After completion of the packing test and determining the final aggregate gradation, the measured packing density and particle size volumes on each sieve size were used in the model to iteratively solve for K and 𝛽𝛽𝑚𝑚. This iterative process was continued until the sum of squared errors (SSE)
between measured and predicted packing density was minimized (Figure F2). The end result of the iterative process is the value of K that produces the best model fit since all other parameters are a function of K, ϕ, and aggregate size volume fractions which are all known parameters now. Figure F2 also shows the predicted and experimental packing densities for all packing tests performed on a particular aggregate type using a particular compaction method. The value of K for each aggregate type and compaction method pair is shown in Table F2. There were some combinations of aggregate type and compaction method that did not converge to a solution. For these combinations, values of K were iterated to 100 however the error did not converge to a minimum for reasonable values of K (Figure F3). Therefore, the K value was considered not applicable and no model fit was proposed for that combination of aggregate type and compaction method. This is likely caused by significant
aggregate breakdown and the model was not able to compensate for this additional packing by simply increasing the packing index (K).
(a) (b)
Figure 22. Error vs. Packing Index for Given Aggregate Type and Compaction Method (a) and Predicted vs. Experimental Packing Densities at K-value that Minimizes SSE for Given Aggregate
Type and Compaction Method (b).
(a) (b)
Figure 23. Error vs. Packing Index (a) and Predicted vs. Experimental Packing Density (b) at K=100 for Manufactured Sand compacted with Gyratory Compactor.
Table F2. Packing Index (K) as a Function of Aggregate Type and Compaction Method Aggregate Type Vibrating Table with Surcharge Weight Modified Proctor Gyratory Compactor
Coarse Dolomite 6.0 10.5 8.5
Trap Rock 4.3 7.5 7.1
River Gravel 7.1 15.8 7.5
Intermediate Dolomite 6.6 N/A* 9.0
Natural Sand 8.0 7.5 12.0
Manufactured Sand 6.7 N/A* N/A*
Average 6.4 10.3 8.8
*N/A signifies that the error did not converge to a minimum and therefore no packing index value could be assigned. These values were excluded from the average K-value determination for each compaction method.
From Table F2, it can be seen that the modified Proctor method of compaction resulted in higher values of packing index than the gyratory compactor, while the vibrating table with the surcharge weight typically led to the lowest packing indices. When using the values of packing index in Table F2 to predict packing density of a particular aggregate type using a particular compaction method, the average packing density error (absolute value) was 0.016. Figure F4 compares the experimental and predicted packing densities for all 320 packing tests performed when the final aggregate gradation was known and the appropriate K-value (Table F2) was used for each aggregate type and compaction method pair. There is good agreement between the two for a wide range of packing densities,
aggregate types, and compaction methods. The K values that minimized model error (Table F2) and the relationship between experimental and predicted packing densities (Figure F4) were developed based on the aggregate gradations after the packing tests were completed (called inverse model calibration here). Attempts were made to calibrate the model with the gradations before packing tests were conducted (Figure F5), which resulted in an average error (absolute value) in packing density of 0.031 (called forward model calibration here). The agreement between experimental and predicted packing densities in Figure F5 (correlation coefficient of 0.82) is not as good as that in Figure F4 (correlation coefficient of 0.96). The experimental and predicted packing densities for the vibrating table with surcharge method in Figure F5 show much better agreement than the other two compaction methods. The difference is likely related to the vibratory table breaks much less particles than the modified Proctor and gyratory compaction methods (Figure F6), and therefore results in a smaller change in the overall gradation. Broken particles (%) is defined as the percentage by weight of particles passing their initial sieve size (after compaction) to the initial weight of the aggregate
sample. A higher value of broken particles indicates a greater weight change in aggregate gradation from pre-compaction to post-compaction.
Figure 24. Comparison of All Predicted and Experimental Packing Densities based on Post-Packing Test Gradations.
Figure 25. Comparison of All Predicted and Experimental Packing Density based on Initial Packing Test Gradations.
The forward packing model (predicting packing density using initial gradation) is unable to account for significant aggregate breakage, since the final gradation is quite different from the initial gradation. However, using the inverse packing model (i.e. knowing the final, compacted gradation) produces much better results (Figure F4). Therefore, use of the model for forward prediction of aggregate packing for the gyratory and modified Proctor compaction methods was not reliable. Although the aggregate packing tests did not result in a comprehensive prediction model in its current functional form, they did reveal insight into the nature of aggregate packing in RCC compaction methods. Figure F6 shows that the modified Proctor compaction method breaks a significantly greater proportion of aggregates relative to the vibrating table and, to a lesser extent, the gyratory compactor. Both the gyratory compactor and modified Proctor compaction methods did result in greater packing densities than the vibrating table with surcharge weight (Figure F7). There was not a consistent trend in
packing density between modified Proctor and gyratory compaction. From Table F3, it can be seen that coarse Dolomite had a higher packing density than trap rock which is likely a result of the fact that Dolomite is a weaker aggregate and therefore fractured more easily to fill in voids. The river gravel produced higher packing densities than the intermediate Dolomite because of the rounded nature of the river gravel that reduces friction and adjacent particle interlock. There was not a consistent and significant difference in packing density of the natural and manufactured sands. Note, all packing tests were done with the aggregate type in the dry condition which definitely led to more particle breakage than would be seen in compacted RCC with any of the 3 compaction methods.
Table F3. Packing Density as a Function of Aggregate Type and Compaction Method Aggregate Type Vibrating Table with Surcharge Weight Modified Proctor Gyratory Compactor
Coarse Dolomite 0.55 0.70 0.64 Trap Rock 0.48 0.57 0.57 River Gravel 0.63 0.73 0.67 Intermediate Dolomite 0.55 0.69 0.62 Natural Sand 0.57 0.61 0.62 Manufactured Sand 0.56 0.65 0.68