The Concepts of Eurocode 7 for Harmonised Geotechnical Design in Europe

Transcription

1 1 The Concepts of Eurocode 7 for Harmonised Geotechnical Design in Europe by Trevor Orr Trinity College Dublin at Politechnika Wrocławska Studia Doktoranckie on 8 th to 12 th February 2010

2 2 Day 2 Development of Eurocode 7 GEO & STR ULSs and Design Approaches Design of Spread Foundations

3 3 Programme Day Monday Tuesday Wednesday Thursday Friday Session 1a 1b 1c 2a 2b 2c 3a 3b 3c 4a 4b 4c 5a 5b 5c Topic Introduction and background to the Eurocodes and Eurocode 7 Basis of design and main features of Eurocode 7 Geotechnical data, characteristic parameter values Development of Eurocode 7 GEO ultimate limit states and Design Approaches Design of spread foundations Calculation models in Eurocode 7 EQU, UPL and HYD ultimate limit states Design of pile foundations Risk and reliability in the Eurocodes Design of retaining structures Design of slopes and overall stability Special features of soil and Geotechnical Design Triangle Associated CEN standards Implementation of Eurocode 7 and future development

4 4 Session 2a Development of Eurocode 7

5 Stages in Development of Eurocode 7 Stage Conception Model Code stage ENV stage ENV trial stage WG1 stage EN stage Implementation Year Initiative for Eurocodes by universities and engineering profession CEC decided on an action programme for the Eurocodes Niels Krebs Ovesen appointed chairman of Eurocode 7 committee First EC7 committee meeting Model Eurocode 7 produced Work began on ENV Work transferred from CEC to CEN ENV published by CEN Trial calculations with ENV and discussions WG1 formed Produced Draft EN Activity WG formed to convert ENV into EN EN published by CEN in 2004 EN published by CEN in 2007 Preparation and publication of national annexes Eurocode 7 to supersede European national codes 29 years from 1st committee meeting to implementation 5

6 Model Code Stage Preparation of limit state geotechnical design code to serve as a model for Eurocode 7 Focused on principles Only a few partial factors proposed 1980 Professor Fukuoka, President ISSMFE, asked Kevin Nash, Secretary General to invite Niels Krebs Ovesen to be Chairman of Eurocode 7 Committee to produce a model code for Eurocode ISSMFE Sub-committee for EC7 formed from 9 EEC countries first meeting in Brussels 1982 ISSMFE Board considered code work not appropriate so sponsorship withdrawn. Committee became ad-hoc committee Committee met 22 times in different EEC countries to draft code and learn about local geotechnical practices 1987 Committee produced Model Code for Eurocode 7

7 Dublin Meeting 1983 by Constance Heijnen Simpson (GB), Lousberg (B) Baguelin (F) Japelli (I) Sadgorski (D), Thorp (D) Farrell (IRL) Nelissen (NL) Orr (IRL) Coumoulos (G) Krebs Ovesen (S) Heijnen (NL)

8 Model Code Committee 1986 Expanded Eurocode 7 Committee Portugal

9 9 Model Code Model Code 1987 Chinese translation of Model Code in 1988

10 10 ENV Stage Preparation of ENV (trial) Eurocode 7 Defined characteristic value Partial factors only on soil strength, not resistance Cases A, B and C with different sets of partial factors 1988 European Commission (CEC) formed a 7-member Drafting Panel for Eurocode 7 with Niels Krebs Ovesen as Chairman 1989 EC decided to transfer Eurocodes to CEN 1990 SC7 formed by CEN to oversee work on Eurocode 7 - Niels Krebs Ovesen appointed convenor of SC7 - Eurocode 7 given reference number EN Completion of ENV after 22 meetings, mostly in Delft - Adoption of ENV by SC7 and CEN 1994 Publication of ENV by CEN

11 Delft Canal and Church Tower 11

12 12 ENV Trial Stage Trial calculations and discussions about ENV - Some CEN countries not happy with ENV - Seminar at Institution of Structural Engineers, London Sept-Oct 1996 to discuss ENV - Some strong views against ENV and partial factors - EC7 is a very strange document. On present evidence, it appears that the method proposed in EC7 needs considerably more development before it can be considered for use - If the present method of EC7 is adopted in this respect it will be a disservice to the industry which will restrain its development for the next decade

13 Eurocode 7 Seminar London

14 14 WG1 Stage Before starting to transform ENV into an EN, SC7 decided work was needed to make Eurocode 7 more acceptable to geotechnical engineers in Europe - Introduced three Design Approaches with partial factors on resistances as well as on soil strength - Introduced sections on failure due to water pressures and seepage 1997 WG1 formed by SC7 - To involve all the CEN countries more directly in the transformation of the ENV into an EN - Ulrich Smoltczyk appointed as convenor - WG1 met 6 times and produced a draft EN 1998 Draft EN produced

15 15 EN Stage Transformation of ENV into EN PT1 established to transform ENV into EN - Ulrich Smoltczyk appointed convenor 2001 Final draft received a unanimous vote of approval from SC7 - Adopted at SC7 meeting in Milan in April - Text translated into 2 other official CEN languages, French and German 2004 January - Issued to all CEN members for formal vote April Positive vote received from all CEN countries - Date of Ratification (DOR)

16 16 Implementation Stage present National implementation of EN Publication of National Annexes for EN Publication of EN Publication of National Annexes for EN Appointment of a Maintenance Group for EN Corrigenda submitted March: Eurocodes with national annexes to supersede existing national standards Beginning of Eurocode Era

17 Irish National Standard Version of EN Irish NA: 2005

18 18 Time for discussion Any questions?

