Numerical Methods in Soil Mechanics 27.PDF

Numerical Methods in Soil Mechanics 27.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 "RISERS "

Structural Mechanics of Buried Pipes

Boca Raton: CRC Press LLC,2000

Figure 27-1 Notation for risers, showing radial pressure on the left side and shearing stress (drag-down) on the right side that is caused by soil compression

CHAPTER 27 RISERS

Risers ar e basically pipes that are buried vertically,

or nearly so In fact, some risers are inclined They

are called risers because they usually "rise" from a

buried tank or pipe Risers serve many purposes:

access (such as manholes and mine shafts),

cleanout, ventilation, collection of gas (methane from

sanitary landfills), standpipes (for water pressure

control), bins (for feeding underground conveyors),

accumulators (to collect entrapped air in water

pipes), etc Most risers are cylinders (usually pipes)

See Figure 27-1 Basic concerns are ring

compression and longitudinal (vertical) thrust The

critical location of both is usually at, or near, the

bottom of the riser

Ring Compression

From Chapter 6, ring compression stress is,

fc = rs x /t

where

fc = circumferential stress in thin-wall riser,

sx = external radial pressure against riser,

r = outside radius of curvature of the riser,

t = wall thickness of the riser

For design, fc must be less than the yield stress of

the riser The safety factor is needed because

pressure, sx, is sensitive to soil properties and to soil

placement, which never assures uniform pressure

Because of soil arching action, sx is neither active

soil pressure, nor radial elastic stress These are

limits only At the lower limit, if a vertical hole were

bored into the ground, and the riser carefully slipped

down into it, sx would be zero down to some depth

below which the free-standing hole collapses

(cave-in) under the soil weight Above this collapse depth,

the only pressure on the riser is hydrostatic pressure

if a water table is above the collapse depth In such

a case, stability analysis applies as discussed in

Chapter 10 The "vacuum" in the pipe is external

hydrostatic pressure The question, of course, is

critical depth of the free-standing bored hole The surest procedure is a test hole

At upper limit, if the soil is cohesionless, the riser

feels radial active pressure,

s = Ksz

where

sx = radial pressure on the riser at depth z,

K = (1+sinj)/(1-sinj) from Mohr circle,

j = soil friction angle,

sz = equivalent vertical stress caused by

compaction of the soil

Active pressure is assumed if the soil is loose and slides into place against the riser If the soil is compacted, sz is roughly equivalent to the precompression stress at reversal of curvature of the stress-strain diagram for the compacted soil See Figure 27-2 This analysis is upper limit because arching action (sx) of the soil around the pipe is ignored In fact, arching action is significant The designer can get a feel for the effect of arching action by an elastic analysis

Elastic theory provides a conservative stress analysis Radial pressure against the riser at depth,

z, is sx Principal stresses on an infinitesimal cube

of soil are shown in Figure 27-3 From elastic theory, strains are:

Eez = s z - n(s x + s y)

Eey = s y - n(s x + s z)

Eex = s x - n(s y + s z) where:

E = modulus of elasticity,

n = Poisson ratio,

e = strains in the directions indicated,

s = principal stresses on the infinitesimal soil

cube in the directions indicated

It is reasonable to assume that horizontal strains, ex

and ey, are zero because the soil is confined

Figure 27-2 Sketch of stress-strain diagrams for soil, showing precompression stresses located where curvature reverses Precompression stresses are approximately equivalent to the effect of compaction (soil density) With no compaction (70% density?) curvature does not reverse

Figure 27-3 Infinitesimal soil cube at the riser

surface, showing the principal stresses sz is the

vertic al soil stress sx is the radial soil pressure on

the riser sy is the circumferential stress which

develops soil arching action

Figure 27-4 Horizontal stress, sx, is equal to the bearing capacity of the soil that resists horizontal movement of the riser into the soil This is the maximum stress that develops when the riser deflects laterally into the soil

horizontally Therefore, sy = s x Solving for

pressure against the riser,

sx = ns z /(1-n) (27.1)

According to elastic theory, pressure on the riser is

sensitive to Poisson ratio, <, as follows:

n sx Applied to:

