Numerical Methods in Soil Mechanics 25.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 "LONG SPAN STRUCTURES" Structural Mechanics of Buried Pipes Boca Raton: CRC Press LLC,2000 Figure 25-1 Two of many typical long-span structures — horizontal ellipse (top), and an inverted pear shape (bottom) to serve as a grade separation for a road over a railroad ©2000 CRC Press LLC CHAPTER 25 LONG SPAN STRUCTURES The term "Long Span" refers to corrugated steel pipes in large diameters The "pipes" are more often non-circular than circular The most common shapes are pipe arch, horizontal ellipse, low profile arch, high profile arch, underpass, and the inverted pear They serve as small bridges and grade separations The structure comprises corrugated steel plates (structural plates) that are bolted together on site The distinguishing feature is the low ring flexibility because of the large radii Moreover, because the plates are bolted together, ring flexibility is less than the theoretical values listed in the AISI Handbook of Steel Drainage & Highway Construction Products From one field test the actual ring stiffness was roughly 80% of theoretical For standard corrugated circular steel pipes, a maximum flexibility factor, FF, is recommended for handling and installation; i.e., FF = D2/EI (25.1) where E = modulus of elasticity = 30(106) psi, D = diameter; i.e., horizontal span (inches), I = moment of inertia of the wall (in 4/inch) From the AISI Manual, recommended maximum values of FF for ordinary installations are: FF = 0.0433 in/lb for factory-made pipe with riveted, welded, or helical seams FF = 0.0200 in/lb for field-assembled pipe with bolted seams in/lb At 80% of theoretical I, FF = 0.043 If the span is increased to 50 ft for this example, FF = 0.118 in/lb Fifty-foot spans are in service The success is based on careful installation For shapes other than circular, AISI publishes modification factors From principles of similitude, FF is not a correct property for buried pipes with distributed soil pressure agains t the ring FF is correct for a concentrated force on the ring which is more typical of handling loads than of buried soil pressures Some design procedures base ring flexibility on the Iowa formula See Appendix B They propose that the EI term (structure) in the denominator must exceed some recommended percentage of the 0.061E'r3 term (soil) This is intended to be minimum ring stiffness for soil-structure interaction In fact, the Iowa formula only predicts ring deflection — not a ring stiffness required for installation Of course, designers specify a maximum allowable ring deflection — but for other reasons than ease of installation Without an elaborate scaffold of stulls, struts, and ties to hold the shape of the structure during installation, a minimum ring stiffness is desirable So required ring stiffness is an economical trade-off with cost of installation The Iowa formula applies to circular rings Most long-span structures are not circular Nevertheless, as in the case of circular rings, the greater the stiffness, the less will be the care required to hold the structure in shape during installation Performance Limits Despite the maximum value of FF = 0.0200 for fieldassembled pipes long-span pipes can exceed 0.02 in/lb if embedment is carefully placed and c ompacted For example, for a 30-ft span of 6x2 structural plate with t = 0.218 inch; the theoretical I = 0.127 in3; and the flexibility factor is FF = 0.035 ©2000 CRC Press LLC The basic performance limits after installation are discussed in Chapters 9, 10, and 13 These include ring compression, soil support, minimum cover, etc But for very flexible long-span structures, additional precautions are required during installation Failures have occurred during construction of the structure and placement of the embedment Installation performance limits include: shape of the structure, unstable soil-structure interaction, and minimum soil cover Shape The structure must be held in shape during placement of the embedment soil Shape can be monitored by hanging plumb bobs inside at appropriate locations such as the crown, and at changes in radius of the plates Because plumb bobs are affected by wind, a laser beam is a better datum for monitoring the shape Measurements by steel tape at any angle from the laser beam to preidentified points on the structure can be monitored The cross section should be monitored at a number of stations throughout the length of the structure because corrugated structures can deflect longitudinally In the case of horizontal ellipses, and profile arches, the top radius is usually a circular arc of about 80o However, the arc angle can vary For pipe arches, the top arc angle is greater than 80o Installers resort to various techniques for holding the structure in shape during placement of the soil Once the structure is assembled on a plane surface bedding, it is essential that support be continuous a) Preshaping the bedding to fit the structure has been tried The procedure is