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FHWA > Engineering > Geotech > Design And Construction Of Continuous Flight Auger Piles > Chapter 5 
Geotechnical Engineering Circular (GEC) No. 8

R_{S} =  N  f_{s,i} π D_{i} L_{i} 
Σ  
i 
Some of the methods presented in this chapter and Appendix A use an average unit sideshear (f_{save}) for the entire pile length, instead of summing individual pile segments. In these cases, the total sideshear resistance is calculated as:
(Equation 5.3)R_{S} = f_{save} π D L
where D is the average diameter of the pile, and L is the pile total embedment length.
The total endbearing resistance (R_{B}) is calculated as:
(Equation 5.4)R_{B} = q_{p}  π D_{B}^{2}  
4 
where q_{p} is the unit endbearing resistance, and D_{B} is the diameter of the pile at the base.
The sideshear component is mobilized with relatively small pile vertical displacements relative to the surrounding soil, typically less than 10 mm (0.4 in.). The endbearing component is fully mobilized with larger displacements, typically at a pile tip movement in the range of 5% to 10% of the pile diameter. Driven piles of comparable axial resistance are likely to mobilize the tip resistance at a smaller vertical displacement due to the inherent preloading at the tip that occurs during installation. Consequently, the loadsettlement curve from a loadtest of a CFA pile may appear somewhat softer than that of a typical driven pile and methods used to interpret ultimate load resistance from loadtests on driven piles could be conservative for CFA piles.
The mobilized side and endbearing resistances can be assessed using Figure 5.1, which is based on a study by Reese and O'Neill (1988) for drilled shafts. The CFA pile resistance at any desired displacement (expressed as a ratio to the diameter) may be obtained from the calculated ultimate resistance for that CFA pile multiplied by the normalized resistance at comparable displacement ratio given in the figure. Reese and O'Neill (1988), AASHTO (2006), and others consider the ultimate endbearing capacity to be mobilized at a tip displacement equal to 5% of the pile diameter. Many studies of CFA pile resistance use a similar definition and the methods presented in this document are also based on the ultimate endbearing capacity defined at a pile tip displacement equal to 5% of the pile diameter, unless otherwise noted.
Elastic compression of the pile under load can have a small effect on the distribution of displacement of the pile relative to the surrounding soil. However, the elastic compression is relatively small for the pile lengths and load levels that are typical of CFA piles, and can often be disregarded. For instance, consider a load of 445 kN (100 kip) acting on a pile 450 mm (18 in.) in diameter and 25 m (82 ft) long, and a pile elastic modulus (E) of 27,500 MPa (4,000 ksi). If half of the load goes to the tip and the sideshear is evenly distributed along the pile length, the average load in the pile would be 0.75 of the load, or 334 kN (75 kips) and the elastic shortening would be 334 kN × 25 m / (A_{pile}E) = 2 mm (0.08 in.), where A_{pile} is the crosssectional area of the pile. Details of the calculation of the elastic compression of a pile are presented in Section 5.5.3.1.
The recommended methods presented for estimation of static axial capacity of single CFA piles assume that a conventional continuous flight auger construction technique will be employed, and construction practices and quality assurance procedures consistent with those recommended herein are adhered to such extent that excessive flighting of soil and ground loosening is avoided. The use of highdisplacement auger cast piles (DD piles) and/or the use of amelioration (introduction of coarse sand or gravel from the ground surface down into the annular area between the borehole wall and the drill stem) could significantly increase the pile capacity, and is discussed subsequently in Section 5.4.
Recommended design procedures are broadly organized by soil type as either cohesive or cohesionless in the subsections that follow. Note that silty soils require judgment on the part of the engineer to evaluate the most reasonable approach to use. In general, these finegrained soils should be classified in response to the anticipated behavior under the load being considered, as to whether the soil is likely to behave more nearly in an undrained or fully drained manner. Depending on this clarification, methods for either cohesive of cohesionless soils must be used. Recommendations are further categorized by the available type of insitu or laboratory test data.
Appendix A summarizes results from comparison studies of different procedures, and provides the basis by which the recommended methods were chosen. Appendix A also summarizes other methods used to predict CFA pile capacities.
Figure 5.1: LoadDisplacement Relationships
(a) Normalized Load Transfer in SideShear (b) Normalized EndBearing Capacity vs. Settlement in Cohesive Soils vs. Settlement in Cohesive Soils
(c) Normalized Load Transfer in SideShear d) Normalized EndBearing vs. Settlement in Cohesive Soils vs. Settlement in Cohesive Soils
Source: Reese and O'Neill (1988)
The design procedures recommended in the following subsections appear to provide good correlations to CFA pile capacity for generalized soil types across the broad scope of North American practice. The design engineer should consider the specific soil composition and construction techniques to be used at their particular site and experience within the local area or geology. The design engineer is encouraged to investigate the formulation of alternative design procedures in order to identify documented procedures that have a basis that may more closely match the specific conditions of their site. While the estimates of capacity derived from static analyses are useful for preliminary design, it must also be emphasized that a well designed loadtesting program is a critical and necessary component for the effective use of CFA piles.
The FHWA 1999 method for drilled shafts is recommended for prediction of both the sideshear and endbearing resistances for CFA piles in cohesive materials. The FHWA 1999 method was originally proposed by Reese and O'Neill (1988) and later modified by O'Neill and Reese (1999).
For a given pile segment, the ultimate unit sideshear resistance (f_{s}) is calculated as:
(Equation 5.5)f_{s} = α S_{u}
where S_{u} is the undrained shear strength of the soil at the pile segment location, and α is a reduction factor that varies as follows:
(Equation 5.6)α = 0.55 for S_{u} / P_{a} ≤ 1.5
where P_{a} is the standard atmospheric pressure (equal to 1 atm or approximately equal to 101 kPa [1.06 ton per square foot or tsf]), for 1.5 < S_{u}/P_{a} ≤ 2.5, α varies linearly from 0.55 to 0.45.
If the bottom of the pile is bearing on clay, the sideshear contribution to the capacity of the bottom onediameter length of the pile is neglected. If the top layer is clayey, there exists the potential for this soil to shrink away from the top of the pile when exposed to the atmosphere. If such a condition is suspected, then the sideshear contribution from this layer should be neglected in the greater of either the top 1.5 m (5 ft) of soil or the depth of seasonal moisture change.
In the FHWA 1999 method, the ultimate unit endbearing resistance (q_{p}) is calculated as:
(Equation 5.7)q_{p} = N_{c}^{*} S_{u}
where S_{u} is the average undrained shear strength of the soil between the pile tip and twopile diameters below the pile tip, and N_{c}^{*} is the bearing capacity factor. The value of N_{c}^{*} is adopted as follows:
(Equation 5.8)N_{c}^{*} = 9
for 200 kPa (2 tsf) ≤ S_{u} ≤ 250 kPa (2.6 tsf), and L ≥ 3D, or
(Equation 5.9)N_{c}^{*} =  4  [ lnI_{r} + 1 ] 
3 
for S_{u} < 200 kPa (2 tsf), and L ≥ 3D.
where L is the pile embedment length below top of grade, and I_{r} is the rigidity index.
Note that values of S_{u} greater than 250 kPa (2.6 tsf) are treated as intermediate geomaterials in accordance with O'Neill and Reese (1999). The rigidity index (I_{r}) is calculated as follows:
(Equation 5.10)I_{r} =  E_{S} 
3 S_{u} 
where S_{u} and the undrained Young's modulus (E_{S}) are those of the soil just below the pile tip. E_{S} is best determined from triaxial testing or insitu testing (such as the pressuremeter test). If E_{S} is not measured, it can be assumed with less accuracy to be a function of S_{u} for design purposes by interpolating between the values given in Table 5.1 below.
S_{u}  I_{r} = E_{s} / ( 3 S_{u} )  N^{*}_{c} 

25 kPa (0.25 tsf)  50  6.5 
50 kPa (0.50 tsf)  150  8.0 
100 kPa (1.00 tsf)  250  8.7 
200 kPa (2.00 tsf)  300  8.9 
Source: O'Neill and Reese (1999)
Although not expected to occur for CFA piles, if the pile embedment length below grade were to be less than three pile diameters, the ultimate unit endbearing resistance (q_{p}) should be reduced according to the FHWA 1999 method, as follows:
(Equation 5.11)q_{p} =  2  1 +  1  L  N_{c}^{*} S_{u} for L < 3D  
3  6  D 
The Coleman and Arcement (2002) method was derived from CFA pile loadtests conducted in mixed soil conditions consisting of mostly alluvial and loessial deposits, and interbedded sands and clays in Mississippi and Louisiana. Section A.2.10 of Appendix A contains further details of the test program. The method may be considered as an alternative for soils of similar geology and properties as described in Appendix A and below. This method provides modifications to the α factor for clays and silts (exhibiting an undrained condition) that may be utilized for estimation of sideshear capacities. The ultimate unit sideshear resistance (f_{s}) is again calculated from the average undrained shear strength (S_{u}), and the α factor as:
(Equation 5.12)f_{S} = α S_{u}
(Equation 5.13a)α =  56.2  (S_{u} in kPa) 
S_{u} 
α =  0.56  (S_{u} in tsf) 
S_{u} 
Coefficients above are rounded from Coleman and Arcement (2002). The valid range of S_{u} for this equation is between about 25 and 150 kPa (0.25 to 1.5 tsf), as shown in Figure 5.2. Note that in the recommended FHWA 1999 method, α would be constant and equal to 0.55 for soils with S_{u} less than approximately 150 kPa [1.5 tsf]), and would reduce to as low as 0.45 for greater values of S_{u}. The design engineer may consider the use of this correlation for similar deposits where it is anticipated that the FHWA 1999 method may be too conservative for similar deposits of clays and silts that are very soft to medium in consistency (i.e., S_{u} up to approximately 50 kPa [0.5 tsf ]).
Figure 5.2: Relationship for the α Factor with S_{u} for Calculating the Unit SideShear for Cohesive Soils for the Coleman and Arcement (2002) Method
Source: Coleman and Arcement (2002)
The TXDOT 1971 Method (Texas Highway Department, 1972) for drilled shafts has shown favorable results in predicting the static axial capacity of CFA piles in stiff clays, which have been overconsolidated by desiccation. The ultimate unit sideshear resistance (f_{s}) in cohesive soils is calculated for a given pile segment simply as a function of S_{u} (i.e., here the α factor is constant at 0.7):
(Equation 5.14)f_{s} = 0.7 S_{u} ≤ 120 kPa (1.25 tsf)
The TXDOT 1971 Method (Texas Highway Department, 1972) for drilled shafts has shown favorable results in predicting the static axial capacity of CFA piles in cohesive soils. However, the method relies on the use of a Dynamic Cone Penetrometer value (N_{TxDOT}) for estimation of ultimate unit endbearing resistance, which is uncommon in most areas outside of Texas. The ultimate unit endbearing resistance (q_{p}) can be determined using the N_{TxDOT} value as follows:
(Equation 5.15)q_{p} (tsf) =  N_{TxDOT} 
8.25 
The design methods for prediction of sideshear and endbearing resistance components in cohesive soils rely almost exclusively on undrained shear strength (S_{u}). When no other types of geotechnical data other than SPTN values are available, the undrained shear strength can be estimated from SPTN values using local or published correlations appropriate for the soil deposit in question. However, this procedure is recommended only in feasibility studies, and not for design, because SPTN values obtained in soils are not highlyreliable in estimating the undrained shear strength.
CPT testing has shown good results in prediction of both endbearing and sideshear of CFA piles, as well as other types of deep foundations. This method of testing has become common in geotechnical soil exploration. For many engineers, the CPT is the preferred tool for use in predicting pile capacities in soils. Current research is focused on developing improved correlations for the use of CPT data in estimating CFA pile capacities, and improved correlations may become available as CPT becomes more widespread in the U.S. market.
The Laboratorie Des Ponts et Chausses (LPC) method for drilled shafts and driven piles, developed by Bustamante and Gianeselli (1981, 1982), is recommended to be used over the previously presented methods for cohesive soils when cone bearing resistance (q_{c}) data from CPT testing. Sideshear resistance estimates can be made using Figure 5.3 for clays and silts exhibiting an undrained condition.
The ultimate unit sideshear in cohesive soils (f_{s}) at a given depth (shown in Figure 5.3 as Maximum friction) is determined from the cone bearing resistance (q_{c}) at that depth (as shown on the Yaxis), and then by interpolation between the limiting curves shown (q_{c} < 1.2 MPa [12.5 tsf] and q_{c} > 5 MPa [52 tsf]) based upon the average q_{c} along the pile length or pile segment length within a cohesive stratum.
The ultimate unit endbearing resistance (q_{p}) in cohesive soils may also be estimated directly from the cone tip resistance (q_{c}) from CPT testing:
(Equation 5.16)q_{p} = 0.15 q_{c}
Figure 5.3: Unit SideShear Resistance as a Function of Cone Tip Resistance for Cohesive Soils  LPC Method
Source: Bustamante and Gianeselli (1982)
The cone tip resistance used in this equation is averaged for a range of two to three pile diameters below the pile tip, whichever gives a lesser average value.
The FHWA 1999 method for drilled shafts is recommended for the prediction of CFA pile capacity in cohesionless soils. The FHWA 1999 method was originally proposed by Reese and O'Neill (1988), and later modified by O'Neill and Reese (1999). This method uses SPT N_{60} values (in blows per 0.3 m or per foot [bpf]) for calculations; these values should be based on 60% hammer efficiency but should not be depth corrected.
The ultimate unit sideshear resistance (f_{s}) of a pile segment is estimated as:
(Equation 5.17)f_{s} = K σ_{v}′ tanφ ≤ 200 kPa (2.0 tsf)
Where K is the lateral earth pressure coefficient, σ′_{v} is the vertical effective stress, and φ is the soil drained angle of internal friction. The β factor is defined as:
(Equation 5.18)β = K tan φ
and is limited to 0.25 ≤ β ≤ 1.2. The β factor for a pile segment is estimated as:
(Equation 5.19a)β = 1.5  0.135 Z^{0.5} for N ≥ 15 bpf
(Equation 5.19b)β =  N  ( 1.5  0.135 Z^{0.5}) for N < 15 bpf 
15 
where Z is the depth (in feet) from the ground surface to the middle of a given soil layer or pile segment.
