Discussion of "Influence of effective parameters of non-orthogonal smeared crack approach in seismic response of concrete arch dams"

Kreuzer 713 The following discussion is not so much on the advanced and interesting approach presented by the authors, Espandar et al., rather than on a general development in seismic analysis of dams. I deeply appreciate the work of Dr. Lotfi, the only author that I know personally. It is this appreciation, which encourages me — a generalist — to take this paper as a hook for the following dialogue. My impression is that the reality in the authors’ minds is the mathematical model. The dam, on which this model is applied, is then a means to an end relating the model to a physical reality. In other words, it is the analyst’s subjective belief that his(her) model is a valid representation for the behavior of the dam. Nothing is wrong with that — but where is the attempt of a proof for this belief, where an engineering judgment about the wide-open outcome of the model? Let me give some examples. Figure 4 shows a 12 s time history of displacements at a crest point of the Shahid Rajaee dam. The variables are the key parameters in the authors’ analysis, namely the “secant and the elastic un/reloading” cases. The authors comment that “extensive cracking of the downstream face [occur] beneath the crest spillway block” and “the drift [of displacements] is more severe in elastic unloading than in secant unloading ...”. Such comments trigger several questions with respect to the anticipated post-earthquake behavior of the dam: • Given the drastic difference in displacements between elastic and secant unloading — which is then, in the authors’ view, the more realistic unloading mechanism for this particular dam? • The radial deformation history in Fig. 4 (upper two diagrams) shows a distinct difference between secant and elastic unloading, i.e., the first seems to indicate a safe behavior (more or less elastic deformations after 12 s), the second not. At 12 s there are about 180 mm irrecoverable radial (downstream?) deformations; this is much compared with the amplitude of the static radial deformation and indicates instability of the central crest section (high tensile strain). much • Cracking will be largely influenced by joint behavior (both behavior of block joints for cross-valley motion and of lift joints for vertical motion). Thus the authors’ cracking criterion (exceeding 1.5 or 3 MPa tensile material strength) might not apply everywhere. • Most laudable is the authors’ use of a fracture energy criterion for tensile strain softening. A value of 600 N/m is assumed, corresponding to a tensile strength of 1.5 MPa, and 2400 N/m for 3 MPa. Which value do the authors consider realistic for Shahid Rajaee dam? Obviously, the four-fold difference in fracture energy is a too wide scatter band for reasonably limiting estimates for postearthquake behavior. (Apparently no fracture energy test results were available.) All of the above relates more or less to the question: How do we value model uncertainties in seismic analysis? In this context, model uncertainty may be taken as the unknown influence of approximations for approaching the true physical behaviour of the dam. It contains two types of impediments: • the innovative part of the model, created in the authors’ imaginations and not yet verified by a sufficient large number of practical applications and test results • the demanding quality–quantity of input parameters, to feed the model Representations of physical phenomena, which cannot be validated empirically, are questionable as they bear the risk of speculative inferences. This requirement complies with a general axiom in scientific methods, where bold conjectures should be verified “by ingenious and severe attempts to refute them ... as a proof that the new theory is a better approximation to truth than the old theory” (Popper 1972). It seems that the strength of modelling seismic phenomena occasionally carries the analyst away to a deductive approach, whereby the main incentive is to create a better algorithm, shunning the inconvenient process of validation. However, validation also signifies to convey complex findings to those, which are finally taking responsibility for dam safety, i.e., the dam owners. The authors’ final statement that

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