Lecture13 Analysis of Single Piles

7/27/2019 Lecture13 Analysis of Single Piles

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Lecture #13

The Analysis of a Single Pile

- Load Transfer Theor ies

- Static Analysis

- Dynamic Analysis


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Introduction:

Pile foundations have been in use since prehistoric times. The Neolithic inhabitants of

Switzerland drove wooden poles in the soft bottoms of shallow lakes 12,000 years ago and

erected their homes on them (Sowers 1979). Venice was built on timber piles in the

marshy delta of the Po River to protect early Italians from the invaders of EasternEurope and at the same time enable them to be close to the sea and their source of

livelihood. In Venezuela, the Indians lived in pile-supported huts in lagoons around the

shores of Lake Maracaibo. Today, pile foundations serve the same purpose: to make it

possible to build in areas where the soil conditions are unfavorable for shallow

foundations.

The commonest function of piles is to transfer a load that cannot be adequately

supported at shallow depths to a depth where adequate support becomes available.

When a pile passes through poor material and its tip penetrates a small distance into a

stratum of good bearing capacity, it is called a bearing pile(Figure 1a). When piles are

installed in a deep stratum of limited supporting ability and these piles develop their

carrying capacity by friction on the sides of the pile, they are called fr iction piles(Figure

1b). Many times the load-carrying capacity of piles results from a combination of points

resistance and skin friction. The load taken by a single pile can be determined by a static

load test. The allowable load is obtained by applying a factor of safety to the failure load.

Although it is expensive, a static load test is the only reliable means of determining

allowable load on a friction pile.


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Different uses of piles: (a) bearing pile, (b) friction pile, (c) piles under uplift.


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(d) piles under lateral loads, (e) batter piles under lateral loads.


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Transfer of L oad.

The way that the load from a column transfers into the soil through the pile has evolved

during the past fifty years, from Terzaghi at the extreme left figure, through to Prieto

(1978) on the extreme right.


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Tension pil esare used to resist moment in tall structures and upward forces (Figure 1c),

and in structures subject to uplift, such as building with basements below the

groundwater level, or buried tanks. For piles under tension both in sands and clays, the

bearing capacity at the tip is lost. For piles of uniform diameter in sands, the ultimate

uplift capacity is made up of the shaft resistance and the weight of the pile.

Laterall y loaded pil essupport loads applied on an angle with the axis of the pile in

foundations subject to horizontal forces such as retaining structures (Figure 1d and e). If

the piles are installed at an angle with the vertical, these are called batter pil es(Figure

1e).

Dynamic load may act on piles during earthquakes and under machine foundations.

During pile driving, the resistance to penetration is a dynamic resistance. When a pile

foundation is loaded by a building, the resistance to penetration is a static resistance. Both

the dynamic resistance and the static resistance are generally composed of point resistance

and skin friction. However in some soils, the magnitudes of the dynamic and static

resistance may not be quite similar. In spite of this difference, frequent use is made ofestimates of dynamic resistance by dynamic formulas and the wave equation for the load

capacity of the pile. Therefore, we also describe an understanding soil action during

loading.


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The Behavior of Soils Around a Dr iven Pi le.

The effect of pile is reflected in remolding the soil around the pile. Sands and clays

respond to pile driving differently. First, we describe the behavior of clays and then the

behavior of sands.

Clays.

The effects of pile driving in clays are listed in four major categories:

1. Remolding or disturbance to structure of the soil surrounding the pile

2. Changes of the state of stress in the soil in the vicinity of the pile

3. Dissipation of the excess pore pressure developed around the pile4. Long term phenomena of strength regain in the soil

The essential difference between the actions of piles under dynamic and static loading is

the fact that clays show pronounced time effects, and hence the show the greatest

difference between dynamic and static action. These effects may be mechanistically

described as follow.

Let us consider piles driven into a deep deposit of a soft impervious saturated clay. Since

a pile has a volume of many cubic feet, an equal volume of clay must be displaced when

the pile is driven.

