Numerical Methods in Soil Mechanics 12.PDF

Numerical Methods in Soil Mechanics 12.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 "RIGID PIPES"

Structural Mechanics of Buried Pipes

Boca Raton: CRC Press LLC,2000

Figure 12-1 Procedure for conducting the three-edge-bearing (TEB) test on rigid pipes The load at failure per unit length of pipe is called the D-LOAD

Figure 12-2 Rigid pipe showing (left) how the ring is forced to support the weight of backfill, W, if the sidefill soil is not compacted; and (right) the basis for the Marston load analysis

CHAPTER 12 RIGID PIPES

Rigid pipes do not deflect enough for deflection to

affect soil pressure against the pipes The soil is a

load on the pipes Rigid pipes include Portland

cement concrete pipes (both reinforced and

unreinforced) and vitrified clay pipes Other pipes

may be rigid under certain conditions Cement

mortar lined and cement mortar coated (CML/CMC)

pipes perform as rigid pipes when buried in loose soil

because pipe stiffness is relatively greater than soil

stiffness In densely compacted soil, CML/CMC

pipes may be flexible, or, according to some

designers, may be semi-rigid

Design of concrete pipes is described in the

Concrete Pipe Design Manual, published by the

Americ an Concrete Pipe Association [ACPA

(1993)] Pipe strengths are specified by standards

The ACPA has wisely left to the manufacturer the

responsibility of making pipe that meets the

standards In general, performance limit is

longitudinal cracking of the pipe wall due to internal

or external pressures

INTERNAL PRESSURE DESIGN

Designers often assume that concrete and clay can

take no tension In fact, both can take tension

Nevertheless, unreinforced concrete or clay pipes are

usually not designed to take internal pressure because

hoop strength is lost if longitudinal cracks form during

curing or handling With tension reinforcement, rigid

pipes serve well as pressure pipes Consider

reinforced concrete pipes If performance limit is

leakage, the reinforcing steel must be pre-tensioned

(or post-tensioned) such that the concrete is in

compression before internal pressure is applied

When internal pressure is applied, the tensioned steel

takes additional tension and stretches This relieves

compression in the concrete The concrete will not

leak until it begins to take tension Therefore, to

avoid leakage, the steel must take the entire internal

pressure Pre-tension force in the steel is,

Ts = Pr/(1 + EsAs /EcAc) (12.1) where

Ts = tension in the steel per unit length of pipe,

P = internal pressure,

r = inside radius,

Ac = area of concrete per unit length,

As = area of steel per unit length,

σ = stress,

E = modulus of elasticity

A safety factor should be included High strength steel is cost effective Small diameter steel rods increase bond between steel and concrete

Procedure specifications for the manufacture of

prestressed pipe are usually left to the manufacturer

The pipeline engineer writes performance

specifications

For typical reinforced concrete pipes, if Ac /As = 100 and Es/Ec = 5, the pre-tension force is Ts = 0.95Pr; or say, conservatively, Ts = Pr With pressure, P, in the pipe, tensile force in the steel is doubled It is prudent

to check maximum stresses in the concrete and steel:

σc = Pr/Ac

σs = 2Pr/As EXTERNAL PRESSURE DESIGN

For rigid pipes, external pressure design is based on loads on the pipe — not stress or strain See Figures 12-1 and 12-2 The following analysis is historical and simplistic It is no longer proposed by ACPA, but

is presented here as the basic rationale for analysis For design,

APPLIED LOAD = ALLOWABLE LOAD

(12.2) APPLIED LOAD = (Wl + Wd) (12.3)

Variation of Lf from class C to class B is based on the width of the bedding.

