Rational seismic design of precast, prestressed concrete piles Andrew Budek-Sc Bud ek-Schmeis hmeisser ser and Gianmario Benzoni The purpose of this research is to develop a rational design methodology for precast, prestressed concrete piles that uses proven seismic design methodology and constitutive modeling to produce detailing requirements that are more economical yet still retain the spirit and meet the Building Code Requirements for strength requirements of Building Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05).
Editor’s quick points n
40
Transverse reinorcement requirements specifed by Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05) or 318R-05) or compressive members penalize precast, prestressed prestressed concrete piles, which typically have large ratios o cover to diameter.
n
This paper develops a rational design method or precast, preprestressed concrete piles using proven seismic design methodology and constitutive modeling to produce economical designs that meet ACI 318-05 strength requirements.
n
The methodology outlined in this paper will require considerable coordination among the precaster, the geotechnical analyst, and the engineer o record.
S e p t e m b e r – O c t o b e r 2 0 0 8 | PCI Journal
Transverse reinforcement requirements specified by ACI 318-05 for compressive members penalize precast, prestressed concrete piles, which typically have large ratios of cover to diameter. These requirements can make prestressed piles uneconomical, even though they have been shown to provide good seismic performance when designed to less stringent specifications. This paper presents a simple design-chart-based methodology that uses current confined concrete models in conjunction with ACI 318-05 performance requirements to allow for lower levels of transverse reinforcement, which will al low for economical pile construction. The design of precast concrete piles is often left to the precaster. If the methodology outlined in this paper is followed, it will require considerable coordination among the precaster, the geotechnical analyst, and the engineer of record. While this may be seen as awkward, the use of more economical and buildable designs will make precast concrete piles more attractive and user friendly. In the long run, this will benefit both the precast concrete industry and the end user.
40
Background and scope of research The equation for the ultimate strength Pu of an axial compression member (column or pile) with spiral reinforcement is given by ACI 318-05 Eq. (10-2). 1
(
P u = 0.80!
' c
0.85 f
( A
g
)
" A st
)
(1)
f y A st
+
where '
f c
= design concrete compressive strength
Ag
= gross member cross-sectional area
Ast
= area of longitudinal reinforcement
Figure 1. This 305-mm-square pile has 19M spiral reinorcement. Note: 19M = no. 6; 1 mm = 0.03937 in.
f y
= yield strength of longitudinal reinforcement
φ
= strength-reduction factor = 0.75
but not less than the minimum specified in section 10.9.3 of ACI 318-05 as Eq. (10-5)
An additional reduction factor of 0.80 is used in Eq. 1 for possible eccentricity of load and a factor of 0.85 accounts for placed concrete having a lower strength than cylinders cured under controlled conditions.
S s
f yt ρ s
ACI 318-05 Eq. (10-2) for column strength is based on maintaining the residual strength of the core after spalling of the cover in a spirally reinforced column. The confinement provided by the spiral steel is expected to provide sufficient support for the core to support the design axial load. This results in a de facto value for the confined con' crete compressive strength according to ACI f cc ACI , which can be back calculated as Eq. (2). ,
'
' f cc , ACI
(
)
0.85 f c A g ! A st =
( Ach ! A st )
(2)
where Ach
Transverse reinforcement ratio ρ t for seismic design is adapted from ACI 318-05 chapter 21.4.4 as Eq. (3) 4 A =
t
'
d s
where At
= area of transverse reinforcement
d ’
= diameter of the confined core
s
= spiral pitch
(4)
= yield strength of the transverse reinforcement = spiral reinforcement ratio
Equation (4) shows that members with a large ratio of gross to core area are penalized by requiring a large spiral reinforcement ratio. For example, a 610-mm-diameter (24 in.) precast, prestressed concrete pile with twentyfour 13.2 mm (0.52 in.) tendons, 76 mm (3.0 in.) cover, 41.3 MPa (6.0 ksi) concrete, and 413 MPa (60 ksi) spiral reinforcement would require a spiral reinforcement ratio of 3.5%. This would call for 10M (no. 3) spirals pitched at 18 mm (0.71 in.). Aside from being uneconomical t o build, this spacing would violate ACI 318-05 minimum pitch requirements of 4d b, where the strand diameter is d b. Another example is the 305 mm (12 in.) square pile shown in Fig. 1, which is reinforced with 19M (no. 6) wire. The force required to turn this wire into a small-diameter spiral is great and is hard on equipment, which makes using this size wire uneconomical.
