arXiv subjects

Brice Lecampion

Publications and source records attributed to Brice Lecampion.

17 recordsLinked to original sources

arXiv2026

Steadily moving semi-infinite fracture in plane poroelasticity

We present a boundary integral formulation for steadily propagating semi-infinite plane strain tensile and shear fractures in poroelastic media. By combining fundamental solutions of plane strain poroelasticity for an instantaneous fluid source and instantaneous edge dislocations (normal and slip modes) with temporal and spatial superposition principles, we derive boundary integral equations for steadily moving fractures under the adopted hydraulic boundary conditions. These equations relate the tractions (normal and shear stresses) and the pore fluid pressure on the fracture surfaces to the fracture opening, slip, and the fluid displacement function. Assuming prescribed traction and pore fluid pressure profiles, we develop a numerical methodology to solve the governing equations for fracture opening, slip, and the fluid displacement function. The formulation is systematically verified on several relevant problems, including a tensile fracture with exponential normal loading, a stress-free tensile fracture with an imposed exponential pore fluid pressure, and a shear fracture under uniform shear loading over a finite region, demonstrating excellent agreement with analytical and semi-analytical solutions. The resulting boundary integral framework provides an accurate and efficient tool for analyzing semi-infinite steadily propagating cracks in permeable poroelastic media. By supplementing the formulation with appropriate closure relations and additional physics, such as lubrication flow in hydraulic fractures or frictional strength evolution in shear fractures, it can be used to investigate a broad range of coupled fracture-fluid problems. The approach may also be adapted to other classes of elasto-diffusive problems by modifying the underlying physical parameters.

physics.geo-ph↗

arXiv2026

Three dimensional simulation of fluid-driven frictional and tensile ruptures on existing discontinuities

We present an implicit, fully-coupled hydro-mechanical solver for the three dimensional simulation of fluid-driven rupture propagation along existing discontinuities. The solver handles simultaneously frictional slip (shear failure) and tensile opening (hydraulic fracture) along arbitrary intersecting fractures and faults in a linearly elastic and impermeable rock matrix. The spatial discretization combines a collocation displacement discontinuity boundary element method for quasi-static elasticity with a Galerkin finite element method for nonlinear pore-fluid diffusion along the discontinuities. Frictional and tensile failure are governed by a poro-elastoplastic cohesive zone like interface law with slip-weakening friction, dilatancy, and tensile strength degradation, integrated via an elastic predictor-plastic corrector scheme. The strong nonlinear coupling between mechanical deformation and fracture permeability is handled via adaptive implicit time-stepping. Efficient block preconditioning of the coupled tangent system, leveraging hierarchical matrix representations of the boundary element operator, is essential to achieve robustness across the full range of fracture behaviors. Accuracy and convergence are demonstrated against a comprehensive suite of analytical and semi-analytical solutions of increasing complexity: fluid-driven frictional ruptures under constant and slip-weakening friction, dilatant ruptures with permeability changes, and penny shaped hydraulic fractures spanning the viscosity-to-toughness transition. The solver is further assessed on two multi-fracture configurations: injection into three intersecting fractures, and a height-confined hydraulic fracture intersecting a strike-slip fault. The proposed framework simultaneously captures frictional slip, dilatancy, permeability evolution, and tensile opening.

physics.geo-ph↗

arXiv2026

Modeling Utah FORGE 2022 EGS Hydraulic Stimulations: Tensile Hydraulic Fractures versus Fluid-Induced Dilatant Shear Ruptures

We investigate two hydraulic stimulation stages performed in April 2022 at the Utah FORGE enhanced geothermal system test site using analytical and numerical models for tensile hydraulic fractures and fluid-induced dilatant shear fractures. The two injection stages differ primarily by the viscosity of the fracturing fluid. Despite similar injection rate schedules and well-head pressure responses, the two stages exhibit markedly different post-shut-in microseismic behavior. The cross-linked gel stage shows sustained microseismic activity for several hours after shut-in, whereas the slickwater stage exhibits an immediate decrease. For the cross-linked gel stage, the located microseismic events reveal the development of a planar radial fracture and allow confident retrieval of the fracture extent evolution with time. We demonstrate that this evolution follows the scalings predicted for viscosity-storage-dominated radial hydraulic fracture by analytical models, providing strong evidence for the development of a planar tensile hydraulic fracture. We further show that leak-off is required to reproduce the fracture extent. In contrast, the immediate arrest observed during the slick-water stage suggests either a transition to a toughness- or leak-off-dominated hydraulic fracture regime, or the development of a fluid-induced shear fracture. We show that the slickwater stage could plausibly correspond to a dilatant shear fracture, provided sufficient dilatancy, whereas this hypothesis is invalidated for the cross-linked gel stage. We confirm these insights using a 3D axisymmetric fully-coupled hydro-mechanical numerical model capable of resolving both tensile and shear failure modes, and including leak-off. Finally, we propagate uncertainties in the in-situ stress state and natural fracture orientations through this numerical model to assess their impact on injection pressures.