For Class B bedding, width of bedding is 0.6(OD)

For Class C bedding, width of bedding is 0.5(OD)

Variation of Lf in class A is based on the percent of area of reinforcing steel:

Reinforced As = 1.0%, Lf = 4.8

Reinforced As = 0.4%, Lf = 3.4

Plain As = 0, Lf = 2.8

Theoretical values of load factors are based on moments at A, which are:

For the TEB load, MA = 0.318 Wf r

For Class A bedding, MA = 0.125 Wf r

For Class D bedding, MA = 0.293 Wf r

Figure 12-3 Loadings on rigid pipes showing the three-edge-bearing test load (TEB) and the three soil loadings identified by the American Concrete Pipe Association, showing the original load factors, Lf, for each Wf = load at failure Failure is a longitudinal crack at point A

Wl = live load on the pipe, per unit length of

pipe,

Wd = dead load,

sf = safety factor,

OD = outside diameter,

ID = inside diameter,

Lf = load factor,

D-load is the load at failure in a three-edge-bearing

test = F-load per unit length Lf = load factor, which

is determined by the bedding and by steel reinforcing

The three-edge-bearing (TEB) test is conducted as

shown in Figure 12-1 The TEB load at failure is

called the D-load In general, failure is the ultimate

(maximum) load on the TEB test pipe However, in

reinforced concrete pipes, failure is often defined as

the TEB load at which longitudinal cracks open to a

width of 0.01 inch The 0.01-inch crack came about

in the 1930s when graduate student, Bill Schlick, was

inspecting reinforced concrete culverts in order to

evaluate their performance This task was assigned

to him by his dean, Anson Marston, of the College of

Engineering, Iowa State College, Ames, Iowa The

only indication of inadequacy that Schlick could

identify was cracking So he put a half-inch-wide

strip of 0.01 steel shim stock in his pocket, and

proceeded to classify adequacy on the basis of crack

widths into which he could insert the 0.01-inch steel

This became the standard It has proven to be better

than happenstance Cracks less than 0.01 inch tend

to close by autogenous healing; i.e., by continued

hydration of the silica gel in the Portland Cement

Cracks greater than 0.01 inch can possibly allow

oxygen to reach and corrode the reinforcing steel

In Equation 12.3, the live load Wl is the effect of live

load on the top of the pipe due to surface live loads

The wheel load is multiplied by an impact factor of

1.5 for highway loadings The dead load Wd is the

vertical soil pressure on the pipe It is usually taken

as the weight of the prism of soil over the pipe

However, Figure 12-2 shows how the entire backfill

load in a trench could be imposed on

the pipe if sidefill soil is not adequately compacted It

is difficult to predict how much of the backfill load is imposed on the pipe Anson Marston pioneered load analysis The theoretical Marston load does not account for soil anomalies such as compaction of soil directly against the top of the pipe Arching action of the soil is ignored A soil arch is formed if the sidefill

is compacted The soil arch supports much of the backfill in the trench At most, the pipe only has to support the prism of soil, γH(OD), above it In fact,

a compacted soil arch relieves the pipe of essentially all of the vertical pressure except for loose soil in the first lift above the pipe Soil arching can be assured

by compacting sidefill up to one soil lift above the top

of the pipe; but avoiding compacting the first lift directly over the pipe This result is backpacking, which protects the pipe from soil pressure concentration, and develops a soil arch

ALLOWABLE LOAD = FAILURE LOAD

(12.4)

FAILURE LOAD is based on the three-edge-bearing test The three-edge-bearing load at failure is the D-load For unreinforced rigid pipes the D-load is the maximum load in lbs per ft of length of pipe For reinforced concrete pipes, the D-load is the load in pounds per ft of length of pipe per ft of ID When the pipe is buried, the soil load is less severe than the D-load Therefore, a load factor, Lf, increases the allowable soil load above the D-load pipe strength

Figure 12-3 shows the four historical loads on rigid pipes At left is a parallel plate load which, for analysis, is tantamount to the TEB load The other three are assumed to be soil loads in service Horizontal soil support is neglected because the rigid ring does not deflect and develop passive soil support For each of the three bedding classes, theoretical failure load, Wf, is found from Appendix A In all cases, Wf is greater than D-load; therefore,

