July-August 2001 1

Kent A. Harries, Ph.D.Assistant ProfessorDepartment of Civil and Environmental EngineeringUniversity of South CarolinaColumbia, South Carolina

Michael F. Petrou, Ph.D.Associate ProfessorDepartment of Civil and Environmental EngineeringUniversity of South CarolinaColumbia, South Carolina

This investigation studied the capacity of square pile-to-pile cap connections where the precast, prestressed pile is simply embedded in the cast-in-place pile cap. Both experimental and analytical results are presented. It is shown that the plain embedment can develop the flexural capacity of the pile without distress to the pile cap or connection region provided that a sufficient embedment length is furnished. Equations for determining the required embedment length are provided. For design purposes, it is recommended that a plain embedment length equal to the width of the embedded pile be used.

Piles, particularly those embedded in soft soils, may be subjected to large lateral deflections in the event of an earthquake. The lateral deflections can result in

high local curvature and moment demands at various loca-tions along the pile length as shown in Fig. 1. Of particular concern is the behavior at the pile-to-pile cap interface.

At this location, very high moment demands result from the assumed fixity of the pile-to-pile cap connection. In order for this behavior to occur as assumed, the connection must be able to transmit lateral forces to the pile and remain essentially rigid. For this discussion, it is assumed that the pile cap may translate but not rotate. If rotation is permitted, the demands on the connection are reduced.

Behavior of Precast, Prestressed Concrete Pile to Cast-in-Place Pile Cap Connections

82 PCI JOURNAL

July-August 2001 83

Severe pile damage has been ob-served in past earthquakes.1,2 Pile de-sign for seismic loading assumes that the pile can develop and maintain its moment capacity through large de-formation demands. Indeed, signifi-cant research1,2 has shown that well-detailed precast, prestressed piles can develop and maintain large moments.

Although a pile may be detailed to resist large forces, it is also necessary that the pile-to-pile cap connection be able to transfer these forces. There are only a few published investigations which report the behavior of the pile-to-pile cap connection. These stud-ies are summarized further on in this paper.

The objective in designing the pile-to-pile cap connection is to provide a connection capable of developing the moment demands on the pile while remaining essentially rigid. Conser-vatively, this requires the connection to be able to develop the theoretical capacity of the pile while remaining elastic. In this paper, the specific case of precast, prestressed piles embedded in cast-in-place pile caps is considered.

PILE EMBEDMENT DETAILSThere are a number of options for

detailing pile-to-cap connections. Fig. 2 shows the connection detail currently used by the South Carolina Depart-ment of Transportation (SCDOT). It is reported that this detail costs close to $800 per pile to fabricate. The objec-tive of the study presented here was to address this issue and determine if less expensive details could provide ad-equate lateral load resisting capacity.

There are a variety of details pro-posed and used in the embedment re-gion of piles in cast-in-place pile caps. Fig. 3 shows a number of these details which are described as follows:

A. No treatment; the pile is simply embedded in the pile cap.

B. Roughening the exterior of the pile (using a rotary or chipping ham-mer, for instance) to provide additional mechanical bond between the pile and pile cap.

C. Grooving (cut or cast in place) the pile surface to provide additional mechanical bond.

D. Embedding vertical dowels in the driving head of the pile (after driving).

Fig. 1. Bending of long piles due to horizontal ground motion (adapted from Joen and Park,1 1990).

Fig. 2. Pile anchorage detail required by SCDOT.

E. Drilling horizontal dowels through the pile.

F. Confining the immediate embed-ment region with hoop or square spiral reinforcement.

G. Confining the immediate em-bedded region with round spiral reinforcement.

H. Exposing the strands and em-bedding them in the cast-in-place concrete. Often, the wires will be

“broomed” (separated) or twisted open to form an annular space (a so-called “olive” anchorage) to im-prove their development.

Typically, embedments will include a combination of these details. For example, the SCDOT detail shown in Fig. 2 incorporates Details B, D, and G. Each additional detail has an as-sociated cost in terms of both money and time.

84 PCI JOURNAL

Studies of Pile Embedment Details

Joen and Park1 reported tests of six pile-to-pile cap connection types. The piles were tested under combined axial load and reversed cyclic lateral loads. The axial load was kept constant at 0.2Ag f ′c for all tests. All piles tested were 16 in. (406 mm) octagonal piles.

