Temperatura inicial

In traditional design calculations such as those largely employed in the BS geotechnical codes, a limit state is avoided by making sure that stresses in materials, eg in the soil beneath a foundation, are kept to working levels. This is ensured by applying a global safety factor in the calculation for a working state design.

For example, in:

E ≤ R/F_S

E is the disturbance or force acting

R is the resistance offered by the structure (eg the bearing pressure beneath the footing)

F_S is a factor to make sure that E is “sufficiently” less than R.

The precise nature and magnitudes of E and R are not often clearly specified in current national geotechnical codes.

Traditionally, FShas been a fairly large number, for example 3 for a simple strip footing and 2-3 for a pile69, 70, 71, 72_{. Through experience, these factor values were found by} testing and from the back-analysis of observations, firstly to prevent failure and secondly to ensure that settlements under working loads remained acceptably small. In the global safety factor method, checking that both ULS and SLS requirements were met was performed in the one calculation. This traditional, “lumped” factor approach merged all the uncertainty into one factor value, as well as providing an element for limiting the strength mobilised and the settlements.

In contrast, the EC7-1 limit state design philosophy73_{clearly separates ULS from SLS.} It also deals rather more rigorously with the identification and treatment of the many uncertainties inherent in a design problem by:

 making a clear distinction between (destabilising) actions from the superstructure and from the ground

 by separating the uncertainties in these actions, with the partial factors for structural actions coming from BS EN 1990 and, for geotechnical actions, from EC7-1  by separating the uncertainty in the (stabilising) reactions from the ground from

that of the structural loads.

At first sight the STR and GEO γMand γRfactor values required in EC7-1 (and reproduced in Table A3.1) might seem quite small when compared with traditional “lumped” factor values. It is important to appreciate that these values have been developed in combination with the γFand γEvalues that are prescribed in BS EN 1990 for the avoidance of a ULS, following calibration studies in which designs using global factors were reproduced. Given the emphasis in EC7-1 on avoiding a ULS, the combination of these γ values will not necessarily be sufficient to avoid an SLS and separate checks will usually be required.

EC7-1 permits the application of additional “model” factors in some calculations. One such is discussed in Section 4.4.1 and illustrated in Examples 4.1 and 4.2.

4

Specific changes in design principles

with examples

4.1

Summary

4.2

Introduction

Chapter 3 presented the general principles of geotechnical design that are different from traditional British practice. In this chapter, we examine some differences that are specific to particular geotechnical elements and structures and give worked examples showing how to apply EC7-1, using DA-1, and how it compares with current practice. The worked examples have been selected to illustrate as clearly as possible the way in which the principles of EC7-1 are applied.

4.3

Spread foundations

The code offers one of three design methods to be adopted:

 a direct method which in principle involves two separate calculations:  a ULS calculation using ground properties

 a settlement calculation to check the SLS requirements.

 an indirect method in which a single calculation (for all limit states) is based on comparable experience (an essential prerequisite), and which uses the results of field or laboratory measurements or other observations and SLS loads

 a prescriptive method, which is usually based on comparable experience of the observation of serviceability performance (see Section 3.3).

Direct calculation method for GEO and STR ULS design

In the fundamental ULS requirement, represented by the familiar inequality:

E_d≤ R_d

Rdmay be calculated using analytical or semi-empirical formulae. Annex D of EC7-1 provides widely-recognised formulae for bearing resistance74_{that apply for}

homogeneous ground, a condition that is only rarely encountered in the UK. 1

EC7-1 requires the serviceability limits for the structure to be clearly identified so that the geotechnical designer is able to demonstrate that settlement of foundations is acceptable.

This is likely to lead to the more frequent need for structural engineers to indicate the tolerable deformations of the super-structure, which has not been common practice.

2 A significant change for pile design involves the introduction of “correlation factors” that are intended to encourage more pile testing and ground investigation.

3 For retaining structures and in contrast to BS 8002, EC7-1 has no specific requirement for a minimum surcharge loading on the retained ground surface.

