study guide for an exam (geotechnical)

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Geotechnical Engineering

8

Piles

Dr Martin Pritchard

Contents:

1. Piles

1.1 Types of piles

1.2 Choice of pile type

1.3 Video links of different pile installation methods

2. Pile design to Eurocode 7

2.1 UK National Annex – partial factors

2.2 Actions

2.2.1 Combinations of actions

2.3 Materials

2.4 Design resistance

2.4.1 Pile shaft resistance

2.4.2 Pile end bearing resistance

3. Table & charts duplicated from formula booklet

4. Summary

5. Worked examples

6. Tutorial questions

British Standards online: BS EN 1997-2: 2007 Eurocode 7 — Geotechnical design — Part 1: General rules. NA to BS EN 1997-1:2004. National Annex UK National Eurocode 7 – Geotechnical design – Part 1: General rules. BS EN 1990:2002 +A1:2005 Eurocode – Basis of structural design (for Table 2, i.e. values).
http://libguides.leedsbeckett.ac.uk/resources/databases

Learning outcomes:

Appreciate theory and design related to the load carrying capacity of piled foundations in various soil types.

Piles

If a shallow foundation (strip, pad or raft) cannot be used to adequately support the given structure over the current ground conditions, then a pile foundation may provide an economic alterative.

A pile can be defined as a long slender structural member that transmits load from its top to the ground, either via:

NB movement has to take place before any load is transferred. Also, in practice piles are often designed as a combination of both pile types. Therefore, the basic equation for the ultimate compressive resistance (Rc) of a pile is:

Equ. 1

Base resistance (Rb): load transmitted through the pile shaft to hard strata beneath, also termed end bearing.

Shaft resistance (Rs): load transmitted to the soil along the length of the pile; termed skin friction in in sands and adhesion in clays.

1.1 Types of piles:

Piles can be classified a number of different ways, such as:

Installation method: driven, bored, jacked or screwed.

Material type: timber, steel or concrete (precast or cast in-situ).

Size: small-diameter bored, large-displacement, under-reamed or mini-piles.

Load carrying capacity: end bearing, friction piles, uplift piles or racking piles.

Precast RC pile

Steel H pile

Shell pile

 

Concrete pile (cast in-situ)

Bored pile (cast in-situ)

Under-reamed bored pile (cast in-situ)

 

1.2 Choice of pile type: Driven or displacement piles (Precast piles):

Advantages:

May be inspected for quality and soundness before driving

Not liable to squeezing or necking

Construction not affected by groundwater

Can be left protruding above ground level (useful in marine structures)

Can withstand high bending and tensile stresses

Can be driven in long lengths

Disadvantages:

Unjointed types cannot easily be varied in length

May break during driving

Uneconomic if the design is governed by driving stresses rather than working stresses

Noise and vibration during driving

Displacement of soil may affect adjacent structures

Cannot be driven in situations of low head room

Bored or replacement piles (In-situ piles):

Advantages:

Length can be varied

Removed soil can be compared with design data

Penetration tests can be carried out in boreholes

Very large bases can be formed in favourable ground

Drilling tools can break up boulders and other obstructions

Pile is designed to working stresses

Very long lengths possible

Little noise and vibration during construction

No ground heave

Disadvantages:

Piles liable to squeezing and necking in soft soils

Special techniques required for concreting in water bearing ground

Concrete cannot be inspected after installation

Enlarged bases cannot be formed in collapsible soil

Cannot be easily extended above ground

Boring may cause instability and settlement of adjacent structures

2. Pile design to Eurocode 7

Eurocode 7 (EC7) is a Limit State Design method

Design compressive force (Fc;d), correctly termed action, is overestimated.

Design resistance (Rc;d) under the worst-case scenario is underestimated.

Both being factored conservatively using partial factors.

Equ. 2

For pile design the overall Rc;d is obtained from the sum of base resistance (Rb) and shaft resistance (Rs).

Direct action is a set of forces or loads applied to a member.

Indirect action is a set of imposed deformations, for example, by temperature and moisture changes

favourable (stabilising) or

unfavourable (destabilising),

Within EC7 the two sub-set of limit state are:

Ultimate Limit State (ULS): considers states associated with collapse, structural failure, excessive deformation or loss of stability of the whole of the structure or any part of it.

