B Schuppener, B Walz, A WeiBETAenbach and K Hock-Berghaus offer a German perspective on the discussion about the present form of Eurocode 7: Geotechnical design.

Introduction

Originally, the principal aim of Eurocode 7: Geotechnical design - Part 1: General rules (ENV1997-1, EC7-1) was to transfer the principles of the original probabilistic safety concept to geotechnical engineering. Under this concept, the shear parameters and c are the relevant basic variables and therefore the relevant partial safety factors are only applied to the shear strength parameters. Thus both the actions and resistances of the ground can contain a safety margin.

Other permanent actions which often play a dominant role in geotechnical engineering, such as the self-weight of the structure or the water pressure, are not factored. The intention was to form a design concept using only a few partial safety factors which could also be applied to a wide variety of problems in foundation engineering. It is known as case C of Eurocode 7 part 1.

However, it was shown that serious problems occurred when using this method to design flexible structures with loading due to water pressure and rigid walls loaded by earth pressure at rest. Therefore, verification for an additional case B was introduced, in which partial safety factors are only applied to the characteristic loads, as is normal practice in structural engineering. In this case the actions of the ground are also factored with a safety factor, when usually the resistance of the ground has no safety factor assigned to it.

Following previous discussions [1] this article presents a critical review of the 'philosophy' and basic concept of the present version of Eurocode 7, with an alternative solution to the problems created therein.

A critical review of the concept of EC7 Part 1

The most controversial parts of EC7 Part 1 are the chapters dealing with the design of geotechnical structural elements. Two separate calculations generally have to be performed for the ultimate limit state, one for case B and a second one for case C. Case B normally applies when determining the size of the cross section of the geotechnical structural element, eg the profile of a sheet pile and the reinforcement of the concrete. Case C normally applies when determining the dimensions eg, the embedding depth of a sheet pile wall or the width of a shallow foundation. The safety factors for the actions and the ground for both cases according to Table 2.1 of EC7 part 1 are shown in Table 1.

The idea of considering cases B and C can be described as follows [2]:

The aim of case C is to provide a design which is safe against unfavourable deviations of soil strength parameters and against uncertainties associated with the geotechnical calculation models while the permanent loading, including the soil weight, is equal to its characteristic (a cautious estimate) value and the variable load is slightly factored. Put simply, what do the sizes and strength of the structure have to be in order to avoid ultimate limit states if the soil and/or the calculation models are worse than expected while the loads are close to their expected value?

The aim of case B is to provide a design which is safe against deviations of the characteristic value of the loadings, or of the effects of the loadings, when the soil strength parameters are equal to their characteristic value. In other words, what do the sizes and the strength of the structure have to be in order to avoid ultimate limit states if the loadings are more unfavourable than expected while the soil strength and the calculation model are close to their expected value?

A formal argument against this 'philosophy' is that in both case B and case C the concept does not comply with the partial safety concept of the Eurocodes for civil engineering. According to the Eurocode concept it must be verified that the design resistances Rd are always equal to or greater than the design actions Sd, the design resistance being defined as the characteristic (or representative) resistance Rk divided by a safety factor R and the design action being defined as the characteristic (or representative) action Sk multiplied by a safety factor S for the actions. For simple cases with only one action and one resistance, this results in the basic equation of the partial safety concept:

Rd = Rk/ R greater than or equal to Sd = Sk . S (1)

It is obvious that the common basis for civil engineering's safety philosophy of applying safety factors on both actions and resistances is abandoned in geotechnical engineering if either safety factor is set to unity. Colleagues and students do not understand why there is this break in the safety concept when it comes to the geotechnical part of structural design calculations. Besides this conceptual discrepancy, there are also a number of inconsistencies, the most evident being described below.

1. The philosophy for cases B and C is not convincing because it cannot guarantee a sufficient safety level for the combination or superposition of the uncertainties of both the material properties (soil and other material) and their actions. Moreover, the concept of cases B and C presents a misleading alternative of actions on the one hand and ground properties on the other. The correct pair is actions and resistances. The ground properties can be found on the left-hand side of equation (1) (eg as the resistance of an abutment for a pipe pusher), on the right-hand side (eg as earth pressure on a tunnel) and on both sides (eg as active and passive earth pressure, both acting on a retaining wall).

2. The investigation of the two cases normally shows that the dimensions of a geotechnical structure will differ more or less in both. These differences are not a result of different modes of failure, but of the two different safety definitions of cases B and C. There is no obvious reason why two different safety definitions should be applied to a single problem and the decision to take the more unfavourable case for design will often lead to uneconomical solutions.

3. Solutions that are not sufficiently safe must be expected if case C becomes relevant and only one partial factor is to be applied, eg when sufficient passive earth resistance Ephd must be verified for cohesionless soil where the permanent actions do not result from earth pressure but from water pressure (see Figure 1). In this case, there is only a factor of = 1.25 on the tangent of the angle of friction k for the passive earth resistance Ephd, compared with a global safety factor as specified in German standards of =1.5 for the construction stage and =2.0 for persistent situations.

