STOCHASTIC ANALYSIS

The latest version of SVFlux implements stochastic analysis of model input parameters. SVFlux accomplishes this by allowing multiple runs of the same problem while varying such soil properties as saturated hydraulic conductivity, the air entry value, the slope of the soil-water characteristic curve, or the slope of the unsaturated portion of the hydraulic conductivity curve, among other parameters. The statistical variation of input parameters allows for accommodation of the natural variability in soil properties may be a result of the natural spatial variation of field soil properties. The resultant change of pore-water pressure, heads, or flow rates may then be observed.

Why do we need stochastic analysis?
The natural world is highly variable. Variability in soil properties may be a result of the natural spatial variation of field soil properties. For example, the variation of saturated hydraulic conductivity is often significant. Variability can also be introduced at the laboratory level. Laboratory testing of the soil-water characteristic curve can result in differences in results depending on the laboratory involved, simple preparation, and the technician performing the test (Zapata, 2000).

Accounting for this variation in finite element models has historically been difficult. Modelers often try to present results representative of a “best guess” or averaged soil properties. Perhaps a “best-case-worst-case” scenario is presented. While both approaches are valid, they lack the mathematical soundness of applying statistical principles to account for model input parameter variability. SVFlux allows the modeling to apply statistical principles to account for potential variation in soil properties. The result is a more comprehensive picture of model performance than previously possible.

What soil properties can be varied?
The specific soil properties that may be varied are shown in Table 1. Any of the variational methods implemented may be applied to these parameters and the resultant changes in pore water pressures, head valves, or flow rates can be plotted.

What Stochastic Methods are Implemented?
SVFlux implements the following types of stochastic methods in both 2D and 3D.

Each method may be applied to any particular soil property. The user can select the method implemented as well as (for most methods) the number of values (and resultant runs) to generate. Variational methods may also be applied to a single soil property or multiple soil properties at once.

So how might this work?
An example of how the stochastic features may work is as follows. A particular engineer has a fairly well defined problem to solve. Geometry and bonding conditions are well-defined. A tempe cell test has been run and a soil-water characteristic cue has been established. A series of falling-head tests were run to establish the saturated hydraulic conductivity.

The falling head test, however, yielded a group of differing measurements. To account for this variability the modeler would typically average the conductivity values and run the model once with the averaged values. With the new features available in SVFlux, the user may now run the model in the following ways:

The first way may be to input all conductivities into the model. The model would then be run multiple times; one time for each input value.

The problem with the first method is that each measurement is weighted equally. A better approach may be to use the Monte Carlo lognormal distribution. With the Monte Carlo method, the user inputs the mean and standard deviation of the laboratory conductivities. SVFlux will then generate a preset number (i.e., 25) random conductivity values that represent the same lognormal distribution. The finite element model is then run 25 times and the variation in heads on flow rates may be plotted.