Numerical Methods in Soil Mechanics 26.PDF

Numerical Methods in Soil Mechanics 26.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 "NON-CIRCULAR LININGS AND COATINGS"

Structural Mechanics of Buried Pipes

Boca Raton: CRC Press LLC,2000

Figure 26-1 Two important deformations of buried flexible pipes.

Figure 26-2 Crack at the invert of the lining caused by increase in radius of curvature

CHAPTER 26 NON-CIRCULAR LININGS AND COATINGS

Linings and coatings are not always circular in cross

section Non-circular pipes are discussed in Chapter

9 Circular linings (encased in host pipes) are

discussed in Chapter 11 Following is a discussion

of the effects of non-circularity on linings and

coatings

Coatings prevent external corrosion of the host pipe

and stiffen the ring The performance limit is

excessive cracking Linings prevent leaks and

stiffen the ring Two basic performance limits of

linings are cracking and collapse (inversion)

Following are two analyses of non-circular linings

and coatings, rigid and flexible.

RIGID LININGS AND COATINGS

Rigid linings and coatings are applied to thin-wall

s teel pipes that are to be buried The linings and

coatings are of high-strength Portland cement

mortar Purposes of the linings and coatings are:

1 to provide adequate stiffness of the pipe in order

to handle and transport the pipe, and to install and

backfill; and,

2 to protect the steel against corrosion and against

abrasion caused by sediment in the fluid flow and

possibly by cavitation

For design, the first two performance limits are hoop

strength against internal pressure and ring

compression strength against external pressure A

third performance limit is ring stiffness The pipe

must be stiff enough to be handled and installed A

fourth performance limit is excessive cracking of the

mortar Pipe engineers consider performance limit

to be crack widths greater than 1/16 inch This is a

rule of thumb that is intended to avoid the break-out

of shards in the lining and to prevent circulation of

corrosive fluid through the crack to the steel

Shards are usually caused by a dent or inversion in

the pipe wall Cracks in the coating that are wider

than 1/16 inch might allow electrically conductive

groundwater and transient electric al currents to get

to the steel

Some pipe engineers still hold to the veryconservative 0.01-inch crack as performance limit.Compared with the 1/16 cr ack (0.0625) the safetyfactor is more than 6 Clearly, a broad safety zone

is available for mitigation

A paradox arises between ring stiffness and mortarcracking Because the mortar is thicker than thesteel, ring stiffness is affected primarily by thickness

of the mortar However, the thicker the mortar, thewider are the cracks at any given ring deflection.The optimum coating thickness between desirablestiffness and undesirable crack width comes fromexperience Both the minimum stiffness and themaximum crack width are related to ringdeformation Of course, ring deformation alsodepends upon loads and embedment soil

Ring deformations in the following analyses a r eeither: a) ellipse, or b) D-bedding See Figure 26-1.The ellipse is the basic deformation under verticalsoil pressure The D-bedding (so-called by rigid pipeindustries) is a worst-case deformation (usuallylabeled "impermissible") The pressure, P, can begreater than the soil prism load when surface liveloads pass over, or when a deflected pipe isrerounded by internal pressure

Notation

r = radius to the neutral surface of circular pipe,r' = maximum (or minimum) radius,

d = ring deflection = D/D where D = 2r,

D = vertical decrease in diameter of deflected

ring,

t = thickness of each lamina in the wall,

w = width of a crack in the mortar (See Figure

26-2),

c = distance from the neutral surface of the wall

to the exposed mortar surface For case analysis, this is the thickness of mortar,either lining or coating

worst-It is sufficiently accurate to assume that the steel is

the neutral surface Whether a radius to the neutral

surface is to the inside or the outside surface of the

steel makes little difference

Crack Width

From the geometry of Figure 26-3, assuming

conservatively that the crack penetrates to the steel,

c is the coating mortar thickness, and the crack

width is w = cDq where Dq = (1/r'-1/r)inch

Substituting with r in inches,

For a derivation of Equation 26.3, see Figure 26-1a

From Appendix A, the maximum moment is at the

invert, B, and is, M = 0.5872Pr2

From mechanics of solids,

if the lining dries out For storing and transportingpipe sections, the ends are often sealed with sheets

of plastic to reduce drying

Hair cracks may develop during backfilling because

of ring deflection Pressure in the pipe rerounds thepipe and closes deflection cracks Cracks narrowerthan 1/16 inch are closed by autogenous healingwhen the mortar is wet Autogenous healing is theformation of silica gel by hydration Small cracks inthe lining usually don't penetrate to the steel

