Numerical Methods in Soil Mechanics 17.PDF

Numerical Methods in Soil Mechanics 17.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 "PARALLEL PIPES AND TRENCHES"

Structural Mechanics of Buried Pipes

Boca Raton: CRC Press LLC,2000

Figure 17-1 Pipe-clad soil column between parallel pipes showing minimum section AA, which must support part of the surface live load W plus the dead load, shown cross-hatched

CHAPTER 17 PARALLEL PIPES AND TRENCHES

When buried pipes are installed in parallel, principles

of analysis for single pipes still apply Soil cover

must be greater than minimum However, the

design of parallel buried pipes requires an additional

analysis for heavy surface loads Consider a

free-body-diagram of the pipe-clad soil column between

two parallel pipes See Figure 17-1 Section AA is

the minimum cross section This column must

support the full weight of the soil mass, shown

cross-hatched, plus part of the surface load W

shown as a live load pressure diagram The soil

column is critical at its minimum section AA at the

spring lines For design, the strength of the column

at section AA must be greater than the vertical load

STRENGTHS

Performance limits of the column are either: 1 ring

compression strength of the pipe wall; or 2

compressive strength (vertical passive resistance) of

the soil at Section AA

1 Ring compression strength of the pipe wall is yield

strength σf For steel pipes, σ f is usually 36 or 42

ksi For rigid pipes, σf is crushing strength of the

wall For plastic pipes, σf depends on temp-erature,

s tress, and service life Manufacturers publish

values

2 Strength of the soil is found as follows Assume

that the embedment is granular and compacted Soil

strength is vertical stress, σy, at slip Horizontal soil

stress is provided by the pipe walls Approximate

soil strength may be found from triaxial soil tests in

which interchamber pressure is equal to the

horizontal pressure, Px, of the pipe against the soil

For circular, flexible pipes at soil slip, Px = Pd = γH

Live load pre s s u r e , P1, has no effect because the

live load is not directly above the pipe If there

should be a water table above Section AA,

compressive soil strength at failure would be the

effective vertical σy confined by

horizontal σx = Kσ y Px = P = σ x + u where u is the water pressure at Section AA

STRESSES

If bond between the soil and the pipe wall could be assured, the column would be analyzed as a reinforced concrete column based on an equivalent (transformed) section But bond between soil and pipe cannot be assured because of fluctuations in temperature, moisture, and loads, all of which tend to break down bond It is assumed that bond is zero Therefore, stresses in the pipe and soil are each calculated independently

DESIGN OF PIPE

Before the soil column is analyzed, the pipe must be adequate See Chapter 6 Design starts with the ring compression equation,

P(OD)/2A = σf /sf, where

OD = outside diameter of the pipe,

A = pipe wall area per unit length of pipe,

σf = ring compression strength of the wall,

sf = safety factor,

P = maximum vertical soil pressure on top of

the pipe

For worst-case ring compression, live load W is directly above the pipe where P = P1 + Pd The live load effect, P1, can be found by Boussinesq or Newmark If W is assumed to be a point load, according to Boussinesq, P1 = 0.477W/H2 See Chapter 4 If live load W is assumed to be a distributed surface pressure, the Newmark integration can be used Soil cover must be greater than minimum by the the pyramid/cone analysis of Chapter 13 In the following it is assumed that the pipe is adequate

DESIGN OF SOIL COLUMN

The following analysis is for flexible pipes Rigid

pipes require modification of the procedure See

Figure 17-1 The vertical load supported by the two

flexible pipe walls at section AA is no less than

2PD/2 = PD So, in the design of the soil column, it

is assumed, conservatively, that the pipe wall

cladding takes a vertical load of PD But this is only

part of the total load The remainder must be

supported by the soil The greatest load occurs

when the heavy live load W is centered above

section AA — not over the top of the pipe At this

location, not only is the live load pressure maximum,

but the portion supported by the pipe wall cladding is

minimum Pipe walls carry dead load, PdD = γHD

Live load, Pl, on the pipes is small enough to be

neglected It is already supported by the ring

stiffness required for minimum cover What cannot

be neglected is the Boussinesq live load on section

AA Soil stress, σy, must be less than strength S'