4 EC7-1 requires that the GDR be updated as observations yield further information about the geotechnical project.

Indirect method for combined ULS and SLS design

A typical indirect method would be based on the results of a field test. While EC7-1 includes an approach using a (pressuremeter) test not commonly used in the UK75_, other, more common indirect methods could be based on the results of the standard penetration test or cone penetration test76_.

Prescriptive method for combined ULS and SLS design

Allowable bearing pressures are prescribed, for simple strip footings, for example in tables in the Building Regulations and the allowable bearing pressures in BS 8004. While a specific example showing the design of a spread foundation has not been included here, aspects such as checking sliding resistance are included in Examples 4.3 to 4.5 on the design of cantilever retaining walls. Example calculations for design against bearing failure may be found elsewhere (Frank et al, 2004 and Driscoll et al, 2005) and are not repeated in this publication.

4.4

Piles

4.4.1

Specific changes/issues

(a) Serviceability:

In EC7-1, pile design by calculation concentrates on ULS avoidance. This means that the values of partial factors for pile resistance (reproduced in condensed form in Table A3.1) have been determined, in combination with characteristic values and the partial factors for actions, to prevent failure, where this is defined as being a settlement of 10 per cent of the pile diameter77,78_.

Most pile design in the UK is based purely on the ULS capacity, estimated from site test data and empirical factors with sufficiently large values to control settlements. In this approach pile capacity essentially corresponds to the asymptote of a load-displacement graph. As there is no direct assessment of pile settlement, the definition of ultimate capacity is inconsistent with the 10 per cent diameter definition of EC7-1 (and

incidentally BS 8004). To control serviceability the ratio of shaft friction to specified pile working load is often set at or above unity to ensure settlements are low, but

serviceability is not explicitly checked.

However, EC7-1 requires a check with structural engineers on the serviceability limits for the structure, which leads to the need to demonstrate the acceptable settlement of piles. As it is not usual to assess pile settlement, this constitutes a major change from routine British practice in pile design. However, EC7-1 requires a check with structural engineers on the serviceability limits for the structure, which leads to the need to demonstrate the acceptable settlement of piles. As it is not usual to assess pile settlement, this constitutes a major change from routine British practice in pile design. In the UK National Annex to EC7-1, BSI has permitted the use of different partial resistance factor (γR, set R4) values depending on the verification of SLS, with a lesser magnitude value being available for explicit verification, for example, see Table A.NA.6 for a driven pile. In this case, the lower γRvalues in R4 may be adopted (a) if the serviceability limit is verified by load tests (preliminary and/or working) carried out on more than one per cent of the constructed piles to loads not less than 1.5 times the representative load for which they are designed, or (b) if settlement is explicitly predicted by a means no less reliable than in (a) (authors italics), or (c) if settlement at the serviceability limit state is of no concern. Note that in particular circumstances EC7-1 also permits settlement calculations to be replaced by

bearing capacity calculations with a higher value of factor so that a sufficiently low

fraction of the ground strength is mobilised (Clause 2.4.8(4)).

Users of EC7-1 who adopt the definition of failure as being a settlement of 10 per cent of the pile diameter may face a dilemma when estimating pile settlement using, for example, the Fleming method79_{(Fleming, 1992). What value of shaft and base} resistance should be used and, if available capacity beyond a settlement of 10 per cent of pile diameter is ignored, how meaningful will the settlement analysis be?

A designer may need to make additional and specific allowance to further limit pile movements80_.

The above remarks apply to single piles and not to piles in groups. EC7-1 has very little to say about pile groups, which are generally designed for serviceability not ULS.

(b) ULS

The other significant change involves the introduction of the use of “correlation factors” ξ81_{. These are intended to provide increasing design benefit, in the form of} reductions in the value of the correlation factor, progressively with either increasing numbers of pile load tests or profiles82_{of ground parameter data. The correlation} factors are used in combination with mean and minimum values of pile test result or ground profile value so as to include some allowance for the variability encountered. In the UK it is likely, given the variability commonly encountered, that ξ will only be used with pile load test results and then only where the test results show reasonable repeatability. In rare circumstances where the local geology is constant, such as an estuarine clay deposit, a consistent set of ground property profiles, obtained using the CPT for example, might permit correlation factors to be used on them.

