*3.1. Traditional Approaches*

Several methods are described in the literature to model the hydro-mechanical behavior of passive margin sediments. They can be sorted into two main families.

A first approach relies on slope stability analysis. It covers a range of methods of increasing complexity, including critical Coulomb wedge theory, infinite slope and limit analyzes, their combinations, and their extensions [45–51]. These methods use slope and pore pressure estimates to compute the shear stress and the rock strength, leading to a likelihood of failure for the wedge. However, they are often based on a strong idealization of the sedimentary stack, notably in terms of geometry, lateral facies variations, and overpressured layers [6]. In addition, this kind of modelling is essentially static. Even when it is implemented in a sequential manner, each time step remains independent from the previous ones, with no consideration of fluid flows and past stress states [52].

A second approach relies on basin simulation technologies [53–59]. From a representation of the basin at the present day, the evolution of its geometry through geological ages is restored with a backward process. Then, the physical variables of interest are computed for each geological event with a forward simulation using this geometrical framework. This methodology can handle a high degree of realism in the description of the sedimentary deposits, notably in terms of slope breaks, truncated layering, lateral lithological heterogeneities, and complex overpressure distribution. The resulting models are also intrinsically dynamic: the simulation results at a given geological age are strongly dependent on the flow and stress history of the margin, and they are also significantly impacted by the evolutive geometry previously restored [60].

Nonetheless, using basin simulation methodologies, it is classical to reduce the stress state to its sole vertical component, to overcome numerical complexity or absence of calibration data [56,57,61,62]. Implicitly, the contribution of lateral e fforts to porosity loss, fluid overpressure build-up and system instability is then estimated as marginal. Horizontal stresses are often considered as direct functions of the burial depth or simple ratios of the vertical stress. In the latter case, the ratios are homogenous in the sedimentary stack or solely variable with depth and lithology [57,63].

The limitations of the usual stress state simplification and their impact on hydro-mechanical simulation results have already been documented [64,65]. Notably, they can imply incorrect estimates for sediment compaction and rock failure likelihood. In a petroleum exploration context, this may produce misleading conclusions on cap rock integrity, migration flowpaths, and present-day overpressure. These observations motivated the design of several alternative methods aiming to better account for the 3D nature of the stress tensor [66,67]. Nevertheless, the focus is traditionally on basins overcoming important lateral tectonic solicitations, with large shortening or extension rates. As a result, the value of integrating non-vertical stresses in the modelling of passive geological settings appears more questionable, especially when considering the associated increase in computation costs. Basin modellers often deal with passive margin sediments as one-dimensional mechanical systems through geological ages [68–70], in line with simplistic models for horizontal stresses computation and the assumption that the maximal principal stress is perfectly aligned with the vertical axis [18].
