6.4 Calculation models
COMMENTARY ON 6.4
BS EN 19971 allows the ultimate bearing 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;
 the results of static pile load tests;
 the results of dynamic impact tests;
 pile driving formulae; and
 wave equation analysis.
6.4.1 Bearing resistance
6.4.1.1 General
6.4.1.1.1 Unless otherwise stated, the total bearing resistance of an individual pile (R_{t}) should be calculated from:
where:
R_{s} is the resistance of the pile shaft; and
R_{b} is the resistance of the pile base.
6.4.1.1.2 The bearing resistance of a pile foundation should be determined for the the appropriate failure criterion corresponding to an ultimate limit state of the foundation.
NOTE BS EN 19971:2004+A1:2013, 7.6.1.1(3) recommends that settlement of the pile top equal to 10% of the pile base diameter be adopted as the failure criterion when it is difficult to define the ultimate limit state.
6.4.1.1.3 The base resistance calculated from models that assume plunging failure of the pile should be reduced appropriately to match failure criterion appropriate to the ultimate limit state of the pile.
6.4.1.2 Models based on ground parameters
6.4.1.2.1 General
COMMENTARY ON 6.4.2.1.1
BS EN 19971 uses several terms that differ from traditional British practice:
 «unit resistance» refers to resistance per unit area (i.e. over an area of 1 m^{2});
 «ultimate unit shaft resistance» (with symbol q_{s}) is equivalent to «limiting shaft (or skin) friction» (traditional symbol f_{s}); and
 «ultimate base resistance» is the same as «limiting endbearing pressure».
A static pile formula based on ground parameters provides an estimate of the ultimate bearing resistance of the pile. The method's accuracy depends on the reliability of the chosen formula, the soil strength data to which it is applied, and sitespecific pile installation methods.
6.4.1.2.1.1 The ultimate bearing resistance of a pile foundation may be calculated from static pile formulae using values of ground parameters obtained from field or laboratory tests on soil and rock.
6.4.1.2.1.2 The consequences of differences between the true ultimate bearing resistance of a pile and its calculated value (which might occur, for example, owing to differences between actual and the assumed ground conditions) should be considered where reasonably foreseeable.
6.4.1.2.1.3 The calculation of ultimate compressive resistance from ground parameters should conform to the «alternative method» given in BS EN 19971:2004+A1:2013, 7.6.2.3.
6.4.1.2.1.4 If this method is used, the characteristic ultimate compressive resistance of an individual pile (R_{c,k}) should be calculated as:
where:
R_{s,k} is the pile's characteristic ultimate shaft resistance; and
R_{b,k} is the pile's characteristic ultimate base resistance.
6.4.1.2.1.5 The characteristic ultimate shaft resistance (R_{s,k}) may be calculated from:
where:
A_{s,j} is the total circumferential area of the pile shaft (in layer j);
q_{s,j} is the average ultimate unit shaft resistance (in layer j) calculated from ground parameters;
n is the total number of layers in contact with the pile shaft; and
γ_{Rd} is a model factor. The value of γ_{Rd} should conform to the UK National Annex to BS EN 19971:2004+A1:2013.
6.4.1.2.1.6 The characteristic ultimate base resistance (R_{b,k}) may be calculated from:
where:
A_{b} is the total crosssectional area of the pile base;
q_{b} is the ultimate unit base resistance calculated from ground parameters; and
γ_{Rd} is a model factor. The value of γ_{Rd} should conform to the UK National Annex to BS EN 19971:2004+A1:2013.
6.4.1.2.1.7 The value of q_{b} should include the contribution due to the total overburden pressure at the level of the pile base.
6.4.1.2.1.8 If the selfweight of the pile is omitted from the calculation of the action, as allowed by BS EN 19971, 7.6.2.1(2), then the overburden pressure should be omitted from the calculation of R_{b,k}, so that:
where:
σ_{v,b} is total overburden pressure at the pile base.
6.4.1.2.1.9 The value of the model factor γ_{Rd} should be taken from the UK National Annex to BS EN 19971:2004+A1:2013.
NOTE The value of the model factor γ_{Rd} given in the UK National Annex to BS EN 19971:2004+A1:2013 varies with the amount of static pile load testing that is available to corroborate the calculation of bearing resistance. Background information about the purpose of the model factor can be found in Decoding Eurocode 7 [47] and Pile design to Eurocode 7 and the National Annex: Part 2 [48].
