CIV350 L5-6 Design Code Principles Annotated(1)

8/13/2019 CIV350 L5-6 Design Code Principles Annotated(1)

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Geotechnical Design Design Code Principles

Design Code Principles

It can be argued that an ‘ideal’ design code should be one based on:

• Performance Based Design (PBD)

• Reliability principles

In practice reliability theory is still an area of research. A pragmatic approach istherefore to work with a simplified method, ideally verified by the overarching framework.

Specific examples of PBD include:

• Limit State Design (e.g. Eurocode).

• Allowable seismic displacement .

Methods of achieving a desired reliability include:

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Methods of design include:

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Limit State Design

Definition

1. Limit State Design involves the analysis of the unexpected states at which the

system has reached an unacceptable or limit state.

2. It ensures that the probability of these limit states being reached is at an appro-priately low level.

The most common limit states used in design are:

1. Ultimate Limit State (ULS)

2. Serviceability Limit State (SLS)

Note:

• A partial factor approach does not necessarily equate to a Limit State method.

• Limit State Design is not directly related to any specific analysis method.

An understanding of limit state design can be obtained by contrasting it with working state design which involves the analysis of the expected, working state to which marginsof safety are applied.

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The Ultimate Limit State (ULS)

Types of ULS

According to EC0 (’Basis of structural design’):

(4)P The following ultimate limit states shall be verified where they arerelevant:

• loss of equilibrium of the structure or any part of it, considered as arigid body;

• failure by excessive deformation, transformation of the structure or anypart of it into a mechanism, rupture, loss of stability of the structureor any part of it, including supports and foundations;

• failure caused by fatigue or other time-dependent effects.

Implementation in Eurocode

Figure 1: Actions and Resistances.

Figure 2: Example probability distributions for Actions and Resistances.

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Consider actions (loads) and resistances (i.e. resistance available at collapse ) asshown for example in Figure 1. In simple terms it is necessary to minimise the overlap inthe probability distribution curves (see Figure 2) for the actions and resistances. This canbe done directly using probability/reliability theory or indirectly (but far more simply)using partial factors. As a general rule it is considered desirable to apply the partial

factors as close to the source of uncertainty as possible.

Definitions of actions, action effects and resis-

tances

There is not currently a full consensus on the definitions of actions, action effects andresistances e.g. for Eurocode. The following definitions were proposed by Smith andGilbert (2011) :

Action A (direct) action is a force or load whose value is independent of the collapse mechanism. Within a defined failure mechanism it may be either favourable (if it opposes collapse) or unfavourable (if it assists collapse).

An example of an action is the dead weight of a foundation or an external structuralload. Variable loads almost always fall into this category. Static water pressuresare also usually regarded as actions.

Action effect The effects of actions can only be defined for a specific failure mecha-nism and are to be taken at a pre-specified location within a design problem. Anaction effect is derived from an ‘action effect model’ which will typically involve

actions and material strength and will act to drive the system to failure. The action effect should assist collapse, and will always be unfavourable. Due to the involvement of material strength, an action effect is considered permanent.

An example of an action effect is an active earth pressure. Note that there isan inconsistency here in Eurocode 7 where it is stated that earth pressures maybe considered as actions (or specifically, geotechnical actions). However in ageneral analysis earth pressures cannot be known until the critical collapse modeis identified. (For hand calculations, the use of closed form solutions such asRankine’s earth pressure equations can serve to mask this issue.)

Resistance A resistance can only be defined for a specific failure mechanism. It must involve material strength in such a way that the mobilised strength opposes the specific failure mechanism being examined. It should be determined using a ‘resis-tance model’ and is taken at a pre-specified location within a design problem (as with action effects).

An example of a resistance is bearing resistance for a footing or passive earthpressure for a retaining wall. Note that a resistance may also be a function of actions. These source actions may or may not oppose the failure mechanism.

Note that the above definitions of action effect and resistance are given in the contextof the geotechnical component of an analysis. For internal structural design checks, it wille.g. typically be found that a resistance is simply a material property and is unaffectedby the failure mechanism.

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Methods of applying partial factors

There are three general methods of applying partial factors, each with its advantagesand disadvantages:

MFA Material Factoring Approach. Partial factors are directly applied to the charac-teristic values of materials in the design calculation. Factors may also be appliedto some actions. Examples in Eurocode 7 are DA1/2 and DA3.

RFA Resistance Factoring Approach (also known as LRFD, load and resistance factordesign). Partial factors are applied to the resultant resistance calculated using thecharacteristic values of materials. Factors may also be applied to some actions. Aspecial case may involve unity factoring of resistance and factoring of actions only.Examples in Eurocode 7 are DA1/1 and DA2.

EFA Action Effect Factoring Approach. Factors are applied to action effects e.g. a

bending moment or tensile force in a structure calculated using characteristic valuesof materials and source actions. Factors may also be applied to the resistancecorresponding to the action effect. Examples in Eurocode 7 are DA1/1* andDA2*, where the * denotes factoring of action effects.