In the FHWA 1999 method, the ultimate unit endbearing resistance (q_{p}) is estimated as:
(Equation 5.20a)q_{p} (tsf) = 0.6 N_{60} for 0 ≤ N_{60} ≤ 75
(Equation 5.20b)q_{p} = 4.3 MPa [45 tsf] for N_{60} > 75
where N_{60} is the SPTN value (bpf) at 60% of hammer efficiency near the tip of the pile, which is typically taken as the average within the depth interval of approximately 1 pile diameter above, to 2 or 3 pile diameters below, the pile tip.
The Coleman and Arcement (2002) method was derived from CFA pile loadtests conducted in Mississippi and Louisiana in mixed soil conditions consisting of mostly alluvial, loessial deposits, and interbedded sands and clays. Section A.6.3 of Appendix A contains further details of the test program. This method provides modifications to the β factor of the recommended FHWA 1999 method for sandy soils and silty soils (exhibiting a drained condition) as follows:
(Equation 5.21)f_{s} = β σ_{v} ≤ 200 kPa (2.0 tsf)
The values of β are computed as follows:
(Equation 5.22)β = 2.27 Z_{m}^{0.67} (for silty soils)
(Equation 5.23)β = 10.72 Z_{m}^{1.3} (for sandy soils)
Where Z_{m} is the depth (in meters) from the ground surface to the middle of a given soil layer or pile segment. The values of β are limited to 0.2 ≤ β ≤ 2.5.
The resulting β values in this method are shown in Figure 5.4, which also shows β values obtained using the FHWA 1999 method for comparison. The higher β factors at shallow depths are most likely a result of the weakly cemented deposits (i.e., with a cohesion of approximately 24 kPa [500 psf]) used in this study; these cemented soils have appreciable strength even when the effective overburden stress is low.
Figure 5.4: Relationship for the β Factor for Calculating the Unit SideShear for Cohesionless Soils for the FHWA 1999 and Coleman and Arcement Methods
Source:Coleman and Arcement (2002)
The LPC method for drilled shafts and driven piles, developed by Bustamante and Gianeselli (1981, 1982), is recommended when the capacities are to be estimated directly from the CPT cone bearing resistance (q_{c}). These estimates can be made using Figure 5.5 for sands and gravel.
The ultimate unit sideshear in cohesionless soils (f_{s}) at a given depth (shown on the Xaxis as Maximum friction) is determined from the cone bearing resistance (q_{c}) at that depth (as shown on the Yaxis), and by the interpolating between the limiting curves shown (q_{c} < 3.5 MPa [36 tsf] and q_{c} > 5 MPa [52 tsf]) based upon the average q_{c} along the pile length or pile segment length within a cohesionless stratum.
The ultimate unit endbearing resistance (q_{p}) in cohesionless soils may also be estimated directly from the cone bearing resistance (q_{c}) from CPT testing, which is typically averaged over two to three pile diameters below the pile tip. According to the LPC method:
(Equation 5.24)q_{p} (MPa) = 0.375 q_{c}
Figure 5.5: Unit SideShear as a Function of Cone Tip Resistance for Cohesionless Soils  LPC Method
Source: Bustamante and Gianeselli, (1982)
CFA piles have been used with success in strong, noncaving materials including vuggy limestones, shales, and other types of weathered or weak rocks. However, it is generally not possible to install CFA piles in such hard material while maintaining a rate of penetration that would normally be required to penetrate caving soil without mining. The use of continuous flight augers to construct CFA piles in weak or weathered rock is thus comparable to drilling an open hole drilled shaft without removing the auger. The potential problem of such practice is for conditions where noncohesive overburden soils are present and will be subject to soil mining of the overburden as the rock socket is drilled. Where cohesive or stable overburden soils permit the installation of CFA piles into weak or weathered rock without problems, it is recommended that computational procedures should follow that of drilled shafts as outlined in O'Neill and Reese (1999). The following subsections present experience with CFA piles installed in vuggy limestone and shale.
For hard rock overlain by soil materials, it may be difficult to construct a CFA pile with sufficient base resistance on the rock without soil mining. Piles should penetrate at least one pile diameter into the rock bearing stratum to utilize endbearing capacity associated with the rock. Even when the overlying soil is cohesive and the risk of soil mining is low, the reliability of the pile/rock interface is uncertain unless penetration of the rock can be assured. Conditions with soil overlying an extremely hard rock formation would be better suited to alternate foundation types, such as a drilled shaft, micropile, or driven steel pile.
For vuggy limestone formations of South Florida, or for similar formations elsewhere, CFA piles may be designed according to the relationships suggested by Frizzi and Meyer (2000). These relationships were derived from over 60 loadtests in the Miami limestone and Fort Thompson limestone formations found in South Florida (Broward and MiamiDade Counties).
Frizzi and Meyer (2000) presented relationships of unconfined compressive strength vs. ultimate unit sideshear resistance, shown on Figure 5.6. The relationship shown on that figure by Gupton and Logan (1984) was based upon drilled shaft experience in Florida limestone, the relationship by Kaderabek and Reynolds (1981) was based on anchor pullout tests performed on rock core specimens, and the relationship developed by Ramos et al. (1994) was developed primarily from fullscale field grout plug tests and limited CFA loadtests in various Florida limestone. The trend lines suggest that the smaller scale anchor tests and grouted plugs tend to mobilize higher sideshear resistance than larger foundations when tested in rock at the lower end of the unconfined compressive strength range; as the intact rock strength increases, they will tend to perform more similarly to drilled shafts. These data suggest that the effect of scale is important in interpreting field test data for drilled foundations in Florida limestone, and design correlations for CFA piles should be based on tests of fullscale piles.
In the Frizzi and Meyer (2000) method, the ultimate unit sideshear resistance for a given pile segment in either the Miami limestone or Fort Thompson limestone formations are correlated to the SPTN_{60}, as shown in Figure 5.7. SPTN_{60} values for calculations should be based on 60% hammer efficiency but should not be depth corrected. The data utilized to develop these relationships were limited to ultimate unit sideshear resistance values not exceeding approximately 9 and 8 MPa (94 to 84 tsf) for the Miami limestone and Fort Thompson limestone formations, respectively. Note that the smaller scale plug tests data from Ramos et al. (1986) again appears to be unconservative when compared to fullscale field loadtest data.
Figure 5.8 presents a relationship of sideshear stress development with displacement from loadtested CFA piles constructed in the Miami limestone and Fort Thompson limestone formations. Note that this data is presented as the ratio of the developed sideshear to the ultimate sideshear resistance (f/f_{max}) vs. the pile displacement (W) expressed as a percentage of the diameter (D). This relationship is compared with curves for drilled shafts proposed by Reese and O'Neill (1988) and with loadtest data published by Semeraro (1982). No modifications or methods for predicting the endbearing capacity were proposed by Frizzi and Meyer (2000). Note that in most cases, the CFA piles mobilized a very high loadcarrying capacity initially (at a very low displacement), after which the load mobilization characteristics become similar to the deflection hardening response shown for granular soil.
Figure 5.6: Unconfined Compressive Strength vs. Ultimate Unit SideShear for Drilled Shafts in Florida Limestone
Source: Frizzi and Meyer (2000)
Figure 5.7: Correlation of Ultimate Unit SideShear Resistance for South Florida Limestone with SPTN_{60} Value
Source: Frizzi and Meyer (2000)
Figure 5.8: SideShear Development with Displacement for South Florida Limestone
Source: Frizzi and Meyer (2000)
For CFA piles socketed into clayshale formations of NorthCentral Texas, or for similar formations elsewhere, the total capacity developed in the socket may be estimated according to the relationships suggested by Vipulanandan et al. (2005). These relationships were derived from eight loadtests of CFA piles socketed into clayshale with unconfined compression strengths (q_{u}) ranging from 100 to 3,000 kPa (1 to 30 tsf) (measured in situ from a Texas Cone Penetrometer value, N_{TxDOT}). Overburden soils were predominantly clay and sandy clay, and thus allowed for construction of the socket without appreciable soil mining effects. The diameter and length of the CFA piles varied from 450 to 600 mm (18 to 24 in.) and 12 to 25 m (40 to 83 ft), respectively.
The loadtest results are presented in dimensionless form for all eight test piles as a relative load capacity (Q / Q_{ult}), which is a function of the relative displacement (ρ / D). This is shown in Figure 5.9 and is represented by the following hyperbolic function:
(Equation 5.25)Q  =  ρ  
D  
Q_{ult}  ρ_{50}  +  ρ  
D  D 
where:
Q  =  resistance at the given displacement (in any consistent units); 
Q_{ult}  =  the ultimate resistance that occurs for very large displacements (in the same, consistent units of Q); 
ρ  =  pile displacement (in any consistent units); 
D  =  diameter of the pile (in the same, consistent units of ρ); and 
ρ_{50}/D  =  the displacementtodiameter ratio at Q/Q_{ult} = 0.5. 
The parameter Q_{ult} was correlated to the unconfined compressive strength (q_{u}) of the clayshale, pile circumference (π D), and socket length (L) and is shown in Figure 5.10 and is represented as:
(Equation 5.26)Q_{ult}  = 0.11  L  + 0.96 
q_{u} π D L  D 
Figure 5.9: Relative Load Capacity vs. Relative Displacement for CFA Sockets in ClayShale
Source: Vipulanandan et al. (2004)
Figure 5.10: Hyperbolic Model Parameter Q_{ult} as a Function of the Unconfined Compressive Strength (q_{u}) for CFA Sockets in ClayShale
Source: Vipulanandan et al. (2004)
The parameter ρ_{50}/D was also correlated to the unconfined compressive strength of the clayshale normalized by the standard atmospheric pressure (in any consistent units) in the equation below.
(Equation 5.27)ρ_{50}  [ in % ] =  15.8 
D  q_{u}  
P_{atm} 
This relationship is shown in Figure 5.11.
To use the Vipulanandan et al. (2004) method, the unconfined compressive strength obtained from the field or laboratory is considered first. After normalizing q_{u} with the atmospheric pressure the ratio ρ_{50}/D is obtained form Figure 5.11 or Equation 5.27. The ultimate capacity is computed using Figure 5.10 or Equation 5.26. With the pile diameter D and socket length L known, and the variables previously presented already determined, the relative load capacity can be the computed for a range of pile displacements. An example in English units is provided to illustrate the method.
Figure 5.11: Parameter ρ_{50}/d as a Function of Unconfined Compressive Strength for CFA Sockets in ClayShale
Source: Vipulanandan et al. (2004)
For:
The following results are obtained using the method described above:
With Equation 5.26, the ultimate capacity is estimated as:
Q_{u} = q_{u} π D L ( 0.11 × L/D + 0.96 ) = 20 × 3.14 × 1.5 × 4.5 ( 0.11 × 3 + 0.96) = 267 tons.
For a pile displacement of 0.25 in. and using Equation 5.25, the mobilized load capacity is estimated to be:
Q  = Q_{ult} [ ρ/D ÷ ( ρ_{50}/D + ρ/D )] = 
= 267 × [ 0.25/18 ÷ ( 0.0079 + 0.25/18 ) ] = 0.64 × 267 = 170 tons. 
Numerous construction techniques and tools have been developed to increase the load capacity over that which is attained from conventional CFA piles for a given soil condition. Most of these systems have been developed by specialty contractors and/or equipment manufacturers, and thus may perform differently depending upon the relative volume of soil displaced in proportion to the pile volume, the magnitude of the permanent increase in lateral stress or soil improvement at the pile/soil interface, the relative roughness of the resulting pile/soil interface, and the effective diameter of the resulting pile. Different techniques may achieve superior results in different types of soil conditions. For example, increased lateral stress and soil densification may be a very desirable effect of installation in sandy soil profiles, while increased roughness or effective diameter may be effective in cohesive soils where densification of saturated cohesive soil is unlikely to occur.
Most of these specific techniques and tools share some common features regarding the mechanisms by which higher capacities may be realized. In general, in DD piles, the drilling spoils and the surrounding soil are displaced laterally or compacted into the borehole wall to varying degrees during auger penetration. The relative volume of soil displaced in proportion to the pile volume determines whether the technique is termed a "high displacement" or a "partial displacement" pile. In cases where an amelioration technique is employed, sand or gravel introduced into the top of the borehole may also be compacted into the borehole wall by specialty tooling. As a result, localized densification of the soil will occur to some limited extent away from the pile, and the effective lateral stresses in the soil surrounding the pile will increase.
A number of studies have attempted to quantify the effects of displacement on surrounding soils during pile construction. Kulhawy (1984) showed that the lateral earth pressure coefficient (K_{o}) may decrease as much as one third (resembling an active lateral earth pressure, K_{a}) for drilled shafts, and may nearly double (resembling a passive lateral earth pressure, K_{p}) for highdisplacement driven piles. Displacement effects have also been quantified by other means. Webb et al. (1994) indicated an increase of 20 to 50% in CPT resistance over the length of pile after the installation of displacement piles in sandy soils. Nataraja and Cook (1983) used SPT to quantify the effects of displacement and concluded that the increased stresses were also a function of the soil uniformity coefficient, overconsolidation ratio, and effective stress conditions before displacement.
The recommended method for estimating axial resistance of DD piles is based on the published work of NeSmith (2002). Caution is warranted in using the correlations presented for DD piles, as the static axial capacity is very sensitive to the construction technique and tooling, and relies heavily on the abilities and experience of the specialty contractors. Improved sideshear resistance and endbearing capacities obtainable with this technique over conventional CFA piles must be verified for the specific site, technique, and equipment using fullscale loadtesting, automated monitoring, and recording equipment for all test and production piles.