physics.geo-ph↗

arXiv2025

FASTDASH: An Implementation of 3D Earthquake Cycle Simulation on Complex Fault Systems Using the Boundary Element Method Accelerated by H-matrices

Fault systems have geometrically complex structures in nature, such as stepovers, bends, branches, and roughness. Many geological and geophysical studies have shown that the geometrical complexity of fault systems in nature decisively influences the initiation, arrest, and recurrence of seismic and aseismic events. However, a vast majority of models of slip dynamics are conducted on planar faults due to algorithmic limitations. We develop a 3D quasi-dynamic slip dynamics model to overcome this restriction. The calculation of the elastic response due to slip is a matrix-vector multiplication in boundary element method, which can be accelerated by using hierarchical matrices. The computational complexity is reduced from the order of O(N^2) to O(N log N), where N is the number of degree of freedoms used. We validate our code with a static crack analytical solution and the SEAS benchmark/validation exercise from Southern California Earthquake Center. We further employ this method on a realistic fault system with complex geometry that was reactivated during the 2023 Kahramanmaras - Turkiye doublet earthquakes, generating slip sequences that closely match real observations.

physics.geo-ph↗

arXiv2024

A Parallelized 3D Geomechanical Solver for Fluid-induced Fault Slip in Poroelastic Media

We present a fully implicit formulation of coupled fluid flow and geomechanics for fluid injection/withdrawal in fractured reservoirs in the context of CO2storage. Utilizing a Galerkin finite-element approach, both flow and poroelasticity equations are discretized on a shared three-dimensional mesh. The fluid flow is assumed to be single-phase. The hydraulic behaviour of fractures is represented through a double-nodes flow element, which allows to efficiently model longitudinal and transversal fracture permeabilities. In addressing the mechanical subproblem, fractures are explicitly modelled using cohesive elements to account for contact, friction and opening phenomena. The nonlinear set of equations is solved implicitly through an iterative partitioned conjugate gradient procedure, extending its traditional application to continuous problems to those involving explicit discontinuities such as faults and fractures. The model's accuracy is verified against analytical solutions for different geomechanical problems, notably for the growth of a frictional slip rupture along a fault due to fluid injection. Such a particularly challenging benchmark for a critically stressed fault is here reproduced for the first time by a finite-element based scheme. The capabilities of the developed parallel solver are then illustrated through a scenario involving CO2 injection into a faulted aquifer. The original solver code, tutorials, and data visualization routines are publicly accessible.

physics.geo-ph↗

arXiv2024

Maximum size and magnitude of injection-induced slow slip events

Fluid injections can induce aseismic slip, resulting in stress changes that may propagate faster than pore pressure diffusion, potentially triggering seismicity at significant distances from injection wells. Constraining the maximum extent of these aseismic ruptures is thus important for better delineating the influence zone of injections concerning their seismic hazard. Here we derive a scaling relation based on rupture physics for the maximum size of aseismic ruptures, accounting for fluid injections with arbitrary flow rate histories. Moreover, based on mounting evidence that the moment release during these operations is often predominantly aseismic, we derive a scaling relation for the maximum magnitude of aseismic slip events. Our theoretical predictions are consistent with observations over a broad spectrum of event sizes, from laboratory to real-world cases, indicating that fault-zone storativity, background stress state, and injected fluid volume are key determinants of the maximum size and magnitude of injection-induced slow slip events.

physics.geo-ph↗

arXiv2024

The Energy Balance of a Hydraulic Fracture at Depth

We detail the energy balance of a propagating hydraulic fracture. Using the linear hydraulic fracture model which combines lubrication flow and linear elastic fracture mechanics, we demonstrate how different propagation regimes are related to the dominance of a given term of the power balance of a growing hydraulic fracture. Taking an energy point of view allows us to offer a physical explanation of hydraulic fracture growth behaviours, such as, for example, the transition from viscosity to toughness dominated growth for a radial geometry, fracture propagation after the end of the injection or transition to self-buoyant elongated growth. We quantify the evolution of the different power terms for a series of numerical examples. We also discuss the order of magnitudes of the different terms for a industrial-like hydraulic fracturing treatment accounting for the additional dissipation in the injection line.

