# 6.4.2 Tensile resistance

COMMENTARY ON 6.4.2

*BS EN 1997-1 allows the ultimate tensile resistance of an individual pile to be determined from any of the following:*

- static pile formulae based on ground parameters;
- direct formulae based on the results of field tests; and
- the results of static pile load tests.

6.4.2.1 Models based on ground parameters

6.4.2.1.1 General

**6.4.2.1.1.1** The calculation of ultimate tensile resistance from ground parameters should conform to the «alternative method» given in BS EN 1997-1:2004+A1:2013, 7.6.3.3.

**6.4.2.1.1.2** When this method is used, the characteristic ultimate tensile resistance of an individual pile (*R*_{t,k}) should be calculated as:

*R*

_{t,k}=

*R*

_{s,k}

where:

*R*_{s,k} is the pile's characteristic ultimate shaft resistance.

**6.4.2.1.1.3** The characteristic ultimate shaft resistance (*R*_{s,k}) should conform to **6.4.1.2.**

**6.4.2.1.1.4** The value of the model factor *γ*_{Rd} should be taken from the UK National Annex to BS EN 1997-1:2004+A1:2013.

6.4.2.1.2 Rock and rock masses

COMMENTARY ON 6.4.2.1.2

*The resistance of a pile foundation in rock depends markedly on the method of pile construction and the roughness of the rock socket in which the pile is located.*

**6.4.2.1.2.1** The equations given in this subclause (**6.4.2.1.2**) should not be used for the verification of the ultimate limit state of piles in rock, unless the parameters used have been corroborated by the results of static pile load tests on similar piles in similar ground conditions.

NOTE The equations given in this subclause can be used for preliminary design without pile testing.

**6.4.2.1.2.2** In weak to medium strong rock, the ultimate unit shaft resistance (*q*_{s}) may be calculated from (see *Piling Engineering (3 ^{rd} edition)* [50]):

where:

*q*_{u} is the rock's unconfined compression strength;

*k*_{1} and *k*_{2} are empirical coefficients that depend on rock and pile type; and

*p*_{ref} is given in Table 4.

NOTE Guidance on the calculation of unit shaft friction in rocks can be found in the ICE manual of geotechnical engineering (2012), Volume II, Chapter 54 [1] and in State of the art report: Analysis and design [68].

**6.4.2.1.2.3** In the absence of reliable test data, values of *k*_{1} and *k*_{2} may be taken from Table 13.

**6.4.2.1.2.4** In weak to medium strong rock, the ultimate unit base resistance (*q*_{b}) may be calculated from (see *Piling Engineering (3rd edition)* [50]):

where:

*q*_{u} is the rock's unconfined compression strength; and

*k*_{3} and *k*_{4} are empirical coefficients that depend on rock type; and

*p*_{ref} is given in Table 4.

NOTE Guidance on the calculation of unit base resistance in rocks can be found in the ICE manual of geotechnical engineering (2012), Volume II, Chapter 54 [1] and in State of the art report: Analysis and design [68].

**6.4.2.1.2.5** In the absence of reliable test data, values of *k*_{3} and *k*_{4} may be taken from Table 13.

**6.4.2.1.2.6** The values of *k*_{1} to *k*_{4} should be selected very cautiously, unless there is static pile load test data to corroborate less cautious values.

**6.4.2.1.2.7** The ultimate unit shaft and base resistances of piles in chalk should be determined in accordance with CIRIA Report C574, Chapter 8 [N2].

NOTE 1 Guidance on piled foundations in weak rocks can be found in CIRIA Research Report 181 [69].

NOTE 2 Guidance on rock-socketed shafts for highway structure foundations can be found in NCHRP Synthesis 360 [70].

*k*

_{1}to

*k*

_{4}for piles installed in rocks

Rock type | Coefficient k_{1} |
Coefficient k_{2} |
Coefficient k_{3} |
Coefficient k_{4} |

(Generic) | 0.63–1.26 ^{A)} |
0.5 ^{A)} |
— | — |

Soft rock | 1.0–1.29 ^{B)} |
0.57–0.61 ^{B)} |
— | — |

Cemented materials | 0.7–2.1 ^{C)} |
0.5 ^{C)} |
15 ^{C)} |
0.5 ^{C)} |

^{A)} Values from Results of tests to determine shaft resistance of rock socketed drilled piers [71].^{B)} Values from A design method for drilled piers in soft rock [72].^{C)} Values from Drilled shaft side resistance in clay soil to rock [73]. |

6.4.2.2 Models based on the results of ground tests

**6.4.2.2.1** The calculation of ultimate tensile resistance from the results of field tests should conform to the main method given in BS EN 1997-1:2004+A1:2013, 7.6.3.3.

