Hydro-Mechanical Properties of an Unsaturated Frictional Material

Chapter 3
Introduction to Process Modeling -
A Statistical Approach
3.1 General
Direct determination of the relation between suction and volumetric water content, saturation
or gravimetric water content from experiments on sand are difficult to handle due to the
narrow soil suction within which the drainage and vice versa imbibition process take place.
That is the relevant range of suctions (e.g. between 0 to 20 kPa) to be measured is relatively
small but the measurement error of the instrument (e.g. tensiometer) may be large. For
this reason the assessment of the error and model validation are of critical importance in
experimental building up the soil-water characteristic curve for sand.
Most models suggested in literature for prediction of the hysteretic nature of the soil-
water characteristic curve are not trivial to use or do not fit the experimental data very well
(see also comparison of experimental and predicted data of sand in Chapter 7). Therefore in
the present chapter a method is proposed that can be used to develop suction-water content
model based on statistical analysis for experimental suction (i.e. total suction, matric suction,
osmotic) and water content (saturation, gravimetric water content) results.
3.2 Steps of Model Building
The main steps to be done for building an appropriate model are given in Fig. 3.1. Basic
assumption for process modeling is the availability of experimental results. However, in the
model selection step diagrams of the experimental data, knowledge of the process and assump-
tions about the process are collected to determine the form of the model, that will be used
for curve fitting. Then the selected model and possible information about the experimental
data, assumptions regarding to the process and a convenient curve fit method are used to
estimate the unknown parameters in the model. Using the model parameter estimates and
the experimental data, the model is assessed wether or not the model assumptions are valid.
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