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Geotechnical Engineering Circular (GEC) No. 8
Design And Construction Of Continuous Flight Auger Piles
Final
April 2007

Chapter 5: Evaluation Of Static Capacity Of Continuous Flight Augered Piles

5.1 Introduction

In many respects, the static capacity of a well-constructed continuous flight auger (CFA) pile can be considered to fall between that of a drilled shaft and a driven pile. This concept is primarily attributed to different changes in lateral stress during the installation of the various pile types. During construction of a drilled shaft, the soil stress tends to reduce or remain unchanged in the vicinity of the pile excavation. During installation of a driven pile, the pile driving process displaces the soil laterally and increases the stresses in the surrounding soil. In the case of conventional CFA pile construction, the stresses in the soil tend to remain near the pre-construction stress values (similar to a drilled shaft), while the construction of drilled displacement (DD) piles tend to increase the stresses in the surrounding soil (similar to driven piles).

It is reasonable to estimate static capacity of CFA piles using methods developed specifically for driven piles and drilled shafts, because the load-settlement behavior of CFA piles are similar. Some methods, however, have been developed specifically for CFA piles, and usually take the form of modifications made to methods previously developed for drilled shafts or driven piles. For these methods, measured pile capacity (via full-scale load-testing) of CFA piles has also been correlated to parameters including, SPT blowcount, CPT cone penetration tip resistance, and soil undrained shear strength.

This chapter provides specific methods of estimating static axial capacity for different soil types and type of strength data. Four comparison studies are available in which several prediction methods were compared to various CFA load-test databases. The methods presented in Section 5.2 were chosen as those that appeared to generally provide reliable and accurate results for conventional CFA piles according to the four studies. Appendix A contains a summary of other analysis methods of estimating static axial capacity of CFA piles that are currently or have traditionally been used in the United States and abroad, and a summary of the four comparison studies to asses the adequacy of various methods. Section 5.3 presents a method for DD piles.

This chapter also presents information on pile group behavior, settlement, and lateral load capacity; this information is also used in Chapter 6 to present a recommended design procedure for CFA piles.

It should be noted that computations of static axial resistance should be considered as estimates to be validated and/or modified on a project-specific basis using the results of load-tests. The guide specification provided in Chapter 8 is written as a performance-based specification, in which the contractor is responsible to compute static resistance, set pile length requirements for a given design axial loading, and verify that the performance requirements are achieved via the use of load-tests.

5.2 Development Of Side-Shear And End-Bearing Resistance With Pile Displacement

Similar to other types of deep foundations, the total axial compressive resistance (RT) of a CFA pile is calculated as the combination of the side-shear resistance (RS), and end-bearing resistance (RB):

(Equation 5.1)

RT = RS + RB

To calculate the total side-shear resistance, the pile length must first be divided into N pile segments. The side resistance of a particular pile segment "i" (of length Li, and diameter, Di) is obtained by multiplying the unit side-shear resistance (fs,i sometimes referred to as load or transfer rate) of the segment by the surface area of the pile segment (π Di Li). The total side-shear resistance is obtained by adding the contribution of all N pile segments as:

(Equation 5.2)
RS =Nfs,i π Di Li
Σ
i

Some of the methods presented in this chapter and Appendix A use an average unit side-shear (fs-ave) for the entire pile length, instead of summing individual pile segments. In these cases, the total side-shear resistance is calculated as:

(Equation 5.3)

RS = fs-ave π D L

where D is the average diameter of the pile, and L is the pile total embedment length.

The total end-bearing resistance (RB) is calculated as:

(Equation 5.4)
RB = qp π DB2 
 
4

where qp is the unit end-bearing resistance, and DB is the diameter of the pile at the base.

The side-shear component is mobilized with relatively small pile vertical displacements relative to the surrounding soil, typically less than 10 mm (0.4 in.). The end-bearing 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 load-settlement curve from a load-test of a CFA pile may appear somewhat softer than that of a typical driven pile and methods used to interpret ultimate load resistance from load-tests on driven piles could be conservative for CFA piles.

The mobilized side- and end-bearing 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 end-bearing 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 end-bearing 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 side-shear 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 / (ApileE) = 2 mm (0.08 in.), where Apile is the cross-sectional area of the pile. Details of the calculation of the elastic compression of a pile are presented in Section 5.5.3.1.

5.3 Recommended Methods For Estimating Static Axial Capacity Of CFA Piles

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 high-displacement 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 fine-grained 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 in-situ 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: Load-Displacement Relationships

(a) Normalized Load Transfer in Side-Shear (b) Normalized End-Bearing Capacity vs. Settlement in Cohesive Soils vs. Settlement in Cohesive Soils

Illustrations showing load-displacement relationships: (a) graphical illustration showing normalized load transfer in side-shear as a function of settlement in cohesive soils, (b) illustration showing normalized end-bearing capacity as a function of settlement in cohesive soils, (c) illustration showing normalized load transfer in side-shear as a function of settlement in cohesive soils, and (d) illustration showing normalized end-bearing as a function of settlement in cohesive soils.

(c) Normalized Load Transfer in Side-Shear d) Normalized End-Bearing vs. Settlement in Cohesive Soils vs. Settlement in Cohesive Soils

Illustrations showing load-displacement relationships: (a) graphical illustration showing normalized load transfer in side-shear as a function of settlement in cohesive soils, (b) illustration showing normalized end-bearing capacity as a function of settlement in cohesive soils, (c) illustration showing normalized load transfer in side-shear as a function of settlement in cohesive soils, and (d) illustration showing normalized end-bearing as a function of 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 load-testing program is a critical and necessary component for the effective use of CFA piles.

5.3.1 Cohesive Soils
5.3.1.1 Recommended Method for Side-Shear and End-Bearing Estimates Using Undrained Shear Strength

The FHWA 1999 method for drilled shafts is recommended for prediction of both the side-shear and end-bearing 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 side-shear resistance (fs) is calculated as:

(Equation 5.5)

fs = α Su

where Su 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 Su / Pa ≤ 1.5

where Pa 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 < Su/Pa ≤ 2.5, α varies linearly from 0.55 to 0.45.

If the bottom of the pile is bearing on clay, the side-shear contribution to the capacity of the bottom one-diameter 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 side-shear 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 end-bearing resistance (qp) is calculated as:

(Equation 5.7)

qp = Nc* Su

where Su is the average undrained shear strength of the soil between the pile tip and two-pile diameters below the pile tip, and Nc* is the bearing capacity factor. The value of Nc* is adopted as follows:

(Equation 5.8)

Nc* = 9

for 200 kPa (2 tsf) ≤ Su ≤ 250 kPa (2.6 tsf), and L ≥ 3D, or

(Equation 5.9)
Nc* =4[ lnIr + 1 ]
 
3

for Su < 200 kPa (2 tsf), and L ≥ 3D.

where L is the pile embedment length below top of grade, and Ir is the rigidity index.

Note that values of Su greater than 250 kPa (2.6 tsf) are treated as intermediate geo-materials in accordance with O'Neill and Reese (1999). The rigidity index (Ir) is calculated as follows:

(Equation 5.10)
Ir =ES
 
3 Su

where Su and the undrained Young's modulus (ES) are those of the soil just below the pile tip. ES is best determined from triaxial testing or in-situ testing (such as the pressuremeter test). If ES is not measured, it can be assumed with less accuracy to be a function of Su for design purposes by interpolating between the values given in Table 5.1 below.