Failure load, W f for each bedding class is the D-load times its D-load factor, L f

Figure 12-4 Effect of diameter on load capacity on an equivalent beam that cracks at point A OD is an overly conservative beam length

Figure 12-5 Backpacking, showing decreased vertical soil pressure on the ring, and limits of soil strength at the spring lines; i.e., active on the left and passive on the right

Sidefill soil support is to be included in the load factor

for Class A bedding What is the revised theoretical

load factor? From Figure 12-3, load factor Lf for

Class A bedding is 2.546 The critical moment is MA

= Wf r/8 Including sidefill support, soil pressure is

the third case of Appendix A for which MA = Wf

r(1-K)/8 Sidefill support is at least active pressure for

which K = (1-sinϕ)/(1+sinϕ) If ϕ = 30o, K = 1/3,

and MA = Wf r/12, including sidefill support, the

revised Lf = 3.820 The sidefill increases L f from

2.546 to 3.820 — a significant 50% increase

EVALUATION OF THE REQUIRED D-LOAD

Taking load factors into account, the rationale for

design of rigid pipes is the equating of applied load to

allowable load; i.e.,

(Wl + Wd) = (D-load)Lf

for non-reinforced pipes, and

(Wl + Wd) = (D-load)Lf (ID)

for reinforced concrete pipes

Resolving these equations, the required D-loads for

buried rigid pipes are:

D-load = (Wl + Wd)/Lf (12.5)

UNREINFORCED RIGID PIPES

D-load = (Wl + Wd)/Lf (ID)

= P(OD)/(ID)Lf (12.5)

REINFORCED CONCRETE PIPES

P is the vertical pressure on the pipe Loads, W, are

based on complex pipe-soil interactions such as pipe

settlement vs soil settlement (positive or negative

projecting pipe), compaction techniques, water table,

bedding, etc W is further complicated by boundary

conditions (trench vs embankment), imperfect trench

conditions (compressible topfill), properties of the

trench wall soil, tunnels (pipes jacked-into-place), etc

Recognizing the complexity as well as the importance

of the soil loading, before 1993, the American Concrete Pipe Association (ACPA) published values for load factor, Lf , based on the ACPA classification

of trench beddings shown at the bottom of Figure

12-3 Note how the load factors, Lf , are about the same

as theoretical values The empirical ACPA load factors are based on the assumption that soil pressure

on the top of the pipe is approximately uniform It is the bedding that causes pressure concentrations Most engineers assume that Class D bedding is

impermissible, a term first proposed by Marston It

is noteworthy that, in general, no safety factor is needed in Equations 12.5 Margins of safety are already in place — soil arching, horizontal support of the pipe by the sidefill, etc An effective way for the designer to capitalize on these margins of safety is to specify a select compacted embedment; and then to enforce it by inspection Experienced installers comply

An additional margin of safety is provided by the ACPA definition of load, W, based on outside diameter In fact, the mean diameter or inside diameter is more nearly correct See Figure 12-4

Failure is a crack at A, due to a moment The clear span that causes the moment is ID, or possibly mean diameter — not OD For reinforced concrete pipes, the D-load is conservatively multiplied by ID — not

OD or mean diameter

Example What height of soil embankment is allowable over a 24-inch vitrified clay pipe of standard strength if the soil weight is 125 pcf and the bedding is Class B? The nominal pipe size is 24 inches From Figure 12-3, the Class B load factor is 1.9 From Table 12-1, the standard strength is 2600 lb/ft Neglecting live load, and substituting values into Equation 12-5, the allowable height of soil is H = 19.76 ft; or say H = 20

ft Clearly, the effect of live load is negligible No safety factor is needed

Backpacking The allowable load on a buried rigid pipe can be

Table 12-1 D-LOADS—ASTM Standards for Rigid Pipe Manufacturers.

