Constitutive damage model for foliated slate under dynamic loading

Foliated rock exhibits pronounced mechanical anisotropy due to inherent weaknesses along foliation planes. The orientation of these planes critically influences the dynamic mechanics of foliated rock, making it a key factor in the stability and safety of rock engineering projects. This research investigated the effects of foliation dip angle ( θ ), and strain rate ( ) on the dynamic mechanical behavior of the slate through dynamic unconfined compression tests using a split-Hopkinson pressure bar (SHPB). The experimental results indicate that increasing the strain rate enhances the material strength, leading to higher peak stress, greater energy absorption, and more extensive fracturing. Observations of the failure modes reveal that the orientation of foliation planes and strain rate significantly influence the failure modes. When the foliation planes are perpendicular to the axial load at θ = 0°, failure at low strain rates is mainly caused by stress wave reflection along the foliation planes. At high strain rates, the failure is dominated by impact-induced splitting. At oblique orientations ( θ = 30°, 45°, and 60°), increasing the dip angle causes a transition from axial splitting to shear failure along the foliation planes. When the foliation planes are parallel to the axial load ( θ = 90°), failure is entirely governed by tensile fracturing along the foliation planes. Based on the experimental results, a constitutive model is developed to characterize the influence of foliation dip angle and strain rates on dynamic mechanics of foliated rock. The model consists of micro-units characterized by an orientation factor ( D ) for foliation-induced anisotropy and a dynamic viscosity coefficient ( η ) for strain rate effects. The strength of micro-units follows a Weibull distribution, capturing the microstructural variability. Parameter sensitivity, calibration methods and model limitations are discussed in detail. Overall, this model provides a robust framework for understanding and predicting the dynamic mechanical behavior of foliated slate.