Assuming that extra dimensions will not be visible at LHC, what motivation will still remain to study them? Many physicists believe that there is little possibility of observing extra dimensions at LHC so that some extra dimension models originally designed to solve hierarchy problem (ADD/Randall-Sundrum) will probably be useless for the original purpose. 
However some people claim that even if unobserved at LHC, these models will not be forgotten and people will continue to use them for other purposes. I am confused here -- if the proposed model fails to solve the very problem it was supposed to tackle, how can such models still be used? Will these not be inconsistent with nature? 
Apart from the confusion, I am interested to know what insight such extra dimension models (RS/ADD) have provided which would be impossible unless such models were developed and studied?     
 A: By way of analogy, you can't observe what's going on inside a black hole.  But you can still make some indirect observations that are consistent with the theories about how a black hole works, such as the observance of radiation (called Hawking Radiation) from just outside the event horizon.
In other words, just because extra dimension models may not be observable, doesn't mean that the theory won't have some orthogonal utility.
A: There is some confusion in this question on what  new physics one expects to see at the LHC. The predominant models with extra dimensions are string theory  models. String models are actively pursued because they allow quantization of gravity and have many group symmetries which can be used to embed the successful Standard Model results of particle physics. They also have at least extra six dimensions than the four we are used to up to now. The grand majority of models compactify these extra dimensions so that they would never be observable at the LHC. 
What these models have also is supersymmetry, and it is the supersymmetric particles which, if found at the LHC, would signal that the string models  with their extra dimensions  are successful. If  no supersymmetric particles are found at the next stage of the LHC this would just mean that the models must modify the models with a  supersymmetric sector to energies larger than the LHC can reach. Nothing definitive will be decided , and we go on to the International Linear Collider to continue the search and test of models. 
Maybe you are thinking of the  models of large extra dimensions where some of the compactified  dimensions could be large enough so that it could result in generating small black holes at the  LHC . If these are not found it just means that these particular models are invalid.