For those most common occasions when design is based on ground test data, EC7-1 provides two calculation methods:

 a procedure in which the bearing resistance is calculated using results from one or more profiles of ground test results83

 an alternative procedure, where the ground test results for all test locations are first combined in order to derive the characteristic values of base resistance and shaft

friction in the various strata84_{, as illustrated in Figure 4.1.}

In another departure from common practice, account should be taken when applying a correlation factor of the ability of the structure connecting the piles to transfer loads from weaker to stronger piles. If structural engineers agree that the structure is able to do so, the value of ξ may be divided by 1.1 provided the resulting value does not fall below 1. EC7-1 differs slightly from BS 8004 in stating that a check of buckling of slender piles is not required if the undrained shear strength, cu, of the soil exceeds 10 kPa, whereas BS 8004 implies that a check is required for culess that 20 kPa.

Here are two examples illustrating features of EC7-1 for the design of piles. The first demonstrates that, at least until the user has become familiar with the code, a

settlement calculation will frequently be necessary to ensure that the design satisfies the SLS. However, since the authors contend that currently most designers do not have sufficient confidence that settlement can explicitly be predicted by a means no less reliable than a pile load test, they cannot justify the adoption of the lower partial factor values given in Table A.NA.6. Over time, however, as settlement calculations are

verified/modified to reflect actual test behaviour (for given soil types) the designer may acquire sufficient experience to use them confidently.

For this reason, Example 4.1 shows a serviceability calculation, as required by BSEN1997-1, but adopts the higher partial factors given in the NA. Example 4.2 illustrates the way in which favourable resistance and unfavourable (downdrag) action are separately factored, with different factor values.

Figure 4.1 Alternative procedures for pile design using profiles of ground properties Calculate characteristic pile resistances for the

different profiles of ground properties, divide mean and minimum values for the resistances by their respective ξ values and take the minimum of these

two results as the characteristic resistance to be factored by γ into the design resistance. Note: this process attempts in a simple way (a) to provide benefit from a greater quantity of data and

(b) to reflect the variability between the ground properties at the locations of the profiles.

Calculate characteristic pile resistances from this single profile of ground properties and apply partial factors for

base (γb) and shaft (γs) to determine

design resistances. Note: an additional “model” factor will

be required, since the ξ factor is not applied in this alternative. The value of

this factor is indicated in the National Annex to EC7-1 (see Endnote 84). More than one

profile of data? This alternative is likely to be most commonly used in UK practice Yes No

Select suitable profiles of ground test data. Number of profiles = n

Find values of ξ3and ξ4

from National Annex, Table A.NA.10, depending on value of n

Assemble available ground test data Note that this option is

not likely unless the ground is locally uniform

Example 4.1 Design of a vertical, pre-cast concrete pile driven into sand and gravel

Project

Subject

Example 4.1

Pre-cast Concrete Driven Pile

Clauses

2.4.7.3.4.2

(2)

Table A.NA.3.

NA.A1.2(B)

(Permanent

Unfavourable)

[1]

7.6.2.1 (2)

Table A.NA.4

Pile D esign

Drive pile in sand and gravel

Note: This example demonstrates how a pile design should be

approached using EC7. The calculation to determine the length of pile

required is shown below. Section 7 of the code should be consulted

when undertaking a complete design to determine which other limit

states should be considered.

Purpose of calculation: To determine length of pile required.

Design Approach 1. (Axia lly loaded piles)

Combination 1: A1 “+” M1 “+” R1

Design Action (Load) (A1)

Partial Factor, Ȗ

G

=

1.35

F

c; d1

=

2000 × 1.35

Note: For transparency in the calculation any difference in the weight of

the pile and the displaced overburden load is not included.

Basic Pile Resistance Factors

Material Factors (M1)

All partial factors = 1.0

Note: No modification to adopted soil parameters is required for the

design of axially loaded piles.

