Relationships between the compaction state and effective stresses are the basis for most quantitative pore-pressure and stress estimates. Common practice uses only a single element of the stress tensor, the vertical stress, for these calculations; mean stress formulations also exist, although they are less widely applied. Using simple models and field data from two distinct stress regimes, we examined the validity and limitations of the vertical-stress approach as well as a mean-stress approach, showing that in complex stress settings, both can perform very poorly. We evaluated a method for incorporating shear stresses into compaction relations by using state boundary surface (SBS) formulations from soil mechanics and demonstrated how the resulting model may be calibrated and applied to field data. This approach was found to perform much better in the complex stress environment, providing more stable calibration behavior and more reliably extrapolating to stress states beyond those present in the calibration data. Although vertical and mean stress compaction models may work well in simple stress environments, we discovered that incorporation of shear stress is necessary for models in complex stress settings. Although the addition of shear stress significantly improves agreement with field data, it also increases the complexity of the model as well as the requirements for calibration data. We therefore evaluated the settings in which each of these three approaches — vertical stress, mean stress, and SBS — may be most appropriate.

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