4. The definitions of the safety factors provide a constant safety level in case B. For case C, however, this can not be achieved by dividing the tangent of the characteristic friction angle (tank) by a safety factor . In the case of actions, Figure 2 demonstrates this for active earth pressure assuming = = 0 ( is the angle between the vertical and the surface of the wall, the inclination of the ground surface behind the wall) and that the angle of wall friction a= 2/3. In case B, the characteristic active earth pressure coefficient is factored by G = 1.35. In case C, the design earth pressure coefficient is determined with the design friction angle (d = arctan ((tank)/), where =1.25.

Figure 2 shows that, by chance, the safety level for the active earth pressure is equal in both cases when the characteristic angle of friction k = 45degrees:

Kad(C) / Kad(B) = Kagh(d)/(Kagh(k) . G) 1

But it also reveals that the safety level for case C falls as the angle of friction decreases. It can be demonstrated that it is impossible to achieve a constant safety level over the range of possible characteristic values of the friction angle k not only for the actions of the ground but also for the resistance of the ground, eg for the passive earth pressure and for the bearing capacity.

5. In case C, it is not possible to calculate an earth pressure coefficient for slope angles d as a reduced design value of the angle of friction d is used. This does not accord with practice.

6. The use of a design friction angle d smaller than the characteristic (representative) angle of friction k produces slip surfaces that do not correspond with those which would in all probability be decisive. This can lead to a misleading interpretation of the real situation both for active and passive earth pressures.

7. Cases B and C are only easy to overlook in simple situations. In complex situations (see Figure 3 for example where hydraulic uplift, anchors and earth pressures have to be taken into account) the average engineer will quickly lose control of the calculation. He will not only have great difficulty in deciding which is case B and which is case C but also which actions are favourable permanent actions, unfavourable permanent actions and variable unfavourable actions respectively.

Proposal for an improvement

The problems described above are avoided in the following concept which is based on the German comments on EC7 part 1. With regard to the design of geotechnical structural elements its main features are:

a single calculation based on the characteristic values of the actions and the resistances.

application of safety factors to neither or c nor directly to the actions but on the characteristic internal forces and bending moments in the last step of the verification of the ultimate limit state (see Table 2).

load cases (LC) to account for different probabilities of failure and the need for different safety levels: LC1 for permanent situations, LC2 for the construction stage or temporary structures and LC3 for accidental situations concerning both actions and resistances (see Tables 2 and 3).

It should be emphasised that the safety factors in Table 3 are only proposed and should be adapted to national experience and safety levels. On the other hand, it must be clear that the partial safety factors given in Eurocodes 2, 3 and 5 apply to the design of structural elements.

The steps of the design procedure proposed in this concept are very similar to those put forward by structural engineers:

1. Selection of the dimensions and the design system of the geotechnical structure (footing, strutted sheet pile wall, piles etc).

2. Determination of the characteristic actions of the structure and of the soil, ie the most realistic and probable actions.

3. Determination of the characteristic effects of the actions Ski, eg 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 for example, for structural elements the characteristic bending moment or the characteristic compressive strength according to the standards for the considered material and for soil, the characteristic bearing capacity of shallow foundations, the characteristic passive earth pressure or the characteristic bearing capacity of piles, anchors and nails deter- mined by calcul- ations, tests or comparable exper- ience.

5. Verification of the ultimate limit state in every relevant cross- section of the structure and in the soil:

obtain the design effects of the actions Sdi: the characteristic effects of the actions are factored by safety factors eg for permanent structures

G= 1.35 and Q = 1.50 (see Table 2).

obtain the internal design resistances Rdi: the characteristic values are divided by their corresponding safety values eg for permanent structures M = 1.10 for steel (see EC2 part 1) and R = 1.40 for soil (see Table 3).

In the last step of the ultimate limit state analyses the basic equation:

Rdi Sdi

is verified. An example of a strutted sheet pile wall is presented in the appendix to illustrate the aforementioned procedure in detail.

The merits of this concept are:

1. The procedure corresponds to the concept of EC2 and EC3 for structural engineering. Thus geotechnical engineering does not need a separate concept as proposed in the present version of EC7 Part 1. This means the procedure can be easily understood and adopted by students and practising engineers, which makes it very user-friendly.

2. 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 (see example in the appendix).

3. The concept is open to 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.

Conclusions

The proposed concept for geotechnical design is simpler and better than that of EC7 Part 1. It guarantees a reasonable mean safety level both for the structural material and the ground when designing structural elements, with the global safety factor 1.5 for steel and 2.0 for the ground for permanent situations. In EC7 Part 1, however, the global safety factor varies between 1.5 and 2.0 for steel and between 1.2 and 3.0 for the ground.

An example is given in the appendix to illustrate the concept. It demonstrates the different steps of the design with the determination of the internal forces and bending moments and the verification of the ultimate limit states and the serviceability limit state.

