Modified Cam-Clay Model for Large Stress Ranges and its Predictions for
Geological and Drilling Processes
Abstract
We modify the Modified Cam-Clay (MCC) model for large stress ranges
encountered in geological applications. The MCC model assumes that the
friction angle (ϕ) and the slope of the compression curve (λ) of a
mudrock are constant and thus predicts constant values for the lateral
effective stress ratio under uniaxial, vertical strain (K0) and
undrained strength ratio (S_u/(σ_v^’ )). However, experimental work
shows that λ, ϕ, and S_u/(σ_v^’ ) decrease and K0 increases
substantially with stress over large stress ranges (e.g., up to 100
MPa). We incorporate the stress dependency of λ and ϕ into the MCC model
and use the new model to predict S_u/(σ_v^’ ) and K0 ratios. The
modified model, with only one additional parameter, successfully
predicts the stress dependency of these ratios. We encode the modified
model and use it for finite-element analysis of a salt basin in the
deepwater Gulf of Mexico. The stresses that the new model predicts
around salt differ significantly from those predicted using the original
model. We incorporate the stress dependency of the friction angle into
the analytical models developed for critical tapers, wellbore drilling,
and the stability of submarine channel levees. We show that the decrease
of the friction angle with stress 1) results in a concave surface for
critical wedges, 2) shifts the drilling window to higher mud weights and
makes it narrower for a vertical wellbore, and 3) causes deep-seated
failure of submarine channel levees at lower angles. Our study could
improve in situ stress and pore pressure estimation, wellbore drilling,
and quantitative understanding of geological processes.