Unified Approach to Thrust Restraint Design Jey K. Jeyapalan, Ph.D., P.E., M.ASCE1; and Sri K. Rajah, Ph.D., P.E., M.ASCE2 Abstract: The design of thrust blocks for water pipelines and sewer force mains vary from one pipe material or standard to another just like the design of pipe wall thickness. This creates tremendous confusion among consulting engineers and owners of projects. The designers and the owners have to look up Design Manual M9 for concrete pipe, Design Manual M11 for welded steel pipe, Design Manual M41 for ductile iron pipe, Design Manual M23 for PVC pipe, and Design Manual M45 for fiberglass pipe. In many countries, water pipeline materials are required to meet a common standard, where design equations are kept the same whereas material properties vary from one pipe material to another. The purpose of this paper is to start from the fundamental principles of fluid mechanics and geotechnical engineering and build the engineering know-how needed to apply the same design methodology for all pipe materials and applications. A step-by-step design methodology is presented. DOI: 10.1061/共ASCE兲0733-947X共2007兲133:1共57兲 CE Database subject headings: Soil-structure interaction; Pipelines; Pipe design; Thrust. Introduction Due to the layout requirements in both above ground and underground pipelines, unbalanced hydrostatic forces known as thrust forces are present at the locations where the pipeline changes either in size or in direction. Examples of such locations include horizontal and vertical bends, tees, wyes, reducers, offsets, bulkheads, pipe bifurcations, and valves. Unless the pipeline is properly restrained to resist the unbalanced forces, either separation can occur at the pipeline joints or pipe wall stresses could approach yield strengths. While providing thrust-resisting supports in an above ground pipeline can resist thrust forces, resisting thrust forces in an underground pipeline is usually accomplished with thrust blocks, restrained joint systems, or a combination of both. Although, various pipe design standards in the American Water Works Association 共1979, 1989, 1996a,b兲 present design equations for the design of thrust restraint systems utilizing thrust blocks and restrained joints in underground pipelines, the equations are often derived with different assumptions and hence are not the same. Considering the theory behind the thrust block design is based on simple statics and does not depend on the type of pipe wall material, the differences in formulations are often confusing and are mostly misunderstood 关for example, see Romer 共1998兲兴. Ironically, the same paper by Romer 共1998兲, in attempting to point out how to avoid common thrust restraint mistakes, made even more fundamental errors, e.g., the definition and use of earth pressure coefficients. In this paper a unified approach independent of pipe wall material or type of pipeline use is presented for the design of thrust restraint systems in an underground pipeline system. Review of Current Design Methodology Thrust Block Design The design of a thrust block can be based on gravity or bearing depending on the source of the unbalanced forces. Bearing-type thrust blocks supporting a horizontal bend and a concave vertical bend are shown in Figs. 1共a and b兲, respectively. A gravitytype thrust block supporting a convex vertical bend is shown in Fig. 1共c兲. The distinction between the bearing and gravity thrust blocks is made based primarily on the mechanism with which the unbalanced forces are resisted. The bearing type thrust blocks are designed to safely transmit the unbalanced thrust forces to the undisturbed soil in bearing using some form of earth pressures. The required bearing area of the thrust block is given by Ab = T Sba 共1兲 where Sba 共=Sb / S f 兲 = design soil bearing strength in the direction of the unbalanced thrust force 共either kN/ m2 or psi兲; 1 Vice President, Camp Dresser & McKee Inc., 100 Great Meadow Rd., Suite 104, Wethersfield, CT 06109. E-mail: jeyapalanjk@cdm.com 2 Senior Soil-Structure Interaction Engineer, URS Corporation, Century Square, 1501 Fourth Ave., Suite 1400, Seattle, WA 98101-1616. E-mail: sriគrajah@urscorp.com Note. Discussion open until June 1, 2007. