ABSTRACT: The discussion on characterization of ground motion is concerned with: alternative representations of time dependence of accelerograms, single- versus multi- component accelerograms, condensed representation and space of accelerograms, consideration of seismic action alternatively at site level and at source level with generalized definition of attenuation, and consideration of past, versus expected, motions. The discussion on specification of seismic conditions is concerned with: recurrence models, case of multi-parameter representations, alternative definitions of design spectra, relationships between alternative representations and alternative approaches to safety verification, consideration of hazard at source level and at site level, and zonation formats.

The specification of seismic conditions represents an essential component of input data to be used in design. The way of specifying seismic input in codes followed a development in parallel with the general development of knowledge in earthquake engineering and engineering seismology, as well as with its gradual implementation in practice. The current stage of advanced ways of specifying seismic conditions in codes is represented by two, well known, reference documents of international importance: the ATC model code (ATC, 1986) and the Eurocode 8 (CEN,1994).

Following considerations are related basically to the formulations adopted in EC-8, due to the environment in which the various problems raised are to be dealt with.

The specification of seismic conditions is intended to forecast, in an appropriate way, seismic events against which structures are to be protected. Two complementary components are to be dealt with in this connection:

Both components referred to are dealt with in some way in design codes, but the solutions adopted may be subject to discussion. Following developments are intended to emphasize the most significant aspects that deserve such a discussion, with the intention to ultimately contribute to what could be considered a consistent approach, providing data that are required by the analysis of seismic risk affecting structures.

The author believes that seismic conditions that are relevant for the earthquake protection of any artifact of man should be specified in a way that satisfies two basic requirements:

The author believes also that, at the current stage, the basic goal of engineering analysis should be, at least in principle, the estimate of seismic risk and, also, that the most relevant way of assessment of seismic risk relies on the use of probabilistic concepts and methods. So, the following developments are pervaded by the idea of using probabilistic concepts in a consistent way, to reach the goal of consistent risk analysis.

The examination of the various cases when seismic conditions are to be specified puts to evidence the considerable variety of situations existing in this field. Some main reasons of this variety are represented by:

In spite of this high variety, there should exist a consistent philosophy of specification of seismic conditions to pervade the actual provisions of codes.

Some needs considered in connection with following developments are:

The aspects subject to discussion are rather of qualitative nature and are dealt with often as questions raised. They should represent essentially a startpoint of debate in WG activities.

The developments presented are concerned essentially with methodological and formal aspects, as well as with the implications of the intention to develop appropriate formats, but not with concrete calibration of input data. The characterization of ground motion is dealt with in Section 2 and the specification of seismic conditions, which relies on the aspects dealt with in Section 2, is dealt with in Section 3. The closing section is devoted to needs of action involved by the intention to contribute to developments emphasized as necessary in Section 2 and 3.

An attempt is made in this section to identify various possibilities or alternative variants of characterizing ground motion during one event, from the viewpoint of several criteria that are relevant to engineering activities. It is intended to contribute to a comprehensive enumeration of criteria and possibilities as well as to a flexible approach, to permit adopting the most suitable variant for every specific case, but to do it on a common conceptual basis.

There are three categories of predictive representations of the time dependence of ground acceleration, used at present for engineering analyses. They are referred to as:

These three categories of representations are referred to explicitly in the EC-8, but the rules of defining and using them are uneven. While comprehensive details are given on the representation R.Sp., little is said about how to specify and use the other two categories of representations. It is necessary to investigate the relationships between the categories referred to and to adopt a consistent conceptual basis in this connection.

It may be mentioned in this connection that design spectra are sometimes used as target spectra in order to generate accelerograms (representation R.Ac.) or power spectrum densities (representation R.St.) but, on the other hand, representations of the category R.St. may be dealt with as fundamental models (which can refer to motions along one or more degrees of freedom) and that response spectra with some specified (conditional) non-exceedance probabilities, or accelerograms (single- or multi- component) can be generated on this basis. On the other hand, a consistent philosophy regarding the relationship between these categories of representations must rely also on the consideration of specification of seismic conditions, essentially in relation to the aspects discussed in Subsection 3. 5.

Going into more details on the representations of category R.St., the alternative possibilities at hand should be considered: fragments of stationary motions, stationary motions amplified by a deterministic function of time, to account for the transient nature of motion, as considered in EC-8, canonic expansion of non-stationary random functions, use of evolutionary power spectrum densities, use of generalized power spectrum densities for non-stationary random functions, use of diagonal representation of the same. The relations between the alternative possible variants must be considered, in order to pass from the one to the other when suitable, using the most appropriate for each purpose (e.g.: for calibration on the basis of records of ground motion, for stochastic dynamic analysis, for generation of artificial accelerograms etc.).