Vertical stress is soil load divided by the

cross-sectional area

σy = Q'/X = S'/sf (17.1)

where

σy = vertical soil stress on section AA,

S' = vertical soil compression strength,

X = width of section AA between pipes,

sf = safety factor,

Q' = Q - γHD = load supported by the soil at

section AA = total load reduced by the

load that is supported by the pipe walls,

γ = unit weight of soil,

H = height of soil cover,

D = diameter of the pipe = 2r,

Q = vertical load on section AA = wd + w1

Per unit length of pipe, Q is the sum of the dead

weight of the cross-hatched soil mass wd, and that

portion w1 of the surface live load W that reaches

section AA See Figure 17-1 The dead load wd

per unit length (1) of pipe is soil unit weight times the

cross-hatched area; i.e.,

wd = (1)[(X+2r)(H+r) - πr2/2]γ (17.2)

The live load w1 is the volume under the live load pressure diagram of Figure 17-1 at section AA It

is calculated by means of Boussinesq or Newmark

as described in Chapter 4 The pyramid/cone punch-through stress analysis does not apply because the cover is not less than minimum I f Boussinesq is justified, the live load w1 per unit length is

w1 = 0.477WX/(H+r)2 (17.3) Example 1

What is the vertical soil stress at section AA of Figure 17-1? The pipes are corrugated steel, 72-inch diameter, 2-2/3 by 1/2 corrugations, t = 0.0598, separated by X = 1.0 ft of soil, with 1.5 ft of soil cover at unit weight of 120 pcf A surface wheel load of W = 20 kips is anticipated From a ring compression analysis, the 20-kip load can pass over each pipe without exceeding yield stress of the pipe Soil cover is greater than minimum In order to evaluate soil stress at section AA, from Equation 17.2, dead load on section AA is wd = 2.08 kips The live load, wl, can be evaluated by Boussinesq Equation 17.3, or by Newmark Figure 4-6 If the dual-wheel print is 1 ft by 2 ft, based on Newmark,

w1 = 4MWX(1 ft)/2ft2, where,

X = width of section AA = 1 ft

w1 = total live load on section AA,

W = wheel load on the surface,

M = f[(L/B), (B/H)] = coefficient from the

Newmark chart Figure 4-6, for each quarter area of surface load W, where,

B = 0.5 ft,

L = 1.0 ft,

H = 4.5 ft = the Newmark H, which is the depth to section AA = 1.5ft + 3 ft

The Newmark denominator, 2 ft2, is the area of surface load W Substituting values, L/B = 2, and B/H = 0.111, the Newmark M = 0.012, and w1 = 0.48 kips The total load on section AA is,

Q = 2.08 + 0.48 = 2.56 kips

The load supported by the soil alone is,

Q' = Q - γHD = 2.56 - 1.08 = 1.48 kips

γHD is the load supported by the pipe walls

Vertical soil stress on section AA is,

σy = 1.48/(1ft)(1ft) = 1480 psf

Could Boussinesq have been used without significant

error? From Chapter 4, if H/B is greater than 3,

Boussinesq is adequate In this case, H/B is 4.5/0.5

= 9 Let's see if it's adequate From Equation 17.4,

w1 = 0.477(20 kips)(1ft)(1ft)/(4.5ft)2 = 0.47 kips

compared to 0.48 kips by Newmark There is no

question that Boussinesq is adequate

Example 2

What is the vertical soil strength at section AA for

the parallel pipes of the example above? The soil

friction angle is φ = 30o The horizontal pressure of

the pipe wall against the soil at section AA is σx =

γH = 180 psf The vertical strength of the soil at

slip is σxK where K = (1+sinφ)/(1-sinφ) = 3

Vertical soil strength is,

S' = 180(3) = 540 psf

The vertical soil stress from Example 1 is 1480 psf

— much greater than the soil strength, 540 psf It

would be necessary to: triple the space between the

parallel pipes, or place concrete between the pipes,

or specify stiffer pipes

Tank spacing:

For multiple parallel tanks, the following are

minimum spacings which must be increased as

needed to accommodate deadmen or anchor slabs

Refer to Chapter 21 on tank anchors If suf ficient

clearance must be allowed for deadmen to be set

outside of the tank shadow; Spacing between

parallel tanks should be no less than one-fourth

tank diameter The live load is assumed to be

HS-20 dual-wheel load with minimum soil cover of 2.25

ft

Rigid Pipes:

Unlike flexible pipes, rigid pipes do not exert pressure, Px = P, against the soil Total load, Q, is supported by the pipe walls in ring compression and the soil in vertical passive resistance It is possible

to analyze the equivalent section by column design See texts on reinforced concrete There is a great difference between the modulus of elasticity of the pipe wall and the modulus of elasticity (compressibility) of the soil

Safety Factors:

