variety of applications since The soil parameters presented include the results of an extensive study of the actual frictional performance of soils on ductile iron, ductile iron encased with polyethylene, and PVC pipe. The theory and application of this design method are outlined in a series of Connections bulletins. These bulletins can be obtained from EBAA Iron Sales. A computer program utilizing all the information provided in these bulletins and this booklet is also available from EBAA Iron Sales. These equations and soil values have proven conservative over the years and are dependent upon accurate soil identification and classification and good installation procedures and inspection. The ultimate responsibility for the identification of soil type, the proper use of the data provided, the final design, and the inspection of the system must rest with the design engineer. 1

2 List of Tables Table Page Number 1 Properties of Soils Used for Bedding to Calculate Fs and Rs 4 2 In Situ Values of Soil Properties for Rs 6 3 Bedding Soil Properties for Fs 6 Restrained Length Tables by Soil Type 4 GW & SW Well Graded Gravels and Sands, Sand/Gravel Mixtures 12 5 GP & SP Poorly Graded Gravels and Poorly Graded Sands 14 6 GM & SM Silty Gravels and Clayey Sands 16 7 GC & SC Clayey Gravels and Clayey Sands 18 8 CL Inorganic Clays of Medium to Low Plasticity In Predominately Dry Soil Above The Water Table 20 9 ML Inorganic Silts, Very Fine Sands, Rock Flour, Silty or Clayey Fine Sands In Predominately Dry Soil Above The Water Table CL Inorganic Clays of Low to Medium Plasticity, Bedded in Granular Materials (GP or SP) Near Saturation Conditions at or Below the Plastic Limit CH Inorganic Clays of High Plasticity, Fat Clays, Bedded in Granular Materials (GP or SP) Near Saturation Conditions at or Below the Plastic Limit ML Inorganic Silts, Very Fine Sands, Rock Flour, Bedded in Granular Material (GP or SP) Near Saturation Conditions at or Below the Plastic Limit MH Inorganic Silts, Micaceous or Diatomaceous Fine Sands or Silts, Elastic Silts, Bedded in Granular Materials (GP or SP) Near Saturation Conditions At or Below the Plastic Limit Fsb For Use With Dead Ends, Tees, and Reducers Nominal Dimensions and Weights 34 List of Figures Figures Page Number 1 The Unified Soil Classification System-ASTM D Horizontal Bend 6 3 Vertical Down Bend Shown on Vertical Offset 6 4 Tee 6 5 Reducer 6 6 Dead End 6 7 ANSI/AWWA C150/A21.50 Trench Conditions 10 2

3 Definition of Terms A Ab Al Ap = Cross sectional area of the pipe, in² = Cross sectional area of the branch of a tee, in² = Cross sectional area of the large side of a reducer, in² = Area based on half of the pipe circumference in contact with the soil, ft²/ft (Ap)b = Area based on full pipe circumference in contact with the soil, ft²/ft As = Cross sectional area of the small side of reducer, in² c = Cohesion of the soil, lbs/ft² D = Outside diameter of the pipe, ft fc = Cohesion modifier coefficient Fs = Frictional resistance acting on the pipeline (acting on half of the pipe diameter), lbs/ft Fsb = Frictional resistance acting on the pipeline (acting on the full pipe diameter), lbs/ft F(sb)l = Fsb on the large side of a reducer, lbs/ft ff = Friction angle modifier coefficient Hc = Mean depth from surface to pipe centerline, ft Kn = Trench compaction modifier Kp = Rankin passive pressure coefficient L = Minimum restrained length for bends, ft Lh = Minimum restrained length for the branch of a tee, ft Ll = Minimum restrained length for the large side of a reducer, ft Lr = Minimum restrained length on each side of the run of a tee, ft P = Internal pressure, lbs/in² Rs = Bearing resistance acting on the pipeline, lbs/ft Sf = Safety factor Su = Undrained shear strength, lbs/ft² T = Resultant thrust force, lbs W = Normal force acting on the pipeline, lbs/ft We = Normal force due to the vertical prism load of the soil, lbs/ft Wp = Normal force due to the weight of the pipe, lbs/ft Ww = Normal force due to the weight of the water in the pipe, lbs/ft F = Internal friction angle of the soil, degrees? = Soil density, lbs/ft³? = Bend angle, degrees s h = horizontal passive soil pressure, lbs/ft² 3

