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  • Writer's pictureSi Shen

Mohr-Coulomb model for soil – when not to use it

The so-called ‘Mohr-Coulomb’ (MC) model is the most widely used constitutive model for simulating soil behaviour. Its theory is easy to understand, widely taught, parameters easy to obtain and calculations quick to perform. However, its limitations must be well understood to avoid dangerous mis-use.

Firstly, it should be noted that the ‘Mohr-Coulomb’ theory in itself is only one piece of the jigsaw in the constitutive model – the yielding criteria. It is used in a ‘linear-elastic-perfectly-plastic’ constitutive model, where the stress-strain relationship develops linearly up to a point of yielding, turning into a yield ‘plateau’ afterwards. Mohr-Coulomb is only used to determine the turning point. So when MC modelled is referred to, a linear-elastic-perfectly-plastic stress-strain behaviour of soil is implied.

Generally speaking, the ‘real’ soil behaviour exhibit the following characteristics:

  • Non-linear stress-strain relationship, starting at very low stress levels

  • Strain-dependent stiffness

  • Time-dependent behaviour, such as consolidation and creep

By comparison, the MC model satisfies none of the above characteristics, but is usually ‘good enough’ for practical use, if used in the appropriate situations.

Generally speaking, MC model is mostly likely to be appropriate (low risk) for the following conditions:

  • Predicting stress in the structure rather than in the ground

  • Predicting ground movement at low stress level. The MC model typically over-predicting movement, which is conservative) The MC model could under-predict ground movement at high stress levels.

  • Where the stress/strain in the ground remains largely constant, without significant fluctuations. In other words, use MC for constant static loading conditions.

  • No significant faulting, ground largely isotropic and homogenous (i.e. behaviour is same in all directions and everywhere)

Be weary of using MC model in the following situations:

  • Prediction of movement of the ground is critical

  • Expected strain of the ground is high. In MC model the stiffness of the ground does not change with strain, and dilatancy increases with strain forever.

  • Significant amount of un-loading and re-loading is involved, because the effective stiffness for un-loading and re-loading is typically quite different, whereas MC model assumes the same.

  • Time-dependent behaviour such as creep is significant to the design

  • MC model does not recognise uniform triaxial compression yielding

Lastly, when using MC model to design for undrained situation, commercial software packages usually offer the option to model soil behaviour with drained (effective) parameters. Be extra careful in this situation and do sensitivity test for using undrained parameters, because this is how Nicoll’s highway collapsed in Singapore.

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