Numerical Methods in Soil Mechanics 12.PDF Numerical Methods in Geotechnical Engineering contains the proceedings of the 8th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE 2014, Delft, The Netherlands, 18-20 June 2014). It is the eighth in a series of conferences organised by the European Regional Technical Committee ERTC7 under the auspices of the International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE). The first conference was held in 1986 in Stuttgart, Germany and the series has continued every four years (Santander, Spain 1990; Manchester, United Kingdom 1994; Udine, Italy 1998; Paris, France 2002; Graz, Austria 2006; Trondheim, Norway 2010). Numerical Methods in Geotechnical Engineering presents the latest developments relating to the use of numerical methods in geotechnical engineering, including scientific achievements, innovations and engineering applications related to, or employing, numerical methods. Topics include: constitutive modelling, parameter determination in field and laboratory tests, finite element related numerical methods, other numerical methods, probabilistic methods and neural networks, ground improvement and reinforcement, dams, embankments and slopes, shallow and deep foundations, excavations and retaining walls, tunnels, infrastructure, groundwater flow, thermal and coupled analysis, dynamic applications, offshore applications and cyclic loading models. The book is aimed at academics, researchers and practitioners in geotechnical engineering and geomechanics.
Anderson, Loren Runar et al "RIGID PIPES" Structural Mechanics of Buried Pipes Boca Raton: CRC Press LLC,2000 Figure 12-1 Procedure for conducting the three-edge-bearing (TEB) test on rigid pipes The load at failure per unit length of pipe is called the D-LOAD Figure 12-2 Rigid pipe showing (left) how the ring is forced to support the weight of backfill, W, if the sidefill soil is not compacted; and (right) the basis for the Marston load analysis ©2000 CRC Press LLC CHAPTER 12 RIGID PIPES Rigid pipes not deflect enough for deflection to affect soil pressure against the pipes The soil is a load on the pipes Rigid pipes include Portland cement concrete pipes (both reinforced and unreinforced) and vitrified clay pipes Other pipes may be rigid under certain conditions Cement mortar lined and cement mortar coated (CML/CMC) pipes perform as rigid pipes when buried in loose soil because pipe stiffness is relatively greater than soil stiffness In densely compacted soil, CML/CMC pipes may be flexible, or, according to some designers, may be semi-rigid Design of concrete pipes is described in the Concrete Pipe Design Manual, published by the Americ an Concrete Pipe Association [ACPA (1993)] Pipe strengths are specified by standards The ACPA has wisely left to the manufacturer the responsibility of making pipe that meets the standards In general, performance limit is longitudinal cracking of the pipe wall due to internal or external pressures INTERNAL PRESSURE DESIGN Designers often assume that concrete and clay can take no tension In fact, both can take tension Nevertheless, unreinforced concrete or clay pipes are usually not designed to take internal pressure because hoop strength is lost if longitudinal cracks form during curing or handling With tension reinforcement, rigid pipes serve well as pressure pipes Consider reinforced concrete pipes If performance limit is leakage, the reinforcing steel must be pre-tensioned (or post-tensioned) such that the concrete is in compression before internal pressure is applied When internal pressure is applied, the tensioned steel takes additional tension and stretches This relieves compression in the concrete The concrete will not leak until it begins to take tension Therefore, to avoid leakage, the steel must take the entire internal pressure Pre-tension force in the steel is, ©2000 CRC Press LLC T s = Pr/(1 + EsAs /EcAc) where Ts = P = r = Ac = As = σ = E = (12.1) tension in the steel per unit length of pipe, internal pressure, inside radius, area of concrete per unit length, area of steel per unit length, stress, modulus of elasticity A safety factor should be included High strength steel is cost effective Small diameter steel rods increase bond between steel and concrete Procedure specifications for the manufacture of prestressed pipe are usually left to the manufacturer The pipeline engineer