"STRUCTURAL ASSESSMENT OF EXISTING CONCRETE BUILDINGS"

Roberto Laranja Jorge de Brito EST - Algarve University DECivil - Instituto Superior Técnico Faro, Portugal Lisbon, Portugal

jb@civil.ist.utl.pt Tel. +351 218418354 Fax. +351 218497650

Summary:

An approach to the general issue of existing concrete structures safety analysis is presented,

referring the most relevant uncertainties and the various ways of characterizing them. The most

relevant uncertainties in the process of structural assessment are referred to. The structural

reliability and reliability index concepts and a procedure to measure them probabilistically are

presented, as well as the basic problem of structural reliability and the semi-probabilistic

approach to safety compliance.

The importance of characterizing the structural materials strength properties is referred and the

main related aspects are pointed out. Methods prescribed in some standards and

recommendations are presented, emphasising those suitable for existing structures safety

analysis. The importance of a priori data, the sources normally used in its acquisition and of the

inspection and tests planning stages is referred. The number of tests (sample dimension) needed

to infer and statistically validate the results is discussed.

The importance of characterizing probabilistically the actions and its effects is stressed. The

code criteria for their quantification are presented and the types of probabilistic distribution and

variability inherent to each action type are succinct described. Some methods for their

quantification in existing structures are pointed out. Special importance is given to the variable

actions quantification, due to the high uncertainties associated, the seismic action specially, in

the process of structural safety assessment. Ways of reducing their nominal values or the

respective safety factors, depending on the degree of uncertainty involved in its quantification,

namely due to the reduction of the existing structure expectable service life, are pointed out.

The probabilistic methodologies developed for structures safety analysis, based on the reliability

classical techniques, namely the second moment methods, of 1st (FORM) and 2nd order (SORM),

and those based on the numerical simulation techniques (Monte Carlo method), are referred,

emphasizing the difficulty in its application to case studies of existing structures assessment.

1. INTRODUTION

The existing reinforced concrete structures safety assessment represents an increased difficulty

as compared with assessing the safety of new structures. The fact that the object of analysis is a

real structure requires and allows a more demanding characterization of the most relevant (and

conditioning in terms of behaviour) parameters, as well as a clearer and more precise definition

of the models used in the assessment of the safety level. A slight variation in the safety level

indexes may mean the transition from an acceptable and safe structural behaviour to an

inadequate one, the reason for which the assessment’s rigour and preciseness are paramount.

Issues such as strength capacity reduction, concrete degradation, reinforcement corrosion and

changes of value or frequency of the actions have to be considered in a realistic way, leading to

the need of approaching the existing structures safety assessment differently from the way

prescribed in the standards that regulate new structures design.

2. UNCERTAINTIES AND RELIABILITY IN STRUCTURAL ASSESSMENT

2.1 Introduction

The structural safety assessment is a strikingly probabilistic problem, since the intervening

variables are generally characterized by their randomness, even though in most cases with

quantifiable probabilistic distributions. This randomness manifests itself in different aspects

during the structure’s service life, such as the number of occurrences, the values that they

assume, in time and space, the degree of repetition or regularity and their effective influence on

the structure. Therefore, the uncertainties related with the actions and with structural strength

may not be enough to allow an adequate study of the safety. It may be necessary to take into

account a wider range of uncertainties, related with environmental aspects, human errors at

design or construction and the prediction of future events [1].

In figure 1 the most relevant uncertainties in structural safety assessment are presented and the

way they interrelate is schematically represented.

An example of this type of uncertainties, difficult to characterize and which clearly influence the

assessment of the structural safety, is the one related to human intervention. As a matter of fact,

design rules are based on the presupposition that people involved in the design and construction

process are honest and competent. Experience shows that this is not always true [2]. Human

involvement in design and dimensioning, documenting, construction, use and maintenance of

the structures introduces a wide range of uncertainties in safety assessment. Human errors can

be divided in errors due to the natural oscillations in professional performance and gross

mistakes [1]. The knowledge of these uncertainties is limited, since they are mostly qualitative.

