obtaining ductile performance from precast, prestressed concrete piles

8/15/2019 Obtaining Ductile Performance From Precast, Prestressed Concrete Piles

1/17Summer 2009 | PCI Journal4

Editor’s quick points

n A parametric study of the inelastic seismic response of precast,

prestressed concrete piles was conducted to determine

whether piles with only light transverse reinforcement could act

as ductile structural elements.

n A nonlinear, inelastic finite-element program written specifically

for this project was used to validate results for both laboratory

and in-place testing.

n The addition of mild-steel longitudinal reinforcement did not

enhance ductility of the piles, though it did increase flexural

strength.

Obtaining

ductile

performancefrom precast,

prestressed

concrete

piles Andrew Budekand Gianmario Benzoni

In general, concrete piles are intended to behave as elastic

structural elements when subjected to seismic loading. Ex-

ceptions include single-pile columns, which are typically

designed to support the development of a subgrade plastic

hinge under seismic loading.1 Elastic behavior is preferred

because of the difficulty of repairing foundations and the

possibility of reinforcing steel being exposed to corrosive

materials due to the extensive cracking and spalling that is

a consequence of plastic hinging.

Prestressed concrete piles were first used as founda-

tion elements in the early 1950s. They offer a number

of advantages to the designer and contractor. Inherently

resistant to tensile stresses, prestressed concrete piles can

be economically fabricated off-site, safely transported,

and easily handled during the pile-driving process. Their

ability to resist tensile stress without cracking is advanta-

geous because inadvertent tensile stresses applied during

construction or service will be less likely to lead to crack-

ing of the concrete, thus reducing the risk of corrosion of

the pile’s steel reinforcement.

Piles carry both axial load and lateral force. Axial load is

resisted by a combination of end bearing and skin fric-

tion (the dominant load-resisting mechanism depends on

the soil characteristics). Lateral forces (for instance, those

imposed by seismic excitation of the superstructure) are

resisted by a combination of shear and bending resistance.

Ideally, a foundation would be designed to remain elastic

under seismic load (as repair of damage to piles after an

earthquake is, at best, difficult), yet this is not normally

practical for pile-column designs, and hinging of piles in a


2/17 6PCI Journal | Summer 2009

s =

4 Ah

d' s= 0.12

f c

'

f yt

0.5+1.25 P

axial

f c' A

g

+ 0.13l

0.01( ) (1)

where

Ah = area of the spiral steel

d' = core diameter

s = spiral pitch

f

c' = concrete compressive strength

f yt = yield strength of the transverse reinforcement

Paxial = axial load

Ag = gross cross-sectional area

ρ l = ratio of area of distributed longitudinal reinforce-

ment to gross concrete area perpendicular to that

reinforcement

However, it is not less than the minimum specified in ACI

318 section 10.9.3, given by Eq. (2).

pile-cap configuration may be difficult to avoid. Thus, the

inelastic behavior of prestressed concrete piles warrants

study. Under lateral loads imposed by an earthquake, an

individual pile (with a fixed head condition) may develop a

moment pattern of the shape in Fig. 1.

Inadequate detailing of early prestressed concrete piles

may have caused inadequate performance in several earth-

quakes, such as the 1964 Alaska2 and 1972 Miyagi-Ken-

Oki3 events. The relation of a pile’s detailing deficiency

to its poor performance has been identified by several

researchers.4–6

Unfortunately, the response to inadequate performance has

been either a complete ban on precast, prestressed concrete

piles in seismic applications or the specification of ex-

tremely conservative amounts of transverse reinforcement,which make precast, prestressed concrete piles uncompeti-

tive in the marketplace.

Piles in seismic regions are governed by the provisions of

the American Concrete Institute (ACI) in Building Code

Requirements for Structural Concrete (ACI 318-05) and

Commentary (ACI 318R-05)7 chapter 21. The minimum

transverse reinforcement ratio ρ s in section 21.4.4 was

modified by Priestly et al.8 as Eq. (1).