Width of Cracks in Mortar Lining Cracks open when the ring is deflected Typicallythe widest cracks are inside the pipe at 6:00 and12:00 o'clock See Figure 26-2 It is reasonable toassume that the inside surface of the steel is theneutral surface In the following analyses, twodeformations are compared: elliptic al, and D-bedding From Equations 26.1, 26.2, and 26.3, therelationship between width of crack, w, and ringdeflection, d, can be found If the ring is deformed,the relationship between w and r’ may be moredependable From inside the pipe, r’ can be found

by laying a horizontal cord (straightedge) at B,

Figure 26-3 Free-body-diagram of a section of pipe wall at spring line The notation shown is used in analysis

of crack width, w, in the mortar coating w = cDq

Figure 26-4 Exposed cracks in a coating that is deflected into an ellipse, shown exaggerated

and measuring the vertical middle ordinate from the

cord to the lining surface Then r' = L2/8e where L

is cord length, and e is the middle ordinate from cord

to pipe surface It is assumed that radius, r', is

circular

Caveat

Once the lining is cracked, a plastic hinge may form

in the steel with a radius smaller than the mean

radius subtended by the cord The plastic hinge can

be analyzed from yield stress of the steel and the

radius of curvature A plastic hinge is recognized

visually as the crimped rim around a dent

Example:

What are the widths of cracks in the lining of a pipe

at the invert? The pipe is nominal 42-inch (inside)

diameter

r = 21.5 inches to the neutral surface (assumed to be

at the inside surface of the steel),

c = 0.5 inch = thickness of the lining

From Equations 26.1, 26.2, and 26.3, in terms of ring

deflection, d, the maximum radii of curvature, r', and

corresponding widths of crack, w, are listed in Table

26-I

CRACKS IN MORTAR COATING

The coating on some steel pipes is tape

Improvements in the protective qualities have made

tape attractive However, if ring stiffness is of

concern, or if increased weight of pipe is desired,

then mortar coating is used

Excessive cracking is performance limit Excessive

cracking allows corrosion of the steel from

aggressive groundwater and electrical currents in

the soil As with linings, cracks are caused either by

ring deflection or by flat spots (dents)

Ring Deflection of Ellipse and D-Bedding:

As a result of ring deflection, the widest cracks in

the coating occur near spring lines Figure 26-4 is

an exaggerated sketch For worst-case analysis, it

is assumed that the neutral surface is near enough to

the outside surface of the steel that the coating isentirely in tension It is noteworthy that thedeflected radius at spring line is roughly the same forthe ellipse and the D-bedding The ellipse isanalyzed in the following

Example:

What is the width of a crack in the 1.5-inch mortarcoating on the following pipe

ID = 72 inches = nominal diameter,

D = 74 inches = outside diameter of steel

(assumed neutral surface, NS)

w = width of crack,

r = 37 = initial circular radius of the NS,r' = deflected radius of elliptical NS at spring

lines,

c = 1.5 from NS to the outside surface of

coating (coating thickness),

d = ring deflection (percent) of elliptical cross

In Table 26-II, e is the middle ordinate from a

twelve inch cord on the inside of the pipe to the

inside surface of the pipe See Figure 26-5 Theneutral surface (NS) is approximately at the outsidesurface of the steel where r = 37 inches If the

Table 26-1 LINING CRACK WIDTHS AS FUNCTIONS OF RING DEFLECTION

at the invert of 42D pipe with 0.5-inch mortar lining

Elliptical deformation D-bedding deformation

by measuring middle ordinate from a cord (straightedge) at the invert

Table 26-2 COATING CRACK WIDTHS — ELLIPSE DEFLECTION

at the spring line, of 72D pipe, 1.5-inch mortar coating

** w = 1/16-inch crack More precisely, d = 25.34%, but such precision is not justified The inaccuracies

of these approximate ellipses increase as ring deflections increase Moreover, the assumption of ellipse isquestionable — especially after the mortar becomes cracked at large ring deflections

K = 3d/(1-2d) = ring deflection factor for ellipse

r' = radius at springline

e = middle ordinate at the invert from a 12-inch cord to the lining

thickness of steel plus lining is 1.0 inch, the inside

radius is r'-1 inch for this 72D pipe with

1.5-inch-thick coating In this example, from geometry, in

terms of the middle ordinate, e, from a 12-inch cord

to the lining,

r'-1 = 18inch2/e (26.7)

