Axial Capacity Methods for Axially Loaded Single Piles
The following axial capacity methods are included in the PileAXL program:
​Driven Piles:
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​(1) API Clay
(2) API COMM Clay
(3) USACE Clay
(4) ICP Clay
(5) NGI Clay
(6) UWA Clay
(7) Alpha Clay
(8) User Clay
(9) API Sand
(10) API RP2GEO Sand
(11) USACE Sand
(12) ICP Sand
(13) Furgo Sand
(14) UWA Sand
(15) NGI Sand
(16) SPT-N Method (Clay and Sand)
(17) LCPC CPT Method (Clay and Sand)
(18) User Sand
(19) General Rock
Bored Piles or Drilled Shafts:
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​(1) FHWA Clay
(2) Alpha Clay
(3) User Clay
(4) FHWA Sand
(6) FHWA Gravels
(8) Beta Sand
(9) SPT-N Method (Clay and Sand)
(10) UWA CPT Method (Clay and Sand)
(11) LCPC CPT Method (Clay and Sand)
(12) User Sand
(13) Weathered Rock - Rowe and Armitage
(14) Weathered Rock - Williams and Pells
(15) Weathered Rock - Zhang and Einstein
(16) Weathered Rock - Pells et al
FHWA Clay - Bored Piles or Drilled Shafts
FHWA Clay method for bored piles or drilled shafts is based on the approach recommended in FHWA manual (O’Neill and Reese 1999). The following equations are adopted in the PileAXL program to calculate the ultimate shaft resistance, fs and ultimate end bearing resistance, fb:
where su is undrained shear strength and pa is the atmospheric pressure (100 kPa).
​where L is pile length and D is the pile diameter. Note that fb cannot be greater than 3800 kPa for bored piles within the cohesive soils according to O’Neill and Reese (1999) and Nc cannot be greater than 9.0.
Alpha Clay - Bored Piles or Drilled Shafts
Alpha Clay method available in the PileAXL program calculates the ultimate shaft resistance (fs) and ultimate end bearing resistance (fb) based on the following equations:
where su is undrained shear strength and α is the adhesion factor which can be defined by the users.
User Clay - Bored Piles or Drilled Shafts
User Clay method in the PileAXL program allows the users to directly define the ultimate shaft resistance (fs) and ultimate end bearing resistance (fb).
FHWA Sand - Bored Piles or Drilled Shafts
For the cohesionless soils, the following equations as recommended in FHWA manual (O’Neill and Reese 1999) are adopted to calculate the ultimate shaft resistance, fs for sand:
where z is the depth below the ground surface, σz' is the effective overburden pressure and ɸ is the effective friction angle of the sand.
The calculation of the ultimate end bearing resistance, fb based on the effective friction angle is carried out by the following equations:
FHWA Gravel - Bored Piles or Drilled Shafts
For the cohesionless soils, the following equations as recommended in FHWA manual (O’Neill and Reese 1999) are adopted to calculate the ultimate shaft resistance, fs for gravel:
where z is the depth below the ground surface, σz' is the effective overburden pressure and ɸ is the effective friction angle of the sand.
The calculation of the ultimate end bearing resistance, fb based on the effective friction angle is carried out by the following equations:
FHWA Gravelly Sand - Bored Piles or Drilled Shafts
For the cohesionless soils, the following equations as recommended in FHWA manual (O’Neill and Reese 1999) are adopted to calculate the ultimate shaft resistance, fs for gravelly sand:
where z is the depth below the ground surface, σz' is the effective overburden pressure and ɸ is the effective friction angle of the sand.
The calculation of the ultimate end bearing resistance, fb based on the effective friction angle is carried out by the following equations:
FHWA Sand Rational Beta - Bored Piles or Drilled Shafts
For the cohesionless soils, the following equations as recommended in Chen and Kulhawy (2002) as described in FHWA-NHI-10-016 (2010) are adopted to calculate the ultimate shaft resistance, fs for granular materials:
where σz' is the effective overburden pressure, ɸ' is the effective friction angle of the sand, σp' is the effective vertical preconsolidation stress, n and m are the empirical constants for correlating SPT values with σp' as suggested by Mayne (2007) and Kulhawy and Chen (2007). The typical values are 0.47 for n and 0.8 for m.