Serviceability Limit State (SLS): considers states that correspond to conditions beyond which specified service requirements are no longer met.

EC7 adopts five distinct ULS that should be sufficiently improbable:

EQU – Loss of equilibrium (tilt or rotation)

STR – Internal failure or excessive deformation (strength of structural material is significant)

GEO – Failure or excessive deformation of the ground (strength of soil or rock is significant)

UPL – Uplift or buoyancy

HYD – Hydraulic heave, erosion or piping

STR and GEO most important for pile design.

EC7 details the three following methods for designing pile foundations:

Testing – results from static or dynamic load tests.

Calculations – empirical or analytical calculation methods.

Observation – observed performance of comparable piles.

 

Despite EC7 giving greater emphasis to determining pile resistance from testing, in UK the majority of pile designs are based on calculations.

2.1 UK National Annex – partial factors

The UK has adopted Design Approach 1 (DA1), which requires two calculations based on different combinations of partial factors:

In combination (or set) 1, partial factors (>1) are applied to actions and small factors to resistance, while ground strengths (when used) are left unfactored.

In combination (or set) 2, partial factors (>1) are applied to resistances with smaller factors applied to variable actions, while permanent actions and ground strengths (when used) are left unfactored.

Table 1: Summary of partial factors (Tables A.NA 6 to 8 combined)

 

Tutorial solution 2: Using EC7 UK-NA, DA1, determine the design actions for the following pile:

10 m

Imposed loads:

FC;Gk = 250 kN (permanent)

FC;QK;1 = 50 kN (imposed)

FC;QK;1 = 10 kN (wind)

Concrete driven pile for a storage area, 0.3 m dia. length = 10 m, gconc = 25 kN/m3

Clay

= 18 kN

Design actions:

Factors to EC7 UK-NA
Set 1 Set 2
Permanent action
Variable action
Factors to EC7 UK-NA
Set 1 Set 2
Permanent action 1.35 1.0
Variable action 1.5 1.3

= 440 kN

= 336 kN

Combinations of actions

From Table 2 – combination factor :

For variable (imposed – storage area) action…

…as the lead action ψ0 = 1.0, as a combined action ψ1 = 0.9.

 

For frequent (wind) variable action…

…as the lead action ψ0 = 0.6, as a combined action ψ1 = 0.2.

 

Representative actions

With the imposed action as the leading variable:

Frep = ψ0Fc;Qk;1 + ψ1Fc;Qk;2 = (50 x 1.0) + (10 x 0.2) = 52 kN

 

With the wind action as the leading variable:

Frep = ψ0Fc;Qk;2 + ψ1Fc;Qk;1 = (10 x 0.6) + (50 x 0.9) = 51 kN

 

Considering the most onerous case, Frep = 52 kN

Factors to EC7 UK-NA
Set 1 Set 2
Permanent action 1.35 1.0
Variable action 1.5 1.3

Chart 2:

Tutorial questions:

Examples of ULS for pile foundations are shown below:

Limit State GEO Compression/Tension/Horizontal Limit State STR Compression/Tension/Horizontal Limit State GEO/STR Buckling/Shear/Bending

Examples of ULS for pile foundations are shown below:

Limit State GEO

Compression/Tension/Horizontal

Limit State STR

Compression/Tension/Horizontal

Limit State GEO/STR

Buckling/Shear/Bending

Combination 1: A1 + M1 + R1 Combination 2: A2 + M1 + R4

NB the “+” sign above implies that the partial factors are to “be combined with”. A = Actions or effects of actions; M = Materials (soil parameters); R = Resistances (from the ground).

BS EN 1997-1:2004 Clause: 2.4.7.3.4

Combination 1: A1 + M1 + R1

Combination 2: A2 + M1 + R4

NB the “+” sign above implies that the partial factors are to “be combined with”. A = Actions or

effects of actions; M = Materials (soil parameters); R = Resistances (from the ground).