NeSmith (2002) studied the results of 22 fullscale compression loadtests and six fullscale pullout tests of DD piles located at 19 different sites throughout the United States. The pile diameters ranged from 0.36 to 0.46 m (14 to 18 in.), with the majority at 0.41 m (16 in.). The pile lengths ranged from 6 to 21 m (20 to 69 ft), with an average length of approximately 13 m (43 ft). A variety of soil conditions were investigated (listed in Table 5.2), which generally ranged from clean sands, fine gravels, to silty and clayey sands. Five of the compression test piles (included as one site in the Piedmont geologic setting in Table 5.2) were from the research conducted by Brown and Drew (2000); the soils at this site consisted of clayey silts to silty clays with around 50% passing the #200 sieve, and represent the soil profile with the highest fines content in the NeSmith (2002) study.
Geologic Setting  Sites  Major Features 

Alluvium in a major river (AR, CA, FL, IA, WA)  5  Loose to dense sand, some gravel, wellgraded (primarily), clean to some silt and clay 
Post Miocene (FL)  4  Loose (primarily) to medium silty, clayey sand 
Barrier Island (Fl, AL, MD)  4  Medium to very dense sand, uniform, clean 
Piedmont (GA)  3  Loose (primarily), silty sand/sandy silt, micaceous (toe in partially weathered rock) 
Glacial Outwash (MN)  1  Loose to medium sand with fine gravel, clean, wellgraded 
Gulf Coastal Plain ( FL)  1  Loose to medium silty clayey sand 
Colma Formation (CA)  1  Medium to very dense silty and clayey sand 
Source: NeSmith (2002)
NeSmith (2002) defined ultimate pile capacity to occur at displacements of 25.4 mm (1 in.) of tip movement, or when the displacement rate of the loading curve reached 0.057 mm/kN (0.02 in./ton), whichever occurred first. While the two stated failure criteria occasionally occurred near the same load, the displacement rate criterion did not govern in any case. In the event that the load was not increased to a level sufficient to reach either of the criteria, the load displacement relationship was extrapolated to ultimate by the method proposed by Chin (1970), and this method was also used to estimate the shaft endbearing component for test piles where no instrumentation was available.
Figure 5.12 (a) and (b) shows correlations of the ultimate unit sideshear (f_{s}) with CPT tip resistance (q_{c}) and SPTN values, respectively. SPTN_{60} values should be based on 60% hammer efficiency but should not be depth corrected. These relationships should only be applied to cohesionless materials in which displacement of the spoils into the borehole wall during construction will result in densification of the surrounding soil. Based on these trends, the ultimate unit sideshear resistance (f_{s}) for a given pile section can be correlated with q_{c} or to SPTN_{60} values as follows:
(Equation 5.28)f_{s} = 0.01 q_{c} + W_{S} for q_{c} ≤ 200 tsf (20 MPa)
(Equation 5.29)f_{S} (tsf) = 0.05 N + W_{S} for N ≤ 50
f_{S} = 0.005 × N + W_{S} for N ≤ 50
where the correlation constant (W_{s}) and limiting ultimate unit sideshear (f_{s}) are as follows:
Note that the recommended method for estimating the ultimate f_{s} from CPTq_{c} values for DD piles (Figure 5.12), are more than twice that predicted by the alternative method (LPC) for computing f_{s} from CPTq_{c} values for conventional CFA piles (Figure 5.5).
The ultimate unit endbearing (q_{p}) was correlated to either CPTq_{c} or SPTN values obtained near the pile tip. SPTN_{60} values should be based on 60% hammer efficiency. These values should be obtained between approximately 4D above and 4D below the pile tip. Figure 5.13 (a) and (b) show the ultimate unit endbearing capacity (q_{p}) data, and the correlations with CPTq_{c} and SPTN values, respectively. Capacities may be estimated according to the following relationships:
(Equation 5.30)q_{p} = 0.4 q_{c} + W_{T} < 19 MPa (200 tsf)
(Equation 5.31)q_{p} (MPa or tsf) = 0.19 N_{60} + W_{T} for N_{60} ≤ 50
where the constant (W_{T}) is as follows:
W_{T} = 0, for q_{p} ≤ 7.2 MPa (75 tsf) and uniform, rounded materials having up to 40% fines.
W_{T} = 1.34 MPa (14 tsf), for q_{p} ≤ 8.62 MPa (89 tsf) and wellgraded angular materials having up to 10% fines.
For soil conditions with material properties falling between the ranges provided above, a linear interpolation between the limiting values should be made.
It is worthwhile comparing the above recommendations for DD piles with that for conventional CFA piles as described in the preceding section. For CFA piles, the recommended method and the alternative method for computing ultimate unit endbearing (q_{p} in units of tsf) from SPTN_{60} values ranged from 0.6 N_{60} to 1.7 N_{60}, respectively. The recommended method for ultimate unit endbearing (q_{p} in units of tsf) from SPTN_{60} values for DD piles ranges from 1.9 N_{60} to 1.9 N_{60} + 14 tsf, depending on soil material properties. Similarly, the alternative method (LPC) for computing the ultimate unit endbearing (q_{p}) from CPTq_{c} values for conventional CFA piles was 0.375 q_{c}_{.} The recommended method for ultimate unit endbearing (q_{p}) from CPTq_{c} values for DD piles ranged from 0.4 q_{c} to 0.4 q_{c} + 14 tsf, depending on soil material properties.
Figure 5.12: Ultimate Unit SideShear Resistance for Drilled Displacement Piles for NeSmith (2002) Method
(a) Correlated to CPT Testing
(b) Correlated to SPT Testing
Note: N in Figure above refers to N_{60}. Source: NeSmith (2002)
Figure 5.13: Ultimate Unit EndBearing Resistance for Drilled Displacement Piles for NeSmith (2002) Method
(a) Correlated to CPT Testing
(b) Correlated to SPT Testing
Note: N in Figure above refers to N_{60}. Source: NeSmith (2002)
The amelioration technique involves introducing coarse sand or gravel into the top of the borehole as the specialty tooling is advanced. A section of reversed auger flights (pitched opposite to the direction of rotation) is situated above the normal auger flights, and a packer (enlarged drill stem) lies in the drill string between these two sets of auger flights. The sand or gravel introduced falls down into the annular between the borehole wall and the drill stem. The reversed flights catch the introduced granular material and force it into the borehole wall.
In addition to densifying the surrounding soil and increasing the effective stress, this technique was shown by Brown and Drew (2000) to be advantageous in silty clays to clayey silts where the soiltopile interface friction angle (δ) would have otherwise been smaller. They found amelioration with sand to increase an individual pile's sideshear resistance by approximately 25% over that of an individual pile constructed without amelioration. However, they found amelioration with sand to increase sideshear by only 16% of a single pile tested individually within a pile group (spaced at 3 pile diameters centertocenter) over that of a similar single pile within a group constructed without amelioration and tested individually within the group. Also, they found amelioration with crushed stone (maximum aggregate size typically 10 mm [0.4 in.]) to increase sideshear resistance of individual piles by approximately 50% over that of an individual pile constructed without amelioration. The introduced freedraining granular material may allow for any excess pore pressures around the pile to be dissipated more rapidly than they would otherwise, as well as potentially increasing the effective diameter of the pile. While both grouping of piles and amelioration both provided marked increases in capacity, their combined effects were not as substantial as the simple sum of the two.
This technique, which may result in substantial improvements to the capacity, relies heavily on the abilities and experience of the specialty contractors, and is typically utilized as only a contractorproposed method. However, with the use of performancebased specifications for contracting as described in Chapter 8, the use of these innovative pile types may be encouraged. Improved capacities obtainable with DD techniques must be verified for the specific site and tooling/technique with fullscale loadtesting and the use of automated monitoring and recording equipment for all test and production piles. Note also that the required resistance may tend to be achieved with shorter piles than anticipated with conventional CFA, and thus group effects and settlement considerations may be controlling issues in some cases. Effects of installation of DD piles with amelioration on adjacent structures may also be a limiting factor in selection of this technique.
The axial compressive capacity of a pile group is not necessarily the sum of the single pile capacity within the group. In pile groups, the zone of influence from an individual pile may intersect with other piles, depending on the pile spacing, as illustrated in Figure 5.14. Evaluations of pile group capacities should also consider potential block failure of the pile group, and the potential contribution of the pile cap to bearing capacity contribution regarding the total capacity of the pile group system (termed occasionally as a pile raft). Finally, the designer should be aware that settlement of a pile group may often exceed that which would be predicted based upon a single pile analysis
Figure 5.14: Overlapping Zones of Influence in a Frictional Pile Group
Source: Hannigan et al. (2006)
The efficiency of a pile group (η_{g}) is defined as:
(Equation 5.32)η_{g} =  R_{ug}  
n  
Σ  R_{u,i}  
i = 1 
where R_{ug} is the ultimate resistance of the pile group, and R_{u,i} is the ultimate resistance of a single pile "i" in the pile group with a total of n piles in the group.
Displacement piles (such as driven piles and to a lesser extent DD piles) generally tend to increase the effective stress of the surrounding soil, and thus can create a pile group capacity greater than the sum of the individual pile capacities when these densified zones of influence surrounding the pile overlap. This soil improvement effect creates an efficiency greater than 1.0. Conversely, excavated piles (such as drilled shafts and conventional CFA piles), generally tend to decrease the effective stress of the surrounding soil, or at best maintain it at the atrest (K_{o}) condition, creating an efficiency less than or equal to 1.0, respectively. Changes in effective stress are more pronounced in cohesionless soils. Note also that installation effects from poorly controlled pile construction resulting in soil mining during drilling can adversely affect the lateral stress of previously installed piles.
Groups of conventional CFA piles may be designed with drilled shaft group efficiencies that may tend to be conservative if proper techniques are used for CFA pile construction, as verified with appropriate construction monitoring. However, the reader is strongly cautioned that if soil mining were to occur, the resulting efficiency for the CFA group would be substantially less than that for a group of drilled shafts in the same soil conditions. Note that cohesionless soils are particularly sensitive to this effect.
The overlapping zones of influence from individual piles in a group, and the tendency for the pile cap to bear on the underlying soils (if in contact) tend to cause the piles, pile cap system, and the soil surrounding the piles to act as a single unit and exhibit a blocktype failure mode (i.e., bearing failure). The group capacity should be checked to see if a blocktype failure mode controls the group capacity, as will be discussed in the next paragraph.
Block failure mode for pile groups generally will only control the design for pile groups in soft cohesive soils or cohesionless soils underlain by a weak cohesive layer. Note that closer spacing of the piles in the group will also tend to increase the potential of the block failure mode.
Cohesionless Soils
In the absence of sitespecific data to indicate otherwise, it is recommended that the AASHTO provisions (AASHTO, 2002) for group efficiencies for drilled shafts in cohesionless soils (AASHTO 10.8.3.9.3) be followed for conventional CFA piles in the same soils. This provision states that regardless of cap contact with the ground:
η = 0.65 for a centertocenter spacing of 2.5 diameters,
η = 1.0 for a centertocenter spacing of 6.0 diameters or more, and
The value of η must be determined by linear interpolation for intermediate spacing.
There is evidence that the recommended values are most likely conservative for CFA piles in cohesionless soils, in circumstances where the pile cap is in firm contact with the ground and contributes significantly to the bearing capacity, and/or when the cohesionless soil is not loosened by the installation process. Results from smallscale field tests in cohesionless soils from diverse locations around the world suggest that an efficiency of 1.0 or greater may be obtained with pile centertocenter spacing of approximately 3 to 4 diameters, and that 0.67 may be a lower bound for group efficiencies. Note that a typical centertocenter spacing of 3 pile diameters would result in a recommended efficiency of 0.7 using the AASHTO (2002) provisions cited above.
Studies of drilled shaft groups in cohesionless soils include Garg (1979), Liu et al. (1985), and Senna et al. (1993). The shafts in these studies did not exceed the range of 125 to 330 mm (5 to 13 in.) in diameter, and from 8 to 24 times their respective diameter in length. While these piles may be considered modelscale for drilled shafts, their sizes approached that typical of CFA piles. Note that all three of the studies sites were performed in either dry sand or sand with fines above the water table. Efficiencies for groups in clean sands below the water table may be lower than reported in the cited studies due to a greater potential for relaxation of lateral stress.
Garg (1979) conducted compression model tests of underreamed shafts in moist, poorlygraded silty sand with SPTN values ranging from 5 to 15. The efficiency vs. the ratio of spacing to diameter (S/B_{shaft}) for 2 and 4 pile groups, both with and without the cap in contact with the ground, are shown in Figure 5.15. Note that the efficiency of a group with its pile cap in contact with the ground is consistently higher than the efficiency of the group with the cap not in contact with the ground.
Liu et al. (1985) conducted model axial compression tests in moist alluvial silty sand, soil density for sideshear resistance was not reported. The group effects on sideshear and endbearing contributions of a 3 by 3 pile group as a function of the ratio of spacing to diameter (spacing/B) are shown in Figure 5.16. The relationship is shown for the cases of the pile cap in contact or not in contact with the ground. Note that the case of the cap in contact with the ground results in lower efficiencies but higher efficiencies for endbearing than with the cap not in contact with the ground for comparable spacingtodiameter ratios.
Figure 5.15: Efficiency (η) vs. CentertoCenter Spacing (s), Normalized by Shaft Diameter (B_{shaft}), for Underreamed Model Drilled Shafts in Compression in Moist, Silty Sand
Source: O'Neill and Reese (1999) (Modified after Garg, 1979)
Figure 5.16: Relative Unit Side and Base Resistances for Model Single Shaft and Typical Shaft in a NineShaft Group in Moist Alluvial Silty Sand
Source: O'Neill and Reese (1999)
Senna et al. (1993) conducted model axial compression tests in clayey sand with SPTN values ranging from approximately 4 at the surface to as high as 18 at the tip depths (6 m [19.7 ft]). Four different group configurations were tested and compared to a single pile response with the resulting efficiencies as shown in Table 5.3. Note that all groups had centertocenter spacing of 3 diameters, and all caps were in contact with the ground.