Table 5.1: Relationship between Undrained Shear Strength, Rigidity Index, and Bearing Capacity Factor for Cohesive Soils for FHWA 1999 Method
SuIr = Es / ( 3 Su )N*c
25 kPa (0.25 tsf)506.5
50 kPa (0.50 tsf)1508.0
100 kPa (1.00 tsf)2508.7
200 kPa (2.00 tsf)3008.9

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 end-bearing resistance (qp) should be reduced according to the FHWA 1999 method, as follows:

(Equation 5.11)
qp =2 1 + 1 L Nc* Su for L < 3D
   
36D
5.3.1.2 Alternative Methods for Side-Shear Estimates Using Undrained Shear Strength

The Coleman and Arcement (2002) method was derived from CFA pile load-tests 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 side-shear capacities. The ultimate unit side-shear resistance (fs) is again calculated from the average undrained shear strength (Su), and the α factor as:

(Equation 5.12)

fS = α Su

(Equation 5.13a)
α =56.2(Su in kPa)
 
Su
(Equation 5.13b)
α =0.56(Su in tsf)
 
Su

Coefficients above are rounded from Coleman and Arcement (2002). The valid range of Su 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 Su less than approximately 150 kPa [1.5 tsf]), and would reduce to as low as 0.45 for greater values of Su. 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., Su up to approximately 50 kPa [0.5 tsf ]).

Figure 5.2: Relationship for the α Factor with Su for Calculating the Unit Side-Shear for Cohesive Soils for the Coleman and Arcement (2002) Method

Graphical illustration showing the relationship for the alpha factor with s sub u for calculating the unit side shear for cohesive soils (i.e., silts and clays) 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 over-consolidated by desiccation. The ultimate unit side-shear resistance (fs) in cohesive soils is calculated for a given pile segment simply as a function of Su (i.e., here the α factor is constant at 0.7):

(Equation 5.14)

fs = 0.7 Su ≤ 120 kPa (1.25 tsf)

5.3.1.3 Alternative Method for End-Bearing Estimates Using Dynamic Cone Penetrometer

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 (NTxDOT) for estimation of ultimate unit end-bearing resistance, which is uncommon in most areas outside of Texas. The ultimate unit end-bearing resistance (qp) can be determined using the NTxDOT value as follows:

(Equation 5.15)
qp (tsf) =NTxDOT
 
8.25
5.3.1.4 Alternative Method for Side-Shear and End-Bearing Estimates Using SPT-N Values

The design methods for prediction of side-shear and end-bearing resistance components in cohesive soils rely almost exclusively on undrained shear strength (Su). When no other types of geotechnical data other than SPT-N values are available, the undrained shear strength can be estimated from SPT-N 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 SPT-N values obtained in soils are not highly-reliable in estimating the undrained shear strength.

5.3.1.5 Alternative Method for Side-Shear and End-Bearing Estimates Using CPT Values

CPT testing has shown good results in prediction of both end-bearing and side-shear 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 (qc) data from CPT testing. Side-shear resistance estimates can be made using Figure 5.3 for clays and silts exhibiting an undrained condition.

The ultimate unit side-shear in cohesive soils (fs) at a given depth (shown in Figure 5.3 as Maximum friction) is determined from the cone bearing resistance (qc) at that depth (as shown on the Y-axis), and then by interpolation between the limiting curves shown (qc < 1.2 MPa [12.5 tsf] and qc > 5 MPa [52 tsf]) based upon the average qc along the pile length or pile segment length within a cohesive stratum.

The ultimate unit end-bearing resistance (qp) in cohesive soils may also be estimated directly from the cone tip resistance (qc) from CPT testing:

(Equation 5.16)

qp = 0.15 qc

Figure 5.3: Unit Side-Shear Resistance as a Function of Cone Tip Resistance for Cohesive Soils - LPC Method

Graphical illustration showing unit side-shear resistance as a function of cone tip resistance for cohesive soils in the 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.

5.3.2 Cohesionless Soils
5.3.2.1 Recommended Method for Side-Shear Estimates Using Pile Depth and End-Bearing Estimates Using SPT-N Values

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 N60 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 side-shear resistance (fs) of a pile segment is estimated as:

(Equation 5.17)

fs = K σv 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 Z0.5 for N ≥ 15 bpf

(Equation 5.19b)
β =N( 1.5 - 0.135 Z0.5) 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 end-bearing resistance (qp) is estimated as:

(Equation 5.20a)

qp (tsf) = 0.6 N60 for 0 ≤ N60 ≤ 75

(Equation 5.20b)

qp = 4.3 MPa [45 tsf] for N60 > 75

where N60 is the SPT-N 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.

5.3.2.2 Alternative Methods for Side-Shear Using Pile Depth

The Coleman and Arcement (2002) method was derived from CFA pile load-tests 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)

fs = β σv ≤ 200 kPa (2.0 tsf)

The values of β are computed as follows:

(Equation 5.22)

β = 2.27 Zm-0.67 (for silty soils)

(Equation 5.23)

β = 10.72 Zm-1.3 (for sandy soils)

Where Zm 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 Side-Shear for Cohesionless Soils for the FHWA 1999 and Coleman and Arcement Methods

Graphical illustration showing the relationship for the ? factor for calculating the unit side-shear for cohesionless soils (i.e., silts and clays) as a function of depth for the FHWA 1999 and Coleman and Arcement methods.

Source:Coleman and Arcement (2002)

5.3.2.3 Alternative Method for Side-Shear and End-Bearing Estimates Using CPT Values

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 (qc). These estimates can be made using Figure 5.5 for sands and gravel.

The ultimate unit side-shear in cohesionless soils (fs) at a given depth (shown on the X-axis as Maximum friction) is determined from the cone bearing resistance (qc) at that depth (as shown on the Y-axis), and by the interpolating between the limiting curves shown (qc < 3.5 MPa [36 tsf] and qc > 5 MPa [52 tsf]) based upon the average qc along the pile length or pile segment length within a cohesionless stratum.

The ultimate unit end-bearing resistance (qp) in cohesionless soils may also be estimated directly from the cone bearing resistance (qc) 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)

qp (MPa) = 0.375 qc

Figure 5.5: Unit Side-Shear as a Function of Cone Tip Resistance for Cohesionless Soils - LPC Method

Graphical illustration showing unit side-shear as a function of cone tip resistance for cohesionless soils (i.e. sand and gravel) in the LPC method.

Source: Bustamante and Gianeselli, (1982)

5.3.3 Other Geo-Materials
5.3.3.1 Introduction

CFA piles have been used with success in strong, non-caving 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 non-cohesive 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 end-bearing 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.

5.3.3.2 Vuggy Limestone

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 load-tests in the Miami limestone and Fort Thompson limestone formations found in South Florida (Broward and Miami-Dade Counties).

