Numerical Methods in Soil Mechanics 16.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 "EMBEDMENT" Structural Mechanics of Buried Pipes Boca Raton: CRC Press LLC,2000 Figure 16-1 Embedment showing a compacted soil arch that supports load and protects the pipe Figure 16-2 Densely compacted "pedestal" of soil on top of a pipe showing the tendency to concentrate the Marston load on the pipe ©2000 CRC Press LLC CHAPTER 16 EMBEDMENT The soil in which a pipe is buried is not just load on the pipe Soil is a major component of the pipe-soil structure Following are a few basic concepts that are useful in evaluating the contribution of soil to the struc-tural performance of buried pipe-soil structures Most undisturbed native soils are stable — even low-strength soils They have settled in place; and, except for earthquakes and landslides, provide a stable medium in which to bury pipes Difference in weights of pipe and soil is usually not great In saturated soil, most pipes tend to float rather than sink The best buried pipe installations are those which disturb the native soil the least A bored tunnel of exact pipe OD into which the pipe is inserted, would cause the least disturbance Microtunneling shows promise, with bore slightly greater than inserted pipe A common installation is a narrow trench with only enough side clearance to align the pipe and to permit placement of em-bedment Regardless of trench width or shape, the embedment is a transfer medium that fits the pipe to the trench and stabilizes pipe-soil interaction Arching action of the soil helps to support the load See Figure 16-1 The soil acts like a masonry arch No cement is needed because the soil is confined in compression Soil protects the pipe In order to create a soil arch, the bedding must be compacted Bedding provides abutments for the s oil arch The sidefill is the soil arch It must be compacted up and over the pipe If mechanical compactors are used, the soil arch should be compacted in lifts of less than one ft on alternate sides of the pipe so that the compaction surfaces are at the same elevation — balanced lifts Soil should not be "pounded" directly on top of the ©2000 CRC Press LLC pipe See Figure 16-2 To so is to create a pedestal that concentrates a Marston load on the pipe The Marston worst-case load can be avoided by compacting a soil arch Full contact of embedment against the pipe should be achieved in order to: a) eliminate voids which could become channels of groundwater flow along the pipe (under the haunches), and, b) reduce concentrations of soil pressure against the pipe As in all structural design, the buried structure has the basic objective of adequate performance at minimum cost Minimum cost is a trade-off between the cost of the structure and the cost of installation Installation costs include: a select soil envelope if required; soil compaction, excavation, alignment, thrust restraints, cross-sectional shape control, etc Of course, the project cost also includes liability, risk, service life, maintenance, repairs, replacement, overhead, insurance, bonds, etc At one extreme, an all-welded, non-corrosive, noncollapsible pipe could be designed which would require no installation costs beyond excavation and backfilling by shoving-it-in The cost of such a pipe is usually enormous At the other extreme, a very low-cost pipe could be designed to just resist internal pressure But the pipe might be so flimsy that the embedment would have to be laid up particle by particle like a masonry arch The masonry arch would carry the loads and protect the flimsy pipe The pipe might have to be retained by mandrels or struts, in order to provide a form for laying up the soil arch The pipe is a liner for a masonry conduit The cost of such installation would be enormous Somewhere between these two extremes is a minimum cost point Pipe costs are available from manufacturers Cost figures for the soil embed- ment and its placement require analysis by the design engineer The basic soil property for embedment is density For select embedment such as pea gravel, compaction can be achieved by merely moving the gravel into place in contact with the pipe For poor embedment, mechanical compaction may be required, and often a slow period for drying the soil to optimum moisture content for compaction Following are suggestions for design of the embedment COMPACTION TECHNIQUES The importance of soil compaction cannot be overemphasized In soil cell tests, the ring deflection of flexible pipes ft in diameter, in an embedment of loose silty sand, was reduced to approximately half by merely stomping soil under the haunches Ring deflection is direc tly related to vertical soil compression Under a given vertical soil pressure, loose soil compresses more than five times as much as compacted soil Below the water table, soil density can be critical At less than critical density, relative shifting of soil particles due to soil movements (vibrations, tremors), tends to "shake down" the soil