Numerical Methods in Soil Mechanics 24.PDF

Numerical Methods in Soil Mechanics 24.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 "LEAKS IN BURIED PIPES AND TANKS"

Structural Mechanics of Buried Pipes

Boca Raton: CRC Press LLC,2000

Figure 24-1 Response (flattening) of a flexible ring due to a hard spot in the embedment.

Figure 24-2 Joggle joint weld showing longitudinal leverage due to an external force that causes a hinge to form and rotate

CHAPTER 24 LEAKS IN BURIED PIPES AND TANKS

Performance limits for buried structures are

excessive deformations One such deformation is a

leak Because of leaks, not only is product lost, but

the soil (or the product) may become contaminated

Craters and landslides have been caused by major

leaks Gas and oil spills and fires could be the

consequences of leaks in fuel lines and fuel tanks

Leaks may occur at gasketed joints due to pinched

gaskets or rolled gaskets, or due to grit under

gaskets Leaks may occur through cracks A leak

in a high-pressure pipeline is a fluid jet that can

backwash sand against the pipe, sand-blast the pipe,

wear through the pipe wall from the outside, and

cause a blow-out Because the cylinder is in contact

with embedment, deformation of the cylinder is

concomitant with movement of the soil — soil slip or

soil compression The soil provides support for

vertical loads and for the cylinder But poor soil

carelessly placed, like a misfit shoe, stresses the

cylinder Installers of buried pipes and tanks use

techniques that minimize deformation of the cylinder

The track record of the installer is important Some

buried fuel tank agencies now require certification of

installers

WELDS IN TANKS

If a pressure-tested cylinder leaks after it is buried,

the leak is due possibly to deformation of a weld

such as a flat spot or a leverage hinge See Figures

24-1 and 24-2 Deformations that cause weld

fractures are usually local and usually occur in the

cylinder Analysis is similar for both pipes and

tanks, but because tanks are more complicated, the

following examples involve tanks

If collapse is the performance limit, heads stiffen the

shell enough that walls are typically thinner in tanks

than in pipes Consequently, under identical burial

conditions, tank shells are more sensitive than pipes

to local deformations caused by non-uniform loads

A comparison of the sensitivities of tank shells and pipes requires similitude of the model and prototype

It is then possible to compare the pressures at equivalent deformations These pressures are inverse measures of sensitivity Let the tank be the

prototype and the pipe be the model Relative

sensitivity indicates the level of care required for handling and installing a prototype tank based on a model pipe experience

Similitude

Similitude is achieved by writing the equation of deformation in terms of dimensionless pi-terms; and then by equating corresponding pi-terms for shell and pipe See Appendix C The pressure that causes critical deformation is a function of the following pertinent fundamental variables

Fundamental variables:

P = external pressure on the tank,

Q = external force on the tank,

d = any and all deflections or movements,

S = yield strength of the wall,

E = modulus of elasticity,

E = 30(106) psi for steel,

D = mean diameter,

r = radius,

w = width of joggle joint overlap,

x = transition length from maximum to

minimum radius of curvature,

I = moment of inertia of the wall cross

section,

I = t3/12 for the plain wall tank cylinder,

L = length of the tank,

t = thickness of the shell,

V = head shear force,

s = normal stress,

t = shearing stress,

n = Poisson ratio = 0.25 for steel

Subscript, r, refers to ratio of model to prototype Pertinent dimensionless pi-terms are:

(P/E) = external pressure term,

(d/r) = deformation term,

(r/t) = ring flexibility term,

(L/r) = length term for the tank,

(rr) = ratio of maximum radius to minimum

radius at flat spots or out-of-roundness,

(1-n2) = 15/16 = Poisson term, where

n = Poisson ratio (assume 1/4),

(d) = ring deflection = ratio of decrease in

vertical diameter to original diameter

Following are the sensitivities of a prototype steel

tank and a model pipe for two cases: without soil

support, and with soil support

I Without soil support

Deformation is collapse under uniform external

pressure The classical equations are:

TANK:

(P/E)(L/r)(r/t)5/2 = 0.8/(1-n2)3/4 = 0.84 (24.1)

PIPE:

(P/E)(r/t)3 = 1/4(1-n2) = 0.234 (24.2)

CORRUGATED PIPE:

(P/E)(r3/I) = 3/(1-n2) = 3.33 (24.3)

Example 1

For a particular steel tank, L/r = 42ft/4.5ft, and r/t =

54in/0.1875in Its collapse pressure is to be

compared with a corrugated steel pipe for which r =

78 inches and I = 0.938 in4/ft What is the relative

sensitivity; i.e., ratio of pressures, Pr, at collapse

From the quotients of Equations 24.3 and 24.1, Pr =

8.24 The pressure at collapse of the pipe is eight

times as great as the pressure at collapse of the

tank Without soil support, the prototype tank is

eight times as sensitive to collapse as the pipe The

heads of the tank provide significant stiffness, but a

good soil embedment is essential

II With Soil Support Sensitivity is deformation of the ring due to a hard spot in the soil See Figure 23-1 From Appendix A, localized ring deformation is of the form, d = kQr2/EI, where Q is the concentrated force, k is a constan t , a n d r2/EI is the flexibility factor — a handling factor with upper limits recommended by AISI (1994) In dimensionless parameters, (d/r) = k(Qr/EI) In Example 1 above, at equal values of (d/r) for model and prototype, the ratio of loads, for prototype and model is, Qr = Ir/rr = 68 The tank is