It is however obvious that its effect is an increase in the structural strength uncertainty due solely

to the structures’ mechanical and geometrical properties (Figure 2).

2.2 Structural reliability basic problem formulation

The structural reliability basic problem formulation involves only the strength, R, and the action,

S, described by their respective probability density functions fR and fS. The probability of failure,

pf, can be generally defined by:

Pf = P[G(R, S) ≤ 0] (1)

where G(R, S) if the limit state function. Therefore, the probability of failure is identified by the

probability of that limit state being violated.

Z

Z

σµ

β =

[ ] ∫+∞

∞−

=≤−= dyyfSRPxF XX )(0)(

If D represents the failure domain, the probability of failure is defined by:

(2)

If R and S are independent, then:

(3)

As the marginal distribution function FX(x), of a generic variable X is given, for x ≥ y, by:

(4)

equation (3) becomes:

(5)

This convolution integral represents every case where strength does not exceed actions.

If R and S are normal independent aleatory variables, variable Z = R - S that defines the safety

margin is also normal aleatory, with a mean value, µZ and a standard deviation, σZ:

µZ = µR - µS 22SRZ σσσ += (6)

where µR, µS, σR and σS are respectively the R and S mean values and standard deviations.

The probability of failure pf may then be expressed by:

(7)

where Φ is the reduced normal law distribution function (nil mean value and unitary standard

deviation); pf can still be represented as:

(8)

where β represents the reliability index:

[ ] ∫ ∫=≤−=D

rsf drdssrfSRPp ),(0

[ ] ∫ ∫+∞

∞−

>

∞−

⋅=≤−=RS

SRf drdssfrfSRPp )()(0

[ ] [ ]

−Φ=≤=≤−=

Z

Zf ZPSRPp

σ

µ000

( ) ( )βσσµµ

−Φ=

Φ=

+

−−

22SR

SRpf

[ ] ∫+∞

∞−

⋅=≤−= dxxfxFSRPp SRf )()(0

(9)

The smaller the value of the reliability index, β, the greater the probability of failure. If β is

known, the probability of failure can be obtained directly from the reduced normal law

distribution function, Φ. In figure 3 the meaning of β is shown schematically.

2.3 Safety assessment semi-probabilistic format

Present normative rules in the structural safety domain, clearly adapted for the design of new

structures, do not take into account the calculation or even an explicit consideration of the

probability of failure or of the reliability index for each structure in particular. It would be too

morose and complex for daily practice. These parameters are normally considered implicitly, in

deterministic methodologies, developed and calibrated for certain structural types, using

probabilistic analyses.

These methodologies constitute a semi-probabilistic approach to safety is associated to so-called

level I safety assessment methods. Safety and adequate service behaviour guarantee is defined

by [3]:

- representative values (nominal or characteristic) of the various aleatory parameters (actions

and strengths), accounting for scatter defined by analytical studies or by acceptance and

quality control rules; they are often associated to a fixed occurrence fractile or probability;

- partial safety factor to be considered in the assessment of limit states, so that the probability

of reaching or going beyond that state are lower than a certain pre-established risk level;

- safety margins, more or less implicit, that are introduced in certain models (and

corresponding formula) used in design.

Safety verification is guaranteed by the satisfaction of the following condition

Sd ≤ Rd or M

kkF

RSγ

γ ≤⋅ (10)

where:

Sd - actions (or action-effects) design value;

Rd - strengths design value;

γF - partial safety factor associated with the actions;

γM - partial safety factor associated with the strengths.

The partial safety factors and the actions characteristic values are defined in the codes as

referred before for certain structures’ types, as a function of the level of risk assumed.

3. STRUCTURAL MA TERIALS MECHANICAL PROPERTIES UPDATING

3.1 Existing data collection

The parameters that characterize the mechanical properties of the structural materials constitute

one of the sets of variables most important for structural safety assessment. The precision on its

characterization is therefore of the utmost importance especially in existing structures.

Usually it is possible to collect data concerning the existing structure, before resorting to tests.