F

c; d1

Berezantsev

et al (1961)

[2]

Kulhawy

(1985)

[3]

7.6.2.3(4)

Table A.NA.6

NA (2007)

A.3.3.2

[4]

[5]

Resistance (R1)

Base resistance formula:

N

q

.V

v

’. A

b

N

q

– bearing capacity factor

V

v

’ – vertical effective stress at the pile toe

A

b

– area of the base of pile

Bearing capacity factor:

I’ = 35q

N

q

= 55 (D/B = 20)

Area of base:

A

b

= [ʌ x (0.6)²] /4 = 0.28m²

Shaft resistance formula:

K

s

.V

v

’. tanG. A

s

K

s

– lateral load factor

V

v

’ – average effective stress on the pil e shaft

tanG - mobilised friction at the pile-soil interface

A

s

– area of the pile shaft

K

s

= 1 (Driven pile, large displacement)

tanG = tan (0.8I’) (Precast concrete)

tanG = 0.53

Design Resistance (R1)

Partial factors for driven piles in compression, Ȗ

b

& Ȗ

s

= 1.0

Model Factor, Ȗ

R;d

= 1.4

Design Base Resistance:

R

b;d1

= (55 x V

v

’

b

x 0.28)/(Ȗ

b

x Ȗ

R;d

)

R

b;d1

= 11V

v

’

b

Design Shaft Resistance:

R

s;d1

= (1 x V

v

’

s

x 0.53 x (0.6 x ʌ x L))/(Ȗ

s

x Ȗ

R;d

)

R

s;d1

= 0.71V

v

’

s

L

Design Compressive Resistance R

c;d

= R

b;d

+ R

s;d

Determination of length of pile to carry prescribed load

Try 15m long pile

[6]

Table A.NA.3

NA.A1.2(C)

(Permanent

Unfavourable)

Table A.NA.4

7.6.2.3(4)

NA(2007)

A.3.3.2

Table A.NA.6

7.6.4.1(1)

Poulos &

Davis (P&D).

Section

5.3.2

R

s;d1

= 0.71 x {[(0+40)/2 x 2] + [(40 + 170)/2 x 13]}

= 998kN

R

c;d1

= 1870 + 998 = 2868kN (> F

c;d1

(2700kN))

Conclusion:

A pile 15m long, 600mm diameter can carry the load of 2000kN under

Combination 1.

Combination 2: A2 “+” M1 “+” R4

Design Action (A2)

Partial Factor, Ȗ

G

= 1.0

F

c;d2

= 2000 ×1.0

F

c;d2

= 2000

Material Factors (M1) for Combination 1 and Combination 2 are the

same, ie M1

Design Resistance (R4)

Model Factor, Ȗ

R;d

= 1.4

Partial factors for driven piles in compression without explicit verification

of SLS. Ȗ

b

= 1.7 and Ȗ

s

= 1.5

Therefore R

c;d2

= R

b;d1

/1.7 + R

s;d1

/1.5

For 17m long pile

R

b;d1

= 11 x (2 x 20 + 15 x 10) = 2090kN

R

s;d1

= 0.71x{[(0+40)/2x2]+[(40+190)/2x15]}=1253kN

R

c;d2

=

2090 1253

+

=

1.7

1.5

2064kN (>F

c;d2

(2000kN))

Conclusion:

A pile 17m long, 600mm diameter can carry the load of 2000kN under

Combination 2

An example of the vertical settlem ent of the pile is det ermined using

procedures developed by Poulos & Davis (1980): Pile foundation analysis

and design (Wiley).

For Floating Pile.

ȕ= ȕ

o

C

k

C

ȣ

R

c;d1

=

2868kN

R

c;d2

=

P&D Fig 5.11

P&D Fig 5.12

P&D Fig 5.13

P&D. Eqn

5.53

P&D

Eqn 5.54

P&D Fig 5.18

P&D Fig 5.19

P&D Fig 5.21

ȕ =P

b

/p = proportion of applied load transferred to pile tip

ȕ

o

= tip load proportion for uncompressible pile

C

k

= correction factor for pile compressibility

C

ȣ

= correction factor for poissons ratio of soil.