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on January 6, 2003; approved on July 27, 2006. This paper is part of the Journal of Transportation Engineering, Vol. 133, No. 1, January 1, 2007. ©ASCE, ISSN 0733-947X/2007/1-57–61/$25.00. Fig. 1. Typical thrust block arrangements JOURNAL OF TRANSPORTATION ENGINEERING © ASCE / JANUARY 2007 / 57 Fig. 2. Thrust forces in most common thrust restraint situations Sb = allowable soil bearing strength 共either kN/ m2 or psi兲; S f = safety factor 共usually taken as 1.5兲; T = unbalanced thrust force resultant 共either kN or lb兲; and Ab = required bearing area of the thrust block 共either m2 or in.2兲. A series of different types of unbalanced force situations and the corresponding unbalanced force resultants are shown in Fig. 2. The gravity type thrust blocks are primarily designed to have sufficient weight to counter the vertical component of the unbalanced forces, while not exceeding the allowable design bearing stresses in the vertical and horizontal directions. The volume of the thrust block, Vg, is given by Vg = S f Ty ␳c 共2兲 where Ty = vertical component of the unbalanced force resultant 共either kN or lb兲; and ␳c = density of concrete to be used in thrust block 共either kN/ m2 or lb/ in.2兲. Restrained Joint System Design As an alternative to providing thrust restraint mechanism using thrust blocks, restrained joint systems may be used. In general, the restrained joint system is a mechanical 共welded or harnessed兲 joint providing longitudinal restraint. The objective of the thrust restraint design using a restrained joint system is to determine the length of the pipe that must be restrained on each side of the point of action of the thrust force. The primary objective of the restrained joint system design is to transmit the unbalanced forces to the surrounding soil with- out overstressing the pipeline wall and without subjecting the pipeline to joint separations. In order to accomplish the transfer of the unbalanced forces to the surrounding soil, friction in AWWA 共1979, 1989, 1996a,b兲 and passive resistance in AWWA 共1996a兲 have been relied upon. A comparison of how the design of restrained joints is handled in various AWWA design manuals is summarized in Table 1 along with the proposed Unified method. The length of the pipe section with restrained joints on each leg is calculated using the sum of the components of the unbalanced forces in the direction of the corresponding leg in some AWWA design manuals 共1979, 1989兲. In some other AWWA design manuals 共1996a,b兲, the length of the pipe section with restrained joints is determined based on the unbalanced force resultant to be transmitted to the soil. Although, it was the intention of the paper by Romer 共1998兲 to use proper restraint to minimize either size or length of the restraint required, the paper fell short of providing a safe solution in most situations arising in the field. For the purpose of this paper, we will evaluate the theory corresponding to a horizontal bend and base our discussion on the merits and demerits of those equations. The design equation for the length of the pipe section with restrained joints from various design manuals for a horizontal bend can be summarized as follows: L= S f Tr n共Fs + Rs/2兲 共3兲 where L = length of the restrained pipe on each side of the bend 共either m or in.