= area of the confined core
! t
¦ A µ f ' 0.45 § g 1¶ c ¨ Ach · f yt
(3)
Another disadvantage of ACI 318-05 chapter 10 requirements for heavy transverse reinforcement in elements with large gross-to-core area ratios is that, when using reinforcement that is readily turned into a spiral, a tight spiral pitch is created. The size of the pitch dictates the maximum size of coarse aggregate used so that an aggregate bond is formed across the core-cover interface. Smaller aggregate results in more shrinkage due to the higher surface area– to–volume ratio of the smaller aggregate. This can result in shrinkage cracks, which might compromise corrosion protection of the prestressing strand and reinforcement. If the size of the aggregate is close to the spiral spacing at the
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Rational design methodology and modeling
Figure 2. This scaled drawing shows the spiral reinorcement that is required or a 610-mm-diameter pile with 76 mm cover rom Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05) Eq. (4) compared with Eq. (3). Note: 1 mm = 0.03937 in.
head of the pile, a weak bond between the core and cover may occur, which can result in spalling of the cover at the pile head during driving, as in the Lindbergh Field Terminal expansion in San Diego, Calif., in the 1990s.2 One of the main advantages of precast, prestressed concrete piles is their resistance to corrosion through the virtual elimination of cracking. A second line of defense is typically a thicker cover than would be found in nonprestressed members, so minor cracking does not reach the reinforcement. Unfortunately, ACI 318-05’s prescriptive approach imposes a penalty on the use of precast, prestressed concrete piles in seismic applications. A graphic example of this can be seen in Fig. 2, which compares the amount of transverse reinforcement mandated by Eq. (4) to that required by Eq. (3) for a representative 610-mmdiameter (24 in.) pile with 76 mm (3.0 in.) cover.
The design of a pile for seismic loading includes the application of both axial load and moment. Use of an interaction diagram is not entirely appropriate for seismic design because successful resistance of seismic loading comes from displacement and curvature ductility rather than strength. It has been shown that curvature demand and, implicitly, provision of adequate curvature ductility control pile response. 3 Interaction diagrams are constructed from a strength basis with ductility capacity implied. To this end, a moment-curvature curve i s required. The Mander model4 has been widely used for seismic design and has been shown to be conservative up to 50%.5 The Mander model is appropriate for assessing the inelastic flexural capacity of prestressed piles for concrete strengths up to 68 MPa (10 ksi). 6,7 In this model, the strength of ' confined concrete f cc is a function of the lateral confining pressure provided by transverse reinforcement f l ' and is given by Eq. (5).
' f cc =
" $ $#
' f c 2.254 1 +
f l ' f c'
!
' l f c'
2 f
% ! 1.254' ' &
(5)
where f l '
2 f =
A
yt t
(6)
d ' s
In developing a rational methodology for seismic desi gn, it is important to stay within the spirit and strength mandates of ACI 318-05, meaning that the confined core should be able to withstand the design axial load after spalling of the cover concrete. In seismic design of piles, specific factors need be considered. First, the design axial load will be less than the maximum specified for compression members in Eq. (1) because of axial load and moment interaction. Seismic moments increase the axial stress in the compression zone above the design axial forces from gravity load only, and global overturning moments on the structure can increase axial load on the compression side during a seismic event. Second, the required displacement ductility demand implies that the section must achieve a given curvature ductility µ ∆, which is calculated by Eq. (7).5
µ !
where Figure 3. A typical pile head confguration uses mild-steel dowels to connect the piles to the superstructure. 42
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=
M u M n
(
+3
µ "
L p
# 1)
L
$ L p ' # 1 0.5 & ) L ( %
(7)
L p
= plastic hinge length
L
= pile length to point of inflection
M u
= ultimate moment capacity
M n
= nominal moment capacity
µφ
= ultimate curvature ductility
Curvature ductility decreases with increasing axial load. Therefore, there is a maximum design axial load that will still allow piles to be designed with sufficient ductility. Third, precast, prestressed concrete piles are generally connected to the superstructure by mild-steel dowels, which are grouted into tubes provided in the head of the pile (Fig. 3). These dowels do not continue t hrough the length of the pile. When calculating the ultimate axial capacity for the pile using Eq. (1), it is not appropriate to include the axial strength contribution of the steel provided for superstructure connection. Two rationales support this approach, the first of which is specific to end-bearing piles. Because the dowels do not extend through the length of the pile, the capacity should be based on the section with minimum axial capacity. This applies to the pile below the termination point of the dowels. The other rationale is appropriate to piles that rely partly on skin friction to transfer axial load into the soil. Seismically loaded piles undergo cyclic lateral deflections that displace soil around the pile shaft. In the upper part of the pile, the soil is inelastically displaced, resulting in gapping, which is the formation of a space between the pile shaft and the soil (Fig. 4). Gapping is assumed to be a phenomenon typical to cohesive soils because cohesionless soils should, by definition, not support the formation of a gap. However, i n practice, cohesionless soils also experience gapping.8 When a gap is formed, axial load will not be transferred from the pile to the soil. However, even below the point at which gapping is no longer seen, there is soil disturbance through elastic deflection of the soil-pile system. This reduces the magnitude of the frictional forces between the soil and pile, which can transfer load. The skin-friction mechanism can be severely degraded, and the lower value of pile capacity (that is, without dowels) should be used for design. Gapping will vary in a pile group. The soil around inboard piles is restrained by the interaction of the soil with the outboard piles. The previous discussion examines the single-pile case, which would be the worst-case scenario for gapping. Because the degree and dist ribution of gapping in a specific pile group would require a detailed soil-structure interaction analysis, it is recommended that the inherent conservativeness of the single-pile assumption for gapping
Figure 4. Dowel termination and potential or gapping are caused by the lateral motion o the pile under seismic loading.