19 Tutorial No. 1 Selection of Characteristic Values 19

20 20 Problem Select characteristic parameter values for design of a spread foundation on sandy soil Given CPT data Location of boreholes relative to foundation Also density of soil

21 21 Responses Received Regarding location of boreholes Consensus: Not considered significant The results of all four tests show high correlation and little local variation Characteristic values at three depths requested on questionnaire Responses for 2m depth Characteristic q c value 17 responses How were characteristic values selected: By eye 32%: By statistical analysis 27% By linear regression 23% Characteristic q c value: Minimum value: 10 MPa Maximum value: 15 MPa Average value: 13.1 MPa

22 22 Soil Characteristic Parameters Characteristic φ value: Minimum value: 32.7 o Maximum value: 48.7 o Average value: 42.0 o Basis for selection: φ = 13.5 logq c + 23 (from EN and most popular) φ = 29 + (q c ) φ = D R (Schmertmann) φ = 16 D R D R + 24 (API) Characteristic E value: Minimum value: 32 MPa Maximum value: 70 MPa Average value: 38.1 MPa 81% said they were confident that their design was sound!

23 How do your results compare? 23

24 24 Session 2b GEO & STR Ultimate Limit States and Design Approaches

25 Ultimate and Serviceability Limit States Definitions of Ultimate and Serviceability Limit States in EN 1990 Basis of Design ULS States associated with collapse or with other similar forms of structural failure SLS States that correspond to conditions beyond which specified service requirements for a structure or structural member are no longer met Responsibility for setting requirements ULS Concerned with risk to people s safety and danger to life Requirements set by society and authorities, e.g. partial factors SLS Concerned with the use of structures,, i.e. their function Requirements set by clients, owners Of limited interest to authorities Little detail in codes 25

26 26 GEO & STR Ultimate Limit States GEO ULS: Failure or excessive deformation of the ground, in which the strength of soil of rock is significant in providing resistance STR ULS: Internal failure or excessive deformation of the structure or structural elements, including e.g. footings, piles or basement walls, in which the strength of structural materials is significant in providing resistance Partial factors for GEO ultimate limit states are used with STR ultimate limit states GEO sometimes gives the loading for STR ultimate limit states GEO & STR Hence one set of partial factors in EN are for verification of GEO and STR ultimate limit states

27 Partial Factors For GEO ultimate limit states must satisfy equation E d < R d Partial factors are applied to either characteristic soil parameters or characteristic resistances to obtain E d and R d Partial factors are grouped into Sets A, M and R in Annex A Set A for partial factors on actions or effects of actions Set M for partial factors on soil parameters Set R for partial factors on resistances Three combinations of sets partial factors are provided in Eurocode 7 for GEO and STR, known as Design Approaches 1, 2 and 3 Each country has to decide and publish in its National Annex which Design Approach or Approaches are to be used for each type of design i.e. whether to factor soils parameters or resistances Poland has chosen to adopt DA1 27

28 28 Design Approaches Design Approach 1 (DA1) Combination 1: Partial factors applied to actions and no partial factors applied to soil strength parameters (DA1.C1) Combination 2: Only a reduced partial factor applied to variable actions and no partial factors applied to soil strengths Except for pile foundations, when partial factors are applied to resistances (DA1.C2) Design Approach 2 (DA2) Partial factors applied to actions and resistances Design Approach 3 (DA3) Partial factors applied to permanent and variable structural actions and to variable geotechnical actions and to soil strength parameters As DA3 has no resistance factors, not used for pile design

29 Combinations of Partial Factors Equations given in Eurocode 7 for combining partial factors DA1 for most situations DA1.C1: DA1.C2: A1 + M1 + R1 A2 + M2 + R1 DA1 for piles and anchors DA1.C1: A1 + M1 + R1 DA1.C2: A2 + (M1 or M2) + R4 DA2 DA3 A1 + M1 + R2 (A1* or A2**) + M2 + R3 * on structural actions ** on geotechnical actions 29

30 Partial Factor Values Parameter Factor DA1(1) DA1(2) DA2 DA3 Partial factors on actions (γ F ) or the effects of actions (γ E ) Set A1 A2 A1 A1* Struct. Actions A2 Geotech Actions Permanent unfavourable action γ G Permanent favourable action γ G Variable unfavourable action γ Q Variable favourable action γ Q Accidental action γ A Partial factors for soil parameters (γ M ) Set M1 M2** M1 M2 Angle of shearing resistance, tanφ' γ tanφ ' Effective cohesion c' γ c' Undrained shear strength c u γ cu Unconfined strength q u γ qu Weight density of ground γ γ γ Partial resistance factors (γ R ) Spread foundations and retaining structures Set R1 R4 R2 R3 Bearing resistance γ R;v Sliding resistance γ R;h Earth resistance retaining structures γ R;e Earth resistance slopes & overall stability γ R;e * For slope and overall stability analyses, actions on the soil (e.g. structural actions, traffic loads) are treated as geotechnical actions by using the set of load factors A2 * M1 is used for calculating design resistances of piles or anchors M2 for calculating unfavourable design actions on piles owing e.g. to negative skin friction or transverse loading 30