This paper is restricted to the most crucial points. There are other detailed comments and proposals, for example on the assessment of characteristic soil parameters, the bearing capacity of piles and anchors as well as the verification of sufficient safety against hydraulic uplift, the bearing capacity of shallow foundations, the earth pressure at rest, sliding, slope stability, failure by boiling and the prestressing of anchor tendons.

References

[1]Gudehus, G & WeiBETAenbach, A; Limit state design of structural parts at and in the ground. Ground Engineering, Sept. 1996, 42-45

[2]Bauduin, C; Internal paper of Working Group 1 of SC7

Appendix: Example of the design of a braced sheet pile wall

Selection of the structural design system and the dimensions of the structure

The embedding depth of the sheet pile wall, its profile and the bearing capacity of the struts have to be determined. For the purpose of the calculation, the wall is assumed to be a beam on two supports. An embedment of t=2.5 m is selected.

2 Determination of the characteristic actions

Kah = 0.224; a = 58.9

Kph = 8.35 according to Caquot/Kerisel

z = 8.00 m:

eagh = 17.0 0.224 8.00 = 30.5 kN/m2

z = 10.50 m:

eagh = 17.0 0.224 10.50 = 40.0 kN/m2

eaghm = 30.5 / 2 = 15.3 kN/m2, assuming a rectangular load distribution

eaph = 100 0.224 = 22.4 kN/m2

hp = 2.00 tan a = 2.00 1.658 = 3,32 m

3 Determination of the characteristic internal forces

A programme for a continuous beam gives the following results:

Action: Permanent Variable

Upper supportAgh,k = 72.7 kN/m Aqh,k = 61.4 kN/m

Field bending moment Mg,k = 172.5 kNm/m Mq,k = 84.1 kNm/m

Lower supportUgh,k = 137.9 kN/m Uqh,k = 13.0 kN/m

Note 1: For the sake of simplicity, the maximum bending moments from both permanent and variable earth pressure are superimposed here although they do not occur at the same depth below ground level. In a more accurate calculation, the distributions of the characteristic bending moments have to be superimposed. In this case, the maximum total moment will be about 7% smaller.

4 Determination of the characteristic resistances

Characteristic strut resistance: Assuming A*k = 500,0 kN for one strut. With a spacing of 2,40 m: Ah,k = 500,0 kN /2,40 m = 208,3 kN/m

Characteristic bending resistance of a sheet pile wall ARBED AZ 18:

Mk = 1800 cm3 240 MN/m2 = 1.80 10-3 m3 240 103 kN/m2 = 432.0 kNm/m

Characteristic passive earth pressure:

Epgh,k =1/2 17.0 8,35 2.502 = 443.6 kN/m

5 Verification of the ultimate limit states

Safety factors:

Retaining structure; load case LC 2 (does not apply to struts):

Partial safety factor for actions: G,sup = 1.20; G,sup = 1.30

Partial safety factor for passive earth pressure: Ep = 1.30

Partial safety factor for steel components: M = 1.10

Struts:

S: AS,d = 1.35 72.7 + 1,50 61.4 = 98.1 + 92.1 = 190.2 kN/m

R: AR,d = 208.3 / 1.10 = 189.4 kN/m 190.2 kN/m

Sheet pile wall:

S: MS,d = 1.20 172.5 + 1.30 84.1 = 207.0 + 109.3 = 316.3 kNm/m

R: MR,d = 432.0 / 1.10 = 392.7 kN/m 316.3 kN/m

Earth support:

S: EphS,d = 1.20 137.9 + 1,30 13.0 = 165.5 + 16.9 = 182.4 kN/m

R: EphR,d = 443.6 / 1.30 = 341.2 kN/m 182.4 kN/m

The bracing is not calculated here.

Note 2: According to the current German practice, the permissible stresses in the design of the struts are not allowed to be increased. Accordingly, the design force of the struts is determined with the partial safety factors for load case LC1. Alternatively, the design force of the strut determined by means of partial safety factors for load case LC 2 could be increased with an adjustment factor = 1.15.

Note 3: Here, the embedding depth of 2,50m is chosen as the necessary length. In order to optimise the design, an iteration can be performed until the bearing capacity of the earth support, ie the design passive earth resistance, equals the design load at the support. In the case presented, an embedding depth of 1.65 m can be obtained. Thus, the design load at the support will decrease by 3% and the bending moment by 7%. If the embedding depth is reduced, the displacement at the base of the wall will increase. This has to be taken into account in the verification of the serviceability limit state.

6 Verification of the serviceability limit state

Under the characteristic actions the continuous beam programme gives a maximum wall deflection of 29mm at a depth z of 5.5m and a deflection of 20mm at the bottom of the excavation. A displacement for the mobilisation of the passive earth pressure must be added to this. As the passive earth pressure is mobilised for about one third and the soil below the bottom of the excavation is slightly overconsolidated, the displacement of the toe of the wall is estimated as:

sF = 0.8 % 2.50 m = 20 mm

This gives a total displacement at the bottom of the excavation of:

ss = 20 + 20 8.0 / 10.50 = 20 + 15 = 35 mm

It is assumed that the displacement of 35 mm can be tolerated.

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