  We study whether and how the energy scalings based on the single-ridge
approximation are revised in an actual crumpled sheet; namely, in the presence
of ridge-ridge interactions. Molecular Dynamics Simulation is employed for this
purpose. In order to improve the data quality, modifications are introduced to
the common protocol. As crumpling proceeds, we find that the average storing
energy changes from being proportional to one-third of the ridge length to a
linear relation, while the ratio of bending and stretching energies decreases
from 5 to 2. The discrepancy between previous simulations and experiments on
the material-dependence for the power-law exponent is resolved. We further
determine the averaged ridge length to scale linearly with the crumpled ball
size $R$, the ridge number as $1/R^2$, and the average storing energy per unit
ridge length as $1/R^{2.364\sim 2.487}$. These results are consistent with the
mean-field predictions. Finally, we extend the existent simulations to the
high-pressure region for completeness, and verify the existence of a new
scaling relation that is more general than the familiar power law at covering
the whole density range.