Indeed, visual inspection may provide a set of useful data on the various aspects of the structure:

- the deterioration state - the observation of the most deteriorated areas (degradation or aspect

change of concrete, reinforcement corrosion, concrete spalling, etc.), as well as of their

deterioration degree, may lead to the definition of critical areas in the structure that may be

subject to special attention when performing the in situ tests;

- excessive deformation or cracking - these phenomena may indicate areas with structural

problems to be analysed carefully;

- structural changes - the detection of changes in shape and dimensions of structural elements

(grooves for piping, columns with their corners bevelled, reduction in the effective depth of

beams, openings in slabs, structural strengthening, etc.);

- the apparent quality of the structure - through the analysis of the structural elements surface

appearance, it is possible to infer qualitatively the level of quality of the structure execution

(surfaces and dimensions regularity, areas with deficient concrete compaction or with

reinforcement without cover, columns lack of verticality, etc.);

- construction errors - relative to dimensions, positioning or shape of the structural elements.

This type of data not only allows a better planning of the tests to be made but also an enhanced

sensitivity to aspects such as the quality of the manufacture and concreting works, the latter

crucial in obtaining an interval for the standard deviation of the concrete compression strength.

The design project and the conformity tests made during the structure construction, if available,

are other important sources of data. The eventual register of results from other tests during and

after construction may obviously contribute to a better characterization of the strength

parameters of the structural materials or of the structure behaviour.

The quantity and quality of data collected at this stage utterly condition the tests campaign to be

performed later on, allowing for example the initial identification of the most troublesome areas,

as well as a clearer idea of the type of tests to be made.

3.2 Definition of the experimental program to evaluate reinforced concrete

After collecting the available data on the structure and the initial inspection, it is necessary to

plan the experimental program. The type, quantity and location of the tests depend on a thorough

analysis of the data available and on the one to be collected. The general state of the structure,

the quantity and quality of the data collected, the aim of the assessment and the available means

are the essential elements at this stage.

The location and number of the tests needed to obtain results representative enough are the

fundamental issues in the tests programming. A statistical approach to this question seems to be

the most adequate, even if not always possible.

Generally, a test aim is to obtain a distribution of values that a pre-determined parameter can

assume, characterized normally by statistical parameters such as the mean value and the standard

deviation. However, the question of the obtained values representativeness is raised, i.e. to know

up to what point the values calibrated from a certain number of experimental results obtained in

selected locations can characterize a property of part or all the structure under analysis.

The need to evaluate the degree of confidence of the results obtained or, inversely, to determine

the minimum number of tests needed so that the results obtained reach a pre-determined degree

of confidence is therefore obvious.

3.3 Results post-treatment

The analysis of the results of the tests must be performed simultaneously with the information

collected from visual inspections of the site, the analysis of the final project elements, reports

from the building site, etc., taking into account the relative importance and the precision level of

the various data and the values available.

A possible way of performing this post-treatment of the results is by resorting to probabilistic

techniques based on a Bayesean approach. According to this approach, the existing estimate of a

parameter, such as the average of a given distribution, can be updated, using the conditioned

probability Bayes theorem and resorting to new data (such as the result of the tests). The

existing estimate is called a priori estimate and the new one is usually called a posteriori (a

priori and a posteriori to the new data).

It must be stressed that, if the parameter under analysis is related to a strength property of the

concrete, every data, i.e. the existing and the new one (such as the one from the tests), must be

referred to a structure, structural element or even a region of an element, where an even

distribution of the referred parameter exists (apart from the scatter assumed as a characteristic of

the material itself).

These techniques further allow considering, besides the variability of the parameters under

analysis, the one inherent to the tests methods themselves, especially those whose results are

related indirectly with the parameter to be assessed, such as the sclerometric and ultra-sounds

propagation tests. This capacity allows defining more realistic distributions for the strength

properties of the materials.

4. ACTIONS QUANTIFICATION

4.1 Introduction

The criteria recommended for the existing structures safety verification consist normally on the

adjustment of the already standardized procedures for new structures to the special features of

existing ones. Since most of them prescribe level I analysis criteria, the adjustments are made on

the characteristic and nominal values of the actions, as well as on the partial safety factors and,

eventually, on the combination factors.