31 31 Comments on DA1 DA1 requires two combinations of partial factors to be considered DA1.C1 and DA1.C2 In principle one has two check both combinations DA1.C1 mainly considers the uncertainty in actions. The partial factors are applied to the actions and not to ground strength parameters DA1.C2 mainly considers the uncertainty in soil parameters. Partial factors are applied to variable loads and soil strength parameters (e.g. c ' or φ') except for pile and anchor design, where the partial factors are applied to the resistance and sometimes to ground strength parameters Usually DA1.C2 is the combination that is relevant for most geotechnical designs so normally partial factors are applied to soil strengths and DA1.C1 is not relevant but beware DA1 considers uncertainty in actions and soil parameters separately good Both DA1 combinations are easy to use in finite element analyses DA1.C2 can be applied using c /φ reduction

32 32 Comments on DA2 Requires only one combination Partial factors applied to soil resistances, not to soil parameters If DA2 used for slope and overall stability analyses the resulting effect of the actions on the failure surface is multiplied by γ E and the shear resistance along the failure surface is divided by γ R,e Not stated specifically in EC7, but partial factor on action from water pressure is applied to the net water pressure force in DA2 Closer to more traditional approach Difficult to apply in finite element analyses Difficult to apply to slope stability analyses using method of slices

33 33 Comments on DA3 Requires only one combination Similar to DA1.C2 except different partial factors applied to structural and geotechnical actions In case of slope stability analyses, actions on the soil (e.g. structural actions, traffic load) are treated as geotechnical actions Only cone calculation required Has been chosen by many countries for slope stability design

34 34 Bridge Pier Bearing capacity or slope stability problem? What partial factors on foundation loads for DA3?

35 Single Source Principle There is the following important note to Clause which is adopted generally in DA1 and DA3: Unfavourable (or destabilising) and favourable (or stabilising) permanent actions may in some situations be considered as coming from a single source. If they are considered so, a single partial factor may be applied to the sum of these actions or to the sum of their effects This is known as the single source principle Useful in the analyses of slope stability Difficult to separate favourable and Centre of rotation unfavourable actions Favourable weight Surcharge Slip surface W f W u Unfavourable weight 35

36 Slope Stability 36 DA1 and DA3 In a drained analysis of the slope in the figure, the disturbing force Wsinα and the resisting force, Wcosα are both functions of the weight of the soil element, W W is treated as coming from a single source In DA1.C1, W k is factored by 1.35 and tanφ k is not factored so both F d and R d contain 1.35W d and there is no margin of safety Hence DA1.C1 is not relevant In DA1.C2, W k is factored by 1.0 and tanφ k is factored by 1.25 so there is a margin of safety DA2 Single source principle not normally adopted in DA2 so it is often difficult to analyse slope stability since part of soil weight is favourable and part is unfavourable F d = W d sinα Require: W d F d R d R d = W d sinα tanφ d W d cosα

37 Water Pressures on Retaining Structures Not stated specifically in EC7, but partial factor on action from water pressure is applied to the net water pressure force in DA2 Total water pressure (DA1 & DA3) Net water pressure (DA2) 37

38 Design Earth Pressures on a Retaining Wall To determine the length of the wall embedment, check the wall stability by taking moments of the design active and passive earth pressure forces, P a,d and P p,d, about the tie rod: Require the wall embedment depth, d Tie rod P a,d z a = P p,d z P This is a GEO ULS geotechnical design, hence one of the Design Approaches must be selected Depending on which Design Approach is adopted, partial factors are either applied to the characteristic actions (earth pressure forces due to permanent and variable loads) or to the characteristic soil parameters (c k ', φ k ') to give design values P a,d and P p,d P a,d z a z p P p,d d 38

39 Design Approach 1 DA1.C1 Active and passive earth pressure forces are both treated as actions Partial action factors γ G = 1.35 and γ Q = 1.5 are applied to the characteristic earth pressure forces obtained using unfactored soil strength parameters c k, φ k For example, if no surcharge P a,d = 1.35 P a,k P p,d = 1.35 P p,k DA1.C2 Partial action factors γ G = 1.0 and γ Q = 1.3 are applied to the earth pressure forces and partial material factors are applied to the soil strength parameters c' = c k /1.4 φ d ' = tan -1 (tanφ k /1.25) Applying partial material factors to reduce c and tanφ increases K a and reduces K p Note: Both P a and P p are increased by the same amount This combination gives no margin of safety for the embedded length (i.e. for geotechnical design) but is relevant to the structural design of the wall Therefore P a,d > P a,k and P p,d < P p,k This combination gives a margin of safety for the geotechnical design of the embedded length of the wall Maximum wall bending moment and shear force DA1.C1 and so is used for but is relevant to the structural design 39