The calculation of the ultimate end bearing resistance, fb based on the effective friction angle is carried out by the following equations:
Beta Sand - Bored Piles or Drilled Shafts
Beta Sand method uses the following equation to calculate the ultimate shaft resistance, fs for sand and gravel:
where β is the factor for shaft resistance input by the users and σz' is the effective overburden pressure.
The calculation of the ultimate end bearing resistance, fb based on the effective friction angle is carried out by the following equations:
SPT-N Method - Driven and Bored Piles
SPT-N method in the PileAXL program calculates the ultimate shaft resistance, fs and ultimate end bearing resistance, fb based on the following empirical relationships for both driven and bored piles:
where N is SPT-N value, α and β are the empirical factors for ultimate shaft resistance and K is the empirical factor for ultimate end bearing resistance.
​The recommended empirical factors of α and β for ultimate shaft resistance and K for ultimate end bearing resistance are summarised in CIRIA Report 143 by Clayton (1995) for different pile types (driven displacement, driven cast-in-place and bored).
UWA CPT Method - Bored Piles and CFA Piles
​CPT method in the PileAXL program calculates the ultimate shaft resistance fs and ultimate end bearing resistance fb based on the following empirical relationships from Doan and Lehane (2021) for bored piles and CFA (continuous flight auger) piles:
Where ft/fc is loading direction parameter, which is 1.0 for compression and 0.8 for tension, Ic is CPT soil behaviour type index, qt is corrected cone tip resistance and pa is atmosphere pressure and is adopted to be 101 kPa.
LCPC CPT Method - Driven and Bored Piles
LCPC CPT method is based on the approach from Bustamante and Gianeselli (1982) where 197 pile tests were reviewed for a wide range of pile and soil types. This method is also known as LCP or LPC method. The ultimate shaft resistance (fs) and ultimate end bearing resistance (fb) are calculated based on the following equations:
where qc is cone tip resistance, αLCPC is the friction coefficient, kc is the end bearing coefficient and qca is the equivalent average cone resistance.
​The recommended empirical factors of α and β for ultimate shaft resistance and K for ultimate end bearing resistance are summarised in CIRIA Report 143 by Clayton (1995) for different pile types (driven displacement, driven cast-in-place and bored).
User Sand - Bored Piles or Drilled Shafts
User Sand method in the PileAXL program allows the users to directly define the ultimate shaft resistance (fs) and ultimate end bearing resistance (fb).
Weathered Rock - Rowe and Armitage - Bored Piles or Drilled Shafts
​Weathered rock – Rowe and Armitage method for bored piles or drilled shafts calculates the ultimate shaft resistance, fs based on the following relationships:
where σc is the unconfined compressive strength (UCS) in MPa, α and β are the factors for shaft resistance. For regular clean sockets (roughness R1, R2 and R3 as defined in the table below). the shaft resistance factors are adopted as below based on Rowe and Armitage (1987):
The shaft resistance factors are adopted as below based on Rowe and Armitage (1987):
​For clean, rough (R4) sockets, the shaft resistance factors are adopted as below based on Rowe and Armitage (1987):
The ultimate end bearing resistance, fb based on Rowe and Armitage (1987) is calculated using the relationship below:
where σc is the unconfined compressive strength (UCS) in MPa and Ncr is the bearing capacity factor which is adopted as 2.5 based on Rowe and Armitage (1987).
The rock elastic mass modulus Em is calculated based on the following relationship:
Weathered Rock - Williams and Pells - Bored Piles or Drilled Shafts
Weathered rock – Williams and Pells method for bored piles or drilled shafts in the PileAXL program calculates the ultimate shaft resistance fs based on the following relationships from Williams and Pells (1981):
where σc is the unconfined compressive strength (UCS), α is a reduction factor influencing the strength of the rock and β is the ratio of shaft resistance of jointed rock mass to shaft resistance of intact rock mass and j is a function of modulus reduction factor .