Figure 1. This drawing shows the pile moment pattern resulting from axial and lateral loads. Note: 1 m = 3.28 ft; 1 kN = 0.225 kip.


3/17Summer 2009 | PCI Journal

s = 0.45

A g

Ah

1

f c

'

f yt

(2)

where

Ah = cross-sectional area of a structural member measured

out to out of transverse reinforcement

In the case of a typical 610-mm-diameter (24 in.) pile,

using twenty-four 13 mm (1 / 2 in.) special tendons and a

76-mm-thick (3 in.) cover, Eq. (1) would be superseded by

Eq. (2), giving a required transverse reinforcement ratio of

3.5%.

This amount of spiral steel reinforcement would lead to

congested construction; the spiral pitch in the plastic hinge

regions using D9.5 (0.348 in. [8.8 mm]) wire would be

18 mm (0.71 in.) (as opposed to 63.5 mm [25 in.] in Fig.

2). This is not acceptable, as ACI 318 specifies Eq. (3).

4d b ≤ s ≤ 6d b (3)

where

d b = main bar diameter

Here, d b is the tendon diameter of 13.2 mm (1 / 2 in.). Use

of D19 (0.49 in. [12 mm]) wire would give an accept-able pitch of 71 mm (2.8 in.), but forming the spiral to the

required 229 mm (9.0 in.) radius would be difficult, slow,

and costly.

If the spacing requirements were relaxed to allow the

use of a lighter-diameter wire at a smaller pitch, another

problem would be created. The use of a small aggregate

size would be mandated by the need to get a good aggre-

gate connection between the core and the cover. Failure to

provide a solid interface could result in spalled cover at the

pile head during driving.

It would, therefore, be advantageous to show that levels of

displacement ductility adequate for competent foundation

performance can be achieved using levels of transverse

reinforcement commensurate with ACI 318 section 21.4.4,

without the restriction that the minimums of section 10.9.3

be met.

The research presented in this paper gives the results of

a parametric study using a pile modeled with transverse

reinforcement slightly less than that required by ACI 318

section 21.4.4. The parameters that varied are axial load,

lateral soil stiffness, and the type of pile-cap connection.

Figure 2. This graph compares the results of the finite-element-model prediction with the in-place pile test. Note: The pile had a 400 mm (16 in.) diameter with 50 mm

(2 in.) of cover, transverse reinforcement ratio = 0.006, longitudinal reinforcement ratio = 0.021, and axial load ratio = 0.1 f c ' A g . A g = gross cross-sectional area; f c

' = con-

crete compressive strength; K = subgrade reaction modulus. 1 m = 3.28 ft; 1 kN = 0.225 kip.



son.13 In these tests, 0.406-m-diameter (1.33 ft) piles wereembedded in soil placed under controlled conditions into a

purpose-built soil box and tested under combined axial and

lateral load. Figure 2 shows the force-displacement enve-

lope and predicted response from the first of these tests.

The general trends of the test results—such as elastic stiff-

ness, beginning of the softening branch, and incipient fail-

ure—are reproduced by the prediction. Some discrepancies

may be attributed to conservative modeling assumptions.

First, the initial stiffness of the test pile was higher than

that predicted. This comes from the action of the small-

strain modulus of elasticity of the soil, which is estimatedat four times the large-strain value.14 This factor-of-four

difference is quite close to that shown in Fig. 2. Second,

the model underpredicted the maximum lateral force by

about 12%. This can be directly attributed to the use of the

28-day concrete strength to generate the prediction, rather

than day-of-test strength. This was the prediction placed

on the plotter at the test site.

Use of the nondimensional system stiffness term KD6 /

D* EI eff was also validated through comparison with this

in-place testing program. One observation from previous

analytical work was that the center of the plastic hinge

Analytical modeling

The analytical models of the soil-pile system used in this

study were based on the nonlinear, inelastic finite-element

modeling of a Winkler beam (a beam on a flexible founda-

tion). The pile was represented using beam elements and

the soil using lateral springs acting at the nodes (Fig. 3).