BS EN 1997-1:2004

Clause: 2.4.7.3.4

Combination 1: A1 + M1 + R1 Combination 2: A2 + M1 + R4

Combination 1: A1 + M1 + R1

Combination 2: A2 + M1 + R4

2.2 Actions (A) The characteristic action (i.e. force or load) value in compression is given by:

𝐹";$ = 𝐹";&$ + 𝜓) 𝐹";+$;) )

+ 𝑊&$

where: 𝐹&$ The characteristic (k) permanent (G) components of F 𝐹+$;) The characteristic (k) variable (Q) components of F for layer, i 𝜓) The combination factor applicable to ‘i’

th variable action 𝑊&$ The pile’s characteristic self-weight (a permanent action)

i Denotes that the ‘sum total’ of variable characteristic actions will be taken for the ‘i’th number of variables

The design value of 𝑭𝒄;𝒅 is therefore given by factoring the characteristic value (Equ. 4), where 𝛾& and 𝛾+ are partial factors on unfavourable permanent and variable actions respectively:

𝐹";1 = 𝛾& 𝐹";&$ + 𝑊&$ + 𝛾+ 𝜓) 𝐹";+$;) )

i

i

i

2.2 Actions (A)

The characteristic action (i.e. force or load) value in compression is given by:

�

;

=�

;

+� �

;;

+�

where:

� The characteristic (

k

) permanent (

G

) components of F

�

;

The characteristic (

k

) variable (

Q

) components of F for layer, i

� The combination factor applicable to ‘i’

th

variable action

� The pile’s characteristic self-weight (a permanent action)

i Denotes that the ‘sum total’ of variable characteristic

actions will be taken for the ‘i’

th

number of variables

The design value of �

�;�

is therefore given by factoring the characteristic value (Equ. 4), where

� and � are partial factors on unfavourable permanent and variable actions respectively:

�

;

=��

;

+�+�

� �

;;

i

i

i

where:

𝑊"# = 𝐴 𝐿 𝛾)*+)

where:

A Area of pile body (m²) – square or circular L Length of pile body (m) 𝛾)*+) Weight density of concrete (kN/m

3)

where: 𝜓- 𝐹);0#;- also known as representative actions 𝑭𝒓𝒆𝒑 are derived

from assembling suitable combinations of characteristic values 𝐹# together with a combination factor (𝝍):

𝐹89: = 𝜓- 𝐹);0#;- -

where:

�= � � �

where:

A Area of pile body (m²) – square or circular

L Length of pile body (m)

� Weight density of concrete (kN/m

3

)

where:

� �

;;

also known as representative actions �

�<�

are derived

from assembling suitable combinations of characteristic values �

together with a combination factor (�):

�=� �

;;

NB the combination factor (𝜓) is always omitted on permanent actions, hence only applied to variable actions. The appropriate combination factor (𝜓) value is taken as less than or equal to one for each action (considering different lead variable to obtain the onerous case), as detailed in Table 2 below (this table has been taken from BS EN 1990:2002+A1:2005).

Table 2: Combination factor (𝝍) values

CEN = European Committee for Standardization (French: Comité Européen de Normalisation) and includes the following member states: Austria, Belgium, Czech Republic, Denmark, Finland, France, Germany, Greece, Iceland, Ireland, Italy, Luxembourg, Malta, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and United Kingdom.

Table 2: Combination factor (�) values

CEN = European Committee for Standardization (French: Comité Européen de Normalisation) and includes the

following member states: Austria, Belgium, Czech Republic, Denmark, Finland, France, Germany, Greece, Iceland,

Ireland, Italy, Luxembourg, Malta, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and United Kingdom.

2.3 Materials (M)

Material (soil) properties are included in EC7 as characteristic values (𝑋#) with a prescribed probability of not being exceeded in a hypothetically unlimited test series. Characteristic material properties 𝑋# are converted into design values 𝑋& by dividing by an appropriate partial factor 𝛾( :

𝑋& = 𝑋# 𝛾(

2.3 Materials (M)

Material (soil) properties are included in EC7 as characteristic values (�) with a prescribed

probability of not being exceeded in a hypothetically unlimited test series. Characteristic material

properties � are converted into design values � by dividing by an appropriate partial factor

�:

�=

�

�

For pile design to the UK National Annex (NA), factored design soil parameters are not used except for unfavourable conditions such as negative shaft friction (NSF), where M2 factors are used in place of M1:

Table 3: Material factors (Table A.NA.4)

Soil properties EC7 & UK NA M1 M2

Friction angle (tan φ’) 1.0 1.25 Effective cohesion (c’) 1.0 1.25 Undrained shear strength (cu) 1.0 1.4 Unconfined compression strength (UCS) 1.0 1.4 Unit weight (γ)* 1.0 1.0 *UK NA gives no factors for unit weight, therefore presume 1.0

For pile design to the UK National Annex (NA), factored design soil parameters are not used

except for unfavourable conditions such as negative shaft friction (NSF), where M2 factors are

used in place of M1:

Table 3: Material factors (Table A.NA.4)

Soil properties

EC7 & UK NA

M1 M2

Friction angle (tan φ’) 1.0 1.25

Effective cohesion (c’) 1.0 1.25

Undrained shear strength (c

u

) 1.0 1.4

Unconfined compression strength (UCS) 1.0 1.4

Unit weight (γ)* 1.0 1.0

*UK NA gives no factors for unit weight, therefore presume 1.0

𝑋" = 𝑋$ 𝛾&

Note on characteristic strength:

The strength of materials, such as concrete, often follow a normal distribution:

The lower or inferior characteristic value 𝑋$;()* is defined as the value of 𝑋 below which 5% of all results are expected to occur. That is, there is a 95% probability that 𝑋 will be greater than 𝑋$;()* . This value is used where overestimate the magnitude of a material property may be unsafe. Typically, this is the norm, and as such 𝑋$;()* is shorten to 𝑋$ . However, in certain situations it will be unsafe to do this and 𝑋$;+,- should be employed. For example, the force acting on a retaining wall should be designed to withstand the upper estimate of the weight density 𝑋$;+,- as this would result in the worst-case scenario. For pile design to the UK National Annex (NA), factored design soil parameters are not used

�=

�

�

Note on characteristic strength:

The strength of materials, such as concrete, often follow a normal distribution:

The lower or inferior characteristic value �

;

is defined as the value of � below which 5% of

all results are expected to occur. That is, there is a 95% probability that � will be greater than

�

;

. This value is used where overestimate the magnitude of a material property may be

unsafe. Typically, this is the norm, and as such �

;

is shorten to �. However, in certain

situations it will be unsafe to do this and �

;

should be employed. For example, the force

acting on a retaining wall should be designed to withstand the upper estimate of the weight

density �

;

as this would result in the worst-case scenario.

For pile design to the UK National Annex (NA), factored design soil parameters are not used

2.4 Design resistance (Rc;d)

From equation 1, the compressive characteristic resistance 𝑹𝒄;𝒌 is obtained from the characteristic shaft friction and end bearing:

𝑅&;' = 𝑅&;);' + 𝑅&;+;' From which, the compressive design resistance 𝑹𝒄;𝒅 is obtained by using partial resistance factors, 𝛾) and 𝛾+:

𝑅&;. = 𝑅&;);' 𝛾)

+ 𝑅&;+;' 𝛾+

where the shaft and base resistances can be calculated from:

𝑅&;);' = 𝐴);0 𝑞);';0 0

𝑅&;+;' = 𝐴+ 𝑞+;'

where: 𝑅&;);' Compressive (c) characteristic (k) resistance (R) of the shaft (s) 𝑅&;+;' Compressive (c) characteristic (k) resistance (R) of the base (b) 𝐴);0 Area of the shaft, i.e. perimeter multiplied by layer, i 𝐴+ Cross-sectional area of the base 𝑞);';0 Unit shaft resistance in layer, i 𝑞+;' Unit base resistance

2.4 Design resistance (R

c;d

)

From equation 1, the compressive characteristic resistance �

�;�

is obtained from the

characteristic shaft friction and end bearing:

�

;

=�

;;

+�

;;

From which, the compressive design resistance �

�;�

is obtained by using partial resistance

factors, � and �:

�

;

=

�

;;

�

+

�

;;

�

where the shaft and base resistances can be calculated from:

�

;;

=�

;

�

;;

�

;;

=�

�

;

where:

�

;;

Compressive (

c

) characteristic (

k

) resistance (R) of the shaft (

s

)

�

;;

Compressive (

c

) characteristic (

k

) resistance (R) of the base (

b

)

