The performance of slabs on moisture reactive soil involves many variables, yet the original authors of AS2870 preposterously prescribed slab design solutions requiring only two input parameters – Site classification and type of construction. Therefore, many practising engineers do not design slabs and footings in the true sense of the term, they simply select a design solution prescribed in AS2870, comfortable in the knowledge that their selections are deemed-to-comply. This widespread practice raises the issue of the engineering community’s professional duty of care to home-owners, as well as technical issues, including but not limited to the following:

- The AS2870 design model is based on analysis of a one-way action beam model for what is obviously a two-way action plate problem.
- Applicable ranges of design Y
_{s}values in AS2870 Table 2.3 are too broad. - Deemed-to-comply slab design solutions are independent of soil stiffness.
- Deemed-to-comply slab design solutions are independent of floor plan dimensions and floor plan shape.

#### In a nutshell

The flawed AS2870 model boils down to using a static analysis method to analyze the dynamic effect of foundation movement. This method treats foundation movement as a static load equal to soil stiffness times an assumed function called the ‘*Mound profile*’. AS2870 recommends the profiles shown at right. It would appear that the profile parameters ‘*Edge distance*‘ (Walsh model) and ‘*Mound exponent*‘ (Mitchell model) have no physical basis. It can be demonstrated from fundamental principles that this static analysis corresponds to superimposing a prefabricated and loaded structure on a building platform that has been shaped into the assumed mound 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.

#### Graphic evidence

The most significant evidence that the AS2870 model is flawed is that it uses linear elastic theory, but graphs of deflection and bending moment versus surface movement exhibit no linearity.

The unusual shapes of the bending moment diagram and soil pressure diagram for the so-called *‘Centre heave’* condition are further evidence of flaws in the AS2870 model. Intuitively, centre heave should produce peak bending moment and peak soil pressure at the centre of the beam, not near the edges. The examples shown here have been taken from Standards Australia Handbook HB28 – 1997, *The design of residential slabs and footings*, pp. 105 – 109.

Last but not least, the graph of movement ratio versus unit stiffness also suggests flaws in the AS2870 model. Clause 4.5.1 in AS2870 suggests 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 Figures 3.1 and 3.4 in AS2870, taking the logarithm of 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 of 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.

## Comments

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