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E L S E V I E R Engineering Geology 39 (1995) 1-3

ENGINBEIR NG GEOLOGY"

Opinion Section

Problems with Logic Trees in earthquake hazard evaluation

E.L. Krinitzsky Geotechnical Laboratory, Waterways Experiment Station, Corps of Engineers, Vicksburg, Miss., USA

Received 31 May 1994; revised version accepted 21 September 1994

Abstract

Logic trees make sense when used in earthquake risk analysis where costs are compared for specific outcomes. However logic trees fail in earthquake hazard analysis when they are used to develop earthquake ground motions for applications in engineering. The failure stems from a misguided attempt to assign numbers for degrees of belief which are personal and indefinable, almost like love or taste, and for which there are neither tests nor measurements. The result is a complicated jumble of egocentric impressions. In contrast, the need in engineering is to have values that are based as much as possible on evidence.

1. Introduction

Logic trees or decision trees have a valid and important place in engineering analyses when they are used to evaluate risk. Fig. 1 is a logic tree that enables the engineer to compare costs incurred for specific outcomes. He can design accordingly to the level of risk that the owner is willing to sustain.

However, logic trees are advocated also as a means for generating earthquake ground motions for engineering applications. Fig. 2, from Power (1994), illustrates the procedure. The presumption is that there is uncertainty in any one method for assigning motions and that the uncertainty must be encompassed by weighing a range of methods and merging them statistically. There are severe problems with this presumption.

First, a maximum credible earthquake for a critical site can be assigned by conservative and defensible practices that will, in a single analysis, cover all reasonable expectations for reliability. Such an analysis, done properly and subjected to

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a peer review, is sufficient to reduce uncertainty to practical levels and provide values that are based on the best available evidence. Resorting to statisti- cal manipulations by logic tree comes from the false assumption that it is necessary for a better result. The procedure is shown in Fig. 2.

2. ProMems

The problems can be summed up as follows: (a) There are dozens of other attenuations that

could have been used (Fig. 2). Following the prin- ciple of uncertainty, they all should have been weighted and evaluated. But the tree would have become unmanageable.

(b) The weighings for the attenuations, and for all other values; are arbitrary and are no more than guesses. What is the justification for 0.5 or 0.7, etc?

(c) The source zones are adapted from the source zones developed by the Electric Power Research

2 E.L. Krinitzsky/Engineering Geology 39 (1995) 1 3

NON- CRITICAL STRUCTURE

E!K EQK o o egT;O

J COST=$18m r ~[

~ J NO COST[ IPROB=0.92 J

.ICOST=$200ml 1 PRO8=0.08 I

Fig. 1. Example of a logic tree, or decision tree used to evaluate risk.

I Catalog A t tenuat ion J Completeness

Model J Method Sources z_ i iRe .c Configuration Magnitude Rate b - va lue

RecuT-reTtce Model

0.0148 Slepp(1972) ; (0.036) / 0.61 (o.s) (o.os6)

0.0100 0.74 (0.288) (0.242)

s.e o.ooee 0.86

Boore & Joyner (0.5) " ~ 0.0044 0.99 / (o.les) (o.248)

1.11 o.0029 (o.o66) (0.021 )

Modified Boore & Joyner (o.s)

EPRI (1986) (O.S)

New Madrid t single zone S_= Reelfoo.._t.t Rift ~ (0.5)

Ouochlta fold belt Gull Coasl

two zones (o.s)

6.3

(0.3)

exponential (t .o)

Fig. 2. Example of a logic tree used to evaluate uncertainty for a probabilistic seismic hazard analysis. (From Power, 1994.)

Institute (EPRI) and Lawrence Livermore National Laboratory (LLNL). These source zones were analyzed by Krinitzsky (1993a) and shown to be illogical and altogether misleading.

(d) The maximum magnitudes with the percen-

rage weighings given to them are completely arbi- trary guesses and could have been made into an almost infinite series of weighted values if the uncertainty principle were followed to its logical conclusion.

E.L. Krinitzsky/Engineering Geology 39 (1995) 1-3 3

(e) The recurrence rate and b-values were shown by Krinitzsky (1993b), under the discussions for central United States, to be totally unsuitable for generating design values.

The relation between uncertainty and probability is a thorny problem in philosophy and the philo- sophical difficulties have been ignored entirely by the advocates of seismic probability. For an appre- ciation of the difficulties, see Foley (1993) under "Degrees of Belief."

One of the principal thorns is called coherence: For two mutually exclusive propositions, it is irrational to claim that the confidence in the prob- ability of one proposition is equal to the confidence in the probability of the other. What are being compared and combined are multiple attitudes. The hang-up is that one cannot have precise and consistent degrees of belief (coherence) in the wide variety of possibilities that make up the logic tree. The less precise the degrees of belief, the less likely will be the coherence. Degrees of belief, resulting in the guesses that are made, cannot be numerically consistent for any individual, let alone for numbers of people. Replicability is not to be expected.

Attempts to correct this difficulty by introducing fine and exact distinctions cause another problem called orderliness. The values dealt with are not transitive, meaning they are not consistent numeri- cal measurements. Also, subjective judgements (guesses) preclude fine distinctions because the content on which such judgements are drawn is subtly personal and indefinable, almost like love or a preference for sweets, for which there are neither tests nor measurements.

The logic tree can be called successful only if the person doing it is a perfect calculator and no one is this perfect calculator. But what of approx-

imations? What of hypothesizing, as is commonly done in science, in order to obtain an approxima- tion of the reality? The problem is that no reality check is available like those in scientific studies. The reality again becomes only a person's sub- jective point of view.

The logic tree is a complicated and uneven jumble of opinions that are egocentric.

3. Conclusions

Logic trees are failures for generating earth- quake ground motions because the procedure gives numbers to degrees of belief that are no more quantifiable than love or taste and for which there are no dependable tests or measurements. The results are purely egocentric. They become far removed from the evidence that should be the basis by which earthquake ground motions are assigned for engineering sites.

References

Foley, R., 1993. Working Without a Net, a Study of Egocentric Epistemology. Oxford University Press, Oxford, 214 pp.

Krinitzsky, E.L., 1993a. Earthquake probability in engineering - - Part 1: The use and misuse of expert opinion. Eng. Geol., 33(4): 257-288.

Krinitzsky, E.L., 1993b. Earthquake probability in engineering - - Part 2: Earthquake recurrence and limitations of Gutenberg-Richter b-values for the engineering of critical structures. Eng. Geol., 36(1): 1-52.

Power, M.S., 1994. Utilization of new developments in ground motion estimation in engineering design practice: Examples for development of site-specific ground motions. Proc. Seminar New Developments in Earthquake Ground Motion Estimation and Implications for Engineering Design Practice, Applied Technology Council, ATC 35-1, San Francisco, Calif., pp. 15-1-15-35.