L/d = 17/0.6 = 28; d

b

/d = 1

ȕ

o

= 0.55

d

b

– diameter of bas e of pile

d – diameter of shaft

Take k=1000 (Ratio stiffness of pile to stiffness of ground)

C

k

= 0.9

Poisson’s ratio, ȣ = 0.3

C

ȣ

= 0.79

So, ȕ = 0.055 x 0.9 x 0.79 = 0.04

Overall load vs settlem ent

Ultimate shaft resistance (unfactored values)

c.f. Equation [5]

P

su

= (0.6 x › x 1 x 0.53 x {[(0 + 40)/2 x 2] + [(40 + 190)/2 x 15]}

= 1763kN

Full shaft yield

P

y1

= P

su

=

1763

= 1836kN

1 – ȕ

1 – 0.04

Settlement at full shaft yield

U

y1

=

I

P

y1

E

s

d

I = I

O

R

k

R

h

R

y

R

k

– correction factor for pile compressibility

R

h

– correction factor for rigid layer (take as 1.0)

R

y

– correction for soil poissons ratio

I

O

– settlem ent influence factor for incompressible pile

L/d = 28, d

0

/d = 1

I

O

= 0.07

K – stiffness ratio soil/pile – take as 1000

R

k

= 1.15

Q

s

= 0.3

R

y

= 0.93

So, based on average soil stiffness of 30MPa

I = 0.07 x 1.15 x 1.0 x 0.93 = 0.075

ȡ

y1

=

0.075 x 1836

(30 x 10

3

_{) x 0.6}

ȡ

y1

= 8mm

Settlement at 2000kN

=

8 x 2000

1836

Overall Conclusion:

1 A pile 17m long, 600mm diameter can carry the load of 2000kN

under Combination 2.

2 Combination 2 is critical as

c;d2< c; d1

c;d2 c;d1

R

R

F

F

3 Settlement analysis has shown the pile will settle less than 10mm

under the working load of 2000kN

NOTE:

1

Traditional pile analysis has been based broadly on obtaining an

appropriate site investigation and then varying the overall factor of

safety dependent on pile testing proposed.

Eg

FofS = 3 – No pile t ests

FofS = 2.5 – Test 1% of working piles

FofS = 2 – Undertake a preliminary pile test

Using this approach it has been expected that settl ement criteria

would be met, without the need for explicit analyses.

2

The equivalent factors of safety for the above analyses are:

Combination 1

Ȗ

G

× Model Factor × Ȗ

(b&s)

= 1.35 × 1.4 × 1.0

Combination 2

Ȗ

G

× Model Factor × Ȗ

(b&s)

= 1.0 × 1.4 × (1.5 to 1.7)

3 The NA states that lower partial factors can be adopted if,

“settlement is explicitly predicted by a method no less relia ble than

a pile load test.”

The authors’ contention is that currently most designers would not have

this degree of confidence. Over tim e, however, as settl ement

calculations are verified/modified to reflect actual test behaviour (for

given soil types) the d esigner may acquire sufficient experience to justify

the adoption of the lower partial factors.

For the above reasons this example shows a serviceability calculation, as

required by BSEN1997-1, but adopts the higher partial factors given in

the NA.

Settlement

= 9mm

FofS = 1.89

FofS =

2.1 to 2.38

Example 4.2 Pile design incorporating negative skin friction (downdrag)

Project

Subject

Example 4.2

Pile design incorporating negative skin friction (downdrag)

Clauses

2.4.7.3.4.2

(2)

7.3.2.2

Table A.NA.3

NA.A1.2(B)

(Permanent

Unfavourable)

[1]

Pile D esign

Bored pile in clay with downdrag

Purpose of calculation: To determine the length of pile required.