40 Design Approaches 2 and 3 DA2 The active earth pressure force, P a is treated as an unfavourable action and the passive earth pressure force, P p is treated as a resistance The design active earth pressure force, P a,d is obtained by applying partial factors γ G = 1.35 and γ Q = 1.5 to the unfavourable characteristic active earth pressure force, P a,k obtained using c k ', φ k The design passive earth pressure force, P p,d is obtained by applying the resistance factor, γ R = 1.4 to the characteristic passive earth pressure force, P a,k obtained using c k ', φ k For example, for no surcharge DA3 DA3 is same as DA1.C2, but γ G = 1.35 and γ Q = 1.5 are applied to unfavourable structural actions while γ G = 1.0 and γ Q = 1.3 are applied to geotechnical actions and partial material factors are applied to reduce soil strength parameters c d = c k /1.4 φ d = tan -1 (tan φ k '/1.25) P a,d = 1.35 P a,k P p,d = P p,k /1.4 Hence using DA2, the overall factor of safety is 1.35 x 1.4 =

41 41 Overview of Design Approaches Philosophically DA1 and DA3 apply the partial factors close to the source of uncertainty the soil parameter values DA1 looks separately at the uncertainties in the actions and the soil parameter values, which is good The DA1 requirement for two separate ULS calculations may discourage some Need to be aware that DA1.C1 does not give any safety margin in some design situations retaining walls and slope stability DA1 and DA3 are much easier to use than DA2 in finite element analyses DA1.C2 and DA3 can be analysed using c/φ reduction Since the overall factor of safety for DA1 ULS designs, particularly for undrained conditions, is lower than in traditional designs, the SLS will have more significance in foundation design

42 42 Discussion Any questions?

43 43 Session 2c Design of Spread Foundations

44 44 Design of Spread Foundations One of the most common geotechnical design situations is the design of spread (i.e. shallow) foundations Term shallow foundations not used in Eurocode 7 because of the difficulty in defining the term shallow Term bearing resistance bearing capacity is used in Eurocode 7 because it is a and involves soil strength Hence equation given is called a bearing resistance equation not a bearing capacity equation Note that bearing resistance in Eurocode 7 is a force (kn) not a stress (kpa)

45 Limit State Requirements Eurocode 7 requires that for each geotechnical design situation it is checked that no relevant limit state is exceeded (Clause 2,1(1)) The ultimate limit states to be considered in the case of spread foundations are (Clause 6.2(1)): Loss of overall stability Bearing resistance failure, punching, squeezing Failure by sliding Combined failure in the ground and the structure Structural failure due to foundation movement Since these ultimate limit states are all situations in which the strength of soil or rock is significant in providing resistance, according to Eurocode 7 they are GEO ultimate limit states (Clause (1)) The serviceability limit states to be considered are: Excessive settlements Excessive heave due to swelling, frost and other causes Unacceptable vibrations 45

46 46 Controlling Limit State It is not always obvious which limit state, ultimate or serviceability, controls a design Controlling limit state depends on the design situation, i.e. it depends on: Loads Soil properties Design approach (i.e. chosen partial factors), and Allowable deformations

47 Example of a Spread Foundation Square pad foundation with vertical central load, Vk = G k + Q k and Q k = 20% G k Dry soil with φ' k = 35 o and E m = 20 MPa Foundation design width, B(m) Design controlled by ULS Design controlled by SLS SLS DA3 DA2 DA1.C Characteristic total foundation load, V k (kn) n this example For loads <~ 1000 kn, ULS controls and for loads >~1000 kn, SLS controls Change occurs at lower loads for DA1 than for DA2 and DA3 47

48 48 Design Methods A direct method, in which separate analyses are carried out for each limit state. When checking against an ultimate limit state, the calculation shall model as closely as possible the failure mechanism, which is envisaged. When checking against a serviceability limit state, a settlement calculation shall be used (Clause 6.4(5)) An indirect method using comparable experience and field or laboratory measurements or observations, chosen in relation to serviceability limit state (i.e. unfactored) loads, so as satisfy the requirements of all relevant limit states i.e. one calculation is used to check that neither a ULS nor an SLS occurs A prescriptive method in which a presumed bearing resistance is used No analysis of stability or deformation is carried (Clause 2.5(1)) out but a presumed bearing resistance is assumed to avoid the occurrence of either a ULS or an SLS Only appropriate for Geotechnical Category 1 structures

49 49 ULS Calculations Need to check that E d R d (Clause (1)) E d = design action effect = design loads in the case of a foundation = a force R d = design resistance and is a force i.e. the above equation is in terms of forces not stresses Hence Eurocode 7 is different from traditional design which checks that the bearing stress does not exceed the allowable stress R d is obtained using a calculation model (equation) and the sets of partial factors for the following Design Approaches: DA1 - Combination 1 Combination 2 DA2 DA3 For all Design Approaches, when relevant, need to consider: Undrained Conditions Drained Conditions

