Abstract
Rockfall is a natural hazard that needs to be rigorously managed along all the major road and railways transport networks by identifying the most appropriate mitigation measures. There has been significant progress in rockfall modelling and rockfall protection systems in recent years but there remains one aspect that is not very well understood and quite challenging to account for in the design of rockfall protection structures, namely the fragmentation of falling blocks upon impact. Rocks often break up upon impact, which leads to a change in size, shape and energy of falling blocks, parameters that affect the design of the protective structures. Before being able to incorporate fragmentation into predictive trajectory models, it is required to better understand the fragmentation process and its likely outcome (number, volume of fragments and their trajectories). To that aim, an innovative experimental setup was developed at the University of Newcastle (Australia) to study rock fragmentation upon impact. The setup was designed to perform controlled vertical drop tests and record the following impact parameters: impact force, impulse, impact duration, velocities (of the block before impact and its fragment after impact) and all components of energy, pre and post impact. Six views (four high-speed cameras and two mirrors) are used for an accurate reconstruction of the 3D trajectory of blocks and fragments, in translation and rotation. This paper presents the validation of the setup via two series of drop tests using mortar spheres. Attention was focused on the evaluation of impact force and impulse from load cells placed under the impacted surface, tracking of translational and rotational velocity and the computation of total kinetic energy (before and after impact) and all components of energy dissipation. The results confirm that the experimental setup and the approach developed can be used to obtain impact force, impulse and to compute the energy balance during the impact and fragmentation and conduct advanced fragmentation testing.
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Abbreviations
- AC:
-
Accelerometer
- \({A}_{j}\) :
-
Area of new surfaces generated by fragmentation
- \(c\) :
-
Dimensional viscosity damping coefficient
- \({Co{R}}_{\text{theo}}\) :
-
Theoretical coefficient of restitution for elastic-perfectly plastic sphere impacting a plane surface
- \({Co{R}}_{\text{exp}}\) :
-
Experimental coefficient of restitution
- \(Co{R}_{w}\) :
-
Coefficient of restitution for elastic wave propagation
- \( {E}_{{k}_{\text{tot}}}^{b}, {E}_{{k}_{\text{tot}}}^{a}\) :
-
Total kinetic energy before and after impact
- \({E}_{{k}_{t}}^{b}, {E}_{{k}_{t}}^{a}\) :
-
Translational component of kinetic energy before and after impact
- \({E}_{{k}_{r}}^{b}, {E}_{{k}_{r}}^{a}\) :
-
Rotational component of kinetic energy before and after impact
- \(f\) :
-
Impact force frequency
- \({f}_{d}\) :
-
Damped natural frequency
- \({f}_{n}\) :
-
Undamped natural frequency
- \(F\) :
-
External force applied to the system
- \({F}_{1}, {F}_{2}, {F}_{3}\) :
-
Forces recorded from the three load cells under the slab
- \({F}_{\text{max}}\) :
-
Force of maximum compression
- \({F}_{T}\) :
-
Transmitted force—sum of the three forces recorded from the load cells
- \({F}_{\text{imp}}\) :
-
Estimated impact force
- \({F}_{\text{imp,LC}}\) :
-
Impact force recorded from the top load cell
- \({h}_{s}\) :
-
Thickness of the slab
- \({I}_{I}, {I}_{II}, {I}_{III}\) :
-
Moments of inertia for the principal axes
- \(J\) :
-
Estimated impulse
- \({J}_{LC}\) :
-
Impulse computed using top load cell data
- \(k\) :
-
Stiffness of the system composed by the slab and three bottom load cells
- \({K}_{Ic}\) :
-
Fracture toughness
- LC1, LC2, LC3:
-
Load cells
- \(m\) :
-
Mass of the sphere
- m i :
-
Mass of fragment i
- \({m}_{\mathrm{s}}\) :
-
Mass of the slab
- \({R}_{1}, {R}_{2}\) :
-
Radius of the sphere and the slab
- \(\tilde{R }\) :
-
Equivalent radius
- S1, S2:
-
Series of drop tests
- \(t\) :
-
Time
- \({v}_{i}\) :
-
Absolute translational velocity of fragment i
- \({v}_{\text{imp}}\) :
-
Impact velocity
- \({v}_{p}\) :
-
Propagation velocity of quasi-longitudinal waves in the slab
- \({v}_{y}\) :
-
Yield velocity
- V1, V2, V3, V4:
-
Physical viewpoints
- V5, V6:
-
Virtual viewpoints
- \({Y}_{1}, {Y}_{2}\) :
-
Young’s modulus of the sphere and the system
- \(\tilde{Y }\) :
-
Equivalent Young’s modulus
- \(z, \dot{z},\ddot{z}\) :
-
Displacement, velocity and acceleration of the slab
- \({z}_{\text{max}}\) :
-
Max displacement of the slab
- \(\alpha\) :
-
Main angle of rotation
- \(\beta\) :
-
Non-dimensional viscous damping coefficient
- \(\gamma\) :
-
Surface energy per unit area
- \(\Delta {E}_{d}\) :
-
Energy loss in deformation
- \(\Delta {E}_{fr}\) :
-
Energy loss to create the fracture surfaces
- \( \Delta {E}_{\text{slab}}\) :
-
Energy loss associated to the elastic displacement of the slab
- \(\Delta {E}_{\text{tot}}\) :
-
Total energy loss associated with the impact
- \(\Delta {E}_{w}\) :
-
Energy loss in elastic wave propagation
- \(\Delta {t}_{\text{imp}}\) :
-
Measurement of the direct impact duration by the pressure sensor
- \(\Delta {t}_{\text{imp,LC}}\) :
-
Measurement of the direct impact duration by the load cell top
- \(\Delta {t}_{T}\) :
-
Transmitted impact duration recorded from the load cells under the slab
- \({\vartheta }_{y}\) :
-
Ratio of mean indentation pressure (assumed fully plastic) to uniaxial yield stress
- \(\lambda\) :
-
Inelasticity parameter
- \({\nu }_{1},{\nu }_{2}\) :
-
Poisson’s ration of the sphere and the slab
- \({\rho }_{1},{\rho }_{2}\) :
-
Density of the sphere and the slab
- \({\sigma }_{c}\) :
-
Unconfined compressive strength
- \({\sigma }_{t}\) :
-
Tensile strength
- \({\sigma }_{y}\) :
-
Yield stress of the impacting material (sphere)
- \({\omega }_{{I}_{i}},{\omega }_{I{I}_{i}},{\omega }_{II{I}_{i}}\) :
-
Rotational velocities around the 3 principal axes of fragment i
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Acknowledgements
The authors would like to acknowledge the financial support of ARC DP160103140, the support of the technical staff at the Civil Engineering laboratory at the University of Newcastle and the help received from Michele Spadari, Toma Canessi, Nathan Fourcade and Giuseppina Ciccone in developing the setup.
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Guccione, D.E., Thoeni, K., Fityus, S. et al. An Experimental Setup to Study the Fragmentation of Rocks Upon Impact. Rock Mech Rock Eng 54, 4201–4223 (2021). https://doi.org/10.1007/s00603-021-02501-3
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DOI: https://doi.org/10.1007/s00603-021-02501-3