Células, dendríticas y microsegregación

3.7.1

The application of safety in limit state design calculations

Current British codes contain a range of different ways of introducing safety into a geotechnical design, from the “working state” method using a global safety factor, generally adopted in BS 8004, to the partial factor method adopted in BS 8081. BS 8002 adopts yet another approach, that of the “(strength) mobilisation factor” whereby movement is limited by reducing in the calculation the value of strength (and thus strain) mobilised in the ground.

Most users of BS 8004 will have performed a design calculation that, by virtue of the (large) global factor of safety employed will have ensured not only that a ULS is avoided but also that settlements are acceptably small. In contrast, EC7-1, in ULS calculations, uses partial factor values that are intended to ensure that geotechnical failure is avoided, and may not be large enough to keep settlements to an acceptable level, particularly for softer, more compressible ground such as normally-consolidated or lightly over-consolidated clay or granular soil49_.

3.7.2

ULS design calculations

The Eurocode design philosophy clearly separates ULS from SLS, and deals rather more explicitly with the identification and treatment of the many uncertainties inherent in a design problem. Since most of EC7-1 is concerned with checking the avoidance of a ULS, this rigour is applied to the uncertainties in the calculation of, for example, bearing capacity from ground strength rather than to settlement calculations for checking the avoidance of an SLS.

ULS design calculations in the Eurocodes involve the following systematic activities:  establishing actions50

 establishing material (ground) properties  establishing (ground) resistances

 setting up calculation models51_{for the relevant ultimate and serviceability limit} states52

 showing in a calculation that limit states will not be exceeded.

Particular care is required when applying partial factors in numerical modelling using computer software.

3.7.3

Actions and their effects

The values of the actions from the superstructure supported by the geotechnical substructure are obtained from BS EN 1991-1-153_{. These values will be characteristic} ones (Fk) and will, in the geotechnical design, be factored by an appropriate partial action factor (γ_F), given in BS EN 1990 and repeated in EC7-1. EC7-1 identifies the geotechnical actions (eg active earth pressures on a retaining wall, and downdrag on piles) and deals with the effects of actions, given the symbol E54_{. EC7-1, in Clause} 2.4.2(2)P states that the values of geotechnical actions to be used shall be selected,

since they are known before a calculation is performed – they may change during that calculation.

A definition of “geotechnical action” has been given in the Glossary, and is based on one provided in BS EN 1990.

Generally, actions may be permanent (eg self-weight of structures or soil), variable (eg imposed loads on the surface of retained ground) or accidental (eg impact loads). It can be argued that EC7-1 promotes better communication between structural and geotechnical engineers by requiring greater awareness of what constitute permanent and variable structural actions. Given the greater emphasis on avoiding unwanted deformations, geotechnical engineers will need to be confident that characteristic values of actions from the structure are sufficiently well reported to them by structural engineers.

It is important to distinguish between actions imposed by the structure on the ground and the effects of geotechnical actions imposed by the ground on the structure. It is

also important to decide if actions are “favourable” (ie act to stabilise the structure) or “unfavourable” (ie act to destabilise the structure) since EC7-1 applies factors of different value depending on the stabilising (or otherwise) effect of the action, see Table A3.1. An unfavourable geotechnical action may have a favourable effect. For example, in the case of an embedded retaining wall, the unfavourable active earth pressure will generate a favourable passive earth pressure, that is a geotechnical resistance55_. Care should be taken when using numerical modelling in a ULS design. The application of ULS γ values of > 1 to actions such as water pressures can lead to physically impossible stress states. In such circumstances it is appropriate to apply partial factors to the effects of actions (moments, shear forces etc). For embedded retaining walls recommended practice is to factor the effects of actions for both serviceability and ultimate states, as the serviceability condition can often be more onerous. This has become accepted practice in the UK although the factors given in Table A.3, for instance, are strictly applicable to the ULS condition.

3.7.4

Geotechnical resistances

Once the characteristic value of the ground strength parameter has been obtained, the appropriate partial factor is applied to arrive at a design value for use in the calculation model that delivers the required geotechnical resistance (Rd)56. Alternatively, the design value of the strength may be assessed directly, without recourse to factoring

characteristic values.

3.7.5

The GEO and STR ULS calculations

All ULS calculations in EC7-1 start from the basic inequality57_:

E_d≤ R_d

where:

E_d is the design value of the effects of all the actions

R_d is the design value of the corresponding resistance of the ground and/or structure.

Design values of the effects of the actions

The effects of an action (such as the bending moments and shear forces in foundations) are functions of the load (action) from the structure, of any geotechnical action that depends on ground properties, and of the geometry of the geotechnical structure:

E_d= E {γ_FF_rep; X_k/γ_M58 _{; a}

d} (this is the so-called “Design Approach 1”–

see below) The meanings of the symbols are:

F_rep the representative59_{(or characteristic F}

k) value of an action (or of the effect of an action)

γF the partial factor for an action (or for the effect of an action, γE60)

X_k the characteristic value of a material (ground) property γ_M the partial factor for the material property

Design values of resistance

In general terms, the design value of the resistance, R_d, of the ground is a function of the design value of the applied load (γFFrep), the ground strength, Xk/γM, and the design value of any relevant geometrical quantity, ad. To obtain Rdthe partial factors may be applied either to ground properties (X_k) or to resistance (R), as follows:

R_d= R {γ_FF_rep ; X_k/γ_M ; a_d} (this is the so-called “Design Approach 1” that

applies generally for geotechnical resistances) or

R_d= R {γ_FF_rep; X_k ; a_d}/γ_R (in “Design Approach 1”, this expression only applies

to the design resistance of piles and anchorages) where γRis a partial factor for the resistance of the ground.