writes performance specifications For typical reinforced concrete pipes, if Ac /As = 100 and Es/Ec = 5, the pre-tension force is Ts = 0.95Pr; or say, conservatively, T s = Pr With pressure, P, in the pipe, tensile force in the steel is doubled It is prudent to check maximum stresses in the concrete and steel: σc = Pr/Ac σs = 2Pr/As EXTERNAL PRESSURE DESIGN For rigid pipes, external pressure design is based on loads on the pipe — not stress or strain See Figures 12-1 and 12-2 The following analysis is historical and simplistic It is no longer proposed by ACPA, but is presented here as the basic rationale for analysis For design, APPLIED LOAD = ALLOWABLE LOAD (12.2) APPLIED LOAD = (Wl + Wd) (12.3) Variation of Lf from class C to class B is based on the width of the bedding For Class B bedding, width of bedding is 0.6(OD) For Class C bedding, width of bedding is 0.5(OD) Variation of Lf in class A is based on the percent of area of reinforcing steel: Reinforced As = 1.0%, Lf = 4.8 Reinforced As = 0.4%, Lf = 3.4 Plain As = 0, Lf = 2.8 Theoretical values of load factors are based on moments at A, which are: For the TEB load, MA = 0.318 Wf r For Class A bedding, MA = 0.125 Wf r For Class D bedding, MA = 0.293 Wf r Figure 12-3 Loadings on rigid pipes showing the three-edge-bearing test load (TEB) and the three soil loadings identified by the American Concrete Pipe Association, showing the original load factors, Lf, for each Wf = load at failure Failure is a longitudinal crack at point A ©2000 CRC Press LLC where Wl = live load on the pipe, per unit length of pipe, Wd = dead load, sf = safety factor, OD = outside diameter, ID = inside diameter, Lf = load factor, D-load is the load at failure in a three-edge-bearing test = F-load per unit length Lf = load factor, which is determined by the bedding and by steel reinforcing The three-edge-bearing (TEB) test is conducted as shown in Figure 12-1 The TEB load at failure is called the D-load In general, failure is the ultimate (maximum) load on the TEB test pipe However, in reinforced concrete pipes, failure is often defined as the TEB load at which longitudinal cracks open to a width of 0.01 inch The 0.01-inch crack came about in the 1930s when graduate student, Bill Schlick, was inspecting reinforced concrete culverts in order to evaluate their performance This task was assigned to him by his dean, Anson Marston, of the College of Engineering, Iowa State College, Ames, Iowa The only indication of inadequacy that Schlick could identify was cracking So he put a half-inch-wide strip of 0.01 steel shim stock in his pocket, and proceeded to classify adequacy on the basis of crack widths into which he could insert the 0.01-inch steel This became the standard It has proven to be better than happenstance Cracks less than 0.01 inch tend to close by autogenous healing; i.e., by continued hydration of the silica gel in the Portland Cement Cracks greater than 0.01 inch can possibly allow oxygen to reach and corrode the reinforcing steel In Equation 12.3, the live load Wl is the effect of live load on the top of the pipe due to surface live loads The wheel load is multiplied by an impact factor of 1.5 for highway loadings The dead load Wd is the vertical soil pressure on the pipe It is usually taken as the weight of the prism of soil over the pipe However, Figure 12-2 shows how the entire backfill load in a trench could be imposed on ©2000 CRC Press LLC the pipe if sidefill soil is not adequately compacted It is difficult to predict how much of the backfill load is imposed on the pipe Anson Marston pioneered load analysis The theoretical Marston load does not account for soil anomalies such as compaction of soil directly against the top of the pipe Arching action of the soil is ignored A soil arch is formed if the sidefill is compacted The soil arch supports much of the backfill in the trench At most, the pipe only has to support the prism of soil, γ H(OD), above it In fact, a compacted soil arch relieves the pipe of essentially all of the vertical pressure except for loose soil in the first lift above the pipe Soil arching can be assured by compacting sidefill up to one soil lift above the top of the pipe; but avoiding compacting the first lift directly over the pipe This result is backpacking, which protects the pipe from soil pressure concentration, and develops a soil arch ALLOWABLE LOAD = FAILURE