Abstract Hydraulic‐test interpretation in fractured rock commonly assumes impermeable confining matrices, an assumption we show is systematically incorrect, even when the matrices are 7–14 orders of magnitude less permeable than the fracture. Fluid injected into a fracture begins to leak into the surrounding rock matrices within milliseconds to seconds, causing the slope of the pressure evolution with respect to the logarithm of time to halve, equivalent to a factor‐of‐two overestimation of fracture transmissivity if leakage is neglected. Here, we investigate the flow regimes induced by constant flow rate water injection into a fracture surrounded by low‐permeability matrices and the implications for hydraulic‐test interpretation. We find that even for a low‐permeability confining rock matrix, leakage is non‐negligible on the pressure evolution due to the small fracture aperture, which leads to a large pressure gradient between the fracture and matrix. Negligible leakage exists only for an extremely short period, and then a transient flow regime arises with a slope of −1/4 in the log‐log derivative plot, that is, flow dimension equal to 2.5. Subsequently, the flow regime becomes radial, with the slope of pressure evolution in a semi‐log plot corresponding to that of a leaky aquifer, that is, twice the actual fracture transmissivity. We validate this finding against step‐rate injection data from the Bedretto Underground Laboratory, for which only the model accounting for matrix leakage reproduces the measured pressure evolution. As a result, one could mistakenly overestimate the fracture transmissivity in injection tests in fractured media if the leaky nature of fractures is not considered.

Coupled thermo-hydro-mechanical (THM) processes in fractured rock are playing a crucial role in geoscience and geoengineering applications. Diverse and conceptually distinct approaches have emerged over the past decades in both continuum and discontinuum perspectives leading to significant progress in their comprehending and modeling. This review paper offers an integrated perspective on existing modeling methodologies providing guidance for model selection based on the initial and boundary conditions. By comparing various models, one can better assess the uncertainties in predictions, particularly those related to the conceptual models. The review explores how these methodologies have significantly enhanced the fundamental understanding of how fractures respond to fluid injection and production, and improved predictive capabilities pertaining to coupled processes within fractured systems. It emphasizes the importance of utilizing advanced computational technologies and thoroughly considering fundamental theories and principles established through past experimental evidence and practical experience. The selection and calibration of model parameters should be based on typical ranges and applied to the specific conditions of applications. The challenges arising from inherent heterogeneity and uncertainties, nonlinear THM coupled processes, scale dependence, and computational limitations in representing field scale fractures are discussed. Realizing potential advances on computational capacity calls for methodical conceptualization, mathematical modeling, selection of numerical solution strategies, implementation, and calibration to foster simulation outcomes that intricately reflect the nuanced complexities of geological phenomena. Future research efforts should focus on innovative approaches to tackle the hurdles and advance the state-of-the-art in this critical field of study.

Hydraulic stimulation of Enhanced Geothermal Systems (EGS) aims at boosting permeability to facilitate fluid circulation, while keeping a low induced seismicity. However, some stimulations have led to poor permeability enhancement or too high induced earthquakes, which suggests that further understanding is needed on poromechanical processes during stimulation. Here, we model a highly-monitored test performed at the Bedretto Underground Laboratory to investigate the impact of fluid injection on permeability enhancement and induced microseismicity. We examine three models: (1) a homogeneous fracture whose transmissivity is manually calibrated to reproduce the observed pressure evolution at the injection borehole (this model fails to capture the spatial distribution of pressure and the corresponding poromechanical processes); (2) an elastic fracture approach, where transmissivity changes locally as a function of fracture aperture following the cubic law (this model overestimates pressure after the onset of fracture slip); and (3) a viscoplastic fracture approach with strain weakening and dilatancy that yields an additional permeability enhancement after shear reactivation. The viscoplastic model captures the spatio-temporal coupled response of the fractured rock to hydraulic stimulation before and after shearing both in terms of pressure and microseismicity. Subsequently to the onset of shear failure, microseismic events occur in every injection cycle as the reactivation front advances when plastic strain and, thus, permeability surpass the previously achieved maximum value. This viscoplastic model permits estimating the extent of the stimulated fracture, the permeability enhancement and its impact on the local state of stress and pore pressure at surrounding fractures, representing a useful tool for the design of effective hydraulic stimulation.