tedious and imperfect Continuous support is not assured In some cases, the structure has been dragged longitudinally a few feet fore and aft to seat (preshape) the bedding b) Well-graded soil can be flushed under the structure from windrows of soil by means of highpressure jets (usually water — sometimes air) Laborers not respond enthusiastically to the requirement of ramming soil under the bottom plates with 2x4 studs c) Flowable soil cement is an increasingly popular option See Chapter 16 An alternate option is elimination of the bottom ©2000 CRC Press LLC plates which are replaced by footings See profile arches in Figure 9-1 The footings must be able to resist the thrust Pry due to pressure P on top of the structure where the radius is ry Because thrust Pry on the footings is at an angle, subbase support of the footings must take into account shear on, and overturning of, the footings, as well as vertical bearing capacity of the subbase Once the structure is bedded, soil is placed and compacted in lifts as described in Chapter 16, keeping soil lifts balanced on the sides of the structure in order to prevent sidewise movement Heavy compactors must be kept outside of the 45o tangent plane as described in Chapter 16 In spite of care in placing embedment, soil pressure on the sides of the structure causes the top of the structure to hump up (uplift) The uplift must be limited and controlled Manufacturers recommend allowable percentages of uplift during installation Part of the uplift can be reversed when soil is placed over the top of the structure — but don't depend on it Sidefill holds the structure close to its "uplifted" shape In some cases, the structure is stulled, strutted, and/or tied to hold it in shape during placement of embedment soil Care is required to prevent damage to the structure such as dents or perforations by stulls and struts when backfill is placed on top of the structure Tie wires (diagonal and horizontal) can be of such a gage that monitoring includes tension (or even the first break) in horizontal wires One project monitored tension in the tie wires by the pitch sound of the wire when plucked If the structure approaches the limits of its uplift, a windrow of soil can be placed (by crane) on top Or additional tie wires can be placed from the crown to the bottom plates or diagonally from the crown to the corner plates or footings Stability Embedment soil must be of good quality in order to assure performance during floods (high water table), earth tremors, excessive surface loads, etc Where groundwater is a problem, soil should have adequate strength (bearing capacity) both when saturated and when dry It must be dense enough that it will not liquefy by earth tremors These precautions are imperative for the small radii at the sides of horizontal ellipses and low profile arches The precautions are reversed for high profile arches, underpasses, and inverted pears Because of the large radius of curvature of the sides, a very small horizontal soil pressure can deform the structure During placement of sidefill, there is no topfill to resist uplift In such cases, horizontal struts can be placed in the structure to prevent horizontal deflection In some cases the side plates can be tied back to deadmen when deflection becomes significant If uplift begins to approach the maximum allowable during placement of sidefill, a windrow of soil placed on top of the structure can arrest or reduce uplift Any scaffolding (stulls, struts, ties) inside the structure should be removed after stability is achieved, but before high soil cover (topfill) is placed over the structure, and before heavy surface loads pass over The basic criterion for stability is minimum cover Of course, compaction of topfill directly over the structure must be done carefully See Chapter 16 Minimum Cover Stabilization of the structure is minimum soil cover to protect the structure from surface wheel loads Minimum cover is analyzed in Chapter 13 for circular flexible pipes The same analyses apply to long spans where the critical radius is the radius of the top plates For analysis by ring compression, the diameter, D, is the span Two additional concerns must be investigated: multiple axle loads and distribution of wheel loads on the structure a) Multiple axle loads can affect soil pressure distribution on top of the structure It may be prudent to analyze the effect of wheel spacing on axles — especially if the load could be moving ©2000 CRC Press LLC longitudinally along the pipe Wheel spacing might justify a finite element analysis or a Castigliano analysis with a more complex soil pressure diagram than was used for circular pipes in Chapter 13 b) In Chapter 13, critical pressure on the pipe due to surface live loads was based on the rationale that a truncated pyramid is punched through the soil cover The live load effect on the pipe was uniform pressure over half of the ring In the case of longspans, the top arch may be so large that the punched-through pressure area is smaller