0.00 0 cork, trash

0.1 0.11sz

0.2 0.25sz

0.3 0.43sz

0.33 0.50sz Assume 0.5sz for waste

0.4 0.67sz for some plastics

0.5 1.00sz constant volume elastics

The radial stress, sx, varies from zero to sz Some

designers use the elastic model with a Poisson ratio

of 0.33, for which radial pressure on the riser is sx

= sz/2 But this rationale applies only to elastic

material Soil is not elastic Based on active soil

pressure against the riser,

sx = s z(1-sinj)/(1+sinj)

If soil friction angle is j = 30o, sx = sz/3 Although

conservative, the coefficient, 1/3, is more reasonable

than the 1/2 used by some designers

If the riser deflects laterally, movement of the riser

causes passive soil resistance From Chapter 4, at

passive soil resistance,

sx = s z (1+sinj)/(1-sinj)

If soil friction angle is j = 30o, sx = 3sz

This is analyzed as pressure on one side of the riser

See Figure 27-4 The only reaction to this force is

cantilever action which may be more critical than

ring compression if the riser can deflect laterally

Design is classical analysis for a vertical cantilever

It may be necessary to locate points of

counterflexure in the deflected riser

Thrust

Thrust is the vertical force on the riser It is caused

by the frictional "drag-down" as the soil compresses Thrust depends upon: pressure against the riser, the coefficient of friction of the soil on riser, and the relative movement (compression) of the soil with respect to the riser A safety factor is required Analysis of the drag-down force is similar to the analysis of silos in Chapter 22 The following design procedure is conservative because soil arching around the riser is neglected in calculating drag-down In the following it is assumed that soil is cohesionless Two soil conditions are analyzed, without compaction and with compaction It is assumed that soil is confined horizontally such that (radial) strains are zero Therefore, sy = s x This is modeled by a confined compression test See Figure 27-3 For design, vertical stress, Q/A, must be less than the yield stress, fc, reduced by a safety factor Q/A = fc /(sf) (27.2) Notation:

Q = total drag-down load on the riser,

A = cross-sectional area of the riser = 2prt,

fc = longitudinal yield stress in the riser,

fz = longitudinal (vertical) stress in the riser,

r = mean radius of the riser,

t = wall thickness of the riser,

sx = radial (active) soil pressure on the riser,

sz = vertical soil pressure at depth, z,

z = depth to soil cube (Figure 3),

K = ratio of sx /s z at soil slip,

= (1- sinj)/(1+sinj) for granular soil,

j = soil friction angle,

m = coefficient of friction, soil on riser,

sf = safety factor

If the soil is cohesive, K must be modified See Chapter 4 The vertical stress, fz, in the riser at depth, z, is an upper limit because horizontal arching

of the soil, sy, is ignored Q is the total

drag-down force of the soil on the riser as soil

compresses It is assumed that the riser is fixed in

length, and is supported on a base that does not

settle See Figure 27-2 At depth, z, vertical stress

in the riser wall caused by drag-down is,

fz = Q/A = Kzmsz /2t (27.3)

UNCOMPACTED SOIL

where

t = msx = vertical shearing stress on riser,

sx = Ksz = radial soil pressure on the riser,

Q = przt = przmK sz = drag-down force

During backfilling, soil "slides" into place against the

riser such that radial pressure in Equation 27.3 is

roughly active soil pressure; i.e., sx = Ks z

K = (1-sinj)/(1+sinj) (27.4)

Uncompacted soil

The active radial pressure is sx = Ks z where s z is

the vertical soil stress at depth z

Example 1

Figure 27-1 shows a riser in uncompacted soil

Therefore, the sx-diagram is a triangle to some

depth, z What is the drag-down force, Qs due to

shearing stresses? The volume under the sx

-diagram is simply the area under the triangle, zsx/2,

times the circumference of the riser, 2pr

Therefore, Qs = mprzs x

Compacted soil

If cohesionless embedment is uniformly compacted

(in lifts), it is reasonable to assume that sz is the

equivalent precompression stress of compaction If

soil is compacted throughout the entire height of the

riser, radial soil pressure on the riser is constant —

not zero to maximum from top-to-bottom

Therefore, the 2 in the denominator of Equation 27-3

cancels, and,

fz = Kzmsz /t (27.5)

COMPACTED SOIL

sz is the precompression stress for samples of the compacted soil It can be found from stress-strain diagrams of laboratory compression tests on compacted soil