兲; Tr = design unbalanced thrust force on one side Table 1. Design Methods for the Thrust Restraint Joints in AWWA Manuals Design method M9 M11 M41 M23 M45 Romer Unified Friction Friction mobilized above the pipe Passive resistance Based on transfer of forces in the direction of the pipe legs Based on transfer of forces in the direction of the unbalanced force resultant Yes Yes No Yes No Yes No No Yes No Yes Yes Yes No Yes Yes No Yes No No Yes Yes No No Yes Yes No No Yes No Yes Yes Yes Yes Yes 58 / JOURNAL OF TRANSPORTATION ENGINEERING © ASCE / JANUARY 2007 that there is a chance that the soil above the pipe might move with the pipe and thereby the friction above the pipe may not fully develop if the cover is shallow. It is important to note that if the soil cover is shallow, in such a case the value of the earth load will be small and the error due to the wrong assumption is also, as a consequence, rather small. However, to be conservative, it is recommended that the friction above the pipe be neglected for pipes with shallow cover. Design Manual M41 includes the pipesoil adhesion in calculating the frictional resistance, whereas other design manuals do not consider it. Design Manual M41 considers the passive resistance in calculating the resistance forces, while other design manuals do not consider this. The design method proposed by Romer 共1998兲, in general, provides conservative design for most common situations. However, for uncommon situations such as bends with an angle greater than 90°, and Wyes with differing diameters in each leg, his method may result in unsafe designs. Also, Romer’s 共1998兲 work fails for the special hypothetical case of the straight pipe, i.e., a bend with a zero bend angle. If applied to such straight pipe segments, Romer’s proposed design methodology would result in restrained joints for the entire pipe and this is simply a fundamental error and would lead a designer to raise serious doubts about the rest of the guidance by Romer 共1998兲. Fig. 3. Schematic showing pipe-soil interaction forces at a horizontal bend of the bend 共either kN or lb兲; n = direction cosine for the angle between the resultant unbalanced force and the direction in which the maximum friction is mobilized; Fs = maximum unit frictional force that could be mobilized in the direction of the unbalanced thrust force resultant 共either kN or lb兲; and Rs = maximum unit bearing resistance 共either kN/ m2 or psi兲, as shown in Fig. 3. The values for the various terms used in Eq. 共3兲 in various design manuals are summarized in Table 2. A factor of safety value of 1.5 is recommended in AWWA Design Manual M41, whereas other design manuals do not recommend any specific values. However, Design Manual M11 points out that since the passive resistance was not included in the formula, this will give an additional safety factor. Considering the uncertainty and variations in the field design parameters, it is prudent to use a factor of safety in the design of the thrust restraint system. As to the design methodology, it is important to ensure that each leg does resist the unbalanced force component along the length of the pipe leg, while satisfying overall equilibrium of the joint. Therefore, it is important that the length of the pipe with restrained joints in each leg satisfies the following conditions: 1. The resultant of the components of the thrust forces in the direction of the leg should be safely transferred to the soil along the pipe-soil interface to avoid joint separations; and 2. The resultant of the unbalanced thrust forces should be safely transmitted to the soil through friction and bearing. In evaluating the unit frictional force, the Design Manual M11 does not consider the friction mobilized above the pipe. Other design manuals, M9, M41, and M45 assume that the friction is fully mobilized above and below the pipe. Romer 共1988兲 notes Unified Design Philosophy After careful evaluation of the existing design methodologies in various AWWA design manuals for the design of thrust restraint systems, a unified method for the design of thrust restraint system using joint restraints is proposed herein. Design of a restrained joint system for a horizontal bend is used to evaluate and present the proposed design philosophy. The