The pile-driving operations may cause the following changes in the clay:


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The soil may be pushed laterally from its original position BCDE to BCDE (Figure 2)

or from FGHJ to FGHJ. If the clay has strength which is lost on disturbance, then

relatively small amount of skin friction exist during driving. Since the pile is being driven

into a saturated impervious clay, the ground surface nay heave considerably because of

the displaced volume of clay. This movement may have a significant effect on adjacent

structures. The piles driven earlier in a multiple-pile installation may heave during thedriving of the later piles. If heave of adjacent structures and/or of the piles already

installed is to be avoided, bored piles are sometimes used.

The displacement and distortion of soil caused by a pile during driving.


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Sands

A pile in sand is usually installed by driving. The vibrations from driving a pile in sand

have two effects:

1. Densify the sand, and2. Increase the value of lateral pressure around the pile.

Penetration tests results in a sand prior to pile driving and after pile driving indicate

significant densification of the sand for distances as large as eight diameters away from

the center of the pile. Increasing the density results in an increase in friction angle.

Driving of a pile displaces soil laterally and thus increases the horizontal stress acting onthe pile. For example, according to Meyerhof (1951) based on analysis of field data the

horizontal stress on pile driven in sand is,

s h = 0.5 sv for loose sand

s h

= 0.1 sv

for dense sand


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Group Action of Pi les.

Piles are driven in groups at a spacing ranging from 3 to 4Bwhere Bis the diameter

or side of a pile. The behavior of piles in a group may be quite different than that of a

single pile if the piles are friction piles. This difference may not be so marked in bearingpiles.

A typical bearing pile usually penetrates a short distance into the soil stratum of good

bearing capacity, and the pile transfers its load to the soil in a small pressure bulb

below the pile tip (Figure 3a). If the stratum in which the piles are embedded and all

strata below it have ample bearing capacity, each pile of the group is capable of carryingessentially the same load as that carried by a single piles. If compressible soils exist below

the pile tips, the settlement of the pile group may be much greater than the settlement

observed in the single pile tests, although the bearing pressure may be smaller than the

allowable value. This is due to the overlap of the zones of increased stress below the tip of

the bearing piles and the pile group is likely to act as a unit (Figure 3b). The total stress

shown by the heavy lines may be several times greater than that under a single pile. Theeffective width of the group is several times that of a single pile. However, if the bearing

stratum is essentially incompressible and there are no softer strata below the pile tips, the

settlement of a group of bearing piles may be essentially equal to the settlements observed

in loading tests on isolated piles. In this case, the piles may, if desired, be spaced about as

closely as it is practicable to drive them.


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Stress condition below tips of piles: (a) a single pile, (b) a group of piles.


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Usually, friction piles are driven in groups, the spacing of piles being from 3 to 4B. A

group of piles may fail under a load per pile less than the failure load of a single pile.

The load carrying capacity of group of piles may be determine by considering failure

along the perimeter of the pile groups.

The load-carrying capacity of the friction pile groups in clay is smaller of the two:

- The sum of the failure load of the individual piles or

- The load carried as in group action and the failure as a pier along the perimeter.


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Negative Skin Friction.

If a pile is driven in a soft clay or recently placed fill and has its tip resting in a dense

stratum (Figure 4), the settlement of both the pile and the soft clay or fill is taking place

after the pile has been driven and loaded. During and immediately after driving, aportion of the load is resisted by adhesion of soft soil with pile (Figure 4a). But, as

consolidation of the soft clay proceeds, it transmits all the load onto the tip of the pile.

In case of a fill, the settlement of the fill may be greater than that of the pile. In the

initial stages of consolidation of the fill, it transmit all the load resisted by adhesion onto

the tip of the pile. A further settlement results in a downward drag on the pile. It isknown as negative skin fr iction(Figure 4b). Both these cases should be recognized in

the field in the design of bearing piles. When this condition occurs, the pile must be

capable of supporting the soil weight as well as all other loads that the pile is designed to

carry. Also, if fill is to be placed around an existing pile foundation, the ability of the

piles to carry the added load should be thoroughly investigated.


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Piles in a soft soil overlying a dense strata: (a) Skin friction immediately and during piledriving, (b) negative skin friction afterwards.