6.4.1.2.2 Coarse soils
6.4.1.2.2.1 In coarse soils, the ultimate unit shaft resistance in layer j (q_{s,j}) may be calculated from effective stress parameters, as follows:
where:
K_{s,j} is an earth pressure coefficient (for layer j) against the pile shaft;
δ_{j} is the angle of interface (also known as «wall») friction between the pile and layer j; and
σ'_{v,j} is the average vertical effective stress acting in the soil in layer j.
6.4.1.2.2.2 In the absence of reliable test data, values of K_{s} may be taken from Table 8. Alternative values of K_{s} may be used, provided there is previously documented evidence of the successful performance of the same type of pile in similar ground conditions using these alternative values.
Pile type  Soil type  Typical coefficient, K_{s} ^{A), B)} 

Large displacement  Precast concrete (solid) Closedended tubular steel Timber Driven castinplace concrete 
(all)  1.0–1.2 
Small displacement  Hsection steel bearing piles Openended tubular steel Helical steel  (all)  80% of large displacement value 
Replacement ^{C)}  Continuous flight auger (CFA)  Clean mediumcoarse sand  0.9 
Fine sand  0.7–0.8  
Silty sand  0.6–0.7  
Interlayered silt and sand  0.5–0.6  
Bored castinplace concrete Micro piles ^{D)}  0.7  
^{A)} K_{s} values may vary due to details of specific installation methods, soil layering, groundwater pressures, and elapsed time between installation and testing. ^{B)} K_{s} values may be superseded by local static pile test data, provided comprehensive documentation is provided (i.e. factual test data, interpretation, local ground conditions, specific pile installation details, etc.). ^{C)} Values taken from the ICE manual of geotechnical engineering (2012), Volume II, Chapter 54 [1]. ^{D)} Higher values of K may be used for micropiles grouted under pressure. 
6.4.1.2.2.3 Values of δ may be estimated from:
where:
φ'_{pk} is the soil's peak angle of shearing resistance;
φ'_{cv} is the soil's constantvolume angle of shearing resistance determined in accordance with 4.6.2.4; and
k_{δ} is a dimensionless coefficient.
6.4.1.2.2.4 In the absence of reliable test data, values of k_{δ} may be taken from Table 9.
Pile type  Coefficient k_{δ}  
Large displacement  Precast concrete (solid) Closedended tubular steel  0.67 
Driven castinplace concrete  0.9  
Timber  0.85  
Small displacement  Steel bearing piles of Hsection Openended tubular steel  0.67 
Helical steel piles  0.67^{A)} or 1.0^{B)}  
Replacement  Continuous flight auger (CFA) Bored castinplace concrete Micro piles  1.0 
^{A)} Value along periphery of steel shaft (soiltosteel boundary). ^{B)} Value along periphery of helices (soiltosoil boundary). 
6.4.1.2.2.5 Depending on the pile installation method, the presence of fine soils overlying coarse soils can adversely affect the angle of interface friction in those underlying coarse soils. The value of δ should be selected appropriately when this is the case.
6.4.1.2.2.6 In coarse soils, the ultimate effective unit base resistance (q'_{b}) may be calculated from effective stress parameters, as follows:
where:
σ'_{v,b} is the vertical effective stress at the pile base; and
N_{q} is a bearing pressure coefficient that depends on the soil's constantvolume angle of shearing resistance, φ_{cv}; the soil's density index, I_{D}; and the vertical effective stress at the pile base, σ'_{v,b}.
NOTE The value of N_{q} can be obtained from a wide range of theories, including those given in Load bearing capacity and deformation of piled foundations [49], Piling Engineering (3rd edition) [50], and The Engineering of Foundations [51].
6.4.1.2.2.7 The density index, I_{D}, (which is defined in BS EN ISO 146882) may be estimated from the results of field tests (e.g. Standard Penetration Test, Cone Penetration Test) using correlations given in BS EN 19972.
6.4.1.2.3 Fine soils
6.4.1.2.3.1 In fine soils, the ultimate unit shaft resistance in layer j (q_{s,j}) may be calculated from effective stress parameters, as follows:
where:
β_{j} is an empirical coefficient (for layer j); and
σ'_{v,j} is the average vertical effective stress acting in the soil in layer j.