be accepted. This would keep t he methodology developed in this paper within the spirit of ACI 318-05. Alternatively, there is justification for including the connecting dowels in the moment capacity of the plastic hinge region at the head of the pile after the cover has spalled. In designing for seismic response, a hinge i s expected to form at the head of the pile. The hinge will have a length of about 0.5 D, in which D is the pile diameter, and the cover concrete is expected to spall. The dowels provided for the connection must be designed to extend t hrough the hinge in order to develop properly for ductile response. This will allow axial load from the superstructure to be transferred through the hinge to the body of the pil e below. Therefore, the ultimate axial capacity of the pile after spalling in the hinge area should include the dowel rei nforcement. Including dowels in the design strength of the pile results in a higher required level of transverse reinforcement and is shown in the following design example. The amount needed when following the methodology derived from the present research is not prohibitive and is far below that called for in ACI 318-05 chapter 10 and Eq. (4). The steps in outlining a rational seismic design procedure for precast, prestressed concrete piles are summarized: 1.
Select a required ductility displacement capacity (typically μ = 3 for piles).
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2.
Assess the needed curvature ductility capacity from Eq. (7), initially assuming M n = M u.
P a
,
core
=
' Ach f cc f + A dowels y
(8)
where 3.
Using an appropriate model for the seismi c loading of confined concrete, develop a set of moment-curvature graphs for the selected pile configuration over a range of axial loads.
4.
Select an appropriate design axial load with sufficient curvature ductility capacity.
5.
Design transverse reinforcement to provide sufficient confining pressure for seismic response.
6.
Verify that the transverse reinforcement provides sufficient confining pressure to allow the core to carry the axial load specified by Eq. (1), which allows for global overturning moments and increased axial loads ca used by residual superstructure drift.
7.
Check that the transverse reinforcement is sufficient for the shear demand.
If, for example, the Mander model is used, the axial capac' ity of the confined core Pax,core can be calculated using f cc from Eq. (5):
Adowels = area of dowels
This assumes that the dowels’ area Adowels and yield strength f y in the plastic hinge region are effective in resisting axial load. To maintain the spirit of ACI 318-05, this must be equal to or greater than the original pile axial capacity from Eq. (1). ' The variable in Eq. (8) is f cc , which is dependent on the degree of confining pressure provided by the transverse Ach clearly has a major influreinforcement. The ratio Agross / ence because the confined core area, which is restrained by the transverse reinforcement, must resist the design axial load for the whole section from Eq. (2). As described above, the axial capacity of the core could also be assisted by the dowels connecting to the cap. ' Using the Mander model, the confined concrete strength f cc ' is explicitly a function of the confining pressure f l provided by the transverse reinforcement and implicitly a function of the spiral pitch. There are two ways to address the devel' opment of the minimum required value of f cc . One way is to ' set up Eq. (9), which will enable f cc to be calculated.
Figure 5. This graph plots the confned concrete strength versus lateral confning pressure or varying design concrete strengths. Note: 1 MPa = 0.145 ksi.
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Figure 6. Plotted is the transverse reinorcement ratio as a unction o lateral confning stress or 420 MPa reinorcement. Note: 1 MPa = 0.145 ksi.
(
0.80!
