  We study supersymmetric extensions of the Standard Model with small R-parity
and lepton number violating couplings which are naturally consistent with
primordial nucleosynthesis, thermal leptogenesis and gravitino dark matter. We
consider supergravity models where the gravitino is the lightest superparticle
followed by a bino-like next-to-lightest superparticle (NLSP). Extending
previous work we investigate in detail the sensitivity of LHC experiments to
the R-parity breaking parameter zeta for various gluino and squark masses. We
perform a simulation of signal and background events for the generic detector
DELPHES for which we implement the finite NLSP decay length. We find that for
gluino and squark masses accessible at the LHC, values of zeta can be probed
which are one to two orders of magnitude smaller than the present upper bound
obtained from astrophysics and cosmology.