​where Em is the elastic modulus of the rock mass and Er is the elastic modulus of the intact rock.
The ultimate end bearing resistance, fb based on Williams and Pells (1981) is calculated using the relationship below:
where σc is the unconfined compressive strength (UCS) in MPa and Ncr is the bearing capacity factor which is adopted as 2.5 as default.
Weathered Rock - Zhang and Einstein - Bored Piles or Drilled Shafts
Weathered rock – Zhang and Einstein method for bored piles or drilled shafts in the PileAXL program calculates the ultimate shaft resistance fs based on the following relationships:
where σc is the unconfined compressive strength (UCS), α and β are the empirical factors for shaft resistance. The empirical factors from a number of researchers have been initially reported by O’Neill et al. (1996) and further summarised in Zhang (2004).
The ultimate end bearing resistance, fb based on Zhang and Einstein (1998) is calculated using the relationship below:
where σc is the unconfined compressive strength (UCS) in MPa.
Weathered Rock - Pells et al (1998) - Bored Piles or Drilled Shafts
Weathered rock – Pells et al method in the PileAXL program calculates the ultimate shaft resistance and end bearing resistance based on the approach from Pells et al. (1998) for Sydney Sandstone and Shale. This design method is based on the rock classification system.
Rock classification for Sydney sandstone (after Pells et al. 1998)
Rock classification for Sydney shale (after Pells et al. 1998)
Once the rock classification is determined, ultimate shaft resistance fs, ultimate end bearing resistance fb and elastic rock modulus can be then obtained using the tables below.
Pile Design parameters for Sydney sandstone (after Pells et al. 1998)
Pile design parameters for Sydney shale (after Pells et al. 1998)
Weathered Rock - Kulhawy and Phoon - Bored Piles or Drilled Shafts
Weathered rock – Kulhawy and Phoon method for bored piles or drilled shafts in the PileAXL program calculates the ultimate shaft resistance fs based on the following relationships:
where σc is the unconfined compressive strength (UCS), ψ is the empirical factor for shaft resistance. Based on Kulhawy and Phoon (1993), the mean value of shaft resistance factor ψ is 2, the lower bound is 1 and the upper bound is 3.
The ultimate end bearing resistance, fb is calculated using the relationship below:
where σc is the unconfined compressive strength (UCS) in MPa and Ncr is the bearing capacity factor which is adopted as 2.5 as default.
Weathered Rock - General Rock - Bored Piles or Drilled Shafts
Weathered rock – General Rock method for bored piles or drilled shafts in the PileAXL program calculates the ultimate shaft resistance fs based on Kulhawy et al. (2005):
where σc is the unconfined compressive strength (UCS), α and β are the empirical factors for shaft resistance and pa is the atmospheric pressure (100 kPa).
The ultimate end bearing resistance, fb is calculated using the relationship below:
where σc is the unconfined compressive strength (UCS) in MPa and Ncr is the bearing capacity factor which is adopted as 2.5 as default.
Weathered Rock - User Rock - Bored Piles or Drilled Shafts
Weathered rock – User Rock method for bored piles or drilled shafts in the PileAXL program allows the users to directly define the ultimate shaft resistance (fs) and ultimate end bearing resistance (fb).
API Clay - Driven Piles
For the cohesive soils, the following equations as recommended in API (2000) are adopted to calculate the ultimate shaft resistance, fs and ultimate end bearing resistance, fb:
where su is undrained shear strength and po' is effective overburden pressure at the point in question.
API COMM Clay - Driven Piles
API COMM Clay method is the method to calculate the ultimate shaft resistance, fs and ultimate end bearing resistance, fb for clays, based on the commentary of API WSD (2000) with the following relationships:
where su is undrained shear strength.
API USACE Clay - Driven Piles
API USACE Clay method is the method to calculate the ultimate shaft resistance, fs and ultimate end bearing resistance, fb for clays, based on EM 1110-2-2906 (USACE, 1991) with the following relationships:
where su is undrained shear strength and α is the adhesion factor which can be determined from the figure below based on the value of undrained shear strength.
