Predicting partial coordination numbers and contact proportions among different contact types is essential for developing theoretical models that link local contact characteristics to the macroscopic mechanical behavior of disordered multicomponent packings. The original Dodds model performs well for binary mixtures with small size ratios but has limited applicability to systems with large size ratios (α > 6.46). This study systematically analyzes the range of small-particle area fractions \(f_{s}\) over which the two-dimensional (2D) Dodds model remains valid for binary mixtures with α > 6.46 under gravity-free packing conditions. The results indicate the model provides reliable predictions when \(f_{s}\) exceeds the optimal value \(f_{s}^{{{\text{opt}}}}\) , which corresponds to the maximum packing density, but exhibits large errors when \(f_{s} < f_{s}^{{{\text{opt}}}}\) , where the discrepancies between the theoretical configuration and the actual packing structure become non-negligible. To address this limitation, a two-stage modification of the Dodds model is introduced. First, a portion of non-rattler small particles is distributed, followed by the redistribution of the remaining ones around the initially placed particles to approximate realistic local configurations. The modified contact statistics are then derived under simplified assumptions. Predictions from both the original and modified models are validated against discrete element method simulations for 2D dense binary assemblies with α = 7, 9, 12, and 16, and experimental data for α = 7, 9. The modified model improves predictions for α > 6.46 and \(f_{s} < f_{s}^{{{\text{opt}}}}\) , providing a framework for extending structural modeling approaches to multicomponent mixtures with large size ratios and to more complex three-dimensional systems.
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