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Practical Numerical Modelling – Lessons from Ancient Greece

At the upcoming Rocscience International Conference 2021 from April 20-21, a panel of experts will debate an important topic – the appropriate use of numerical modelling in geotechnical practice. The panellists will share differing perspectives, and the audience will enrich the discussion, curated by a moderator, by asking questions or contributing thoughts.

To allow conference participants to know some of the opinions ahead of time and prepare for the discussion, the panellists' positions will be posted on the conference website before the discussion date. Conference registrants can even send in questions or contributions before the start, and we will strive to share as many of them as possible during the discussion. As we prepare for April, we would like to share some food for thought on numerical modelling to prepare us for the day.

Models - their Purposes

As we know, models are simplified representations of real-world systems intended to help us understand the systems. Models are founded on relevant theory and knowledge and simplifying assumptions.

Building a model helps engineers to understand the problem they are trying to solve. It also allows us to identify how various factors combine to influence the behaviour of the system. We also use modelling tools to help us organize information on our problems and predict the system's future behaviours under different inputs or conditions.

Today, engineers do most of their modelling with computer software. It is one of their most powerful tools for deepening their understanding of geotechnical problems, fixing them, or improving designs. In theory, numerical modelling can handle a broad range of geotechnical problems. Troubles begin when they are employed blindly.

Limitations in Models

Modelling ALWAYS excludes specific details of the real-world. The critical question is what level of detail to include or exclude. If we exclude essential information, we risk making the model too simplistic, which will not deepen our understanding. On the other hand, if we include too much detail, the model becomes too complicated, time- and resource-consuming. As Michael Levitt, professor of structural biology at Stanford University (co-winner of the 2013 Nobel Prize for chemistry, explained in a Nature article) that “The art is to find an approximation simple enough to be computable, but not so simple that you lose the useful detail.”

The limitations and errors in geotechnical models arise from the following:

  1. Simplification of actual problems (e.g., excavation geometries) when building numerical models
  2. Approximations and idealizations made in the development of the governing equations
  3. Assumptions on the nature and behaviour of geological materials (e.g., the postulation that a rock mass, which comprises intact rock and discontinuities, can be represented with a continuum), and
  4. Uncertainties in the values and distribution of input parameters (e.g., the variability of strength properties in space and uncertainty in scaling parameters from laboratory-size testing to the field.)

These errors and limitations of models likely led the statistician, George Box, to state that “all models are wrong, but some are useful.” Good models improve insight into geotechnical excavations and structures' behaviour and help experienced engineers develop suitable mitigating measures.

Significant modelling problems arise when engineers frame questions incorrectly and mischaracterize problems. These errors are the most dangerous because they leave the real problem unaddressed, waste resources, and impede learning. Users of numerical modelling need significant knowledge and experience to avoid such misuse and abuse.

Healthy Skepticism – a Critical Skill for Engineering Modelling

Geotechnical engineers acquire essential knowledge such as engineering mechanics, CAD and numerical methods during their education, and practical technical skills on the job. However, one critical skill is often omitted – healthy skepticism towards their work and those of others. In modelling, this skill is indispensable. Without it, engineers are likely to be swayed by the seductive beauty of computer-generated graphics and the attractiveness of other modelling outcomes. Modellers must always judge results against observations, experience, and engineering judgment.

Misuse and Abuse of Numerical Modelling

We will now discuss a few typical instances of ways in which engineers and management misuse or abuse models.

The Illusion of Accurate Predictions

In our opinion, one of the most counterproductive aspects of numerical modelling in geotechnical engineering is the illusion of accurate predictions. Some specialists argue that given the large uncertainties and sometimes crude approximations in numerical models, geotechnical engineers are much better off providing order of magnitude predictions than offering “accurate” predictions. These often end up at the centre of debates and can distract engineers from understanding a problem or system. Geotechnical engineers should ensure that they do not underestimate uncertainty.

Accounting for uncertainty implies that good numerical modelling should consider more than one set of deterministic parameters and assumptions, which produce one set of results. Engineers must run their models many times to establish a range of possible outcomes.