Finite-element analysis (FEA) for inelastic soil-pile inter-

action has been verified through field studies.9 FEA was

chosen due to its flexibility in representing both pile and

soil properties.

Budek et al. used nonlinear, inelastic constitutive models

for both the pile and soil and described them in detail.1

Briefly, the change in flexural stiffness of the pile as

inelastic action took place was extracted from the moment-

curvature data as the slope of the moment-curvature curve.

Lateral load was applied in a series of steps. The elements’

flexural stiffnesses were modified as necessary after each

load step, according to the elements’ respective average

moment. Pile yield was defined by tendon stress reaching

85% of its ultimate value.

A bilinear soil model was used in which the lateral stiff-

ness of the soil (that is, individual spring stiffness) was re-

duced to one-fourth of its original value when the displace-

ment at a node associated with a given spring exceeded

25.4 mm (1 in.).

Soil stiffness as expressed by the subgrade reaction modu-

lus K ranged from 3200 kN/m3 to 48,000 kN/m3

(20 kip/ft3 to 300 kip/ft3). The nondimensional system stiff-ness KD6 / D* EI eff is used to describe the properties of the

soil-pile system. It includes cracked-section flexural stiff-

ness EI eff of the pile shaft, and normalizes the pile diameter

D against a reference pile diameter D* of 1.83 m (6.0 ft).

Budek et al. describes its derivation.10

The FEA program used was written specifically for this

research program and was validated through comparison

with laboratory testing10–12 and against results from in-place

testing.9,13

The laboratory testing program consisted of a series of 16tests,10 which included a number of precast, prestressed

concrete pile shafts of a size and configuration similar to

those examined in this study. The purpose of the investiga-

tion was to characterize the effect of external confinement

(as may be provided by competent soil) on the flexural

ductility available in the pile shaft at the subgrade hinge

(Fig. 1). The finite-element model in this study successful-

ly predicted pile-shaft response under the imposed loading.

The analytical model was further validated by comparison

with a series of four in-place tests of free-head reinforced

concrete pile-columns performed by Chai and Hutchin-

Figure 3. The prestressed pile analytical model is shown with indicated forces.

The notch in the cap of the prestressed model is for illustrative purposes, to allow

the top spring to be shown. Note: K 1 = subgrade reaction modulus associated with

node 1; K 2 = subgrade reaction modulus associated with node 2; K 3 = subgrade

reaction modulus associated with node 3; K 4 = subgrade reaction modulus as-

sociated with node 4; K 5 = subgrade reaction modulus associated with node 5; K n

= subgrade reaction modulus associated with node n; K n -1 = subgrade reaction

modulus associated with node n – 1.



center of the plastic region after testing, fall almost directly

on the curves.

In this study, the structure was modeled as a 0.61-m-

diameter (2 ft) continuous pile. Depth to the pile base was

set at 24.4 m (80 ft), which is equal to 40 D and exceedsthe depth corresponding to long-pile response. The pile

head was assumed to connect to a cap at ground level.

Axial load varied from zero to 0.4 f

c' Ag to represent forces

from global overturning moments transferred from the

superstructure.

The pile section used in the analysis was a typical 0.61-m-

diameter (2 ft) round pile as used in California. Figure

2 shows the details. A transverse reinforcement ratio of

1% was chosen for this study, slightly less than the 1.2%

that would result from the use of Eq. (1). Nominal effec-

tive section prestress after losses was 9.3 MPa (1.35 ksi).Figure 5 shows the section geometry.

Three different types of pile–pile cap connections were

considered: pile head embedded in cap, tendons embed-

ded in cap, and tendons stressed through cap. Each was

examined with and without the presence of mild-steel

longitudinal bars providing dowel reinforcement through

the pile-cap connection and down through the area of the

subgrade plastic hinge (Fig. 4). The piles’ flexural respons-

es were analyzed using the Mander15 model for confined

concrete modified for prestressed sections. Modifications

allowed for appropriate positioning of tendons with the

in the pile shaft (that is, the subgrade hinge) would move

toward the surface as plasticity progressed from the origi-

nal location of the point of maximum subgrade moment.

