Creating a model of your antenna (not too much different than your little diagram) with all nearby associated metal can be done with the NEC2 (or, NEC4) antenna modeling software. It is the best way to compute the effect of nearby conductors. In fact, there are no formulas or easy fill-in-the-blanks methods to do this.
NEC2 is easy to use but without a nice 3rd party output processing program, such as EZNEC (http://eznec.com) it is hard to make use of the results. These 3rd party output programs will create graphs to show SWR on the antenna and radiation propagation field and show currents on the antenna (and other things).
There are a variety of tutorials available that show you how to do this and they are easily found by googling NEC2. Note, you can probably get a Free Trial Use of EZNEC that will allow you to do the model and display the graphic results. EZNEC runs on Windows PCs only.
I personally do not use EZNEC although I did years ago. I use Mathematica as my 3rd party graphic display of result data produced by NEC2. Technically I use NEC4 but NEC2 should be able to do everything you need to do. NEC2 is freely available on the Internet, NEC4 is source licensed from Lawrence Livermore Laboratories. I purchased my single-user license for $300 about five years ago. Not sure if it is still priced the same though.
In my own antenna analysis work I always use NEC to produce the model and evaluate the results. I have found that results of NEC (NEC2 or NEC4) to be very close to actual measurements that I can make on the antenna after I put it up.
NEC4 does a better job of ground modeling and much more accurate for conductors close to the ground (inches or under) as you might use with a radial counterpoise for a 1/4 wave vertical. However, NEC2 is quite adequate for just about all uses being mindful of where the model starts to show weakness.