Rare-earth dodecaborides RB₁₂ (R=Tb, Dy, Ho, Er, Tm) are all characterized by a controversial and unresolved magnetic and specific-heat anomaly at low temperature (T_C≈3-22 K) except LuB₁₂ with closed f-shell. Although the bump feature in magnetic susceptibilities resembles that of antiferromagnetically ordered R³⁺ ions, no definite magnetic structure was identified by either neutron scattering or Mössbauer spectra. The anomalies in susceptibilities, entropy, and low temperature neutron diffraction pattern all pointed to the amplitude-modulated nature of complex magnetic structure. In view of the rather small crystal-field-splitting energies of the order of meV, we propose to treat crystal-field-splitting (CFS) energy as an order parameter rather than a quantum mechanical quantity. In this way, we found that not only the magnetic and specific-heat anomalies can be explained properly by a gradual quenching of R orbital moments, but also the low temperature satellite peaks of neutron scattering spectra can be understood in terms of the spontaneously (111) dimerised structure and inelastically absorbed rattling phonon modes.