Its terminal location when the ultimate inelastic capacity

of a free-head pile is known (in which the subgrade hinge

controls response) can therefore be predicted. It is consis-tently at a depth of 70% of the point of maximum subgrade

elastic moment, a value that is insensitive to either soil

stiffness or above-grade height of the pile head. The actual

depth is, of course, a function of both of these variables.

Figure 4 shows curves predicting subgrade hinge depths

for the above-grade heights tested in the relevant range of

nondimensional system stiffness for the four tests con-

ducted by Chai and Hutchinson. The depths of the centers

of the plastic hinges, determined by digging down to the

Figure 4. This graph compares the predicted and observed plastic-hinge depths from in-place pile tests. Note:D = pile diameter; H = depth of plastic hinge.

Figure 5. This drawing illustrates the prestressed concrete pile section.

Note: f c ' = concrete compressive strength; D9.5 = 8.8 mm. 1 mm = 0.394 in.; 1 m

= 3.28 ft; 1 MPa = 0.145 ksi.



was handled similarly. Active prestress went from zero

to its full value over the transfer length, and the effect of

stressing the tendons was modeled by applying an extra

increment of axial load to each section (in addition to the

design load), such that the combination of this additional

axial and prestress load would remain constant (that is,

40% of prestress at 40% of d b was supplemented by an

axial load equivalent to 60% of the prestressing force).

Strain penetration of the longitudinal reinforcement into

the cap is an important part of modeling. In the response of

actual structures it permits a larger rotation at the pile-cap

connection. It was modeled in this study by decreasing the

stiffness of the pile’s top element as yielding of the tensile

reinforcement occurred.

For plastic hinges forming against supporting members,

such as footings or cap beams, theoretical and experi-

mental studies have led to the development of Eq. (4) for

plastic hinge length l p.8

l p = 0.08 L + 0.022 f yd bl (4)

correct level of prestressing force applied through the sec-

tion analysis, which produced the moment-curvature data

used as input for the FEA.

Previous experimental work 6,16–20 has shown that similar

pile-cap connections can support ductile response up to a

displacement ductility level of six.

Modeling of the different connections was addressed

through variation of either section prestress or axial load

in calculating moment-curvature data. For the pile head

embedded in the cap, full prestress was assumed at the

bottom of the cap (that is, full transfer was assumed at the

interface) (Fig. 6). To model embedment of the tendons,

effective prestress was assumed to go from zero at the top

of the pile to its full value at the end of the transfer length

of 115d b.21,22 This part of the pile was, therefore, modeled

in 10 sections, adding 10% of the effective prestress each

time. Therefore, the input data for this case consisted of 11

sets of moment-curvature data (output from the Mander

model analysis) applied to the relevant section of the pile.

The practice of stressing the tendons through the pile cap

Figure 6. Three prestressed concrete pile–pile cap connections were considered in this study and are shown without reinforcing steel dowels. Note: The nominal embed-ment length of a pile head embedded in cap is two pile diameters. d b = main bar diameter.



Figure 7. This graph compares Eq. (1) results with nominal design values for a prestressed pile with head embedded in cap with no nonprestressed, longitudinal reinforce-

ment. Note: A g = gross section area; D = pile diameter; D * = reference pile diameter; EI eff = cracked-section bending stiffness of the pile; f c ' = concrete compressive

strength; K = subgrade reaction modulus; P axial = axial load.

Figure 8. This graph plots the moment versus height for a pile head embedded in cap with no reinforcing dowels. Note: f c '

= concrete compressive strength; K = subgradereaction modulus; P axial = axial load. 1 m = 3.28 ft; 1 kN = 0.225 kip.



where

L = distance from the critical section to the point of con-

traflexure (point A in Fig. 1)

f y = yield strength

d bl = longitudinal bar diameter

The first term in Eq. (4) represents the spread of plasticity

resulting from variation in curvature with distance from the

critical section and assumes a linear variation in moment

with distance. The second term represents the increase in

effective plastic hinge length associated with strain pen-

etration into the supporting member.

