LSD2000: International Workshop on Limit State Design in Geotechnical Engineering Melbourne, Australia, 18 November 2000
Stability analysis for shallow foundations Eurocode 7 and the new generation of DIN codes B. Schuppener Federal Waterways Engineering and Research Institute, Karlsruhe, Germany U. Smoltczyk Böblingen Germany ,
ABSTRACT: The relevant features of Eurocodes 0 and 7 – the concept of limit states and the partial factor method – are described. In particular it is shown how the factors of safety are to be introduced in the three approaches proposed by the new version of Eurocode 7 for the verification of ultimate limit states. The approach adopted in the new generation of geotechnical DIN codes and the basic principles of the new DIN 1054 are then presented. The main features are that the partial factors on the actions of the ground and of the structure have the same value and only one single calculation is required to verify a limit state. Moreover Germany favours the approach, in which the partial factors are neither applied to ϕ´ or c´ nor directly to the actions but to the action effects and the characteristic values of the resistances in the last step of the verification of the ultimate limit states of geotechnical structures. Based on a long tradition three design situations are introduced to account for different probabilities of failure and the need for different safety levels. The procedures and results of the three approaches specified in Eurocode 7 are compared taking the dimensioning of the width of the foundation of a cantilever stem wall as an example.
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INTRODUCTION
In future, verification of ultimate limit states by calculation will be performed in accordance with the partial factor concept throughout the entire construction sector in Europe. To put it simply, the concept states that it must be verified that the design value Rd of the resistance is greater than the design value Ed of the actions or the action effects: Rd ≥ Ed However, it turned out that the member states were unable to reach a consensus of opinion on the implementation of this limit state equation in geotechnical design in the draft of Part 1 of Eurocode 7 (ENV 1997-1, 1994). The principal criticism expressed not only by Germany but also by other European countries concerned the intended procedure for verifying the stability of foundations by calculation. The procedure involves the use of two different stability analyses – the investigation of cases B and C. Firstly, this attracted criticism as it would have doubled the amount of effort required to verify the stability of foundations by calculation after implementation of EC 7. Secondly, the safety philosophy on which the procedure was based was strongly criticised in Germany and other member states (Gudehus and Weissenbach, 1996, Schuppener et al., 1998, Stocker, 1997, Weissenbach et al. 1999). After lengthy discussions, a compromise was reached by which the new version of EC 7 would in future not specify a single procedure only but would give member states a choice of three different approaches to verifying the stability of foundations by calculation. Each state would then have to specify, in a National Application Document (NAD), which of the three approaches was to be applied. In a NAD the suggested partial safety values of EC7 will either have to be confirmed or altered if necessary according to national experience.
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LIMIT STATES AND PARTIAL FACTOR METHOD OF EUROCODES 0 AND 7
The revised EC 7 and the new versions of the German geotechnical codes are based on Eurocode 0 (prEN 1990, draft July 2000) which contains provisions that are applicable to all areas of building and civil engineering and thus do not have to be specified again separately in each Eurocode. In particular, this includes the definition of the limit states for which verification is required in building and civil engineering and how the partial factors are to be applied in stability analyses and introduced into limit state equations. There are two possible approaches when determining the design values of resistances and actions of the ground: In the Material Factor Approach the partial factors γ m are applied to the characteristic values of the material properties of the structure or the ground to determine the design value of the resistance R d of the structure or the ground or the design value of the action of the ground E d. Thus the following equations are derived for resistances and actions of the ground: Rd = R {(tan ϕk ) / γ m, ck / γ m} Ed = E {(tanϕk ) / γ m, ck / γ m} where: R is a function describing the resistance of the ground - e.g. passive earth pressure, bearing capacity or sliding resistance of a footing - determined with factored values of the characteristic shear parameters ϕk and ck , E is a function describing the action of the ground - e.g. active earth pressure - determined with factored values of the characteristic shear parameters ϕk and ck , γ m is the partial factor for the shear parameters of the ground taking account of the possibility of unfavourable deviations of the shear parameters from their characteristic values and uncertainties in modelling the resistance and/or actions. In the Resistance and Action Factor Approach the design values of the resistances R d and actions Ed are determined by applying the partial factors γ R and γ E to the characteristic values of the resistance Rk and of the actions or action effects E k of the structure or the ground: Rd = Rk / γ R Ed = Ek ⋅ γ E where γ R is the partial factor for the resistance of the ground, taking account of the possibility of unfavourable deviations of the shear parameters from their characteristic values and uncertainties in modelling the resistance, γ E is the partial factor for the actions or action effects taking account of the possibility of unfavourable deviations of the shear parameters from their characteristic values and uncertainties in modelling the resistance and/or actions. The Material Factor Approach was the only approach specified in the previous version of EC 7 (ENV 1997-1 (1994)). As the Resistance and Action Factor Approach has now been introduced in EC 0 (prEN 1990, draft July 2000) for building and civil engineering as a whole, there are no longer any obstacles to applying it in geotechnical engineering and including it in the new version of EC7. This now enables two other verification approaches to be included as alternatives to the methods used hitherto in Case B and Case C (see table 1).