The dependence on the system of parameters defining the degrees of freedom of ground-structure(s) interface(s) must rely on the identification of the system of these degrees of freedom, as relevant from the view point of requirements of engineering analysis. One can identify in this connection a sequence of characteristic cases of increasing complexity:

The number of components of ground motion considered depends upon the way in which engineering analyses are conducted. The reference situation is the consideration of one single component of (horizontal) translations motion. There are, nevertheless, situations in which the consideration of motion along several DoF (degrees of freedom) of the ground-structure interface is necessary. One case is that of structures with compact foundations, for which several components of translation, perhaps of rotation too, must be considered if 3D analyses are to be performed (e.g.: Part 3 of EC-8). Another case is that of multi-support structures, like long bridges (dealt with e.g. in Part 2 of EC-8). While these alternative possibilities are related to cases when a single structure is considered, considerations could be extended to multi-component systems, like networks, lifelines etc.. It is appropriate to discuss these latter aspects further on in Subsection 3 5.

It may be noted that, while representations of categories R.Ac. and R.St are suited for motions with an arbitrary number of DoF, the representation R.Sp. is confined inherently to the case of a single DoF. Solutions adopted in EC-8 (Parts 2 and 3) in order to extend data to the case of defining the input for motion along several DoF rely essentially on models of category R.St.. This adds to the arguments in favour of the importance of these representations and of their extensive and consistent use. Given these facts, as those discussed in previous subsection, the problem is raised whether it would not be suitable to recognize explicitly in codes this fundamental role of stochastic representations and to think of appropriate adaptation of formats specifying the seismic input.

Experience shows that a past motion is never identically repeated in future. On the other hand, it may be stated quite often that two different accelerograms are rather similar, or strongly dissimilar. Considering just single-component motion, criteria like predominant frequencies, bandwidth, duration etc. can be used for such comparisons. One can state, further on, that accelerograms accepted to be rather similar pertain to a common class and one can think of classification of accelerograms. This has obvious implications for hazard characterization and such aspects are dealt with in Subsection 3.3.

In case the option for defining different classes of accelerograms is accepted, some technique to define or identify a class must be adopted. In case of single component accelerograms one could start perhaps from such approaches as using running Fourier spectra or evolutionary power spectrum densities and to adopt a discretized system of characterization. Expected motions pertaining to a definite class should differ only from the viewpoint of an amplitude-type parameter, to be defined in appropriate terms, with consequences for hazard characterization, as defined in Subsection 3.3.

Going on, starting from an accepted condensation technique, one could define a space of accelerograms, to be used as a background for more comprehensive hazard characterization.

 2.5. Action at source level vs. action at site level. Attenuation.

Codes for practice, related to the design of structures, consider always seismic action at site level, be it for individual events, or for sequences of expected events, which involve hazard considerations. There are reasons, nevertheless, to consider in some cases characterization of seismic events at source level too. Two main reasons should be considered in this view:

Without going into hazard considerations, which are dealt with in Subsection 3.5, the need of specifying the way in which source-specific phenomena must be characterized is to be recognized. In case one considers just the global size of an earthquake, parameters like seismic moment, or a magnitude, are in principle sufficient. More is nevertheless necessary to be known or specified about an earthquake, especially about a big one. As a first example: the adoption of the instrumental hypocentre as a reference for the source position is not satisfactory, given the fault length which may be of the order tens, if not hundreds of kilometers. The reference source point for defining attenuation is, thus, a problems by itself. Another problem is represented by the rupture propagation which influences considerably the radiation pattern. Seismic hazard at source level should consider, thus, not just recurrence of various values of magnitude, seismic moment etc., but also recurrence of various types of earthquake mechanisms. Deriving of site hazard characteristics relies, at its turn, as known, on appropriate specification of attenuation. Improvement of definition of attenuation would lead, of course, to more correct and certain specification of hazard at site level.

Information on past ground motions represents a fundamental source of knowledge, which must be used, as far and consistently as possible, for the characterization of future motions. The ways of characterizing past motions are not the same as those of characterizing future motions. To give just an example, a recorded accelerogram represents a hard fact, while a design accelerogram is just a kind of illustration of possible future accelerograms. As another example, there is a considerable difference between response spectra of actual accelerograms on one hand and design spectra on the other hand. While response spectra for actual accelerograms represent hard facts, design spectra (should) represent some kind of envelope (in a probabilistic sense) of future spectra.

