<p>Using triangles enables high-fidelity DEM (discrete element model) simulation of granular materials with complex shapes, but processing the particle–particle interaction becomes a major computational bottleneck due to the huge number of triangles. The Energy-Conserving Contact Model (ECCM) calculates contact features from intersection segments, which accommodates both concave and convex polyhedral particles. However, efficient implementation strategies with multiple Graphics Processing Units (GPUs) in distributed super computers remain underexplored. As a result, existing polyhedral particle simulations are typically constrained to laboratory scale problems, limiting their applicability to industrial scale systems. This work proposes a DEM framework to enable scalable simulations of both concave and convex polyhedral particle systems by parallel computing with multiple GPUs. Performance is improved by the GPU-oriented data layout to store and communicate the polyhedral particles, the fine-grained parallelization for the contact pair, and the localization of contact detection and calculation by the local grid for each polyhedral particle. Validation and verification are conducted by experiments and simulations of differently shaped polyhedra in packing and rotating drum experiments. The proposed framework demonstrates excellent performance of parallel computing on up to 16 NVIDIA RTX 4090 GPUs, with nearly ideal linear weak scaling scalability when computing 2 × 10⁷ rock particles modelled by 1.2 × 10¹⁰ triangles and more than 80% strong scaling efficiency.</p>