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Table 1: Sets of partial factors for the approaches 1 to 3 to verify ultimate limit states of foundations and retaining structures according to EC0 and EC7 –1
Approach
Action or action effects of the structure
1 Case B Case C 2 3
of the ground
γ G = 1.35, γ G,fav = 1.00, γ Q = 1.50 γ G = 1.00, γ Q = 1.30 γ G = 1.35, γ G,fav = 1.00, γ Q = 1,50 γ G =1.35, γ G,fav =1.00, γ Q =1.50
Resistance of the ground
γ ϕ = 1.00, γ c = 1.00 γ ϕ = 1.25, γ c = 1.25 γ Ep = γ Gb =1.40, γ Sl = 1.10 γ ϕ =1.25, γ c =1.25
Approach 1 corresponds to the approach originally specified in EC 7 according to which two analyses - referred to as “Case B” and “Case C” – were required. Case B of Approach 1 is primarily intended to cover the uncertainties in the actions. Partial factors are therefore applied to all actions – both of the structure and of the ground – with a distinction being made between unfavourable permanent (γ G), favourable permanent (γ G,fav) and variable loads (γ Q). It aims to provide a safe geotechnical design in the event of unfavourable deviations of the actions from their characteristic values, while the characteristic values of the angle of friction ϕ´k and cohesion c´k are taken as soil parameters (γ ϕ = γ c = 1.00) . In Case C of Approach 1, it is principally the uncertainties in the material characteristics that are investigated. The partial factors on the soil parameters γ ϕ and γ c are therefore greater than 1. In contrast, it is assumed that the permanent actions correspond to the c haracteristic values while the variable actions are slightly higher than the characteristic values, providing a conservative design. Approach 2 corresponds to the joint proposal put forward by Germany and France in which a single analysis is deemed sufficient. The same partial factors are applied to the actions and action effects of the structure and the soil in this approach, γ G being taken as 1.35 for permanent loads and γ Q as 1.50 for variable loads. The partial factors for soil resistances vary between γ Ep = γ Gb = 1.40 for passive earth resistance and ground bearing capacity and γ Sl = 1.10 for sliding. The values chosen ensure that the level of safety is equivalent to that provided by the former global safety concept. In approach 2 geotechnical design thus takes account of the unfavourable deviations of the resistance of the soil and the actions of both the soil and of the structure from their characteristic values by applying partial factors greater than 1 to both the actions and the resistances in the inequation for geotechnical ultimate limit states. This approach thus corresponds in content and form to the partial safety concept specified in EC 0 for the verification of stability by calculation in all areas of structural design in building and civil engineering. In Approach 3, both the actions and the resistances of the ground are determined using the design shear parameters, i.e. partial factors are applied to the characteristic shear parameters. The actions due to the structure are dealt with in the same way as in Approach 2.
