Soil properties are inherently variable and this variability needs to be factored in simulations and analysis. The spatial variability of soil can be modeled using realizations of random fields which can then be used for Monte Carlo simulations. While some software programs such as Rocscience Slide and Optum G2 offer random field analysis, they are restricted to 2D simulations and random field creation is often limited in flexibility.
For situations where 3D random fields are required, the user will have to generate their own fields and input into the software (if user inputs are allowed). For my work on corrosion in inhomogeneous soil, I generated 3D random fields and input the realizations into COMSOL Multiphysics as a point cloud. I used the excellent
GeoStatTools (GSTools) Python library (Sebastian Müller & Lennart Schüler. GeoStat-Framework/GSTools. Zenodo.https://doi.org/10.5281/zenodo.1313628) for this purpose. This library can be used to generate random fields based on several covariance models. Once the random fields are generated using this method, the rest is simply data manipulation and formatting to match the input format for a particular software. For my purpose, I generated a random field based on the standard normal distribution (Mean=0, Std.dev=1) so that I can transform it to any soil property (including log-normally distributed parameters by transformation by log values). I formatted the output field as a text file containing columns for the three spatial coordinates and the corresponding density value from the random field. This file can be input as a point cloud to COMSOL.
For example, the random field realization from a standard normal distribution after input to COMSOL is shown below:
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Input random field realization
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Note the layered profile which is typical of most soil and rock and is obtained by specifying a relatively larger correlation length in horizontal plane (x and y directions) compared to the vertical (z) direction.
The degree of saturation field obtained by transformation using the soil water retention variables for a given value of suction, and the corresponding electrical conductivity (obtained from Archie's law) distribution is shown below:
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Transformed fields |
An input realization can be used to generate a field for any soil or rock variable. I have shared below the Python code to generate random fields in 3D with the option to control properties such as field size, correlation lengths in 3 Cartesian coordinate axes, resolution of generated point cloud and rotation angle.
The code may be directly pasted into a Jupyter notebook and the properties such as spatial correlation length in the three axes (x, y and z), the field size, resolution (points per meter) and the rotation angle can be changed according to requirements. When the code is run, a text file will be created at the specified location.