Configuration  2 × 1 Pile Bent  3 × 1 Pile Bent  3 Triangular Pile Group  4 Square Pile Group 
Efficiency  η = 1.1  η = 1.1  η = 1.04  η = 1.0 
While these studies have limitations with respect to application to CFA pile design in cohesionless soils, they suggest that there may be circumstances in which the AASHTO (2002) specifications would result in a significantly conservative estimate of group capacity. The group effects of CFA pile installation in cohesionless soil are generally attributed to reductions in lateral stress and/or reductions in soil relative density. For granular soils with considerable fines or light cementation and pile construction that is conducted with care to avoid potential reductions in lateral stress, it may be worthwhile to include an evaluation of group effects into the test pile program. Effects of pile installation on soil density or stress should be reflected in postconstruction insitu tests (SPT or CPT) within the pile group. Likewise, verification tests of an interior pile should provide a representative indication of a typical pile within a group after installation of the entire group. If reliable interpretations from a wellconceived test pile program can demonstrate that negative group effects are less severe than indicated by the AASHTO recommendations for drilled shafts, then an alternate approach may be justified on a projectspecific basis.
Cohesive Soils
It is recommended that the AASHTO (2002) provisions for group efficiencies for drilled shafts in cohesive soils (AASHTO 10.8.3.9.2) be followed for conventional CFA piles in similar soils. This provision states that, regardless of cap contact with the ground, the efficiency should be determined from a block failure mode, and that the efficiency be limited to η = 1.0, or:
(Equation 5.33)η_{g} =  R_{Block}  ≤ 1  
n  
Σ  R_{u,i}  
i = 1 
The resistance of the block failure (R_{Block}) mode can be simply estimated as the sum of the sideshear resistance contribution from the peripheral area of the block, as shown in Figure 5.17, and the endbearing capacity contribution from the block footprint area:
(Equation 5.34)R_{Block} = 2 f_{s} [ D Z + B ] + q_{p} ( Z B )
where: D, Z, and B are the depth, length, and width of the block, respectively, f_{s} is the ultimate unit sideshear resistance of the block, R_{u,i} is the individual pile ultimate resistance and q_{p} is the ultimate unit endbearing capacity for the block, R_{u,i} is estimated as described in Section 5.3 for conventional CFA piles.
Most often, the limiting piletosoil friction angle (δ) is used to conservatively calculate shear resistance for the entire peripheral surface of the block at corresponding depths, rather than a combination of piletosoil (δ) and soiltosoil (φ) friction angles. The ultimate unit endbearing capacity for the block is similar to that determined for a single pile; however, the ultimate unit endbearing capacity of the block must take into account that the influence zone of the block is deeper than that of a single pile. This may be accounted for by assuming a zone of approximately 2 to 3 times Z, and determining q_{p} by the methods presented in Section 5.3 for this deeper zone of influence.
Figure 5.17: Block Type Failure Mode
Source: Hannigan et al. (2006)
Pile in a Strong Layer with a Weak Underlying Layer
If a weak formation is present, the group efficiency should be checked to ascertain whether a group efficiency of less than 1.0 is warranted. The group efficiency may be checked as described in Section 5.5.2.1.2, where the individual pile ultimate resistance (R_{u,i}) is estimated as described in Section 5.3 (for conventional CFA piles) and the block extends to the weak layer. It should be noted that a weak layer below the pile group will, in most cases, present a significant consideration from the standpoint of group settlement as outlined in section 5.5.3.3. Settlement considerations may require that minimum pile penetration be achieved to an elevation below the compressible layer.
The efficiency of DD pile groups are comparable to that of driven displacement pile group. The recommendations included in this section are consistent with recommendations for the design of driven pile groups. In general, even a modest amount of displacement with intermediate DD piles can result in the conditions required to avoid the negative installation effects associated with conventional drilled foundations. For conditions where positive displacement of at least 15% of the pile volume is achieved, the methods in the sections below are recommended.
Cohesionless Soils
It is recommended that the AASHTO provisions for group efficiencies for driven piles in cohesionless soils (see, AASHTO 10.7.3.10.3 in AASHTO, 1996) be followed for DD piles in the same soils. This provision states that η = 1.0 regardless of cap contact with the ground.
Groups of driven displacement piles typically exhibit a group efficiency greater than 1.0 (especially for cohesionless soils). However, a group efficiency of 1.0 is typically used in the interest of a conservative design. Likewise, groups of DD piles have typically exhibited a group efficiency greater than 1.0; however the group efficiency should also be limited to 1.0. Adequate spacing for DD piles may be considered to be approximately 3 pile diameters on centers or more.
For cohesionless soils, the DD pile group efficiency is recommended to be taken as 1.0 if a weak deposit is not encountered in the underlying formation. If a weak formation is present, the group efficiency should be checked to ascertain whether a group efficiency of less than 1.0 is warranted. The group efficiency may be checked with the equation in Section 5.5.2.1 where the ultimate resistance of the block (R_{Block}) is estimated as described in Section 5.5.3, while the individual pile ultimate resistance (R_{u,i}) is estimated as described in Section 5.4 (for auger displacement piles).
Cohesive Soils
A study by Brown and Drew (2000) of fullscale DD piles in the Piedmont geologic setting of the National Geotechnical Experimentation Site (NGES) (clayey silts to silty clays), suggested that DD piles behave like neither driven displacement piles nor conventional CFA piles, but inbetween these extremes. Although not tested as a group, comparisons showed an increase in unit sideshear resistance of approximately 100% of the single interior pile within a 5pile group (spaced at 3 pile diameters centertocenter) over an isolated pile. Also tested and compared was an isolated pile and a 5pile group (spaced at 3 pile diameters centertocenter), all of which were constructed using an amelioration technique with coarse sand. The same comparison yielded an increase in unit sideshear resistance of 90% for the single interior central pile of the fivepile group over the isolated pile.
For cohesive soils with undrained shear strengths greater than 100 kPa (1 tsf) or for groups with the pile cap in firm contact with the ground, the DD pile group efficiency may be taken as 1.0. For the condition of cohesive soils with undrained shear strengths less than 100 kPa (1 tsf) and the pile cap not in firm contact with the ground, a group efficiency should be linearly interpolated in accordance with the pile spacing as follows: adopt an efficiency of 0.7 for a pile spacing of 3 diameters oncenters and increase to an efficiency of 1.0 for a pile spacing of 6 diameters or greater oncenters.
In all cases, a block failure mode should be checked to see if it governs the efficiency. The group efficiency for this mode should be checked with the equation shown in the previous section, where again, the ultimate resistance of the block (R_{Block}) is estimated as described in Section 5.5.3, while the individual pile ultimate resistance (R_{u,i}) is estimated as described in Section 5.4 (for auger displacement piles).
Piles in a Strong Layer with a Weak Underlying Layer
If a weak formation is present the group efficiency should be checked to ascertain whether a group efficiency of less than 1.0 is warranted. The group efficiency may be checked as described in Section 5.5.2.1, where the individual pile ultimate resistance (R_{u,i}) is estimated as described in Section 5.4 (for auger displacement piles). Note that a potentially problematic condition may exist if the overlying strong layer is capable of stopping the penetration of DD piles. If the piles are terminated at this shallow "refusal" depth, the group effect must be checked for punching shear through into the underlying weak layer using the block failure concept described in the previous section. However, it is likely that settlement concerns could be significant, and these issues must be addressed as outlined in the following sections.
The development of resistances with pile displacements of individual piles was discussed in Chapter 5.2. Displacements of individual piles at ultimate resistances (or in limited cases the load development with pile displacement) derived from many studies and prediction methods were presented in Section 5.3 and Appendix A. However, the settlement of a pile group is likely to be many times greater than the settlements predicted with the assumption that the piles act individually, especially for cases where the soils near the pile tips are more compressible.
The greater settlement of the pile group is attributed to a deeper zone of influence for the pile group than that for a single pile. The group effect of the piles mobilize a much deeper zone than that of a single pile, as illustrated in Figure 5.18.
Settlement of pile groups can be attributed to a combination of elastic compression of the piles and settlement of the surrounding soils. Settlement of the surrounding soils primarily consists of nearly instantaneous compression for purely cohesionless soils, and primarily timedependant consolidation for purely cohesive soils. Note that layered systems of soils may contain appreciable amounts of both compression and consolidation settlements.
Figure 5.18: Deeper Zone of Influence for EndBearing Pile Group than for a Single Pile
Source: Hannigan et al. (2006), after Tomlinson (1994)
Design engineers, who must consider pile foundation settlements, should carefully consider the magnitude and timing of the application of loads and their effect on the structure. For instance, the dead load of the column, pier cap, and perhaps other portions of the bridge structure may be in place, therefore, settlement due to these loads may be complete before the final connections of any settlementsensitive portions of the structure are made. It may be possible that only settlements resulting from loads are imposed after the girder bearing plates are set are of significance to the structure.
Simplified methods for estimating pile group settlement are presented in the following sections. The methods presented were formulated for driven pile groups and are considered to be generally representative of CFA and DD pile group settlements. The deeper zone of influence for a pile group is unlikely to be significantly affected by differences in installation between piles of different types, although differences in individual pile stiffness and mobilization of capacity can affect settlements to some degree.
The elastic compression of the pile is a function of the imposed load, pile stiffness, and the load transfer characteristics from the pile to the surrounding soil.
Defining the stiffness ratio as:
(Equation 5.35)S_{R} =  L  ×  E_{soil}  
B  E_{pile} 
where: L = pile embedment depth, B = pile diameter, E_{soil} = average Young's modulus of the soil, and E_{pile} = Young's modulus of the pile.
For many practical problems, a pile may be considered "rigid" if its stiffness ratio (S_{R}) is approximately S_{R} ≤ 0.010. In these cases, the elastic shortening of the pile is likely to be very small compared to the settlements of the soil in which the pile is embedded. Otherwise, elastic compression (Δ) should be estimated and included in settlement calculations. This compression should be subtracted from the pile total displacement when determining the development of sideshear or endbearing developed stresses at values less than ultimate.
The elastic compression of a pile (Δ) may be calculated as the sum of elastic compression of "n" pile segments as follows:
(Equation 5.36)Δ = 
 Q_{i}  L_{i}  
A_{i}  E_{i} 
Where: L_{i}, A_{i}, and E_{i} are the length, average crosssectional area, and average composite modulus, respectively, for each of the pile segments. Q_{i} is the average axial load at the pile segment. The load at the top pile segment would be the total imposed load to that individual pile, and would reduce in magnitude down to the mobilized endbearing load at the pile tip in accordance with the load transfer response of the pile to soil system. If downdrag or uplift were to occur, the load distribution would be as described in Section 5.7.
The load imposed to an individual pile could become a complex solution if the pile cap were to provide a contribution to the total capacity of the pile group system (i.e., a pile raft as described in Section 5.5.4), and the group was subject to eccentric effects. However, to estimate the load imposed to the individual pile for purposes of elastic compression calculations, it may be sufficient to simply divide the total load of the pile group by the number of piles.
For many practical problems, an estimate of elastic shortening may be made using simplified assumptions regarding the load distribution in the pile. For example, a constant load transfer rate (i.e., a uniform unit sideshear stress along the entire length of the pile) and axial load supported entirely in side friction would result in a triangular distribution of load in the pile vs. depth ranging from the maximum load at the pile top to 0 load at the pile toe. For this condition, the elastic compression may be computed as:
(Equation 5.37)Δ =  1  ×  Q_{max} × L_{pile}  
2  A_{pile} × E_{pile} 
Where: Q_{max} is the total maximum imposed load and L_{pile} and A_{pile} are the pile total length and crosssectional area, respectively.
An upper bound (other than the possibility of downdrag) is represented by a pile acting as a freestanding column with no load transfer along the entire length of the pile and the total maximum imposed load to the pilesupported in endbearing. For this condition, Equation 5.38 provides an upper bound estimate of elastic shortening in the pile.
(Equation 5.38)Δ_{max} =  Q_{max} × L_{pile} 
A_{pile} × E_{pile} 
Note that downdrag or soil swell conditions could present a more significant pile load, and for such a case Q_{max} would be determined as described in Section 5.7.
Equations 5.37 and 5.38 can be used to quickly estimate the potential magnitude of elastic shortening and determine if a more complete evaluation of load distribution is justified for the purpose of computing settlement.
Meyerhof (1976) recommended that the compression settlement of a pile group (S_{group}) in a homogeneous sand deposit (not underlain by a more compressible soil at greater depth) be conservatively estimated by the correlations to either SPTN values or to CPTq_{c} values. If the group was underlain by cohesive deposits, timedependant consolidation settlements would be needed, as described in the following section. The method proposed by Meyerhof (1976) does not distinguish 60% hammer efficiency for Nvalues. However, the 60% correction is recommended.
For SPTN values in cohesionless soils:
(Equation 5.39)S_{group} =  0.96 p_{f} I_{f} B  for sands 
N_{60}′ 
S_{group} =  1.92 p_{f} I_{f} B  for silty sands 
N_{60}′ 
For CPT q_{c} values in cohesionless saturated soils:
(Equation 5.41)S_{group} =  42 p_{f} I_{f} B 
q_{c} 
where:
S_{group}  =  estimated total settlement (in.); 
p_{f}  =  foundation pressure (tsf), which is obtained as the group load divided by group area on plan view; 
B  =  width of pile group (ft); 
D  =  pile embedment depth below grade (ft) 
I_{f}  =  influence factor for group embedment = 1  D/(8B) ≥ 0.5; 
N_{60}′  =  average corrected SPTN value (bpf per 0.3 m) within a depth B below the pile tip level; and 
q_{c}  =  average static cone tip resistance (tsf) within a depth B below the pile tip. 