Examples

Retaining wall anchored in rock

Consider a propped retaining wall retaining stiff clay, with the base of the wall embeddedin rock. Which is the appropriate design approach to use?

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Footing on sand

Consider the 2m wide strip footing placed on the surface of a sand layer of strengthφ = 40o and γ = 16 kN/m2 as shown in Figure 4. Calculate the design load.

Figure 4: Footing on sand.

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Rigorous analysis of ULS problems using yield sur-faces or interaction diagrams

Definition

1. An interaction diagram or yield surface may be defined for a system as well as fora material.

2. A common yield surface used for a material in soil mechanics is the Mohr-Coulombcriterion (see Figure 5) . The surface is defined by the equation τ = c + σ tan φ.If at any point, |τ | < c + σ tan φ the soil is not yielding at that point. If τ = c + σ tan φ the soil is yielding. Conditions where |τ | > c + σ tan φ are notpossible.

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S h e a r

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Normal stress σn

τ = c + σn tan φImpossible state

Stable state

Yield state

Figure 5: Mohr-Coulomb yield surface.

3. Similarly such a surface may be defined for a system such as the undrained sta-bility of a strip footing founded on a clay soil subjected to combined vertical V and horizontal H loading per unit length, with full adhesion on the footing/soilinterface. This problem is depicted in Figure 6, and the yield surface/interactiondiagram in Figure 7. States inside the surface are stable, states on the surface areyielding, states outside are not possible.

4. It is possible to plot one surface for all possible combinations of footing width Band soil strength cu by normalising (and non-dimensionalising) the loads per unitlength V and H by dividing by cuB. For this particular problem, the soil unitweight does not influence the solution.

5. Simple states are visible on the surface e.g. for purely vertical loading (H = 0),failure occurs when V /cuB = 5.14, and for purely horizontal loading (V = 0),failure occurs when H/cuB = ±1.0.

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H

V

θ

Figure 6: V-H loading on a footing.

6. For undrained problems, the direction in which the system moves at failure (when

its loading condition meets the yield surface) is perpendicular to the yield surfaceat that point.

7. When using interaction diagrams do not measure angles directly off a graph unlessit is plotted to exactly identical scales on each axis. This will usually not be thecase. It is preferable to calculate angles using trigonometry.

Checking the ULS

An Ultimate Limit State analysis must ensure that the problem state analysed using

design parameters must not be at the collapse or ULS state. There are two broadapproaches to check this:

1. If the yield surface for the system is known, then it is simply necessary to checkthat the design state is inside the yield surface.

2. If the yield surface for the system is not known then it is necessary to show thatthe system at its design state must be ‘perturbed’ unfavourably to reach its ULS.

In order to undertake a ‘perturbation’ based ULS analysis it is necessary to drivethe design state to collapse by some means. This can be done implicitly or explicitly.In many conventional analyses the process is typically implicit. In a general numerical

analysis it must be done explicitly.There are three general ways to drive a system to ULS:

1. Increase an existing unfavourable load or loads in the system (multiply load byadequacy factor a). This applies commonly to RFA methods.

2. Reduce a material strength (divide strength by adequacy factor a). This appliescommonly to MFA methods.

3. Impose an additional unfavourable load in the system (multiply additional load byadequacy factor a). This applies commonly to EFA and RFA methods.

The system passes the design criterion if a ≥ 1.0 in the first two cases and if a ≥ 0.0in the latter case.If design parameters can only be determined following an analysis then the system

must be perturbed using Method 3. This typically applied to Action/Resistance factoringmethods (RFA). This will be examined in more detail later.

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Example - footing with inclined loading (Eurocode factoring)

Problem definition

A footing founded on undrained soil is subjected to characteristic permanent loads perunit length V k = 2.3cukB and H k = 0.15cukB. It is required to assess this usingEurocode 7. Figure 8 depicts the yield surface for this footing for combined horizontaland vertical loading.

Design Approach 1 Combination 1 - Action factoring (RFA special case)

1. Apply partial factors to characteristic actions to obtain the design state. In thiscase the factors on permanent actions are 1.35. Therefore the design state (pointD1C1) is displaced from the characteristic state (point K).

2. Check that this point lies within the design yield surface, which in this case is the

unfactored yield surface since DA1/1 has unit partial factors on material properties.

If the yield surface is not known in advance, the ULS test can be undertaken by oneof the following methods:

1. Apply Method 1, increasing the existing (unfavourable) design load by a factor a,and show that a > 1.0 to reach yield (ULS1).

2. Apply Method 3, applying an additional (unfavourable) load which is factored bya, and show that a > 0.0 to reach yield. E.g. path from D1C1 to ULS1a

Design Approach 1 Combination 2 - Material factoring (MFA)

In a material factoring method, the design yield surface is reduced in size relative to theunfactored yield surface using the material factor (dashed line in Figure 8). Note thatthis means that the value cu used to normalise the design actions in the graph shouldstill be taken as the characteristic value.

1. Apply partial factors on actions to obtain the design state. In this case the factorson permanent actions are 1.0. Therefore the design state (point D1C2) is thesame as the characteristic state (point K).