Design Approach 1. (Axia lly loaded piles)

Combination 1: A1 “+” M1 “+” R1

Characteristics values of Actions

Applied force, F

k

= 1000KN

Negative s kin friction, S

D

= D C

u

(take adhesion factor, D = 1)

= C

u

Downdrag force, F

nsf;k

= › x 0.6 x 4 x 20

= 150.8KN

Design Actions (A1)

Partial factor, Ȗ

G

= 1.35 (for both applied and downdrag force)

Applied force, F

d1

= 1000 × 1.35 = 1350kN

Downdrag force, F

nsf;d1

= 150.8 x 1.35 = 203.6kN

Total downward force, F

c;d1

= 1350 + 203.6

Note: For transparency in the calculation any difference in the weight of

the pile and the displaced overburden load is not included.

Skempton

(1951)

B/L = 1,

D/B>5

Table A.NA.4

Undrained

Shear

Strength

[2]

[3]

7.6.2.3

Table A.NA.7

7.6.2.3 (8)

NA (2007)

A.3.3.2

[4]

[5]

[6]

[7]

Basic Pile Resistance Factors

Pile Base: 9 C

u

Pile Shaft: Į C

u

For this case, adopt Į = 0.5

Pile Shaft: 0.5 C

u

Design Soil Parameters (M1)

Partial factor

Ȗ

cu

= 1.0

C

u;d

= C

u;k

/1.0

C

u;d

= C

u;k

Characteristic Resistance (R1)

Base Resistance: R

b;k

= 9.C

u;d

.A

b

Shaft resistance: R

s;k

= 0.5.C

u;d

.A

s

Note: C

u

is the average undrained shear strength of the clay along the

pile shaft.

Design Resistance (R1)

Note: Data obtained from ground test results

Partial factors for bored piles

Ȗ

b

= 1.0

Ȗ

s

= 1.0

Note: When d eriving characteristic values for pile design from ground

parameters partial factors have to be corrected by a Model Factor.

Model Factor,Ȗ

R;d

= 1.4

Partial factors for pile resistance for bored piles:

Ȗ

b

× Ȗ

R;d

= 1.0 × 1.4 = 1.4

Ȗ

s

× Ȗ

R;d

= 1.0 × 1.4 = 1.4

Design Base Resistance:

R

b;d

= (9/1.4) C

u;d

.A

b

= 6.4 C

u;d

.A

b

Design Shaft Resistance:

R

s;d

= (0.5/1.4) C

u;d

.A

s

= 0.36 C

u;d

.A

s

Design Compressive Resistance: R

c;d

= R

b;d

+ R

s;d

Determination of length of pile to carry prescribed load

Try L

R

= 17m

R

c;d1

=

[6.4 × (60 + 17 × 8) × (› × (0.6)

2

)/4] + [0.36 × (60

[8]

2.4.7.3.4.2

(2)

Note 2

Table A.NA.4

(Undrained

Shear

Stength)

[9]

Table A.NA.3

NA.A1.2(C)

(Permanent

Unfavourable)

[10]

7.6.2.3 (4)

Table A.NA.7

NA (2007)

A.3.3.2

[11]

[12]

R

c;d1

=

355kN + 1477Kn = 1831kN (>F

c;d1

(1554kN))

Conclusion

A pile 21m long, 0.6m diameter can carry the load of 1000kN with

downdrag force of 151kN under Combination 1.

Combination 2: A2 “+” (M1 or M2) “+” R4

M1 – For calculating pile resistance

M2 – For calculating unfavourable actions ie downdrag

Design Soil Parameters (M2)

Partial factor, Ȗ

cu

= 1.4

C

u;d

= C

u;k

x 1.4 = 28kPa

Note 1: The use of factors for set M2 in Table A.NA .4 is explicit when

negative skin friction is deri ved directly from shear strength, ie C

u

, but in

this case as it is unfavourable the factor is used as a multiplier rather

In document PLANEAMIENTO DE SISTEMAS DE DISTRIBUCIÓN CON GENERACIÓN DISTRIBUIDA A BASE DE GAS NATURAL USANDO RECOCIDO SIMULADO OSCAR MAURICIO LAVERDE SAAVEDRA (página 34-57)