In spite of the fundamental differences between actual and expected (predicted) accelerograms, it is necessary to make use of compatible ways in characterizing the two categories of entities. Ways of global characterization of recorded motions in terms of effective duration or bandwidth, as well as use of techniques like those corresponding to running Fourier spectra or evolutionary power spectrum densities would help, obviously, in calibrating the parameters of condensed representations, as referred to in Subsection 2.4. There occur frequent situations in which instrumental information about past motion is scarce, if not totally missing. Concepts like intensity, or frequency dependent intensity, as defined in some alternative ways in (Sandi & Floricel, 1998), could be considered in order to use macroseismic information for assessing spectral characteristics of past motion. Some connections with condensed representations, as referred to in Subsection 2.4, could be considered in this connection too.

Hazard characterization and specification of seismic conditions represent, as known, a fundamental prerequisite in the adoption of earthquake protection measures. As also known, probabilistic tools are widely recognized at present as a basis for deriving hazard characteristics in a way to be compatible with the needs of control and limitation of risk to structures. The characterization of hazard and the specification of seismic conditions must be compatible with the characterization of seismic action during one event on one hand and with engineering needs on the other hand. Following developments start from these general requirements.

Stochastic process models are widely accepted for the characterization of the expected sequences of seismic events at various places, under various conditions etc.. Codes in force, which present often references to the concept of return period, rely on the simple model provided by Poissonian stochastic processes, which is based, at its turn, on the assumption of no probabilistic dependence between different cases of occurrence of seismic events. This assumption on independence is, of course, in disagreement with the physics of earthquake generation and attempts were made to use also other categories of models, accounting for the dependence of occurrence of future events on the occurrence of past ones. The consideration of non-Poissonian models appears to be attractive for structures intended to be in service for a short time, in areas with quite well known seismicity. On the other hand, knowing about the difficulties of calibrating even parameters of Poissonian recurrence models, the calibration of non-Poissonian models, which involve more parameters and more information, would raise considerably increased difficulties. The problem of criteria of option between alternative possibilities is raised in this connection.

The recurrence of earthquakes is related in codes to a single, scalar, parameter (intensity, reference acceleration). The aspects dealt with in Subsection 2.4 pointed out the need of a multi-parameter characterization of ground motions and, consequently, after discussing the possibilities of condensation of information, the possibility of defining a space of (possible) accelerograms. In case one uses a space of possible accelerograms, discretized in some appropriate way, it becomes necessary to replace techniques based on the use of one scalar parameter characterizing one event, by techniques based on the use of several scalar parameters or of one vectorial parameter for the same purpose. Even in case when one accepts Poissonian models, this requires a generalization of techniques of analysis. One could specify, e.g., return periods for events pertaining to different classes of motions etc.

According to current concepts, it is desirable to define design spectra with a specified (uniform upon an interval of oscillation frequencies), limited, exceedance probability. This approach, which is appropriate in case the semi-probabilistic design philosophy (see also Subsection 3.5) is accepted, must be considered nevertheless in connection with situations in which several classes of motions are defined. Developing a unique design spectrum, to envelope (in a probabilistic sense) all classes of possible motions, becomes in such situations unsuitable, because it reflects impossible events. If such an envelope spectrum is used e.g. as a target spectrum for developing design accelerograms, this will lead at its turn to impossible accelerograms. The problem is thus raised to formulate an option about in which cases to replace one design spectrum (with specified exceedance probability) by means of several spectra.

The need of using probabilistic tools in the analysis of structural safety (or, conversely, of risk) is widely recognized at present. The verification of structural safety and reliability can be made at present using alternative probabilistic approaches of three different levels, referred to as:

P.1: the semi-probabilistic approach (which is widely implemented at present in the regulatory basis of structural design, among other, in the Eurocodes);

P.2: the simplified probabilistic approach (which is based on the use of some standard distributions and of some standard functions, like differences or ratios, of loading and resistance characteristics respectively, and was used in several cases for the calibration of partial safety factors used in the P.1. approach);

P.3: the consistent probabilistic approach (which is based on the use of various appropriate probabilistic models for the factors determining the risk of failure and on the use of appropriate rules of combining the functions characterizing these models).

It must be mentioned at this place that the approach of P.3 type is compatible with the needs of explicit estimates of seismic risk and that this can transcend the boundaries of mechanical phenomena in structures, going up to estimates of risk of impact of various other natures.

It may be mentioned here that design spectra with controlled exceedance probability correspond essentially to a P.1 approach to structural safety and that an attempt to provide compatibility with a P.3 approach would impose to reconsider and redefine the concept of design spectra. On the other hand, it is hard to relate representations of categories R.Ac. or R.St. to a P.1 approach. These representations are much more compatible with a P.3 approach.