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BASIC PRINCIPLES OF THE NEW GERMAN GEOTECHNICAL CODE DIN 1054
Apart from the basic concepts specified in EC0 and EC7, priority has been given in German geotechnical coding to the principle that the concept applied in the verification of geotechnical limit states should be as similar as possible to that applied in the verification of structural limit states. In most cases the same engineer will perform the geotechnical as well as the structural verifications for foun-
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dations and retaining walls, so switching from one concept to another must be avoided. This meant that - the values of the partial factors on the actions of the ground and those of the structure should be the same (see table 2) and - only a single calculation based on the characteristic values of the actions and the resistances should suffice to verify a limit state – instead of the two Cases B and C proposed in the draft of EC7 published in 1994. Moreover, Germany favoured the Resistance and Action Factor Approach in which the safety factors are neither applied to ϕ´ or c´ nor directly to the actions but to the characteristic action effects (internal forces, bending moments, etc.) and the characteristic values of the resistances in the last step of the verification of the ultimate limit state. Design Situations to account for different probabilities of failure and the need for different safety levels constitute the fourth important feature of German geotechnical coding (also see prEN 1990) in accordance with a long tradition of design situations in geotechnical DIN codes and other geotechnical recommendations. There are Design Situation 1 (DS1) for permanent situations, Design Situation 2 (DS2) for the stage of construction or transient structures and Design Situation 3 (DS3) for accidental situations concerning both actions and resistances (see table 2 and 3). Table 2: Proposed partial safety factors on action effects Ek Actions
Symbol
DS1
DS2
DS3
Permanent actions including water, active earth pressure Unfavourable variable actions
γ G γ Q
1.35 1.50
1.20 1.30
1.00 1.00
Table 3: Proposed partial safety factors on resistances Rk of the ground Resistances
Symbol
DS1
DS2
DS3
Passive earth pressure and ground bearing resistance Sliding Pile resistance in compression (from pile tests) Pile resistance in tension (from pile tests) Pull-out resistance of grouted anchors Shear parameter: tan ϕ´ and c´ (only for slope stability)
γ Ep, γ Gb γ Sl γ Pc γ Pt γ A γ ϕ , γ c
1.40 1.10 1.20 1.30 1.20 1.30
1.30 1.10 1.20 1.30 1.15 1.20
1.20 1.10 1.20 1.30 1.10 1.10
Experience in Germany has shown that the former global safety concept has hitherto ensured that foundations could be designed economically and with an adequate degree of safety. It is for this reason that the safety level used hitherto in the global safety concept has been selected as a base quantity and the partial factors of the new partial safety concept calibrated against it. This was done by “splitting” up the global factor η in two partial factors – γ R for the resistance and γ G,Q a mean value for permanent and variable actions and action effects: (1) η = γ R ⋅ γ G,Q The partial factors for the resistance of the ground γ R were then determined by means of equation (1), inserting the value η of the old global safety concept and the prescribed partial safety factors γ G,Q for permanent and variable actions specified in Eurocode 0 (ENV 1990, draft October 1999): γ R = η / γ G,Q The steps of the design procedure proposed by the German geotechnical DIN codes are very similar to those put forward by structural engineers: 1. Estimated sizing and assessment of the static design system of the geotechnical structure (footing, retaining wall, strutted sheet pile wall, piles etc). 2. Determination of the characteristic actions of the structure and of the soil, i.e. the most realistic and probable actions. -4-
3. Determination of the characteristic action effects Eki, e.g. strut-, anchor- or supporting-forces, the resultant characteristic forces in the base level of a footing or in the earth pressure support of a wall etc. 4. Determination of the characteristic resistances Rki e.g.: - for structural elements: the characteristic bending moment or the characteristic compressive strength according to the standards for the considered material, - for soil: the characteristic bearing capacity of shallow foundations, the characteristic passive earth pressure or the characteristic bearing capacity of piles, anchors and nails determined by calculations, tests or comparable experience. 5. Verification of the ultimate limit state in every relevant cross section of the structure and in the soil: − The design effects of the actions Edi are obtained by multiplying the characteristic effects E ki of the actions by partial safety factors e.g. for permanent structures with γ G = 1.35 for permanent actions and γ Q = 1.50 for variable actions (see table 2) − The design resistances Rdi are obtained by dividing the characteristic values Rki by their corresponding safety factors for the structure (e.g. for steel see Eurocode 2 (EN 1992 (1991)), for concrete see Eurocode 3 (EN 1992 (1992)) and for soil (see table 3). The basic equation: Σ Rdi ≥ Σ Edi is verified in the final step of the ultimate limit state analyses. If it is not fulfilled the sizing shall be improved. The merits of this concept for the geotechnical and structural verifications of foundations and retaining walls are: 1. As this calculation works with characteristic values of actions, which are also used for the verification of the serviceability limit state, no separate calculation is necessary for the input of the determination of the displacements. 2. The concept is open for all analytical methods of verification. Steps 3 and 4 allow for the classical methods, the theory of elasticity, ultimate load method, spring models, the finite element method and cinematic element method. 3. The procedure corresponds to the concept of the Eurocodes for structural engineering (EN 1992 Eurocode 2 (1991), EN 1993 Eurocode 3 (1992). Thus geotechnical engineering does not need a separate concept as proposed in the 1994 version of Eurocode 7. The procedure can t herefore easily be understood and adopted by students and practising engineers, which makes it very user-friendly.