In the first expression, the design value of the resistance is obtained by applying the partial factor γM> 1 to the characteristic values of the ground strength parameters ck′ and ϕk′ or cu;ketc. If actions play a role in the resistance, design values of actions (γF F_rep) are introduced into the calculation of R_d61_.

In the second expression, the design value of the resistance is obtained by applying the partial factor γ_R> 1 to the resistance obtained using characteristic values of the ground strength parameters62_{. If actions play a role in the resistance, design values of actions} (γFFrep) are introduced in the calculation of Rdbut with γG= 1 for permanent actions (and γ_Q= 1.3 for variable actions), so that the expression becomes:

R_d= R {F_rep ; X_k ; a_d}/γ_R

During the development of EC7-1 there was much debate about the different forms of these expressions. In order to reach consensus among the EU member states, EC7-1 settled on three alternative design approaches (DAs), each using different forms of the expressions and, sometimes, different recommended partial factor values. In the National Annex to BS EN 1997-1 only Design Approach 1 (DA-1) is permitted. Appendix A3 explains how DA-1 is applied and provides a reference to explanations of the other two design approaches.

3.7.6

Serviceability limit state design

EC7-1, while requiring a more explicit consideration of settlement and serviceability limits than some BS codes, does not prescribe how settlements are to be calculated, although a simple elasticity method is outlined in Annex F63_{of the Eurocode}64_{. It} should be remembered that settlements are notoriously difficult to calculate with any accuracy and that use of relatively simple elasticity methods is best left to a suitably experienced geotechnical engineer.

Limit state design requires that the occurrence of a serviceability limit state is sufficiently improbable. Serviceability limit states may be checked in two ways:  by calculating the design values of the effects of the actions E_d(eg deformations,

differential settlements, vibrations etc) and comparing them with limiting values, Cd  by a simplified method, based on comparable experience.

normally be equal to their characteristic values, that is the γ_Fand γ_Mvalues will be equal to 1. In cases where differential settlements are calculated, a combination of upper and lower characteristic values of deformation moduli should be considered, to account for any local variations in the ground properties.

It should be appreciated that it may not be appropriate, notwithstanding that different γ values will be applied to arrive at a design values, to adopt the same characteristic value of strength in both ULS and SLS calculations. To do so may result in unreasonable estimates of forces and moments in the SLS.

In a perfect world, limiting values of deformations, Cd, might be specified as design requirements for each supported structure. EC7-1 lists a series of items to take into account when establishing limiting values of movement65, 66_{but does not recommend} any specific values of limiting deformations. However this is not remarkable since nor do current BS codes67_.

As a simple alternative to performing serviceability checks using calculations, EC7-1 permits the designer to show that a sufficiently low fraction of the ground strength is mobilised to keep deformations within the required serviceability limit. This simplified method requires the existence of comparable experience with similar soil and structure. This clearly restricts the circumstances in which the simplified method may be applied to conventional structures and foundations in familiar ground conditions. The

simplified method is applied in EC7-1 to spread foundations, to pile foundations and to retaining structures. EC7-1 gives no indication of what is a “sufficiently low fraction of ground strength”68_{. However, for spread foundations the code states: 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 should be calculated (see 2.4.8(4)). 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. Clause 6.6.1(16). It should be noted that

even when the ratio exceeds 2, non-linear and scale effects can play an important role in determining settlement.

3.7.7

The EQU limit state

EC7-1 stipulates that the following inequality must be satisfied:

E_dst;d≤ E_stb;d+ T_d

This means that the design value of the destabilising action E_dst;d(eg the overturning moment from earth or water pressures) should be less than the design value of the stabilising action Estb;d(eg the restoring moment due to the weight of the structure) plus any contribution from the design value of shearing resistance, T_d, on the sides of structures in the ground (the contribution from Tdshould be of minor significance).

3.7.8

The UPL limit state

The UPL limit state applies in circumstances such as where a new building basement will be excavated below the water-table so that uplift pressures may be resisted by piling the basement slab.

To check that failure will not occur, EC7-1 requires the following inequality to be satisfied:

V_dst;d≤ G_stb;d+ R_d

where Vdst;dis the sum of Gdst;dand Qdst;d, the design values, respectively, of the permanent and variable destabilising actions, such as water pressures under the structure and any other upward or pull-out force. Gstb;dand Rdare the design values of the stabilising permanent actions, such as the weight of the structure and/or of the ground, and the resistance of any additional structures such as holding-down piles or anchorages.

Example 4.8 illustrates the design of a structure subjected to uplift water pressures.

3.7.9

The HYD limit state

The resistance to failure by heave due to seepage of water in the ground is checked using either stresses or forces as the variables. As it does not depart from current best practices in the UK, design to avoid this limit state is not discussed further in this book. Further guidance may be found in Frank et al (2004).

3.8

The difference between DA-1 and traditional design