�

;

Area of the shaft, i.e. perimeter multiplied by layer, i

� Cross-sectional area of the base

�

;;

Unit shaft resistance in layer, i

�

;

Unit base resistance

where: 𝑅";$;% Compressive (c) characteristic (k) resistance (R) of the shaft (s) 𝑅";&;% Compressive (c) characteristic (k) resistance (R) of the base (b) 𝐴$;( Area of the shaft, i.e. perimeter multiplied by layer, i 𝐴& Cross-sectional area of the base 𝑞$;%;( Unit shaft resistance in layer, i 𝑞&;% Unit base resistance

- by calculation: Model factor 𝜸𝑹𝒅 A model factor should be applied to ensure that the results of the design calculation are either accurate or err on the safe side. This model factor should be applied to the shaft and base resistance calculated using characteristic values of soil properties. Hence, Equation 10 becomes:

𝑅%;' = 𝑅%;);* 𝛾) 𝛾-;'

+ 𝑅%;/;* 𝛾/ 𝛾-;'

In accordance with A3.3.2 of NA to EN1997-1 the value of the model factor 𝜸𝑹 should be 1.4, except that it may be reduced to 1.2 if the resistance is verified by a maintained load test taken to the calculated, unfactored ultimate resistance (i.e. to failure).

- by calculation:

Model factor �

�N

A model factor should be applied to ensure that the results of the design calculation are

either accurate or err on the safe side. This model factor should be applied to the shaft

and base resistance calculated using characteristic values of soil properties. Hence,

Equation 10 becomes:

�

;

=

�

;;

� �

;

+

�

;;

� �

;

In accordance with A3.3.2 of NA to EN1997-1 the value of the model factor �

�

should

be 1.4, except that it may be reduced to 1.2 if the resistance is verified by a maintained

load test taken to the calculated, unfactored ultimate resistance (i.e. to failure).

2.4.1 Pile shaft resistance

Effective stress approach – granular soils

𝑞" = 𝜎%& 𝐾" tan𝛿 Total stress approach – cohesive soils

𝑞" = 𝛼 𝑐/ where: 𝑞" Shaft resistance 𝜎%& Average effective stress on the pile shaft 𝑤ℎ𝑒𝑟𝑒 𝜎% = 𝛾&ℎ 𝐾" Lateral load factor 𝑡𝑎𝑛𝛿 Mobilised friction at the pile-soil shaft 𝛼 Adhesion factor 𝑐/ Undrained shear strength

2.4.1 Pile shaft resistance

Effective stress approach – granular soils

�=� � tan�

Total stress approach – cohesive soils

�=� �

where:

� Shaft resistance

� Average effective stress on the pile shaft �ℎ�O� �=�ℎ

� Lateral load factor

�?�[ Mobilised friction at the pile-soil shaft

� Adhesion factor

� Undrained shear strength

2.4.2. Pile base resistance

Effective stress approach – granular soils

𝑞" = 𝑁% 𝜎() Total stress approach – cohesive soils

𝑞" = 𝑁* 𝑐, where: 𝑞" Base resistance 𝑁% Bearing capacity factor (obtained from chart 2 below) 𝑁* Bearing capacity factor = 9 𝜎() Vertical effective stress at the pile toe 𝑐, Undrained shear strength 𝜙 Angle of shear resistance (used to obtain Nq)

2.4.2. Pile base resistance

Effective stress approach – granular soils

�=�

�

Total stress approach – cohesive soils

�= � �

where:

� Base resistance

� Bearing capacity factor (obtained from chart 2 below)

� Bearing capacity factor = 9

� Vertical effective stress at the pile toe

� Undrained shear strength

� Angle of shear resistance (used to obtain N

q

)

3.0 Table & charts (duplicated form formula booklet)

Pile material

𝜹 Ks

∅ ≤35o ∅ >35o Steel 20 0.5 1.0 Concrete 3/4 ∅ 1.0 2.0 Wood 2/3 ∅ 1.5 4.0

Table 6:

Chart 1:

Bearing capacity factor Nq Berezantsev, et. al. (1961)

3.0 Table & charts (duplicated form formula booklet)

Pile

material

�

Ks

∅≤35

o

∅>35

o

Steel 20 0.5 1.0

Concrete 3/4 ∅ 1.0 2.0

Wood 2/3 ∅ 1.5 4.0

Table 6:

Chart 1:

Bearing capacity factor N

q

Berezantsev, et. al. (1961)

An adhesion factor, a, of 0.45 may be used for bored piles in many clays, although for short bored piles in heavily fissured clays an adhesion factor, a, of 0.3 is more usual.

