Lesson 11 - Exercise: Modeling Complex Container Failure

To build on what we discussed in the previous Lesson, in this Lesson we will work through a simple Exercise in which we use multiple failure modes and shift the failure distribution.

To do this, we are going to start with the previous Exercise we did in this Unit.  You should have saved it as to the “MyModels” subfolder of the “Contaminant Transport Course” folder on your desktop as ExerciseCT19.gsm. If you don’t have the model that you built, open and look at the worked out Exercise (ExerciseCT19_Multiple_Vaults.gsm in the “Exercises” subfolder).

Recall that in this model, the Source represents 100 concrete vaults (i.e., essentially square boxes). The vaults are filled with grout, and three contaminants (X, Y and Z) are disposed of within the grout (that degrades over a fixed duration). None of the species decay. Y has a specified solubility limit (and X and Z are infinitely soluble).  Z partitions onto the grout after it is exposed (X and Y do not).  

Water flows vertically through each vault after it fails. Prior to the failure of the concrete walls the flow through the walls (and hence the grout inside the vault) is insignificant. No mass is transferred out of the vault until it fails.

The failure distribution for the vaults is described using a Weibull distribution. We are simply going to make two changes to this model:

1. Delay the Weibull failure distribution by 3 years.
2. Create a second failure distribution that represents early failures of a fraction of the vaults due to poor construction.  It should be defined as an Exponential distribution with an Expected Lifetime of 1 year and a Probability of 0.25.

Stop now and try to build and run the model.

Once you are done with your model, save it to the “MyModels” subfolder of the “Contaminant Transport Course” folder on your desktop (call it ExerciseCT20.gsm). If, and only if, you get stuck, open and look at the worked out Exercise (ExerciseCT20_Complex_Vault_Failure.gsm in the “Exercises” subfolder) to help you finish the model.

Let’s walk through the model now.

The Outer Barrier Failure should look like this for the Weibull failure mode:

You should have created a second failure mode that looks like this:

If you run the model and plot the Release Rate, it should look similar to this (due to the small number of vaults, there will be variability in the failure times, so each realization will look a bit different):

The key point to notice is that the release rate is quite complex with two peaks (one due to early failures associated with bad construction and a second due to the later failures).