Probabilistic Analysis

SoilVision modeling software and probabilistic analysis.

SoilVision Systems is a pioneer in the application of probabilistic analysis methods to finite element modeling. Our company has been the first to implement these features commercially available finite element geotechnical software package. The features allow the user to set up a sequence of model runs in which model input parameters vary through a range. This "range" of an input parameter can be used to perform a deterministic sensitivity analysis or a probabilistic analysis.

1. Why are multiple model runs important?
2. How does it work?
3. How does this help in a deterministic analysis?
4. How does this help in a probabilistic analysis?

5. Research Papers

1. Why are multiple runs important?

"The acceptable level of uncertainty depends on the application and for waste containment purposes that uncertainty is often greater than desired. We have discovered this when numerical modeling is compared to definitive field data. While a single model run can be useful for preliminary evaluation, I continue to think that a sensitivity analysis approach offers considerable advantages in understanding the importance of the various design parameters to performance."

William H. Albright, PhD
Desert Research Institute
Reno, NV

The running of multiple model runs is critical for the user to gain an appreciation for what the model is actually saying. If multiple model runs are not performed it will often lead to a misinterpretation of what the model is actually saying.

For example, if a model run is performed which indicates a flowrate of 5 gal/min what is the result if the hydraulic conductivity of one or more of the layers is increased? What if it has been measured wrong? The accuracy of measuring hydraulic conductivity may be up to one order of magnitude. How do we reasonably represent this in our modeling software?

The majority of consulting modeling projects now require a representation of uncertainty through a deterministic or probabilistic sensitivity analysis. Our finite element products help the consultant perform these types of analysis easily and quickly.

2. How does it work?

This feature works by allowing the user to define model inputs of one or more of the model parameters as a list of values, or as a list of values , or as a list of values consistent with a Monte Carlo analysis.

This system then allows the user to define model inputs in light of a deterministic sensitivity analysis or a probabilistic analysis. Subsequent model output can also be plotted as a function of the model input "stage". The figure below shows the general concept of this feature of analysis.

For example, the user may want to plot flow through an earth dam when hydraulic conductivity of a certain soil layer has been statistically described by a mean and standard deviation. The user would then input the mean and standard deviation. The user would then input the software and generate a Monte Carlo normal distribution of the hydraulic conductivity. The model would then run multiple times (once for each parameter) and the resulting variation in flux could be plotted.

3. How does this help in a deterministic analysis?

It is reasonable in many deterministic analysis for the user to want to obtain an idea for how model output changes as a function of model input.

For example, assume the user is performing an analysis of a waste rock pile and wants to determine the influence of the air-entry value (AEV) of the waste rock on flow deep in the pile. In this case the user would merely input a range of values for the AEV between 0.5 and 12 kPa (or some other relevant variation) and output the resulting impact on a certain flux section.



4. How does this help in a probabilistic analysis?

In a full probabilistic analysis the user may input the mean and standard deviation of a model input parameter such as hydraulic conductivity, air entry value, residual water content, Young's modulus, or some other input parameter. A random normal distribution of the input data is then generated and a separate model run is performed for each model run. The resulting impact on any model flux section or pressure at a point may be plotted.

5. Research Papers

Fredlund, M.D. - 2004
"Finite Element Stochastic Analysis"
57th Canadian Geotechnical Conference and 5th Joint IAH-CGS Conference, October 24-27, 2004, Quebec, QC, Canada