Analyses of the soil column with pipe wall cladding, are conservative Longitudinal resistance of the pipes and soil cover is neglected Also the arching action of the soil cover is neglected Safety factors can be small

PARALLEL TRENCH Buried flexible pipes depend on the embedment for stability Compacted soil at the sides supports and stiffens the top arch What happens to a buried flexible pipe when a trench is excavated parallel to it? What is the stability of the trench? At what minimum separation between the pipe and the parallel trench will the pipe collapse? What are the variables that influence collapse? Answers to these questions were the objectives of an experiment at USU in 1968 In order to reduce the number of variables, ring stiffness was assumed to be zero Results were conservative because no pipe has zero ring stiffness For the most flexible plain steel pipes, D/t is less than 300 For the test pipes, D/t was 600

in an attempt to approach zero stiffness It was necessary to hold the pipes in shape on mandrels during placement of the backfill

Vertical Trench Walls Figure 17-2 is the cross section of a buried, flexible pipe with an open cut vertical trench wall parallel to

it If trench wall AB is cut back closer and closer to the buried pipe, side cover X decreases to the point where the sidefill soil is no longer able to

Figure 17-2 Vertical trench wall parallel to a buried flexible pipe showing the soil wedge and shear planes that form as the pipe collapses

Figure 17-3 Formation of a soil prism on the pipe during ring deflection as the soil wedge is thrust into the trench

provide the lateral support required to retain the

flexible ring The ring deflects, thrusting out a soil

wedge as indicated in Figure 17-3 As the ring

deflects, a soil prism breaks loose directly over the

ring The soil prism collapses the flexible ring In

order to write pi-terms to investigate this

phenomenon, the pertinent fundamental variables

must be identified Ring stiffness is ignored

because the ring is flexible In fact, at zero ring

deflection, the ring stiffness has no effect anyway

The remaining fundamental variables are:

Basic Fundamental Variables Dimensions

X = minimum side cover (minimum L

horizontal separation between

pipe and trench at collapse),

H = height of soil cover over L

the top of the pipe,

Z = critical depth of trench in L

vertical cut (vertical sidewalls)

Critical depth, Z, is a convenient measure of soil

strength It is defined as the maximum depth of a

trench at which the walls stand in vertical cut At

greater depths the trench walls slip or cave in

Critical depth Z may be determined by excavation

in the field, or it may be calculated from the

dimensionless stability number, Zγ/C See Figure

17-6

2C/γZ = tan(45o - ϕ /2) (17.4)

where

Z = critical depth of trench in vertical cut,

γ = unit weight of soil (pcf),

C = soil cohesion (psf),

ϕ = soil friction angle of the trench wall

Z can be found from Equation 17.4 if soil

properties, γ, C, and ϕ , are provided by laboratory

tests

To investigate the four fundamental variables,

three pi-terms are required One possible set is (X/D), (H/D), and (H/Z) Tests show that (H/D)

is not pertinent Only (X/D) and (H/Z) remain as pertinent pi-terms Results of the tests are as follows

For a vertical trench wall excavated parallel to a flexible pipe,

1 Failure is sudden and complete collapse

2 The ring collapses under a free-standing prism

of soil that breaks loose on top of the pipe

3 If the ring has some stiffness, and if soil cover

H is not great enough to collapse the ring, soil may slough off the pipe into the trench This is not considered failure because the soil can be replaced during backfilling

Test data are plotted in Figure 17-4, which shows (X/D) as a function of (H/Z) The best fit straight line equation is, X/D = 1.4(H/Z) The probable error in X/D is plus or minus 0.1, so probable error

in side soil cover, X, is roughly plus or minus D/10 Because field conditions may be less reliable than laboratory conditions, the safety factor should be two Therefore, the minimum side cover, X, might

be specified as,

Of interest in Figure 17-4 are the data points indicated by squares These do not represent collapse The ring stiffness for the test pipes was great enough that part of the shallow soil cover merely sloughed off the pipes after the soil wedge fell into the trenc h If ring stiffness were to be included as a fundamental variable, ring deflection would have to be included Then the coefficient

of friction between pipe and soil should also be included as a fundamental variable

If the pipe has significant ring stiffness, the height

of soil cover that it can support without collapse can be found for uniform vertical pressure with

Figure 17-4 Cover term X/D as a function of soil strength term H/Z for a vertical trench wall excavated parallel to a very flexible buried pipe