physics.geo-ph↗

arXiv2023

Fluid-mediated impact of soft solids

A viscous, lubrication-like response can be triggered in a thin film of fluid squeezed between a rigid and flat surface and the tip of an incoming projectile. We develop a comprehensive theory for this viscous approach stage of fluid-mediated normal impact, applicable to soft impactors. Under the assumption of mediating fluid being incompressible, the impacting solid displays two limit regimes: one dominated by elasticity and the other by inertia. The transition between the two is predicted by a dimensionless parameter, which can be interpreted as the ratio between two time scales that are the time that it takes for the surface waves to warn the leading edge of the impactor of the forthcoming impact, and the characteristic duration of the final viscous phase of the approach. Additionally, we assess the role of solid compressibility and elucidate why nearly-incompressible solids feature (a) substancial "gliding" prior to contact at the transition between regimes, (b) the largest size of entrapped bubble between the deformed tip of the impactor and the flat surface, and (c) a sudden drop in entrapped bubble radius past the transition between regimes. Finally, we argue that the above time scale ratio (a dimensionless number) can govern the different dynamics reported experimentally for a fluid droplet as a function of its viscosity and surface tension.

cond-mat.soft↗

arXiv2023

Rock anisotropy promotes hydraulic fracture containment at depth

We report laboratory experiments and numerical simulations demonstrating that the anisotropic characteristics of rocks play a major role in the elongation of hydraulic fractures propagating in a plane perpendicular to bedding. Transverse anisotropy leads to larger hydraulic fracture extension in the parallel-to-bedding/divider direction compared to the perpendicular-to-bedding/arrester direction. This directly promotes vertical containment of hydraulic fractures in most sedimentary basins worldwide even in the absence of any favorable in-situ stress contrasts or other material heterogeneities. More importantly, the ratio of the energy dissipated in fluid viscous flow in the fracture to the energy dissipated in the creation of new surfaces is found to play a critical role on fracture elongation, with fracture-energy dominated hydraulic fractures being the most elongated while the viscous dominated ones remain more circular. These results open the door to a better engineering and control of hydraulic fractures containment at depth in view of the competition between material anisotropy and injection parameters (fluid viscosity and rate of injection).

physics.geo-ph↗

arXiv2023

Fluid-driven slow slip and earthquake nucleation on a slip-weakening circular fault

We investigate the propagation of fluid-driven fault slip on a slip-weakening frictional interface separating two identical half-spaces of a three-dimensional elastic solid. Our focus is on axisymmetric circular shear ruptures as they capture the most essential aspects of the dynamics of unbounded ruptures in three dimensions. In our model, fluid-driven aseismic slip occurs in two modes: as an interfacial rupture that is unconditionally stable, or as the quasi-static nucleation phase of an otherwise dynamic rupture. Unconditionally stable ruptures progress through four stages. Initially, ruptures are diffusively self-similar and the interface behaves as if it were governed by a constant friction coefficient equal to the static friction value. Slip then accelerates due to frictional weakening while the cohesive zone develops. Once the latter gets properly localized, a finite amount of fracture energy emerges along the interface and the rupture dynamics is governed by an energy balance of the Griffith's type. In this stage, fault slip transition from a large-toughness to a small-toughness regime. Ultimately, self-similarity is recovered and the fault behaves again as having a constant friction coefficient, but this time equal to the dynamic friction value. When slow slip is the result of a frustrated dynamic instability, slip also initiates self-similarly at a constant peak friction coefficient. The maximum aseismic rupture size varies from a critical nucleation radius (shear modulus divided by slip-weakening rate) to infinity near the limit that separates the two modes of aseismic sliding. We provide analytical and numerical solutions for the problem solved over its full dimensionless parameter space. Due to its three-dimensional nature, the model enables quantitative comparisons with field observations as well as preliminary engineering design of hydraulic stimulation operations.

