Soil behaviours for the choice of constitutive models

Constitutive models are essentially a mathematical description of certain mechanical behaviours of a soil (or rock). They paint a picture of what a soil’s behaviour looks like in aspects relevant to the design. When studying a constitutive model, it is important to drill deeper to understand the underlying soil behaviour the model attempts to simulate.

Constitutive models of a wide variety of complexity have been published over many decades. You’ll see that after so many years, the simplest constitutive models are still the most popular choice, as they are easier to use, with relevant parameters easier to obtain from common test procedures, and the whole methodology easier to demonstrate compliance with codes.

However, simpler constitutive models are usually more idealised and generalised, which means they deviate from the ‘real’ behaviour further. More advanced constitutive models are developed to make up the drawbacks of simpler models, bringing the simulated behaviour closer to reality, suitable for specific given situations.

The holy grail in choosing what constitutive model to use lies in the balance between efficiency and accuracy, which means determining the boundaries around what aspects of behaviour matter to the results and what others to disregard.

This post lists out some commonly seen elements of soil behaviour relevant to constitutive modelling:

• Differentiation between drained and undrained behaviour

  • Drained behaviour represents a state after pore water pressure self-balances by the flow of pore water, thus generates no excess pore water pressure

  • Undrained behaviour represents a state before any pore water pressure is able to flow and try to self-balance, thus generates excess pore water pressure, affecting the effective stress state of the soil and ultimately its mechanical behaviour

  • The above two states are the two extremes on a linear scale. The intermediate states between them are the various degrees of consolidation.

• Differentiation between shear behaviour and volumetric behaviour. Classic linear elastic mechanics has the two coupled but in reality they behave differently:

• Shear has a mode of strength failure (e.g. the Mohr-Coulomb failure criteria) whereas volumetric failure doesn’t happen under normal regimes of soil mechanics

• Shear stiffness generally reduces as strain goes higher whereas volumetric stiffness increases as strain goes higher

• Confining stress dependent strength and stiffness (the compaction effect). This means there are differences between primary loading and re-loading. Primary loading consolidates the soil and results in plastic strain. Unloading and re-loading of the soil is an elastic process but with a much higher stiffness. With more compaction (primary consolidation) comes:

  • Higher friction angle, relative to critical state angle (not a given constant)

  • Lower void ratio

  • Higher volumetric stiffness and shear stiffness

  • Lower water content

  • Lower permeability

• Post-yield softening, which can happen to dense soils. Where shear strength reduces after the yielding point, using perfectly plastic model may over estimate the strength of the soil.

• Shear-strain-dependent shear stiffness. The more shear strain there is, the lower the shear stiffness is. The ‘stiffness degradation curve’ is an illustration of this phenomenon.

• Volumetric change due to shear.

  • Over consolidated clay and dense sand tend to have dilatancy

  • Loose soils tend to contract (negative dilatancy)

  • This affects pore water pressure in the undrained condition.

  • Volumetric changes affect undrained soil strength. Dilatant soils have undrained strength higher than drained strength. Contracting soils have the opposite.

• Anisotropy – the behaviour of soil in the vertical direction can be different from that of the horizontal direction. This can be due to the way the soil is deposited, consolidated or weathered.

• Rate and cycles of loading. The faster a soil is loaded, the stiffer it tends to be. Cyclic loadings tend to soften a soil. This is pertinent to structures that are subject to significant dynamic loadings, such as wind load, wave load, blast load and accidental impact load.