4 Bearing Resistance Rankin Passive Pressure theory for soils states s h =?H ckp + 2c vkp where Kp=tan²(45+F/2) Therefore, the bearing resistance along the pipeline is denoted by the term Rs and is represented as Rs=Kns hd Frictional Resistance The frictional resistance acting on a pipeline, Fs, can be determined by an adaptation of Potyondy s equation. Fs=Ap(fcc)+Wtan(fFF) Where Ap=pD/2 W=2We+Wp+Ww When analyzing the branch of a tee, reducers, or dead ends, the full pipe circumference should be taken into account since the full surface of the pipe is moving longitudinally into the soil. This modified version of the frictional force is denoted as pfs Fsb=(Ap)b(fcc)_+Wtan(fFF) where (Ap)b=pD The friction values for the soil should always be based on the soil that is in contact with the pipe. The pipe friction tests also indicated that ductile iron pipe encased with polyethylene film slips inside of the polyethylene encasement. This lends itself to conventional friction theory where the coefficient of friction of polyethylene on a ductile iron pipe surface was determined to be the tangent of 14 degrees. Therefore, for PE encased ductile iron pipe Fs=Fsb=Wtan 14=0.249W Table 1 lists the properties for most soils. Figure 1 lists the soils classifications for ASTM D2487 SOIL fc c ff F Trench Type GROUP DI PVC (psf) DI PVC (deg) (pcf) GW, SW GP, SP GM, SM GC, SC CL ML TABLE 1. PROPERTIES OF SOILS USED FOR BEDDING TO CALCULATE Fs AND Fs Kn 4

5 5

Special Soil Conditions The values in Tables 2 and 3 are for near saturated, undisturbed soils, type CL, ML, CH, and MH with pipe surrounded with sand or gravel having a minimum Standard Proctor

HORIZONTAL BEND Vertical Down Bend L=SfPAtan(φ/2) Fs Soil c=su Kn Group (psf) (pcf) 3 4 5 CL 450 100.60.

6 Special Soil Conditions The values in Tables 2 and 3 are for near saturated, undisturbed soils, type CL, ML, CH, and MH with pipe surrounded with sand or gravel having a minimum Standard Proctor Density of 80% or greater. While these values are conservative for most situations, a competent soils engineer should be contacted for pipelines in wetlands, river bottoms, etc. FIGURE 2. HORIZONTAL BEND Vertical Down Bend L=SfPAtan(φ/2) Fs Soil c=su Kn Group (psf) (pcf) CL CH ML MH (note: The above values are for undisturbed soil) TABLE 2: IN SITU VALUE OF SOIL PROPERTIES Rs Soil Group fc C fφ φ GP & SP TABLE 3. BEDDING SOIL PROPERTIES FOR Fs Bends The resultant thrust force for bends is Horizontal Bend T=2PAsin(φ/2) L=SfPAtan(φ/2) Fs+ ½Rs FIGURE 3. VERTICAL DOWN BEND SHOWN ON VERTICAL OFFSET For vertical offsets use the equation for the vertical down bend for the upper bend and the equation for thehorizontal bend for the lower bend. Tees Lb=Sf(PAb-RsLr) Fsb FIGURE 4. TEE 6

7 Reducers Restrained length on the large side. Lt=SfP(Al-As) (Fsh)l FIGURE 5. REDUCER Dead Ends L=SfPA Fsb FIGURE 6. DEAD ENDS 7

8 REFERENCES Potyondy, J.G.; Skin Friction Between Various Soils and Construction Materials, Geotechnique, London, England, Volume II, No. 4, December 1961, PP Kennedy, Harold Jr., Shumard, Dennis D., and Meeks, Cary M.; Investigation of Pipe-To-Soil Friction and Its Affect on Thrust Restraint For PVC and Ductile-Iron Pipe, Presented at AWWA Distribution Systems Symposium, September Carlesen, Rodger J.; Thrust Restraint for Underground Piping Systems, Ductile Iron Pipe News, CIPRA, Spring DIPRA; Thrust Restraint Design for Ductile -Iron Pipe, Second Edition, Lambe, T. William, and Whitman, Robert V.; Soil Mechanics, Series in Soil Engineering, Massachusetts Institute of Technology, John Wiley and Sons, New York, ASTM D 2487; Classification of Soils for Engineering Purposes. Uni-Bell Plastic Pipe Association; Handbook of PVC Pipe, Design, and Construction, Dallas, Texas. 8