The alternative approaches P.1 to P.3 are connected not only with safety verification or risk analysis, but also with the techniques of deriving parameters or functions used in the specification of seismic conditions. Examples of semi-probabilistic procedures:

The recurrence of seismic events can be dealt with:

The hazard representations at one or the other of the levels referred to will be determined by the nature of the systems dealt with in engineering analyses. While in case of objects like buildings or other individual structures it is suitable to use, as an input, data concerning the hazard at site level, for multi-component systems, like lifelines, a consistent approach requires to use, as an input, data concerning the hazard at source level.

It is widely accepted at present that the most appropriate way to derive hazard characteristics at site level consists of the use of data at source level, to be converted on the basis of attenuation laws, specific for the zone dealt with (Cornell, 1968). Unfortunately, this conversion is performed routinely with consideration of deterministic attenuation laws (obtained as average attenuation laws on the basis of regression analysis). The lack of explicit consideration of attenuation randomness, as put to evidence by authors of various attenuation laws (Esteva, 1976) is bound to lead to underestimates of hazard at site level (see also considerations of previous subsection on this subject).

Returning to the aspects referred to in Subsection 2.5, the choice between hazard specified at site level and hazard specified at source level is discussed again from a complementary viewpoint. In case of a multi-component system, like a lifeline, hazard characterization should reflect the possibilities of alternatives radiation patterns during future earthquakes. This has implications for risk analysis, as put to evidence by the analytical developments of (Sandi, 1986). A consistent approach to risk analysis under such conditions would imply the development of probabilistic attenuation models related simultaneously to several sites, which involve at their turn multi- dimensional distributions. The difficulties of calibrating such attenuation laws are obvious, but this does not mean that their importance should be neglected.

Seismic zonation of a territory involves, according to current procedures, partition of a territory into zones for which seismic conditions are stated to be homogenous. In the case of advanced codes the zones referred to are expressed in probabilistic terms, in the sense that design parameters referred to (e.g. reference accelerograms) correspond to an explicitly specified, fixed, return period. This approach provides limited information and cannot be satisfactory in cases when different return periods should be considered for various categories of limit states and/or classes of importance of structures. Nor is it appropriate in case when a P.3 approach is intended, in order to conduct explicit risk analyses. A solution to be considered is to specify zonation in more complete terms, i.e. to specify not values of design parameters for a fixed return period, but design parameters as explicit functions of return periods.

The developments of Subsection 3.4 were related to the case of at least partial acceptance of a semi-probabilistic philosophy in specifying design spectra. The considerations of previous subsection, which were aimed to bring zonation closer to the needs of improved code formats, to make possible more consistent conventional safety verifications, but also to the needs of risk analysis, raise the problem of reconsidering the format of design spectra too. Design spectra should be defined in such a generalized frame as functions also of return periods, besides oscillation periods and damping.

This paper was intended to initiate activities of an EAEE Working Group on characterization of ground motion and specification of seismic conditions. It was presented essentially as a list of problems to play a brainstorming role.

The list of topics referred to is extensive and cannot be dealt with entirely, in-depth, within a limited time interval, so some selection should be made.

A group involved in this field should start by selecting some topics that appear to be feasible, in the sense of obtaining some useful results. These could be start-of-art reports related to some topics, proposals to develop some research projects, proposals to improve codes.

Cornell, C. A. 1968. Engineering seismic risk analysis. Bull. SSA, Vol. 58.

Crandall, S. H. 1963. Random vibration. Vol. 2 Cambridge: The Mit Press.

Esteva, L. 1976. Seismicity. Seismic risk and engineering decisions. Amsterdam-Oxford-New York: Elsevier.

Pugachov, S. V. 1960. Teoriya sluchaynykh funktsiy i eio primeneniya v zadachakh avtomaticheskogo regulirovaniya (2-nd ed.) Moscow: GIFML.

Sandi, H. (WG Convenor) 1986. Report to the 8-th ECEE of the EAEE WG 5 + 10 on Vulnerability and Risk Analysis for Individual Structures and for Systems. Proc.8-th ECEE, Vol. 7. Lisbon: LNEC.

Sandi, H. & Floricel, I. 1998. Some alternative instrumental measures of ground motion severity. Proc. 11-th ECEE Paris.

ATC 1986. Tentative provisions for the development of seismic regulations for buildings, ATC 3-06 (2-nd printing). Redwood City: ATC.

CEN 1994. Eurocode 8. Design provisions for earthquake resistance of structures - Part.1 European prestandard ENV 1998-1. Brussels: CEN.