Frizzi and Meyer (2000) presented relationships of unconfined compressive strength vs. ultimate unit side-shear 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 full-scale field grout plug tests and limited CFA load-tests in various Florida limestone. The trend lines suggest that the smaller scale anchor tests and grouted plugs tend to mobilize higher side-shear 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 full-scale piles.

In the Frizzi and Meyer (2000) method, the ultimate unit side-shear resistance for a given pile segment in either the Miami limestone or Fort Thompson limestone formations are correlated to the SPT-N60, as shown in Figure 5.7. SPT-N60 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 side-shear 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 full-scale field load-test data.

Figure 5.8 presents a relationship of side-shear stress development with displacement from load-tested CFA piles constructed in the Miami limestone and Fort Thompson limestone formations. Note that this data is presented as the ratio of the developed side-shear to the ultimate side-shear resistance (f/fmax) 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 load-test data published by Semeraro (1982). No modifications or methods for predicting the end-bearing capacity were proposed by Frizzi and Meyer (2000). Note that in most cases, the CFA piles mobilized a very high load-carrying 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 Side-Shear for Drilled Shafts in Florida Limestone

Graphical illustration showing unconfined compressive strength as a function of ultimate unit side-shear for drilled shafts in Florida limestone based on results from three references. Figure shows range of unconfined compressive strength Miami Limestone and Fort Thompson Limestone.

Source: Frizzi and Meyer (2000)

Figure 5.7: Correlation of Ultimate Unit Side-Shear Resistance for South Florida Limestone with SPT-N60 Value

Graphical illustration showing the correlation of ultimate unit side-shear resistance for South Florida limestone with SPT-N sub 60 value based on data provided by various authors. Figure shows proposed relationships for Miami Limestone and Fort Thompson Limestone.

Source: Frizzi and Meyer (2000)

Figure 5.8: Side-Shear Development with Displacement for South Florida Limestone

Graphical illustration showing side-shear development, in terms of a normalized value, with respect to a normalized displacement for South Florida Limestone. Figure shows proposed range for CFA piles in South Florida. Figure shows data from various authors.

Source: Frizzi and Meyer (2000)

5.3.3.3 Clay-Shale

For CFA piles socketed into clay-shale formations of North-Central 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 load-tests of CFA piles socketed into clay-shale with unconfined compression strengths (qu) ranging from 100 to 3,000 kPa (1 to 30 tsf) (measured in situ from a Texas Cone Penetrometer value, NTxDOT). 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 load-test results are presented in dimensionless form for all eight test piles as a relative load capacity (Q / Qult), 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
  
Qultρ50+ρ
  
DD

where:

Q=resistance at the given displacement (in any consistent units);
Qult=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
ρ50/D=the displacement-to-diameter ratio at Q/Qult = 0.5.

The parameter Qult was correlated to the unconfined compressive strength (qu) of the clay-shale, pile circumference (π D), and socket length (L) and is shown in Figure 5.10 and is represented as:

(Equation 5.26)
Qult= -0.11L+ 0.96
  
qu π D LD

Figure 5.9: Relative Load Capacity vs. Relative Displacement for CFA Sockets in Clay-Shale

Graph illustrating relative load capacity a function of relative displacement for CFA sockets in clay-shale. Figure shows typical range of relative displacement.

Source: Vipulanandan et al. (2004)

Figure 5.10: Hyperbolic Model Parameter Qult as a Function of the Unconfined Compressive Strength (qu) for CFA Sockets in Clay-Shale

Graph illustrating hyperbolic model parameter Q sub ult as a function of the unconfined compressive strength q sub u for CFA sockets in clay-shale and the normalized length of the pile. Figure shows the minimum normalized length of pile recommended by Texas DOT.

Source: Vipulanandan et al. (2004)

The parameter ρ50/D was also correlated to the unconfined compressive strength of the clay-shale normalized by the standard atmospheric pressure (in any consistent units) in the equation below.

(Equation 5.27)
ρ50[ in % ] =15.8
  
Dqu
 
Patm

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 qu with the atmospheric pressure the ratio ρ50/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 ρ50/d as a Function of Unconfined Compressive Strength for CFA Sockets in Clay-Shale

Graph illustrating parameter rho sub 50 over d as a function of unconfined compressive strength for CFA sockets in clay-shale.

Source: Vipulanandan et al. (2004)

For:

  • a pile with diameter D = 1.5 ft;
  • drilled into clay shale of qu = 20 tsf; and
  • a socket L = 3 D = 4.5 ft.

The following results are obtained using the method described above:

  • for ratio qu/Patm = 20;
  • Equation 5.27 results ρ50/D = 0.79%.

With Equation 5.26, the ultimate capacity is estimated as:

Qu = qu 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= Qult [ ρ/D ÷ ( ρ50/D + ρ/D )] =
= 267 × [ 0.25/18 ÷ ( 0.0079 + 0.25/18 ) ] = 0.64 × 267 = 170 tons.

5.4 Static Axial Capacity Of Drilled Displacement Piles

5.4.1 Introduction

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 (Ko) may decrease as much as one third (resembling an active lateral earth pressure, Ka) for drilled shafts, and may nearly double (resembling a passive lateral earth pressure, Kp) for high-displacement 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, over-consolidation ratio, and effective stress conditions before displacement.

5.4.2 Recommended Method Using SPT-N Values or CPT Data

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 side-shear resistance and end-bearing capacities obtainable with this technique over conventional CFA piles must be verified for the specific site, technique, and equipment using full-scale load-testing, automated monitoring, and recording equipment for all test and production piles.

NeSmith (2002) studied the results of 22 full-scale compression load-tests and six full-scale 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.

Table 5.2: Soil Conditions Investigated for Drilled Displacement Piles
Geologic SettingSitesMajor Features
Alluvium in a major river (AR, CA, FL, IA, WA)5Loose to dense sand, some gravel, well-graded (primarily), clean to some silt and clay
Post Miocene (FL)4Loose (primarily) to medium silty, clayey sand
Barrier Island (Fl, AL, MD)4Medium to very dense sand, uniform, clean
Piedmont (GA)3Loose (primarily), silty sand/sandy silt, micaceous (toe in partially weathered rock)
Glacial Outwash (MN)1Loose to medium sand with fine gravel, clean, well-graded
Gulf Coastal Plain ( FL)1Loose to medium silty clayey sand
Colma Formation (CA)1Medium 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 end-bearing component for test piles where no instrumentation was available.

Figure 5.12 (a) and (b) shows correlations of the ultimate unit side-shear (fs) with CPT tip resistance (qc) and SPT-N values, respectively. SPT-N60 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 side-shear resistance (fs) for a given pile section can be correlated with qc or to SPT-N60 values as follows:

(Equation 5.28)

fs = 0.01 qc + WS for qc ≤ 200 tsf (20 MPa)

(Equation 5.29)

fS (tsf) = 0.05 N + WS for N ≤ 50

fS = 0.005 × N + WS for N ≤ 50

where the correlation constant (Ws) and limiting ultimate unit side-shear (fs) are as follows:

  • Ws = 0, and fs ≤ 0.16 MPa (1.7 tsf) for uniform, rounded materials having up to 40% fines.
  • Ws = 0.05 MPa (0.5 tsf) and fs ≤ 0.21 MPa (2.2 tsf) for well-graded angular materials having up to 10% fines.
  • For soil conditions with material properties falling between the provided ranges, a linear interpolation between the limiting values should be made.