Two specimens were provided with a 32 in. (813 mm) embedment having Details B and G (see Fig. 3). Another two specimens had 24 in. (610 mm) embedments with Details G and H (exposed strand left straight). A fifth specimen had a 36 in. (914 mm) em-bedment with Details G and H (ex-posed strand provided with an “olive” anchorage). The final specimen was provided with only a 2 in. (51 mm) embedment and Details D and G.

The theoretical capacity of the pile was obtained in each test and only the sixth detail showed significant distress to the pile cap and the embedment re-gion, which led to a significant decay of the load-deflection response of the pile.1

Sheppard2 summarized the results of both experimental and post-earthquake

field investigations. Two embedment details were presented as being ad-equate for the pile-to-pile cap connec-tion to behave in a desirable manner. The first suitable detail is H; the sec-ond is D. It is implied that confining Detail G is also provided.

Curiously, the details presented by Sheppard show minimal embedment of the pile, similar to the sixth speci-men described by Joen and Park.1 As such, it would appear that the details recommended by Sheppard may be inadequate for severe seis-mic loading. No experimental results concerning this aspect are reported by Sheppard.

PLAIN PILE-TO-PILE CAP EMBEDMENT

The objective of this study is to in-vestigate the behavior of a plain em-bedment (Detail A in Fig. 3). In this detail, the capacity of the pile is de-veloped along the length of the em-bedment. The pile-to-pile cap connec-tion should be designed such that it

is adequate to develop the theoretical moment capacity of the pile. Note that the scope of this study is restricted to driven precast, prestressed piles em-bedded in cast-in-place pile caps.

There are two proposed models, namely, Mattock and Gaafar3 and Marcakis and Mitchell,4 for determin-ing the capacity of the pile-to-pile cap connection. Both models assume that a rigid body (pile) is embedded in a cast-in-place concrete monolith (pile cap). Both models are based on the mobilization of an internal moment arm between bearing forces Cf and Cb as shown in Fig. 4.

Mattock and Gaafar3

A parabolic distribution of bearing stresses is assumed for Cb, and Cf is computed by a uniform stress equal to 0.85f ′c. The bearing stresses are distrib-uted over the width of the embedded pile, b. Following these assumptions and calibrating the calculated stresses against experimental data, the required embedment length, Le, may be deter-mined from:

Fig. 3. Proposed pile embedment details.

July-August 2001 85

V fb

bbL

a

L c

V fb

bbL

a

L

u c e

e

u c e

e

= ′ ′

−

+−

= ′ ′

−

+−

54

0 58 0 22

0 88

4 5

0 58 0 22

0 88

0 66

1

1

0 66

1

1

.

.

. .

.( )

.

. .

.

β

β

β

β

psi units

(1a)

MPa units

(1b)

c

( )

V fb

bbL

a

L c

V fb

bbL

a

L

u c e

e

u c e

e

= ′ ′

−

+−

= ′ ′

−

+−

54

0 58 0 22

0 88

4 5

0 58 0 22

0 88

0 66

1

1

0 66

1

1

.

.

. .

.( )

.

. .

.

β

β

β

β

psi units

(1a)

MPa units

(1b)

c

( )

where a is the shear span of the pile (distance from pile cap to assumed point of zero moment) and β1 is the concrete stress block factor defined in ACI 319-99, Section 10.2.7.3.5

It is suggested that the shear span be increased by an amount equal to the concrete cover, c, to account for pos-sible spalling of the soffit of the pile

Fig. 4. Analytical methods for determining capacity of embedment.

cap as shown in Fig. 4. The value of b′ is given by Mattock and Gaafar as the width of the element into which (in this case) the pile is embedded.

This value is intended to account for the spreading of the compressive stresses away from the embedment as indicated in Fig. 4(b). For a single pile in a pile cap, this value is taken as the width of the pile cap. For a pile group, this value may be conservatively taken as the pile spacing.

Marcakis and Mitchell4

Using slightly different assumed stress distributions shown in Fig. 4(b), Marca-kis and Mitchell4 proposed the following expression for determining the required embedment length, Le. This expression has also been calibrated against experi-mental data:

Vf b L c

e

L c

uc e

e

=′ ′ −( )

+−

0 85

13 6

..

