When estimating the magnitude of horizontal stresses, elastic properties are often assumed constant over geologic time. In addition, the successive build-up of a formation and its burial history are often not considered despite playing an important role. In this paper, 2D finite element analysis is used to model the successive build-up of a formation with visco-elastic material that hardens with depth. Zero lateral strain and extensional lateral strain boundary conditions are explored. In all cases horizontal stresses are lower than vertical stress. Effective stress ratios are elevated in visco-elastic cases compared to elastic reference cases.

The ability of a visco-elastic material to dissipate deviatoric stresses may cause variations in effective stress ratios imposed by layers with different Poisson’s ratios to be much less pronounced than in corresponding linear elastic models. Extensional lateral strain boundary conditions lead to further reduced vertical to horizontal effective stress ratios because of reduced lateral confinement. These two mechanisms, viscous relaxation, which equalizes stress, and extensional lateral strain, which decreases horizontal stress, may operate simultaneously to determine the resulting magnitude of horizontal stress and of effective stress ratio. Depending on the stress regime, they may work in concert with or in opposition to each other. In the cases considered here, variations in horizontal stress magnitudes are smaller than predicted by linear elastic models, and thus hydraulic fractures may be less confined within low-stress intervals than customarily predicted.


Estimates of horizontal stress magnitudes are often based on elastic properties under the assumption that present-day geometry and material properties are constant over time. In many cases, estimates of horizontal stress magnitudes do not completely agree with simple predictive theory. For a formation in a normal faulting environment in the Gulf of Mexico, in-situ effective stress data does not correlate with previously published fracture gradient models [1]. Instead, the effective stress ratio appears to be bound on the lower end by K=0.33, which corresponds to a Coulomb failure coefficient of µ=0.60, and on the higher end by K=1, which represents the isotropic stress limit. The differences likely result from a combination of effects such as a complicated burial history (e.g., [2]), time-dependent tectonic forces, pore pressure variations due to fluid migration, visco-plastic deformation (e.g., [3]), diagenesis and viscous relaxation (e.g., [4]).

As material is deposited in a sedimentary basin and subsequently buried, material parameters change with time or, equivalently, depth. In a simple deposition and burial scenario the most recent deposits, e.g. unconsolidated sands in an oceanic basin, can effectively dissipate differential stresses by viscous creep. As material subsides to greater depth and becomes increasingly compacted, it effectively hardens and loses the ability to deform viscously. This paper presents tests of how viscous relaxation and depth-dependent hardening during the formation of a sedimentary basin can influence resulting horizontal stress magnitudes.

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