50 Partial Factor Values 50 Parameter Factor DA1(1) DA1(2) DA2 DA3 Partial factors on actions (γ F ) or the Set A1 A2 A1 A1* A2 effects of actions (γ E ) Struct. Geotech Actions Actions Permanent unfavourable action γ G Permanent favourable action γ G Variable unfavourable action γ Q Variable favourable action γ Q Accidental action γ A Partial factors for soil parameters (γ M ) Set M1 M2* M1 M2 Tan angle of shearing resistance, tanφ' γ tanφ ' Effective cohesion c' γ c' Undrained shear strength c u γ cu Unconfined strength q u γ qu Weight density of ground γ γ γ Partial resistance factors (γ R ) Spread foundations Set R1 R1 R2 R3 Bearing resistance γ R;v

51 51 SLS Calculations SLS calculations Need to check that E d C d (Clause 2.4.8(1)) E d = the design effect of the action, e.g. foundation settlement Obtained using a calculation model, e.g. settlement analysis For SLS calculations, partial factors normally equal to 1.0 (Clause 2.4.8(2)) i.e. characteristic (unfactored) parameters are used C d = the serviceability criterion, e.g. limiting values of foundation movement / maximum allowable settlement

52 Actions and Design Situations (Clauses and 2.2) 52 Main Actions Permanent and variable loads from the supported structure Other actions to be considered Water pressures Note that water pressures may be part of the loading and part of the resistance to determine effective stresses Uplift water pressure forces are favourable actions Need care when applying partial factors to water pressures Removal of load or excavation of ground Soil swelling or shrinkage Movements due to creeping soil masses Movements due to self compaction Design Situations Ground water level major effect on bearing resistance Drained and undrained conditions need to check both, where relevant

53 53 Design and Construction Considerations Eurocode 7 provides a list of factors to be considered (a checklist) when choosing the depth of a spread foundation (Clause 6.4(1)). These include: Reaching an adequate bearing stratum The depth above which damage may occur due to shrinkage or swelling of clay soils or heave due to frost The level of the ground water table Possible ground movements and strength due to seepage, climatic effects or nearby construction or excavation Scour The presence of soluble materials, e.g. karstic limestone

54 Basic Equations and Calculation Models 54 Ultimate limit state Equilibrium equation to be satisfied for bearing resistance or sliding failure E d R d Serviceability limit state Serviceability condition to be satisfied E d C d No calculation models are given in the code text for R d or E d Only principles are given as to how these should be calculated and how to obtain design values Some calculation models for resistance and settlement are given in Annexes D and F These are informative annexes, not code text The national annex for a country must state if the informative annexes are mandatory or optional BUT, if you don t use them your design is not to Eurocode 7!

55 Bearing Resistance Calculation Model 55 Bearing resistance equations (Annex D): - Undrained conditions: R u / A = (π + 2)c u b c s c i c + q - Drained conditions: R d / A = c N c b c s c i c + q N q b q s q i q γ B N γ b g s g i g F V, F H M, P W 2 V d A W 1 A V A H The model for bearing resistance failure is a rectangular plastic stress block at the limiting stress beneath the foundation, similar to the plastic stress block in the ultimate limit state design of a concrete beam R d Actions and resistance on a spread foundation (from Designers Guide to Eurocode 7 by Frank et al.) The design bearing resistance force, R d acts through the centre of this stress block over effective foundation area, A

56 Settlement Calculations 56 Generally a separate settlement calculation is required to check that a serviceability limit state is sufficiently unlikely Components of settlement to consider on saturated soils (Clause 6.6.2(2)): Undrained settlements (due to shear deformation with no volume change) Consolidation settlements Creep settlements Note words of caution in Eurocode 7 (Clause 6.6.1(6)): settlement calculations should not be regarded as accurate but as providing an approximate indication Settlement equation (Annex F2: Adjusted elasticity method): merely s = p B f / E m where: B = foundation width E m = the design value of the modulus of elasticity f = the settlement coefficient p = the bearing pressure, linearly distributed on the base of the foundation

57 57 Overall Factors of Safety For conventional structures founded on clay, one should calculate the ratio, OFS u of the bearing resistance of the ground at its initial undrained shear strength, i.e. at its characteristic (unfactored) c u,k value, to the applied serviceability loading (Clause 6.6.2(16)): OFS u = R u,k / V k If OFS u < 3: Settlement calculation should always be undertaken If OFS iu < 2: Settlement calculation should take account of non-linear stiffness This is similar to traditional design where an overall factor of safety of 3 is often used with an undrained analysis to ensure settlements are acceptable and no settlement calculations are carried out However, overall factors of safety of designs for undrained conditions carried out using the Eurocode 7 partial factors are usually much less than 3

