Numerical Methods in Soil Mechanics 25.PDF

Numerical Methods in Soil Mechanics 25.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 "LONG SPAN STRUCTURES"

Structural Mechanics of Buried Pipes

Boca Raton: CRC Press LLC,2000

Figure 25-1 Two of many typical long-span structures — horizontal ellipse (top), and an inverted pear shape (bottom) to serve as a grade separation for a road over a railroad

CHAPTER 25 LONG SPAN STRUCTURES

The term "Long Span" refers to corrugated steel

pipes in large diameters The "pipes" are more often

non-circular than circular The most common

shapes are pipe arch, horizontal ellipse, low profile

arch, high profile arch, underpass, and the inverted

pear They serve as small bridges and grade

separations The structure comprises corrugated

steel plates (structural plates) that are bolted

together on site The distinguishing feature is the

low ring flexibility because of the large radii

Moreover, because the plates are bolted together,

ring flexibility is less than the theoretical values listed

in the AISI Handbook of Steel Drainage &

Highway Construction Products From one field

test the actual ring stiffness was roughly 80% of

theoretical

For standard corrugated circular steel pipes, a

maximum flexibility factor, FF, is recommended for

handling and installation; i.e.,

where

E = modulus of elasticity = 30(106) psi,

D = diameter; i.e., horizontal span (inches),

I = moment of inertia of the wall (in4/inch)

From the AISI Manual, recommended maximum

values of FF for ordinary installations are:

FF = 0.0433 in/lb for factory-made pipe with riveted,

welded, or helical seams

FF = 0.0200 in/lb for field-assembled pipe with

bolted seams

Despite the maximum value of FF = 0.0200 for

field-assembled pipes long-span pipes can exceed 0.02

in/lb if embedment is carefully placed and

c ompacted For example, for a 30-ft span of 6x2

structural plate with t = 0.218 inch; the theoretical

I = 0.127 in3; and the flexibility factor is FF = 0.035

in/lb At 80% of theoretical I, FF = 0.043 If the span is increased to 50 ft for this example, FF = 0.118 in/lb Fifty-foot spans are in service The success is based on careful installation For shapes other than circular, AISI publishes modification factors

From principles of similitude, FF is not a correct property for buried pipes with distributed soil

pressure agains t the ring FF is correct for a concentrated force on the ring which is more

typical of handling loads than of buried soil pressures

Some design procedures base ring flexibility on the Iowa formula See Appendix B They propose that the EI term (structure) in the denominator must exceed some recommended percentage of the 0.061E'r3 term (soil) This is intended to be minimum ring stiffness for soil-structure interaction

In fact, the Iowa formula only predicts ring deflection — not a ring stiffness required for installation Of course, designers specify a maximum allowable ring deflection — but for other reasons than ease of installation Without an elaborate scaffold of stulls, struts, and ties to hold the shape of the structure during installation, a minimum ring stiffness is desirable So required ring stiffness

is an economical trade-off with cost of installation

The Iowa formula applies to circular rings Most long-span structures are not circular Nevertheless,

as in the case of circular rings, the greater the stiffness, the less will be the care required to hold the structure in shape during installation

Performance Limits

The basic performance limits after installation are discussed in Chapters 9, 10, and 13 These include ring compression, soil support, minimum cover, etc But for very flexible long-span structures, additional precautions are required during installation Failures

have occurred during construction of the structure

and placement of the embedment Installation

performance limits include: 1 shape of the

structure, 2 unstable soil-structure interaction, and

3 minimum soil cover

1 Shape

The structure must be held in shape during

placement of the embedment soil Shape can be

monitored by hanging plumb bobs inside at

appropriate locations such as the crown, and at

changes in radius of the plates Because plumb

bobs are affected by wind, a laser beam is a better

datum for monitoring the shape Measurements by

steel tape at any angle from the laser beam to

pre-identified points on the structure can be monitored

The cross section should be monitored at a number

of stations throughout the length of the structure

because corrugated structures can deflect

longitudinally

In the case of horizontal ellipses, and profile arches,

the top radius is usually a circular arc of about 80o

However, the arc angle can vary For pipe arches,

the top arc angle is greater than 80o

Installers resort to various techniques for holding

the structure in shape during placement of the soil

Once the structure is assembled on a plane surface

bedding, it is essential that support be continuous

a) Preshaping the bedding to fit the structure has

been tried The procedure is tedious and imperfect

Continuous support is not assured In some cases,

the structure has been dragged longitudinally a few

feet fore and aft to seat (preshape) the bedding

b) Well-graded soil can be flushed under the

structure from windrows of soil by means of

high-pressure jets (usually water — sometimes air)

