[THE EXPLANATION]: 
 
^||. The Equestria Girls portal (both) work like a Stargate (from the tv series "Stargate"): The person/object must completely cross a "barrier" [the "event horizon"], before any transformation & transportation can happen entirely at once.  
 -> The "barrier" is constantly pushing away, so any pasive matter like air, rain/snow, water or sand will be deflected/rejected [while an active living body (or a solid object with enough momentum) will advance through it). 
 
. The body initially goes into an "intermediate space" inside the portal (where the passage of time is extremely slow), so any bodypart that enters "first" stops sending or receiving nerve signals from the brain [it does not "feel" like anything, literally (it is not like a "missing" bodypart, but more like extreme sedation)].  
 -> Once the head goes inside, the rest of the body either has enough momentum to fully complete the crossing, or it is eventually pulled out by the barrier [this is what happened to human!Pinkie near the end of Rainbow Rocks]. 
 
. With the body fully inside the "intermediate space" (before even a single heartbeat could happen in the time_dilation), the equivalent of an A.I. performs an analysis to decide how to transform it into one of the current "native species" of "the other side" (that is safe/compatible with its ecology), adding attributes/skills/abilites & even "extras" like magic if necesary.   
-> Then magical processes DESTROYS the body to the subatomic level, sending all of its matter/energy to "the other side", alongside with all the "information" necesary to reconstruct it with the "new specifications" (plus the "original" configuration data to be encripted & stored inside the new body for the future use of any other "portal" that follows apropiate safety protocols). 
 
. On "the other side", a similar process happens in reverse [building a "new pony body" atom_by_atom inside a safe "intermediate space" before releasing it].  
-> For the traveler it feels like sudden brief loss of conciousness, followed by spatial confusion and quick regaining of awareness (as the new nerves on the hooves re-connect with the spine & the new neurons in the horse_brain re-synchronize).||^  
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In the Equestria Girls Special "Spring Breakdown"; the feet of human!Dash were not even touching the surface of the "barrier" on top of the portal (that is now "facing up" after falling to the side), because it is hidden by a dense mix of water & sand. When Sunset & Sci!Twilight arrived & attempted to help her get out of that quicksand trap, her efforts made her sink even more, starting to push against the barrier enough to cause some of the sand around her leg to pass through it [efectively removing some of the "sustentation" that was still keeping her head out of the quicksand].  
-> Luckily, Sunset managed to see the effect of a "portal" activation when this happened. 
 
. It would had being IMPOSSIBLE for Sunset to take Dash out there by herself (as it is equivalent of lifting her whole weight using only her arms); while Sci!Twi could had used her telekinesis to help, she was fully occupied barely containing an agressive plant_monster.   
.  With Dash at a serious risk of asfixiation/drowning happening soon; plus Sunset & Sci!Twi at risk of being eaten, the only options were to "run away" (leaving Dash to her certain death); or risking going all of them through this "mysterious hidden portal" to %wherever% it may lead [not necesary Equestria], with the hope that the "transformation protocols" would give them new bodies that could survive the inmediate enviroment conditions "on the other side". 
 
  Sunset had no time to explain all of this, so she just pushed Dash down (with enough force for gravity to do the rest, pulling her body and a lot of sand through the barrier), followed by Sunset & Sci!Twi joining the temporary "drainage" of quicksand before the barrier could manage to stop it completely [since at that point it would become extremely difficult for them to "dive down" to reach the barrier, getting "stuck" like Dash was moments before].  
-> The 3 girls (& a few tons of sand & water) were "processed" by the magic & sent to Equestria in a "single package" [as seen when the portal fully activated moments later, releasing a "beam" of energy to clear its entrance from the detected "debris" (another safety protocol)]. 
 
  
[In Equestria]: The "other side" had a portal inscribed on a block of stone (just like the pedestal at C.H.S.), inside a deep cavern with a (rather convenient) ammount of empty space next & "below" it to accomodate all the quicksand at the bottom.  
-> The girls emerged on Equestria (as ponies) from the portal in a horizontal direction [instead of "keeping falling" like when they entered], but because there was no "floor" in front of the portal, they inmediatly fell (again) a few meters down (on top of a pile of humid sand that absorbed most of the impact).