Equation 26.7 provides a means from inside the pipe

to estimate the width of cracks in the coating For

this example, if inside the pipe, e = 0.625, from

Equation 26.7, r' = 29.8 in, which is then substituted

into Equation 26.5 to find that w = 0.01 inch A list

of values appears in Table II for this particular

example The procedure applies to other

mortar-coated pipes

Excessive Crack Widths

What is excessive crack width? For linings,

experienced pipeline engineers say "any crack wider

than 1/16 inch." A more conservative specification

is the 0.01-inch crack Water in the pipe causes the

lining to expand and close cracks Autogenous

healing (hydration of silicates in the mortar) seals

small cracks For coatings, also, the 0.01-inch crack

is conservative For 1/16 inch coating cracks,

conditions for corrosion are affected by: electrical

ground current, the water table, and water quality

Cracks in coatings do not penetrate to the steel if the

only loads are soil pressure It might be argued that

when the pipe is pressurized internally, the steel

stretches, and cracks in the coating widen and

penetrate to the steel However, pressure in the

pipe rerounds the pipe So cracks in the coating are

narrowed by the pressure.

It is noteworthy that cracks are widest when the

pipe is emptied after hydrotests In service, with

pressure in the line, cracks are narrow Cycles of

dewatering cause pipe-soil interaction to stabilize at

crack widths that are less than they were

immediately after hydrotests Over time, the soil

migrates into place against the pressure-stiffened

pipe Thereafter the soil holds the pipe in its circular shape Consequently, service life is notshortened by cycles of dewatering

a flat spot in a coating The crack at B in the middle

of the flat spot is not a problem because it opens tosteel — not to groundwater The two cracks at theends of the flat spot each open at roughly half themiddle crack width Therefore, if the lining is half asthick as the coating, the crack widths, w, in thecoating are roughly equal to the crack widthmeasured in the lining at the middle of the flat spot

If the flat spot is circular rather than long, cracks inthe lining appear as a starburst Of course, crackwidths cannot be pr edicted precisely The aboverationale is conservative

Flexible Linings and CoatingsDevelopment of flexible linings and coatings, such asepoxies and tapes, is significant Not only iscorrosion resistance achieved, but resistance toimpacts and pipe deformations is impressive Abackhoe tooth can dent a mortar-lined steel pipeleaving a starburst in the mortar lining, but withoutdamage to the tape coating

Inversion AnalysisOne cause of inversion is a concentrated reaction,

Q, (hard spot) See Figure 26-7 From Appendix A,the moment at B is, MB = 0.3Qr For worst-caseanalysis, mortar-to-steel bond is discounted Forinversion analysis, see Figure 26-8 In the examplethat follows, the data are:

Figure 26-5 Procedure for finding ring deflection of an elliptical pipe by laying a 12-inch cord, at the springline and measuring e.

Figure 26-6 Exaggerated sketch of flat spot in a mortar coating

Figure 26-8 Equivalent wall section in mortar for stiffness analysis of the mortar coating at invert, B.

Q = P(OD) + W per unit length,

P = soil pressure on the pipe,

W = wt (pipe + contents) per unit length,

sf = 1200 psi = yield strength of mortar,

n = 7.5 = Es /Em,

Es = 30(106) psi = mod/elast, steel,

Em = 4(106) psi = mod/elast, mortar,

tl = 0.75 = thickness of the lining,

ts = 0.32 = thickness of the steel,

tc = 1.50 = thickness of the coating,

rl = 36.38 = radius to center of lining,

rs = 36.91 = radius to center of steel,

rc = 37.82 = radius to center of coating

Example:

What is the line reaction, Q, at inversion? First, find

the moment resisting ring stiffness of the critical

mortar coating as a fraction of the total ring stiffness

which must resist moment, MB = Qr/4 See Figure

26-7 and Appendix A Total ring stiffness =

The last column, Emb(t/r)3, is ring stiffness, 12EI/r3,

where moment of inertia is I = bt3/12 For ratios, the

12 is factored out

Moment in the Coating: (Coating is critical)

Mc = (250/305)MB = 0.82MB = Qr/4 Coating yields

(i.e., cracks) at Mc = s f (tc)2/6 = 450 lbin/in Since r

= 37.82 for the coating, Q = 570 lb/ft Q is the

critical line load that cracks the coating The weight

of pipe and contents is W = 2370 lb/ft Clearly, the

reaction must not be the concentrated Q-reaction of

Figure 26-7 The pipe must be supported by soil

under the haunches As soon as the coating cracks

at the invert, the lining and steel let go, and the

Q-reaction is distributed over an area

Remedies

Coating Ideally, wherever cracks are excessive in the mortarcoating, the pipe could be uncovered and re-rounded

by internal pressure Then the embedment could becarefully re-compacted while the pipe is circular If

it is not practical to pressurize the pipe, it may bepossible to reround the pipe by carefully monitoringring deflection during re-compaction of sidefill soil