' + Ach f cc
Adowels f y " 0.80! # 0.85 f c' A g " A st % = 0 $ &
)
(
)
(9)
Then Eq. (6) can be solved using root-finding methods to obtain the confining pressure f l , which can then be used to solve for the spiral pitch required to develop the appropriate axial capacity of the core. This is, however, a relatively cumbersome approach for design. '
It is more convenient to plot f c as a function of design concrete strength f c' using Eq. (5) and extract the lateral confining pressure (Fig. 5). Given a required lateral confining pressure, the designer can then enter another chart in which the transverse reinforcement ratio ρ t is plotted versus the lateral confining pressure for a given transverse steel strength, substituting Eq. (10) into Eq. (6). ! s
4 A =
t
'
d s
and 1972 Miyagi-ken-Oki10 earthquakes. The potential development of critical shear is also forecast by inelastic analysis.6,11 It is, therefore, reasonable to use the ACI-mandated maximum value of 413 MPa (60 ksi) for transverse reinforcement. Figure 6 plots the lateral confining pressure of a Grade 420 (Grade 60) spiral versus the transverse confining ratio, which shows that with an increase in confining ratio, there is an increase in lateral confining pressure. The pile shear demand and capacity should also be checked. Typical design procedure assesses the shear demand as the overall base shear on the superstructure and divides it evenly among the piles. Although this model is not correct, it is conservative. Variation in axial force will draw shear to the more heavily loaded (stiffer) piles, but the shear strength of these piles will be enhanced by the increased axial load. Also, passive soil pressure against a foundation slab can resist a significant amount of shear, decreasing the load on the piles. The design process is summarized as follows:
(10)
The upper part of fixed-head prestressed concrete piles can be shear critical, as shown in the 1964 Alaska9
1.
Select a preliminary pile design, specifying transverse reinforcement using Eq. (3) and a design axial load that will provide the curvature ductility needed in Eq. (7) to provide the desired displacement ductility µ ∆.
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Figure 7. This graph plots the nondimensional system stiness versus the pile depth to fxity or equivalent column modeling. Source: Data rom Budek, Priestley, and Benzoni 2000.
2.
Calculate the maximum axial load from Eq. (1), disregarding the influence of dowels used to connect the pile to the superstructure but including the effect of prestress.
3.
Use Eq. (9) to determine the required value of f cc .
4.
Using the design concrete strength and t he needed confined concrete strength, extract the required lateral confining pressure from Fig. 5.
5.
Use Fig. 6 to determine the required transverse reinforcement ratio.
6.
Check that the transverse reinforcement ratio exceeds that required by Eq. (3).
The foundation supports a 1.83-m-diameter (6 ft), 5-mhigh (16.4 ft) circular cantilever column with an ultimate moment capacity of 25,000 kN-m (18,400 kip-ft). The column carries an axial load of 21,700 kN (4880 kip). For this column, base shear V can be estimated as the shear required to attain the ultimate moment capacity of the column at the base, thus M
7.
Check that the transverse reinforcement provides sufficient shear capacity to develop the full moment capacity of the pile-superstructure connection.
Design example Consider a foundation consisting of a grade-level slab supported on batterless precast, prestressed concrete piles driven into medium-soft cohesionless soil, which has a subgrade reaction modulus of 25,600 kN/m 3 (163 kip/ft3).
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V
=
u
H
25,000 =
5
=
5000 kN (1100 kip)
(11)
where M u
= ultimate moment capacity
H
= height of column
Passive soil pressure against the sides of the foundation will be neglected. A design displacement ductility of µ ∆ = 3.0 for the foundation is appropriate. For design, the pile may be modeled using an equivalent depth–to–fixity approach. Figure 7 plots the nondimensional system stiffness for an equivalent column versus
the depth to fixity. The nondimensional system stiffness is calculated by KD5 / D* EI eff
where K
= subgrade reaction modulus of the soil
EI eff = pile’s effective cracked-section bending stiffness D
= pile diameter
D*
= reference pile diameter of 1.83 m (6 ft)
This results in an equivalent model column with a height of d f + H , where d f is effective depth to fixity. For a gradelevel slab, H = 0.
Figure 8. This diagram depicts the design example’s oundation plan view. Note: Dimensions are in meters. 1 m = 3.28 t.
The initial design steps are identical for rational or prescriptive design:
erties of the pile for varying axial load ratios, calculated using the Mander model.
1.
Initially, design the pile for an axial capacity, neglecting the contribution of the dowels connecting the pile to the superstructure.
2.
Use Fig. 7 to develop an equivalent column model of the pile.
Given D = 0.61 m (2.0 ft), K = 25,600 kN/m3, modulus of elasticity E = 30.4 GPa (4410 ksi), and the effective moment of inertia I eff = 0.5 I gross (where I gross is the gross section moment of inertia), an equivalent column height of 5.5 D can be extracted from Fig. 7.
3.
Design the transverse reinforcement as per the requirements of ACI 318-05 section 21.4.1.
4.
Perform a moment-curvature analysis to ensure that the pile has the required transverse reinforcement to provide sufficient curvature-ductility capacity with the specified length to contraflexure from the equivalent column model.
