16.2.2 Boyce Model

The model proposed by Boyce [11] describes the nonlinear elastic behavior of granular materials under repeated loading. The relationships between the isotropic and shear strain invariants and the hydrostatic and effective deviatoric stresses read

$$\begin{cases} \varepsilon _{\mathrm{v}} &= \dfrac{1}{K_{1}} ... ...\, G_{1}} \left( \dfrac{p}{p_{0}} \right)^{\!n-1} q \end{cases}$$ (16.12)

with the reference pressure p₀ with a value equal to -1 kPa and the reference values of the compression and shear moduli, K₁ and G₁ respectively. These reference values as well as the value of the power n are determined by experiments, with the factor $\beta$ given by (16.11).