Consolidation settlement of cohesive soils is generally associated with sustained loads and occurs as excess pore pressure dissipates (primary consolidation). For purpose of discussion in this section, the time rate of settlement will not be addressed directly. Design for a total magnitude of settlement for the full sustained dead load on the structure would represent a conservative approach to settlement in cohesive soils. For most structures, a portion of the dead load will be in place (pile cap, column, pier cap, etc.), and consolidation for that portion of the load may be nearly complete, before settlementsensitive portions of the structure (above the girder bearing plates) are in place. Should computed settlements for total sustained dead load be found to significantly affect the design, it may be prudent to evaluate the time rate of the settlement for construction loads to more accurately assess the postconstruction settlements. Time rate of primary consolidation is a topic covered in most geotechnical texts and in the FHWA Soils and Foundations Workshop Manual (FHWA NH106088).
The consolidation settlement is driven by the load exerted on the pile group and resulting stress distribution into the soil below and around the pile group. The actual stress distribution in the subsurface can be affected by many factors including the soil stratigraphy, relative pile/soil stiffness, pile to soil load transfer distribution, pile cap rigidity, and the amount of load sharing between the cap and the piles. For most practical problems, a simplified model of stress distribution is sufficient to estimate pile group settlements. The equivalent footing method is presented below as a simplified method to estimate vertical stress with depth in the soil below the pile group.
Terzaghi and Peck (1967) proposed that pile group settlements could be evaluated using an equivalent footing situated 1/3 of the pile embedment depth (D) above the pile toe elevation, and this equivalent footing would have a plan area of the pile group equal to the width (B) times the pile group length (Z). The pile group load over this plan area is then the bearing pressure transferred to the soil through the equivalent footing. The same load is then assumed to spread within the frustum of the pyramid of side slopes of 1 (horizontal): 2 (vertical), thus reducing the bearing pressure (p_{d} with depth) with depth as the area increases. This concept is illustrated in Figure 5.19.
In some cases, the depth of the equivalent footing should be adjusted based on soil stratigraphy and load transfer mechanism to the soil, rather than fixing the equivalent footing at a depth of 1/3 D above the pile toe for all soil conditions. Figure 5.20 presents the recommended location of the equivalent footing for a variety of load transfer and soil resistance conditions.
The cohesive soils below the equivalent footing elevation are broken into layers, and the total consolidation settlement is the sum of the settlements of each layer. A plot of the relationship between void ratio (e) and logarithm of the vertical effective consolidation stress (p) determined in the laboratory is used to estimate the consolidation settlement. Multiple laboratory curves may need to be generated to accommodate the different layers depending on the soil consistency and maximum past pressures. The settlement of each layer may be calculated as presented in the three following equations. A generic example of this consolidation curve is shown in Figure 5.21 to illustrate the terms in these equations.
Figure 5.19: Equivalent Footing Concept for Pile Groups
Source: Hannigan et al. (2006)
The settlement (S_{i}) for an overconsolidated cohesive soil layer, where the pressure after the foundation pressure increase is greater than the soil preconsolidation pressure (p_{o} + Δ_{p} > p_{c}), is obtained as:
(Equation 5.42)S_{i} = H  C_{r}  log  p_{c}  + H  C_{c}  log  p_{σ} + Δp  
1 + e_{0}  p_{0}  1 + e_{0}  p_{c} 
The settlement (S_{i}) for an overconsolidated cohesive soil layer, where the pressure after the foundation pressure increase is less than the soil preconsolidation pressure (p_{o} + Δ_{p} < p_{c}), is obtained as:
(Equation 5.43)S_{i} = H  C_{r}  log  p_{0} + Δp  
1 + e_{σ}  p_{σ} 
Figure 5.20: Pressure Distribution Below Equivalent Footing for Pile Group
a) Toe Bearing Piles in Hard Clay or in Sand Underlain by Soft Clay
b) Piles Supported by Shaft Resistance in Clay
c) Piles Supported by Shaft Resistance in Sand Underlain by Clay
d) Piles Supported by Shaft and Toe Resistance in Layered Soil Profile
Notes:
Source: Cheney and Chassie (1993) and Hannigan et al. (2006)
Figure 5.21: Typical e vs. Log p Curve from Laboratory Consolidation Testing
Source: Hannigan et al. (2006)
The settlement for a normally consolidated cohesive soil layer (p_{o} = p_{c}) is:
(Equation 5.44)S_{i} = H  C_{c}  log  p_{o} + Δp  
1 + e_{o}  p_{o} 
where:
S_{i}  =  total settlement; 
H  =  original thickness of layer; 
C_{c}  =  compression index; 
C_{r}  =  recompression index; 
e_{o}  =  initial void ratio; 
p_{o}  =  effective overburden pressure at midpoint of stratum, prior to pressure increase; 
p_{c}  =  estimated preconsolidation pressure; and 
Δ  =  average change in pressure. 
If the soil were underconsolidated (i.e., p_{o} > p_{c}), the consolidation process due to loads imposed prior to placement of the foundation would continue, and this would result in an additional downdrag load to the pile group, as discussed in Section 5.7.
CFA piles behave essentially as drilled shafts in response to uplift. CFA piles can be particularly efficient in uplift because their long, slender shape maximizes sideshear for a given volume of grout or concrete. A limiting factor for uplift may be the ability to place sufficient reinforcing steel; however, a single highstrength bar can be placed full length in most circumstances.
Uplift forces may be exerted on CFA piles by either an applied external uplift force or due to swelling of surrounding soils. Note that an uplift resistance is provided in response to the case of externally applied loads, while an uplift load is applied to the pile in the case of swelling soils.
The ultimate upward sideshear resistance may be determined as a portion of the ultimate downward sideshear resistance using the methods for axial compression loading on CFA piles recommended in this chapter, but with opposite sign (direction). For piles in cohesive soils subjected to uplift, the upward resistance may be estimated as the same magnitude as the downward resistance. For piles in cohesionless soils subjected to uplift, the upward directed sideshear from the pile can produce a potential reduction in effective stress in the vicinity of the pile. The ultimate uplift sideshear resistance in cohesionless soils can be maintained up to 100%. However, it has been determined in numerous studies that the remaining sideshear resistance range from about 70 to 100% of the downward ultimate resistance. It is recommended that to obtain the ultimate sideshear resistance in cohesionless soils for uplift the sideshear resistance used for compressive loading be multiplied by a factor of 0.8. Note that appropriate safety factors still need to be applied to obtain the allowable uplift resistance.
The uplift resistance of a pile group should be determined in accordance with AASHTO (1996) for service load design that states that the group uplift should be determined as the lesser of:
Soil uplift on a pile is most often caused by the swelling of expansive soils, or may also occur through ice jacking (frost heave, or upward load imposed from an ice sheet frozen to the pile or column/pier). When the uplift force is caused by the swelling of surrounding soils, it should be considered as a load to the pile and may be determined equal to the ultimate downward sideshear values on the CFA piles, using the methods recommended herein [but opposite sign (direction)]. Note that a reduction factor should not be applied to cohesionless soils when the uplift is a soil load because the reduction in effective stress around the pile would not be anticipated in such a condition.
Although published results are limited, lateral loadtests have shown that CFA piles behave essentially like drilled shafts when the differences between the pile material properties are accounted for (i.e., differences in grout or concrete used for CFA piles and amount of reinforcing steel). References for lateral loadtests on CFA piles include O'Neill et al. (2000) in overconsolidated clays in Coastal Texas, and Frizzi and Meyer (2000) in the dense Pamlico sand and Miami limestone (vuggy) formations are typical of South Florida.
Because of structural capacity limitations related to reinforcement, CFA piles generally do not provide large resistances to lateral loading compared to that which can typically be developed with drilled shafts and driven pile groups. Typically, a reinforcing cage is set to only a sufficient depth to accommodate the section of pile where the bending stresses are at or near the maximum, with a single bar often set through the centerline of the pile to the full pile depth. For applications requiring greater reinforcement than is practical from reinforcing cages, it is possible to reinforce CFA piles with structural steel sections such as H or pipe, similar to micropile construction techniques.
In the construction of CFA piles, the reinforcing cages are typically set into the freshly placed grout or concrete except for the special case of some types of screw piles where the cage is placed through the hollow auger. Placing the reinforcing cages in freshly placed grout can limit the amount of steel that can be penetrated into the grout to the pile full depth. This limitation is affected by soil conditions and the concrete or grout mix properties.
CFA piles constructed in cohesive soils generally provide for greater penetration ability for a full reinforcing steel cage (often to 45 m [150 ft] or more), as the water in the concrete or grout mix is better retained and thus workability is better maintained. Conversely, freedraining cohesionless soil will allow bleed water from the concrete or grout mix to escape into the surrounding soil; this rapid fluid loss limits the insitu workability of the remaining grout. Penetration ability for a full reinforcing steel cage in freedraining soils (e.g., sand) may thus be limited, especially if the sand is dry.
CFA piles typically have a diameter in the range of 0.35 to 0.60 m (14 to 24 in.) and are rarely constructed in excess of 0.9 m (36 in.) in diameter. When accounting for concrete cover of the reinforcing steel (particularly in aggressive environments), this leaves little room for a rebar cage diameter to provide a crosssectional moment to resist the bending stresses.
It is possible to design groups of CFA piles to include batter piles to enhance lateral stiffness and capacity of the group, as may be done with driven piles. Analyses of a CFA pile group may be performed in a similar manner to other deep foundation types, using computer codes such as GROUP (Ensoft, 2006) or FBPier (BSI, 2003). However, the use of batter piles can be limited by concerns relating to ground movement from settlement and by the increased construction difficulty associated with placing a rebar cage within a batter CFA pile. The use of batter piles over water is not a typical CFA pile application.
In the special case of a secant or tangent pile wall constructed using CFA piles, the procedures for analysis are similar to other types of deep foundation elements. The differences for CFA piles are in the sizes and depth limitations, along with the need to install reinforcement after the grout or concrete is in place.
The py method is recommended for lateral load analyses of vertical CFA piles and pile groups. The py method is a general method for analyzing laterally loaded piles with combined axial and lateral loads, including distributed loads along the pile, nonlinear bending characteristics (including cracked sections), layered soils and/or rock, and nonlinear soil response. The method utilizes a numerical solution to the governing equations, and a variety of software is available to perform the analyses.
A physical model for a vertical laterally loaded pile is shown in Figure 5.22. The pile is modeled as a simple beam with boundary condition specified as pile head loads, as shown. The soil has been idealized by a series of nonlinear springs with depth that provide reaction to the external loading imposed at the head. At each pile depth (x) the soil reaction (p) resisting force per unit length along the pile) is a nonlinear function of (y) lateral deflection, which is dependent on the soil shear strength and stiffness, piezometric surface, pile diameter, depth, and whether the loading is static (monotonic) or cyclic.
Although the curves have been shown as bilinear in the preceding figure, actual py curves used for design are usually more complexcurvilinear functions. The nonlinear soil resistance (p) as a function of displacement (y) has been derived from instrumented fullscale loadtests in a variety of soils. From these instrumented tests and simple theory of passive earth pressure response around a pile, empirical correlations of py response with soil properties have been developed for different soil types. Computer programs for lateral load analyses of piles contain many of these models, and allow the user to input a userdeveloped curve of any shape (presumably based on local experience, correlations with insitu tests, latest research in a specific geology, etc.).
Lateral models for soils are correlated with basic strength and stiffness information obtained during the geotechnical investigation. For example, cohesive soils will require input profiles to the depth along the pile of shear strength (S_{u}), a stiffness parameter associated with strain at a compressive stress equal to 50% of the compressive strength from uniaxial strength testing (ε_{50}), and unit weight (γ). Cohesionless soils will require input profiles of soil friction angle (φ), subgrade modulus (k), and unit weight (γ). Ground water elevation must also be defined.
Figure 5.22: py Soil Response of Laterally Loaded Pile Model
Source: O'Neill and Reese (1999)
A more detailed description of many lateral soil models may be found in Reese (1986) and O'Neill and Reese (1999).
Note that loss of soil resistance due to scour or liquefaction must be considered as a part of the lateral load analysis. In some cases, it may be necessary to consider the loss of soil resistance when calculating the axial capacity of piles. Conditions in which liquefaction results in loss of soil resistance along a significant portion of the pile length could be problematic for CFA piles of small diameter due to the inherent limitations of bending capacity and reinforcement in small diameter piles.
For these analyses, the pile is modeled as a beamcolumn with a distributed load along the length of the beam produced by the elastic (spring) foundation. The governing differential equations for the solution of a beam on an elastic foundation were derived by Hetenyi (1946). For the general case of combined lateral and axial loading, the following governing differential equation applies:
(Equation 5.45)EI  d^{4}y  + P_{x}  d^{2}y   p  w = 0 
dx^{4}  dx^{2} 
where:
x  =  distance along pile length; 
P_{x}  =  axial load; 
y  =  lateral deflection at a point with coordinate x; 
p  =  lateral soil reaction, (measured as a force per unit length of pile); 
EI  =  flexural rigidity of pile; 
E  =  pile elastic modulus; 
I  =  movement of inertia of pile crosssection; and 
w  =  distributed load along the length of the pile (due to either soil or water, if any). 
Available computer codes typically discretize the pile and soil into a number of segments and nodes (i.e., finite difference, finite elements) via numerical methods to obtain solutions to complex problems. The numerical methods can handle great complexity and offer the advantage of their relative simplicity to the user. In these models, the solution produces computed soil resistance (p), shear (V), moment (M), pile slope (S), and pile deflection (y) at each node along the pile. The beam equations for shear, moment, and slope are derived as follows (FHWARD85106):
(Equation 5.46)V = EI  d^{3}y 
dx^{3} 
M = EI  d^{2}y 
dx^{2} 
S =  dy 
dx 
In addition to the axial load, the boundary conditions at the pile head must be specified by a lateral force (P_{t}) and a moment (M_{t}), as shown in Figure 5.22. Alternatively, these conditions may be specified in terms of lateral displacement, slope, or a rotational restraint, relating the slope at the top of the pile to the pile head moment. A freehead condition is represented by a specified lateral force and moment, as shown in Figure 5.22. This condition might be representative of a CFA pile used to support a soundwall, sign, light pole, or any similar freestanding structure that is cantilevered above a single CFA pile. For groups of CFA piles incorporated into a rigid cap, the rotational stiffness of the group and a full moment connection into the cap would result in a pile top condition approaching that of a fixed head pile (i.e., pile head is completely restrained). A fixedhead condition might be specified by using a lateral force and a slope at the pile head of zero. Computer software for modeling pile groups can be used to specify the group loads and incorporate the appropriate boundary condition for each pile into the group solution.