Table 12-1 is still used for some conservative pipeline design and analysis However, in its 1993 Concrete Pipe

Technology Handbook, the American Concrete Pipe Association (ACPA) has abandoned the load factor

concept in favor of an ASCE design procedure The ASCE procedure is based on tests and on finite element analysis that include sidefill soil support and boundary conditions — both pipe and trench — and on soil type and compaction, etc

doubled by backpacking Backpacking is

compressible material against the pipe Styrofoam

has been used Uncompacted soil has been used

Bales of straw and leaves have been tried with

questionable success The concept, called imperfect

trench method, is that backpacking is similar to

packing used to protect fragile products for shipment

Organic material may be suspect, but uncompacted

soil is effective Assuming that the embedment is

cohesionless, soil failure (soil slip) is incipient if the

ratio of maximum to minimum principal stresses is

greater than K = (1+sinϕ)/(1-sinϕ), where ϕ = soil

friction angle

The performance limit of a rigid pipe depends upon

failure of the sidefill soil See the unit cube of soil B

at the spring lines in Figure 12-5 Soil failure can be

either active or passive If the horizontal pressure Px

of the pipe against the soil at B is less than σy /K, the

s oil slips at active resistance, and the pipe wall

collapses inward This is shown on the left side of

Figure 12-5 If the horizontal pressure, Px of the pipe

against the soil at B is greater than σyK, the soil slips

at passive resistance, and the pipe wall collapses

outward This is shown on the right side of Figure

12-5 If the height of backpacking is equal to the OD,

and the stiffness is half as great as the embedment,

the pressure on the pipe is half of what it would be

without the backpacking In Figure 12-5, half of the

backpacking is shown above, and half below the pipe

Accordingly, some designers conservatively specify

half a diameter of backpacking above and below

The compressibility should be no more than half the

compressibility of the embedment In order to

prevent passive soil slip at B, the embedment must

not be excessively compressible The backpacking

must retain soil arches over and under the pipe This

rationale is conservative

An alternate evaluation of height of backpacking is

the classical equation for stresses around a hole with

radial stress, σy, and tangential stress, σ x,

σx/σ y = (ρ2+r2)/(ρ2-r2) (12.5)

See cube, C, at the top of an imaginary soil vault in

Figure 12-5 What is radius ρ at which σx /σ y = 3, assuming that soil friction angle is 30o? The rationale

is that a soil vault forms over the backpacking It is stable at such radius, ρ, that σx < Kσ y But backpacking is needed to prevent soil particles from falling from the vault From Equation 12.5, ρ = 1.414r With a safety factor of two, a good rule of thumb for pipe protection is,

Height of backpacking should be at least half the pipe diameter Backpacking under the pipe is not

necessary

Another rule of thumb is,

Backpacking permits twice the pressure P at top

of the pipe For deep burial, maximum height of soil

over the pipe can be doubled

Example Using typical values, let backpacking pressure on top

of the pipe be σy /2 For embedment at the spring lines, K = 3 What are the limiting ratios of horizontal

to vertical soil pressure on the pipe under high cover? See Figure 12-5

For active soil pressure, RATIO = 2σx /σ y = 4/3; which is improbable because the rigid ring is usually stiff enough resist the 4/3 ratio

of horizontal to vertical pressures

For passive soil resistance, RATIO = 2σx/σ y = 6; which is impossible σ y /2 is less than σx The ring could not fail outward if σ y/2

on top is less than σx on the side Backpacking allows a broad range of tolerance

MARSTON LOAD

In the analysis of soil loads on buried rigid pipes, the Marston load is still used by some pipeliners Con-sider a rigid pipe in a trench as shown in Figure 12-2 The load, W, is the weight of backfill in the trench minus the frictional resistance of the trench walls

Figure 12-6 Comparison of soil pressures against rigid and flexible pipes.

Figure 12-7 Details of reinforced concrete pipes