Laborers do not respond enthusiastically to the

requirement of ramming soil under the bottom plates

with 2x4 studs

c) Flowable soil cement is an increasingly

popular option See Chapter 16

An alternate option is elimination of the bottom

plates which are replaced by footings See profile arches in Figure 9-1 The footings must be able to resist the thrust Pry due to pressure P on top of the structure where the radius is ry Because thrust Pry

on the footings is at an angle, subbase support of the footings must take into account shear on, and overturning of, the footings, as well as vertical bearing capacity of the subbase

Once the structure is bedded, soil is placed and compacted in lifts as described in Chapter 16, keeping soil lifts balanced on the sides of the structure in order to prevent sidewise movement Heavy compactors must be kept outside of the 45o

tangent plane as described in Chapter 16 In spite of care in placing embedment, soil pressure on the sides of the structure causes the top of the structure

to hump up (uplift) The uplift must be limited and controlled Manufacturers recommend allowable percentages of uplift during installation Part of the uplift can be reversed when soil is placed over the top of the structure — but don't depend on it Sidefill holds the structure close to its "uplifted" shape

In some cases, the structure is stulled, strutted, and/or tied to hold it in shape during placement of embedment soil Care is required to prevent damage

to the structure such as dents or perforations by stulls and struts when backfill is placed on top of the structure Tie wires (diagonal and horizontal) can be

of such a gage that monitoring includes tension (or even the first break) in horizontal wires One project monitored tension in the tie wires by the pitch sound of the wire when plucked

If the structure approaches the limits of its uplift, a windrow of soil can be placed (by crane) on top Or additional tie wires can be placed from the crown to the bottom plates or diagonally from the crown to the corner plates or footings

2 Stability Embedment soil must be of good quality in order

to assure performance during floods (high water

table), earth tremors, excessive surface loads, etc

Where groundwater is a problem, soil should have

adequate strength (bearing capacity) both when

saturated and when dry It must be dense enough

that it will not liquefy by earth tremors These

precautions are imperative for the small radii at the

sides of horizontal ellipses and low profile arches

The precautions are reversed for high profile arches,

underpasses, and inverted pears Because of the

large radius of curvature of the sides, a very small

horizontal soil pressure can deform the structure

During placement of sidefill, there is no topfill to

resist uplift In such cases, horizontal struts can be

placed in the structure to prevent horizontal

deflection In some cases the side plates can be tied

back to deadmen when deflection becomes

significant If uplift begins to approach the

maximum allowable during placement of sidefill, a

windrow of soil placed on top of the structure can

arrest or reduce uplift

Any scaffolding (stulls, struts, ties) inside the

structure should be removed after stability is

achieved, but before high soil cover (topfill) is placed

over the structure, and before heavy surface loads

pass over The basic criterion for stability is

minimum cover Of course, compaction of topfill

directly over the structure must be done carefully

See Chapter 16

3 Minimum Cover

Stabilization of the structure is minimum soil cover to

protect the structure from surface wheel loads

Minimum cover is analyzed in Chapter 13 for

circular flexible pipes The same analyses apply to

long spans where the critical radius is the radius of

the top plates For analysis by ring compression, the

diameter, D, is the span Two additional concerns

must be investigated: multiple axle loads and

distribution of wheel loads on the structure

a) Multiple axle loads can affect soil pressure

distribution on top of the structure It may be

prudent to analyze the effect of wheel spacing on

axles — especially if the load could be moving

longitudinally along the pipe Wheel spacing might justify a finite element analysis or a Castigliano analysis with a more complex soil pressure diagram than was used for circular pipes in Chapter 13

b) In Chapter 13, critical pressure on the pipe due to surface live loads was based on the rationale that a truncated pyramid is punched through the soil cover The live load effect on the pipe was uniform pressure over half of the ring In the case of long-spans, the top arch may be so large that the punched-through pressure area is smaller than the top arch More complicated analysis may be required