The foundation in the design example can be supported by nine precast concrete piles of 610 mm (24 in.) diameter with a design concrete compressive strength of 41.3 MPa ' (6.0 ksi), loaded to 20% of f c Ag (Fig. 8). Each pile carries an axial load of 2432 kN (546.8 kip). Typical pile detailing includes twenty-four 13.2 mm (0.52 in.) strands stressed to 1061 MPa (153.9 ksi) a fter losses and 76 mm (3.0 in.) of cover to the strands. Transverse reinforcement is provided by 10M (no. 3) ASTM A82 wire spaced at 63.5 mm (2.5 in.) from ACI 318-05 section 21.4.1 and Eq. (3), which results in a transverse reinforcement ratio of ρ t = 0.01 (1%). Eight 29M (no. 9) Grade 420 (Grade 60) bars provide connection of the piles to the slab. The prestressing tendons in the example are cut at the end of the pile. Thus, effective prestress in the pile decreases from its nominal value to zero over the flexural transfer length of the tendons, approximated at 115 tendon diameters.6 Figure 9 shows the moment-curvature prop-
Equation (7) relates curvature ductility to displacement ductility capacity. For the pile under consideration, Fig. 9 gives an ultimate curvature ductility of µφ = 6, and M u / M n = 1.1. The curvature ductility is obtained by dividing the ultimate curvature (on the x -axis) by the curvature at yield. The ratio of ultimate to nominal moment capacity is obtained by dividing the ultimate moment of the section as obtained from the moment-curvature analysis by the nominal moment capacity as calculated from standard concrete flexural methods. The plastic hinge length L p can be conservatively calculated as 0.5 D, as for a column hinge forming against a foundation. 5 The column length L can be calculated by dividing the equivalent column depth to fixity from Fig. 7 by 2 because Fig. 7 represents a fixedfixed column. Thus, L = 2.75 D, and applying Eq. (7), the displacement ductility µ ∆ = 3.57, which is greater than the specified minimum of 3.0.
Rational design The rational design procedure outlined will be used to determine the amount of transverse reinforcement needed for adequate flexural and shear performance. The steps to calculate the needed transverse reinforcement for flexural response are as follows. 1.
' Calculate the required confined concrete strength f cc of the confined core concrete such that the core will
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Figure 9. This graph plots the moment-curvature properties calculated by the Mander model or the 610-mm-diameter pile used in the design example at var ying axial load ratios. Note: 1 mm = 0.03937 in.; 1 m = 3.28 t; 1 kN = 0.225 kip.
meet the requirements of ACI 318-05 section 10.3.5.3 in developing the full strength of t he gross section, assuming that the strength of the confined core will ' reach f cc as specified by the Mander model. Equation ' (9) calculated f cc as 48.6 MPa (7.05 ksi).
calls for a transverse reinforcement ratio of 2.1%. This is considerably higher than that calculated from Eq. (3) but is still less than the ACI 318-05 minimum of 3.5% (Eq. [4]). In this case, 13M (no. 4) wire could be used at a pitch of 54 mm (2.1 in.), which is still economical to build.
2.
Use Fig. 5 to obtain the required confining pressure of 1.5 MPa (0.22 ksi).
3.
Use Fig. 6 and a confining pressure of 1.5 MPa (0.22 ksi) to obtain the transverse reinforcement ratio ρ t = 0.008 (0.8%).
Next, shear capacity of the pile should be assessed. While it is customary to assess the shear demand by dividing the total seismic shear on the foundation by the number of piles, it is more correct to ensure that the piles’ shear capacity is sufficient to allow the development of their full flexural strength.
4.
This is lighter reinforcement than initially specified from Eq. (3), so assume 1% transverse reinforcement.
This procedure allows the use of the initial spiral pitch of 63.5 mm (2.5 in) with 10M (no. 3) wire, which is constructable. This design meets the spirit of ACI 318-05 in supplying the full axial capacity of the section from Eq. (10-2) less the axial strength contribution of the dowels. If, however, it is desired to include the dowels in the design strength of the pile, Eq. (2) can be used to calculate ' a required confined concrete compressive strength f cc of 63.4 MPa (9.20 ksi). Using the outlined procedure, a confining pressure of 4.4 MPa (0.64 ksi) is needed, which
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As mentioned, the inelastic response of piles has been shown to result in higher shear demands t han indicated through elastic analysis. If flexural hinging occurs in the pile shaft, the point of maximum moment in the shaft will move upward, toward the pile head. This will reduce the shear span between the maximum moment at the pilesuperstructure connection and the point of maximum subgrade moment. The upward movement of the point of maximum moment in the shaft with the onset of plasticity is independent of soil stiffness. The point of maximum plastic moment in the shaft is at a depth 70% of that calculated through elastic analysis. Figure 10 shows the moment pattern for the example pile section and loading for first yield at the pile head, elastic analysis to maximum moment at the pile head, and inelastic analysis to maximum moment.
