Passive core catchers have been proposed as a means for retaining the core debris following a hypothetical core disruptive accident in a fast reactor. The core debris which may be in the form of a molten pool is passively retained in a sacrificial bed of high melting temperature material placed inside or outside the reactor vessel. Recently, it has been suggested that composite sacrificial beds with a low-melting-temperature zone inside the main high-melting-temperature bed may be more effective in retaining the pool than simple beds. It was argued that the inner zone would quickly melt and dilute the pool so that further growth into the main bed would be slowed. Hence, the main objective of this work has been to examine the composite bed concept to ascertain its efficacy vis-a-vis simple sacrificial beds.