68 times as sensitive as the pipe to hard spots in the embedment Racks must not bear against the tank Bedding must be uniform

Deformations at welds cause most of the structural leaks in buried tanks For uniform internal or external pressure, circumferential welds must resist longitudinal stress — but longitudinal stress is only half as great as circumferential stress Butt welds can be made nearly as resilient as the parent metal, and they can tolerate deformation But they are expensive Consequently, longitudinal joints are often joggle joints — usually welded on the outside only See Figure 24-2 If the seam is not seriously deformed, such welds are adequate When the weld

is deformed, three conditions develop which could fracture the weld: leverage, shear, and gap

Leverage — A hard spot force on a joggle joint causes a leverage hinge as shown in Figure 24-2 From tests, a joggle joint in 1/4-inch steel, stick welded with E-6024 rod, loaded as a simply supported beam of 3-inch span; fractured when a line force at mid-span reached 230 lb per inch of weld Stresses were concentrated at the corner of the weld which became vulnerable to leverage — a typical cause of leaks in fuel tanks

Shear — When the cylinder is deformed,

c ircumferential shearing stress, t , develops on the neutral surface of the wall If wall thickness is doubled, and the deformation remains the same, the

shearing stress is doubled In joggle joints, shear in

the weld is increased even more For the typical

joggle joint of Figure 24-3,

t = Ewt2(1/ro - 1/r)/2bx (24.4)

where x is the length of transition from minimum to

maximum radius of curvature The transition is

usually visible as a localized crimp for which length,

x, is very short — an inch or two — at the ends of

a flat spot

Example 2

A flat spot occurs in the joggle joint of a steel tank

What is the shearing stress in the weld? Shearing

yield stress is usually about 20 ksi

Given:

E = 30(106) psi,

w = 1 inch = minimum recommended

pene-tration of the joggle joint spigot into the bell,

t = 0.1875 inch (3/16 inch),

ro = original radius of curvature,

= 54 inches (minimum),

r = infinity at the flat spot (maximum),

x = length of transition from minimum to

maximum radius

Substituting into Equation 24.4, t = 52 kips/x(inch)

If the transition length is x = 2.5 inches, shearing

stress in the weld is 20 ksi (shearing yield stress)

For 3/16 steel, it is more likely that x is less than 2.5

inches In such a case, the weld yields and could

crack if its ductility limit is exceeded

If the "flat spot" were not flat, but had a radius of

curvature twice the original tank radius, the shearing

stress would be t = 26 kips/x(inch) which is half of

the stress at a flat spot If the radius of curvature

were inverted, shearing stress in the weld would be

greater At the ends of a flat spot, the radius of

curvature is less than the original radius Therefore,

actual shearing stress is greater than the values

above

If the ring were deflected into an ellipse, see Figure

24-4,

t = (Ext/pr)(1/rx - 1/ry) (24.5) where the minimum and maximum radii of curva-ture are:

rx = r(1-d)2/(1+d),

ry = r(1+d)2/(1-d) (24.6) Substituting the values from Example 2, ring deflection at yield is 76.8% Clearly, some small elliptical ring deflection is not a cause of shearing cracks in welds It is noteworthy that ring deflec-tion of the shell causes other complic adeflec-tions such as head shear (guillotine) and increased potential for inversion, both of which could contribute to cracked welds These are analyzed separately under "Head Shear" and "Inversion Analysis."

Gap — In forming a joggle joint, one end of the can

is deformed into a spigot of smaller diameter such that it can be inserted into the mating can See

Figure 24-5 This usually leaves a gap as shown When a hard spot in the soil deforms the ring, the gap tends to narrow under the hard spot, and widen

at other locations Widening of the gap may crack the weld or, at least, compound the effect of shearing stress caused by change of radius Worse than the elliptical ring show n is the accumulation of gap at the crimped ends of a flat spot — again where shearing stress is maximum Once a weld is cracked, the crack propagates and opens Also, if a hard spot bears against the joggled can, but not the mating can, the crack tends to open In either case, the crack widens and leakage increases

In order to minimize the effect of a gap, typical standards require that outside circumference of the joggle spigot be 1/32 to 3/32 inch smaller than the inside circumference of the mating bell Even 3/32-inch difference can cause a gap to accumulate if the joint is welded continuously without first "tack welding" or "wedging" the gap with shims (or screw drivers) Large gaps are sometimes “slugged;” i.e., the gap is partially filled with a bar