Figure 10. The moment pattern is s hown or the design example pile section and loading or the inelastic, elastic, and yield moments. Note: 1 m = 3.28 t; 1 kN = 0.225 kip.
The difference in shear in the upper part of the pile is evident by examining the different slopes of the moment curve between the maximum moment under elastic and inelastic analysis. A linearization of the slope of the moment curve gives a shear span of four pile diameters D, which is substituted into Eq. (12) to calculate shear.
V =
1250 + 1050
(
)
4 0.61
=
943 kN (212 kip)
(12)
This is greater than the 555 kN/pile (125 kip/pile) specified by Eq. (11). The shear strength of the section at the pile head (where there is assumed to be no effective prestress) is calculated by Eq. (13), which is in chapter 11 of ACI 318-05:
V = ! (V c
+
V s )
" P axial % " = ! $ 1 + ' $ A 14 # g & $ #
f c' 6
' % % " ( At f yt d ' ( 0.8 A g ) + ! $ ' s ' 2$ ' # & &
where V c
= nominal shear strength provided by concrete
V s
= nominal shear strength provided by shear reinforcement
Paxial = axial load
A designed load of 0.2 f c' Ag is reasonable for design. Axial load corresponding to 0.2 f c' Ag is 2432 kN (546.8 kip), V c = 462 kN (104 kip), and V s = 332 kN (74.6 kip), so the total shear capacity of each pile is 794 kN (219 kip). Applying the strength-reduction factor φ = 0.75, the ultimate shear capacity of each pile is 731 kN (164 kip). This is greater than the demand of 555 kN/pile (125 kip/pile) but below the nominal moment capacity of the pile. It can be inferred from this calculation that the column will undergo a flexural failure before the piles reac h their nominal moment capacity, which is the desired mechanism. Detailing for this mechanism remains within the spirit of rational design because the superstructure will fail before the piles. Pile shear failure is thus a capacity-protected action.
(13) This analysis clearly makes a de facto assumption that shear will be divided equally among the piles in the group. This may not be the case because overturning moments generated in a foundation under seismic l oading can increase the axial load on some piles, attracting shear to them, while decreasing it on others. While shear demand increases with increasing axial load, shear strength increas-
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rizes these results. The capacity is above the demand, and the design is acceptable. Table 1 was calculated under the assumption that pile shear failure was an action protected by column capacity. If it is desired to provide shear reinforcement to support the ultimate moment capacity of the piles, the required spacing for 10M (no. 3) wire to achieve the nominal moment capacity can be calculated using Eq. (15).
' " $ A s f yt d
" $ 72 (413) ( 457 ) ' & ) ( 0.80) & ) 2 & V # V ) 2 % 974 # 462 ( c ( % '
s
=
!
=
= 33 mm (1.3 in.)
(15)
where Figure 11. This diagram illustrates the eect o overturning moments on axial orce distribution in the piles. I support rom the soil beneath the piles is neglected, the compression piles will see an increase in axial orce, while the tension piles will see the same decrease in axial load.
As = the area of shear reinforcement
This gives a transverse reinforcement rat io of 1.88%, which is more reinforcement than required by fle xural design. The reinforcement for this pile is governed by shear design. The spacing of 33 mm (1.3 i n.) is both difficult to construct and smaller than is desirable under ACI 318-05 spacing guidelines, so 13M (no. 4) wire could be spaced at 60 mm (2.4 in.) instead. This is not an onerous requirement. The reinforcement required is just over half that called for by the prescriptive design of ACI 318-05 section 10.9.3. The shear capacity will be in excess of the demand.
es as well, and the assumption of an equal division of shear force among the piles may be unnecessarily conservative.5 To verify this, consider the e ffect of overturning moments on the axial force distribution in the piles, and, hence, the shear strength. If support from the soil beneath the piles is neglected, the compression piles will see an increase in axial force POT calculated by Eq. (14). P OT
26,500 ! 1 $ =
4.88
#" 3& %
=
1748 kN/pile (393.0 kip/pile)
(14)
As indicated in Fig. 10, fixed-head piles may develop a second plastic hinge, which can form at a distance of up to 10.8 m (35.4 ft) below grade level. This secondary hinge is formed as a result of moment redistribution down the pile shaft after the rotational stiffness at the pile head is reduced. While the secondary hinge is not likely to have a large influence on overall pile performance, it should be properly detailed for ductile behavior.
The tension piles will see the same decrease in axial load (Fig. 11). This results in an axial load of 4159 kN (935.0 kip) (0.342 f c' Ag) in the compression piles and an ' axial load of 663 kN (149 kip) (0.542 f c Ag) in the tension piles. The axial force on the middle row of piles is unchanged. Thus, new values for V c can be calculated using Eq. (12).