grains into a smaller volume If this loose soil is saturated, the volume decrease of the soil skeleton leaves only the non-compressible water to carry the loads The soil mass becomes liquefied and the pipe may collapse On the other hand, at greater than critical density, any shifting of soil particles only tends to "shake-up" soil grains such that the soil volume tries to increase But the confined, saturated embedment cannot increase in volume Consequently, intergranular stresses increase, and the shearing strength increases Depending on the soil type, critical density is no more than 85% (AASHTO T-99 or ASTM D698) Below the water table, it is usually prudent to compact the soil to a density above critical Ninety percent density is often specified to add a margin of safety The sidefill should be placed in balanced lifts to retain the cross section and alignment of the pipe ©2000 CRC Press LLC A caveat is suggested in the use of water to compact the soil The soil must be free-draining and must be dewatered such that seepage stresses help to compact the soil Flotation of the pipe must be avoided Another caveat applies to all compaction techniques As the size of buried structures increases, contractors are prone to extrapolate those installation techniques they have learned by experience with smaller structures Installation techniques cannot be scaled-up so simply An ant can carry many times its own weight An elephant cannot carry a load equal to its weight A whale cannot carry itself, but must be buoyed up by water From the similitude of scale-up, the unit weight of soil varies with length scale ratio See Appendix C For example, suppose a contractor has experience in backfilling 6-ft-diameter flexible pipes with no difficulty and less than 2% ring deflection Now he is to backfill a 12-ft-diameter pipe To scale-up to 12-ft from his 6-ft pipe experience, he must imagine that the soil he placed around the 6-ft pipe weighed twice as much — like iron filings or ball bearings Clearly, he would have to be more careful when installing the 12-ft pipe to control ring deflection Following are techniques for compacting soil Select Embedment Carefully graded select soil falls into place at densities greater than critical density The only requirement is to actually move the soil in against the pipe — including that hard-to-reach zone under the haunches — in order to achieve intimate contact between embedment and pipe Jetting Soil density greater than critical can be achieved by jetting This technique is particularly attractive for soil compaction about large buried structures Soil is placed in high lifts, such as to ft, or to the spring line (mid-height) of large diameter pipes A "stinger" pipe (1 inch? diameter, and or ft long, attached to a water hose) is injected vertically down to near bottom of the soil lift A high-pressure water jet moves the soil into place at a density greater than critical if the soil is free-draining and immediately dewatered Jet injections are made on a grid every few feet Five-ft grids have been used successfully for 5- or 6-ft lifts of cohesionless soil Gang jets can be mounted on a tractor See Figure 16-3 They can be injected into a lift of sidefill up to the spring line In order to fill holes left when jets are withdrawn, the stingers are vibrated A second lift up to the top is jetted in a similar manner The technique works well in sand Flushing Soil densities greater than critical can be achieved if soil is moved by a high-pressure water jet (fire hose) used to flush soil down a slope into place against the pipe This method is shown schematically on the right side of Figure 16-3 where a windrow of soil is placed adjacent to the pipe A laborer with a highpressure water jet plays the stream onto the inside slope of the windrow until a soil slide develops This soil slide can be directed by the jet into place against the pipe with enough energy to fill in the voids Of course, the water must drain out rapidly for best compaction Windrows are added on both sides simultaneously in order to keep the soil in balance This method is very effective in mountain soils that were deposited by the flushing action of tumbling stream flow Ponding (Flooding) The least effective method (yet often adequate) for compaction is ponding or flooding A lift of freedraining soil is placed up to the spring line of the pipe, then the soil is irrigated Enough water must be applied that the lift of soil is saturated The soil should be free-draining and must be dewatered to settle the soil The pipe must not float out of alignment A second lift to the top of the structure, and ponded, is often specified The compaction mechanism is downward seepage stress which compacts the soil Soil is washed into voids and under the haunches of the pipe High-Velocity Impact Soil compaction as well as controlled placement can ©2000 CRC Press LLC be achieved by blowing, slinging, or dropping the soil into place With the proper gradation of soil particle size, and