Local Average Subdivision method in svslope

Question

Hello. 
 I have a question regarding the Local Average Subdivision method functionality which generates random values for different segments along different slip surfaces of a slope in each Monte Carlo iteration, though I have spent lots of time understanding this technique . Actually, I do not understand how does it generate random values in each MC iteration in a Floating approach ? Could you please clarify this as different slip surfaces have different lengths in each MC iteration, so how a two-segment slip surface random values can be equivalently converted to become random values of a three-segment slip surface in an MC iteration using the LAS method ? 
 
 For example, there are two slip surfaces(with different lengths, e.g. 5 and 7 meters) in each Monte Carlo iterations(no of iterations=2000). How LAS approach generates random values for soil cohesion for each segment of two slip surfaces considering SOF value of 2 meters, so the two resulting factors of safety can be compared at the end of each iteration?

Faseel Khan · Answer

Our Local Average Subdivision (LAS) method is only used to generate the 2-D random field for 2D-Spatial Variability as stated in our theory manual, not for 1D Spatial Variability. 
 SVSLOPE uses Local Average Subdivision (LAS). This approach is a fast and accurate method of generating a homogeneous Gaussian scalar random process in one, two, or three dimensions. The resulting discrete process represent local average of a homogeneous random function defined by its mean and covariance function, the averaging being performed over incremental domains formed by different levels of discretization of the field. The approach is motivated first by the need to represent engineering properties as local averages (since many properties are not well defined at a point and show significant scale effect), and second to be able to easily condition the field to incorporate known data or change resolution within sub-regions. 
 In two dimensions, a rectangular domain is defined and the subdivision proceeds by dividing rectangles into 4 equal areas at each stage. In order to preserve the exact &lsquo;within cell&rsquo; covariance structure, three random noises are added to three of the cell quadrants and the fourth quadrant is determined such that upwards averaging is preserved. 
 In two dimensions, a rectangular domain is defined and the subdivision proceeds by dividing rectangles into 4 equal areas at each stage. In order to preserve the exact &lsquo;within cell&rsquo; covariance structure, three random noises are added to three of the cell quadrants and the fourth quadrant is determined such that upwards averaging is preserved. 
 More details on this feature can be found in the slope stability theory manual 2021 Section 18.3. 
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