LOAD (12.4) FAILURE LOAD is based on the three-edge-bearing test The three-edge-bearing load at failure is the Dload For unreinforced rigid pipes the D-load is the maximum load in lbs per ft of length of pipe For reinforced concrete pipes, the D-load is the load in pounds per ft of length of pipe per ft of ID When the pipe is buried, the soil load is less severe than the D-load Therefore, a load factor, Lf, increases the allowable soil load above the D-load pipe strength Figure 12-3 shows the four historical loads on rigid pipes At left is a parallel plate load which, for analysis, is tantamount to the TEB load The other three are assumed to be soil loads in service Horizontal soil support is neglected because the rigid ring does not deflect and develop passive soil support For each of the three bedding classes, theoretical failure load, Wf, is found from Appendix A In all cases, Wf is greater than D-load; therefore, Failure load, Wf for each bedding class is the Dload times its load factor, Lf Figure 12-4 Effect of diameter on load capacity on an equivalent beam that cracks at point A OD is an overly conservative beam length Figure 12-5 Backpacking, showing decreased vertical soil pressure on the ring, and limits of soil strength at the spring lines; i.e., active on the left and passive on the right ©2000 CRC Press LLC Example Sidefill soil support is to be included in the load factor for Class A bedding What is the revised theoretical load factor? From Figure 12-3, load factor Lf for Class A bedding is 2.546 The critical moment is MA = Wf r/8 Including sidefill support, soil pressure is the third case of Appendix A for which MA = Wf r(1K)/8 Sidefill support is at least active pressure for which K = (1-sinϕ)/(1+sinϕ) If ϕ = 30o, K = 1/3, and MA = Wf r/12, including sidefill support, the revised Lf = 3.820 The sidefill increases Lf from 2.546 to 3.820 — a significant 50% increase EVALUATION OF THE REQUIRED D-LOAD Taking load factors into account, the rationale for design of rigid pipes is the equating of applied load to allowable load; i.e., (Wl + Wd) = (D-load)Lf for non-reinforced pipes, and (Wl + Wd) = (D-load)Lf (ID) for reinforced concrete pipes Resolving these equations, the required D-loads for buried rigid pipes are: D-load = (Wl + Wd)/Lf UNREINFORCED RIGID PIPES D-load = (Wl + Wd)/Lf (ID) = P(OD)/(ID)Lf REINFORCED CONCRETE PIPES An additional margin of safety is provided by the ACPA definition of load, W, based on outside diameter In fact, the mean diameter or inside diameter is more nearly correct See Figure 12-4 Failure is a crack at A, due to a moment The clear span that causes the moment is ID, or possibly mean diameter — not OD For reinforced concrete pipes, the D-load is conservatively multiplied by ID — not OD or mean diameter (12.5) Example (12.5) P is the vertical pressure on the pipe Loads, W, are based on complex pipe-soil interactions such as pipe settlement vs soil settlement (positive or negative projecting pipe), compaction techniques, water table, bedding, etc W is further complicated by boundary conditions (trench vs embankment), imperfect trench conditions (compressible topfill), properties of the trench wall soil, tunnels (pipes jacked-into-place), etc Recognizing the complexity as well as the importance ©2000 CRC Press LLC of the soil loading, before 1993, the American Concrete Pipe Association (ACPA) published values for load factor, Lf , based on the ACPA classification of trench beddings shown at the bottom of Figure 123 Note how the load factors, Lf , are about the same as theoretical values The empirical ACPA load factors are based on the assumption that soil pressure on the top of the pipe is approximately uniform It is the bedding that causes pressure concentrations Most engineers assume that Class D bedding is impermissible, a term first proposed by Marston It is noteworthy that, in general, no safety factor is needed in Equations 12.5 Margins of safety are already in place — soil arching, horizontal support of the pipe by the sidefill, etc An effective way for the designer to capitalize on these margins of safety is to specify a select compacted embedment; and then to enforce it by inspection Experienced installers comply What height of soil embankment is allowable over a 24-inch vitrified clay pipe of standard strength if the soil weight is 125 pcf and the bedding is Class B? The