If collapse goes to completion in a momentum-only (no supports) inelastic configuration, then the entire event can be considered a single inelastic collision in the sense that the final velocity of the debris pile just before hitting ground is that given by a collision between the upper block and the lower block as point masses - ignoring gravitational effects, of course. So, in a horizontal arrangement of inelastic slabs, a single impactor hitting a line of 99 masses has the collective debris zone speed reduced to 1/100th that at the final collision. Makes perfect sense.
It also provides another means of validation of calibration obtained under other conditions. Here, the initial downward speed can jacked up to ridiculous amounts, so long as the time step is made sufficiently small. I chose a single top slab v0 of 1000 m/s to slam into 99 floors below under a variety of circumstances. In the stepwise model, it's only necessary to set support energy to zero to run with momentum-only, but the physics sim is like real life in that a stucture with no supports will fall uniformly at g. It would be possible to make the supports disappear at the right moment but it's more effort than I care to expend on it. The solution to get momentum-only is to turn gravity off. This is one of the cases presented next.
The graph below is a plot of top slab velocity vs time for 7 different impact scenarios all at 1000 m/s (plus delta for drop height of 0.8*3.7m in gravity cases). The green lines are with support in 1 g field, the red line is no support in zero g, and the blue are with support in zero g. Three support capacities corresponding to FOS of 1,5 and 10 were used in zero and 1g. The stretch and maxwell numbers are 0.196 and 0.0237 (@ FOS = 1).
Of the seven cases, the momentum only red line cannot arrest because it's the only one which has no support. This exemplifies the kind of collision transaction alluded to above. By completion, it's equivalent to a single inelastic collision between two bodies of masses m and 99m. When support fail energy is added, the results change in a regular way about the special trajectory of the red line except for arrest.
Three of the six remaining cases arrest, two under zero g and one in gravity. The one in gravity is the arrest case portrayed in the second graph of the earlier post. The similar case in the stepwise model does not arrest. What are the differences?
1) In the physics simulation, the slabs are connected by joints that are short travel non-linear springs. Several things remain in characterizing their dynamic behavior but this exercise has shown their energy consumption under failure to be consistent under a variety of settings. In high FOS trials, the bottom slabs are observed to recoil significantly with each impact above, indicating the joints absorb energy. They seem to be highly damped, like a shock absorber. This is an energy sink not accounted for in the stepwise crush calculator, but it could be in a generic way.
2) The slabs collide mostly inelastically in the physics simulation, but not perfectly so. There is a repulsive skin depth because singularities don't solve well in any system, and there is some elasticity. Because of this, the slabs in the debris zone will be loosely packed instead of artificially and unrealistic welded on collision. This results in a vertical newton's cradle sort of affair when impacts occur, and these repeated inelastic collisions dissipate energy.
Item 1 is not really characterized in any way other than the appearance of damping. The propagation of shock waves through this medium is undoubtedly peculiar to this bizarre structure of 1D semi rigid spheres and highly dissimilar to any real macroscopic system of interest.
Item 2 is quite a bit more realistic for physical slabs like tiles than the analytical model of accretion, however the analytical model may be more like real buildings than rigid slab approximations. To the extent that debris was loose, it applies but doesn't go far enough, it just hints at what the characteristics are in a discrete 1D model with relatively small numbers of particles.