Figure 5.23 illustrates a computed solution for a pile that is restrained against rotation at the pile head and is subjected to a lateral shear force. The moment is observed to be a maximum at the pile head due to the rotational restraint; the pile slope approaches zero at the pile head.
Figure 5.23: Example Deflection and Moment Response of Laterally Loaded Pile Model
The nonlinear py relationship described earlier is implemented at each node by using a secant modulus (E_{s}), as indicated below:
(Equation 5.49)E_{s} =  p 
y 
Therefore, at each node (i) along the length of the pile, the value of soil reaction (p_{i}) is expressed as the secant modulus multiplied by the deflection (or E_{si} y_{i}). Because the py response is nonlinear, an iterative solution is used to repetitively update the secant modulus so as to track the nonlinear relation of p at a range of differing values of y. This method of successive approximation using a secant modulus is computationally intense but very stable, and allows py curves to incorporate features such as strainsoftening, loss of resistance due to cyclic loading, and other deflectiondependent effects on soil resistance that may be observed in experiments.
Nonlinear stressstrain relationships are also available for both the steel and the concrete materials in a computer solution. The assumed stress strain relationship built into most programs for the steel is shown in Figure 5.24, while that for concrete is shown in Figure 5.25.
Figure 5.24: Typical StressStrain Relationship Used for Steel Reinforcement
Source: O'Neill and Reese (1999)
For steel, the value of yield stress (f_{y}) is the same in compression (positive or +, in the sign convention adopted herein) and in tension. Reinforcing steel used is usually Grade 60 with a yield stress of 413 MPa (60 ksi) and a modulus (E) of 200,000 MPa (2,900 ksi). By definition, the yield strain is the yield stress divided by the modulus (ε_{y} = f_{y} /E).
Figure 5.25: Typical StressStrain Relationship Used for Concrete
Source: O'Neill and Reese (1999)
For concrete, the compressive strength depends on the mobilized compressive strain. First, the compressive strength increases up to the reduced ultimate compressive strength (f″_{c}), which is taken as a percentage of the 28day cylinder compressive strength. The strength is expressed as
(Equation 5.50a)f_{c} = f″_{c}  2  ε    ε  2  for: ε < ε_{o}  
ε_{o}  ε_{o} 
f_{c} = 0.85 f″_{c} for: ε < 0.038
f_{c} = linearly interpolated for ε_{o} ≤ ε ≤ 0.038
With:
(Equation 5.51)f″_{c} = 0.85 f′_{c}
(Equation 5.52)ε_{o} =  1.7 f′_{c} 
E_{c} 
Where f′_{c} is the concrete compressive strength at 28 days, and E_{c} is the initial tangent slope of the stressstrain area. The value E_{c} can be estimated as:
(Equation 5.53a)E_{c} = 57,000 f′_{c} (psi)
or
(Equation 5.53b)E_{c} = 151,000 f′_{c} (kPa)
The ultimate tensile strength of concrete (f_{r}) is estimated as
(Equation 5.54a)f_{r} = 7.5 f′_{c} (psi)
or
(Equation 5.54b)f_{r} = 19.7 f′_{c} (kPa)
The authors' experience from observed behavior of instrumented loadtests on drilled shafts suggests that the computed modulus using the equations above tends to be somewhat conservative for concrete. Sand cement grout without coarse aggregate may have a slightly lower modulus than that of concrete of similar strength.
The bending stiffness (EI) of the beam column system is not actually constant once cracking occurs in the concrete or grout. As the bending moment at any of the steel reinforced sections increases to the point at which tensile stresses at one side of the pile exceeds the tensile strength of the concrete or grout, the section cracks, and the value of EI is reduced significantly at that cracked section. Note that a uniform, concentric axial compressive load (P_{x}) will produce a uniform compressive stress (P_{x} × Area). The superposition of this uniform compressive stress to the stress distribution produced by the bending moment on the uncracked section will allow for a larger bending moment at the point of crack initiation and beyond. Computer programs for lateral load analyses can include the reduction in stiffness. Figure 5.26 illustrates an example of computed EI as a function of moment for the case of an axial load of varying magnitude.
Figure 5.26: Variation of Pile Stiffness (EI) with Bending Moment and Axial Load
The pmultiplier (P_{m}) method is recommended to account for group effects on lateral load response. For closely spaced piles in a group, values of soil resistance for a given py relationship are multiplied by a pmultiplier less than 1 (i.e., P_{m}<1), as shown in Figure 5.27. Therefore, the lateral capacity of the pile group at a given deflection level is less than the sum of the individual pile lateral capacities at that deflection. Also, the lateral deflection at a given load is greater than the deflection of an individual pile at the same load per pile. The value of this multiplier is dependent on the location of the pile within the group and the spacing of the pile group. "Front Row" piles are those that push into the soil without any piles ahead of them, and thus are the least affected by the presence of the other piles. "Second Row" piles are affected to a greater extent than the front row piles; "Third and Subsequent Rows" piles are the most affected by the group interaction. The group interaction may be described as the piles in the back pushing the soil forward into the area that is being vacated by the piles in front of them (often referred to as a "shadowing" effect).
Values of pmultipliers (P_{m}) are provided in Table 5.4 for cyclic loading and static loading.
Figure 5.27: The pmultiplier (P_{m})
Source: Hannigan et al. (2006)
Soil Type^{(1)}  Test Type  Pile Spacing (Cent.Cent.)  P_{m} for Rows: 1 2 3+  Reported Lateral Group Efficiencies  Deflection (mm)  Reference 

Stiff Clay  Field Study  3B  .70 .50 .40  N/A  51  Brown et al. (1987) 
Stiff Clay  Field Study  3B  .70 .60 .50  N/A  30  Brown et al. (1987) 
Medium Clay  Scale Model (Cyclic Load)  3B  .60 .45 .40  N/A  600 (at 50 cycles)  Moss (1997) 
Clayey Silt  Field Study  3B  .60 .40 .40  N/A  2560  Rollins et al. (1998) 
V. Dense Sand  Field Study  3B  .80 .40 .30  75%  25  Brown et al. (1998) 
M. Dense Sand  Centrifuge Model  3B  .80 .40 .30  74%  76  McVay et al. (1995) 
M. Dense Sand  Centrifuge Model  5B  1.0 .85 .70  95%  76  McVay et al. (1995) 
Loose M. Sand  Centrifuge Model  3B  .65 .45 .35  73%  76  McVay et al. (1995) 
Loose M. Sand  Centrifuge Model  5B  1.0 .85 .70  92%  76  McVay et al. (1995) 
Loose F. Sand  Field Study  3B  .80 .70 .30  80%  2575  Ruesta and Townsend (1997) 
Note: (1) V = very, M = medium, F = fine
Computer programs such as GROUP (Ensoft, 2006) or FBPier (BSI, 2003) may be used to analyze the entire group of piles for a given axial, lateral, and moment loading applied to the pile cap. These codes compute the group pmultipliers by multiplying individual pmultipliers (P_{m}) and py curves for individual piles. Recent studies (Brown and O'Neill 2003) suggest that a simplified approach to the use of pmultipliers is suitable for design, particularly when considering that the direction of loading may not be known. A single pmultiplier equal to the average value of all the pile row pmultipliers in the group provides a reasonably accurate indication of the overall group deflection and stiffness. The shear and maximum moment distribution in individual piles within the group was found to deviate from the computed average response using the simplified method by no more than 20% in typical cases. The simplified analysis also allows the analysis of a single pile to be used to anticipate the lateral response of a typical pile within the group, with a 20% increase in computed maximum bending moment recommended for design in order to account for variations within the pile group.
Analyses of an individual pile within the group can be performed using a computer code such as LPILE (Ensoft, 2006), but with pmultipliers applied to the individual py curves to account for group action. Within a group of piles connected to a common cap, a full moment connection to the cap would provide rotational restraint to the top of the pile so that the horizontal translation of the cap is modeled as a lateral shear or displacement at the pile head combined with a slope of zero. The lateral load resistance of the pile group is then equal to the sum of the lateral load resistance of the individual piles.
The structural capacity of CFA piles should be checked in the same manner, and to the same requirements as drilled shafts. While both types of foundations are reinforced, castinplace structural elements, some differences exist. Drilled shafts often have larger diameters and consist of nonredundant single shafts designed to support individual columns. On the other hand, CFA piles are typically used in groups with relatively small lateral and bending stresses on a perpile basis. However, CFA piles can also be used as individual foundations for soundwalls, signs, or light pole structures where the design is dominated by flexure. The structural integrity should be checked for axial loading (including potential uplift loads), as well as bending and shear induced by lateral loading.
The following sections describe the necessary steps for structural analysis and design of CFA piles based on the axial load requirements and bending stresses computed as a result of the lateral analyses using the py method. Note that the geotechnical design of CFA piles is outlined in accordance with allowable stress design (ASD). However, most states use the load and resistance factor design AASHTO specifications (AASHTO, 2006) for the structural design of reinforced concrete members. Structural design of CFA piles is outlined in accordance with LRFD as is typical of structural design of other reinforced concrete members in AASHTO (2006). To compute bending moments in the pile for structural design, the lateral load analyses must include factored load cases.
Reinforcing steel for CFA piles typically consists of two different sections: 1) a top section that consists of a full cage configuration of multiple longitudinal bars and transverse spirals or ties; and 2) a bottom section that consists of a single longitudinal bar along the centerline of the pile that extends the full length of the pile.
An adequate section of steel reinforcement of CFA piles for the purpose of axial uplift loading is often accomplished by the insertion of a single bar down the center of the freshly placed grout or concrete column. Virtually any size bar needed to satisfy the structural requirements can typically be inserted to full depth. Highstrength, threaded rods can be used in CFA piles similarly to the use with micropiles.
The top section of reinforcement must extend to a depth that is below the area where large bending moments take place. It is recommended that the depth of full cage reinforcement be set to the inflexion point in the displacement profile (i.e., second point of zero displacement with depth), obtained from lateral load analysis. For instance, the pile shown in Figure 5.23 would require a reinforcing cage extending to approximately 7.5 m (25 ft) below the top of the pile. If this were a pile that extended to a depth of 15 or 18 m (50 or 60 ft) below grade, it would be unnecessary to install a full length cage. When relatively short piles are used and the computed deflection profile does not cross the zero axis at a second point, a full length reinforcing cage should be used.
For ease of cage installation with both a top section cage and central bar only, the transverse reinforcement is often not included in approximately the bottom 1.2 m (4 ft) of the cage, and the longitudinal bars are bent inward toward the single bar at the center of the shaft to form a "tapered section" in the cage. In such case, the tapered section should not be counted as part of the cage length to the required minimum depth.
Within the zone where the full cage is installed, the minimum longitudinal reinforcement area should be not less than 1% of the gross concrete area (A_{g}) of the pile. However, in the event that the pile size is larger than necessary to support the computed loads from a structural (not geotechnical) standpoint, then a reduced effective area (A_{g}′) may be used to determine the minimum longitudinal reinforcement and design strength as outlined in the O'Neill and Reese (1999) recommendations for drilled shafts and per section 10.8.4 of the ACI code (ACI, 2004). The reduced effective area (A_{g}′) is the area of concrete sufficient to provide the required axial strength and, in all cases, must be limited to not less than one half of the gross concrete area (A_{g}).
If the reinforcement includes a central bar, this bar must extend throughout the top section cage. If a central bar is used, the area of the central bar may be included in the analysis of structural capacity and minimum requirements of the top cage section.
The design of reinforced concrete piles for bending and axial forces follows procedures used for analysis and design of short columns. Figure 5.28a schematically illustrates the section of a reinforced concrete column loaded parallel to its axis by a compressive force P and moment M. The distribution of strains across the cross section at the instant the ultimate load is reached are shown in Figure 5.28b. The internal forces within the pile, shown in Figure 5.28c, must be in equilibrium with the nominal strength, represented by the combined P and M. The internal forces are related to the strains by the modulus. For any of the bars with strains in excess of the yield strain (i.e., equal to the yield strength divided by the elastic modulus), the stress at failure is taken as the yield stress of the bar.
Figure 5.28: Circular Column (Pile) with Compression Plus Bending
The analysis of the combinations of P and M to produce failure is called a strain compatibility analysis; the plot of these load combinations at failure is an interaction diagram. Details and examples of the calculations involved in the analysis described above is covered in most textbooks on reinforced concrete design.
Satisfactory pile designs are those where all combinations of axial loads and bending moments are contained within the factored ultimate resistance interaction diagram for all critical pile sections, and where the transverse shear requirements are met. The interaction diagram is a plot of all combinations of axial and bending forces on a column that would result in structural yield of the column. The factored interaction diagram would lie inside the interaction diagram of ultimate resistance and are obtained by multiplying the "ultimate" interaction diagram by resistance factors for axial and bending.
To calculate the required amount of longitudinal reinforcement, the interaction diagram must be determined. The maximum bending moment and axial load calculated from the lateral analysis of the pile foundation are compared against the factored interaction diagram. Figure 5.29 shows a typical interaction diagram, both with the nominal and the factored ultimate resistances.
The nominal ultimate resistance interaction diagram, shown as the solid line in Figure 5.29, should be obtained for all critical pile sections. Computer programs for lateral analyses typically include options for generating this interaction diagram at specified pile sections.
