SIGMA/W Chapter 2: Numerical Modeling
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2 Numerical Modeling: What, Why and How
2.1 Introduction
The unprecedented computing power now available has resulted in advanced software products for
engineering and scientific analysis. The ready availability and ease-of-use of these products makes it
possible to use powerful techniques such as a finite element analysis in engineering practice. These
analytical methods have now moved from being research tools to application tools. This has opened a
whole new world of numerical modeling.
Software tools such as SIGMA/W do not inherently lead to good results. While the software is an
extremely powerful calculator, obtaining useful and meaningful results from this useful tool depends on
the guidance provided by the user. It is the user’s understanding of the input and their ability to interpret
the results that make it such a powerful tool. In summary, the software does not do the modeling, the user
does the modeling. The software only provides the ability to do highly complex computations that are not
otherwise humanly possible. In a similar manner, modern day spreadsheet software programs can be
immensely powerful as well, but obtaining useful results from a spreadsheet depends on the user. It is the
user’s ability to guide the analysis process that makes it a powerful tool. The spreadsheet can do all the
mathematics, but it is the user’s ability to take advantage of the computing capability that leads to
something meaningful and useful. The same is true with finite element analysis software such as
SIGMA/W.
Numerical modeling is a skill that is acquired with time and experience. Simply acquiring a software
product does not immediately make a person a proficient modeler. Time and practice are required to
understand the techniques involved and learn how to interpret the results.
Numerical modeling as a field of practice is relatively new in geotechnical engineering and, consequently,
there is a lack of understanding about what numerical modeling is, how modeling should be approached
and what to expect from it. A good understanding of these basic issues is fundamental to conducting
effective modeling. Basic questions such as, What is the main objective of the analysis?, What is the main
engineering question that needs to answered? and, What is the anticipated result?, need to be decided
before starting to use the software. Using the software is only part of the modeling exercise. The
associated mental analysis is as important as clicking the, buttons in the software.
This chapter discusses the “what”, “why” and “how” of the numerical modeling process and presents
guidelines on the procedures that should be followed in good numerical modeling practice. It should be
noted now that some of the examples in this chapter pertain to stress-deformation analysis while others
relate to seepage analysis. While the actual type of analyses may differ, the concepts illustrated apply to
all engineering analyses.
2.2 What is a numerical model?
A numerical model is a mathematical simulation of a real physical process. SIGMA/W is a numerical
model that can mathematically simulate the real physical process of ground volume change in response to
self or external loading. Numerical modeling is purely mathematical and in this sense is very different
than scaled physical modeling in the laboratory or full-scaled field modeling.
Rulon (1985) constructed a scale model of a soil slope with a less permeable layer embedded within the
slope and then sprinkled water on the crest to simulate infiltration or precipitation. Instruments were
inserted into the soil through the side walls to measure the pore-water pressures at various points. The
results of her experiment are shown in Figure 2-1. Modeling Rulon’s laboratory experiment with SEEP/W
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