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Equations for estimating the static pile capacity:

Meyerhofs Method: Qp= Ap q Nq

Vesics Method: Qp= Ap (c Nc + o N)

Janbus Method: Qp= Ap (cNc + qNq)

Coyle and Castellos: Qp= q Nq Ap

Nordlund Method: Qu= Rs + Rt


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Q ult

rsh

rt

Static Analysis.

Disregarding the weight of soil displaced versus the new concrete and/or steel

introduced, the ultimate pile load Qul tis,

tip bearing shaft frictionQul t = A tx rt + Ashx rsh

In granular soils, the laterally displaced material

compacts the soil around the shaft. Therefore,

Qul t

=(ox N

q) x A

t+(Kx

ox tan) x A

sh

i

where o

is the effective stress at each level

considered,

K( for driven piles) is 1.00 to 2.5, K( for shafts) is 0.25to 0.70 (that is, loose to dense) and

= for in-situ shafts

= 2/3 for driven concrete piles

= 1/3 for driven steel piles

where is the friction angle between the soil and the

pile or the shaft.


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Both rtand rshincrease with depth, but not indefinitely. They stabilize at a particular

value at a depth that is approximately 20 pile diameters. Alternatively, the values for rtand rsh can be found from:

rt = 5 Nq tan

( tons / m

2

)and rsh= rt

11090705040a f

15090703020Nq

4036333028f

>5030-5010-304-100-4N (S.P.T.)

very dense sanddense

sand

medium

sand

loose

sand

very loose sandRelative density

Parameter

TABLE 1. Relationship betweenN(SPT) and for piles in sand.


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Buckling of Piles.

The buckling of fully embedded piles, under the influence of vertical loads only, appears

to be rare. Long, unsupported lengths of timber and H-pile sections have been shown to

be vulnerable to buckling failures. However, modern pile practices use very longunsupported lengths of piles for offshore structures; therefore, buckling of piles may

become important.

Two cases must be recognized. First, the pile is perfectly vertical and there is no

eccentricity in the vertical load. These are ideal situations and may not be fully realized

in practice. There is eccentricity both due to pile driving as well as due to vertical loadbeing not at the center of the section.

However, when a lateral and a vertical load are applied simultaneously the deflections

due to lateral loads result in automatic eccentricity of the vertical loads. Pile with large

eccentricities tend to deflect laterally quite rapidly at low loads. The lateral deflection of

the pile produces soil reactions which may exceed the bearing capacity of the soil.Slender piles sections have a low ultimate bearing capacity resistance because the

bearing capacity is proportional to the pile width.


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Dynamic analysis of pile capacity:

1. The rational pile formula (the basic formula);

2. The Danish formula;

3. Eytelwein formula;

4. Engineering News formula (the most used); and

5. The Wave equation.

Pile driving studies are required for effective design of constructible pile foundations.

Perhaps the oldest method of estimating load capacity of driven piles is to use the

dynamic formula. These formulae relate the measured permanent displacement of thepile at each blow of the hammer, to the pile capacity. They are considered outdated and

seldom used today in pile capacity calculations. Load tests and the use of the wave

equation are more reliable methods of measuring load capacity and are the most

frequently used.


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The Method of I nstallation.The traditional method of inserting piles into the ground is to use the various types of

pile-driving hammers. Drop hammers, single acting hammers, double acting hammers,

diesel hammers and vibratory pile drivers are the principal types of hammers that have

been commonly used in the pile-driving industry.

Drop Hammer. Drop hammers are weights which are raised and allowed to fall freely on

the head of the pile. The hammer is controlled by guides during the fall in order to

ensure axial and square impact. The manner in which the operator releases the hammer

has an important effect on the velocity at impact, and thus on the effective energy

delivered by the blow. Single-Acting Hammer. The single acting hammer uses steam orair pressure to raise the ram, which then falls under gravity imparting its blow to the

head of the pile. Sufficient pres-sure must be supplied to raise the ram to the top of its

stroke, and thus trip the valve. Energy can be reduced to meet special driving conditions

by adjusting external valve slide bars. Double-acting hammer. Double acting hammers

utilize steam or air to power both the up and down strokes of the hammer ram.