(consistent units) (2)

where e is the eccentricity from the

point of zero moment to the center of the effective embedment as shown in Fig. 4(b).

Marcakis and Mitchell define b′ based on a “strut-and-tie” approach as being the effective width to the as-sumed “tie” steel, limited by a value of 2.5b [see Fig. 4(b)].

Eq. (2) has been adopted in Chap-ter 6 of the PCI Design Handbook6 for the design of embedded structural steel haunches or brackets in precast concrete. The same method has also successfully been applied to the de-sign of moment-resisting connections for steel beams embedded in concrete core walls7 and may be reasonable extended to the embedment of any essentially rigid body in a concrete embedment.

EXPERIMENTAL PROGRAMThe objective of this experimen-

tal program is to demonstrate that no special details are needed when em-bedding prestressed piles into cast-in-place pile caps provided that the embedment length is sufficiently long.

86 PCI JOURNAL

The pile-to-pile cap connection must be adequate to develop the probable moment capacity of the embedded pile without significant deterioration.

The connection must remain stiff enough so that rotation of the pile within the embedment does not con-tribute significantly to the overall drift of the pile-to-pile cap assembly. Ad-ditionally, the deterioration of the con-nection region should not allow the expected hinging of the pile to migrate into the embedded region.

In this program, piles are embed-ded into cast-in-place pile caps. The embedded portions of the piles are not prepared in any particular way; they are simply placed within the pile cap forms and the pile cap concrete

Fig. 5. Prestressed concrete pile [18 in. (450 mm) square] used in present study.

Fig. 6. Detail of

24 in. (610 mm) embedment.

is placed around them. No dowels or confinement reinforcement beyond that provided by the cast-in-place pile cap are provided.

Pile DetailsTwo 18 in. (450 mm) square by 18

ft (5.49 m) long piles were fabricated simultaneously in the 40 ft (12.2 m) prestressing bed located in the Univer-sity of South Carolina Structures Lab-oratory. These piles were prepared for an ongoing study of strand slippage.8 The piles used in this study had the lowest observed strand end slip of all 22 piles available to this experimental program.

The 28-day concrete compressive strength of the Type I ready-mixed

concrete was 6700 psi (46.2 MPa). The piles were prestressed with eight 1/2 in. (12.7 mm) diameter low-relaxation strands. Each strand had an initial pre-stressing force of 31 kips (138 kN), equivalent to 0.75fpu. The strands were released 43 hours after casting when the concrete compressive strength was 4500 psi (31 MPa). The strands were confined with W6 (0.276 in.) plain wire spiral. The strand layout and spi-ral details are shown in Fig. 5.

The predicted nominal moment ca-pacity of the piles corresponding to an axial load of 200 kips (890 kN) is 285 ft-kips (386 kN-m). All pre-dictions presented in this paper were made using the plane section analysis program RESPONSE-2000.9

Pile Cap DetailsEach pile was embedded in a 7 x

3 x 7 ft (2.14 x 0.92 x 2.14 m) cast-in-place pile cap. Each pile cap was reinforced with No. 7 bars on the top and bottom and No. 3 ties at 6 in. (152 mm) spacing in the transverse direc-tion and through the depth of the pile cap (see Fig. 6).

The concrete compressive strength and primary reinforcing details of each pile cap was different for each test. The details of the first pile test are rep-resentative of what may be expected in the field in South Carolina. The details for the second test were purposely se-lected to represent very poor in situ conditions. Pile cap data are provided

July-August 2001 87

in Table 1.

Embedment Details

The embedment length of Pile No. 1 was selected to be 24 in. (610 mm), the value desired by the SCDOT. The embedment length of Pile No. 2 was 18 in. (457 mm). This value was felt by the SCDOT to be the minimum ac-ceptable embedment length. Required embedment lengths calculated from Eqs. (1) and (2) are shown in Table 1.

Based on current practice, and as-suming typical pile cap material properties and details, an embedment length of approximately 12 in. (305

Fig. 7. Test setup to simulate seismic loading of pile-to-pile cap assembly.

Concrete EmbedmentRequiredembedmentlength compressive length Specimen Primarysteel strength provided Eq.(1) Eq.(2)

Pile No. 1 6 - No. 7 bars 5000 psi 24 in. 12.4 in. 11.9 in. top and bottom (34.5 MPa) (610 mm) (316 mm) (303 mm)

Pile No. 2 4 - No. 7 bars 3000 psi 18 in. 14.0 in. 14.8 in.