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GEOTECHNICAL DESIGN OF A CANTILEVER STEM WALL – A COMPARISION OF THE THREE APPROACHES
4.1 Geometry and loads The procedures and results of the three design approaches specified in EC 7 (EN 1997-1, 2000) will be compared taking as an example the design of a cantilever stem wall (see figure 1) which has already been used by Simpson & Driscoll (1998) for comparative calculations. The width B of the foundation slab of the cantilever stem wall is to be determined. In geotechnical design, this is done by demonstrating that the limit state equations with the required partial factors are satisfied for both bearing resistance failure and for sliding for the width B selected in advance. The earth pressure is determined in accordance with DIN 4085-100 (1996). In the stability analysis, the active earth pressure acting on a fictitious vertical wall is applied at the end of the foundation slab of the cantilever stem wall. The bearing capacity of the ground is calculated using the formulae given in DIN 4017-100 (1996). The partially mobilised passive earth pressure in front of the wall, E phmob,d = Eph / γ Ep, is taken to be an favourable action when verifying bearing resistance failure in all three approaches.
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1)
pk = 5 kN/m²
β = 20° Fictitious wall to determine the action due to active earth pressure
h = 6,0 m
1)
0,95 m 0,7 m
This part of the variable action must only be considered in the structural design of the wall
B=? Figure 1: Cantilever stem wall, dimensions and loads 4.2 Design according to Approach 1 Each of the calculations – Case B and Case C - is performed with design values. Owing to the stabilising moment, the action due to the self-weight of the soil acting on the foundation slab is assumed to be favourable (γ G,fav = 1.00) in Case B - while the action due to the self-weight of the retaining wall is unfavourable (γ G = 1.35). Determination of the design ground bearing resistance is based on the vertical and horizontal components and the eccentricity of the design value of the resultant action effect in the base level of the foundation. The results of both analyses are shown in table 4. The calculation demonstrates that Case C is relevant for the design of the foundation width B in approach 1. Owing to the higher design values of the shear parameters, the design bearing resistance R Gb,d of Case B is nearly three times higher than in Case C while in both cases the vertical components V d of design value of the resultant action effects differ only to a small extent. 4.3 Design according to Approach 2 In Approach 2 the calculations to determine the resultant action effect at the base level of the foundation are performed with characteristic values. The determination of the characteristic ground bearing resistance is then based on the characteristic values of the vertical and horizontal components and the eccentricity of the resultant action effect at the base level of the foundation. The partial factors are not introduced until the final step of the calculation when the limit state equations for bearing resistance failure and sliding are verified. No distinction is made between favourable and unfavourable permanent actions, in accordance with DIN 1054, a single partial factor γ G = 1.35 being applied to all permanent action effects instead. If a distinction between favourable and unfavourable permanent actions is to be made in accordance with EC 7 the determination of the bearing resistance must be based on the design value of the resultant action effect in the base level of the foundation. The results of both analyses are given in table 4. 4.4 Design according to Approach 3 In Approach 3, all calculations are performed with design values as in approach 1. The action due to the self-weight of the soil acting on the foundation slab is taken to be favourable ( γ G,fav = 1.00) owing to the resultant stabilising moment while the action due to the self-weight of the retaining wall is unfavourable (γ G = 1.35). Determination of the design ground bearing resistance is based on the vertical and horizontal components and the eccentricity of the design value of the resultant action effect in the base level of the foundation. The results are shown in table 4.
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Table 4: Results of the comparative stablility calculations Approach 1 Approach 2 Case B Case C DIN 1054 EC7 Width of foundation B [m] 5,00 5,00 3,40 3,80 Verification of safety against bearing resistance failure Vertical component Vd of the resultant 806 717 605 601 action effect in the base level [kN/m] Inclination of the resultant action effect 0.34 0.40 (0.36) 0.39 tanδ=Hd /Vd (Hk /Vk ) Bearing resistance RGb,d [kN/m] 2177 734 616 627 Degree of mobilisation f Gb = Vd / RGb,d 0.37 0.98 0.98 0.96 Verification of safety against sliding Sliding resistance RSl,d [kN/m] 559 393 291 327 Design value of the horizontal actions ΣHd 301 305 260 270 [kN/m] Degree of mobilisation f Gl = ΣHd /RSl,d 0.55 0.78 0.89 0.83
Approach 3 4,90 773 0.37 767 1.01 422 306 0.73
4.5 Results and conclusions In all three approaches, safety against ground bearing resistance failure is relevant for the design of the width B of the foundation. The smallest foundation dimension B resulting from the application of Approach 2 is 3.40 m if DIN 1054 is followed and each permanent action – favourable and unfavourable - is multiplied by the same partial factor γ G = 1.35. If the proposal given in EC 7 is followed and a factor of only γ G,fav = 1.00 is applied to the self-weight of the soil acting on the foundation, the angle of the resultant action effect tan δ increases and the bearing resistance therefore decreases. This is not compensated for by the reduction of the vertical component Vd of the design value of the resultant action effect in the base level of the foundation, resulting in a wider foundation with a width B = 3.80 m being required.