ICP Clay - Driven Piles
ICP Clay Method is based on the empirical pile design method proposed by Jardine et al (2005) in Imperial College, UK. The main feature of this method is that the calculation of end bearing resistance (qb) is mainly based on the cone tip resistance (qc) from the cone penetration tests (CPT/CPTu).
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The ultimate shaft resistance or skin friction (τf) along the pile can be determined using the following relationships for both closed-ended and open-ended piles:
Note that h/R or h/R* is the normalized distance from the pile tip. h is the relative depth to the pile toe from the calculation location. For open-ended pile, the equivalent radius of R* shall be used according to the equation below:
Note that Router is the outer radius of the pipe section and Rinner is the inner radius of the pipe section.
St is the clay sensitivity parameter which is defined as the clay’s peak intact undrained shear strength value divided by its remoulded undrained shear strength. This parameter is generally between 4 and 8 for deep-water marine deposits and around unity for glacial tills.
Note that this loading factor (Kf/Kc) is constant regardless of the direction of loading or drainage conditions.
The ultimate bearing resistance qb for closed-ended piles in clay is calculated using the following relationships:
qc is averaged 1.5 pile diameters above and below the pile toe level.
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The ultimate bearing resistance qb for open-ended piles in clay is calculated using the following relationships:
For rectangular and H section piles with non-circular sections, the following equation is used to calculate the ultimate end bearing resistance:
NGI Clay - Driven Piles
​NGI Clay method is based on the approach proposed in Karlsrud et al. (2005). For the cohesive soils, the following equations are adopted to calculate the ultimate shaft resistance, fs based on the strength ratio of ψ which is the ratio between the undrained shear strength (su) and effective vertical stress (po'):
The following equations are adopted to calculate the ultimate end bearing resistance, fb:
su is undrained shear strength, po' is effective overburden pressure at the point in question and Ip is the plasticity index (in %).
UWA Clay - Driven Piles
UWA Clay method is based on the approach proposed by Lehane et al. (2013) The following equation is adopted in the program to calculate the ultimate shaft resistance fs:
where qt is the corrected cone tip resistance, qc is the cone tip resistance, α is the cone area ratio, u2 is pore pressure acting at the filter zone, h is the relative depth to the pile toe from the calculation location, σv' is the effective vertical stress, δf is the interface angle of friction at failure, Router is the outer radius of the pipe section and Rinner is the inner radius of the pipe section.
The calculation of ultimate end bearing resistance fb of UWA Clay method is the same as ICP Clay method in the PileAXL program.
Alpha Clay - Driven Piles
Alpha Clay method available in the PileAXL program calculates the ultimate shaft resistance (fs) and ultimate end bearing resistance (fb) based on the following equations:
where su is undrained shear strength, α is the adhesion factor which can be defined by the users and Nq is the bearing capacity factor which can be defined by the users.
API Sand - Driven Piles
For the granular soils, the following equations as recommended in API (2000) are adopted to calculate the ultimate shaft resistance (fs) and ultimate end bearing resistance (fb) based on the following equations:
where K is the coefficient of lateral pressure and usually assumed to be 0.8 for open-ended pipe piles or 1.0 for plugged or close-ended pipe piles, δ is the friction angle between the soil and pile, β is the shaft friction factor, Nq is the bearing capacity factor and po' is effective overburden pressure.
The following table is extracted from API (2000) and adopted in the PileAXL program for the values of interface friction angle, δ and bearing capacity factor, Nq.
API RP2GEO Sand - Driven Piles
For API RP2GEO Sand method, the following equations as recommended in API (2011) are adopted to calculate the ultimate shaft resistance (fs) and ultimate end bearing resistance (fb) based on the following equations:
where β is the shaft friction factor, Nq is the bearing capacity factor and po' is effective overburden pressure.
The following table is extracted from API (2011) and adopted in the PileAXL program for shaft friction factor β and bearing capacity factor, Nq.