**6.4.2.2.2** When this method is used, the characteristic ultimate tensile resistance of an individual pile (*R*_{t,k}) should be calculated as the smaller of the following two values:

where:

*ξ*_{3} and *ξ*_{4} are correlation factors that depend on the number of tests performed;

(*R*_{t,calc})_{mean} is the mean calculated ultimate tensile resistance of the pile; and

(*R*_{t,calc})_{min} is the minimum calculated ultimate tensile resistance of the pile.

**6.4.2.2.3** The calculated ultimate tensile resistance of an individual pile (*R*_{t,calc}) should be determined from:

*R*

_{t,calc}=

*R*

_{s,calc}

where:

*R*_{s,calc} is the calculated ultimate shaft resistance.

**6.4.2.2.4** The calculated ultimate shaft resistance (*R*_{s,calc}) should conform to **6.4.2.2.**

**6.4.2.2.5** The values of the correlation factors *ξ*_{3} and *ξ*_{4} should be taken from the UK National Annex to BS EN 1997-1:2004+A1:2013, Table A.NA.10.

6.4.2.3 Models based on static pile load tests

**6.4.2.3.1** The ultimate tensile resistance of a pile foundation may be calculated directly from the results of static pile load tests.

**6.4.2.3.2** The calculation of ultimate tensile resistance from static pile load tests should conform to BS EN 1997-1:2004+A1:2013, 7.6.3.2.

**6.4.2.3.3** If this method is used, the characteristic ultimate tensile resistance of an individual pile (*R*_{t,k}) should be calculated as the smaller of the following two values:

where:

*ξ*_{1} and *ξ*_{2} are correlation factors that depend on the number of tests performed;

(*R*_{t,m})_{mean} is the mean measured ultimate tensile resistance of the pile; and

(*R*_{t,m})_{min} is the minimum measured ultimate tensile resistance of the pile.

**6.4.2.3.4** The values of the correlation factors *ξ*_{1} and *ξ*_{2} should be taken from the UK National Annex to BS EN 1997-1:2004+A1:2013, Table A.NA.10.

6.4.3 Transverse resistance

6.4.3.1 Models based on ground parameters

6.4.3.1.1 General

COMMENTARY ON 6.4.3.1.1

*BS EN 1997-1 recommends that the following failure mechanisms should be considered when verifying the transverse resistance of an individual pile:*

- for short piles, rotation or translation as a rigid body (termed the «short pile mechanism»); and
- for long slender piles, bending failure of the pile, accompanied by local yielding and displacement of the soil near the top of the pile (termed the «long pile mechanism»).

**6.4.3.1.1.1** The calculation of ultimate transverse resistance from ground parameters should conform to BS EN 1997-1:2004+A1:2013, 7.7.3.

**6.4.3.1.1.2** The characteristic ultimate transverse resistance of an individual pile (*R*_{tr,k}) should be calculated from:

*R*

_{tr,k}= min(

*R*

_{tr,short,k},

*R*

_{tr,long,k})

where:

*R*_{tr,short,k} is the characteristic ultimate transverse resistance of an individual pile rotating or translating as a rigid body (the «short pile mechanism»); and

*R*_{tr,long,k} is the characteristic ultimate transverse resistance of an individual pile that fails in bending near its head (the «long pile mechanism»).

6.4.3.1.2 Coarse soils

**6.4.3.1.2.1** In coarse soils, the characteristic ultimate unit transverse resistance of a pile (*R*_{tr,k}) may be calculated using Broms' method [74] from an expression of the form:

*R*

_{tr,k}= func{

*φ*

_{k},

*γ*

_{k},

*B,L,e,M*

_{Rk}}

where:

func{…} denotes a function of the enclosed variables;

*φ*_{k} is the soil's characteristic angle of shearing resistance;

*γ*_{k} is the soil's characteristic weight density;

*B* is the pile's breadth;

*L* is the pile's embedded length;

*e* is the eccentricity of the transverse load applied to the pile; and

*M*_{Rk} is the pile's characteristic ultimate bending resistance.