The graphs below detail the adhesion factors for driven piles

(Tomlinson, 2001)

Chart 3:

An adhesion factor, a, of 0.45 may be used for bored piles in many clays, although for short bored

piles in heavily fissured clays an adhesion factor, a, of 0.3 is more usual.

The graphs below detail the adhesion factors for driven piles

(Tomlinson, 2001)

Chart 3:

- by testing: Characteristic resistances also may be derived from static load tests, ground test results or from dynamic impact tests. In addition, the UK National Annex (NA) has reconsidered the partial factor system for piling recommended in EC7 in light of concerns that the system does not reflect UK current practice and in certain circumstances may be too conservative, and in other cases yielded unsafe design.

Static load tests (BS EN 10997-1:2004 – section 7.6.2.2): The design resistance Rc;d can also be obtained directly from static load testing by applying correlation factors (𝝃) from Tables 4 or 5 or the total resistance factor ( 𝜸𝒕) from Table 1.

𝑅(;* = 𝑅(;, 𝛾.

𝑅(;* = 𝑅(;/;, 𝛾/

+ 𝑅(;1;, 𝛾1

or

- by testing:

Characteristic resistances also may be derived from static load tests, ground test results

or from dynamic impact tests. In addition, the UK National Annex (NA) has reconsidered

the partial factor system for piling recommended in EC7 in light of concerns that the

system does not reflect UK current practice and in certain circumstances may be too

conservative, and in other cases yielded unsafe design.

Static load tests (BS EN 10997-1:2004 – section 7.6.2.2):

The design resistance R

c;d

can also be obtained directly from static load testing by

applying correlation factors (�) from Tables 4 or 5 or the total resistance factor ( �

�

)

from Table 1.

�

;

=

�

;

�

�

;

=

�

;;

�

+

�

;;

�

or

The characteristic resistance is obtained from the static load test data using the following:

𝑅";$ = 𝑅";& &'()

𝜉+ 𝑜𝑟

𝑅";& &/) 𝜉0

For stiff & strong structures use 1 +.+ ≮ 1.0 for redistribution

Ground test results (BS EN 10997-1:2004 – section 7.6.2.3): The characteristic resistance can also be obtained from empirical relationships with ground test results using the following similar relationship:

𝑅";$ = 𝑅";"(6 &'()

𝜉7 𝑜𝑟

𝑅";"(6 &/) 𝜉8

For stiff & strong structures use 1 +.+ ≮ 1.0 for redistribution

Dynamic impact tests (BS EN 10997-1:2004 – section 7.6.2.4): The characteristic resistance can also be obtained from dynamic impact test data using the following similar relationship:

𝑅";$ = 𝑅";& &'()

𝜉9 𝑜𝑟

𝑅";& &/) 𝜉:

Values of 𝜉 may also be multiplied by a model factor (𝛾<): • 0.85 when using dynamic impact tests with signal matching. • 1.10 when the test includes pile head displacement • 1.20 if no measurement of pile head displacement.

NB subscript m = measured cal = calculated

The characteristic resistance is obtained from the static load test data using the

following:

�

;

=

�

;

�

�c

�

;

�

For stiff & strong structures use

.

≮1.0 for redistribution

Ground test results (BS EN 10997-1:2004 – section 7.6.2.3):

The characteristic resistance can also be obtained from empirical relationships with

ground test results using the following similar relationship:

�

;

=

�

;

�

�c

�

;

�

For stiff & strong structures use

.

≮1.0 for redistribution

Dynamic impact tests (BS EN 10997-1:2004 – section 7.6.2.4):

The characteristic resistance can also be obtained from dynamic impact test data using

the following similar relationship:

�

;

=

�

;

�

�c

�

;

�

Values of � may also be multiplied by a model factor (�):

• 0.85 when using dynamic impact tests with signal matching.