Figure 7 shows that Eq. (4) overestimates the plastic hinge

length for the hinge occurring at the pile–pile cap connec-

tion. Using typical values from an elastic analysis for depthto point of contraflexure at yield for a pile with the pile head

embedded into the cap (both with and without reinforcing

dowels), the plastic hinge length is substantially greater than

that resulting from the present inelastic analysis.

Used in this context, Eq. (4) demonstrates one of the

inaccuracies associated with elastic analyses of piles:

when yielding is reached in the pile’s critical section, the

structure softens and a lesser depth of soil needs to be mo-

bilized, thus moving the point of contraflexure toward the

surface. If an appropriate correction is made, Eq. (4) gives

a reasonable prediction of l p.

The second term in Eq. (4), representing strain penetration,

is straightforward in cases in which dowels are present

because the dowels’ yielding is concurrent with the yield

point of the structure. Where prestressing tendons alone

form the longitudinal steel, however, interpretation of

strain penetration is complicated by the fact that tendons

in general require a development length about twice that ofdeformed, nonprestressed reinforcing steel. Also, ultimate

tensile strains in prestressing steel are about half those of

ordinary reinforcing steel, and even this is compromised

by proximity to anchorages, with their attendant stress ris-

ers. Thus, the strain penetration length should be consider-

ably longer in the case of prestressing steel. Accordingly,

in this study the strain penetration length for prestressing

tendons was assumed to be roughly equivalent to that

resulting from the use of ordinary reinforcing bar of twice

the diameter of the prestressing steel used, in this case

455 MPa (Grade 60) 29M (no. 9) deformed bar.

Results

Flexural responseand moment patterns

The response of piles to lateral loading is best introduced

through examination of moment patterns. In the case of

a fixed-head pile, the maximum moment, which controls

overall response, is generated at the pile-cap connection,

and a secondary moment maximum forms below grade.

Modeling inelastic pile response resulted in the formation

of a plastic hinge at the pile-cap connection, after which

Figure 9. This graph plots the moment versus height for a pile head embedded in cap with no reinforcing dowels. Note: A g = gross section area; f c ' = concrete compres-

sive strength; K = subgrade reaction modulus; P axial = axial load. 1 m = 3.28 ft; 1 kN = 0.225 kip.



Analyses of other end conditions and considering the

presence of dowels show similar trends. Ultimate moment

versus height for three levels of axial load Paxial (0,

0.2 f

c' Ag, and 0.4

f c' Ag) and the yield moment for the pile

shafts is represented. Increasing soil stiffness increased the

the moment was redistributed into the shaft. This resulted

in the formation of a secondary hinge in the shaft. Figures

8 through 10 demonstrate this, and the effect of varying

soil stiffness and axial load on pile response is represented

for the case of the pile head embedded into the cap.

Figure 10. This graph plots the moment versus height for a pile head embedded in cap with no reinforcing dowels. Note: A g = gross section area; f c ' = concrete compres-

sive strength; K = subgrade reaction modulus; P axial = axial load. 1 m = 3.28 ft; 1 kN = 0.225 kip.

Figure 11. This graph plots the moment versus height in comparing plastic and elastic analyses for a pile head embedded in cap with reinforcing dowels. Note: The plastic

analysis implies the development of a subgrade hinge. A g = gross section area; f c '

= concrete compressive strength; K = subgrade reaction modulus; P axial = axial load.1 m = 3.28 ft; 1 kN = 0.225 kip.



Figure 12. This graph plots the shear versus height in comparison of elastic and inelastic analyses for pile head embedded in cap with reinforcing dowels. Note: A g = gross

section area; f c ' = concrete compressive strength; K = subgrade reaction modulus; P axial = axial load. 1 m = 3.28 ft; 1 kN = 0.225 kip.