6.4.1.2.3.2 In the absence of reliable test data, values of β for fine soils may be estimated from (see Shaft friction on piles in clay: a simple fundamental approach [52] and Bearing capacity and settlement of pile foundations [53]):
for normally consolidated clays 
for overconsolidated clays 
where:
φ is the soil's angle of shearing resistance; and
R_{O} is the soil's overconsolidation ratio, given by R_{O} = p'_{v,max} /p'_{v};
p'_{v} is the effective overburden pressure; and
p'_{v,max} is the maximum effective overburden pressure that the soil has previously been subjected to.
6.4.1.2.3.3 Alternatively, the ultimate unit shaft resistance in layer j (q_{s,j}) may be calculated from total stress parameters, as follows:
where:
α_{j} is an empirical coefficient (for layer j) that depends on the strength of the soil, the effective overburden pressure acting on it, pile type, and method of execution; and
c_{u,j} is the undrained shear strength of the soil in layer j.
NOTE Equation (40) is an empirical relationship between undrained shear strength measured using historical sampling and laboratory test practice (e.g. quick undrained triaxial compression texts on 100 mm diameter samples) and test data from static pile load tests using maintained load.
6.4.1.2.3.4 For piles located in ground that is subject to a reduction in stress (for example, within the zone of influence of deep excavations), equation (40) should only be used if allowance is made for this stress relaxation.
6.4.1.2.3.5 Values of α should be obtained from previous evidence of acceptable performance in static load tests on the same type of pile of similar length and crosssection and in similar ground conditions.
6.4.1.2.3.6 In the absence of reliable test data, values of α may be estimated from one of the methods given in this subclause (6.4.1.2.3).
6.4.1.2.3.7 In the absence of reliable test data, values of α for replacement piles (denoted α_{repl}) may be estimated from:
where:
c_{u} is the undrained shear strength of the fine soil;
p_{ref} is 100 kPa; and
k_{1} and k_{2} are coefficients whose values may be taken as 0.45 and 1.0, respectively.
6.4.1.2.3.8 For replacement piles in glacial tills, the values of k_{1} and k_{2} in equation (41) may be taken as 0.75 and 0.75, respectively (see Piling in 'boulder clay' and other glacial tills [54]).
6.4.1.2.3.9 For bored piles in stiff overconsolidated clays (such as London, Gault, Lias, Oxford and Weald Clays), provided the bore is left open for less than 12 hours, then α_{repl} may be taken as 0.5 (see Foundations no. 1 [55]).
6.4.1.2.3.10 Alternative values of α_{repl} may be used, provided there is previously documented evidence of the successful performance of the same type of pile in similar ground conditions using these alternative values.
6.4.1.2.3.11 In the absence of reliable test data, values of α for displacement piles (denoted α_{disp}) may be estimated from:
where:
c_{u} is the undrained shear strength of the fine soil;
σ'_{v} is the effective vertical stress (overburden pressure) acting on the soil; and
m is 0.25 for c_{u}/σ'_{v} ≥ 1 and 0.5 for c_{u}/σ'_{v} < 1
6.4.1.2.3.12 Alternative values of α_{disp} may be used, provided there is previously documented evidence of the successful performance of the same type of pile in similar ground conditions using these alternative values.
6.4.1.2.3.13 In fine soils, the ultimate unit base resistance (q_{b}) may be calculated from total stress parameters, as follows:
where:
N_{c} is a bearing pressure coefficient that depends on the depth of the pile base; and
c_{u,b} is the undrained shear strength of the soil at the pile base.
6.4.1.2.3.14 In the absence of reliable test data, the value of N_{c} may be calculated from:
where:
k_{1} is a coefficient that accounts for insufficient embedment of the pile toe; and
k_{2} is a coefficient that accounts for the stiffness of the bearing statum.
6.4.1.2.3.15 The value of k_{1} in equation (44) should be calculated from:
where:
L is the depth of embedment of the pile toe into the bearing stratum; and
B is the pile breadth (or diameter).
6.4.1.2.3.16 Values of k_{2} should be taken from Table 10.
Pile type  Undrained shear strength of soil, c_{u}
kPa 
k_{2}  9 × k_{2} 
Bored, CFA ^{A)}  ≤25  0.72  6.5 
50  0.89  8  
≥100  1.0  9  
Driven ^{B)}  1.11  10  
^{A)} Values based on FHWA Report No. NHI10016 [56]; k_{2} may be interpolated for intermediate values of c_{u}. ^{B)} Value based on Salgado [51]. 