with the proper amount of water, the soil has the consistency of concrete If this "concrete" is dropped from an adequate height, it will flow by impact under the haunches of the pipe It sets up like low-grade concrete Air-dry cohesionless soil will ricochet and tumble under the haunches, at uniform density, if dropped from sufficient height See Figure 16-4 Better control is achieved if the embedment is "shot-creted" into place or if dry soil is blown or slung into place Vibration Loose soil can be compacted by vibrating it with vibroplates and vibrating rollers on each soil lift Some compaction of the embedment can be achieved by vibrating the pipe itself Concrete vibrators are designed for placement of concrete The purpose is to "flow" the concrete into voids, and to remove air pockets Concrete vibrators are effective in placement of embedment around pipes if enough water is mixed with the soil to form a viscous mix like concrete The contractor may saturate a lift of sidefill and then settle it with concrete vibrators This technique places, but does not compact, the soil Saturated soil is noncompressible; therefore, "non-compactable" A method called saturated-internally-vibrated (SIV) is the vibration of the saturated embedment by concrete vibrators The method is expensive If the soil is not free-draining, particles flow into place, but settle only under buoyant weight The result is the same as ponding The soil gradation must be controlled just as concrete aggregate is controlled Flotation must be avoided Soil Cement (Flowable Fill) and Slurry Under some circumstances, the best way to assure support under the haunches is by flowable fill (soil cement or slurry) The pipe is aligned on mounds Flowable fill is poured into the haunch area on one side of the pipe Full contact is assured when the flowable fill rises on the other side of the pipe Figure 16-3 Compaction of backfill by jetting (left) and by flushing (right) Figure 16-4 Soil compaction by high-velocity impact (drop) ©2000 CRC Press LLC Recommended slump is about 10 inches or a flowability of 12-inch diameter Flowable fill can be mixed on site, or grout can be delivered in ready-mix trucks The minimum height of flowable fill is about 60o of bottom arc (say D/10) above which the angle of repose of embedment fills in under the haunches If flowable fill is required to a depth greater than flotation depth, it can be poured in lifts Some agencies specify compressive strength of 200 psi Less strength (40 psi?) may be desirable to reduce stress concentration, and to facilitate subsequent excavations Flowable fill should not shrink excessively However, cracks not cause distress of the pipe Mechanical Compaction Mechanical compaction of the soil in lifts (layers) is an effective method for compaction Mechanical compactors densify the soil by rolling, kneading, pressing, impacting, vibrating—or any combination Sales instructions are available on mechanical compactors and on procedures such as optimum heights of soil lifts, moisture content, etc Efficiencies of various compactors in various soils have been studied In order to retain shape and alignment of the structure, heavy equipment (compactors, loaders, scrapers, etc.) must not operate close to the structure — especially flexible structures LIGHT AND HEAVY EQUIPMENT ZONES If the buried structure is so flexible that heavy compactors can deform it, then only light compactors can be used close to it Especially vulnerable are flexible structures with a large side radii such as an acorn-shaped railway underpass and egg-shaped sewer Heavy compactors must remain outside of planes tangent to the structure and inclined at an angle less than 45o + ϕ/2 from horizontal See Figure 16-5 Soil cover, H, greater than minimum is required above the structure The heavy equipment zone is often specified as shown on Figure 16-5 Operators should be reminded that a large structure gives a false illusion of strength It ©2000 CRC Press LLC achieves its strength and stability only after the embedment has been placed about it Because the structure cannot resist high sidefill pressures during soil placement, operators should think, "If it were not there, how far back from the edge of the sidefill would I keep this equipment in order not to cause a soil slope failure?" The answer is found from experience and from the tangent plane concept A margin of safety is usually applied to the 45o+ϕ/2 plane by specifying a 45o tangent plane The minimum cover, Hmin, for various types and weights of equipment can be determined by the methods suggested in Chapter 13 As a rule of thumb, the minimum soil cover should not be less than ft for H-20 truck loads, D8 tractors, etc For scrapers and s uper-compactors, ft of soil may be a more comfortable minimum TRENCH WIDTH The trench only needs to be wide enough to align the pipe and to place embedment between pipe and trench wall If ring deflection is excessive, or if the pipe has less than minimum soil cover when surface