9 HOW TO USE THE TABLES TO DETERMINE THE RESTRAINED LENGTH, L Tables 4 through 13 have been formulated for horizontal 90 degree bends having a pressure in the pipeline of 100 psi. A 1.5 safety factor has also been applied. Step 1: Identify the soil along the route of the proposed pipeline and classify it according to the Unified Soil Classification System. This can be done through an engineering soil survey. If a detailed soil survey is not available, refer to the published soil surveys of the U.S. Department of Agriculture Soil Conservation Service, County Soil Survey. These useful publications contain information on the soils in almost every country of the U.S. Step 2: Determine the test pressure of the proposed line. All calculations should be done using the test pressure since the test pressure is usually the maximum pressure the line should see in its lifetime. Step 3: Determine the pipe size and depth of cover. Step 4: Turn to the table covering the appropriate soil classification for the particular location to be considered. Note that the soil types will probably vary along the pipeline and that separate calculations should be made for each type encountered. Step 5: Locate the appropriate pipe type, pipe size, trench type (see Figure 7), and depth of cover in the table and obtain the corresponding L. Step 6: Multiply the selected value of L by the ratio of the test pressure of the pipeline to 100 psi (i.e., given a test pressure of 250 psi, multiply L by 2.5). Step 7: Determine the angle of horizontal bend required and multiply the L value from Step 6 by the appropriate factor given below. For example: If the bend angle is 45 degrees, multiply L from the chart by this pressure ratio (Step 6) and by The new product is the length of pipe to be restrained on both sides of the bend. Every joint within the prescribed length must be restrained: all fitting joints, pipe joints, valve joints, couplings, sleeves, etc. Offsets, tees, Dead Ends, and Reducers The equations and tables can also be utilized to calculate L for offsets, tees, reducers and dead ends. Step 1: Assuming the test pressure, depth of cover, and soil classification have been determined, turn to the section of the handbook covering the fitting in question. The equations for these fittings contain Rs, Fs, and Fsb. Use Tables 4 through 13 to determine Rs for the particular soil classification, pipe size, and depth of cover. Use Table 14 to determine Fsb. Step 2: The table values of Rs, Fs, and Fsb can now be used in the appropriate equation, along with the test pressure and other variables. Notes on Table Values These tables are to be used with soils that are unsaturated or near saturated. Saturated soil conditions should be calculated using the values given in Tables 1 through 3. For horizontal bends other than 90 degrees, multiply the given length by one of the following coefficients: 45 degrees ½ degrees ¼ degrees Units Fs and Fsb lbs/ft Rs lbs/ft Size-nominal pipe size, in. Depth-depth of bury to the top of the pipe, ft. L-restrained length, ft. Pipe Classifications DI-bare ductile iron pipe DI/PE-polyetheylene encased ductile iron pipe PVC-polyvinyl chloride pipe 9