The main reason for the much lower foundation width that results when applying Approach 2 is the much higher design ground bearing resistance R Gb,d that results for the same loads and dimensions when applying the two other approaches. In the approach laid down in DIN 1054, the design ground bearing resistance RGb,d is determined by first calculating the characteristic ground bearing resistance RGb,k using the characteristic shear parameters ϕ’k and c’k . The design bearing resistance RGb,d = RGb,k / γ Gb is then obtained by dividing the the characteristic ground bearing resistance by the partial factor for the bearing resistance failure, γ Gb = 1.40. In contrast, RGb,d is determined using the design values of the shear parameters ϕ’d and c’d in approaches 1 and 3. In the case we are dealing with here, a reduction in the angle of friction ϕ’k = 32.5° to ϕ’d = 27.0° lowers the ground bearing resistance to around half of that determined when a characteristic angle of friction ϕ’k = 32.5° is applied. The greater foundation widths obtained using approaches 1 and 3 are thus due on the one hand to the additional safety included when dealing with the favourable permanent actions and on the other hand to the greater level of safety in respect of the bearing resistance resulting from the proposed partial factors for the shear parameters. The difference between approach 1 (Case C) and approach 3 when establishing the required foundation width B is insignificant in the example we are dealing with here. Approach 3 results in a somewhat smaller width B despite the higher vertical component Vd of the action effect in the base level of the foundation as the angle of the resultant (tan δ) decreases and thus the bearing resistance increases, which influences the results in the way shown here. To sum up, it can be said that a far more economical shallow foundation design is obtained when following Approach 2 with the partial factors specified in DIN 1054. The partial factors for the actions due to the structure and the ground as well as those for the ground resistances have been specified such that the level of safety provided by the global safety concept used hitherto is maintained. The safety level of this concept has been tried and tested in practice for decades. Thus, applying the partial factors specified in DIN 1054 to the design of geotechnical structures not only ensures an adequate de-
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gree of safety, it is also considerably more economical, as the comparison with the other approaches has illustrated. The detailed numerical calculations according to the three approaches can be ordered from the author by email:
[email protected].
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REFERENCES
DIN 4017-100 (1996) Berechnung des Grundbruchwiderstandes von Flachgründungen Teil 100: Berechnung nach dem Konzept mit Teilsicherheitsbeiwerten, Beuth, Berlin DIN 4085-100 (1996) Berechnung des Erddrucks Teil 100: : Berechnung nach dem Konzept mit Teilsicherheitsbeiwerten, Beuth, Berlin DIN 1054 (1999) Standsicherheitsnachweise im Erd- und Grundbau, Draft February 2000, Beuth, Berlin ENV 1997-1 Eurocode 7 (1994): Geotechnical design, Part 1: General rules. European Committee for Standardisation (CEN) Brussels EN 1997-1 Eurocode 7 (2000): Geotechnical design, Part 1: General rules. European Committee for Standardisation (CEN) Brussels, draft April 2000 prEN 1990 Eurocode 0 - Basis of design (1999), European Committee for Standardisation (CEN) Brussels, draft July 2000 EN 1992 Eurocode 2 (1991) Design of concrete structures, European Committee for Standardisation (CEN) Brussels EN 1993 Eurocode 3 (1992) Design of steel structures, European Committee for Standardisation (CEN) Brussels Gudehus, G. & Weißenbach, A. (1996) Limit state design of structural parts at and in the ground, Ground Engineering Schuppener, B., Walz, B., Weißenbach, A., Hock-Berghaus, K. (1998), EC7 – A critical review and a proposal for an improvement: a German perspective, Ground Engineering, Simpson, B. & Driscoll, R. (1998) Eurocode 7 – a commentary. Construction Research Communications Ltd., London Stocker, M. (1997) Eurocode 7 – all problems solved? European Foundations, a Ground Engineering Publication Weißenbach, A., Gudehus, G. and Schuppener, B. (1999) Proposals for the application of the partial safety factor concept in geotechnical engineering, geotechnik special issue: German contributions to European standardization
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