cond-mat.soft↗

arXiv2023

Three-dimensional buoyant hydraulic fractures: finite volume release

In impermeable media, a hydraulic fracture can continue to expand even without additional fluid injection if its volume exceeds the limiting volume of a hydrostatically loaded radial fracture. This limit depends on the mechanical properties of the surrounding solid and the density contrast between the fluid and the solid. Self-sustained fracture growth is characterized by two dimensionless numbers. The first parameter is a buoyancy factor that compares the total released volume to the limiting volume to determine whether buoyant growth occurs. The second parameter is the dimensionless viscosity of a radial fracture at the time when buoyant effects become of order 1. This dimensionless viscosity notably depends on the rate at which the fluid volume is released, indicating that both the total volume and release history impact self-sustained buoyant growth. Six well-defined propagation histories can be identified based on these two dimensionless numbers. Their growth evolves between distinct limiting regimes of radial and buoyant propagation, resulting in different fracture shapes. We can identify two growth rates depending on the dominant energy dissipation mechanism (viscous flow vs fracture creation) in the fracture head. For finite values of material toughness, the toughness-dominated limit represents a late-time solution for all fractures in growth rate and head shape (possibly reached only at a very late time). The viscosity-dominated limit can appear at intermediate times. Our three-dimensional simulations confirm the predicted scalings and highlight the importance of considering the entire propagation and release history for accurate analysis of buoyant hydraulic fractures.

physics.flu-dyn↗

arXiv2022

Injection-induced aseismic slip in tight fractured rocks

We investigate the problem of fluid injection at constant pressure in a 2D Discrete Fracture Network (DFN) with randomly oriented and uniformly distributed frictionally-stable fractures. We show that this problem shares similarities with the simpler scenario of injection in a single planar shear fracture, investigated by Bhattacharya and Viesca (2019); Viesca (2021) and whose results are here extended to include closed form solutions for aseismic moment as function of injected volume Vinj. Notably, we demonstrate that the hydro-mechanical response of the fractured rock mass is at first order governed by a single dimensionless parameter T associated with favourably oriented fractures: low values of T (critically stressed conditions) lead to fast migration of aseismic slip from injection point due to elastic stress transfer on critically stressed fractures. In this case, therefore, there is no effect of the DFN percolation number on the spatio-temporal evolution of aseismic slip. On the other hand, in marginally pressurized conditions (T > 1), the slipping patch lags behind the pressurized region and hence the percolation number affects to a first order the response of the medium. Furthermore, we show that the aseismic moment scales Vinj^2 in both limiting conditions, similarly to the case of a single planar fracture subjected to the same injection condition. The factor of proportionality, however, depends on the DFN characteristics in marginally pressurized conditions, while it appears to be only mildly dependent on the DFN properties in critically stressed conditions.

physics.geo-ph↗

arXiv2022

Post-injection aseismic slip as a mechanism for the delayed triggering of seismicity

Injection-induced aseismic slip plays an important role in a broad range of human-made and natural systems, from the exploitation of geo-resources to the understanding of earthquakes. Recent studies have shed light on how aseismic slip propagates in response to continuous fluid injections. Yet much less is known about the response of faults after the injection of fluids has stopped. In this work, we investigate via an hydro-mechanical model the propagation and ultimate arrest of aseismic slip during the so-called post-injection stage. We show that after shut-in, fault slip propagates in pulse-like mode. The conditions that control the propagation as a pulse and notably when and where the ruptures arrest are fully established. In particular, critically-stressed faults can host rupture pulses that propagate for several orders of magnitude the injection duration and reach up to nearly double the size of the ruptures at the moment of shut-in. We consequently argue that the persistent stressing of increasingly larger rock volumes caused by post-injection aseismic slip is a plausible mechanism for the triggering of post-injection seismicity -- a critical issue in the geo-energy industry. We discuss evidence that supports this mechanism based on documented cases of post-injection-induced seismicity.

physics.geo-ph↗

arXiv2020

Propagation of a plane-strain hydraulic fracture accounting for a rough cohesive zone

The quasi-brittle nature of rocks challenges the basic assumptions of linear hydraulic fracture mechanics (LHFM): linear elastic fracture mechanics and smooth parallel plates lubrication fluid flow. We relax these hypotheses and investigate the growth of a plane-strain hydraulic fracture in an impermeable medium accounting for a rough cohesive zone and a fluid lag. In addition to a dimensionless toughness and the time-scale of coalescence of the fluid and fracture fronts as in the LHFM case, the solution now also depends on the in-situ-to-cohesive stress ratio and the intensity of the flow deviation induced by aperture roughness. The solution is appropriately described by a nucleation time-scale, which delineates the fracture growth into a nucleation phase, an intermediate stage and a late time stage where convergence toward LHFM predictions finally occurs. A highly non-linear hydro-mechanical coupling takes place as the fluid front enters the rough cohesive zone which itself evolves during the nucleation and intermediate stages. This coupling leads to significant additional viscous flow dissipation. As a result, the fracture evolution deviates from LHFM solutions with shorter fracture lengths, larger widths and net pressures. These deviations ultimately decrease at late times as the lag and cohesive zone fractions both become smaller. The deviations increase with larger dimensionless toughness and in-situ-to-cohesive stress ratio, as both further localize viscous dissipation near the fluid front located in the rough cohesive zone. The convergence toward LHFM can occur at very late time for realistic values of in-situ-to-cohesive stress ratio encountered at depth. The impact of a rough cohesive zone appears to be prominent for laboratory experiments and short in-situ injections in quasi-brittle rocks with ultimately a larger energy demand compared to LHFM predictions.