10 10

11 RESTRAINED LENGTH TABLES TABLE SOIL TYPE AND DESCRIPTION PAGE 4 GW & SW WELL GRADED GRAVELS AND WELL 12 GRADED SANDS 5 GP & SP POORLY GRADED GRAVELS AND POORLY 14 GRADED SANDS 6 GM & SM SILTY GRAVELS AND SILTY SANDS 16 7 GC & SC CLAYEY GRAVELS AND CLAYEY SANDS 18 8 CL INORGANIC CLAYS OF LOW TO MEDIUM PLASTICITY 20 - IN PREDOMINATELY DRY SOIL ABOVE THE WATER TABLE 9 ML INORGANIC SILTS, VERY FINE SANDS, ROCK FLOUR 22 - IN PREDOMINATELY DRY SOIL ABOVE THE WATER TABLE 10 CL INORGANIC CLAYS OF LOW TO MEDIUM PLASTICITY, 24 BEDDED IN GRANULAR MATERIALS (GP or SP) NEAR SATURATION CONDITIONS AT OR BELOW THE PLASTIC LIMIT 11 CH INORGANIC CLAYS OF HIGH PLASTICITY, FAT CLAYS, 26 BEDDED IN GRANULAR MATERIALS (GP or SP) NEAR SATURATION CONDITIONS AT OR BELOW THE PLASTIC LIMIT 12 ML INORGANIC SILTS, VERY FINE SANDS, ROCK FLOUR, 28 BEDDED IN GRANULAR MATERIALS (GP or SP) NEAR SATURATION CONDITIONS AT OR BELOW THE PLASTIC LIMIT 13 MH INORGANIC SILTS, MICACEOUS OR DIATOMACEOUS 30 FINE SANDS OR SILTS, ELASTIC SILTS, BEDDED IN GRANULAR MATERIALS (GP or SP) NEAR SATURATION CONDITIONS AT OR BELOW THE PLASTIC LIMIT 14 Fsb FOR USE WITH DEAD ENDS, TEES, AND REDUCERS NOMINAL PIPE DIMENSIONS AND WEIGHTS 34 11

12 THRUST RESTRAINT DESIGN TABLE 4 SOIL TYPE: GW & SW WELL GRADED GRAVELS AND SANDS, SAND/GRAVEL MIXTURES. (SEE ASTM D2487 FOR MORE DETAILED SOIL DESCRIPTION) SOIL PARAMETERS: SYSTEM DESIGN PARAMETERS: PHI: 36 DEGREES DESIGN PRESSURE: 100 PSI COHESION; 0 PSF BEND ANGLE THETA: 90 DEGREES GAMMA: 110 PCF SAFETY FACTOR: 1.5 ANSI/AWWA C150/A21.50 TRENCH TYPE 3 TYPE 4 TYPE 5 DI PVC DI PVC DI PVC fφ fc Kn SIZE DEPTH Fs DI Fs DI/PE Fs PVC Rs L L DI DI/PE PVC Rs DI DI/PE PVC Rs DI DI/PE L PVC

13 THRUST RESTRAINT DESIGN TABLE 4 SOIL TYPE: GW & SW

14 THRUST RESTRAINT DESIGN TABLE 5 SOIL TYPE: GP & SP POORLY GRADED GRAVELS AND POORLY GRADED SANDS (SEE ASTM D2487 FOR MORE DETAILED SOIL DESCRIPTION) SOIL PARAMETERS: SYSTEM DESIGN PARAMETERS: PHI: 31 DEGREES DESIGN PRESSURE: 100 PSI COHESION: 0 PSF BEND ANGLE THETA: 90 DEGREES GAMMA: 110 PCF SAFETY FACTOR: 1.5 ANSI/AWWA C150/A21.50 TRENCH TYPE 3 TYPE 4 TYPE 5 DI PVC DI PVC DI PVC fφ fc Kn

15 THRUST RESTRAINT DESIGN TABLE 5 SOIL TYPE: GP & SP

16 THRUST RESTRAINT DESIGN TABLE 6 SOIL TYPE: GM & SM SILTY GRAVELS AND SILTY SANDS (SEE ASTM D2487 FOR MORE DETAILED SOIL DESCRIPTION) SOIL PARAMETERS: SYSTEM DESIGN PARAMETERS: PHI: 30 DEGREES DESIGN PRESSURE: 100 PSI COHESION: 0 PSF BEND ANGLE THETA: 90 GAMMA: 110 PCF SAFETY FACTOR: 1.5 ANSI/AWWA C150/A21.50 TRENCH TYPE 3 TYPE 4 TYPE 5 DI PVC DI PVC DI PVC fφ fc Kn