58 Overall Factors of Safety for Design Approaches 58 Examine overall factors of safety for different Design Approaches Consider a design situation where V k = 60%G k + 40%Q k DA1.C1, DA2, DA3: V d = γ F V k = (1.35x x0.4) V k = 1.41 V k DA1.C2: V d = (1.0x x0.4) V k = 1.12 V k DA1.C1: R u,d = R (c u,k / γ M ) = R u,k / 1.0 DA1.C2, DA2, DA3: R d = R (c u,k / γ M ) or R u,k / γ R = R u,k / 1.4 Design equation is V d = R d, i.e. γ F V k = R u,k / γ R or R u,k / γ M Hence OFS u = R u, k / V k = γ F x (γ M or γ R ) DA1.C1 DA1.C2 DA2 DA3 γ F x (γ M or γ M ) 1.41 x x x x 1.4 OFS u = R u,k / V k All OFS u values < 2.0, hence settlement calculations are required if a Eurocode 7 design is based only on undrained bearing resistance

59 Limiting Values of Foundation Movement 59 Eurocode 7 provides limiting values of foundation movement in Annex H Examples include: The maximum acceptable relative rotations (in a sagging mode) for normal routine open framed structures, infilled frames and load bearing or continuous brick walls are unlikely to be the same but are likely to range from about 1/2000 to about 1/300, to prevent the occurrence of an SLS in the structure. A maximum relative rotation of 1/500 is acceptable for many structures The relative rotation likely to cause a ULS is about 1/150 For normal structures with isolated foundations, total settlements up to 50 mm are often acceptable. Larger settlements may be acceptable provided the relative rotations remain within acceptable limits and provided the total settlements do not cause problems with the services entering the structure, or cause tilting etc.

60 Conclusions 60 Eurocode 7 provides a comprehensive framework with the principles for design of spread foundations The designer of spread foundations is explicitly required to: Consider all relevant limit states Consider both ULS and SLS Consider both drained and undrained conditions (where relevant) Distinguish between actions on the foundation and resistances Treat appropriately: Forces from supported structure (permanent or variable) Forces due to water pressure (actions not resistances) Since overall factors of safety for ULS design are generally lower than traditionally used for foundation design, it is likely that settlement considerations and hence SLS requirements will control more foundation designs, particularly on cohesive soils and when using DA1 Eurocode 7 is likely to encourage foundation designers to focus more on SLS considerations

61 61 Thank you Discussion Any questions?

62 Spread Foundation Design Example 62

63 Spread Foundation Example G k = 900,kN, Q k = 600,kN GWL d = 0.8 m B =? Design Situation: Square pad foundation for a building, 0.8m embedment depth; groundwater level at base of foundation. Central vertical load. Maximum allowable settlement is 25mm. Characteristic values of actions: Permanent vertical load = 900 kn + weight of foundation Variable vertical load = 600 kn Concrete weight density = 24 kn/m 3. Characteristic values of ground properties: Overconsolidated glacial till, c u,k = 200 kpa, c' k = 0kPa, φ' k = 35 o, γ k = 22kN/m 3 SPT N = 40 Require foundation width, B To satisfy both ULS (drained and undrained conditions) and SLS Using partial factors values in Irish NA for all Design Approaches 63

64 Using Direct Design Method 64 ULS calculations for 3 Design Approaches Need to check that E d R d Since only vertical loads, design action effect = design loads: E d = V d Obtain R d using the sets of partial factors for the following Design Approaches: DA1 - Combination 1 Combination 2 DA2 DA3 For all Design Approaches need to consider: Undrained Conditions Drained Conditions SLS calculation Need to check that E d C d Calculate E d, the action effect, i.e. the settlement, with characteristic (unfactored) parameters

65 Partial Factor Values 65 Parameter Factor DA1(1) DA1(2) DA2 DA3 Partial factors on actions (γ F ) or the Set A1 A2 A1 A1* A2 effects of actions (γ E ) Struct. Geotech Actions Actions Permanent unfavourable action γ G Permanent favourable action γ G Variable unfavourable action γ Q Variable favourable action γ Q Accidental action γ A Partial factors for soil parameters (γ M ) Set M1 M2* M1 M2 Tan angle of shearing resistance, tanφ' γ tanφ ' Effective cohesion c' γ c' Undrained shear strength c u γ cu Unconfined strength q u γ qu Weight density of ground γ γ γ Partial resistance factors (γ R ) Spread foundations Set R1 R1 R2 R3 Bearing resistance γ R;v

66 Undrained Conditions 66 eneral Equation for undrained bearing resistance R u / A in Annex D R u / A = (π + 2) c u b c s c i c + q o obtain the design undrained bearing resistance R u,d for all Design Approaches, the elevant partial factors are applied and all parameters are design values: R u,d = ( A ((π + 2)c u,d b c,d s c,d i c,d + q d )) / γ R here, for undrained conditions, a non-inclined foundation base, a square foundation nd vertical loading: A = effective foundation area (reduced area with load acting through its centre) = B 2 b c,d = 1.0 s c,d = 1.2 i c,d = 1.0 Substituting known values in Eqn. D.1 and noting q d = γ d x d = (γ k / γ γ ) x d: R u,d / A = ( B 2 ( 5.14 x (200 / γ c u ) x 1.0 x 1.2 x (22 / 1.0) x 0.8) ) / γ R = ( B 2 ( 6.17 x 200 / γ c u ) ) / γ R General Equation for bearing resistance: R u,d = ( B 2 ( / γ c u ) ) /γ R