loads pass over, the soil at the sides can slip Ring inversion is incipient If there is any possibility of soil liquefaction, the embedment should be denser than critic al density With a margin of safety, 90% standard density (AASHTO T-99 or ASTM D698) is often specified In loose saturated soil, liquefaction can be caused by earth tremors Soil compaction may or may not be required depending upon the quality of the embedment For example, gravel falls into place at densities greater than 90% Loss of embedment (piping) should be prevented Piping is the wash-out of soil particles by groundwater flow The Marston load on a pipe is the weight of backfill in the trench, reduced by frictional resistance of the trench walls The narrower the trench, the lighter is the load on the pipe The pipe has to be strong enough to support the load Marston neglected the strength contribution of the sidefill — both horizontal support of the pipe, and vertical support of backfill Trenches are kept narrow for rigid pipes Figure 16-5 Light and heavy equipment zones during the placement of backfill soil showing, of particular concern, the light equipment zone into which no heavy equipment is allowed Figure 16-6 Infinitesimal soil cube, B, at spring line, showing conditions for soil slip when Px = Kσ y ©2000 CRC Press LLC When flexible pipes came on the market, Spangler observed that a flexible ring depends upon support from sidefill soil His observation led to the inference that, if the trench is excavated in poor soil, the trench walls cannot provide adequate horizontal support The remedy appeared to be wider embedment (a wider trench) especially in poor native soil In fact, a wide trench is seldom justified — either by experience or by principles of stability From Chapter 9, P xr x = Pyry If the deflected ring is elliptical, ry /rx = (1+d)3/(1-d)3 When ring stiffness is taken into account, Pxrx is less than Pyry The contribution to the support of load P by ring stiffness can be included in the analysis if ring deflection is significant But ring stiffness is ignored in conservative flexible pipe design As long as the ring is circular, theoretically, the embedment needs little horizontal strength Practically, good sidefill adds a margin of safety See Figure 16-6 where the infinitesimal soil cube B is in equilibrium as long as pipe pressure Px does not exceed sidefill soil strength, σx For stability, Px < σ x = Kσ y (16.1) where K = (1+sin φ)/(1-sin φ), and φ is the friction angle at soil slip If sidefill soil is granular and denser than critical, its friction angle is no less than 30°, for which K = From Equation 16.1, the safety factor against soil slip is no less than three because Px = P Example Suppose the trench walls are poor soil; with blow count less than four What should be the trench width for a flexible pipe? See Figure 16-7 If the friction angle of sidefill is φ = 35°, then the soil shear plane is at angle (45°-φ/2) = 27.5° and P x is transferred to the trench wall by a soil wedge with 1:2 slopes as shown If ring deflection is less than 5% and the width of sidefill is half the pipe diameter, the pressure on the trench wall is about P/2 as ©2000 CRC Press LLC shown, and can be supported by trench walls with a blow count less than four The trench width in poor soil does not need to be greater than twice the diameter of the flexible pipe The margin of safety is increased by: stiffness of the ring, shearing resistance of soil on pipe, and arching action of the soil Both ring stiffness and ring deflection can be included in the analysis of Px, if greater accuracy is required In fact, the pressure, P/2 on the trench wall of Figure 16-7 is only approximate According to both Boussinesq and Newmark, pressure on the trench wall is not uniform, and the maximum pressure is 0.7P But these elastic analyses not represent either particulate mechanics or passive resistance at punch-through Moreover, from experiments, the soil wedge of Figure 16-7 does not remain intact during punch-through It is sheared into three wedges as discussed in Chapter 17 As long as the pipe is nearly circular, in poor native soils, the trench does not need to be wider than half a diameter on each side for both rigid and flexible pipes If ring deflection of a flexible pipe is no more than 5%, the effect of ring deflection can be neglected On a rigid pipe Pd is the Marston load (Marston 1930) On a flexible pipe, Pd is more nearly the prism load, γ H (Spangler 1941 and 1973) Dead load is roughly three-fourths as great on a flexible pipe as on a rigid pipe The height of soil cover, H, is not a pertinent variable in the analysis of trench width As soil load is increased, the pressure on the pipe increases; but the strength of the sidefill soil increases in direct proportion See Equation 16.1 A good rule of thumb for width of sidefill is: In poor soil, specify a minimum width of sidefill of half a diameter, D/2, from the pipe to the walls of the trench, or from the pipe to the windrow slopes