Table 1. Pile cap and embedment details and requirements.

mm) is required to develop the 285 ft-kip (386 kN-m) capacity of the piles used. These calculations are based on a shear span (a in Fig. 4) equal to 12 ft (3.66 m). Based on these calcula-

tions, it is expected that the embed-ment lengths provided are sufficient to develop the piles used. A photograph of the embedment region of Pile No. 1 prior to casting the pile cap is shown

0.1f ′c Ag

88 PCI JOURNAL

in Fig. 6.

Test Setup

The pile-to-pile cap assembly was tested as a cantilever beam in the horizontal position. The test setup is shown in Fig. 7. Each pile-to-pile cap assembly was tested under constant axial load and reversed cyclic lateral load. The 200 kip (890 kN) axial load, equal to 0.092Ag f ′c, was applied using a load following mechanism that does not impose secondary moment effects on the column.

The axial load was kept constant throughout the test using a regulated hydraulic power supply. The reversed cyclic lateral loads were applied at a distance of 146 in. (3.7 m) from the soffit of the pile cap. This loading is representative of a pile having a shear span of 146 in. (3.7 m) or point of fix-

ity approximately 24 ft (7.3 m) below the pile cap soffit.

This shear span was thought to be typical of partially exposed 18 in. (457 mm) piles [see Fig. 1(a)]. Shorter piles will place less demand on the embed-ment region and longer 18 in. (457 mm) piles are not common. Pile deflections were recorded at the point of application of the lateral load.

Load History and Experimental Observations

The lateral load is cycled three times at each load or displacement level. The load-deflection response of each pile is shown in Fig. 8. The predicted pile moment capacity of 285 ft-kips (386 kN-m) is shown as a horizontal dotted line. The piles were cycled at two elastic load levels; ±7 kips (±85 ft-kips) and ±14 kips (±170 ft-kips)

Fig. 8. Applied load versus deflection responses for piles tested.

[(±31 kN (±115 kN-m) and ±62 kN (±230 kN-m)].

In each test, the piles were first ob-served to crack at the pile-to-pile cap interface at an applied load of 13.9 kips (62 kN), corresponding to an ap-plied moment of 169 ft-kips (230 kN-m) at the crack location. The predicted load to cause cracking of the piles is 136 ft-kips (185 kN-m).

Loading continued to the “yield” load level. Yielding was defined as a significant change in the load-deflec-tion response of the pile. The yield displacement, δ, was found to be ap-proximately 1 in. (25.4 mm), corre-sponding to a pile drift of 0.7 percent. The applied load to cause a deflection of δ = 1 in. was 20.2 kips (90 kN) or 246 ft-kips (332 kN-m) and 17.8 kips (79 kN) or 217 ft-kips (293 kN-m) for Pile No. 1 and No. 2, respectively.

The predicted moment to cause sig-nificant nonlinearity of the pile section response is 240 ft-kips (326 kN-m). At this load, cracks were observed in the piles at approximately 12 and 26 in. (305 and 660 mm) from the pile cap soffit.

Beyond yield, the piles were cycled three times each to displacements equal to 1.5δ, 2δ and 3δ. Pile No. 2 was also cycled to 2.5δ in sequence. No lateral or axial load capacity decay or stiffness degradation was noted through these cycles as can be seen in Fig. 8. The peak load val-ues recorded during testing were 24.9 kips (111 kN) or 303 ft-kips (410 kN-m) and 21.5 kips (96 kN) or 262 ft-kips (354 kN-m) for Pile No. 1 and No. 2, respectively.

While attempting the initial cycle to 4δ, Pile No. 1 experienced a flexural failure due to crushing of the extreme compression concrete (see Fig. 9). At this point, the axial capacity of the pile was affected. The axial load regulator was unable to sustain the 200 kip (890 kN) axial load without further driv-ing the compressive failure. The final monotonic load response to a peak deflection of approximately 5 in. (127 mm), corresponding to a 3.4 percent drift, is shown in Fig. 8(a).