67 Design for DA1.C1 Undrained Conditions Design Approach 1 Combination 1 Check V d R d for a 1.32 m x 1.32 m pad Design value of the vertical action V d = γ G (G k + G pad;k ) + γ Q Q k = γ G (G k + A γ c d) + γ Q Q k where G pad;k = characteristic weight of the concrete pad, γ c = weight density of concrete, A = B 2 = pad cross-sectional area, d = depth of the pad and γ Q = partial factor on variable actions Substituting values for parameters gives: = 1.35 ( x 24.0 x 0.8) x 600 = kn V d Design value of the bearing resistance R d = ( ( / γ )) / γ c u R = (1.742( / )) / 1.0 = kn The ULS design requirement V d R d is fulfilled as kn < kn DA1 = 1.32 m 67

68 Design for DA1.C2 Undrained Conditions 68 Design Approach 1 Combination 2 Check V d R d for a 1.39 m x 1.39 m pad Design value of the vertical action V d = γ G (G k + G pad;k ) + γ Q Q k = 1.0 ( x 24.0 x 0.8) x 600 = kn Design value of the bearing resistance R d = ( ( / ) ) / 1.0 = kn The ULS design requirement V d R d is fulfilled as kn < kn DA1 = 1.39 m Since B = 1.39m for DA1.C2 > B = 1.32m for DA1.C1 DA1 Design Width for Undrained Conditions: DA1 = 1.39m (given by Combination 2)

69 Designs for DA2 Undrained Conditions 69 Design Approach 2 Check V d R d for a 1.57 m x 1.57 m pad Design value of the vertical action V d V d = γ G (G k + A γ c d) + γ Q Q k = 1.35 ( x 24.0 x 0.8) x 600 = kn Design value of the bearing resistance R d = ( ( / γ ) ) / γ c u R = (2.465( / )) / 1.4 = kn The ULS design requirement V d R d is fulfilled as kn < kn. DA2 Design Width for Undrained Conditions: DA2 = 1.57 m

70 70 Designs for DA3 Undrained Conditions Design Approach 3 Check V d R d for a 1.56 m x 1.56 m pad Design value of the vertical action V d = γ G (G k + G pad;k ) + γ Q Q k = 1.35 ( x 24.0 x 0.8) x 600 = kn Design value of the bearing resistance R d = ( ( / ) ) / 1.0 = kn The ULS design requirement V d R d is fulfilled as kn < kn DA3 Design Width for Undrained Conditions: DA3 = 1.56 m

71 Drained Conditions eneral Equation for drained bearing resistance R / A in Annex D, Eqn. D.2: R d / A = c N c b c s c i c + q N q b q s q i q γ B N γ b γ s γ i γ n this example the c terms are ignored as c = 0. o obtain the design resistance R d, for all Design Approaches, relevant partial factors re applied and all parameters are design values: R d = (A (q d N q,d s q,d γ d B N γ,d s γ,d ) ) / γ R here: A = effective foundation area = B 2 N q;d = e πtanφ d tan 2 (π/4 + φ d /2) N γ;d = 2 (N q -1) tanφ d s q;d = 1 + sin φ' d s γ;d = 0.7 φ' d = tan -1 (tan φ' k / γ M ) = tan -1 (tan35/1.25) = 29.3 o ssuming ground water level at ground surface, for γ = 22 kn/m 3, γ w = 9.81 kn/m 3 nd since γ γ = 1.0: γ d = (γ - γ w ) / γ γ = ( ) / 1.0 = kn/m 3 q d = γ d d = x 0.8 = 9.75 kpa ence: R d = (B 2 (9.75 N q,d s q,d x B N γ,d s γ,d ) ) / γ R = (B 2 (9.75 N q,d s q,d B N γ,d s γ,d ) ) / γ R 71

72 Design for DA1.C1 Drained Conditions Design Approach 1 Combination 1 Check V d R d for a 1.62 m x 1.62 m pad Design value of the vertical action V d = γ G (G k + γ c A d) + γ Q Q k = 1.35 (900 + ( ) x x x 600 = kn Note: Submerged weight of foundation used. Alternatively could use total weight of foundation and subtract uplift force due to water pressure under foundation Design value of the bearing resistance R d,d = ( B 2 (q d N q,d s q,d + 0.5γ d B N γ,d s γ,d )) / γ R = ( (9.75 x 33.3 x x 1.62 x x 0.7) )/ 1.0 = kn The ULS design requirement V d R d is fulfilled as kn < kn DA1.C1 = 1.62 m 72

73 Design for DA1.C2 Drained Conditions Design Approach 1 Combination 2 Check V d R d for a 2.08 m x 2.08 m pad Design value of the vertical action V d = γ G (G k + γ c A d) + γ Q Q k = 1.0 (900 + ( ) x x 0.8) x 600 = kn Design value of the bearing resistance R d = (9.75 x x x 2.08 x x 0.7) / 1.0 = kn The ULS design requirement V d R d is fulfilled as kn < kn B = 2.08m for DA1.C2 > B =1.62m for DA1.C1 DA1.C2 = 2.08 m DA1 Design Width Drained Conditions: DA1 = 2.08m (given by Combination 2) 73