CAVEAT — Usually, compacted soil does not compress with respect to the riser Therefore, shearing stresses, t , do not develop The very purpose of compaction is to prevent relative settlement of soil with respect to the riser The above rationale applies to "unusual" cases of relative movement

Structural Analysis of the Pipe

Figure 27-1 (right) shows loads on the pipe ring due

to soil and riser The ring can be analyzed by closed form integration See Appendix A Such analyses are conservative, however, because arching of the soil is ignored, both longitudinal and circumferential Moment, thrust, and shear in the ring make possible the stress analysis of the ring Plastic analysis is more relevant than elastic analysis Stress concentrations at the intersection of riser and pipe are critical

Surface Live Loads

If a live surface load can pass over the riser, the riser must support the entire load If a concentrated dual-wheel load is located at a point on the rim of the riser, the riser can be analyzed as a short column with both an axial load and a moment due to the eccentricity of load from the neutral axis of the riser The maximum stress is usually at or near the top It must be less than yield stress reduced by a safety factor Localized buckling could reduce the critical load, P The maximum stress, from classical mechanics, is the familiar,

fc = P/A + Mc/I = 3P/2prt, approximate (27.6) where

P = dual-wheel load,

A = 2prt = cross sectional area of the riser,

M = Pr = moment of force on the riser,

I/c = ptr3/r = ptr2

If the live surface load is not on the riser, but is

located on soil adjacent to the riser, the problems are

vertical force on the riser, and non-uniform radial

pressures

Ring Compression:

The ring compression pressure, sx, under the wheel

load may greater than the passive resistance of the

soil around the rim The riser rim could invert

Approximate analysis is possible, but is usually not

justified

Thrust

If live loads ar e anticipated, either the riser must be

able to support the loads, or loads must be kept off

the riser Manholes in roads support wheel loads

It is common practice to place a collar around the

rim of the riser See Figure 27-5 The collar is not

attached to the riser Therefore, it bears on soil

The collar usually rises above the surface like a curb

so wheel loads do not roll onto the riser See Figure

27-5 The collar keeps the wheel load far enough

away from the riser that radial soil pressure is not

excessive Vertical soil stress, sz, next to the riser

can be calculated using the Boussinesq procedure

See Chapter 4 Radial stress is sx = Ksz Radial

stress is reduced by increasing distance, R, from the

riser See Figure 27-6

Example 2

Assume that an HS-20 dual- wheel load is P = 16

kips with tire pressure of 105 psi is located at

distance, R, from the riser The depth to the

infinitesimal soil cube is Z Assume that the soil is

cohesionless with a soil friction angle of 30o for

which K = 1/3 Values from Boussinesq are plotted

in Figure 27-6 Clearly, sx is reduced dramatically

as R increases Shown for comparison is a plot for

R = 0; i.e., the wheel is on soil at the edge of the

riser Theoretically, sx approaches infinity on the

soil surface where Z = 0 because Boussinesq

assumes a point load In fact, the dual-wheel load is

spread over an area The maximum pressure is

simply tire pressure, 105 psi, for which sx = 35 psi = K(105 psi)

The effect of non-uniform radial stresses on the ring can be analyzed, if necessary, by the Castigliano equation See Appendix A

Drag-down shearing stress caused by the wheel load is, t = msx

See Figure 27-1 Again, the problem is evaluation of radial stresses, sx; and, again, for cohesionless soil, the major distinction is between uncompacted and compacted soil; i.e., between active soil pressure, Equation 27.3, and equivalent precompressed soil pressure, Equation 27.5 The drag-down shearing force is mtimes the volume under the sx-diagram; i.e.,

Qs = m sxdA (27.7) See Figure 27-5 For a concentrated wheel load, P, radial soil stress, sx, at depth Z varies with radii, R, from the wheel load (P-axis) to the riser Moreover,

sx is the radial component of the Boussinesq stress

at R and Z The boundaries of the pressurized area

to be integrated depend upon ring stiffness It is reasonable to assume an area equal to Z times one-eighth of the circumference (45o arc) At each depth, Z, radial stress, sx , is K times the vertical stress, sz, and is assumed to be constant around the

45o arc at depth Z

Example 3

A riser is buried in uncompacted soil Roughly what

is the drag-down force, Qs, due to the wheel load P

= 16 kips at R = 10 inches from the edge of the riser? Radius of the riser is r = 16 inches

