fig4 one core assembly may consist of three tunnel cores 6 all joined to a common frame 15 by means of the connectors 18 the horizontal tubes 13 are preferably also connected to the frame 15 by coupling means 19 so that the tubes 13 can also be withdrawn from the compost stack 1 at the same time as the tunnel cores 6 are withdrawn thus each core assembly includes three tunnel cores 6 and two horizontal tubes 13 see fig2 the frame 15 supports all of these elements in cantilever fashion and the frame itself is provided with supporting wheels 16 and a hitch 17 so that the core assembly and frame unit may be withdrawn readily normally each stack will initially utilize a plurality of core assemblies and corresponding frames 15 disposed in side by side relation and properly positioned for forming the tunnels 2 and passage 4 as the building of the stack progresses from one end to the other the core assembly first covered may be withdrawn and transported to a new site then the second core assembly covered may also be withdrawn and transported to a new site and so on thus there is a progressive withdrawal of core assemblies and transportation thereof to a new site making the process a continous one in order to support the end walls of the compost stack 1 the wall support elements 20 21 are preferably employed which are so constructed as to provide practically complete access of the surrounding air to the compost material accordingly the wall elements have slats 22 distributed over their height and secured to uprights 23 these slats consist preferably of planks secured between posts the slats are preferably inclined downwards towards the side adjacent to the compost stack the.