Figure 5.29: Example Interaction Diagram for Combined Axial Load and Flexure
Source: O'Neill and Reese (1999)
The factored axial resistance (i.e., the intersection of the solid line with the P_{x}axis for axial compressive load only) is obtained as follows:
(Equation 5.55)P_{n} = β P_{S} = β [ 0.85 f′_{c} ( A_{g}  A_{s} ) + f_{y}A_{S} ]
where:
P_{n}  =  nominal ultimate axial resistance; 
f′_{c}  =  compressive concrete strength at 28days; 
f_{y}  =  yield strength of the longitudinal reinforcing steel; 
A_{g}  =  gross crosssectional area of concrete; 
A_{s}  =  crosssectional area of the reinforcing steel; and 
β  =  reduction factor to account for the possibility of small axial load eccentricities. β = 0.85 for spiral transverse reinforcement, and β = 0.80 for tied transverse reinforcement. 
Because resistance factors are different for pure axial and bending, the interaction diagram used for design involves transitional factors for cases with combined axial and bending. A transition point is defined by the axial load P′ in Figure 5.29, which is defined as:
(Equation 5.56)P′ = 0.133 f′_{c} A_{g}
The factored resistance interaction diagram (shown as the dashed line in Figure 5.29) is obtained above the P′ line by simultaneously multiplying the nominal ultimate axial resistance (P_{x}) and the nominal ultimate flexural resistance (M_{x}) by a resistance factor (φ),
(Equation 5.57)P_{r} = φ P_{x} and M_{r} = φ M_{x}
where φ = 0.75 for either spiral or tied transverse reinforcement (AASHTO, 2006)
The factored flexural resistance for pure flexure (i.e., P_{x} = 0) is determined as 0.9 of the nominal ultimate flexural resistance, or 0.9 M. For locations between P_{x} = 0 and P_{x} = P′, the factored resistance is obtained by multiplying the nominal ultimate flexural resistance by a factor linearly interpolated between φ = 0.9 (for P_{x} = 0) and φ = 0.75 (for P_{x} = P′). In most cases for CFA piles with large bending moments, bending controls the structural design and the computed combinations of axial forces and bending moments lie close to the P_{x} = 0 side of the diagram.
The pile design should first be checked to determine if the concrete section has adequate shear capacity without shear reinforcement. The factored shear resistance (φ V_{n}) of the concrete section can be determined as follows:
(Equation 5.58)φ V_{n} = φ V_{c} A_{V}
Where:
V_{n}  =  nominal (computed, unfactored) shear resistance of section; 
φ  =  capacity reduction factor for shear, usually equal to 0.85; 
A_{V}  =  crosssectional area that is effective in resisting shear; and 
V_{c}  =  concrete shear strength. 
The crosssectional area that is effective in resisting shear can be evaluated for a circular CFA pile as:
(Equation 5.59)A_{V} = B  B  + 0.58 r_{ls}  
2 
where
(Equation 5.60)r_{ls} =  B   d_{c}   d_{b} 
2  2 
where:
r_{ls}  =  radius of the ring formed along the centroids of the longitudinal bars; 
B  =  pile diameter; 
d_{c}  =  depth of concrete cover; and 
d_{b}  =  diameter of longitudinal bars. 
The concrete shear strength can be estimated as:
(Equation 5.61a)V_{c} =  1 + 0.00019 φ  P  f′_{c} (f′_{c} in psi)  
A_{g} 
V_{c} =  0.166 + φ 0.000032  P  f′_{c} (f′_{c} in MPa)  
A_{g} 
Where P = axial load and A_{g} = gross concrete area.
For a pure bending case (i.e., P_{x} = 0), this reduces to: V_{c} = f′_{c} (f′_{c} in psi) or V_{c} = 0.166 f′_{c} (f′_{c} in MPa).
If the factored shear resistance is greater than the factored shear load for the critical sections (as determined from py analyses), the minimum area of transverse reinforcement recommended below is adequate. If the factored shear resistance is less than the factored shear load, then: a) the pile diameter should be increased; or b) the shear reinforcing must be analyzed specifically to ensure that sufficient shear capacity is provided. The latter is likely to be an unusual circumstance for a CFA pile under normal conditions because bending moments associated with high shears are likely to control pile diameter.
If a spiral is used for the transverse reinforcement, the minimum reinforcement ratio (ρ) will be determined in accordance with the AASHTO code as:
(Equation 5.62)ρ_{S} = 0.45  A_{g}   1  f′_{c}  
A_{c}  f_{y} 
where:
ρ_{S}  =  Volume of spiral steel per turn/Volume of concrete core per turn; 
=  Volume of spiral steel per turn = area of bar × π × diameter of spiral hoop;  
=  volume per turn of concrete core = A_{c} × pitch of spiral;  
A_{c}  =  crosssectional area of concrete inside spiral steel = 0.25 × π × (core diameter)^{2}; 
A  =  gross crosssectional area of concrete of pile cross section; 
f′_{c}  =  concrete compressive strength at 28days; and 
f_{y}  =  yield strength of the spiral reinforcing steel. 
If a tied bar is used for the transverse reinforcement, the minimum requirement is:
The vertical spacing of the tied bars shall not exceed the lesser of:
Where the pile with minimum transverse reinforcement has inadequate shear resistance, the pile design may be changed to: (1) a larger diameter pile; (2) higher concrete compressive strength; or (3) transverse reinforcement greater than the minimum to increase the shear resistance. The required area of transverse steel is determined as follows:
(Equation 5.63)A_{vs} =  S V_{steel}  
f_{y}  B  + 0.58 r_{ls}  
2 
Where:
A_{vs}  =  required area of transverse steel; 
S  =  longitudinal spacing of the ties (spiral pitch); 
V_{steel}  =  nominal shear resistance of transverse steel (equal to total nominal shear resistance needed less shear resistance provided by concrete); 
f_{y}  =  yield strength of steel; and 
r_{ls}  =  radius of the ring formed along the centroids of the longitudinal bars on cross section. 
The concrete cover requirements of Section 5.12.3 AASHTO (AASHTO, 2006) apply for CFA piles. For watertocement ratios (W/C) between 0.40 and 0.50, the minimum cover of concrete or grout over the longitudinal bars must be 75 mm (3 in.) and 100 mm (4 in.) for aggressive environments (e.g., exposure to salt water). The required cover for transverse reinforcement may be less than that required for longitudinal bars by no more than 12 mm (0.5 in.). Transverse reinforcement greater than 13 mm (0.5 in.) would thus necessitate greater cover than longitudinal bars. This is rarely the case for CFA piles, as they typically have transverse reinforcement no greater than 13 mm (0.5 in.).
For W/C ratios greater than or equal to 0.50, the cover requirements must be increased by a factor of 1.2. For W/C ratios less than or equal to 0.40, the cover requirements may be decreased by a factor of 0.8. However, low W/C ratios can pose constructability problems with reinforcement.
Centering devices must be used with CFA pile construction to maintain alignment of the steel reinforcing cages that are being inserted into the freshly placed concrete or grout. The centering devices for full cages are similar to the centering devices used for drilled shaft construction, and most often plastic "wheels" that are installed around the transverse reinforcement. The central longitudinal bar is typically centered with a set of skids such that the arrangement of skids is axissymmetric around the central bar. Note that the orientation of either wheels or skids must be such that they roll or easily slide, respectively, along the borehole wall without scraping into the soil.
Where seismic loadings govern design, there may be several considerations that influence the design of a deep foundation. A complete discussion of the design of deep foundations for seismic loading is beyond the scope of this manual. However, it is appropriate to summarize herein the major points that may affect the selection and design of CFA piles for projects where seismic loads are significant.
For many transportation structures, design for seismic loading may only include a simple equivalent static analysis of lateral loads at the top of the foundation due to inertial effects on the structure. For such cases, the analysis and design may proceed as outlined in Sections 5.6.2 and 5.6.3. It is possible that seismic loads could include a component of pile uplift load in some cases. If piles are subjected to uplift loading, a full length center bar may be required as described in Section 5.6.4.1.
Where seismic loads and soft ground conditions are present, it may be necessary to consider bending stresses in the pile due to seismicallyinduced lateral ground movements. The most significant in this case is liquefaction and lateral spreading. Seismicallyinduced lateral ground movements could produce large bending stresses at great depth below the top of the pile. Therefore, reinforcement may need to be installed at great depths in a CFA pile to ensure that the pile retains axial load capacity during and after the seismic event. A single center bar is not sufficient in such cases. The use of a continuous steel pipe for reinforcement can provide good flexural capacity and ductility in such cases and may be considered where deep reinforcing cages may be problematic to install.
CFA piles will be subjected to a downdrag load (i.e., shear stress reversal) when the soils in contact with the upper portion of the pile move downward relative to the pile. Downdrag loads are fully developed at relatively small displacements, of only approximately 2.5 to 13 mm (0.1 to 0.5 in.). CFA piles behave similarly to drilled shafts in response to downdrag and analysis should be conducted in accordance with the methods of determining the ultimate sideshear values on the CFA piles as recommended herein. One difference with CFA piles is that they will always be used in groups and group behavior for downdrag and uplift may control.
Some examples of cases where downdrag can occur are illustrated in Figure 5.30. Note that overlying loose sand, shown as case (a), may be especially problematic if the loose sand is submerged and is in a seismically active area. A high liquefaction potential, coupled with the limited flexural capacity of CFA piles at great depths may preclude their use. Overlying soft clay, shown as case (b), may only be a problem if a surface load is added or if excess pore pressures exist within the clay following the CFA pile installation to drive the consolidation process. Recently placed fill, shown as case (c), may most commonly be encountered in highway design when an abutment and fill are placed around the CFA columns or the supported column/pier.
The range of forces that may develop against vertical piles when downdrag is occurring is shown schematically in Figure 5.31. The limitstate on the left occurs when the combination of the applied load and downdrag load produces both sideshear and endbearing resistance failures in the founding stratum. The limitstate on the right occurs when a greater load is applied to the same pile shown on the left. The load on the right has been increased a sufficient amount such that the increased pile deflection is then greater than the settlement of the surrounding soil, and thus the entire pile has now been moved down relative to the soil. In such a case, downdrag no longer acts to load the pile.
Although the limitstate on the right side of Figure 5.31 represents the true ultimate geotechnical limitstate for strength, this condition can only exist when the settlement of the pile exceeds that of the ground surface that may be on the order of several inches to several feet. Therefore, the limitstate on the left side is customarily considered to be the strength limitstate for sustained loads. Downdrag conditions can be such that settlement considerations (i.e., serviceability limit state) rather than geotechnical strength conditions control design. Downdrag forces can add significantly to axial forces within the pile and thus can have a significant effect on pile structural design and material strength requirements.
Figure 5.30: Examples of Cases of Downdrag
Source: O'Neill and Reese (1999)
The downdrag force should be considered as a permanent load for analysis. This force is the force added to the pile above the neutral plane (defined below) by way of negative (i.e., downward) sideshear. The pile resistance is then the positive (upward) sideshear and endbearing located below the neutral plane. To correctly differentiate between the downdrag loads and pile resistances, the location of the neutral plane must be determined. The neutral plane is defined at the depth along the pile where there is zero relative movement between the soil and the pile. Therefore, at the neutral plane, there is no load transfer from the soil to the pile.
It may be sufficient to assume that the neutral point lies at the top surface of the strong lower layer in Figure 5.32 if the top layer is relatively weak and causes the downdrag. Note that this assumption is conservative. This condition is shown as details (c) and (d) in Figure 5.32 and is discussed in O'Neill and Reese (1999). Figure 5.32(c) shows the relative movement between the pile and the soil (i.e., negative sign means downdrag). Figure 5.32(d) shows the distribution of resistances along the pile. Better estimates of the neutral point may be obtained with the iterative methodology, as shown in parts (e) and (f) in Figure 5.32. In this case, the neutral point will be located where the endbearing resistance (R_{Bd}) matches that value predicted by static analyses or loadtests. The location of the neutral point may be obtained after only a few trial depths provided that the pile behaves elastically and the load transfer functions are simple.
Figure 5.31: Potential Geotechnical Limit States for Piles Experiencing Downdrag
Source: O'Neill and Reese (1999)
When downdrag is anticipated to occur around a pile group, it is usually sufficient for design purposes to use an equivalent pier method where the depth of the pier is the same as for individual piles, and the perimeter of the pier is that of the pile group, as shown in Figure 5.33. The neutral plane may then be determined by the iterative procedure previously described with the equivalent pier dimensions and the equivalent elastic modulus (E_{e}) calculated as follows:
(Equation 5.64)E_{e} = E_{c}  A_{piles}  + E_{st}  1   A_{piles}  
A_{group}  A_{group} 
Where:
E_{e}  =  average Young's modulus of equivalent pier within the compressible layer; 
E_{c}  =  Young's modulus of pile (concrete or grout); 
E_{st}  =  Young's modulus of geomaterial between piles; 
A_{piles}  =  crosssectional area of all the piles in the group; and 
A_{group}  =  crosssectional area of the pile group, not including overhanging cap area. 
Note that for typical spacing of 3 pile diameters centertocenter in groups of piles, the downdrag loads occur only around the perimeter of the group, and do not develop against interior piles.
Figure 5.32: Mechanics of Downdrag: Estimating the Depth to the Neutral Plane
Source: O'Neill and Reese (1999)
Figure 5.33: Mechanics of Downdrag in a Pile Group
Source: O'Neill and Reese (1999)
This section presents two example problems that illustrate the estimation of the axial capacity of CFA piles. The first example is on the estimation of the axial capacity of a conventional CFA pile in cohesive soils. The second example is on the estimation of the axial capacity of conventional CFA and DD piles in cohesionless soils. In these example problems, all quantities are expressed in English units only.
Problem Statement
Conventional CFA piles of 18 in. nominal diameter are being considered for use to provide support for a highway interchange in a Coastal Plains area. A subsurface investigation, as described in the example problem of Chapter 6 (section 6.7.4, part A), provided information necessary to develop the generalized soil profile at the pier location shown in Figure 5.34. The bottom of the proposed pile cap is at a depth of 4 ft. An allowable stress design (ASD) is to be used with a safety factor of 2.0, as detailed in Chapter 6 (section 6.7.4 Part D). Note that a safety factor of 2.0 is used, as fullscale loadtesting will be implemented to verify (or modify if necessary) the pile capacity estimates. Details of the safety factor selection criteria will be presented subsequently in Chapter 6. Provide a hand calculation of the allowable static axial capacity at a pile depth of 60 ft.
