# Zone property-distribution

Hi everyone,
the new version of flac2d has a command below to assign the gaussian-distribution of the zone properties:
`zone property-distribution cohesion 600 deviation-gaussian 10`
So what is the inside process when I solve the model with fos command? Is the fos result a deterministic or probabilistic?

Hi Sullivan. The question is somewhat not clear to me, what do you mean by “what is the inside process”? Are you wondering about how the FOS value is calculated? You can read about the logic behind in Strength Reduction Procedure in FLAC and 3DEC — Itasca Software 9.0 documentation

I don’t see any conceptual difference in running a single model with regularly set material properties or material properties set via a (random) distribution. Within the FOS logic, material properties of each zone will be reduced by a given strength reduction factor, leading to a weaker material but also with a distribution of properties. So, I think even when prescribing material properties via distribution, you would still get deterministic FOS for a given set.

Now, if you have multiple runs, and in each of them have different material properties but within a distribution, the results for FOS values (or distribution), in my opinion, would be undetermined (meaningless) rather than deterministic or probabilistic. I think a lot depends on many other parameters of the model (e.g., geometry) and where you would get weaker spots. I haven’t run such cases but maybe there are some research papers dealing with this subject. This would be interesting to investigate.

thanks Apya!
I am just wondering, what is the mean to assign a distributed material params while the result is deterministic?

I really don’t know what is inside the generation of the property mentioned in command. Maybe you could post some image of the cohesion distribution at the model to see if it incorporates any spatial correlation or not.

In the context of probabilistic analyses, one run of the cohesion random field would represent a realization (or potential reality) of its spatial distribution.
Suppose cohesion (x) is a random variable or field, then any scalar function f(x) would also be a random variable. In our case, FS(x) is a function of x and then a random variable as well. In other words, if you run one model using a realization of x then your resulting FS would be a realization of the random variable FS(x). If you want to know the full distribution of FS(x) you might think of using any approximation or simulation method (e.g. Monte Carlo). That process should involve a higher number of runs considering different scenarios of x.