The presence of the secondary hinge does influence shear. Because shear is quantified as the slope of the moment curve, the high-shear region in the upper part of the pile will extend down to the secondary hinge.
A pushover analysis of an equivalent portal frame system with column stiffness assigned as per the pile stiffnesses obtains an estimation of the distribution of shear force among the piles of varying stiffnesses. Table 1 summa-
Table 1. Pile shear capacities and demands or overturning moment Pile row
P axial /pile,
kN
V c , kN
Shear demand/pile, kN
Factored shear capacity/ pile, kN
Compression
4159
567
771
786
Middle
2432
462
555
707
Tension
663
350
318
623
Note: 1 kN = 0.225 kip. P axial = axial load, V c = nominal shear capacity provided by concrete. 50
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Prescriptive design
The design process consists of the following steps:
The initial design procedure for prescriptive design is identical to that used for rational design. The differences lie in the calculation of the amount of transverse reinforcement required to develop the design axial load after spalling of the cover concrete.
1.
Provide a preliminary assessment of displacement ductility capacity.
2.
Select a pile design with reinforcement and a design axial load that allows curvature ductility capacity to enable the development of the required displacement ductility capacity, as per Eq. (3).
3.
Calculate the required confined concrete compressive strength such that the confined core will have the same capacity as the additional section from Eq. (1).
4.
Use a design chart such as Fig. 5 to calculate the required lateral confining stress given the required confined concrete strength and the design concrete strength.
5.
Calculate the required transverse reinforcement ratio from a design chart such as Fig. 6, given a specified transverse reinforcement strength.
6.
Check that the transverse reinforcement requirement meets the minimum from Eq. (3).
7.
Verify that the transverse reinforcement is sufficient for the shear demand for capacity-protected actions—either V max at superstructure failure or the full flexural capacity of the piles.
The steps used in prescriptive reinforcement design are as follows: 1.
Design transverse reinforcement per ACI 31805 section 21.4.1 or 10.9.3, whichever gives the greater amount of reinforcement.
2.
Evaluate shear based on dividing the seismic base shear evenly among the piles.
3.
Check that the transverse reinforcement provided is enough to carry V from Eq. (12).
Using current detailing practice, the transverse reinforcement will be chosen to meet the criteria of ACI 318-05 section 21.4.1 Eq. (3) but will not be less than that specified by section 10.9.3 Eq. (4). In this example, use of Eq. (4) with 10M (no. 3) wire would require a spiral pitch of 17.5 mm (0.689 in.), which is prohibitively tight for construction and concrete placement. It also violates the minimum pitch requirements of ACI 318-05, which would set a minimum spacing of 4d b, which is 52.8 mm (2.08 in.) based on the prestressing strand diameter and 116 mm (4.57 in.) based on the dowel diamet er. If 13M (no. 4) wire is used, the pitch increases to 32 mm (1.3 in.), which is still too small. Use of 16M (no. 5) results in a workable pitch of 49 mm (1.9 in.). However, turning 16M (no. 5) spiral is difficult. The amount of transverse reinforcement provided by prescriptive design is clearly more than enough to carry the calculated shear loads.
The suggested approach can result in significant cost savings, have no impact on structural safety or reliability, and validate that the use of structural elements would be uneconomical under current ACI guidelines.
References 1.
American Concrete Institute (ACI) Committee 318. Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05) . Farmington Hills, MI: ACI.
2.
Oldcastle Precast. 1996. Personal communication.
3.
Banerjee, S., J. F. Stanton, and N. M. Hawkins. 1987. Seismic Performance of Precast Concrete Bridge Piles. Journal of Structural Engineering, V. 113, No. 2: pp. 381–396.
4.
Mander, J. B., M. J. N. Priestley, and R. Park. 1988. Observed Stress-Strain Behavior of Confined Concrete. Journal of Structural Engineering, V. 114, No. 6: pp. 1827–1849.
Conclusion In the foregoing research, a rational seismic design approach for precast, prestressed concrete piles was developed and remained within the spirit of ACI 318-05. This methodology uses a proven model for confined concrete (the Mander model) and relies on a n ACI approach for validation. Implementation of this methodology is simple, requiring the use of two design charts and the generation of pile moment-curvature relationships, which are required for seismic design in any event.
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5.
6.
7.
8.
9.
Priestley, M. J. N., F. Seible, and G. Calvi. 1996. Seismic Design and Retrofit of Bridges. New York, NY: John Wiley and Sons.