To harness the immense potential of geothermal energy for non-intermittent baseload power, low-permeability crystalline hot rocks need to be hydraulically stimulated to create Enhanced Geothermal Systems (EGS) that enable economically profitable fluid flow rates. However, hydraulic stimulation is usually associated with seismic activity that has led to project cancellation in a few occasions. To improve our understanding of the coupled hydro-mechanical (HM) processes behind stimulation during both injection and post-injection stages (after shut-in), we numerically analyze three different stimulation protocols: constant-rate, step-rate, and cyclic injection with and without bleed-off after shut-in (and between cycles for the cyclic protocol). Simulation results show that the injection protocol has a higher influence on the HM response of the fracture than the total volume of injected water, which challenge scaling laws that relate the injection volume with the expected maximum magnitude of the induced earthquakes. The trade-off between maximizing permeability enhancement, while minimizing induced seismicity is not straightforward. In particular, bleeding-off the well after injection restricts induced seismicity, but at the expenses of limiting permeability enhancement. When considering stimulation of a single fault, all protocols yield comparable slip rates and, thus, magnitude of the induced earthquake, with the constant-rate injection being the fastest to induce the largest earthquake. The small differences in the HM response to hydraulic stimulation do not permit identifying a protocol that performs better than the others.

Fractures control fluid flow, solute transport, and mechanical deformation in crystalline media. They can be modeled numerically either explicitly or implicitly via an equivalent continuum. The implicit framework implies lower computational cost and complexity. However, upscaling heterogeneous fracture properties for its implicit representation as an equivalent fracture layer remains an open question. In this study, we propose an approach, the Equivalent Fracture Layer (EFL), for the implicit representation of fractures surrounded by low-permeability rock matrix to accurately simulate hydromechanical coupled processes. The approach assimilates fractures as equivalent continua with a manageable scale (>> 1 mu m) that facilitates spatial discretization, even for large-scale models including multiple fractures. Simulation results demonstrate that a relatively thick equivalent continuum layer (in the order of cm) can represent a fracture (with aperture in the order of mu m) and accurately reproduce the hydromechanical behavior (i.e., fluid flow and deformation/stress behavior). There is an upper bound restriction due to the Young's modulus because the equivalent fracture layer should have a lower Young's modulus than that of the surrounding matrix. To validate the approach, we model a hydraulic stimulation carried out at the Bedretto Underground Laboratory for Geosciences and Geoenergies in Switzerland by comparing numerical results against measured data. The method further improves the ability and simplicity of continuum methods to represent fractures in fractured media.

Geo-energies, such as geothermal energy, geologic carbon storage, and subsurface energy storage, will play a relevant role in reaching carbon neutrality and allowing net-carbon removal towards the midcentury. Geo-energies imply fluid injection into and/or production from the subsurface, which alter the initial effective stress state and may destabilize fractures and faults, thereby inducing seismicity. Understanding the processes that control induced seismicity is paramount to develop reliable forecasting tools to manage induced earthquakes and keep them below undesired levels. Accurately modeling the processes that occur during fracture/fault slip leading to induced seismicity is challenging because coupled thermo-hydro-mechanical-chemical (THMC) processes interact with each other: (1) fluid injection causes pore pressure buildup that changes total stress and deforms the rock, (2) deformation leads to permeability changes that affect pore pressure diffusion, (3) fluids reach the injection formation at a colder temperature than that of the rock, which cools down the vicinity of the well, causing changes in the fluid properties (density, viscosity, enthalpy, heat capacity) and cooling-induced stress reduction, (4) the injected fluids are not in chemical equilibrium with the host rock, leading to geochemical reactions of mineral dissolution/precipitation that may alter rock properties, in particular, the shear strength. In the framework of GEoREST (www.georest.eu), a Starting Grant from the European Research Council (ERC), we aim at developing forecasting tools for injection-induced seismicity by developing methodologies to efficiently simulate the coupled THMC processes that occur as a result of fluid injection, which allows us to improve the understanding of the mechanisms that trigger induced seismicity. To this end, we use the fully coupled finite element method software CODE_BRIGHT, which includes capabilities like friction following the Mohr-Coulomb failure criterion with strain weakening and dilatancy, enabling simulations of fracture/fault reactivation. Our investigations have already contributed to the understanding of the processes that induced the seismicity at the Enhanced Geothermal System (EGS) at Basel, Switzerland, at the Castor Underground Gas Storage, Spain, and the reservoir-induced seismicity at Nova Ponte, Brazil. To achieve scalability and speed up the calculations to eventually manage induced seismicity in real time, we intend to incorporate efficient state-of-the-art linear solvers, like HYPRE and PETSc, in CODE_BRIGHT.