Pile No. 2 was cycled once at 3.5δ and twice at 4δ before failing while being pushed to 5δ for the first time. In this case, the failure appeared to be

0.1f ′c Ag

0.1f ′c Ag

July-August 2001 89

rupture of at least one of the strands. After testing, the pile was broken off from the pile cap and no strand rup-tures were evident. It is believed, in this case, that the loud noise and ac-companying decrease in lateral load that occurred on the cycle to 5δ may have resulted from the catastrophic slipping of a strand. Two views of Pile No. 2 near the end of testing are shown in Fig. 10.

Pile No. 2 behaved somewhat dif-ferently from Pile No. 1. Most of the deflection of Pile No. 2 was accounted for by the significant opening of the crack at the pile-to-pile cap interface as shown in Fig. 10(a). The deflec-tion of Pile No. 1, on the other hand, derived from the more uniform open-ing of cracks at the interface and at 12 and 16 in. (305 and 406 mm) from the pile-to-pile cap interface. It is believed that this differing behavior is entirely due to the piles and is not related to the pile-to-pile cap connections.

Pullout Test

It is possible that piles may experi-ence tensile loads during a seismic event. It is clearly undesirable for the pile to separate from the pile cap in these instances. The question arises as to whether the cyclic loads imposed on the embedment region causes a

Fig. 10. Pile No. 2 near end of test.

Fig. 9. Pile No. 1 [24 in. (610 mm) embedment] at displacement of +5 in. (127 mm) (3.4 percent drift).

“ratcheting” induced degradation of the embedment region resulting in the possibility of the pile pulling out of the pile cap.

To test this hypothesis, an ad hoc pullout test was devised. After the completion of the reversed cyclic load tests, Pile No. 1 was fitted with a col-lar and an attempt was made to re-move the pile from the pile cap. A di-rect axial tension of 75 kips (334 kN) was applied to the pile. There was no evidence of distress or movement of the pile away from the pile cap at this load. This test was not repeated for

Pile No. 2 since it was assumed that a strand had been ruptured.

SUMMARY OF EXPERIMENTAL RESULTS

Each pile behaved very much as was expected. Observed cracking, yielding, and ultimate capacities were very close to those predicted for the 18 in. (457 mm) piles. There was no observable damage to the embedment region in either test. Pile curvature data mea-sured relative to the pile cap indicated that neither rotation of the pile cap nor

(a) Pile No. 2 [18 in. (457 mm) embedment] at displacement of -4.5 in. (114 mm) (3.1 percent drift).

(a) Pile No. 2 [18 in. (457 mm) embedment] at displacement of +5.5 in. (140 mm) (3.8 percent drift).

90 PCI JOURNAL

rotation of the embedment region had a significantly measurable effect on the recorded deflections of the pile.

In essence, the pile cap provided the desired rigid end condition for the can-tilevered pile. It is clear that the 24 and 18 in. (610 and 457 mm) embedments provided were sufficient to develop the capacity of the piles with no special embedment details. This conclusion was expected based on past research of embedded members in cast-in-place concrete.3,4,7

For practical reasons, it is not be-lieved that embedment lengths shorter than 18 in. should be specified. The SCDOT expects the tolerance on em-bedment lengths to be ±6 in. (±152 mm). Similarly, embedment lengths longer than 24 to 30 in. (610 to 762 mm) are also impractical without sig-nificantly affecting the design and construction of pile caps. For instance, pile caps in South Carolina have been standardized to be 36 in. (914 mm) deep, making the longest practical em-bedment length approximately 30 in. (762 mm).

Application to Other Pile Sizes

The experimental program has indi-cated that practical construction issues

are more likely to control the specified embedment length than are capacity requirements. Fig. 11 shows curves generated from Eqs. (1) and (2) for the moment capacity of the embed-ment for varying embedment lengths and square pile sizes. Figs. 11(a) and (b) show the capacity to embedment length relationships for piles having a shear span of 12 ft (3.66 m) [similar to Fig. 1(a)], while Figs. 11 (c) and (d) show the similar relationship for piles having a short shear span of 4 ft (1.22 m) [Fig. 1(b)].

Note that for all calculations shown in Fig. 11, the concrete compressive strength, f ′c, of the pile cap has been assumed to be 5000 psi (34.5 MPa), the load spreading factor [see Fig. 4(b)] is 2 (thus b′ = 2b) and 3 in. (76 mm) of concrete cover has been as-sumed.

