# Consideration of the Volumetric Changes that Accompany Rock Mass Failure

• Bre-Anne Louise Sainsbury
Technical Note

## Introduction

Some numerical modelling packages are able to calculate numerical solutions in both a large-strain and small-strain mode. In small-strain mode, grid-point co-ordinates are not updated during mechanical calculations; in large-strain mode, grid-point coordinates are constantly updated. The application of a small-strain mode is most useful when controlling boundary and applied conditions and large displacements are expected in relation to the grid size. As a result of the small-strain calculation mode, modification of the density and bulking/dilational behaviour of the rock mass during volumetric expansion is required to be considered as constitutive model behaviour. A summary of validated volumetric behaviours that can be used for large-deformational modelling in small-strain calculation mode is provided below.

## Rock Mass Constitutive Behaviour

### Density

Volumetric expansion of a rock mass can occur as a result of fracture, separation and rotation during dilation under shear...

## Keywords

Volumetric change Numerical model Small strain Constitutive behaviour

## List of symbols

$${\rho _{\text{d}}}$$

Dynamic rock mass density (kg/m3)

$${\rho _{\text{s}}}$$

Initial rock mass in situ density (kg/m3)

$$\eta$$

Porosity

$${\eta _{{\text{eqiv}}}}$$

Equivalent porosity

$${\eta _{{\text{max}}}}$$

Maximum porosity achieved by a rock mass. Default 0.4.

$${\varepsilon _{{\text{vsi}}}}$$

Volumetric strain increment

$${\varepsilon _{{\text{vsi(max)}}}}$$

Maximum volumetric strain achievable by a rock mass

Ψ

Dilation angle (degrees)

$${\psi _{{\text{dyn}}}}$$

Dynamic dilation angle (degrees)

ϕ

Friction angle (degrees)

$${\sigma _{{\text{ci}}}}$$

Intact Unconfined Compressive Strength (MPa)

$${\sigma _3}$$

Minor principal stress magnitude (MPa)

$${E_{{\text{dyn~}}}}$$

Dynamic deformation modulus (GPa)

$${E_{{\text{in}}\,{\text{situ}}}}$$

Initial peak in situ rock mass deformation modulus (MPa)

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