However, in the areas of medium to high seismic risk, the most significant change caused by the

adjustments to the design codes is the one related to seismic action effects [4]. Indeed, the great

uncertainty associated with the definition and quantification of its effects on the structure leads

to very conservative code procedures. In the analysis of existing structures, the high economic

pressure coupled with other aspects forces the consideration of lower levels of demand that are

reflected in code recommendations. Recent European codes, namely the Eurocodes, already

introduce some rules concerning existing structures.

4.2 Dead loads

4.2.1 Representative values

Dead loads are usually those due to volume distributed loads, such as the structural elements

own weight, and to loads distributed over the outer surface, resulting from permanence of non-

structural elements such as linings, partition walls and fixed equipment. Due to these effects

being added, the global dead load variability is lower than the one due to each individual part. It

has also been found that the variability of this type of loads in the whole is more due to the non-

structural materials and the fixed equipment than to the structural materials own weight [1].

When evaluating existing structures, these loads may be characterized more accurately than at

the design stage, by resorting to in situ measurements, of the structural elements geometric

variability, the density of the materials, namely of the concrete, and also the type and

dimensions of the non-structural materials.

4.2.2 Partial safety factors

Most international codes prescribe for the design of new structures in general a safety factor for

dead loads, γf,G, equal to 1.5, when their effects are unfavourable. In the case of reinforced and

prestressed concrete structures, this factor may be reduced to 1.2 for prestress, when it is not

conditioning for the structure’s safety, and 1.35 for the other dead loads, as long as they are very

accurately quantified [4]. This last value is also the one prescribed by EC1 [5] for dead loads in

general with an unfavourable effect and for all limit states that do not involve global balance.

When the uncertainties associated to this type of actions are reduced through measurements and

accurate testing in existing structures, namely in what concerns structural elements dimensions

and density of the materials, it is thus possible to consider for this factor the value 1.35. For this

type of situations, CEB [6] states that it is possible to proceed with a reduction of the partial

safety factor to a value γf,G,exist, even though no guidance is given to quantify it. Another

document from CEB [7] proposes that in such cases one may consider:

γf,G,exist = γf,G - 0.1 (11)

Some recent international codes on this subject adopt a broader perspective, by considering

fundamental aspects in the process of analysis and verification of the safety, such as the quality

of the inspection made, the extent and quality of the in situ tests performed, the potential

collapse mechanisms and their possible consequences.

The Canadian National Building Code, for instance, allows the change of the reliability index

adopted for new structures, βC, considering a factor, ∆, obtained as a function of the aspects

referred above [4]. The reliability index for existing structures, βexist, is obtained by:

βexist = βC - Σ∆i (12)

where ∆i values are as in Table 1. Since the reliability index is changed, an adjustment is made

to the code safety factors, see Table 2.

Even though this method allows greater flexibility than in new structures, it demands a greater

professional judgement from the structural engineer, as it involves the evaluation of subjective

aspects such as inspection quality and probability of personal injuries.

4.3 Live loads

4.3.1 Representative values

Concerning actions time-dependent and besides the seismic action, live loads assume a great

importance in the general issue of safety assessment of structures, and namely in buildings. For

this type of structures, live loads’ modelling considers the following basic assumptions [8]:

- the variability of live load is independent in time and in space;

- discreet live loads are defined by an equivalent load uniformly distributed; therefore, the

effect of the load on the pavement is defined and not its nominal value;

- the time dependency is considered through two components: the sustained component that

represents the mean value of the load between the several occupancies and considers heavy

equipment, furniture and frequently people’s weight; and the transient component that

represents special loads that act only during very short periods (Figure 4).

In each moment, the live load global value will be the sum of the two components. The extreme

values of the global load may result from this sum in three different ways [9]:

- the maximum sustained value throughout the service life plus the maximum transient value

within the occupancy;

- the maximum transient value throughout the service life plus the instantaneous sustained

value;

- the maximum sustained value throughout the service life plus the maximum transient value

in the same period.

