In a nutshell
The flawed AS 2870 model boils down to treating the dynamic effect of foundation movement as a static load equal to soil stiffness times an assumed function defined as the. ‘Mound profile’. The static analysis method corresponds to superimposing a prefabricated structure on a building platform that has been pre-distorted into an assumed profile, and then analyzing the combined static effects of dead load, live load, and assumed foundation movement load. Mathematically correct as these static solutions are, they solve a hypothetical problem.
The following example for the so-called ‘Centre heave’ condition has taken from from Standards Australia Handbook SAA HB28 – 1997, ‘The design of residential slabs and footings’, pp 105-109. Please click on images below to enlarge.
The most significant engineering evidence that the AS 2870 model is flawed is that it uses linear elastic theory, but graphs of deflection and bending moment versus surface movement exhibit no linearity whatsoever.
The unusual shapes of the bending moment diagram and soil pressure diagram are further evidence that the AS 2870 model is flawed. Engineers intuitively expect the maximum bending moment and maximum soil pressure for the centre heave condition to be at the centre of the beam, not near the edges.
The graph of movement ratio versus unit stiffness also suggests that the AS 2870 model is flawed. AS 2870 Clause 4.5.1 claims this graph covers a huge range of design parameters. Actually, it appears that the graph is an empirical fit to standard slab design solutions in AS 2870 Figure 3.1 and Figure 3.4, taking the logarithm of what is defined as ‘Unit stiffness’ on the horizontal axis of the graph to get a straight line. Admittedly the term within the brackets of the logarithm is the sum of the second moments of area of the gross (that is, not cracked) cross-sections through the webs of the stiffening beams divided by the overall width of the slab, but to call this ‘Unit stiffness’ is misleading, and taking the logarithm of a number involving units of measurement breaches fundamental principles of mathematics.