Tunneling in classical mechanics According to a classical mechanics a particle that do not have enough energy will not be able to surmount a potential barrier. 
But what if we have a lot of particles(e.g. electrons)? They can interact with each other(Coulomb's law) and transfer enough energy for some of them to surmount a barrier. 
Does it explain a tunneling phenomenon without quantum theory?
 A: This will help:

Please note that the energy is the same , inside and outside the barrier. Also it works on one particle. Your "model" would give a  statisticacl gaussian distribution for the probability of finding the tunneling particle whereas alpha decays of a nucleus, for example, have an exponential fall off distribution.
No, tunneling is a quantum mechanical phenomenon.
A: Well as all the comments they have given,the answer should be no.
Tunneling in quantum mechanics state that even you are given only one electron now, it still has some probability to surpass the potential and finally detected in which the classical physics can ever and never gives an explanation.
And in the case you take as an example, you should first notice that since the particles are electron,they are so small that you can't ignore the  wave characteristics,thus the particle shouldn't be deal with classical physics in anyway.
And then if they interact just like what you say, they have "different" energy now even if you maintain the potential barrier! So this is a totally different case from the former one and you can't say this is a quantum tunneling if you have now a system of larger energy, so large that it might surpass the potential barrier and even in the classical case they will go through the barrier.
And just like Jon said: you might even change the barrier since at reality you are changing the total system.
So tunneling can only be explained in quantum mechanics, and has no similar case in classical view
A: You are quite correct that interactions between electrons can cause them to jump a potential barrier. For example thermionic emission is a good example of this. However this is a quite separate process from quantum tunneling.
Consider some collection of electrons - we'll use the electrons in the conduction band of a metal as an example. To get an electron out of the metal requires an energy called the work function, and this energy is typically a few electron volts. The thermal energy available to the electrons is $kT$, but at room temperature $kT$ is only about 0.025 eV. That suggests we would require 40 times room temperature or about 12000K to get thermionic emission, but actually we get emission at only a few hundred degrees C.
The reason for this is that $kT$ is the average energy of the electrons and some electrons have energies lower than this while some have energies higher than this. Electrons scatter off each other in a basically random way and as a result some can get very high energies.
The probability that an electron will have an energy $E$ is given by the Boltzmann distibution:
$$ P \propto e-{E/kT} $$
For energies a lot higher than $kT$ the probability is very small, but then there are a lot of electrons in a metal. The result is that even at relatively low temperatures some electrons will escape.
So interactions between electrons can indeed allow a few of them to jump a potential barrier. However this happens because those few electrons have an energy higher than the barrier. Quantum tunneling is a completely different process and allows an electron to jump a barrier even when it doesn't have enough energy to jump the barrier.
