This morning I've been testing a variety of adhesives on SPS foam to discover if any of these would eat the foam,  but also to see if any created a stronger bond compared to the other. I thought this experiment might help others, so here 'tis.  FYI - for what I need to achieve on this model: My structure will include ~ 25 brick piers that will be set into the foam. The piers will be attached to the structure and only give the appearance of actually supporting the structure in the ground. I will drill slightly over-sized, shall holes in the foam to accept the piers. The holes will be ~ 1/2" deep and the piers will only be ~ 1/4" deep in the holes (just enough to appear below grade) I need to use an adhesive or something similar to fill the voids around and beneath the piers. When dry, the piers will be firmly secured on both ends.

The adhesives were spread around ranging from a feathered edge to something thick.  I wasn't sure if the thicker concentrations would make a difference in eating the foam or not. I left the spreader stick in place to test the bond. The caulk really wasn't being tested as an adhesive per se, but I may need to use a little caulk so it got thrown into the mix.   The other materials are E6000, Elmer's PVA, Gorilla brand wood glue, Aleene's Original Tacky Glue, and Clear Gorilla glue.

Just a note about the Clear Gorilla Glue. This stuff is supposed to be clamped up for a couple hours and claims to be fully cured in 24 hours. For the purposes I've used this adhesive, clamping wasn't practical, so I did not clamp. It's very slow to dry but I'll say this: don't use this glue on anything you don't want to be permanent!  In my experience in using about a half bottle, this is awesome stuff!

The results after about 3 hours: 

• The E6000 ate the foam within 20 minutes - no good! 
• The caulk is not eating the foam, but I'm a little baffled. This particular caulk is designed for finishing wood trim, which I've used quite a bit of, and this caulk is typically set within 30 minutes. For some reason today, after 3 hours, its really just now skinned over good. Maybe its the thick concentration but I won't be using this particular caulk (but still need to test a couple other caulks I have).
• Similar story with the thick application of PVA ... rather slow to set up and the bond wiggles around a bit. The PVA is not eating the foam, but I'm not impressed for what I need to achieve on this model.
• The Tacky Glue is not eating the foam and is well on its way to drying clear as promoted. The bond is looking very good; I suspect by this time tomorrow I'll be very happy with the bond. 
• The Clear Gorilla Glue is not eating the foam and is performing just as I expected - clear as advertised and the bond is fantastic. I've never spread this glue as thick as I did for this test. After 3 hours it feels dry to the touch but the texture feels like hard rubber. I'm thinking it'll be hard as a rock tomorrow.
• The Gorilla brand wood glue: WOW, WOW, and WOW!  First, it was dry to the touch in about an hour and felt like a hard shell on the foam. But the bond blows me away ... that stick is really stuck! As wood glue seeps into the grain of wood, I get the impression it also seeped into the grain of the foam and has really bonded the grain/fibers of the wood and foam.  
• Summary: Wood glue, then Clear Gorilla Glue, then Tacky Glue. 

But I needed one more test to see which of these worked best to fill a hole like I described above.  The second photo shows holes drilled into foam and filled with the three adhesives.  They've been setting there for about an hour and a half.  The level of the wood glue has dropped a bit, but does not seem to be eating the foam. My assumption is the wood glue is seeping into the surround pores of the hole causing the level to drop a bit. Unfortunately the Clear Gorilla Glue seems to be melting the foam at this heavy of a concentration. The level also dropped a bit and I can feel a little tack on the bottom of the foam. The Tacky Glue level has not dropped, it doesn't appear to be eating the foam, and it seems to be setting up nicely.  I'll have to let this test play out until this evening to see what really happens, but if the level of the Tacky Glue doesn't drop, the Tacky Glue is likely what I'll be using.