Figure 13. This graph shows the depth of maximum subgrade moment of the three pile–pile cap connections tested with no dowel reinforcement. Note: A g = gross sec-

tion area; D = pile diameter; D* = reference pile diameter; EI eff = cracked-section bending stiffness of the pile; f c '

= concrete compressive strength; K = subgrade reactionmodulus; P axial = axial load.


11/17Summer 2009 | PCI Journal4

Figures 13 and 14 show the depth of the point of maxi-

mum subgrade moment for piles without and with longitu-

dinal mild-steel reinforcement, respectively. This is an im-

portant parameter, as it shows the length of pile for which

detailing for inelastic flexural action should be provided in

the form of increased levels of transverse reinforcement.

Depth of the maximum subgrade moment or hinge, if oneforms, is strongly affected by system stiffness but weakly by

structural details such as the presence of mild-steel reinforce-

ment or the specific type of pile-cap connection evaluated.

The maximum depth seemed to approach a limiting value as

system stiffness (functionally, in the case of the piles exam-

ined in this study, soil stiffness) increased. The overall range

was from 9 diameters (for soft soils) to 4 diameters. The anal-

ysis was not extended for softer soils on the assumption that

pole behavior (that is, rotation of the pile as a whole) would

begin to take place as stiffness was dropped to low levels.

Comparison of pile-cap connections

Figure 15 compares ultimate moment patterns for the

three pile–pile cap configurations examined in which

reinforcing dowels were not included: pile head embedded

in cap, prestressing tendons embedded in cap, and ten-

dons stressed through cap. Figure 16 examines the effect

of the presence of longitudinal mild-steel reinforcement

maximum magnitude of the subgrade moment. Stiffening

soil reduced the shear span between the two moment maxi-

mums, which required greater mobilization of the pile-

shaft flexural capacity at the subgrade moment maximum.

Also, lower axial load with a commensurate reduction of

section flexural strength placed more demand on the pile

shaft to assist in resisting the applied moment.

The effect of moment redistribution can only be assessed

through an inelastic analysis. Figures 11 and 12 show an

important aspect of this. Figure 11 compares an inelastic

analysis and an elastic analysis of the system with the

maximum flexural strength. The ultimate moments at the

pile head are similar, but the shaft maximum predicted

by elastic analysis was much lower. The consequence of

this is seen in Fig. 12, which shows the difference in shear

predictions from inelastic and elastic analyses.

The redistribution of moment down the pile shaft after for-

mation of the hinge at the pile-cap connection created much

higher levels of shear (approaching twice as much, in the

worst cases) in the pile shaft, which was missed by a purely

elastic analysis. The increase in shear was also caused by

the point of maximum moment in the shaft moving upward,

toward ground level, as the subgrade hinge formed. This

effect reduced the shear span and has been previously ob-

served in both analytical10 and experimental13 studies.

Figure 14. This graph shows the depth of maximum subgrade moment of the three pile–pile cap connections tested with dowel reinforcement. Note: A g = gross section

area; D = pile diameter; D* = reference pile diameter; EI eff = cracked-section bending stiffness of the pile; f c '

= concrete compressive strength; K = subgrade reactionmodulus; P axial = axial load.



Figure 15. This graph compares ultimate inelastic moment patterns for different pile–pile cap connections with no reinforcing dowels. Note: A g = gross section area; f c ' =

concrete compressive strength; K = subgrade reaction modulus; P axial = axial load. 1 m = 3.28 ft; 1 kN = 0.225 kip.

Figure 16. This graph compares ultimate inelastic moment patterns for different pile–pile cap connections with reinforcing dowels. Note: A g = gross section area; f c '

=concrete compressive strength; K = subgrade reaction modulus; P axial = axial load. 1 m = 3.28 ft; 1 kN = 0.225 kip.



Figure 17. This graph shows the displacement ductility capacity versus the nondimensional system stiffness for different pile–pile cap connections with no reinforcing

dowels. Note: 3200 kN/m3 < K < 48,000 kN/m3 (20 kip/ft3 < K < 300 kip/ft3). A g = gross section area; D = pile diameter; D * = reference pile diameter; EI eff = cracked-

section bending stiffness of the pile; f c ' = concrete compressive strength; K = subgrade reaction modulus; P axial = axial load.

