  Radio relics are giant ($\sim$Mpc) synchrotron sources that are believed to
be produced by the (re)acceleration of cosmic-ray electrons (CRe) by shocks in
the intracluster medium. In this numerical study, we focus on the possibility
that some radio relics may arise when electrons undergo diffusive shock
acceleration at multiple shocks in the outskirts of merging galaxy clusters.
This multi-shock (MS) scenario appears viable to produce CRe that emit visible
synchrotron emission. We show that electrons that have been shocked multiple
times develop an energy spectrum that significantly differs from the power-law
spectrum expected in the case of a single shock scenario. As a consequence, the
radio emission generated by CRe that shocked multiple times is higher than the
emission produced by CRe that are shocked only once. In the case explored in
this paper, the radio emission produced in the two scenarios differ by one
order of magnitude. In particular in the MS scenario, the simulated relic
follows a KGJP spectral shape, consistent with observation. Furthermore, the
produced radio emission is large enough to be detectable with current radio
telescopes (e.g. LOFAR, JVLA).