Figure 17-5 Trench wall sloped at angle of repose for which the soil is stable, but the flexible ring requires either some ring stiffness or a minimum cover

no side support See Appendix A, from which

moment = Pr2/4 = σ I/c For plain steel pipes

based on elastic theory, at yield stress,

P = 16σf I/cD2 (17.6)

where

P = vertical soil pressure at collapse,

I = moment of inertia of the wall cross

section,

D = pipe diameter = 2r,

c = half the distance to wall surface from

the neutral surface = t/2 for plain pipes,

t = wall thickness of plain pipes,

σf = yield strength of the pipe,

m = D/t = ring flexibility for plain pipes

P = (8σf /3m2) for plain pipes (17.7)

Based on plastic theory (plastic hinging),

P = 24σf I/cD2 (17.8)

P = 4σf /m2 for plain pipes (17.9) Vertical ring deflection at plastic hinging is,

d = 0.01PD3/EI where

d = ∆/D = ring deflection,

∆ = decrease in vertical diameter,

P = vertical pressure on the ring,

D = circular pipe diameter,

EI = wall stiffness per unit length of pipe

Sloped Trench Walls

Figure 17-5 shows a flexible pipe in cohesionless soil for which the slope is angle of repose ~ ϕ Pressure distribution on the ring is triangular as shown Maximum moment at A can be found by Castigliano's equation However, it is sufficiently accurate to find equivalent moment MA = Pr2/4 for average uniform pressure, Px = rγ See

Figure 17-6 Rationale for finding critical depth, Z, of a vertical open cut in a trench wall in brittle soil with cohesion, C, and soil friction angle, ϕ ; 2C/γZ = tan(45o - ϕ/2)

~

Appendix A The required section modulus is,

I/c = MA(sf)/σ f

where σf is yield stress

EXCAVATION

Depth of the excavation must include

"overexcavation" required to remove unstable

subbase material It should be replaced by

approved bedding material Some tank

manufacturers consider soil to be unstable if the

cohesion is less than C = 750 psf bas ed on

unconfined compression test, or if the bearing

capacity is less than 3500 psf In the field, bearing

capacity is adequate if an employee can walk on

the excavation floor without leaving footprints A

muddy excavation floor can be choked with gravel

until it is stable These are conservative criteria

for soil stability

Of greater concern are OSHA safety

requirements for retaining or sloping the walls of

the trench Excavations for tanks are usually

short enough that OSHA trench requirements

leave a significant margin of safety Longi-tudinal,

horizontal soil arching action is significant

These criteria for bearing capacity and cohesion

are equivalent to a vertical trench wall over 20 ft

deep Bearing capacity of 3500 psf can support

more than 29 ft of vertical trench depth at soil unit

weight of 120 pcf Cohesion of 750 psf can

support a vertical open cut trench wall that is more

than 20 ft deep

Critical Depth of Vertical Trench Wall

Granular soil with no cohesion cannot stand in

vertical cut Much of the native soil in which

pipes and tanks are buried have cohesion

Therefore, the wall of the excavation can stand in

vertical open cut to some critical depth, Z See

Figure 17-6 (left) Greater depth will result in a

"cave-in" starting at the bottom corner, O, where

the slope of the failure plane is (45o+ϕ /2) For a two-dimensional trench analysis, the infinitesimal soil cube, O, is subjected to vertical stress, γZ, where,

γ = soil unit weight,

Z = critical depth of vertical trench wall,

ϕ = soil friction angle,

C = soil cohesion

The Mohr circle is shown in Figure 17-6 (right) The orientation diagram (x-z) of planes on which stresses act, is superimposed, showing the location

of the origin, O The strength envelope slopes at soil friction angle ϕ from the cohesive strength, C

At soil slip, the Mohr stress circle is tangent to the strength envelope From trigonometry,

tan(45o - ϕ/2) = 2C/γZ

This is the critical depth Equation 17.4

From tests, Equation 17.4 provides a reasonable analysis for brittle soil If the soil is plastic, soil slip does not occur until shearing stresses reach shearing strength C Consequently, in plastic soil, the critical depth equation is 2c/γZ = 1 Below the water table, critical depth is essentially doubled

Example What is the critical depth, Z, of a vertical, open-cut, trench wall if,

C = 750 lbs/ft2,

γ = 120 lbs/ft3,

ϕ = 30o? Substituting into Equation 17-4, Z = 22 ft This is

a lower limit if the soil has some plasticity (is not brittle) Excavations for tanks are almost never greater than 20 feet

Example

Suppose that a sloped trench wall exposes a pipe

as shown in Figure 17-5 Pressure, Px, must be resisted by ring stiffness What is the required wall thickness for a 72-inch plain steel pipe?