Lining Linings tend to expand in a moist environmentthereby reducing crack widths One basic concern

is cracks so wide (>1/16 inch) that water couldcirculate through cracks to the steel Another basicconcern is shards of lining that might break out.Break-out would require suction such as theBernoulli effect Loose shards can be detected bythe flat, hollow sound when the lining is rapped with

a hard object at locations of multiple cracks, parallel

or starburst Wide cracks may be associated withinversions (Q-reactions) or flat spots (dents) If thepipe is not uniformly bedded, but is propped up onhigh spots, and if ring deflection is excessive duringinstallation, hydrotests tend to reround the pipe byforcing it down against the high spots The resultcould be inversion at the high spots, and the potentialfor shards to form

General Uniform bedding is essential Ring deflection duringinstallation should be limited by specification Goodembedment should be placed with care The reasonfor an embedment is remembered as P5 — packingfor placing, positioning and protecting the pipe Infact, the embedment is part of the conduit — not justpressure on a pipe

Example 1

A tape-coated, mortar-lined steel pipe is installedand hydrotested Then it is inspected and found to

have excessive ring deflection and flat spots at

various locations under the haunches Maximum

allowable ring deflection was conservatively

specified as 3% The embedment had been placed

by covering the pipe with sand, then jetting down to

the level of the invert with high-pressure water jets

that flush soil under the haunches What caused

excessive ring deflection and flat spots? What can

be done to remedy or mitigate it?

Class pipe: 150 to 200

D = 43 inches to neutral surface of the wall,

t = 0.175 = thickness of the steel,

tl = 0.500 = thickness of the lining,

E = 30(106) psi = mod/elast, steel,

El = 3(106) psi = mod/elast, mortar lining,

n = 0.3 = Poisson ratio,

rs = 21.59 = mean radius of steel,

rm = 21.25 = mean radius of mortar lining,

r = 21.5 = approximate radius to NS,

t = 0.2645 = wall thickness of equivalent

unlined steel pipe

Design of the Pipe — OK

1 Hoop tension stress under internal pressure is not

excessive

2 Ring compression stress due to external soil

pressure is OK

3 Composite ring stiffness is approximately EI/r3

= 4.59 psi For the steel only, EI/r3 = 1.33 psi For

the mortar lining only, EI/r3 = 3.26 psi The

composite ring stiffness is the sum, 4.59 psi It is

assumed that there is no bond between mortar lining

and steel Because there may be bond, and because

shrinkage cracks are disregarded, values for ring

stiffness are not precise The composite ring

stiffness of 4.59 is equivalent to D/t = 163 for

unlined steel pipes Steel pipe engineers recommend

a maximum D/t = 288, or, with care in installation, up

to D/t = 325 Ring stiffness is OK

4 Ring deflection is limited by specification to a

maximum of 3% to be sure that the lining will not

crack excessively Small cracks (less than inch-wide) close in time by autogenous healing(hydration of the silicates in the cement.)

1/16-5 Cracks should be no wider than 1/16 inch Figure26-2 shows a crack in the lining at the invert Figure26-9 shows crack width, w, as a function of ringdeflection, d, when the pipe is deflected into anellipse The ordinate at right is the ratio of radii,maximum ry to mean circular, r The width of crack,

w, can be found either as a function of the ratio ofradii, ry /r; or as a function of ring deflection, d Themaximum radius, ry, of a flat spot or inversion in thepipe can be found by measuring the ordinate to thepipe wall from the middle of a cord of known length

In this pipe (r = 21.5, t = 0.59 lining to center of thesteel), for a 1/16- inch crack to open, the pipe wall

must invert to a radius of ry = -17 in See Figure26-10 For cracks to occur in the steel, radius rymust be less than 2.5t Manufacturers recommend

a lower limit of ry = 7t

6 Longitudinal stresses are caused by temperaturechange, internal pressure change, and longitudinalbending moment Beam action is not anticipated ifthe pipe is supported by soil bedding and soil underthe haunches The longitudinal design is OK

Installation and Hydrotesting

1 The buried pipe-soil interaction has stabilized.The sidefill is compacted to 90% standard density.Soil arching action has been achieved No increases

in deformations or stresses are anticipated Themaximum ring deflections and flat spots occurredduring installation or hydrotesting

2 Flat spots were discovered in the invert SeeFigure 26-11 The result could be disbonding andspalling of the lining due the Bernoulli lift and tovibrations (turbulence) in water flow Long flatspots should be rerounded and lining replaced ifwidth of the flat spot is greater than roughly b = 5inches Circular flat spots should be rerounded andlining replaced if diameter of the flat spot is greater