Discrete and Indiscrete Rigid Block Methods

DISCRETE RIGID BLOCK
This method makes significant improvements on the basic limit analyses formulations (Livesley,1978), it takes into account much more complex mechanisms than the basic method which comprises of various positions on the four hinges required for collapse. Livesley pioneered discrete rigid block limit analysis concerning masonry structures, the arch structure is realised with a series of rigid blocks.
The structure is divided into a number of discrete rigid blocks connected by zero thickness and tensile strength joints. The virtual displacements compatible with the kinematic laws of the system of rigid blocks are able to be considered. The modelling of sliding friction in plastic analyses can be problematic and a load factor satisfying both static and kinematic constraints is not always obtainable. This often means that the amount of dilatancy which accompanies the sliding between block is unrealistic.
The load spreading through the fill and the passive fill restraint has been attempted to be included in subsequent works, the use of vertical retaining wall theory has been used to model the passive restraint provided by the backfill.  For frictional materials it has been suggested that this is a 1/3 of the factor applied for classical earth pressures, this provides a reasonable assumption where four hinge failures are concerned as stated by (Gilbert, 2007).


INDISCRETE RIGID BLOCK
This method is an intermediate step between basic limit analysis methods and discrete rigid block methods (Hodgson, 1999).This approach differs from the discrete method as it takes into account that not all rigid blocks undergo movements relative to each other. This therefore allows for much shorter analysis times for longer and more complex methods.