this is a very delicate topic, because both technical performances and work safety are involved.
First of all you must know geotechnical properties of the muck, grain size distribution, minerals, shape of fragments, moisture content, geometrical characteristics, local meteo and climatic conditions.
Then it is necessary to know the pile forming procedure (belt, dump, strata etc). Testing is necessary to know basic physical and geomechanical properties of muck forming the pile and surrounding area.
Loading machines act from the bottom of the piles and this is always a concern, not only for performance of the loader (this machine is selected on productivity issues) but also for evolution of stability.
Take great care and caution when dealing on this subject.
Your question is very generic. However many characteristics like angle of repose, loose denstity, pile distribution etc.
If I understood your question right you need a controlling muckpile characteristic that you can change to see its impact on machinery. If this is the question, muck pile size distribution is the only characteristic that can help you.
Now, How to measure it? Image analysis softwares (wipfrag/splitdesktop) help in quick size distribution. Another passive method will be using the your primary crusher flow rate correlation with particle size distribution.
You can incorporate as many parameters as you can and present their relationship to machine performance, but as a mining engineer I think only thing we can control is particle size distribution by better blast design.
Machine performance is again a very generic term, you want to evaluate it from which prospect etc.
For the repose angle and bulk density is not difficult. From a little conic pile, you can measure the perimeter, calculate the radius; measure the height and than calculate the angle. There are in literature some ways to determine bulk density. See:
Lopez, J.; Vercik, A.; Costa, E.J.X. Meios granulares e experimentos simples para a sala de aula. Rev. Brasileira de Ensino de Física, v.30, n.1. 2008.
Lopez, J.; Demarchi, T.; Akamatsu, M.; Vercik, A. Estudo comparativo de algumas propriedades dinâmicas de líquidos e grãos na sala de aula. Revista Brasileira de Ensino de Física, v.32, n.1. 2010.