74 Design for DA2 Drained Conditions 74 Design Approach 2 Check V d R d for a 1.87 m x 1.87 m pad Design value of the vertical action V d V d = γ G (G k + γ c A d) + γ Q Q k = 1.35 (900 + ( ) x x 0.8) x 600 = kn Design value of the bearing resistance R d = ( (9.75 x 33.3 x x 1.87 x x 0.7)) / 1.4 = kn The ULS design requirement V d R d is fulfilled as kn < kn DA2 Design Width Drained Conditions: DA2 = 1.87 m

75 Design for DA3 Drained Conditions 75 Design Approach 3 Check V d R d for a 2.29 m x 2.29 m pad Design value of the vertical action V d = γ G ( G k + γ c A d ) + γ Q Q k = 1.35 (900 + ( ) x x 0.8) x 600 = kn Design value of the bearing resistance R d = (9.75 x x x 2.29 x x 0.7 ) / 1.0 = kn The ULS design requirement V d R d is fulfilled as < kn DA3 Design Width - Undrained Conditions: DA3 = 2.29m

76 Summary of ULS Designs Undrained width (m) Drained width (m) ULS Design Width DA1.C1 (1.32) (1.62) DA1.C DA DA For this example Drained conditions give the larger design widths Considering undrained and drained conditions (design width): DA1.C2 is larger than DA1.C1 DA3 gives largest width for ULS (2.29m) DA2 gives smallest width for ULS (1.87m) Considering just undrained conditions: DA2 gives the largest width for ULS (1.57m) DA1 gives smallest width for ULS 76

77 SLS Design 77 Is it always necessary to calculate the settlement to check the SLS? In SLS Application Rules, Eurocode 7 states that: For spread foundations on stiff and firm clays calculations of vertical displacements (settlements) should usually be undertaken For conventional structures founded on clays, the ratio of the bearing capacity of the ground, at its initial undrained shear strength, to the applied serviceability loading (OFS u ) should be calculated If this ratio is less than 3, calculations of settlements should always be undertaken. If the ratio is less than 2, the calculations should take account of non-linear stiffness effects in the ground i.e. if OFS u < 3, one should calculate settlement If OFS u < 2, one should calculate settlement accounting for non-linear stiffness For undrained designs of foundations with permanent structural loads only DA1 give F i = 1.4 while DA2 and DA3 give F i = Hence settlement calculations are needed

78 OFS u Ratios ULS design (drained) width (m) OFS u using drained width = R u,k / V k = B 2 ULS undrained width (m) OFS u using undrained width = R u,k / V k = γ F x γ M/R DA DA DA Calculating the undrained OFS ratio using the design width i.e. the drained design width: OFS u = R u,k / V k = A ( (p + 2) c u,k b c s c ic + qc ) / Vc = B2 x ( 5.14 x 200 x 1.0 x 1.2 x x 0.8) / ( ) = B2 x ( ) / 1500 = B In this example, using design (i.e. drained) widths: For DA1, OFS = u 3.60 ( > 3 ) Settlement need not be calculated For DA2, OFS u = 2.91 ( < 3 ) Settlement should be calculated For DA3, OFS u = 4.37 ( > 3 ) Settlement need not be calculated But using the undrained widths OFS u values are all less than 2.0, - much lower than value of 3 often used in traditional designs 78

79 Settlement Calculations Components of settlement to consider on saturated soils: Undrained settlements (due to shear deformation with no volume change) Consolidation settlements Creep settlements The form of an equation to evaluate the total settlement of a foundation on cohesive or non-cohesive soil using elasticity theory, referred to as the adjusted elasticity method, is given in Annex F: s = p B f / E m where: E m = design value of the modulus of elasticity f = settlement coefficient p = bearing pressure Assume E m = E = 1.5N = 1.5 x 40 = 60 MPa f = (1 ν 2 ) I where ν = 0.25 and I = 0.95 for square flexible uniformly loaded foundation Then f = ( ) x 0.95 = p = (G k + Q k )/B 2 = ( ) / B 2 = 1500 / B 2 Hence settlement: where B is in m s = p B f / E m = (1500 / B 2 ) x B x x 1000 / = / B mm 79

80 Calculated Settlements ULS design width (m) OFS u Settlement ( mm ) s = / B DA DA DA In this example, using adjusted elasticity method and ULS design widths, the calculated settlements, s for all the Design Approaches are less than 25 mm The SLS design requirement E d C d is fulfilled as for each DA, s < 25 mm Note words of caution in EN : Settlement calculations should not be regarded as accurate but as providing an approximate indication merely 80

81 81 Conclusions In the example considered: ULS design: For each Design Approach, the drained condition determines the foundation width SLS design: The calculated settlements are less than the allowable settlement of 25mm, so that the SLS condition is satisfied using the design widths obtained using all the Design Approaches The ratio R u,k / V k for the ULS drained design widths is greater than 3 for DA1 and DA3 so settlement calculations are not required

82 82 Thank you for your attention Discussion Any questions?