Fabrice Golfier

Cyclic fluid pressurization can promote repeated fault reactivation and transient permeability changes, a behavior often discussed within the fault‐valve concept in which faults alternate between acting as hydraulic barriers and conduits. To investigate the micromechanical processes involved during fluid induced reactivations, we simulate cyclic fluid injection into a pre‐sheared granular gouge using a discrete element model. The simulations reproduce key behaviors observed in laboratory and in situ studies and reveal pronounced cycle‐to‐cycle variability in the onset of reactivation and slip magnitude. Some cycles generate large slip episodes, whereas others produce comparatively small slip under similar loading conditions. Micromechanical analysis of force‐chain evolution reveals a strong inverse correlation between slip magnitude and the population of load‐bearing chains, with sparser force‐chain backbones generating larger slip events. Our results highlight the role of micromechanical processes in controlling macroscopic cyclic fault behavior, offering a physically grounded perspective on fault‐valve behavior.

We study an optimal control problem motivated by the physical process of mixing a soluble substance into a viscous fluid, such as dissolving sugar in coffee by stirring with a spoon. The fluid motion is modeled by the incompressible Navier–Stokes equations, while the transport of the dissolved substance is described by an advection–diffusion equation. The control variable represents the imposed stirring action, modeled here as a distributed body force acting throughout the fluid domain. The objective is to achieve fast and efficient homogenization while minimizing the energetic cost of stirring. We first establish the well-posedness of the coupled system under suitable assumptions on the data and the control. Using the direct method of the calculus of variations, we prove the existence of at least one optimal control. Subsequently, we derive first-order necessary optimality conditions through an extended Lagrangian formalism, which yields a coupled system involving the primal state (velocity, pressure, and concentration) and the adjoint states. The gradient of the cost function is explicitly computed, providing the foundation for gradient-based optimization algorithms. Finally, we implement a gradient-based numerical method and validate it on a two-dimensional test case: for a localized concentration blob stirred by a physically bounded distributed force, the optimal control reduces the terminal spatial variance of the concentration by approximately 99% relative to the uncontrolled (purely diffusive) case, and by approximately 96% relative to a constant forcing of comparable energy. The influence of the regularization parameter on the temporal structure of the optimal forcing is also discussed. The proposed framework offers a rigorous and quantitatively validated approach for optimizing mixing processes in various industrial and natural applications.

In this paper, three simple test cases are presented to demonstrate the ability of the smoothed particle hydrodynamics (SPH) method to handle damage initiation and propagation in elastic solids, both with and without coupling to the fluid flow. In contrast to other approaches based on non-local damage models in the context of finite elements, SPH retains the local formulation of the damage model, while the non-local regularisation is achieved numerically by weighted interpolations. All governing equations for both fluid flow and solid mechanics with infinitesimal strain are discretised in the same SPH framework, together with a thermodynamics-based damage model with unilateral effects. This implementation is tested on a pre-cracked domain that is dynamically loaded in tension, leading to crack bifurcations or multiple bifurcations. It is shown that the number of secondary branches depends on the characteristic length h of the SPH method. For the case of a penny-shaped crack in a purely elastic medium loaded with a pressurised fluid, it is shown that the crack opening profile calculated with SPH is very close to the analytical quasi-static solution. Finally, a simple case of hydrofracking is simulated, and it is found that the critical fluid pressure required to initiate damage propagation is within 10% of the classical Griffith criterion. This paper concludes that the SPH method can be reliably used to simulate more complex phenomena, such as drainage within realistic pore geometries of Callovo-Oxfordian clay.

The peridotite massifs of New Caledonia are characterised by complex hydrodynamics influenced by intense inherited fracturing, uplift, and erosion. Following the formation of the erosion surfaces and alteration processes, these processes drive chemical redistribution during weathering; particularly lateritisation and saprolitisation. Magnesium, silica, and trace elements such as nickel and cobalt—released as the dissolution front advances—are redistributed through the system. New observations and interpretations reveal how lateritic paleo-land surfaces evolved, and their temporal relationship with alteration processes since the Oligocene. Considering the geometry of discontinuity networks ranging from micro-fractures to faults, the transfers occur in dual-permeability environments. Olivine dissolution rates are heterogeneously due to differential solution renewal caused by erosion and valley deepening. Differential mass transfer occurs between mobile regions of highly transmissive faults, while immobile areas correspond to the rock matrix and the secondary fracture network. The progression of alteration fronts controls the formation of boulders and the distribution of nickel across multiple scales. In the saprolite, nickel reprecipitates mostly in talc-like phases, as well as minor nontronite and goethite with partial diffusion in inherited serpentine. The current nickel distribution results from a complex interplay of climatic, hydrological and structural factors integrated into a model across different scales and times.