*5.2. Stress States*

With the iterative hydro-mechanical coupling, a stress tensor is computed in each cell of the basin model at each geological event. It represents the total stresses endured by the passive margin sediments during this event. In this study, we note *S* as this stress tensor, *X* the distality axis oriented from onshore to offshore, and *Z* the depth axis oriented downward. Consequently, *SXX* corresponds to the horizontal stress, *SZZ* to the vertical stress, and *SXZ* to the shear stress. We use the sign convention with positive compressive stresses. The stress tensor is then diagonalized to determine the principal stresses. We note *SMAX* the maximum principal stress and *SMIN* the minimum one. In addition, effective stresses are computed from total stresses and pore pressure values using Terzaghi's theory [101]. The resulting tensor is noted *S*.

We note *p* the confinement pressure, or average effective stress, computed from *S*:

$$p' = \frac{1}{3} \times (\mathcal{S}\prime\_{XX} + \mathcal{S}\prime\_{YY} + \mathcal{S}\prime\_{ZZ}) \tag{1}$$

With the confinement pressure, it is possible to isolate the deviatoric part *Q* of the effective stress tensor:

$$Q = S' - p' \times I \tag{2}$$

In rock mechanics, the multidimensional nature of the stress states is then commonly characterized by the equivalent deviatoric stress *q*, defined as follows:

$$q = \sqrt{\frac{3 \times Q \times Q}{2}}\tag{3}$$

The value of this equivalent stress is not necessarily meaningful on its own, and should be compared to the confinement pressure, notably in rock failure predictions. However, from a physical standpoint, a rise in deviatoric stress can be related to two phenomena: (1) development of shear stresses, leading to the rotation of the principal stress system, and (2) higher anisotropy in the principal stresses, leading to a more strongly extensional tectonic regime [102]. Consequently, in the following, we evaluate the significance of these two mechanical e ffects in our models and consider their variability through space and time, in relation to the lithology and geometry of the sediments deposited.

### 5.2.1. Shear Stress and Rotation of Principal Stresses

The shear stress in the present day simulated on the base case model is presented in Figure 4. The highest absolute values are concentrated in a deep area, located beneath the center of the continental slope. These values are quite moderate, as they do not exceed 3.5 MPa (Figure 4a). However, they appear much more significant when expressed as a ratio of the vertical e ffective stress. On the base case model, the shear stress in the present day represents up to 40% of the vertical e ffective stress (Figure 4b). The greatest ratios are simulated in the area of strongest shear but also in the inferior part of the overlying lowstand wedges, where the vertical e ffective stress is lowered by high overpressure.

**Figure 4.** Shear and rotation of principal stresses simulated on the base case scenario. (**a**) present-day shear: absolute values; (**b**) present-day shear: ratios of vertical effective stress; (**c**) overview of the rotation of the principal stress system through time from six geological events; vertical exaggeration × 2.

Shear stresses reflect on the local rotation of the principal stress system, measurable by the angle from vertical for the orientation of the maximal principal stress. Figure 4c presents these rotations in the margin sediments through geological time, as simulated on the base case model. Rotations up to 32◦ are observed. The highest rotation angles are found in the area of highest absolute shear, deep beneath the center of the continental slope. However, strong rotations are also simulated in much shallower areas, due to low vertical stresses and sloping geometries for the deposits. These shallow zones of principal stress rotation mostly appear downslope during the deposition of the lowstand system tracks, and upslope during the deposition of highstand system tracks.