Example

An inverted pear was designed as a railroad grade separation Nomenclature and dimensions are shown in Figure 25-2 Data are:

Structure: 6x2 corrugated sectional plate

D = 28 ft = span,

ry = 25 ft = top radius,

σf = 36 ksi = steel strength,

E = 30(106) psi elastic modulus,

t = 0.218 = nominal steel thickness,

A = 3.2 in2/ft = wall cross-sectional area,

I = 1.523 in4/ft = theoretical moment of inertia,

from the AISI Handbook of Steel

Drainage & Highway Construction Products,

S = 1.376 in3/ft = I/c

Soil:

γ = 100 pcf = soil unit weight,

ϕ = 30o,

H = 3 ft of soil cover, Load:

a) Find dual-wheel load, W, if it is assumed to

be concentrated at midspan

σ = PD/2A where P = Pd + Pl

Pd = 300 psf dead load of soil cover,

Pl = 0.12 W/ft2 = 0.477W/H2 by Boussinesq, Substituting values and solving, W = 66 kips If the wheel load is HS-20 load (16 kips), the safety

Figure 25-2 Nomenclature and dimensions for a long-span, pear-shaped structure to serve as a road grade separation The dimensions are used in the example and problems in this chapter This structure meets clearance requirements of the American Railroad Engineering Association (AREA) a) If the specified soil cover is 3 ft, what is the allowable surface load, W, based on ring compression?

3'

factor in ring compression is 4 What about multiple

axles?

b) During installation, with compacted select soil

cover of only 2 ft, there arises a need for a

dual-wheel truck to pass over the structure What is the

allowable dual-wheel load, W, based on slip of soil

wedges? If the structure is not deformed, stiffness

is negligible From the dimensions of Figure 25-2,

soil pressures against the structure are as shown in

Figure 25-3 (top) Critical soil wedges are shown

in Figure 25-3 (bottom) Ignoring shear, the soil

resistance at point C on the corner plates (shoulder)

is 4.745 ksf = 33 psi Assuming that the dual tire

print is 7x22 inches, and the truncated pyramid

slopes at 1h:2v, the live load area at A is

(7+24)(22+24) = 1426 in2 At punch-through,

P = Pd + Pl = 1.39 psi + W/1426in2

Because Pr is constant all around the perimeter of a

flexible structure, at the corner , C , Pc = 4.17P

Substituting values and solving, W = 9.3 kips Allow

an axle load of 18 kips to cross — with care and

restraint of corners (shoulders).

Safety Factor

Fortunately, the concerns for long-span structures

are worst-case Soil placement and compaction is

usually done with care Analysis neglects

longitudinal soil arching Neglected also, is the

longitudinal beam strength of the corrugated

structure Despite the accordion configuration of

corrugations, the structure has some longitudinal

strength Therefore, safety factors can be small In

minimum cover tests, the punch-through load is

greater by a factor of two than is predicted by soil

slip analysis A surface load test was performed on

a long-span structure, 6x2 corrugation, 0.218

structural plate, 12-ft top radius, with 20 inches of

well-compacted select soil cover A single-axle

dual-wheel load punched through when the axle

weight was finally raised to 168 kips Failure was

catastrophic

PROBLEMS

25-1 What is the maximum dual-wheel load at soil slip for the above example of a pear-shaped structure if soil cover is assumed to be the specified minimum H = 3 ft? The tire print is 7x22 inches a) Check ring compression at A,

b) Ring compression at maximum span, c) What is load, W, at minimum cover?

(W = 7.6 kips) 25-2 Problem 25-1 considers only the top arch Now consider the corner (shoulder) plates of 6 ft radius What is the maximum dual-wheel load, W,

if the shoulder plates are supported by soil of 100 pcf and friction angle of 30o? Analyze for both horizontal equilibrium and vertical equilibrium Include the hold-down force of the top arch on the

25-3 A long-span ellipse is a bridge over a stream During a flood, the bridge is partially plugged, causing the water table to overflow the road surface What must be the friction angle of the granular soil at the spring lines when an HS-20 dual-wheel load of 16 kips passes over? See sketch Inside the ellipse is essentially empty

(ϕ = 32.6o)

Figure 25-3 Pear-shaped long-span showing soil pressures (top) and the pressure diagrams for the soil wedge slip analysis (bottom) The soil cover of H = 2 ft is less than minimum in this example