Note that the recommended method for estimating the ultimate fs from CPT-qc values for DD piles (Figure 5.12), are more than twice that predicted by the alternative method (LPC) for computing fs from CPT-qc values for conventional CFA piles (Figure 5.5).

The ultimate unit end-bearing (qp) was correlated to either CPT-qc or SPT-N values obtained near the pile tip. SPT-N60 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 end-bearing capacity (qp) data, and the correlations with CPT-qc and SPT-N values, respectively. Capacities may be estimated according to the following relationships:

(Equation 5.30)

qp = 0.4 qc + WT < 19 MPa (200 tsf)

(Equation 5.31)

qp (MPa or tsf) = 0.19 N60 + WT for N60 ≤ 50

where the constant (WT) is as follows:

WT = 0, for qp ≤ 7.2 MPa (75 tsf) and uniform, rounded materials having up to 40% fines.

WT = 1.34 MPa (14 tsf), for qp ≤ 8.62 MPa (89 tsf) and well-graded 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 end-bearing (qp in units of tsf) from SPT-N60 values ranged from 0.6 N60 to 1.7 N60, respectively. The recommended method for ultimate unit end-bearing (qp in units of tsf) from SPT-N60 values for DD piles ranges from 1.9 N60 to 1.9 N60 + 14 tsf, depending on soil material properties. Similarly, the alternative method (LPC) for computing the ultimate unit end-bearing (qp) from CPT-qc values for conventional CFA piles was 0.375 qc. The recommended method for ultimate unit end-bearing (qp) from CPT-qc values for DD piles ranged from 0.4 qc to 0.4 qc + 14 tsf, depending on soil material properties.

Figure 5.12: Ultimate Unit Side-Shear Resistance for Drilled Displacement Piles for NeSmith (2002) Method

(a) Correlated to CPT Testing

Graphs illustrating ultimate unit side-shear resistance for drilled displacement piles for NeSmith (2002) method: (a) correlated to CPT testing, and (b) correlated to SPT testing. The figures also show results from various sources and show recommended relationships for clean, angular soil and for dirty, rounded, and uniform soil.

(b) Correlated to SPT Testing

Graphs illustrating ultimate unit side-shear resistance for drilled displacement piles for NeSmith (2002) method: (a) correlated to CPT testing, and (b) correlated to SPT testing. The figures also show results from various sources and show recommended relationships for clean, angular soil and for dirty, rounded, and uniform soil.

Note: N in Figure above refers to N60. Source: NeSmith (2002)

Figure 5.13: Ultimate Unit End-Bearing Resistance for Drilled Displacement Piles for NeSmith (2002) Method

(a) Correlated to CPT Testing

Graphs illustrating ultimate unit end-bearing resistance for drilled displacement piles for NeSmith (2002) method: (a) graph correlated to CPT testing, and (b) graph correlated to SPT testing. The figures also show results from various sources and show recommended relationships for clean, angular soil and for dirty, rounded, and uniform soil.

(b) Correlated to SPT Testing

Graphs illustrating ultimate unit end-bearing resistance for drilled displacement piles for NeSmith (2002) method: (a) graph correlated to CPT testing, and (b) graph correlated to SPT testing. The figures also show results from various sources and show recommended relationships for clean, angular soil and for dirty, rounded, and uniform soil.

Note: N in Figure above refers to N60. Source: NeSmith (2002)

5.4.3 Amelioration

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 soil-to-pile interface friction angle (δ) would have otherwise been smaller. They found amelioration with sand to increase an individual pile's side-shear resistance by approximately 25% over that of an individual pile constructed without amelioration. However, they found amelioration with sand to increase side-shear by only 16% of a single pile tested individually within a pile group (spaced at 3 pile diameters center-to-center) 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 side-shear resistance of individual piles by approximately 50% over that of an individual pile constructed without amelioration. The introduced free-draining 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 contractor-proposed method. However, with the use of performance-based 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 full-scale load-testing 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.

5.5 Group Effects On Static Axial Compression Load Resistance Of CFA Piles

5.5.1 Introduction

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

Graphical illustration showing overlapping zones of influence in a frictional pile group.

Source: Hannigan et al. (2006)

5.5.2 Group Efficiencies

The efficiency of a pile group (ηg) is defined as:

(Equation 5.32)
ηg =Rug
 
n 
ΣRu,i
i = 1 

where Rug is the ultimate resistance of the pile group, and Ru,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 at-rest (Ko) 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.

5.5.2.1 Conventional CFA Pile Groups

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 block-type failure mode (i.e., bearing failure). The group capacity should be checked to see if a block-type 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 site-specific 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 center-to-center spacing of 2.5 diameters,

η = 1.0 for a center-to-center 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 small-scale 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 center-to-center spacing of approximately 3 to 4 diameters, and that 0.67 may be a lower bound for group efficiencies. Note that a typical center-to-center 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 model-scale 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, poorly-graded silty sand with SPT-N values ranging from 5 to 15. The efficiency vs. the ratio of spacing to diameter (S/Bshaft) 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 side-shear resistance was not reported. The group effects on side-shear and end-bearing 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 end-bearing than with the cap not in contact with the ground for comparable spacing-to-diameter ratios.

Figure 5.15: Efficiency (η) vs. Center-to-Center Spacing (s), Normalized by Shaft Diameter (Bshaft), for Underreamed Model Drilled Shafts in Compression in Moist, Silty Sand

Graphical illustration showing pile efficiency as a function of center-to-center spacing, normalized by shaft diameter, 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 Nine-Shaft Group in Moist Alluvial Silty Sand

Two graphical illustrations showing the unit side and base resistances for model single shaft and typical shaft in a nine-shaft group in moist alluvial silty sand. The figure shows the unit side and base resistances as functions of the normalized spacing the effects of the presence of the pile cap.

Source: O'Neill and Reese (1999)

Senna et al. (1993) conducted model axial compression tests in clayey sand with SPT-N 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 center-to-center spacing of 3 diameters, and all caps were in contact with the ground.

Table 5.3: Efficiency (η) for Model Drilled Shafts Spaced 3 Diameters Center-to-Center in Various Group Configurations in Clayey Sand (Senna et al, 1993)
Configuration2 × 1 Pile Bent3 × 1 Pile Bent3 Triangular Pile Group4 Square Pile Group
Efficiencyη = 1.1η = 1.1η = 1.04η = 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 post-construction in-situ 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 well-conceived 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 project-specific 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)
ηg =RBlock≤ 1
 
n 
ΣRu,i
 i = 1  

The resistance of the block failure (RBlock) mode can be simply estimated as the sum of the side-shear resistance contribution from the peripheral area of the block, as shown in Figure 5.17, and the end-bearing capacity contribution from the block footprint area:

(Equation 5.34)

RBlock = 2 fs [ D Z + B ] + qp ( Z B )

where: D, Z, and B are the depth, length, and width of the block, respectively, fs is the ultimate unit side-shear resistance of the block, Ru,i is the individual pile ultimate resistance and qp is the ultimate unit end-bearing capacity for the block, Ru,i is estimated as described in Section 5.3 for conventional CFA piles.