D
= pile diameter
D*
= reference pile diameter
Budek, A. M., G. Benzoni, and M. J. N. Priestley. 1997. Experimental Investigation of Ductility of In-Ground Hinges in Solid and Hollow Prestressed Piles. Report no. SSRP 97/17. La Jolla, CA: Department of Structural Engineering, University of Ca lifornia at San Diego.
E
= modulus of elasticity
EI eff
= pile’s effective cracked-section bending stiffness
f y
= yield strength of the longitudinal reinforcement
f yt
= yield strength of the transverse reinforcement
f c'
= design concrete compressive strength
' f cc
= confined concrete strength
f l '
= lateral confining pressure provided by transverse reinforcement
H
= height of column
I eff
= effective moment of inertia
I gross
= moment of inertia for the gross section
K
= subgrade reaction modulus of soil
L
= pile length to point of inflection
L p
= plastic hinge length
M n
= nominal moment capacity
M u
= ultimate moment capacity
P
= load
Budek, A. M., M. J. N. Priestley. 2005. Experimental Analysis of Flexural Hinging in Hollow Marine Prestressed Pile Shafts. Coastal Engineering Journal, V. 47, No. 1: pp. 1–20. Chai, Y. H., and T. C. Hutchinson. 2002. Flexural Strength and Ductility of Extended Pile-Shafts—Experimental Study. Journal of Structural Engineering, V. 128, No. 3: pp. 595–602. Kachedoorian, R. 1968. Effects of March 27, 1964 Earthquake on the Alaska Highway System. U.S. Geological Survey professional paper 545-C. Washington, DC: U.S. Department of the Interior.
10. Kishida, H., T. Hanazato, and S. Nakai. 1980. Damage of Reinforced Precast Piles during the MiyagiKen-Oki Earthquake of June 12, 1972. In Proceedings of the Seventh World Conference on Earthquake Engineering. 11. Budek, A. M., M. J. N. Priestley, and G. Benzoni. 2000. Inelastic Seismic Response of Bridge DrilledShaft RC Pile/Columns. Journal of Structural Engineering, V. 126, No. 4: pp. 510–517.
Notation
Pax,core = axial load at the confined core
Ach
Paxial
= axial load
POT
= axial force increase if support from soil under piles is neglected
= cross-sectional area of the confined core or area measured out-to-out of transverse reinforcement
Adowels = area of dowels
52
Ag
= gross member cross-sectional area
Pu
= ultimate strength
As
= area of shear reinforcement
s
= spiral pitch
Ast
= area of longitudinal reinforcement
V
= shear strength
At
= area of transverse reinforcement
V c
= nominal shear capacity provided by concrete
d b
= strand diameter
V max
= maximum shear capacity at superstructure failure
d f
= effective depth to fixity
V s
= nominal shear capacity provided by shear reinforcement
d ’
= diameter of confined core
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φ
= strength-reduction factor
µ ∆
= displacement ductility
µφ
= ultimate curvature ductility
ρ l
= ratio of area of distributed longitudinal reinforcement to gross concrete area perpendicular to that reinforcement
ρ s
= ratio of volume of spiral reinforcement to total volume of core confined by the spiral (measured out-to-out of spirals)
About the authors Andrew Budek-Schmeisser, P.E., PhD, is assistant professor for the Department of Civil and Environmental Engineering at the New Mexico Institute of Mining and Technology in Socorro, N.Mex. Gianmario Benzoni, PhD, is research scientist for the Department of Structural Engineering at the University of California at San Diego in La Jolla, Calif.
ρ t
= ratio of area distributed transverse reinforcement to gross concrete area perpendicular to that reinforcement
uneconomical, even though they have been shown to provide good seismic performance when designed to less stringent specifications. This paper presents a simple design-chart-based methodology that uses current confined concrete models in conjunction with ACI 318-05 performance requirements to allow for lower levels of transverse reinforcement, which will allow for economical pile construction.
Keywords Code, design, pile, prestressed, reinforcement, seismic.
Review policy Synopsis The purpose of this research is t o develop a rational design methodology for precast, prestressed concrete piles that uses proven seismic design methodology and constitutive modeling to produce detailing requirements that are more economical yet still retain the spirit and meet the strength requirements of Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05) .
This paper was reviewed in accordance with the Precast/Prestressed Concrete Institute’s peerreview process.
Reader comments Please address any reader comments to PCI Journal editor-in-chief Emily Lorenz at elorenz@pci .org or Precast/Prestressed Concrete Institute, c/o PCI Journal, 209 W. Jackson Blvd., Suite 500, Chicago, IL 60606. J
Transverse reinforcement requirements specified by ACI 318-05 for compressive members penalize precast, prestressed concrete piles, which typically have large ratios of cover to diameter. These requirements can make prestressed piles
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