design equations for the length of the pipe section for a horizontal bend with restrained joints can be derived from force balance equations. As noted earlier, the AWWA design manuals differ as to how the thrust force is resisted and the directions in which the resisting forces act. Various forces acting on a typical bend in a buried pipeline and the direction in which those forces act are shown in Fig. 3. Particularly, the frictional forces are mobilized in the opposite direction of the resultant thrust force, adhesive forces are mobilized in the longitudinal direction of the pipe over its perimeter, and passive resistance forces are mobilized in the transverse direction of the Table 2. Comparison of Design Equations for the Design of Thrust Restraint Joints in Different Design Manuals Design method Factor of safety 共S f 兲 Design unbalanced force 共Tr兲 Unit frictional force 共Fs兲 M9 M11 M41 M23 M45 Romer 1.0 PA共1 − cos共␪兲兲 1.0 PA共1 − cos共␪兲兲 1.5 2PA Sin共␪ / 2兲 1.5 2PAS Sin共␪ / 2兲 1.0 PA Sin共␪ / 2兲 1.0 PA 共2We + W p + Ww兲 . ␮ 共We + W p + Ww兲 . ␮ ␲Df cC 2 + 共2We + W p + Ww兲 . ␮ K n P pD ␲Df cC 2 + 共2We + W p + Ww兲 . ␮ K n P pD 共2We + W p + Ww兲 . ␮ 共We + W p + Ww兲 . ␮ 0 0 Unit bearing 0 0 resistance 共Rs兲 1.0 1.0 0.2 to 1.0 0.4 to 1.0 1.0 1.0 Kn Note: We = unit earth load on pipe 共kN/m or lb/ft兲; Wp = unit weight of pipe 共kN/m or lb/ft兲; Wwunit weight of water 共kN/m or lb/ft兲; ␲Df cC / 2 = unit adhesive resistance between soil and pipe 共kN/m or lb/ft兲; f c = ratio of pipe-soil adhesion to soil cohesion; C = soil cohesion 共kN/ m2 or lb/ ft2兲; D = diameter of the pipe 共m or ft兲; ␮ = frictional coefficient; Kn = empirical reduction factor for coefficient of passive resistance; P p = design value of passive soil pressure 共kN/ m2 or lb/ ft2兲; ␪ = bend deflection angle 共deg兲; P = design internal pressure 共kN/ m3 or psi兲; and A = cross-sectional area of the pipe 共m2 or in.2兲. JOURNAL OF TRANSPORTATION ENGINEERING © ASCE / JANUARY 2007 / 59 pipe. The force balance equation in the direction of the pipe leg is written as follows: L1 = S f 关PA共1 − cos共␪兲兲兴 ␲Df cC ␮关2␣We + W p + Ww兴sin共␪/2兲 + 2 共4a兲 and the force balance equation in the direction of the resultant unbalanced thrust force is written as follows: L2 = S f ⌊PA sin共␪/2兲⌋ 1 ␲Df cC sin共␪/2兲 + Kn P pD cos共␪/2兲 ␮关2␣We + W p + Ww兴 + 2 2 共4b兲 where 0.5艋 ␣ 艋 1.0= parameter describing the degree of mobilization of friction above the pipe; ␣ = 0.5 denotes no friction is mobilized above the pipe and ␣ = 1.0 denotes that friction is fully mobilized above the pipe. The value of ␮ that defines the friction coefficient between the outer surface of the pipe and the surrounding soil has been known to vary in the range of 0.25艋 ␮ 艋 0.40 based on the type of soil, degree of compaction, moisture content, and the type of coating on the pipe. The remaining notations used in these equations are consistent with the notations defined in Table 2. A factor of safety of 1.5 or higher is recommended for the design of thrust restraint systems. Care should be exercised in the selection of soil parameters used in the design, especially when the designer wants to take advantage of the adhesive and passive resistances from the soil. The design length of the pipe with restrained joints on each side of the bend, L, is given by the higher value obtained from Eqs. 共4a兲 and 共4b兲, i.e. L = max兵L1,L2其 共4c兲 both. Pipeline designers should recognize that the movement in pipe against the soil needed to mobilize fully the benefit of passive soil resistance is ten times that of the movement needed to produce an active soil pressure condition. A conservative approach is to use Rankine’s at-rest earth pressure estimates, assuming that the pipe will not move much into the surrounding soil during its design life. Summary The paper provides a summary of thrust restraint design equations and critically examines those equations for consistency and technical adequacy. A unified approach is outlined for thrust restraint design for a horizontal bend. The proposed design approach for a thrust restraint system using restrained joints can be summarized in a series of steps as follows: 1. Conduct geotechnical investigation along the pipeline alignment, review bore hole logs, plans, profiles, and establish soil parameters. 