Most often, the limiting pile-to-soil 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 pile-to-soil (δ) and soil-to-soil (φ) friction angles. The ultimate unit end-bearing capacity for the block is similar to that determined for a single pile; however, the ultimate unit end-bearing 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 qp by the methods presented in Section 5.3 for this deeper zone of influence.

Figure 5.17: Block Type Failure Mode

Illustration showing 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 (Ru,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.

5.5.2.2 Drilled Displacement Pile Groups

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 (RBlock) is estimated as described in Section 5.5.3, while the individual pile ultimate resistance (Ru,i) is estimated as described in Section 5.4 (for auger displacement piles).

Cohesive Soils

A study by Brown and Drew (2000) of full-scale 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 in-between these extremes. Although not tested as a group, comparisons showed an increase in unit side-shear resistance of approximately 100% of the single interior pile within a 5-pile group (spaced at 3 pile diameters center-to-center) over an isolated pile. Also tested and compared was an isolated pile and a 5-pile group (spaced at 3 pile diameters center-to-center), all of which were constructed using an amelioration technique with coarse sand. The same comparison yielded an increase in unit side-shear resistance of 90% for the single interior central pile of the five-pile 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 on-centers and increase to an efficiency of 1.0 for a pile spacing of 6 diameters or greater on-centers.

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 (RBlock) is estimated as described in Section 5.5.3, while the individual pile ultimate resistance (Ru,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 (Ru,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.

5.5.3 Settlement of Pile Groups

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 time-dependant 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 End-Bearing Pile Group than for a Single Pile

Illustration showing deeper zone of influence (i.e., heavily stressed zone) for end-bearing 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 settlement-sensitive 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.

5.5.3.1 Elastic Compression of the Pile

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)
SR = L × Esoil 
  
BEpile

where: L = pile embedment depth, B = pile diameter, Esoil = average Young's modulus of the soil, and Epile = Young's modulus of the pile.

For many practical problems, a pile may be considered "rigid" if its stiffness ratio (SR) is approximately SR ≤ 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 side-shear or end-bearing 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 =
n
Σ
i = 1
Qi - Li
 
Ai - Ei

Where: Li, Ai, and Ei are the length, average cross-sectional area, and average composite modulus, respectively, for each of the pile segments. Qi 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 end-bearing 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 side-shear 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 ×Qmax × Lpile
  
2Apile × Epile

Where: Qmax is the total maximum imposed load and Lpile and Apile are the pile total length and cross-sectional area, respectively.

An upper bound (other than the possibility of downdrag) is represented by a pile acting as a free-standing column with no load transfer along the entire length of the pile and the total maximum imposed load to the pile-supported in end-bearing. For this condition, Equation 5.38 provides an upper bound estimate of elastic shortening in the pile.

(Equation 5.38)
Δmax =Qmax × Lpile
 
Apile × Epile

Note that downdrag or soil swell conditions could present a more significant pile load, and for such a case Qmax 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.

5.5.3.2 Compression Settlement in Cohesionless Soils

Meyerhof (1976) recommended that the compression settlement of a pile group (Sgroup) in a homogeneous sand deposit (not underlain by a more compressible soil at greater depth) be conservatively estimated by the correlations to either SPT-N values or to CPT-qc values. If the group was underlain by cohesive deposits, time-dependant consolidation settlements would be needed, as described in the following section. The method proposed by Meyerhof (1976) does not distinguish 60% hammer efficiency for N-values. However, the 60% correction is recommended.

For SPT-N values in cohesionless soils:

(Equation 5.39)
Sgroup =0.96 pf If Bfor sands
 
N60′ 
(Equation 5.40)
Sgroup =1.92 pf If Bfor silty sands
 
N60′ 

For CPT qc values in cohesionless saturated soils:

(Equation 5.41)
Sgroup =42 pf If B
 
qc

where:

Sgroup=estimated total settlement (in.);
pf=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)
If=influence factor for group embedment = 1 - D/(8B) ≥ 0.5;
N60′ =average corrected SPT-N value (bpf per 0.3 m) within a depth B below the pile tip level; and
qc =average static cone tip resistance (tsf) within a depth B below the pile tip.
5.5.3.3 Consolidation Settlement in Cohesive Soils

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 settlement-sensitive 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 post-construction settlements. Time rate of primary consolidation is a topic covered in most geotechnical texts and in the FHWA Soils and Foundations Workshop Manual (FHWA NH1-06-088).

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 (pd 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

Illustration showing equivalent footing concept for pile groups. Figure shows the increase in the size of the loaded area under the tip of the pile group.

Source: Hannigan et al. (2006)

The settlement (Si) for an overconsolidated cohesive soil layer, where the pressure after the foundation pressure increase is greater than the soil preconsolidation pressure (po + Δp > pc), is obtained as:

(Equation 5.42)
Si = H Crlog pc  + H Cclog pσ + Δp  
    
1 + e0p01 + e0pc

The settlement (Si) for an overconsolidated cohesive soil layer, where the pressure after the foundation pressure increase is less than the soil preconsolidation pressure (po + Δp < pc), is obtained as:

(Equation 5.43)
Si = H Crlog p0 + Δp  
  
1 + eσpσ

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

Illustrations showing 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, and (d) piles supported by shaft and toe resistance in layered soil profile.

c) Piles Supported by Shaft Resistance in Sand Underlain by Clay
d) Piles Supported by Shaft and Toe Resistance in Layered Soil Profile

Illustrations showing 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, and (d) piles supported by shaft and toe resistance in layered soil profile.

Notes:

  1. Plan area of perimeter of pile group = (B)(Z).
  2. Plan area (B1)(Z1) = projection of area (B)(Z) at depth based on shown pressure distribution.
  3. For relatively rigid pile cap, pressure distribution is assumed to vary with depth as above.
  4. For flexible slab or group of small separate caps, compute pressures by elastic solutions.

Source: Cheney and Chassie (1993) and Hannigan et al. (2006)

Figure 5.21: Typical e vs. Log p Curve from Laboratory Consolidation Testing

Illustration showing typical curve of void ratio as a function of the log of pressure from laboratory consolidation testing.

Source: Hannigan et al. (2006)

The settlement for a normally consolidated cohesive soil layer (po = pc) is:

(Equation 5.44)
Si = H Cclog po + Δp  
  
1 + eopo

where:

Si=total settlement;
H=original thickness of layer;
Cc=compression index;
Cr=recompression index;
eo=initial void ratio;
po=effective overburden pressure at midpoint of stratum, prior to pressure increase;
pc=estimated preconsolidation pressure; and
Δ=average change in pressure.

If the soil were underconsolidated (i.e., po > pc), 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.