From Figure 27-6 by counting squares, the area under the (R=10) curve is roughly 100 lb/in A 45o arc of the riser is pr/4 = 12.5 inches The stress volume is approximately (12.5 in)(100 lb/in) = 1.25 kips The shearing drag-down force is 1.25(m) kips

If the coefficient of friction is m =

Figure 27-5 Collar for preventing excessive soil pressures on the riser due to surface wheel loads, showing principal stresses on an infinitesimal soil cube at the riser surface and at depth, Z

Figure 27-6 Radial pressures, sx, acting on the riser, as a function of depth, Z, and distance, R, from a 16-kip wheel load to the riser

0.5, the drag-down force is Qs = 625 lbs If R is

decreased to 5 inches, the area under the sx-curve

is roughly 2.5 times as large The down-drag force

is (2.5)(625 lbs) = 1.56 kips, a quarter of the wheel

load Keep wheel loads away from the edge of the

riser

Risers in Sanitary Landfills

Sanitary landfills pose unique problems because of

compressibility of waste material Properties of the

waste vary Unit weight of waste is typically g = 75

pcf Some engineers design for 80 pcf to include

variable water content and non-homogeneity

Vertical compression can be as much as 30%

Temperature can vary from below freezing to 120o

F Landfills spread horizontally as the height rises

The rise is gradual (over many years) Design of

risers must take into account lateral deflection due to

spreading of the sanitary landfill, and drag-down

(friction as the waste compresses)

Drag-down

For lack of accurate values, the drag-down

"coefficient" is sometimes set at 0.5; i.e., half the

vertical pressure of the waste at any given depth

The result is a triangular drag-down shear diagram

(t -diagram) as shown on the right side of the riser in

Figure 27-1 where t is 0.5(sz), and where s z = gz

Because sanitary landfills are usually high, z can be

a large value To relieve the riser of large

drag-down thrust, and to protect the riser, a "chimney" of

compacted, select backfill is sometimes specified

with the riser serving as the "flue." An alternative

could be a telescoping riser See Figure 27-7 It

may be prudent to provide flanges on each stick of

pipe Analysis shows that friction should hold the

sticks in place However, variations in temperature

cause the sticks to lengthen and shorten, both of

which cause incremental creep downward Flanges

resist downward creep Flanges can be placed

anywhere on the larger diameter telescoping sticks

Some designers use pipes with the bell on one end to

serve as a flange for the larger diameter sticks

Flanges on the smaller diameter sticks must be far

enough from the ends to allow telescoping by insertion of the smaller diameter pipe into the larger diameter pipe

The required bearing area of the flanges can be analyzed as follows Area times bearing capacity of the soil (trash) must exceed the frictional drag-down plus the weight of each stick This design procedure

is conservative because downward creep and telescoping both reduce or eliminate drag-down Safety factors are not needed

Resistance to Live Loads When a live load passes over a riser supported by a buried pipe or tank, the question arises as to how much of the load is felt If the riser is non-compressible (no slip joints or corrugated sections), the entire live load could be supported by the pipe or tank If the riser is compressible, it shortens under the live load The load, or part of the load, is supported by frictional resistance of the waste That frictional resistance is analyzed the same way as drag-down, except that it is reversed in direction Lateral Deflection

If insertion clearance is not adequate between the larger and smaller sticks, lateral deflection of the riser may bind contiguous sticks At worst, the bending moment could fracture the ends Lateral deflection can be accommodated by shortening the lengths of the sticks and the insertions, and by increasing the annular space between the smaller and larger diameter sticks Gaskets at the insertions may or may not be required to prevent influx of leachate or soil The length of the sticks may be determined by the rate of rise of the sanitary landfill Telescoping sticks facilitate rise, but the stick added for each lift must be limited in length depending on the method of support A mound of select granular soil around the base of the added stick may adequately support short sticks Otherwise, tie wires are needed

Foundation for the Riser

In some cases, the weight of the riser and the

drag-Figure 27-7 Diagrammatic sketch of a telescoping riser to accommodate compression of the waste in sanitary landfills, shown here with flanges to resist incremental creep downward The flanges do not necessarily have to be at midlength of the sticks