Solution
The sideshear resistance (R_{S}) for a pile embedment depth of 60 ft is estimated with the use of the recommended method detailed in Section 5.3.1.1. Note that a spreadsheet solution for the capacity with a range of pile depths is given in Appendix B. The sideshear contributions from the top soil layer (classified as medium gray clay or CH), and the bottom soil layer (classified as stiff to very stiff tan clay or CL to CH) are estimated. The top 5 ft of sideshear is disregarded from the top soil layer estimate, and the bottom 1diameter (1.5 ft) of sideshear is disregarded from the bottom soil layer estimate, as per the recommended method. Note that if either the bottom of the pile cap (at a depth of 4 ft for this example) or an evaluation of the depth of seasonal moisture change were at a depth in excess of 5 ft, then this larger depth would be discounted from the contribution to the sideshear resistance. From Equation 5.2:
R_{s} =  N  f_{s,i} π D_{i} L_{i} = f_{s (Top Layer)} π D L_{(Top Layer)} + f_{s (Bottom Layer)} π D L_{(Bottom Layer)} 
Σ  
i 
where:
D  =  1.5 ft (the same for both top and bottom layers); 
L_{(Top Layer)}  =  29 ft  5 ft = 24 ft (note the top 5 ft are disregarded for sideshear resistance); 
L(_{Bottom Layer})  =  60 ft  1.5 ft  29 ft = 29.5 ft (note the bottom 1 diameter or 1.5 ft is disregarded for sideshear resistance); 
f_{s}  =  α S_{u,ave}; f_{s} is estimated from Equation 5.5 for both the top and bottom layers, as shown below. Note that this will yield an ultimate unit sideshear resistance. 
The maximum undrained shear strength, S_{u,max}, for this profile is 2.5 ksf, which yields a ratio of S_{u,max}/P_{a} ≈ 1.25. Therefore, α = α_{(Top Layer)} = α_{(Bottom Layer)} = 0.55, from Equation 5.6.
S_{u,ave}_{(Top Layer)} = 0.6 ksf from the idealized soil profile shown in Figure 5.34. Note that the stiffer, desiccated surficial soils (within the top 5 ft zone) were not included in this average in the idealized soil profile.
S_{u,ave}_{(Bottom Layer)} = (1.50 ksf + 2.07 ksf)/2 = 1.79 ksf from the idealized soil profile shown in Figure 5.34. Note that 2.07 ksf in the above calculation was linearly interpolated at a depth of 58.5 ft (60 ft embedment depth  1.5 ft exclusion zone at tip).
f_{s (Top Layer)} = 0.55 × (0.60 ksf) = 0.33 ksf
f_{s (Bottom Layer)} = 0.55 × (1.79 ksf) = 0.98 ksf
Then, it results:
R_{S} = (0.33 ksf) × π × (1.5 ft) × (24 ft) + (0.98 ksf) × π × (1.5 ft) × (29.5 ft)
R_{S} = 37.3 kips + 136.2 kips = 173.5 kips
The endbearing resistance (R_{B}) for a pile embedment depth of 60 ft is estimated per the recommended method detailed in Section 5.3.1.1. The endbearing resistance is estimated for the bottom soil layer according to Equation 5.4:
R_{B} = q_{p}  π D^{2}  
4 
where:
D  =  1.5 ft, the nominal diameter of the pile 
q_{p}  =  N^{*}_{c} S_{u} from Equation 5.7 
S_{u (ave)}  =  (2.10 ksf + 2.14 ksf) / 2 = 2.12 ksf = 1.06 tsf from the idealized soil profile shown in Figure 5.34. The values 2.10 ksf and 2.14 ksf in the above calculation were linearly interpolated at depths of 60 ft (pile tip) and 63 ft (2 diameters below the pile tip), respectively 
N_{c}^{*}  =  8.71, as interpolated from Table 5.1 for an undrained shear strength of 2.12 ksf = 1.06 tsf 
q_{p}  =  (8.71) × (2.12 ksf) = 18.46 ksf 
R_{B}  =  (18.46 ksf) × (π/4) × (1.5 ft)^{2} = 32.6 kips 
The total axial resistance (R_{T}) for a pile embedment depth of 60 ft is the sum of the sideshear resistance and the endbearing resistance, according to Equation 5.1:
R_{T} = R_{S} + R_{B} = 173.5 kips + 32.6 kips = 206.1 kips
Note that this is the ultimate geotechnical axial resistance.
The allowable static axial resistance (R_{allowable}) is obtained in accordance with ASD and a Safety Factor, SF = 2.0.
R_{allowable} = R_{T} / SF = (206.1 kips) / 2.0 = 103.1 kips
Problem Statement
Both conventional CFA piles and DD piles, both with a nominal diameter of 18 in., are being considered for use to provide support for a bridge over a small stream within a flood plain. A subsurface investigation provided information to develop the generalized soil profile at the pier location, shown in Figure 5.35, in terms of SPTN values, soil descriptions, and unit weights. N values are assumed to correspond to 60% hammer efficiency. While the pier location is usually accessible by trackmounted equipment, extreme high tides have been known to bring the water level up to that indicated on the figure. The hydraulic engineer for the project has indicated that potential scour exists at the pier to a depth of 6 ft. The bottom of the proposed pile cap is also proposed at a depth of 6 ft. An ASD is used with a safety factor of 2.5. Details of the safety factor selection criteria will be presented subsequently in Chapter 6. Provide a hand calculation of the ultimate static axial resistance and the allowable static axial resistance for both pile types at a depth of 17 ft in accordance with ASD.
Solution
Hand solutions for conventional CFA piles and DD piles are presented subsequently, both at a pile depth of 17 ft. Note that spreadsheet solutions of both piles types are given in Appendix B for the capacity with a range of pile depths.
For both pile types, the pile will be divided into 6 segments with the bottom of these segments at depths of 3.25, 5.75, 8.25, 10.75, 13.25, and 17 ft, respectively. These depths correspond to the midpoint between depths of reported SPTN values. It follows then that the midpoint of each pile segment is at depths of 1.63, 4.5, 7.0, 9.5, 12.0, and 15.1 ft, respectively.
Figure 5.34: Soil Profile S_{u} vs. Depth for Example Problem of CFA Pile in Cohesive Soil
Conventional CFA Pile Calculations
The sideshear resistance (R_{S}) for a pile embedment depth of 17 ft is estimated following the recommended method detailed in Section 5.3.2.1. The pile cap and the potential scour both dictate that the sideshear contribution be discounted to a depth of 6 ft. Further, the solution in this example has assumed a worstcase "bed"scour, where the top 6 ft has been disregarded in the calculation of the effective stress distribution and β with depth. Note that if the scour was anticipated to be only "localized", the top 6 ft do not need to be disregarded in calculating effective stresses and β. From Equation 5.2:
R_{s} =  N  f_{s,i} π D_{i} L_{i} 
Σ  
i 
Figure 5.35: Soil Profile SPTN vs. Depth for Example Problem of CFA Pile and DD Pile in Cohesionless Soil
For this example with N = 6 pile segments and a constant nominal pile diameter, it results:
R_{s} = D  6  f_{s,i} L_{i} 
Σ  
i 
where:
D  =  1.5 ft (the same for both top and bottom layers) 
f_{s}  =  K σ_{v}′ tan φ = β σ_{v}′ from Equations 5.17 and 5.18 
and β = 1.5  0.135 Z^{0.5} (from Equation 5.19) and Z is the depth to the middle of each pile segment (in ft). Note that β is limited to the following range
0.25 < β < 1.2, and
σ_{v}′ = (γ_{sat}  γ_{water}) Z = (120 pcf  62.4 pcf) Z (ft)
Pile Segment 1: Disregarded (above scour and pile cap)
Pile Segment 2: Disregarded (above scour and pile cap)
Pile Segment 3: f_{s}_{(3)} = (1.2) × (0.120  0.0624 kcf) × (7  6 ft) = 0.07 ksf (β limited to 1.2)
Pile Segment 4: f_{s}_{(4)} = (1.2) × (0.120  0.0624 kcf) × (9.5  6 ft) = 0.24 ksf (β limited to 1.2)
Pile Segment 5: f_{s}_{(5)} = [1.5  0.135 × (12  6)^{0.5}] × (0.120  0.0624 kcf) × (12  6 ft) = 0.40 ksf
Pile Segment 6: f_{s}_{(6)} = [1.5  0.135 × (15.1  6)^{0.5}] × (0.120  0.0624 kcf) × (15.1  6 ft) = 0.57 ksf
R_{S} = π (1.5 ft) × {(0.07 ksf) × [(2.5 ft  (6  5.75 ft)] + (0.24 ksf) × (2.5 ft) + (0.40 ksf) × (2.5 ft) + (0.57 ksf) × (3.75 ft)}
R_{S} = 18.4 kips
The endbearing resistance (R_{B}) for a pile embedment depth of 17 ft is estimated following the recommended method detailed in Section 5.3.2.1. From Equation 5.4:
R_{B} = q_{p}  π D^{2}  
4 
where:
D  =  1.5 ft is the nominal diameter of the pile 
q_{p} (ksf)  =  0.6 N_{ave} from Equation 5.20 
N_{ave}  =  (22 + 26 blows/ft)/2 = 24 blows/ft, from the N values at the tip and 5 ft below the tip. 
q_{p}  =  0.6 × (24) × (2 ksf/ 1 tsf) = 28.8 ksf 
R_{B}  =  (28.8 ksf) × (π/4) × (1.5 ft)^{2} = 50.9 kips 
The total axial resistance (R_{T}) for a pile embedment depth of 17 ft is the sum of the sideshear resistance and the endbearing resistance, according to Equation 5.1:
R_{T} = R_{S} + R_{B} = 18.4 kips + 50.9 kips = 69.3 kips
Note that this is the ultimate geotechnical axial resistance.
The allowable static axial resistance (R_{allowable}) is obtained for a Safety Factor, SF = 2.5:
R_{allowable} = R_{T} / SF = 69.3 kips / 2.5 = 27.7 kips
DD Pile Calculations
The sideshear resistance (R_{S}) for a pile embedment depth of 17 ft is estimated following the recommended method detailed in Section 5.4.2. The pile cap and the potential scour both dictate that the sideshear contribution be discounted to a depth of 6 ft. From Equation 5.2:
R_{s} =  N  f_{s,i} π D_{i} L_{i} 
Σ  
i 
For this example with N = 6 pile segments and a constant nominal pile diameter is results:
R_{s} = π D  6  f_{s,i} L_{i} 
Σ  
i 
where:
D  =  1.5 ft (the same for both top and bottom layers) 
f_{s} (ksf)  =  (0.05 N) (2 ksf/ 1 tsf) + W_{T}, from Equation 5.31, and limited to N_{60} ≤ 50. 
W_{T}  =  0 for 6pile segments, all lying within the soil layer (silty fine sand). Note that f_{s} would be limited to 3.4 ksf for wellrounded and poorlygraded soils, and limited to 4.4 ksf for angular wellgraded soils. If the pile segments had been into the last layer (i.e., Shelly sand), W_{T} = 1 ksf for these angular, wellgraded soils. See Section 5.4.2 for details pertaining to the selection of W_{T}. 
Pile Segment 1: Disregarded (above scour and pile cap)
Pile Segment 2: Disregarded (above scour and pile cap)
Pile Segment 3: f_{s}_{(3)} = (0.05) × (19 blows/ft) × (2 ksf/1 tsf) + (0 ksf) = 1.90 ksf
Pile Segment 4: f_{s(}_{4)} = (0.05) × (24 blows/ft) × (2 ksf/1 tsf) + (0 ksf) = 2.40 ksf
Pile Segment 5: f_{s}_{(5)} = (0.05) × (25 blows/ft) × (2 ksf/1 tsf) + (0 ksf) = 2.50 ksf
Pile Segment 6: f_{s}_{(6)} = (0.05) × (22 blows/ft) × (2 ksf/1 tsf) + (0 ksf) = 2.20 ksf
R_{S} = π × (1.5 ft) × [(1.90 ksf) × (2.5 ft(6  5.75 ft)) + (2.40 ksf)(2.5 ft) + (2.50 ksf)(2.5 ft)+ (2.20 ksf)(3.75 ft)]
R_{S} = 116.7 kips
The endbearing resistance (R_{B}) for a pile embedment depth of 17 ft is estimated according to the recommended method detailed in Section 5.4.2. From Equation 5.4:
R_{B} = q_{p}  π D^{2}  
4 
where:
D  =  1.5 ft, the nominal diameter of the pile 
q_{p} (ksf)  =  1.9 N_{(ave)} (2 ksf/1 tsf) + W_{T}, from Equation 5.33 and limited to N_{60} ≤ 50. 
N_{ave}  =  (25 + 22 + 26 + 9) / 4 = 20.5 blows/ft, from the SPTN values 6.25 ft above and 10 ft below the tip. Note that q_{p} would be limited to 150 ksf for wellrounded and poorlygraded soils and limited to 178 ksf for angular, wellgraded soils. 
q_{p}  =  1.9 × (20.5) × (2 ksf/1 tsf) + 0 = 77.9 ksf 
R_{B}  =  (77.9 ksf) × (π/4) × (1.5 ft)^{2} = 137.7 kips 
The total axial resistance (R_{T}) for a pile embedment depth of 17 ft is the sum of the sideshear resistance and the endbearing resistance according to Equation 5.1:
R_{T} = R_{S} + R_{B} = 116.7 kips + 137.7 kips = 254.4 kips
Note that this is the ultimate geotechnical axial resistance.
The allowable static axial resistance (R_{allowable}) is obtained in for a Safety Factor (SF = 2.5).
R_{allowable} = RT/SF = 254.4 kips / 2.5 = 101.7 kips
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