5.5.4 Uplift of Single CFA Piles and CFA Pile Groups

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 side-shear 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 high-strength 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 side-shear resistance may be determined as a portion of the ultimate downward side-shear 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 side-shear from the pile can produce a potential reduction in effective stress in the vicinity of the pile. The ultimate uplift side-shear resistance in cohesionless soils can be maintained up to 100%. However, it has been determined in numerous studies that the remaining side-shear resistance range from about 70 to 100% of the downward ultimate resistance. It is recommended that to obtain the ultimate side-shear resistance in cohesionless soils for uplift the side-shear 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:

  1. The design allowable uplift capacity of a single pile times the number of piles in the group. The design uplift capacity of a single pile has been specified above. The design allowable uplift should be taken as one third of the ultimate, if determined by a static analysis method, or one half, if determined by a load test.
  2. Two thirds of the effective weight of the group and soil contained within a block defined by the perimeter of the pile group and the embedded length of the piles (see Figure 5.17).
  3. One half of the effective weight of the pile group and soil contained within a block defined by the perimeter of the pile group and the embedded pile length plus one half of the total soil shear resistance on the peripheral surface of the pile group (see Figure 5.17).

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 side-shear 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.

5.6 Lateral Resistance And Structural Capacity Of CFA Piles

5.6.1 Behavior and Limitations of CFA Piles

Although published results are limited, lateral load-tests 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 load-tests on CFA piles include O'Neill et al. (2000) in over-consolidated 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, free-draining cohesionless soil will allow bleed water from the concrete or grout mix to escape into the surrounding soil; this rapid fluid loss limits the in-situ workability of the remaining grout. Penetration ability for a full reinforcing steel cage in free-draining 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 cross-sectional 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 FB-Pier (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.

5.6.2 Lateral Analyses Using the p-y Method

The p-y method is recommended for lateral load analyses of vertical CFA piles and pile groups. The p-y method is a general method for analyzing laterally loaded piles with combined axial and lateral loads, including distributed loads along the pile, non-linear bending characteristics (including cracked sections), layered soils and/or rock, and non-linear 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 non-linear 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 bi-linear in the preceding figure, actual p-y curves used for design are usually more complex-curvilinear functions. The nonlinear soil resistance (p) as a function of displacement (y) has been derived from instrumented full-scale load-tests in a variety of soils. From these instrumented tests and simple theory of passive earth pressure response around a pile, empirical correlations of p-y 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 user-developed curve of any shape (presumably based on local experience, correlations with in-situ 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 (Su), a stiffness parameter associated with strain at a compressive stress equal to 50% of the compressive strength from uniaxial strength testing (ε50), 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: p-y Soil Response of Laterally Loaded Pile Model

Illustration showing p-y 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 beam-column 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)
EId4y+ Pxd2y- p - w = 0
  
dx4dx2

where:

x=distance along pile length;
Px=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 cross-section; 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 (FHWA-RD-85-106):

(Equation 5.46)
V = EId3y
 
dx3
(Equation 5.47)
M = EId2y
 
dx2
(Equation 5.48)
S =dy
 
dx

In addition to the axial load, the boundary conditions at the pile head must be specified by a lateral force (Pt) and a moment (Mt), 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 free-head 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 free-standing 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 fixed-head 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

Two graphs illustrating example deflection and moment response of a laterally loaded pile model.

The nonlinear p-y relationship described earlier is implemented at each node by using a secant modulus (Es), as indicated below:

(Equation 5.49)
Es =p
 
y

Therefore, at each node (i) along the length of the pile, the value of soil reaction (pi) is expressed as the secant modulus multiplied by the deflection (or Esi yi). Because the p-y 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 p-y curves to incorporate features such as strain-softening, loss of resistance due to cyclic loading, and other deflection-dependent effects on soil resistance that may be observed in experiments.

Non-linear stress-strain 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 Stress-Strain Relationship Used for Steel Reinforcement

Illustration showing typical stress-strain relationship used for steel reinforcement.

Source: O'Neill and Reese (1999)

For steel, the value of yield stress (fy) 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 (εy = fy /E).

Figure 5.25: Typical Stress-Strain Relationship Used for Concrete

Illustration showing typical stress-strain 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 28-day cylinder compressive strength. The strength is expressed as

(Equation 5.50a)
fc = f″c 2 ε - ε 2 for: ε < εo
  
εoεo
(Equation 5.50b)

fc = 0.85 f″c for: ε < 0.038

fc = linearly interpolated for εoε ≤ 0.038

With:

(Equation 5.51)

f″c = 0.85 f′c

(Equation 5.52)
εo =1.7 f′c
 
Ec

Where f′c is the concrete compressive strength at 28 days, and Ec is the initial tangent slope of the stress-strain area. The value Ec can be estimated as:

(Equation 5.53a)

Ec = 57,000 f′c (psi)

or

(Equation 5.53b)

Ec = 151,000 f′c (kPa)

The ultimate tensile strength of concrete (fr) is estimated as

(Equation 5.54a)

fr = 7.5 f′c (psi)

or

(Equation 5.54b)

fr = 19.7 f′c (kPa)

The authors' experience from observed behavior of instrumented load-tests 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 (Px) will produce a uniform compressive stress (Px × 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

Graphical illustration showing variation of pile stiffness with bending moment and axial load.

5.6.3 Lateral Analyses of CFA Pile Groups

The p-multiplier (Pm) 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 p-y relationship are multiplied by a p-multiplier less than 1 (i.e., Pm<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 p-multipliers (Pm) are provided in Table 5.4 for cyclic loading and static loading.

Figure 5.27: The p-multiplier (Pm)

Illustration showing the p-multiplier concept for a number of pile groups.

Source: Hannigan et al. (2006)

Table 5.4: P-Multipliers (Pm) for Design of Laterally Loaded Pile Groups
Soil Type(1)Test TypePile Spacing
(Cent.-Cent.)
Pm for Rows:
1 2 3+
Reported Lateral Group EfficienciesDeflection
(mm)
Reference
Stiff ClayField Study3B.70 .50 .40N/A51Brown et al. (1987)
Stiff ClayField Study3B.70 .60 .50N/A30Brown et al. (1987)
Medium ClayScale Model (Cyclic Load)3B.60 .45 .40N/A600 (at 50 cycles)Moss (1997)
Clayey SiltField Study3B.60 .40 .40N/A25-60Rollins et al. (1998)
V. Dense SandField Study3B.80 .40 .3075%25Brown et al. (1998)
M. Dense SandCentrifuge Model3B.80 .40 .3074%76McVay et al. (1995)
M. Dense SandCentrifuge Model5B1.0 .85 .7095%76McVay et al. (1995)
Loose M. SandCentrifuge Model3B.65 .45 .3573%76McVay et al. (1995)
Loose M. SandCentrifuge Model5B1.0 .85 .7092%76McVay et al. (1995)
Loose F. SandField Study3B.80 .70 .3080%25-75Ruesta and Townsend (1997)

Note: (1) V = very, M = medium, F = fine

Computer programs such as GROUP (Ensoft, 2006) or FB-Pier (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 p-multipliers by multiplying individual p-multipliers (Pm) and p-y curves for individual piles. Recent studies (Brown and O'Neill 2003) suggest that a simplified approach to the use of p-multipliers is suitable for design, particularly when considering that the direction of loading may not be known. A single p-multiplier equal to the average value of all the pile row p-multipliers 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 p-multipliers applied to the individual p-y 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.

5.6.4 Structural Capacity

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, cast-in-place structural elements, some differences exist. Drilled shafts often have larger diameters and consist of non-redundant 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 per-pile 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 p-y 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.