Figure 24-5 Joggle joint in a tank showing how the gap becomes narrower under hard spots and wider at soft spots in the embedment Wide gaps also tend to accumulate at the ends of continuous welds

of reinforcing steel before it is welded "Slugged"

welds are to be avoided

Installers of tanks, especially long tanks, try to avoid

hard spots in the embedment which might cause flat

spots in the tank Longitudinal deflections of tanks

must be restricted by leveling the bedding and by

carefully placing embedment under the haunches of

the tank A flat hard bedding, rocks in the

embedment, frozen soil, and loose soil under the

haunches — all can cause flat spots in tank shells

Inversion Analysis

A major problem with flat spots is the potential for

inversion For conservative analysis, the flat spot is

a beam with fixed ends See Figure 24-6 The

maximum moment is at the ends where Mmax =

PL2/12 But at the formation of a plastic hinge, Mp

= 3SI/2t = St2/4 Equating,

(L/t)2 = 3S/P (24.7)

From the geometry of Figure 24-6,

(L/t) = (D/t)sin(q/2) (24.8)

where q is the arc angle of the flat spot between

plastic hinges Eliminating L/t between the two

equations, and substituting a known value for S,

pressure, P, can be found as a function of angle, q,

and ring flexibility, (D/t)

cylinders for which S = 36 ksi The analysis is

conservative because soil support is neglected

Arching action of the top of the cylinder is also

neglected even though the "flat spot" may not be

completely flat Noteworthy is the increase in

pressure P at inversion when D/t is decreased A

common upper limit for plain pipe is D/t = 288 For

mortar-lined pipes, upper limits are usually not more

than D/t = 240 Noteworthy also is the increase in

angle q as D/t is decreased Soil support increases

as q increases, but the beam analysis loses

accuracy The beam inversion model is reasonably

accurate up to roughly q = 45o Beyond that, a stability analysis is more relevant because of increased soil support and arching of the top of the pipe

Head Shear Heads stiffen the shell, but they also cause head shear when, under soil load, a head shears down past the flexible shell like a guillotine The shell deflects easily under backfill load But heads remain circular This causes distress in the head-to-shell welds at the bottom of the tank where head shear tends to curl the flange (knuckle) and crack the weld

as shown in Figure 24-8 If the seam is a joggle joint, a leverage hinge may form For analysis, the effective shearing load on each head is soil pressure,

P, acting over an area of a tank diameter times roughly one diameter longitudinally P = Pd+Pl where Pd is dead load pressure and Pl is live load pressure Shearing load is:

Reaction is developed under the shell If sidefill soil compresses vertically, the shell deflects, and the heads shear down past it Analysis must consider weld strength and resistance of the flange to bending Distress in the weld is exacerbated by deflections of the head and shell both of which bend the flange Unfortunately, the 90o flange angle is bent (reduced) the most on the invert where head shear is greatest

Example 3 Consider the steel tank, D = 9 ft, L = 42 ft, t = 3/16 inch What is the shearing force, V, between the head and the shell due to a soil cover of 3 ft with unit weight of 120 pcf? From Equation 24.9, V = 29.16 kips — enough to distort a 3/16-thick knuckle and weld

From field experience, the shear load, V, is also felt

at the first joint from the head Many of the leaks in steel fuel tanks are cracks in the bottom at this joint The joint between the first and second cans

Figure 24-6 Model for beam analysis of a flat spot (exaggerated) in a flexible cylinder, showing the moment diagram and the geometry The flat spot is shown here at the top of the cylinder, but may occur anywhere When a flat spot does occur, it is usually at the invert

Figure 24-7 Pressure at beam inversion of flat spots on steel cylinders as a function of ring flexibility, D/t, and angle of the flat spot, q, (beam length)

Figure 24-8 Failure of a circumferential weld due to a stiff head that shears down past a flexible shell Steel tank standards call for a minimum of 1.5-inch flange and 0.5-inch penetration into the shell

does not have the benefit of a head to give it

strength Yet it may be subjected to much of the

shear force, V

Precautions

In order to avoid cracks in welds, attention should be

directed to the following:

1 Careful handling and installation in order to avoid

flat spots,

2 Well-compacted embedment that does not

com-press or slip under anticipated loads,

3 Sound welds with enough toughness that they can

yield without cracking under slight deformation

4 Control of internal vacuum and high external

water table

Additional safeguards to prevent or mitigate leaks include the following:

1 Double containment tanks or coated tanks,

2 Sniffer systems such as a vent between the product tank and the double containment tank

3 Diligent monitoring of contents to discern any loss,

4 Sensor devices in the path of any possible leakage plume,

5 Control of surface loads and high water table

Longitudinal Beam Action

Stress in the welds can be exacerbated by longitudinal beam action See Figure 24-9 The

Figure 24-9 Typical conditions for longitudinal stresses in a tank caused by concentrated supports — on the ends of the tank (top) and at the tie-downs (bottom) due to a high water table or flood