  To investigate the factors that control the success and/or failure of solar
eruptions, we study the magnetic field and 3-Dimensional (3D) configuration of
16 filament eruptions during 2010 July - 2013 February. All these events, i.e.,
erupted but failed to be ejected to become a coronal mass ejection (CME), are
failed eruptions with the filament maximum height exceeding $100 Mm$. The
magnetic field of filament source regions is approximated by a potential field
extrapolation method. The filament 3D configuration is reconstructed from three
vantage points by the observations of STEREO Ahead/Behind and SDO spacecraft.
We calculate the decay index at the apex of these failed filaments and find
that in 7 cases, their apex decay indexes exceed the theoretical threshold
($n_{crit} = 1.5$) of the torus instability. We further determine the
orientation change or rotation angle of each filament top during the eruption.
Finally, the distribution of these events in the parameter space of rotation
angle versus decay index is established. Four distinct regimes in the parameter
space are empirically identified. We find that, all the torus-unstable cases
(decay index $n > 1.5$), have a large rotation angles ranging from $50^\circ -
130^\circ$. The possible mechanisms leading to the rotation and failed eruption
are discussed. These results imply that, besides the torus instability, the
rotation motion during the eruption may also play a significant role in solar
eruptions.
