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# Spatial Variability

Spatial Variability Analysis is a sub-option of the Probabilistic Analysis in Slide2.

To enable spatial variability analysis:

1. Select Project Settings > Statistics > Probabilistic Analysis
2. Select the Spatial Variability Analysis checkbox.
3. You may choose a Covariance Function and Mesh Size option (see below).

## Covariance Function

Three covariance functions are available with spatial variability: Markovian, Markovian 1D Separable, and Gaussian. During the random field generation using the Local Average Subdivision method, the covariance functions are used to calculate the covariance value between cells in the field. This is where the correlation length input is taken into account. Each method uses a different equation to model the reduction of covariance with distance.

• Markovian: covariance = variance * exp( -tau ), where tau = sqrt[ (2*X/CLX)^2 + (2*Y/ CLY)^2 ]
• Markovian 1D Separable: covariance = variance * rX * rY, where rX = exp(-2|X|/CLX), rY = exp(-2|Y|/CLY)
• Gaussian: covariance = variance * rX*rY, where rX = exp( -pi*(X/CLX)^2 ), rY = exp( -pi*(Y/CLY)^2 )

## Automatically Calculate Mesh Size

The mesh size in a random field must meet two requirements: 1) it is recommended that it be at least half of the smaller correlation length (X or Y), and 2) each material layer must have a sufficient amount of cells to correctly represent the variability (for example a thin horizontal layer should not have just one row of cells because this would not take into account the vertical variability). Slide2 uses an algorithm that automatically calculates the mesh size for each layer in order to satisfy these requirements. It is recommended that this checkbox is not turned off. However, the user may turn off the checkbox if they want to define their own mesh size for spatially variable materials in the Material Statistics dialog.

## Analysis Type

Due to the nature of a spatially variable probabilistic analysis, you must use the Overall Slope Analysis Type option. This is because for each sampling a new random field of material properties is generated for the spatially variable materials. Therefore the critical slip surface search must be repeated for each new random field.

## Spatial Variability Tutorial

After you have enabled spatial variability analysis in Project Settings, you must define correlation lengths for your spatially variable materials in the Material Statistics dialog. For an overview of Spatial Variability Analysis in Slide2 and a step-by-step tutorial example, see the spatial variability tutorial.