Both Eqs. (1) and (2) yield simi-lar results. Eq. (2) tends to result in slightly more conservative embedment capacity values.

The calculated embedment capaci-ties are lower for shorter shear spans, where the shear-to-moment ratio at the pile-to-pile cap interface is high [see Figs. 11(c) and (d)]. As the shear span increases, the embedment capacity in-

creases at a decreasing rate. For the geometry shown in Fig. 11, increasing the shear span beyond 12 ft (3.66 m) has little effect on the capacity of the embedment.

Fig. 12 shows the same results from Eqs. (1) and (2) for 18 and 36 in. (457 and 914 mm) square piles. Superimposed on these relationships is the range of probable pile moment capacities.

Based on the data shown in Figs. 11 and 12, it is proposed that provid-ing a minimum embedment length equal to the width of the pile will conservatively result in an embed-ment having sufficient capacity to develop the pile. Furthermore, such an embedment may reasonably be assumed to provide a rigid end condi-tion for the top of the pile. Certainly, the pile embedment requirement may be significantly reduced for piles hav-ing a long shear span.

Additional Embedment Details

The inclusion of additional embed-ment details, such as those discussed previously and shown in Fig. 3, will increase the capacity of the embed-ment to some extent. For instance, the method for designing embedded steel

Fig. 11. Embedment capacity predictions of varying pile sizes having varying embedment lengths.

f ′c

f ′c

f ′c

f ′c

July-August 2001 91

haunches contained in the PCI Design Handbook6 includes guidance for de-termining the additional embedment capacity resulting from the inclusion of horizontal dowels [see Fig. 3(e)]. It is felt, however, that these additional details will not significantly enhance the capacity of the embedment even though they may be beneficial in pro-viding post-failure continuity in the event of extremely large lateral deflec-tions of the pile.

Application to Other Pile Shapes

The previous discussion applies to square piles. It is felt, however, that the discussion may be extended to other typical pile shapes using the pro-jected pile width in place of the square pile dimension b. It is cautioned, how-ever, that unlike square piles, round or octagonal piles will develop bearing forces directed radially from the em-bedment. This may result in greater deterioration of the pile cap and em-

bedment region.It is not believed that this discussion

can be extended beyond prestressed concrete piles. For instance, it is not advocated that the analyses presented here are applicable to large caisson-to-pier cap connections despite the geometric similarities. No analysis or experiments of other pile shapes or sizes has been carried out. Data from embedment tests on smaller embedded sections6 having a width less than 12 in. (305 mm) do correlate well with the presented equations.

Strand Development Length

In this study, it has been assumed that the design capacity of the pile-to-pile cap embedment is based on devel-oping the capacity of the pile. Implicit in this assumption is that the capacity of the pile is actually attainable at the pile-to-pile cap interface. This requires full development of the prestressing strand at this location.

Fig. 12. Comparison of embedment capacity and pile capacity.

With relatively short embedment lengths this may not be possible.8 It has been suggested that a pile should have an embedment length equal to the strand development length to en-sure that the capacity of the pile is available at the face of the pile cap.10

It is felt that the provision of an embedment length equal to the strand development length is impractical in most cases because it would result in very deep pile caps. Note that the maximum moment demand on a pile may not occur at the pile-to-pile cap interface1 (see Fig. 1), in which case full development of the strand at the face of the pile cap may be unneces-sary.

The embedment calculations pro-posed here will result in a conserva-tive pile cap design. This is desirable because it leads to a “weak pile, strong pile cap” behavior that permits easier inspection and repair in the event of damage from an earthquake.

CONCLUSIONS AND RECOMMENDATIONS

Based on the results of this investi-gation, the following conclusions and recommendations can be made. These conclusions apply to square prestressed piles smaller than 36 in. (914 mm) em-bedded in cast-in-place pile caps.

1. The simple plain embedment of a precast, prestressed pile into a cast-in-place pile cap can be designed to de-velop the required capacity of the pile.

2. The required plain embedment length may be conservatively deter-mined from either Eqs. (1) or (2). Eq. (2) is proposed in Chapter 6 of the PCI Design Handbook6 for the design of embedded steel haunches or brackets in precast concrete. This is analogous to the embedment of precast, prestressed piles in cast-in-place pile caps.

