Volumetric behaviour of soil

Soil is predominantly a shear material. Whilst its shear behaviour is well taught and known, its volumetric behaviour is not so, but can be very important in many instances. This blog post explains some key points related to the volumetric behaviour of soil.

Laying down some fundamentals first:

Whilst shear behaviour describes the soil’s change in shape, volumetric behaviour describes the soil’s change in size.

Young’s modulus expresses the change in volume from uni-axial stress change; bulk modulus expresses the change in volume from isotropic stress change, i.e. uniformly from all directions.

In the normal range of soil mechanics, it is assumed that the volume of the soil particles does not change (incompressible); water itself is also incompressible; the only that can result in changes in the soil volume is the change of pore space (void ratio); by way of change of pore space, pore water flow in or out of a soil body (the consolidation process).

Then we can describe the soil’s volumetric behaviour:

The drained condition permits volume change of soil. The soil’s volume can change from two sources:

1. Isotropic compression.

o   The more a soil is compressed, the harder it is to compress it further. The bulk stiffness increases as the void ratio decreases.

o   The first time the soil is subject to a compressive stress that is the highest it has ever experienced, it is called ‘primary consolidation’. This process induces plastic volumetric strain

o   When unloaded, the soil does not bounce back to its original volume due to the plastic strain, but a small proportion of it. This unloading part is largely elastic.

o   When reloaded, the soil strains largely elastically until the highest ever loading it has experienced. Any loading even higher than this level will count as primary consolidation again.

2. Shear.

o   Initially loose soils tend to contract when sheared, as the particles become better compacted, reducing pore space. This behaviour is not reflected in the ‘Mohr-Coulomb’ model but can be captured in more advanced constitutive models such as Cam-Clay

o   Initially dense soils tend to dilate when sheared, as the particles are forced to break out of their well-compacted status, increasing pore space. This can be expressed as ‘dilation angle’.

In undrained analysis, there is no volume change. Any tendency of volume change when drained leads to the generation of excess pore water pressure instead at the undrained phase. In undrained condition, initially loose/soft soils generate positive excess pore water pressure that reduces the shear capacity; initially dense/stiff soils generate negative excess pore water pressure that increases the shear capacity.

In undrained analysis, the bulk modulus of a soil is practically infinity. Young’s modulus is not infinity but a given value since uni-axial strain can still happen without changing volume. Since volume is kept constant, any shortening in one direction will be made up by the bulging out in the lateral directions (the Poisson’s effect) and the Poisson’s ratio has to be 0.5 – 2X0.5=1.

Drawbacks of the ‘Mohr-Coulomb model’ related to volumetric behaviour

Firstly, the so-called ‘Mohr-Coulomb model’ is a linear-elastic-perfectly-plastic constitutive model, with the ‘Mohr-Coulomb’ part being the shear failure criterion.

A major implicit assumption of the ‘Mohr-Coulomb model’ is that the volumetric behaviour is linear elastic. Simply put, the soil material behaves as if it is a sponge. This obviously is different from the real soil behaviour, but still can be useful within a carefully chosen range.

Outside of its useful range, this model can lead to grossly inappropriate outcomes of the analysis not matching general principles of geotechnics or even common sense, such as ground heaving up around the excavation of a shaft rather than settling down.

This model can also lead to inaccurate generation of excess pore water pressure in undrained analysis. This has two major implications: 1) it can lead to underestimation of soft soils’ undrained shear capacity as the excess pore water pressure generated is not adequately accounted for; 2) and any subsequent consolidation analysis will set off on the wrong base.