nominal pipe size is 24 inches From Figure 12-3, the Class B load factor is 1.9 From Table 12-1, the standard strength is 2600 lb/ft Neglecting live load, and substituting values into Equation 12-5, the allowable height of soil is H = 19.76 ft; or say H = 20 ft Clearly, the effect of live load is negligible No safety factor is needed Backpacking The allowable load on a buried rigid pipe can be Table 12-1 D-LOADS—ASTM Standards for Rigid Pipe Manufacturers Table 12-1 is still used for some conservative pipeline design and analysis However, in its 1993 Concrete Pipe Technology Handbook, the American Concrete Pipe Association (ACPA) has abandoned the load factor concept in favor of an ASCE design procedure The ASCE procedure is based on tests and on finite element analysis that include sidefill soil support and boundary conditions — both pipe and trench — and on soil type and compaction, etc ©2000 CRC Press LLC doubled by backpacking Backpacking is compressible material against the pipe Styrofoam has been used Uncompacted soil has been used Bales of straw and leaves have been tried with questionable success The concept, called imperfect trench method, is that backpacking is similar to packing used to protect fragile products for shipment Organic material may be suspect, but uncompacted soil is effective Assuming that the embedment is cohesionless, soil failure (soil slip) is incipient if the ratio of maximum to minimum principal stresses is greater than K = (1+sinϕ)/(1-sinϕ), where ϕ = soil friction angle See cube, C, at the top of an imaginary soil vault in Figure 12-5 What is radius ρ at which σ x /σ y = 3, assuming that soil friction angle is 30o? The rationale is that a soil vault forms over the backpacking It is stable at such radius, ρ, that σ x < Kσ y But backpacking is needed to prevent soil particles from falling from the vault From Equation 12.5, ρ = 1.414r With a safety factor of two, a good rule of thumb for pipe protection is, The performance limit of a rigid pipe depends upon failure of the sidefill soil See the unit cube of soil B at the spring lines in Figure 12-5 Soil failure can be either active or passive If the horizontal pressure Px of the pipe against the soil at B is less than σy /K, the s oil slips at active resistance, and the pipe wall collapses inward This is shown on the left side of Figure 12-5 If the horizontal pressure, Px of the pipe against the soil at B is greater than σyK, the soil slips at passive resistance, and the pipe wall collapses outward This is shown on the right side of Figure 12-5 If the height of backpacking is equal to the OD, and the stiffness is half as great as the embedment, the pressure on the pipe is half of what it would be without the backpacking In Figure 12-5, half of the backpacking is shown above, and half below the pipe Accordingly, some designers conservatively specify half a diameter of backpacking above and below The compressibility should be no more than half the compressibility of the embedment In order to prevent passive soil slip at B, the embedment must not be excessively compressible The backpacking must retain soil arches over and under the pipe This rationale is conservative Another rule of thumb is, Height of backpacking should be at least half the pipe diameter Backpacking under the pipe is not necessary Backpacking permits twice the pressure P at top of the pipe For deep burial, maximum height of soil over the pipe can be doubled Example Using typical values, let backpacking pressure on top of the pipe be σ y /2 For embedment at the spring lines, K = What are the limiting ratios of horizontal to vertical soil pressure on the pipe under high cover? See Figure 12-5 For active soil pressure, RATIO = 2σx /σ y = 4/3; which is improbable because the rigid ring is usually stiff enough resist the 4/3 ratio of horizontal to vertical pressures For passive soil resistance, RATIO = 2σx/σ y = 6; which is impossible σ y /2 is less than σx The ring could not fail outward if σ y /2 on top is less than σx on the side Backpacking allows a broad range of tolerance MARSTON LOAD An alternate evaluation of height of backpacking is the classical equation for stresses around a hole with radial stress, σy, and tangential stress, σ x, σx/σ y = (ρ2+r2)/(ρ2-r2) ©2000 CRC Press LLC (12.5) In the analysis of soil loads on buried rigid pipes, the Marston load is still used by some pipeliners