2. For each thrust restraint location based on the soil parameters from investigation, establish design soil parameters ␮, f c, C, Kn, and P p. 3. Based on cover, size of pipe, soil conditions, estimate the value of ␣. 4. Calculate the unit loads from soil, pipe, and fluid. 5. Determine the value of factor of safety. 6. Calculate the value of L1 by writing force balance equations in the direction of the leg. 7. Repeat Step 6 for each leg, if size of pipe or component of the force in the direction of the leg is different. 8. Calculate the value of L2 by writing force balance equations in the direction of the unbalanced thrust force resultant. 9. By comparing results obtained in Steps 6–8, determine the value of L for each leg. Example Determination of Soil Parameters The soil parameters needed to complete design calculations should start with soil borings and standard in situ geotechnical testing followed by laboratory testing. Pipe-soil adhesion resistance estimates would rely on the vast body of published literature on pile-soil interaction. Engineering properties such as unit weight, cohesion intercept, friction angle, and friction coefficient under appropriate loading and drainage conditions would come from either in situ tests, or laboratory tests, or a combination of Calculate the minimum pipe length that needs to be restrained for the following conditions: PVC pipe; D = 0.2 m 共8 in.兲; D0 = 0.228 m 共9 in.兲; P = 10 bars 共150 psi兲; bend angle, ␪ = 45°; soil cover, Hc = 2.13 m 共7 ft兲; USCS is GC-SC; unit weight of soil, ␥ = 15.7 kN/ cm2 共100 pcf兲; angle of internal friction, ␾ = 25°; ␮ = 0.3; Fc = 0.2; C = 10.8 kN/ m2 共225 psf兲; Kn = 0.60; ␣ = 0.75; We = ␥. Hc Do= 7.66 kN/ m 共525 lb/ ft兲; W p = small; Ww = 0.41 kN/ m 共28 lb/ ft兲; and P p = ␥HcN␾ + CQ = 100⫻ 7 ⫻ tan2共45− ␾ / 2兲 + 225 tan共45− ␾ / 2兲 = 20.4 kN/ sm 共427 lb/ sf兲 L1 = 1.5关150 ⫻ 64.33 ⫻ 共1 − 0.707兲兴 = 8.8 m 共29 ft兲 关0.3共2 ⫻ 0.75 ⫻ 525 + 0 + 28兲sin共22.5兲 + 22 ⫻ 0.75 ⫻ 0.2/225/共7 ⫻ 12 ⫻ 2兲兴 L2 = 1.5关150 ⫻ 64.33 sin共22.5兲兴 = 4.9 m 共16 ft兲 关0.3共1.5 ⫻ 525 + 0 + 28兲 + 53 sin共22.5兲 + 0.5 ⫻ 0.6 ⫻ 427 ⫻ 0.75 cos共22.5兲兴 60 / JOURNAL OF TRANSPORTATION ENGINEERING © ASCE / JANUARY 2007 Use 8.8 m 共29 ft兲 for each leg of the pipe to carry the unbalanced forces from the 45° bend. thrust block and thrust restraint mistakes practicing engineers make in their pipeline projects. References Recommendations The principles of fluid mechanics, statics, and geotechnical engineering should govern the design of thrust blocks and thrust restraint systems. The use of equations, which are dependent on the type of pipe material, should be avoided. The effect on the surrounding soil is not dependent upon whether the pipe is made of steel, concrete, fiberglass, or ductile iron other than the fact that soil-pipe interaction principles are always at work in controlling the design. A unified design methodology to all pipe materials is given in this paper. This approach will help avoid most common American Water Works Association 共AWWA兲. 共1979兲. Manual M9, concrete pressure pipe, Denver. American Water Works Association 共AWWA兲. 共1989兲. Manual M11, steel pipe—A guide for design and installation, Denver. American Water Works Association 共AWWA兲. 共1996a兲. Manual M41, ductile-iron pipe and fittings, Denver. American Water Works Association 共AWWA兲. 共1996b兲. Manual M45, fiberglass pipe design, Denver. Romer, A. E. 共1998兲. “Avoiding common thrust restraint mistakes.” Proc., ASCE Conf. on Pipelines in the Constructed Environment, J. P. Castronovo and J. A. Clark, eds., San Diego, 97–102. 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