physics.flu-dyn↗

arXiv2020

PyFrac: A planar 3D hydraulic fracture simulator

Fluid driven fractures propagate in the upper earth crust either naturally or in response to engineered fluid injections. The quantitative prediction of their evolution is critical in order to better understand their dynamics as well as to optimize their creation. We present a Python implementation of an open-source hydraulic fracture propagation simulator based on the implicit level set algorithm originally developed by Peirce & Detournay (2008) -- "An implicit level set method for modeling hydraulically driven fractures". Comp. Meth. Appl. Mech. Engng, (33-40):2858--2885. This algorithm couples a finite discretization of the fracture with the use of the near tip asymptotic solutions of a steadily propagating semi-infinite hydraulic fracture. This allows to resolve the multi-scale processes governing hydraulic fracture growth accurately, even with relatively coarse meshes. We present an overview of the mathematical formulation, the numerical scheme and the details of our implementation. A series of problems including a radial hydraulic fracture verification benchmark, the propagation of a height contained hydraulic fracture, the lateral spreading of a magmatic dyke and the handling of fracture closure are presented to demonstrate the capabilities, accuracy and robustness of the implemented algorithm.

cs.CE↗

arXiv2020

Time-lapse reconstruction of the fracture front from diffracted waves arrivals in laboratory hydraulic fracture experiments

4D acoustic imaging via an array of 32 sources / 32 receivers is used to monitor hydraulic fracture propagating in a 250~mm cubic specimen under a true-triaxial state of stress. We present a method based on the arrivals of diffracted waves to reconstruct the fracture geometry (and fluid front when distinct from the fracture front). Using Bayesian model selection, we rank different possible fracture geometries (radial, elliptical, tilted or not) and estimate model error. The imaging is repeated every 4 seconds and provide a quantitative measurement of the growth of these low velocity fractures. We test the proposed method on two experiments performed in two different rocks (marble and gabbro) under experimental conditions characteristic respectively of the fluid lag-viscosity (marble) and toughness (gabbro) dominated hydraulic fracture propagation regimes. In both experiments, about 150 to 200 source-receiver combinations exhibit clear diffracted wave arrivals. The results of the inversion indicate a radial geometry evolving slightly into an ellipse towards the end of the experiment when the fractures feel the specimen boundaries. The estimated modelling error with all models is of the order of the wave arrival picking error. Posterior estimates indicate an uncertainty of the order of a millimeter on the fracture front location for a given acquisition sequence. The reconstructed fracture evolution from diffracted waves is shown to be consistent with the analysis of $90^{\circ}$ incidence transmitted waves across the growing fracture.

physics.geo-ph↗

arXiv2014

Confined flow of suspensions modeled by a frictional rheology

We investigate in detail the problem of confined pressure-driven laminar flow of neutrally buoyant non-Brownian suspensions using a frictional rheology based on the recent proposal of Boyer et al., 2011. The friction coefficient and solid volume fraction are taken as functions of the dimensionless viscous number I defined as the ratio between the fluid shear stress and the particle normal stress. We clarify the contributions of the contact and hydrodynamic interactions on the evolution of the friction coefficient between the dilute and dense regimes reducing the phenomenological constitutive description to three physical parameters. We also propose an extension of this constitutive law from the flowing regime to the fully jammed state. We obtain an analytical solution of the fully-developed flow in channel and pipe for the frictional suspension rheology. The result can be transposed to dry granular flow upon appropriate redefinition of the dimensionless number I. The predictions are in excellent agreement with available experimental results, when using the values of the constitutive parameters obtained independently from stress-controlled rheological measurements. In particular, the frictional rheology correctly predicts the transition from Poiseuille to plug flow and the associated particles migration with the increase of the entrance solid volume fraction. We numerically solve for the axial development of the flow from the inlet of the channel/pipe toward the fully-developed state. The available experimental data are in good agreement with our predictions. The solution of the axial development of the flow provides a quantitative estimation of the entrance length effect in pipe for suspensions. A analytical expression for development length is shown to encapsulate the numerical solution in the entire range of flow conditions from dilute to dense.

cond-mat.soft↗