of the embedment in an embankment See Figure 16-8 In good soil, width of sidefill can be less, provided that the embedment is placed at adequate density Figure 16-7 Approximate punch-through soil wedge showing how pressure P is transferred to the trench wall where it is distributed and reduced by roughly half in a trench of width 2D Figure 16-8 Cross-sectional sketch showing how the recommended width of embedment cover is D/2 for both trench and embankment if the installation is in poor soil ©2000 CRC Press LLC Soil Particle Migration Following are five concerns for embedments: Wheel loads over a pipe with less than minimum soil cover, Water table above the pipe, and/or vacuum in the pipe, Migration of soil particles out of the embedment, Voids left by a trench shield, or sheet piling, Embedment on a sidehill Wheel Loads Figure 16-9 shows a wheel load on a pipe with minimum soil cover The angle of punch-through in cohesionless soil is about 1h:2v The punch-through is approximately a truncated cone for a single tire, or a truncated pyramid for a dual wheel Vertical pressure on the pipe is P = Pd+Pl where Pd = γ H, is dead load, and Pl is live load Pl = Q/(B+H)(L+H) for load, Q, on a rectangular tire print area, LxB (about 22x7 inches for HS-20 dual wheel) Sidefill soil strength must support the pipe under this live load However, minimum cover of compacted granular soil is about H = ft for HS-20 dual wheel, and H = ft for the single wheel of a scraper Manufacturers of large steel pipes with mortar linings recommend that a margin of safety of 1.5 ft be added to the minimum cover Recommended minimum cover is 2.5 ft for HS-20 loads and 4.5 ft for scraper wheel loads With soil cover greater than minimum, wheel load pressure is less than Pl = W/2H2 In fact, a soil arch will support wheel loads Punch-through does not occur Trench width could be critical — but only if the sidefill embedment were so poor that it could not support wheel loads anyway Water Table See Figure 16-10 When the water table is above the pipe, sidefill soil strength is effective (buoyant) strength, σ x = K σ y The effective vertical soil stress is σy = σ y - u, where u is the pore water pressure; i.e., u = γ wh, where γ w is the unit weight of water and h is the height of the water table (head) above the spring line of the pipe If the pipe tends to float, for analysis, P is the hydrostatic buoyant pressure on the bottom of the pipe, P = γ w(h+r), rather than soil pressure on top ©2000 CRC Press LLC Soil particle migration is generally a function of either: a) groundwater flow that washes trench wall fines into the voids in a coarser embedment; or, b) wheel loads and earth tremors that shove or shake coarser particles from the embedment into the finer soil of the trench wall If fines migrate from trench wall into embedment, the trench wall may settle, but the pipe is unaffected If embedment particles migrate into the trench wall, the shift in sidefill support may allow slight ring deflection This could occur only if the trench wall soil is loose enough, or plastic enough, that the embedment particles can migrate into it Soil particle migration is unusual, but must be considered Remedies include: a) embedment with enough fines to filter out migrating particles in groundwater flow; and, b) trench liners Geotextile liners may be required under some circumstances Trench Box (Voids in the Embedment) Soil should be in contact with the pipe in order to avoid piping (channels of groundwater flow) under the haunches Voids are avoided if the embedment is flowable fill — a good idea when trench widths are too narrow for placement of soil under the haunches Flexible pipes tend to squat slightly into the bedding The increased radius of the bottom, ry , must neither be great enough to cause spalling of the mortar lining, nor great enough that the relationship Pyry = Pxrx causes Px to exceed sidefill support capability Constructors have clever ways to "chuck" soil down under the haunches: J-bar it, or vibrate it, flush it, etc It is sometimes proposed that the bottom of the trench be shaped to fit the pipe But the effort does not justify the cost and does not assure uniform support Voids left by the withdrawal of sheet piling or trench shield not affect the pipe if the tips of the piles or shield are above the spring lines of the pipe See Figure 16-11 Sidehill Embedment Figure 16-12 shows a pipe on a sidehill What is Figure 16-9 Dual-wheel load passing over a pipe buried under minimum soil cover showing a sidefill wedge at incipient soil slip Figure 16-10 Free-body-diagram of an empty flexible pipe buried below the water table ©2000 CRC Press LLC Figure 16-11 Comparison of soil slip planes when a trench box is withdrawn from trench bottom (left side) and springlines (right side) where soil slip planes are above the pipe and have no effect on the pipe Voids in the sidefill can occur and cause ring deflection if the trench box is at the bottom of the trench Figure 16-12 Pipe buried