Figure 18. This graph shows the displacement ductility capacity versus the nondimensional system stiffness for different pile–pile cap connections with reinforcing dowels.

Note: A g = gross section area; D = pile diameter; D * = reference pile diameter; EI eff = cracked-section bending stiffness of the pile; f c '

= concrete compressive strength; K =subgrade reaction modulus; P axial = axial load.



Prestressed concrete piles can be considered to be ductile

structural elements. This has been shown experimentally

through previous research and has been verified through

the analytical work described in this study. With appropri-

ate detailing, prestressed concrete piles may be used as

energy-dissipating elements in structures in which ductile

behavior may be demanded. Detailing that would allow

sufficient ductility capacity can be specified in both rein-forcement specification (through relevant design codes)

and location (through knowledge of the location of the

point of maximum subgrade moment).

The ductility capacity of prestressed concrete piles is

limited by the performance of the soil-pile system. Con-

sideration of ductile response of individual parts (pile-cap

connection or pile shaft) may be misleading. Ductility is

affected by both the connection type chosen and axial load.

The connection type is intrinsic to the structure of which

the piles form a part, but axial load may be subject to

variation in a given pile.

Equation (4) is inappropriate for plastic hinges forming in

pile shafts because of the following:

Inelastic curvature can be expected to spread both•

above and below the critical section.

The slope of the moment profile at the section of•

maximum moment is zero, invalidating the assump-

tion of a linear decrease in moment with distance from

the critical section.

There should be no strain-penetration effect. This is•because there should be no significant slip of tension

reinforcement past the critical section (which results

in the strain-penetration effect for a fixed-base plastic

hinge) due to the approximate symmetry of the mo-

ment profile about the critical section.

Analytical modeling, validated by in-place testing, has

shown that the plastic hinge forming in a pile shaft will

be located at a depth 70% of that predicted by an elastic

analysis to maximum pile capacity. Results of previous

experimental work have shown that a precast, prestressed

concrete pile-shaft plastic hinge can give displacementductility in excess of six for a pile of the configuration and

reinforcement levels examined in this study.

The transverse reinforcement requirements given by ACI

318 section 21.4.1 applied to piles of the configuration

examined in this study will allow the piles to perform as

structural elements of limited ductility. It is therefore rec-

ommended that transverse reinforcement that would sup-

port formation of a plastic hinge in the pile shaft (ideally

equal to that provided at the pile-cap connection) should

on moment patterns for these configurations. Curves are

shown for both soft and stiff soil at a moderate axial load.

The greatest demand on the pile shaft was from embedding

the tendons into the pile cap (Fig. 15) due to the reduced

flexural strength of the embedded tendon condition. In

this case, prestress was assumed to be developed over the

transfer length of 115d b, beginning at the bottom of the cap

and extending upward into the cap. The effective prestressforce at the connection is, therefore, zero, which gives a

lower strength and flexural stiffness over the plastic hinge

length of 0.5 D at the pile-cap connection, requiring greater

mobilization of the pile shaft. The transfer length was

about 2.2 pile diameters, so the active prestress over the

hinge length of 0.5 D did not exceed 30% of total prestress.

The presence of reinforcing dowels in the three categories

of pile–pile cap connection reduced the differences between

subgrade moment maxima (Fig. 16). In both cases, the dif-

ferences between subgrade moment maximums among the

different end conditions were larger for softer soils.

System ductilities

Figures 17 and 18 show displacement ductility as a func-

tion of nondimensional system stiffness, axial load, and

pile-cap connection type. Figure 17 shows displacement

ductility capacity for piles without longitudinal mild-steel

reinforcement, and Fig. 18 shows displacement ductility

capacity for piles with mild-steel reinforcement. Accord-

ing to these two figures, displacement ductility capacity is

relatively insensitive to the parameters studied. The plots

lie on a fairly narrow range.