NOTE Guidance on the precise form of the function to be used in equation (66) can be found in textbooks, such as The engineering of foundations [51] and Piles and pile foundations [75].

**6.4.3.1.2.2** Alternatively, the characteristic ultimate unit transverse resistance of a pile in coarse soils may be calculated using Brinch Hansen's closed-form solution (see *The ultimate resistance of rigid piles against transversal forces* [76]).

NOTE Guidance on the use of Brinch Hansen's method can be found in textbooks, such as Pile design and construction [77].

6.4.3.1.3 Fine soils

**6.4.3.1.3.1** In fine soils, the characteristic ultimate unit transverse resistance of a pile (*R*_{tr,k}) may be calculated using Broms' method [78] from an expression of the form:

*R*

_{tr,k}= func{

*c*

_{u,k},

*B,L,e,M*

_{Rk}}

where:

*c*_{u,k} is the soil's characteristic undrained shear strength; and the other symbols are as defined for equation (66).

NOTE Guidance on the precise form of the function to be used in equation (67) can be found in standard textbooks, such as The engineering of foundations [51] and Piles and pile foundations [75].

**6.4.3.1.3.2** Alternatively, the characteristic ultimate unit transverse resistance of a pile in fine soils may be calculated using Brinch Hansen's closed-form solution (see *The ultimate resistance of rigid piles against transversal forces* [76]).

NOTE Guidance on the use of Brinch Hansen's method can be found in textbooks, such as Pile design and construction [77].

6.4.3.2 Models based on the results of field tests

The calculation of ultimate transverse resistance from the results of field tests should conform to BS EN 1997-1:2004+A1:2013, 7.7.3.

6.4.3.3 Models based on static pile load tests

**6.4.3.3.1** The ultimate transverse resistance of a pile foundation may be calculated directly from the results of static pile load tests.

**6.4.3.3.2** The calculation of ultimate transverse resistance from static pile load tests should conform to BS EN 1997-1:2004+A1:2013, 7.7.2.

6.4.4 Settlement

**6.4.4.1** The settlement of a pile foundation may be calculated using any of the following models, as appropriate:

- theory of elasticity (see
*Pile foundation analysis and design*[79]); - t-z curves (see
*Analysis and design of shallow and deep foundations*[80]); - hyperbolic stress-strain model (see
*A new method for single pile settlement prediction and analysis*[81]); - numerical models, including:
- the interaction-factor method (see
*An analysis of the vertical deformation of pile groups*[82]); - the boundary element method (see
*Non-linear analysis of pile groups*[83]); - finite element method;
- wave equation analysis, provided the validity of the analysis has been demonstrated by previous evidence of acceptable performance in static load tests on the same pile type, of similar length and cross-section, and in similar ground conditions; or
- other appropriate models not listed here.

**6.4.4.2** In order to conform to BS EN 1997-1:2004+A1:2013, 7.4.1, the validity of the pile settlement model that is used for design should be demonstrated by static pile load tests in comparable situations.

NOTE 1 Guidance on the calculation of settlement for single piles can be found in the ICE manual of geotechnical engineering (2012), Volume II, Chapter 54 [1].

NOTE 2 Guidance on the calculation of settlement of pile groups can be found in the ICE manual of geotechnical engineering (2012), Volume II, Chapter 55 [1].

6.4.5 Lateral displacement

**6.4.5.1** The lateral displacement of a pile foundation may be calculated using any of the following models, as appropriate:

- theory of elasticity (see
*Pile foundation analysis and design*[79]); - p-y curves (see
*Single piles and pile groups under lateral loading*[84]); - subgrade reaction models;
- numerical models, including:
- the interaction-factor method (see
*An analysis of the vertical deformation of pile groups*[82]); - the boundary element method (see
*Non-linear analysis of pile groups*[83]); - the finite element method; or
- other appropriate models not listed here.

**6.4.5.2** Owing to rapid degradation of mobilized stiffness with pile head movement when using linear elastic and subgrade reaction models, preference should be given to an alternative method of calculating lateral displacement of a pile foundation.

**6.4.5.3** Local near surface ground conditions can have a significant influence on an individual pile's response to lateral loading.

**6.4.5.4** Pile head fixity can have a significant influence on a pile group's response to lateral loading.