17 THRUST RESTRAINT DESIGN TABLE 6 SOIL TYPE: GM & SM

18 THRUST RESTRAINT DESIGN TABLE 7 SOIL TYPE: GC & SC CLAYEY GRAVELS AND CLAYEY SANDS (SEE ASTM D2487 FOR MORE DETAILED SOIL DESCRIPTION) SOIL PARAMETERS: SYSTEM DESIGN PARAMETERS: PHI: 25 DEGREES DESIGN PRESSURE: 100 PSI COHESION: 225 PSF BEND ANGLE THETA: 90 DEGREES GAMMA: 100 PCF SAFETY FACTOR: 1.5 ANSI/AWWA C150/A21.50 TRENCH TYPE 3 TYPE 4 TYPE 5 DI PVC DI PVC DI PVC fφ fc Kn

19 THRUST RESTRAINT DESIGN TABLE 7 SOIL TYPE: GC & SC

20 THRUST RESTRAINT DESIGN TABLE 8 SOIL TYPE: CL INORGANIC CLAYS OF MEDIUM TO LOW PLASTICITY IN PREDOMINATELY DRY SOIL ABOVE THE WATER TABLE (SEE ASTM D2487 FOR MORE DETAILED SOIL DESCRIPTION) SOIL PARAMETERS: SYSTEM DESIGN PARAMETERS: PHI: 20 DEGREES DESIGN PRESSURE: 100 PSI COHESION: 250 PSF BEND ANGLE THETA: 90 DEGREES GAMMA: 100 PCF SAFETY FACTOR: 1.5 ANSI/AWWA C150/A21.50 TRENCH TYPE 3 TYPE 4 TYPE 5 DI PVC DI PVC DI PVC fφ fc Kn

21 THRUST RESTRAINT DESIGN TABLE 8 SOIL TYPE: CL PREDOMINATELY DRY SOIL

22 THRUST RESTRAINT DESIGN TABLE 9 SOIL TYPE: ML INORGANIC SILTS, VERY FINE SANDS, ROCK FLOUR, SILTY OR CLAYEY FINE SANDS PREDOMINATELY DRY SOIL ABOVE THE WATER TABLE (SEE ASTM D2487 FOR MORE DETAILED SOIL DESCRIPTION) SOIL PARAMETERS: SYSTEM DESIGN PARAMETERS: PHI: 29 DEGREES DESIGN PRESSURE: 100 PSI COHESION: 0 PSF BEND ANGLE THETA: 90 DEGREES GAMMA: 100 PCF SAFETY FACTOR: 1.5 ANSI/AWWA C150/A21.50 TRENCH TYPE 3 TYPE 4 TYPE 5 DI PVC DI PVC DI PVC fφ fc Kn

23 THRUST RESTRAINT DESIGN TABLE 9 SOIL TYPE: ML PREDOMINATELY DRY SOILS

24 THRUST RESTRAINT DESIGN TABLE 10 SOIL TYPE: CL INORGANIC CLAYS OF LOW TO MEDIUM PLASTICITY, BEDDED IN GRANULAR MATERIALS (GP or SP) NEAR SATURATION CONDITIONS AT OR BELOW THE PLASTIC LIMIT (SEE ASTM D2487 FOR MORE DETAILED SOIL DESCRIPTION) SOIL PARAMETERS: SYSTEM DESIGN PARAMETERS: PHI: 0 DEGREES DESIGN PRESSURE: 100 PSI COHESION: 450 PSF BEND ANGLE THETA: 90 DEGREES GAMMA: 100 PCF SAFETY FACTOR: 1.5 ANSI/AWWA C150/A21.50 TRENCH TYPE 3 TYPE 4 TYPE 5 DI PVC DI PVC DI PVC fφ fc Kn

25 THRUST RESTRAINT DESIGN TABLE 10 SOIL TYPE: CL NEAR SATURATION BEDDED IN GRANULAR MATERIAL

Depth of Bury Tables 9B-5. A. General. B. Rigid Pipe Assumptions. Design Manual Chapter 9 - Utilities 9B - Trench Design

Depth of Bury Tables 9B-5. A. General. B. Rigid Pipe Assumptions. Design Manual Chapter 9 - Utilities 9B - Trench Design Design Manual Chapter 9 - Utilities 9B - Trench Design 9B-5 Depth of Bury Tables A. General The depth of bury tables on the following pages are based upon the design methodology from the various pipe material