on an infinite slope of cohesionless soil, showing the infinitesimal cube for conjugate stresses and the resulting diagram of approximate stresses on the ring ©2000 CRC Press LLC the minimum soil cover for stability? Cement stabilized soil may be one remedy Assume that the pipe is flexible With no cover H, the soil slope would slide into the flexible pipe From Rankine's analysis of conjugate axes, F/P = K = cosi - (cos 2i - cos 2φ)1/2 cosi + (cos 2i - cos 2φ)1/2 (16.2) Soil pressures on the ring are shown at the left of Figure 16-12 Py is based on prism load More reasonable is a wedge load lifted by the ring Average Px = γ K(H+r) It acts slightly below the spring line Using prism load, for ring stability γ Hcos 2i = γ K(H+r), from which, H(cos 2i - K) = Kr (16.3) Example For a worst case, assume that angle i is the angle of repose of the slope which is nearly equal to the soil friction angle, φ Let φ = 30o = i K = 1, and, H = -r/sin 2φ H goes negative The flexible ring is unstable More reasonable is an uplifted wedge load But the height, H, of the wedge is unknown A value for the load is assumed — say Py = γ Hcos 2φ Substituting into Equation 16.3, H = 2r = D From this H, the wedge load can be calculated to see if it is twice the prism load as assumed Not many iterations are justified because the assumptions are loose If angle i is less than angle of repose, φ = 30o, then typical results for the conservative prism load would be: For i = 20o, H = 5.7r For i = 10o, H = 1.9r These are improbable upper limits, for this worstcase scenario Iteration for wedge loads would result in lower, more reasonable, values of H Any ring stiffness would further reduce the values of H Example How much live load, Pl, (in addition to dead load) can a flexible pipe resist if, for the embedment at slip, K = (1+sin φ)/(1-sin φ) = 2? At the spring line, ©2000 CRC Press LLC the vertical soil pressure is no less than the weight of soil, i.e., σz = γ (H + D/2) If the flexible pipe ring remains circular, the horizontal pressure against the soil at soil slip is 2γ (H + D/2) If the circular ring is perfectly flexible, vertical soil pressure on the top of the pipe is equal to the horizontal pressure and is also 2γ (H + D/2) Dead load pressure on the top of the pipe is γ H So the pipe is capable of resisting a live load of Pl = 2γ (H + D/t) - γ H = γ (H + D) REFERENCES Marston, Anson (1930) The Theory of External Loads on Closed Conduits in the Light of the Latest Experiments Bul 96, Engr Exp Sta., Iowa State College Spangler, M.G (1941) The Structural Design of Flexible Pipe Culverts Bul 153, Engr Exp Sta., Iowa State College Spangler, M.G and R.L Handy (1973) Soil Engineering, 3ed Intex Educational Publishers Watkins, R.K and M.G Spangler (1958) Some characteristics of the modulus of passive resistance of soil: A study in similitude Proceedings, Highway Research Board 37, 576 PROBLEMS 16-1 What will be the increase in ring deflection of a very flexible pipe when the trench shield is pulled ahead after the pipe has been embedded and backfilled with dry sand to a height above the pipe of about H = 1+ meter? The pipe is meters in diameter, in a trench 2.6 meters wide, with vertical trench walls shored up by a shield with walls 100 mm thick The shield walls reach the level of the bottom of the pipe The angle of repose (soil friction angle) is 30o Soil unit weight is 120 pcf 16-2 For the flexible pipe of Problem 16-1, what is the horizontal pressure against the trench walls at the level of the spring lines? 16-3 At one location, a flexible storm drain happens to be embedded in soft clay at the sides (sidefill) See the sketch below, Figure 16-13 By analyzing the free-body-diagram of an infinitesimal cube of clay at the spring lines, what is the safety factor against collapse of the pipe due to sand backfill above the pipe? Surface loads are not anticipated The drain keeps water out of the sand backfill Pipe: Diameter = 24 in., Pipe stiffness = Clay: Unit wt = 120 pcf, Cohesion = 100 psf, ϕ = Backfill: Specific gravity = 2.7, Void ratio = 0.4, ϕ = 30° 16.4 What is the diameter of pipe in Problem 16-3 at incipient collapse of the ring vertically? Assume that the height of cover of the backfill sand is still meters Assume that: Trench: Depth = ft (H = ft) Figure 16-13 Cross section of a very flexible pipe embedded in clay (left), and the Mohr circle for the clay (right) ©2000 CRC Press LLC ... tries to increase But the confined, saturated embedment cannot increase in volume Consequently, intergranular stresses increase, and the shearing strength increases Depending on the soil type,... ponding or flooding A lift of freedraining soil is placed up to the spring line of the pipe, then the soil is irrigated Enough water must be applied that the lift of soil is saturated The soil. .. actually move the soil in against the pipe — including that hard-to-reach zone under the haunches — in order to achieve intimate contact between embedment and pipe Jetting Soil density greater