The probability of occurrence of the last hypothesis is very small compared with the first two,

around 17% [1]. The probabilistic model that characterizes the global load must however take

into consideration these three possibilities, which shapes it into a complex formulation

aggravated by the fact that the individual distribution are of different types. Indeed, the

distributions that better describe the maximum sustained, transient and maximum transient

components are type I (Gumbel’s law) extreme values ones, while the sustained component

adjusts itself better to a Gamma law [9].

However, it is possible to model the global load value in a more simplified even though less

accurate way by resorting to a type I extreme values distribution, whose distribution function is:

(13)

From the characteristic values given by the codes and knowing some distribution probabilistic

parameters, it is possible to define the distribution function for a pre-determined live load. For

the live load in residential buildings, for example, for the characteristic value, 2.0 kN/m2, F(2) =

0.95. For this type of live load, values of the variation coefficient between 0.3 [4] and 0.4 [10]

( )( )( )

−−−

=≤=uxe

exXobxFα

Pr)(

are quoted. With this data and considering a variation coefficient of 0.4, it is possible to define

the respective distribution function for an expected 50-year service life:

(14)

Assuming that the instantaneous global load values are independent and that their occurrence

constitutes a stationary process, it is possible to obtain this live load’s distribution function,

FT(q), for a service life, T, different from 50 years:

(15)

Thus, for the situation of the safety assessment of an existing structure, it is possible to obtain

the representative value of the live load as a function of its design remaining life, maintaining

the code concept of characteristic value, Qk, i.e. guaranteeing a probability of exceedance less

than 5%. Figure 5 presents a graphical representation of this variation.

4.4 Seismic actions. Quantification according to Eurocode 8, part 1-4

4.4.1 Introduction

The European Pre-standard ENV 1998-1-4:1995, Eurocode 8 [12], aims at defining criteria for

the assessment of existing structures’ behaviour when subjected to earthquakes, describing the

approach to selecting intervention measures and defining criteria for structural repair and

strengthening situations.

Assessment consists on assuring seismic action resistance to existing structures, damaged or not,

by resorting to linear, non-linear or approximate non-linear analysis methods, considering the

seismic and the non-seismic actions for the assumed design remaining life. The actions and their

partial safety factors can be modified considering an eventual reduction of the service life and a

decrease of the degree of uncertainty related to dead loads and to structural materials properties.

( )( )( )

−−−

=≤=93887.028002.0

Pr)(qe

eqQobqF

( )TT qFqF

50)()( =

4.4.2 Basic principles

The basic model for defining the seismic action is the one prescribed in EC8 - Part 1-1 [13] and

Part 1-2 [14] for new structures’ design, with the particularity of admitting the possibility of

reducing the effective peak ground acceleration, ag, as long as:

- the structure is not included in importance category I;

- the structure’s residual service life is less than the one considered in new ones;

- the structure is strengthened or demolished at the end of its design remaining life.

The possibility of having higher values of the exceedance probability of the ag value during the

reference period considered (equal to the new structures service life) is also admitted. For the

remaining actions, the values to be considered should not be altered, i.e. they are the same as for

new structures.

4.4.3 Combination of actions

Combining the seismic action with the remaining ones is made according to EC8 - Part 1-1:

(16)

where:

γI - importance factor depending on the importance category;

Emod - seismic action modified according to 3.3.2;

G - dead loads characteristic values;

P - prestress action long-term value;

Qik - live loads characteristic values;

ψ2i - combination factors relative to the live loads.

There is no corrective factor either for the seismic action or the remaining ones, which means

that possible changes of the partial safety factors mentioned in 4.4.1 is reserved to the factors

iki

iI QPGE ∑Ψ+++± .. 2modγ

related with the materials strength properties.