5.6.4.1 Longitudinal Reinforcement

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. High-strength, 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 (Ag) 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 (Ag) 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 (Ag) 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 (Ag).

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

Illustration showing the strain and stress distributions of a circular column (pile) under combined compression and 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

Graphical illustration showing example of an interaction diagram for a concrete section for combined axial load and flexure. Figure shows both nominal ultimate and factored interaction curves.

Source: O'Neill and Reese (1999)

The factored axial resistance (i.e., the intersection of the solid line with the Px-axis for axial compressive load only) is obtained as follows:

(Equation 5.55)

Pn = β PS = β [ 0.85 f′c ( Ag - As ) + fyAS ]

where:

Pn=nominal ultimate axial resistance;
f′c=compressive concrete strength at 28-days;
fy=yield strength of the longitudinal reinforcing steel;
Ag=gross cross-sectional area of concrete;
As=cross-sectional 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 Ag

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 (Px) and the nominal ultimate flexural resistance (Mx) by a resistance factor (φ),

(Equation 5.57)

Pr = φ Px and Mr = φ Mx

where φ = 0.75 for either spiral or tied transverse reinforcement (AASHTO, 2006)

The factored flexural resistance for pure flexure (i.e., Px = 0) is determined as 0.9 of the nominal ultimate flexural resistance, or 0.9 M. For locations between Px = 0 and Px = P′, the factored resistance is obtained by multiplying the nominal ultimate flexural resistance by a factor linearly interpolated between φ = 0.9 (for Px = 0) and φ = 0.75 (for Px = 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 Px = 0 side of the diagram.

5.6.4.2 Shear Reinforcement

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 Vn) of the concrete section can be determined as follows:

(Equation 5.58)

φ Vn = φ Vc AV

Where:

Vn=nominal (computed, unfactored) shear resistance of section;
φ=capacity reduction factor for shear, usually equal to 0.85;
AV=cross-sectional area that is effective in resisting shear; and
Vc=concrete shear strength.

The cross-sectional area that is effective in resisting shear can be evaluated for a circular CFA pile as:

(Equation 5.59)
AV = B B+ 0.58 rls 
 
2

where

(Equation 5.60)
rls =B- dc -db
  
22

where:

rls=radius of the ring formed along the centroids of the longitudinal bars;
B=pile diameter;
dc=depth of concrete cover; and
db=diameter of longitudinal bars.

The concrete shear strength can be estimated as:

(Equation 5.61a)
Vc = 1 + 0.00019 φP f′c (f′c in psi)
 
Ag
(Equation 5.61b)
Vc = 0.166 + φ 0.000032P f′c (f′c in MPa)
 
Ag

Where P = axial load and Ag = gross concrete area.

For a pure bending case (i.e., Px = 0), this reduces to: Vc = f′c (f′c in psi) or Vc = 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 p-y 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)
ρS = 0.45 Ag- 1  f′c 
  
Acfy

where:

ρS=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 = Ac × pitch of spiral;
Ac=cross-sectional area of concrete inside spiral steel = 0.25 × π × (core diameter)2;
A=gross cross-sectional area of concrete of pile cross section;
f′c=concrete compressive strength at 28-days; and
fy=yield strength of the spiral reinforcing steel.

If a tied bar is used for the transverse reinforcement, the minimum requirement is:

  • #3 tied bars may be used for cages with longitudinal reinforcing smaller than # 11 bars
  • #4 tied bars may be used for cages with longitudinal reinforcing of #11 bars or larger.

The vertical spacing of the tied bars shall not exceed the lesser of:

  • the pile diameter; or
  • 300 mm (12 in.).

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)
Avs =S Vsteel
 
fy B+ 0.58 rls 
  
2

Where:

Avs=required area of transverse steel;
S=longitudinal spacing of the ties (spiral pitch);
Vsteel=nominal shear resistance of transverse steel (equal to total nominal shear resistance needed less shear resistance provided by concrete);
fy=yield strength of steel; and
rls=radius of the ring formed along the centroids of the longitudinal bars on cross section.
5.6.5 Concrete or Grout Cover and Cage Centering Devices

The concrete cover requirements of Section 5.12.3 AASHTO (AASHTO, 2006) apply for CFA piles. For water-to-cement 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 axis-symmetric 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.

5.6.6 Seismic Considerations

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 seismically-induced lateral ground movements. The most significant in this case is liquefaction and lateral spreading. Seismically-induced 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.

5.7 Downdrag In CFA Piles

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 side-shear 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 limit-state on the left occurs when the combination of the applied load and downdrag load produces both side-shear and end-bearing resistance failures in the founding stratum. The limit-state 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 limit-state on the right side of Figure 5.31 represents the true ultimate geotechnical limit-state 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 limit-state on the left side is customarily considered to be the strength limit-state 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

Illustration showing example 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) side-shear. The pile resistance is then the positive (upward) side-shear and end-bearing 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 end-bearing resistance (RBd) matches that value predicted by static analyses or load-tests. 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

Illustration showing 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 (Ee) calculated as follows:

(Equation 5.64)
Ee = Ec Apiles + Est 1 -Apiles 
  
AgroupAgroup

Where:

Ee=average Young's modulus of equivalent pier within the compressible layer;
Ec=Young's modulus of pile (concrete or grout);
Est=Young's modulus of geomaterial between piles;
Apiles=cross-sectional area of all the piles in the group; and
Agroup=cross-sectional area of the pile group, not including overhanging cap area.

Note that for typical spacing of 3 pile diameters center-to-center 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

Illustration showing the distribution of load transfer along a pile under downdrag. Figure illustrates the concept of the neutral plane.

Source: O'Neill and Reese (1999)

Figure 5.33: Mechanics of Downdrag in a Pile Group

Illustration showing mechanics of downdrag in a pile group.

Source: O'Neill and Reese (1999)

5.8 Example Problems: Axial Capacity Of Single Piles

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 full-scale load-testing 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.

5.8.1 Conventional CFA Pile in Cohesive Soils

Solution

The side-shear resistance (RS) 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 side-shear 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 side-shear is disregarded from the top soil layer estimate, and the bottom 1-diameter (1.5 ft) of side-shear 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 side-shear resistance. From Equation 5.2:

Rs =Nfs,i π Di Li = fs (Top Layer) π D L(Top Layer) + fs (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 side-shear 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 side-shear resistance);
fs=α Su,ave; fs is estimated from Equation 5.5 for both the top and bottom layers, as shown below. Note that this will yield an ultimate unit side-shear resistance.

The maximum undrained shear strength, Su,max, for this profile is 2.5 ksf, which yields a ratio of Su,max/Pa ≈ 1.25. Therefore, α = α(Top Layer) = α(Bottom Layer) = 0.55, from Equation 5.6.

Su,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.