The Illusion of Complexity being Better than Simplicity

In the era of relatively cheap, fast computers and numerical modelling software, it is now possible for firms and their engineers, including the young and the inexperienced, to build models of such complexity that no one knows what the models actually represent. There is a tendency to make models more and more complicated just because they can be quickly built. In doing so, these engineers include everything they can think of, run the model once on a powerful computer with lots of memory, and then interpret the results without critical questioning.

Sometimes engineers and management deceive themselves that because models are complicated, they must be meaningful. Such presumption can lead to severe and dreadful errors. Good engineers always compare their model results to order-of-magnitude estimates and observed behaviour before accepting the outcomes. Even simple models (such as elastic models) lead to a deep appreciation of problems in the hands of these skilled engineers. After all, in the 1960s, engineers safely landed humans on the moon using the simple slide rule. (We must note, though, that bad engineering can also be done with simple models.)

The Illusion of Models being Right Just because They are Built

Due to the ubiquity of software, many models are built today based on user manuals. These manuals explain how to set up and run models rather than provide knowledge on underlying physical principles or behaviour. If the primary purpose of modelling is to clarify, not to confuse, to elucidate rather than obfuscate, this situation requires urgent addressing.

As alluded to above, the illusion of models being right just because they are built often arises when numerical modelling software tools are used by engineers not familiar with the software. It also appears when inexperienced engineers disappear into the world of computer simulations to escape interactions with other engineers and explain their reasoning.

In our opinion, to produce meaningful numerical modelling results, users must understand the mathematical and engineering principles underlying the software. Users must also have practical experience, including sound engineering judgment and how design works in the field. Without such knowledge, it is difficult for users to

  • Decide which features must be modelled, ignored, or simplified
  • Determine which assumptions are appropriate for a given problem or circumstance
  • Understand the picture results are painting, and
  • Accurately convey results and limitations to the design team, senior engineers, and management.

We cannot overemphasize this fact – designs or analyses with models we do not understand are DANGEROUS!

Who then Should Model – the Generalist Engineer or the Dedicated Modelling Specialist?

We want to address another dimension of modelling – the role of specialist modellers. Who should perform numerical modelling? Should it be done by the designers of any geotechnical engineering excavation or structure? Or should it be done by specialists focused on modelling?

In our opinion, for general problems, it is best to have design engineers who are familiar with the software (who properly appreciate the mechanics and limitations of the software) to conduct their own modelling. However, for more complicated analyses, such as nonlinear three-dimensional ground-structure interactions, it may be better to use specialized modelling experts. These specialists must tightly collaborate with the designers.

Lessons from Ancient Greece

We will conclude our conversation by examining an expression used when engineers blindly approach numerical modelling and accept its results. People describe such engineers as using models as oracles. However, a thoughtful look at how Ancient Greeks viewed oracles tells a different story that can actually help us in our modelling.

There are several accounts of ways in which Ancient Greeks dealt with uncertainty, particularly regarding the future. One way was to visit an oracle – a temple or holy place where someone with supernatural ability could provide insights into affairs. To ensure that they got the most useful oracle responses, Greeks had to phrase their questions carefully before visiting the oracle. They had to think wisely about the various ways in which their futures could unfold as part of this exercise.

Scholars tell us that the oracles often responded with riddles, which had to be solved. A response could be full of vivid imagery and could be puzzling. The one who consulted an oracle had to figure out what the answer meant and try to fit it into a likely future outcome. Based on this, the "client" would then decide what to do.

I cannot think of a better way to prepare to use models and better use modelling results than how the Ancient Greeks consulted oracles and used their responses. We must carefully prepare our questions and needs before we start modelling. It is only after such careful exercise should we begin to build our models.

Next, numerical modelling answers can present puzzling (and sometimes contradictory) outcomes amidst all the beautiful pictures. We must think carefully about these results and appropriately interpret them before converting them into practice.

Last Words

The 90-minute panel discussion on numerical modelling at RIC2021 promises to be highly interactive, lively, and insightful. You cannot miss it!

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