• 1.10 when the test includes pile head displacement

• 1.20 if no measurement of pile head displacement.

NB subscript

m

= measured

cal

= calculated

Values for 𝜉 depend on the number of test with values decreasing as the number of tests increases, and are obtained from the following table(s): Table 4: EC7 (Tables A.9 to A.11 combined):

No of tests

Static load tests

Ground test results

Dynamic impact tests

𝜉" 𝜉# 𝜉$ 𝜉% 𝜉& 𝜉' 1 1.4 1.4 - - 2 1.3 1.2 1.35 1.27

1.6 1.5 3 1.2 1.05 1.33 1.23 4 1.1 1.0 1.31 1.20 5 1.0 1.0 1.29 1.15

1.5 1.35 7 1.27 1.12 8 9 10

to 14 1.25 1.08

1.45 1.23

15 to 19

1.42 1.25

≥20 1.4 1.25

Values for 𝜉 depend on the number of test with values decreasing as the number of tests increases, and are obtained from the following table(s): Table 4: EC7 (Tables A.9 to A.11 combined):

No of tests

Static load tests

Ground test results

Dynamic impact tests

𝜉" 𝜉# 𝜉$ 𝜉% 𝜉& 𝜉' 1 1.4 1.4 - - 2 1.3 1.2 1.35 1.27

1.6 1.5 3 1.2 1.05 1.33 1.23 4 1.1 1.0 1.31 1.20 5 1.0 1.0 1.29 1.15

1.5 1.35 7 1.27 1.12 8 9 10

to 14 1.25 1.08

1.45 1.23

15 to 19

1.42 1.25

≥20 1.4 1.25

Table 5: NA to BS EN 1997-1:2004 (Tables A.NA 9 to 11 combined):

No of tests

Static load tests

Ground test results

Dynamic impact tests

𝜉" 𝜉# 𝜉$ 𝜉% 𝜉& 𝜉' 1 1.55 1.55 - - 2 1.47 1.35 1.47 1.39

1.94 1.90 3 1.42 1.23 1.42 1.33 4 1.38 1.15 1.38 1.29 5 1.35 1.08 1.36 1.26

1.85 1.76 7 1.33 1.20 8 9 10

to 14 1.30 1.15

1.83 1.70

15 to 19

1.82 1.67

4. Summary: Characteristic values (k) have not had partial factors applied to them. Design values (d) have had partial factors applied to them.

Subscript: G = permanent Q = variable C = compressive i = denotes the sum total

g = partial factors: to EC7 or EC7 UK-NA

A = Actions (loads or forces = F) M = Materials R = Resistances Actions:

𝐹#;% = 𝛾( 𝐹#;() + 𝑊() + 𝛾, 𝜓. 𝐹#;,);. .

Combination 1: A1 + M1 + R1 Combination 2: A2 + M1 + R4

DA1

Materials: Partial factors for materials are 1.0 therefore design strengths are identical to their characteristic values.

Resistances:

Calculation:

𝑅";$ = &';(;) *( *,;-

+ &';/;) */ *,;-

𝑅";0;1 = 𝐴0;3 𝑞0;1;33 𝑅";5;1 = 𝐴5 𝑞5;1

𝑞0 = 𝜎78 𝐾0 tan𝛿 (sands) or 𝑞0 = 𝛼 𝑐@ (clays) 𝑞5 = 𝑁B 𝜎78 (sands) or 𝑞5 = 𝑁" 𝑐@ (clays)

𝜓" = combination factor (for imposed actions – omitted for permanent actions)

SLS = Proof load test on 1% of the working piles 𝛾%;' = model factor (applied to design based on calculations, i.e. 1.4 which can be reduced to 1.2 when pile tested to failure)

Static load tests: 𝑅#;% = '(;) )*+,

-. 𝑜𝑟

'(;) )1, -2

Ground test results: 𝑅#;% = '(;(+3 )*+,

-4 𝑜𝑟

'(;(+3 )1, -5

Dynamic impact tests: 𝑅#;% = '(;) )*+,

-6 𝑜𝑟

'(;) )1, -7

𝜉 = correlation factor (related to the number of piles tested, applied to mean & min. values)