Su,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).

fs (Top Layer) = 0.55 × (0.60 ksf) = 0.33 ksf

fs (Bottom Layer) = 0.55 × (1.79 ksf) = 0.98 ksf

Then, it results:

RS = (0.33 ksf) × π × (1.5 ft) × (24 ft) + (0.98 ksf) × π × (1.5 ft) × (29.5 ft)

RS = 37.3 kips + 136.2 kips = 173.5 kips

The end-bearing resistance (RB) for a pile embedment depth of 60 ft is estimated per the recommended method detailed in Section 5.3.1.1. The end-bearing resistance is estimated for the bottom soil layer according to Equation 5.4:

RB = qp π D2 
 
4

where:

D=1.5 ft, the nominal diameter of the pile
qp=N*c Su from Equation 5.7
Su (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
Nc*=8.71, as interpolated from Table 5.1 for an undrained shear strength of 2.12 ksf = 1.06 tsf
qp=(8.71) × (2.12 ksf) = 18.46 ksf
RB=(18.46 ksf) × (π/4) × (1.5 ft)2 = 32.6 kips

The total axial resistance (RT) for a pile embedment depth of 60 ft is the sum of the side-shear resistance and the end-bearing resistance, according to Equation 5.1:

RT = RS + RB = 173.5 kips + 32.6 kips = 206.1 kips

Note that this is the ultimate geotechnical axial resistance.

The allowable static axial resistance (Rallowable) is obtained in accordance with ASD and a Safety Factor, SF = 2.0.

Rallowable = RT / SF = (206.1 kips) / 2.0 = 103.1 kips

5.8.2 Conventional CFA and Drilled Displacement Piles in Cohesionless Soils

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 SPT-N values, soil descriptions, and unit weights. N values are assumed to correspond to 60% hammer efficiency. While the pier location is usually accessible by track-mounted 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 SPT-N 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 Su vs. Depth for Example Problem of CFA Pile in Cohesive Soil

Graphical illustration showing profile of soil undrained shear strength with depth for example problem of CFA pile in cohesive soil.

Conventional CFA Pile Calculations

The side-shear resistance (RS) 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 side-shear contribution be discounted to a depth of 6 ft. Further, the solution in this example has assumed a worst-case "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:

Rs =Nfs,i π Di Li
Σ
i

Figure 5.35: Soil Profile SPT-N vs. Depth for Example Problem of CFA Pile and DD Pile in Cohesionless Soil

Graphical illustration showing profile of SPT-N with depth for example problem of CFA pile and drilled displacement pile in cohesionless soil.

For this example with N = 6 pile segments and a constant nominal pile diameter, it results:

Rs = D6fs,i Li
Σ
i

where:

D=1.5 ft (the same for both top and bottom layers)
fs=K σv tan φ = β σv from Equations 5.17 and 5.18

and β = 1.5 - 0.135 Z0.5 (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

σv = (γsat - γwater) 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: fs(3) = (1.2) × (0.120 - 0.0624 kcf) × (7 - 6 ft) = 0.07 ksf (β limited to 1.2)

Pile Segment 4: fs(4) = (1.2) × (0.120 - 0.0624 kcf) × (9.5 - 6 ft) = 0.24 ksf (β limited to 1.2)

Pile Segment 5: fs(5) = [1.5 - 0.135 × (12 - 6)0.5] × (0.120 - 0.0624 kcf) × (12 - 6 ft) = 0.40 ksf

Pile Segment 6: fs(6) = [1.5 - 0.135 × (15.1 - 6)0.5] × (0.120 - 0.0624 kcf) × (15.1 - 6 ft) = 0.57 ksf

RS = 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)}

RS = 18.4 kips

The end-bearing resistance (RB) 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:

RB = qp π D2 
 
4

where:

D=1.5 ft is the nominal diameter of the pile
qp (ksf)=0.6 Nave from Equation 5.20
Nave=(22 + 26 blows/ft)/2 = 24 blows/ft, from the N values at the tip and 5 ft below the tip.
qp=0.6 × (24) × (2 ksf/ 1 tsf) = 28.8 ksf
RB=(28.8 ksf) × (π/4) × (1.5 ft)2 = 50.9 kips

The total axial resistance (RT) for a pile embedment depth of 17 ft is the sum of the side-shear resistance and the end-bearing resistance, according to Equation 5.1:

RT = RS + RB = 18.4 kips + 50.9 kips = 69.3 kips

Note that this is the ultimate geotechnical axial resistance.

The allowable static axial resistance (Rallowable) is obtained for a Safety Factor, SF = 2.5:

Rallowable = RT / SF = 69.3 kips / 2.5 = 27.7 kips

DD Pile Calculations

The side-shear resistance (RS) 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 side-shear contribution be discounted to a depth of 6 ft. From Equation 5.2:

Rs =Nfs,i π Di Li
Σ
i

For this example with N = 6 pile segments and a constant nominal pile diameter is results:

Rs = π D6fs,i Li
Σ
i

where:

D=1.5 ft (the same for both top and bottom layers)
fs (ksf)=(0.05 N) (2 ksf/ 1 tsf) + WT, from Equation 5.31, and limited to N60 ≤ 50.
WT=0 for 6-pile segments, all lying within the soil layer (silty fine sand). Note that fs would be limited to 3.4 ksf for well-rounded and poorly-graded soils, and limited to 4.4 ksf for angular well-graded soils. If the pile segments had been into the last layer (i.e., Shelly sand), WT = 1 ksf for these angular, well-graded soils. See Section 5.4.2 for details pertaining to the selection of WT.

Pile Segment 1: Disregarded (above scour and pile cap)

Pile Segment 2: Disregarded (above scour and pile cap)

Pile Segment 3: fs(3) = (0.05) × (19 blows/ft) × (2 ksf/1 tsf) + (0 ksf) = 1.90 ksf

Pile Segment 4: fs(4) = (0.05) × (24 blows/ft) × (2 ksf/1 tsf) + (0 ksf) = 2.40 ksf

Pile Segment 5: fs(5) = (0.05) × (25 blows/ft) × (2 ksf/1 tsf) + (0 ksf) = 2.50 ksf

Pile Segment 6: fs(6) = (0.05) × (22 blows/ft) × (2 ksf/1 tsf) + (0 ksf) = 2.20 ksf

RS = 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)]

RS = 116.7 kips

The end-bearing resistance (RB) 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:

RB = qp π D2 
 
4

where:

D=1.5 ft, the nominal diameter of the pile
qp (ksf)=1.9 N(ave) (2 ksf/1 tsf) + WT, from Equation 5.33 and limited to N60 ≤ 50.
Nave=(25 + 22 + 26 + 9) / 4 = 20.5 blows/ft, from the SPT-N values 6.25 ft above and 10 ft below the tip. Note that qp would be limited to 150 ksf for well-rounded and poorly-graded soils and limited to 178 ksf for angular, well-graded soils.
qp=1.9 × (20.5) × (2 ksf/1 tsf) + 0 = 77.9 ksf
RB=(77.9 ksf) × (π/4) × (1.5 ft)2 = 137.7 kips

The total axial resistance (RT) for a pile embedment depth of 17 ft is the sum of the side-shear resistance and the end-bearing resistance according to Equation 5.1:

RT = RS + RB = 116.7 kips + 137.7 kips = 254.4 kips

Note that this is the ultimate geotechnical axial resistance.

The allowable static axial resistance (Rallowable) is obtained in for a Safety Factor (SF = 2.5).

Rallowable = RT/SF = 254.4 kips / 2.5 = 101.7 kips

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Updated: 04/07/2011
 

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