Overview

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In geotechnical engineering, soils are multiphase materials - composed of solid particles, water, and air. Their behaviour is complex, and simulating it numerically requires different types of constitutive models depending on the level of detail and physical processes being considered.

In numgeo, we distinguish between the following model families:

1. Mechanical Models

   These models govern the mechanical response of the soil, typically by updating the (effective) stress at time \(t = t_0 + \Delta t\). In the simplest case, the model computes the stress increment \(\Delta \sigma\) as a function of the strain increment \(\Delta \varepsilon\). More advanced models account for additional factors such as: void ratio \(e\), current stress state \(\sigma\), degree of saturation \(S\) or Other internal state variables These models are critical when simulating non-linear, path-dependent behaviour, such as plasticity or cyclic loading.

2. Hydraulic Models

   Hydraulic models describe the soil-water retention behaviour, i.e., how water is held within the pores of the soil. Basic models relate suction \(s\) to the effective degree of saturation \(S\) (or \(S^e\)). More advanced formulations also incorporate changes in void ratio (or volumetric changes), allowing the retention curve to evolve during deformation. These models are essential when dealing with partially saturated soils and unsaturated flow processes.

3. Permeability Models

   Permeability models define the intrinsic permeability of the soil - a property that quantifies the ease with which a fluid can move through the pore network. This property reflects the size and connectivity of pores. It is a material property and does not depend on the fluid type. Note: Permeability should not be confused with hydraulic conductivity, which also includes fluid properties.

4. Relative Permeability Models

   In saturated soils, the hydraulic conductivity is often treated as constant. However, in unsaturated conditions, it can vary by several orders of magnitude depending on the degree of saturation. numgeo handles this variability using the concept of relative permeability, which modifies the intrinsic permeability based on the current saturation state. These models are particularly important in coupled analyses involving unsaturated flow.

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Each model family is explained in more detail in the respective sections.

• Mechanical Models

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  Govern the mechanical response of the soil, updating the (effective) stress \(\boldsymbol{\sigma}\) at time \(t = t_0 + \Delta t\)

  Read more...

• Hydraulic Models

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  Describe the soil-water retention behaviour

• Permeability Models

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  Define the intrinsic permeability of soils

• Relative Permeability Models

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  Consider the effect of saturation on the hydraulic conductivity