The most prominent general trends were an increase in

ductility capacity with both axial load and soil stiffness

(expressed here as nondimensional system stiffness). Inclu-

sion of mild-steel reinforcement had a significant effect.

Comparing Fig. 17 and 18 shows that such reinforcement

both increased ductility at the lower end of its range and

decreased it at the top end of the range.

In both cases, embedding the pile head into the cap gave

the largest displacement ductility capacity. For piles with-

out mild-steel reinforcement, the maximum range of ductil-

ity for this case was from 2.5 to 4. With reinforcement, therange was about 2.7 to 3.4.

Embedding the tendons (and dowels, where present) gave

the next-highest ductility, followed by the rarely used prac-

tice of stressing the tendons through the footing.

Conclusion

The results from this research program allow the formula-

tion of several conclusions.



11. Budek, A. M., M. J. N. Priestley, and G. Benzoni.

2004. The Effect of External Confinement on

Flexural Hinging in Drilled Pile Shafts. Earthquake

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from an elastic analysis.

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Notation

Ah = cross-sectional area of a structural member mea-

sured out to out of transverse reinforcement

Ag = gross cross-sectional area

Ah = area of the spiral steel

d' = core diameter

d b = main bar diameter

d bl = longitudinal bar diameter

D = pile diameter

D* = reference pile diameter

EI eff = cracked-section bending stiffness of the pile

f

c' = concrete compressive strength

f y = yield strength

f yt = yield strength of the transverse reinforcement

H = depth of plastic hinge

K = subgrade reaction modulus, expression of soil

stiffness

l p = plastic hinge length

L = distance from the critical section to the point of

contraflexure

Paxial = axial load

s = spiral pitch

ρ l = ratio of area of distributed longitudinal reinforce-

ment to gross concrete area perpendicular to that

reinforcement


17/17

About the authors

Andrew Budek, P.E., PhD, is an

assistant professor for theDepartment of Civil and Environ-

mental Engineering at New

Mexico Institute of Mining and

Technology in Socorro, N.Mex.

Gianmario Benzoni, PhD, is a

research scientist for the Depart-

ment of Structural Engineering at

the University of California at

San Diego in La Jolla, Calif.

Synopsis

A parametric study of the inelastic seismic response

of precast, prestressed concrete piles was conducted

to determine whether piles with only light transverse

reinforcement could act as ductile structural elements.

A nonlinear, inelastic finite-element program written

specifically for this project was used to validate results

for both laboratory and in-place testing. The study

examined single piles using several types of pile-cap

connections, the addition of mild-steel reinforcement,

varying levels of axial load, and a range of soil stiff-ness.

The piles were modeled with 1% transverse reinforce-

ment, which is less than 1 / 3 of that required by ACI

318. The results indicated that modest levels of trans-

verse reinforcement will allow for ductile response.

Assuming that the pile-cap connection is detailed to

allow and support the formation of a plastic hinge,

with subsequent redistribution of moment down the

shaft to form a secondary subgrade hinge in the pile

shaft, the pile configurations analyzed provided aminimum displacement ductility of 2.

The addition of mild-steel longitudinal reinforce-

ment did not enhance ductility, though it did increase

flexural strength. The optimum pile-cap connection to

maximize ductility is embedment of the pile head into

the cap. Rotation capacity is maximized by embed-

ment of the prestressing tendons and any mild-steel

longitudinal reinforcement present into the pile cap.

Keywords

Ductility, footing, pile, seismic, soil structure, trans-

verse reinforcement.

Review policy

This paper was reviewed in accordance with the

Precast/Prestressed Concrete Institute’s peer-review

process.

Reader comments

Please address any reader comments to PCI Journal

editor-in-chief Emily Lorenz at [email protected] orPrecast/Prestressed Concrete Institute, c/o PCI Journal,

209 W. Jackson Blvd., Suite 500, Chicago, IL 60606. J

obtaining ductile performance from precast, prestressed concrete piles

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