4.4.4 Reduction of the effective peak ground acceleration

In Annex C of EC8 - Part 1-4, a possible way to reduce the value ag as a function of the

structure’s design remaining life is presented. According to some scientific results, the effective

peak ground acceleration can be obtained by:

(17)

where Tm is the average return period obtained by:

(18)

where:

Lt - reference period, i.e. the structure’s service life;

Pf - probability of exceeding the value of ag, within period Lt;

k1, k2 - location dependent parameters.

Maintaining the probability of exceedance of ag, and considering k1 = 1.0 in accordance with the

National Application Document (DNA) of Portugal for EC8 [15], the corrective factor for a

fixed design remaining life, Lt,res, is:

(19)

where res,tL,ga is the effective peak ground acceleration to be considered for Lt,res.

In Figure 6 the variation of the corrective factor with Lt,res is presented, admitting that Lt = 50

years, in accordance with the DNA.

EC8 - Part 1-4 also allows the increase of the accepted value of the exceedance probability of ag

during the structure’s service life but it does not refer the criteria to which it should comply.

( )2log1 kmTkg ea +⋅=

)1( f

tm PLn

LT−

−=

= tLrestL

g

restLg ea

a ,log,,

−

−

=)sup,1ln(

)1ln(log

sup,, fPfP

g

fPg ea

a

Admitting an exceedance probability, Pf,sup, higher than the one defined in EC8, for a 50-year

period, the reduction in the value of ag is:

(20)

where sup,, fPga is the effective peak ground acceleration to be considered for Pf,sup.

Figure 7 presents the variation of the corrective factor with the accepted exceedance probability.

The return period stated in EC8 - Part1.1, 475 years, corresponds to an exceedance probability

of 10% in 50 years, i.e., according to Figure 7, the maximum nominal acceleration to be

considered would be only 45 % of the value obtained for ag according to the Portuguese DNA.

Ii is interesting to note that in the United States and according to the recent codes on existing

structures safety assessment, the quantification of the seismic action is made for an exceedance

probability of 10% over a reference period of 50 years [17]. The recent Canadian codes

prescribe the same exceedance probability and reference period [4].

5. SAFETY ASSESSMENT

In 2.2 a formulation of the structural reliability basic issue was presented. However, usually it is

not possible to reduce the structural reliability problem to the simplified formulation stated in

(1), that relates strength, R, and action, S, by considering them independent variables. As a

matter of fact, R is usually dependent on the structural materials properties or on the structure

itself, while S depends on the actions, the materials density and eventually on the structure’s

dimensions, all of these usually aleatory variables. There are also situations where it is not

possible to consider R and S as independent, namely when the action-effect is favourable (it is

against the effects that lead to failure), or when the structure or the structural elements’

dimensions simultaneously condition the values of the action and the strength.

The generalization of the reliability issue leads to the need to resort to structural analysis

probabilistic techniques such as the First and Second Order Reliability Methods (FORM and

SORM, respectively) or numerical simulation techniques based on the Monte Carlo Method.

However, these techniques are mostly appropriate to calibrate the partial safety factors used in

level I analyses that are prescribed by almost every structural safety code, namely those for

reinforced concrete structures. In simple and easy to model structures they also allow the

calibration of the most relevant parameters of structural behaviour.

However, it has been found out that the application of this type of analyses to existing structures

case studies becomes very time-consuming, complex and therefore unattractive, specially if it

involves some overall complexity of the intervening actions and their combination, the

structures’ dimension and geometrical characteristics and the nature of the materials involved.

This leads to the common practice of using deterministic techniques, based on semi-

probabilistic code-based safety formulations. However, in these cases and given the nature of

the problems involved, reliable tools must be used in order to reduce as much as possible the

errors inherent to the set of uncertainties involved and the models used.

Whenever possible, the update of intervening actions and combinations, as well as of strength

properties as described in chapters 3 and 4, is recommended. Structural analysis methods that

allow the accurately enough reproduction of the structures’ response, in terms of action-effects

and deformations, ought to be used. The most advanced methods available today, based on non-

linear spatial dynamic analyses using accelerograms and structural elements finite elements

modelling, usually yield a great volume of results, whose post-treatment can become time-

consuming and complex.