3. Conservatively, the required em-bedment length to develop the flexural capacity of a pile may be taken as the width of the pile. A minimum absolute embedment length of 12 in. (305 mm) is recommended.

4. Due to the prestressing strands not being developed at the pile-to-pile cap interface, the flexural capacity of the pile may not be available at this location. This condition must be in-

f ′c

f ′c

92 PCI JOURNAL

vestigated by the designer. 5. The pile-to-pile cap embedment

length proposed here should be inter-preted as the minimum embedment re-quired to attain the theoretical capacity of the pile. The flexural capacity at the pile-to-pile cap interface is determined from the flexural capacity of the pile, which is affected by the strand develop-ment length provided at this location.

ACKNOWLEDGMENTS

This investigation was funded by the South Carolina Department of Trans-portation (SCDOT).

The authors would like to thank the entire staff of the USC Structures Lab-oratory for their assistance in prepar-ing the piles, pile caps, and assisting with the tests; and SMI-Owen Steel for assisting with the fabrication of the reaction frame.

The authors would also like to ac-knowledge Terry Koon, the Seismic

Special Projects Engineer at SCDOT, Jeff Mulliken, a Project Engineer at the LPA Group in Columbia, South Carolina, and Lewis Ryan of United Contractors in Chester, South Caro-lina. Their assistance is greatly ap-preciated.

Lastly, the authors wish to thank the PCI JOURNAL reviewers for their helpful and constructive comments.

T h e o p i n i o n s , f i n d -i n g s , a n d c o n c l u s i o n s e x -

pressed in this paper are those of the authors and do not necessarily reflect those of the South Carolina

Department of Transportation.

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Prestressed Concrete Piles and Pile-Pile Cap Connections,” PCI JOURNAL, V. 35, No. 6, November-December 1990, pp. 42-61.

2. Sheppard, D. A., “Seismic Design of Prestressed Concrete Pil-ing,” PCI JOURNAL, V. 28, No. 2, March-April 1983, pp. 21-49

3. Marcakis, K., and Mitchell, D., “Precast Concrete Connections with Embedded Steel Members,” PCI JOURNAL, V. 25, No. 4, July-August 1980, pp. 88-116.

4. Mattock, A. H., and Gaafar, G. H., “Strength of Embedded Steel Sections as Brackets,” ACI Journal, V. 79, No. 2, March-April 1982, pp 83-93.

5. ACI Committee 318, “Building Code Requirements for Struc-

tural Concrete (ACI 318-99),” American Concrete Institute, Farmington Hills, MI, 1999.

6. PCI Design Handbook: Precast and Prestressed Concrete, Fifth Edition, Precast/Prestressed Concrete Institute, Chicago, IL, 1999.

7. Harries, K. A., Mitchell, D., Cook, W. D., and Redwood, R. G., “Seismic Response of Steel Beams Coupling Re-inforced Concrete Walls,” ASCE Journal of the Struc-tural Division , V. 119, No. 12, December 1992, pp. 3611-3629.

8. Wan, B., Petrou, P., Harries, K. A., and Hussein, A. A., “‘Top Bar’ Effect in Prestressed Concrete Piles,” submitted for publi-cation to ACI Structural Journal.

9. Bentz, E. C., and Collins, M. P., “RESPONSE-2000 Rein-forced Concrete Sectional Analysis Using the Modified Com-pression Field Theory Computer Program, Release 1.0.0.1,” University of Toronto, Toronto, Ontario, Canada.

10. Shahawy, M.A., and Issa, M., “Effect of Pile Embedment on the Development Length of Prestressing Strands,” PCI JOUR-

NAL, V. 37, No. 6, November-December 1992, pp. 44-59.

APPENDIX – NOTATIONa = shear span of pile taken as distance from pile cap soffit

to point of zero momentb′ = effective width of concrete compression blockb = width of pile, also bearing width of the embedment

c = depth of concrete coverCf = resultant bearing (compressive) force in embedmente = eccentricity from midspan of beam to center of

embedmentf ′c = specified concrete compressive strengthLe = embedment length of pile inside pile capVu = shear force on pilexb = length of compression block at back of embedment

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xf = length of compression block at front of embedment

β1 = ratio of average concrete com-pressive strength to maximum stress

δ = deflection at yield stress of pile