Di ff erential acting hammer. Differential acting hammers use steam, air, or hydraulic

pressure to raise and force down the ram. This type of ram differs from a double acting

hammer in that on the down stroke the cylinder, both above and below the piston, is

under equal pressure and the exhausts only on the upward stroke.


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Diesel hammer. Diesel hammers consist of a cylinder or casing, ram, anvil block, and

simple fuel injection system. To start the operation, the ram is raised in the field as

fuel is injected near the anvil block, then the ram is released. As the ram falls, the air

and fuel compress and become hot because of the compression: when the ram is near

the anvil, the heat is sufficient to ignite the air -fuel mixture. The resulting

explosion(1) advances the pile and (2) lifts the ram.

Vibratory hammmer. The principle of the vibratory driver is two counter-rotating

eccentric weights. The driver provides two vertical impulses of as much as 700 kN at

amplitudes of 6 to 50 mm each revolution-one up and one down. The downward pulse

acts as with the pile weight to increase the apparent gravity force. The pile insertion isaccomplished by the push-pull of the counter-rotating weights, which increases the

pore water pressure to a point where the shear strength approaches zero; the soil in

the immediate vicinity of the pile behaves as a viscous fluid.


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Pile driving cushions.


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The Dynamic Formulae.

The driving formula are based on an energy balance between the input energy of the

hammer and the work required to move the pile a small distance. Although the use of the

driving formula is not common practice, the Hileyform of the equation is sometimesused in small projects. Even though it is a well known fact that the results of the dynamic

formula are unreliable and their validity is a controversial subject, engineers use the

formula as a quick reference or starting point to determine the pile capacity. The

following examples illustrate how the formula are used.

TABLE: Basic Pile-driving Formulas

(Qv)b

all = 2E/s+0.1(WD/W)(Qv)b,c

all= 2WH/s+0.1(WD/W)

(Qv)c

all = 2WH/s+1

(Qv)a

all = 2E/s+0.1(Qv)a,c

all = 2WH/s+0.1

For Double-Acting HammerFor Single-Acting HammerFor Drop Hammer


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where,

a Use when driven weights are smaller than striking weights;

b Use when driven weights are larger than striking weights;

c This is based on the most commonly used formula, known as the Engineering NewFormula;

and,

Qal l= allowable pile load in pounds;

Wr= weight of striking parts of hammer (ram) in pounds;

H= effective height of fall (of the ram) in pounds;

E= actual energy delivered by the hammer per blow in foot-pounds;s= average net penetration in inches per blow for the last six inches of driving set; and

WD= driven weights including piles.

Since the appearance of the Engineering News formula in 1893, over 400 dynamic driving

formulas have been proposed. Few have been proven useful, and only two will be

considered as relevant here, the Hiley formula, proposed in 1930 and used considerablyin the United States, and the Janbu formula (1962), used extensively in Europe and

adopted there as a standard in 1978. The original ENR formula of 1893 was developed

for wood piles in sand using a simple drop hammer.


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One simple and widely used pile-driving formula is known as the Engineering-News

formula given by:

Qal l= 2WrH

2 + C

or Qal l= 2E

2 + C

where Qal l= allowable pile capacity,

Wr= weight of ram,

H= height of fall of ram, ft.

s= amount of pile penetration per blow, in./blowC= 1.0 for drop hammer

C= 0.1 for steam hammer

E= driving energy

The Engineering-New formula given before has a built-in factor of 6. Tests have shown

that this formula is not reliable for computing pile loads, and it should be avoided exceptas a rough guide.


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Another pile-driven formula is Knaumas, the Danish formula. It is given by:

Qult = ek (Ek)

s + 0.5 so

where Qul t = ultimate capacity of the pile

ek = efficiency of pile hammer

Ek = manufacturers' hammer energy rating

s = average penetration of the pile from the last few driving blows

so = elastic compression of the pile

so = 2ekEkL

AE

L = length of pile

A = cross-sectional area of pile

E = modulus of Elasticity of pile material

Statistical studies indicate that a factor of safety of 3 should be used as a field control

during pile driving to indicate when desired pile driving to indicate when desired pile

capacity has been obtained.