The structural analysis methods that consider in a simplified way the structures non-linear

response, in terms of action-effects and deformations, are the most adequate, specially if they

allow the consideration of their hysteretic damping and the identification of the cross-sections or

elements where the response is inadequate or conditioning in terms of the limit states at stake.

One of the methods of this type that has been gaining support in the two last decades but mostly

recently, having been adopted code-wise in several countries such as the United States and

Japan, is the so-called Capacity Spectrum Method, proposed by Freeman in 1978 [17], that

consists basically in the following:

• a simplified representation of the non-linear response of the structure to the seismic

action, obtained by a set of static linear analyses, through the ration spectral

acceleration-displacement, Sa-Sd, of an equivalent single degree of freedom system,

SDFS;

• a simultaneous representation of the ratio Sa-Sd and of the elastic response spectrum

converted to the Sa-Sd shape;

• through an iterative process, the elastic response spectrum is successively corrected,

taking into account the hysteretic damping of the structure (which itself depends on

the spectrum), until a modified response spectrum is obtained in which the response

of the structure equals the action. The intersection point of the modified response

spectrum with the Sa-Sd curve of the structure is called the Design Point, whose

coordinates represent the maximum spectral acceleration and displacement of the

SDFS equivalent to the structure.

6. CONCLUSIONS

The evaluation of the structural materials strength properties is paramount in the process of

verifying an existing structure safety. Indeed, since they are the only variable entities directly

measurable and consequently allowing a greater accuracy in its quantification, their importance

is increased. Their quantification accuracy is in principle dependent only on the quality and

dimension of the experimental tests and the thoroughness of the structures’ inspections. This is

indeed the greatest difficulty in the evaluation process, since the definition of a test program

conditions at the very beginning the accuracy of the experimental results obtained.

Some variable actions such as the live loads can also be estimated with greater accuracy in

existing structures, since they depend on aspects directly assessed at the site.

In general it is possible to decrease the uncertainties involved in the quantification of actions in

relation with the values prescribed in the codes, usually aimed at new structures. The criteria

adopted in codes comprise certain structural typologies and consider typical values of the aspects

that condition the actions’ values. The definition of typologies presupposes a wide range of the

intervening parameters and is therefore conservative. In an existing structure these parameters

can be defined more accurately and therefore it is acceptable to consider less conservative values.

If the models the codes are based on are known, it is possible to act on the parameters most

susceptible to alterations and thus obtain more reasonable values for the structure under analysis.

7. REFERENCES

1. Melcher’s, R. E. - Structural reliability: Analysis and predictions. John Wiley & Sons, 1999.

2. Ferry-Borges, J.; Castanheta, M. - Structural safety. Course 101, National Laboratory of Civil Engineering (LNEC), 1985, Lisbon.

3. Henriques, A. R. - Application of new concepts in structural concrete safety design. (in Portuguese) Civil Engineering PhD Thesis, Engineering Faculty of the Porto University, 1998, Porto.

4. Allen, D. E. - Limit states criteria for structural evaluation of existing buildings. Canadian Journal of Civil Engineering, 1991, 18(6): 995-1004.

5. ENV 1991-1-1 - Eurocode 1: Basis of design and actions on structures - Part 1: Basis of design. CEN, 1994.

6. CEB - Assessment of concrete structures and design procedures for upgrading. Comité Euro-International du Béton, 1983, Bulletin d’Information No. 162.

7. CEB - Redesign for concrete structures. Comité Euro-International du Béton, 1989, GTG-21,

Redesign of Concrete Structures Task Group.

8. Peir, J.; Cornell, C. A. - Spatial and temporal variability of live load. Journal of the Structural Division, ASCE, 1973, 99(ST5): 903-922.

9. Chalk, P. L.; Corotis, R. B. - Probability model for design live loads. Journal of the Structural Division, ASCE, 1980, 106(ST10): 2017-2030.

10. Calgaro, J. A. - Introduction aux eurocodes: Sécurité des constructions et bases de la théorie de la fiabilité. Presses de l'École Nationale des Ponts et Chaussées, 1996.