than the top arch More complicated analysis may be required Example An inverted pear was designed as a railroad grade separation Nomenclature and dimensions are shown in Figure 25-2 Data are: Structure: 6x2 corrugated sectional plate D = 28 ft = span, ry = 25 ft = top radius, σf = 36 ksi = steel strength, E = 30(106) psi elastic modulus, t = 0.218 = nominal steel thickness, A = 3.2 in 2/ft = wall cross-sectional area, I = 1.523 in4/ft = theoretical moment of inertia, from the AISI Handbook of Steel Drainage & Highway Construction Products, S = 1.376 in 3/ft = I/c Soil: γ = 100 pcf = soil unit weight, ϕ = 30o, H = ft of soil cover, Load: a) Find dual-wheel load, W, if it is assumed to be concentrated at midspan σ = PD/2A where P = Pd + Pl Pd = Pl = 300 psf dead load of soil cover, 0.12 W/ft2 = 0.477W/H2 by Boussinesq, Substituting values and solving, W = 66 kips If the wheel load is HS-20 load (16 kips), the safety 3' Figure 25-2 Nomenclature and dimensions for a long-span, pear-shaped structure to serve as a road grade separation The dimensions are used in the example and problems in this chapter This structure meets clearance requirements of the American Railroad Engineering Association (AREA) a) If the specified soil cover is ft, what is the allowable surface load, W, based on ring compression? ©2000 CRC Press LLC factor in ring compression is What about multiple axles? b) During installation, with compacted select soil cover of only ft, there arises a need for a dualwheel truck to pass over the structure What is the allowable dual-wheel load, W, based on slip of soil wedges? If the structure is not deformed, stiffness is negligible From the dimensions of Figure 25-2, soil pressures against the structure are as shown in Figure 25-3 (top) Critical soil wedges are shown in Figure 25-3 (bottom) Ignoring shear, the soil resistance at point C on the corner plates (shoulder) is 4.745 ksf = 33 psi Assuming that the dual tire print is 7x22 inches, and the truncated pyramid slopes at 1h:2v, the live load area at A is (7+24)(22+24) = 1426 in At punch-through, P = Pd + Pl = 1.39 psi + W/1426in Because Pr is constant all around the perimeter of a flexible structure, at the corner , C , Pc = 4.17P Substituting values and solving, W = 9.3 kips Allow an axle load of 18 kips to cross — with care and restraint of corners (shoulders) Safety Factor Fortunately, the concerns for long-span structures are worst-case Soil placement and compaction is usually done with care Analysis neglects longitudinal soil arching Neglected also, is the longitudinal beam strength of the corrugated structure Despite the accordion configuration of corrugations, the structure has some longitudinal strength Therefore, safety factors can be small In minimum cover tests, the punch-through load is greater by a factor of two than is predicted by soil slip analysis A surface load test was performed on a long-span structure, 6x2 corrugation, 0.218 structural plate, 12-ft top radius, with 20 inches of well-compacted select soil cover A single-axle dual-wheel load punched through when the axle weight was finally raised to 168 kips Failure was catastrophic ©2000 CRC Press LLC PROBLEMS 25-1 What is the maximum dual-wheel load at soil slip for the above example of a pear-shaped structure if soil cover is assumed to be the specified minimum H = ft? The tire print is 7x22 inches a) Check ring compression at A, b) Ring compression at maximum span, c) What is load, W, at minimum cover? (W = 7.6 kips) 25-2 Problem 25-1 considers only the top arch Now consider the corner (shoulder) plates of ft radius What is the maximum dual-wheel load, W, if the shoulder plates are supported by soil of 100 pcf and friction angle of 30 o? Analyze for both horizontal equilibrium and vertical equilibrium Include the hold-down force of the top arch on the shoulder plates (W = 1.6 kips) 25-3 A long-span ellipse is a bridge over a stream During a flood, the bridge is partially plugged, causing the water table to overflow the road surface What must be the friction angle of the granular soil at the spring lines when an HS-20 dualwheel load of 16 kips passes over? See sketch Inside the ellipse is essentially empty (ϕ = 32.6o) Figure 25-3 Pear-shaped long-span showing soil pressures (top) and the pressure diagrams for the soil wedge slip analysis (bottom) The soil cover of H = ft is less than minimum in this example ©2000 CRC Press LLC ... 0.061E'r3 term (soil) This is intended to be minimum ring stiffness for soil- structure interaction In fact, the Iowa formula only predicts ring deflection — not a ring stiffness required for installation... soil- structure interaction, and minimum soil cover Shape The structure must be held in shape during placement of the embedment soil Shape can be monitored by hanging plumb bobs inside at appropriate... footings must take into account shear on, and overturning of, the footings, as well as vertical bearing capacity of the subbase Once the structure is bedded, soil is placed and compacted in lifts