2. Check that this point lies within the factored yield surface (dashed line surface inFigure 8 ).

Note that it is in general, preferable to plot a design (factored) yield surface sincenormalisation is not always possible by a material strength (e.g. by tan φ).

Design Approach 2 - Action and Resistance factoring (RFA)

Design approach 2 (DA2) is not used in the UK, but is used in other parts of Europe.It is examined here in order to illustrate the wider principles of Ultimate Limit StateDesign.

In this case:

1. In DA2, actions are factored in the same way as in DA1/1. Therefore the designstate (in terms of actions) is the same as D1C1.

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2. It is necessary to determine the resistance in order to apply factors to it. In DA2,the factor is 1.4 for bearing failure, and 1.1 for the special case of horizontal sliding.

3. The resistance is normally that available at yield, however it may be a pre-yieldstate.

4. In order to determine the resistance it is necessary to specify a failure mode.

5. For this problem, this approach therefore requires multiple checks on multiplefailure modes, unlike previous cases for which all failure modes can be checked byone calculation. Three examples are given below. It is possible for some directionnot to comply with the Eurocode and other to comply:

(a) A check against perturbation in the same direction as the load, leads tothe path to ULS1 (coordinates V k = 4.81cukB and H k = 0.31cukB). Thecharacteristic loading in the direction of the load is E k = 2.30cukB (length

of the line from the origin to K). The characteristic ULS resistance Rk,ULS is4.82cukB (length of the line from the origin to ULS1). Hence the Eurocodecheck is 1.35 × 2.30 ≤ 4.82/1.4, i.e. 3.11 ≤ 3.44 and so the criterion issatisfied.

(b) A check against a horizontal perturbation leads to the path 2a. The char-acteristic ULS resistance Rk,ULS is 0.97cuB. The characteristic horizontalaction H k is 0.15cuB. Hence the Eurocode check is 1.35× 0.15 ≤ 0.97/1.4,i.e. 0.20 ≤ 0.69 and so the criterion is satisfied.

(c) A check against vertical perturbation leads to path 2b. The ULS resistanceRULS is 4.94cuB. The vertical characteristic action H k is 2.3cuB. Hence

the Eurocode check is 1.35 × 2.3 ≤ 4.94/1.4, i.e. 3.11 ≤ 3.53 and so thecriterion is also satisfied.

Relationship to global factors used in older codes

In older design codes, global factors of safety were often used. It is incorrect simply tostate that a design has a factor of safety of X as this gives no information on what thefactor of safety is applied to. Several different definitions of factors of safety are used ingeotechnical engineering. Three in common usage are listed below:

1. Factor on load.2. Factor on material strength.

3. Factor defined as ratio of resisting forces (or moments) to disturbing forces (ormoments).

The calculation process used to determine each of these factors for any given problemwill in general result in a different failure mechanism, and a different numerical factor.Each FOS must therefore be interpreted according to its definition.

In the context of partial factor methods such as Eurocode, it is possible to quotean overdesign factor over and above the margin of safety given using partial factors.However this also must be clearly defined.

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Problems

1. Consider the undrained stability of a 2m wide strip footing, founded on a clay soil of undrained strength cu = 50kN/m2, with full adhesion on the footing/soil interface.Determine the magnitude of the collapse load, and the initial displacement velocity

direction for the following load inclinations (θ in Figure 6), where the load is appliedto the centre of the footing:

(a) 45o

(b) 5o

2. A 1.5m wide footing founded on a clay soil of undrained strength cu = 60kN/m2

is subjected to an inclined load of 360 kN/m at an angle θ of 10o. How muchadditional horizontal loading is required to produce collapse.

3. A 1m wide footing founded on a clay soil of characteristic undrained strength

cu = 70kN/m2 is subjected to an inclined characteristic permanent load of 170kN/m at an angle of 5o, and a characteristic variable horizontal load of 20 kN/m.

(a) Show that the loading satisfies the Eurocode Design Approach 1 criteria.

(b) Determine the overdesign factor (adequacy factor) for the combined load.

4. Repeat 1, 2 and 3 above using the LimitState:GEO software, in this case assumingthat you do not know the yield surface in advance. Remember that in the software,loads are applied as stresses not loads per unit width.

AnswersNote that if results are scaled off the provided interaction diagrams, then answers withina few percent of the given answers are acceptable.

1. (a) 141 kN/m, horizontal velocity direction (b) 467 kN/m, velocity direction in-clined approx 33o downwards to horizontal.

2. 8 kN/m

3. (b) 1.06 for DA1/2. (DA1/1 gives an overdesign factor of 1.15).

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Figure 7: VH interaction surface for a footing subjected to an inclined load. Solid

line is yield surface.

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K, D1C2

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ULS1

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Figure 8: VH interaction surface for a footing subjected to an inclined load. Solid

line is yield surface, dashed line is yield surface subjected to a material factor.

CIV350 L5-6 Design Code Principles Annotated(1)

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