Consider a rigid pipe in a trench as shown in Figure 12-2 The load, W, is the weight of backfill in the trench minus the frictional resistance of the trench walls Figure 12-6 Comparison of soil pressures against rigid and flexible pipes Figure 12-7 Details of reinforced concrete pipes ©2000 CRC Press LLC Based only on soil friction angles, the evaluation of W is logical Less logical are assumptions, such as: rigid trench walls, no sidefill soil support, no pipe settlement, no soil arch over the pipe, etc Without soil arching, the load on the pipe continues to increase directly as the height of soil cover in-creases This relationship has limitations Marston provided adjustment factors, which are based on additional assumptions The imprecisions of soil properties, density, and placement, are usually greater than the precision achieved by applying adjustment factors For explanation of the Marston load, see Spangler (1973), Chapters 25 and 26 ACPA DESIGN PROCEDURE The above rationale for rigid pipe performance has been adjusted and refined by ACPA to respond to neglected factors, and to refine simplistic assumptions Sidefill support is now included, soil types are taken into account, etc COMPARISON OF SOIL PRESSURES ON RIGID AND FLEXIBLE PIPES Shown in Figure 12-6 are cross sections of a rigid and a flexible pipe The ring deflects 6% during backfilling Assuming elliptical deflection, hori-zontal pressure on the flexible pipe is Px = 1.5P Horizontal pressure on the rigid pipe is active pressure, P/3 The vertical pressure on top is greater than P, but not more than 2P One exception ob-tains if the first lift of soil over the pipe is heavily compacted against the pipe, leaving pressure concentration on top that could exceed 3P The pressure on the bottom is often more critical because of difficulty in placing soil under the haunches These problems are anticipated by designers Updated ACPA (1993) software are available REFERENCES ACPA (1993), Concrete Pipe Technology Handbook, American Concrete Pipe Association Spangler, M.G and Handy, R.L., (1973), Soil Engineering, 3ed, IEP ©2000 CRC Press LLC PROBLEMS 12-1 What is the Marston load on the rigid pipe of Figures 12-2 and 12-3 if the backfill soil is sand loosely dumped into place? Data are as follows: Pipe Trench OD = 36 inches, H = ft, ID = 30 inches B = ft Soil φ = 20o = friction angle, γ = 100 pcf What is the required pipe strength (D-load)? Assume that as soil is dumped into the trench, it slides in against the pipe and trench walls at active horizontal soil pressure; i.e., the horizontal soil stress is σy /K where K = (1+sinφ)/(1-sinφ) and φ = soil friction angle 12-2 A four-ft (ID) reinforced concrete pipe is to serve as a culvert under 2.5 ft of granular soil cover If sf is and bedding is Class B, what class pipe is required? t = 4.8 inches Performance limit is 0.01 inch crack Assume HS-20 dual-wheel load and soil unit weight of 120 pcf (Class IV) 12-3 Using a programmable computer for iterations, find the maximum allowable height of prismatic soil cover H, assuming γ = 125 pcf, for minimally reinforced concrete culvert as shown in Figure 12-7, with only one cage of circumferential #3 rebars spaced at inches in the center of the 6- inch-thick wall, and with 26 longitudinal #3 rebars equally spaced on the outside of the cage Properties of materials are listed on the Figure 12-4 Using a PC find the area of cage rebars per ft of pipe length required for balanced design of the pipe wall, i.e., σs/σ c = Ss /Sc in Problem 12-3 12-5 If soil is carefully placed and compacted under the haunches, what is the allowable height of soil cover in Problem 12-3 if full soil support of the ring is assured such that for the sidefill, the horizontal soil pressure is Px = Py /3? 12-6 Derive Equation 12.1 ... bedding For Class B bedding, width of bedding is 0.6(OD) For Class C bedding, width of bedding is 0.5(OD) Variation of Lf in class A is based on the percent of area of reinforcing steel: Reinforced... failure (soil slip) is incipient if the ratio of maximum to minimum principal stresses is greater than K = (1+sinϕ)/(1-sinϕ), where ϕ = soil friction angle See cube, C, at the top of an imaginary soil. .. cracks at point A OD is an overly conservative beam length Figure 12-5 Backpacking, showing decreased vertical soil pressure on the ring, and limits of soil strength at the spring lines; i.e.,