11. Laranja, R.; Brito, J. de - Reinforced concrete structures safety assessment: Dead and live loads quantification. (in Portuguese) BE2000 - National Structural Concrete Meeting, Engineering Faculty of the Porto University, 2000, Porto.

12. ENV 1998-1-4 - Eurocode 8: Design provisions for earthquake resistance of structures - Part 1-4: Strengthening and repair of buildings. CEN, 1995.

13. ENV 1998-1-1 - Eurocode 8: Design provisions for earthquake resistance of structures - Part 1-1: General rules and rules for buildings - Seismic actions and general requirements for structures. CEN, 1994.

14. ENV 1998-1-2 - Eurocode 8: Design provisions for earthquake resistance of structures - Part 1-2: General rules and rules for buildings - General rules for buildings. CEN, 1994.

15. Carvalho, E. C. et al. - Definition of the seismic action within the National Application Document (DNA) of Eurocode 8. (in Portuguese) 4th National Meeting on Seismology and Seismic Engineering, EST - Algarve University, 1999, Vol. 2: 77-94.

16. Laranja, R.; Brito, J. de - Reinforced concrete structures safety assessment: Seismic action quantification. (in Portuguese) REPAR2000 - National Meeting on Conservation and Rehabilitation of Structures, LNEC, 2000, Lisbon.

17. ATC - Seismic evaluation and retrofit of concrete buildings. Applied Technology Council, California Seismic Safety Commission 1996, ATC 40, Vol. 1.

Decision Phenomenological

Modelling

Prediction

Statistical

Physical Human factors

Figure 1: Uncertainties in structural assessment (adapted from [1])

fR(r) .

r rd

Original fR( r)

Modification due to human intervention

Figure 2: Human intervention effects in strength density function (adapted from [1])

β . σ Z

Z = R - S

p f

Z < 0

0

Failure

µ Z

Safe

f(Z)

Z > 0

Figure 3: Probability density function of safety margin Z = R - S and safety index (adapted from [2])

Qqp)

Time fQq

Qqp

Sustained loads Qqp

(Qi)

fQi

Qi

Time Transient loads Qi

Figure 4: Live loads modelling

0

0,25

0,5

0,751

1,25

1,5

1,75

2

10 15 20 25 30 35 40 45 50

Vida útil residual [anos]

Qk,exist [KN/m2]

Figure 5: Variation of Qk,exist with the structure design remaining life (adapted from [11])

Design remaining life [years]

0,5

0,6

0,7

0,8

0,9

1,0

20 25 30 35 40 45 50

Vida útil residual, L t res [anos]

(a g,Lt,res ) /a g

Figure 6: Reduction of ag with the structure design remaining life (adapted from [16])

Design remaining life, Lt,res [years]

0,30,40,50,60,70,80,9

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Probabilidade de excedência admitida [%]

(a g,Pf,sup )/a g

Figure 7: Reduction of ag with the accepted probability of exceedance (adapted from

[16])

Accepted probability of exceedance [%]

Table 1: Reliability index, βC,, corrective factors ∆i [4]

Assessment factor ∆i

Inspection performance - ∆1

No inspection nor design drawings

Inspection for identification / location

Satisfactory inspection or dead loads measurement

Structural system behaviour - ∆2

Failure leads to collapse, likely to injure people

Intermediate situation

Failure local only very unlikely to injure people

Risk category of failure - ∆3

Very high

High n = 100 to 1000

Normal n = 10 to 99

Low n = 0 to 9

-0.40

0.00

0.25

0.00

0.25 (a)

0.50 (a)

(b)

0.00

0.25

0.50

(a) - except when the seismic action acts

(b) - use prescribed values for new structures

n - Probable maximum number of people exposed to failure in situations of

normal occupancy

Table 2: Safety factors, γf,G,exist, for structural assessment and upgrading of existing

buildings [4]

Σ∆i Safety factors

γf,G,exist

-0.40

0.00

0.25

0.50

0.75

1.00

1.25

1.35

1.25

1.20

1.16

1.12

1.08

1.05