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Example 1.

Find the allowable load on a steel pipe pile that was driven by a 5000 lb drop hammer

having a 6.5 feet free fall. The pile-driving record showed 12 blows for the last foot of

driving into the granular soil. Of these 12 blows, the last six inches had seven blows.Determine the allowable load on the pile.

Solution.

W = 5000 lb, H = 6.5 feet

s = set or penetration in inches per blow = 6/7 = 0.86 inches / blow

Qal l= 2 WH / (s+1) (from table for drop hammer)

= (2)(5000)(6.5) / (0.86 +1) = 34.8 kips


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Example 2.

A steel HP 14x73 pile was installed by using a Delmag D-22 double acting hammer

having a rated energy of 39,800 ft-lb. Driving records showed 54 blows for the last 9

inches of driving. Estimate the allowable load on this pile.

Solution.

E = 39,800 ft-lb, s = 9/54 = 0.167 in./blow

Qal l= 2E / (s + 0.1) = (2)(39,800) / (0.167 + 0.1) = 298 kips


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Example 3.

Select a suitable driving hammer for a

highway bridge that will be supported on

14 x 14 square precast prestressedconcrete piles (PSPC) at a mid stream, and

establish the driving criterion for a 50-ton

capacity pile with a FS=3.

Solution.

Design load Qal l= 100 kips

Concrete pile length L = 50 feet

Width of pile b = 14 in,

and assume that the driving cushion is

made up of plywood boards, so that thecoefficient of restitution for plywood n = 0.4

River

Marl

Limestone

25

15

10Pile(s)

14 x 14

PSPC


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Weight of the pile Wp= (14/12)2(50 feet)(0.150 kips/ft3) = 10.2 kips

Try a, Weight of the ram Wr= 14 kips (for an MKT S-14, see table on next slide)

Check the ratio of Wr / Wp = 14 / 10.2 = 1.37 < 1.5 which is satisfactory.

The MKT S-14 hammers energy HE= 37.5 ft-kips

The height of fall of the ram h= HE/ Wr= 37.5 / 14 = 2.67 feet

and that hammer has an efficiency e = 0.9.

The elastic compression of the pile cap, sc= 0.37 in

The elastic compression of the pile itself, sp= 0.006 L = 0.006(50) = 0.30 in

The elastic compression of the soil, ss= 0.10 in

Table of most commonly used hammers.


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752054.37439-603.06.629DieselDelmag D-39

833060.18140-603.27.132DieselKobe K-32

4160304180-842.35.123DieselLink Belt 520

44303243481.8418DieselMKT C-826

22201622480.929DieselMKT C-826

270019.5261303.06.529HydraulicRaymond 0-30

500036491036.41462DifferentialVulcan 140C

340024.5331113.6836DifferentialVulcan 80C

33302433953.6836CompoundMKT C-826

265019.126952.3522Double-actingMKT 11B-3

222016221102.3522Double-actingMKT C-5

520037.551606.41462Single-actingMKT S-14

226016.322602.3522Single-actingMKT S-5

623604506106068150668Single-actingVulcan 3150 CT

16630120163601840178Single-actingVulcan 040

338024.466503.47.533Single-actingVulcan, Raymond 0

20801520602.3522Single-actingVulcan, Raymond 1

kgfmft-kipskNmMin.103kgkipskN

BlowPerEnergyperWt. RamTypeHammer

Blows

b e o os co o y used e s.


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2

2

12 ( )

(0.5)( ) ( )

12(14)(0.90) [(14) (0.40) (10.2)]300(0.5)[(0.37) (0.30) (0.10)] (14 10.2)

0.49

125 50 .

R R Pu

c p s R P

W e W n W Q

s s s s W W

kipss

s inches per blow

or blows per foot driving criterion for a ton designs

+=

+ + + +

+=+ + + +

=

= =

Lecture13 Analysis of Single Piles

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