Fractures control fluid flow and the coupled geomechanical response of geological media in many geo-engineering applications. For instance, fractures dominate fluid flow and deformation in enhanced geothermal systems, underground radioactive waste repositories, and CO2 storage. Coupled thermo-hydro-mechanical processes in rock masses are a result of perturbations in the pore pressure, as in fluid injection and/or production, and/or temperature, as in cold fluid injection and disposal of radioactive waste. For example, fractures open as a result of pore pressure increase, which simultaneously increases permeability and reduces overpressure. Geo-engineering and geo-energy applications involve a large portion of rock masses that include several fractures. Numerical computations of coupled processes occurring in rock masses while considering a large number of fractures pose several challenges. In this study, we firstly focus on a simple problem to fully understand the hydro-mechanical behavior of a single fracture subjected to a constant injection flow rate. We use the FEM software CODE_BRIGHT, which solves the thermo-hydro-mechanical governing equations in a fully coupled way. Since standard FEM can solve equations in continuum media, we investigate the behavior of a single fracture by analyzing the hydro-mechanical parameters that control the fracture response in a continuum fashion. However, simulating fractures with the real aperture is not simply feasible, hence, we search the equivalent properties of thicker fractures that are more feasible to be discretized in large-scale models with several fractures. As the pore pressure increases inside a fracture, the fracture aperture increases and enhances its transmissivity. The embedded model uses variable permeability as a function of the cubic law. The simulation results show that a continuum approach can represent a fracture with a relatively large thickness (in the cm order) instead of the real aperture dimension (in the order of the micron).

The authors acknowledge funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Program through the Starting Grant GEoREST (www.georest.eu) (Grant agreement No. 801809).

The authors acknowledge funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Program through the Starting Grant GEoREST (www.georest.eu) (Grant agreement No. 801809).

Contamination of soil and underground waters is a common environmental problem. Arsenic is a toxic chemical used widely in chemical industrial applications. New methods such as solidification/stabilization developed as requiring much space and propagation of materials in primary treatment methods caused interim methods for disposal of contamination to become inappropriate. The aim of this study was to investigate the use of cement kiln dust (CKD) and lime dust in solidification/stabilization process for arsenic-contaminated soils. Laboratory-prepared samples spiked with arsenic were made and treated with CKD and lime dust ranging from 15 to 30 wt% and 5–15 wt%, respectively. The effectiveness of treatment was evaluated at 28 days of curing based on the solidification/stabilization tests including unconfined compression test, toxicity characteristic leaching procedures (TCLP), and scanning electron microscopy (SEM). The results show that, though lime dust has a minor effect on samples strength, it has a significant effect on arsenic sorption. On the other hand, CKD causes immobilization of arsenic in the soil, as well as a major effect on soil strength. Based on the results, samples with 20 wt% CKD and 5 wt% lime dust have the optimized correlation between strength and acceptable level of Arsenic leakage in the TCLP test.

This paper is focused on the simulation of the lateral spreading phenomenon and the anticipated maximum surface displacements of sloping ground. An innovative numerical methodology is proposed employing a generalized plasticity model implemented in a finite element code (Chan, 1988) which has been thoroughly validated against VELACS centrifuge liquefaction experiments (Arulanandan & Scott, 1993). The results of numerical analysis compared with experimental measurements indicate that the proposed numerical model has the capability to simulate the lateral spreading phenomenon. This model has been used for a parametric study. In parametric analyses, different factors have been investigated and their effects on magnitude of soil deformation have been studied.

This paper is focused on the simulation of the lateral spreading phenomenon and the anticipated maximum surface displacements of sloping ground. An innovative numerical methodology is proposed employing a generalized plasticity model implemented in a nite element code, which has been thoroughly validated against VELACS centrifuge liquefaction experiments. Lateral spreading is the term used to refer to the development of large horizontal ground displacements due to earthquake induced liquefaction, in the case of even small free ground surface inclination or small topographic irregularities. Recent earthquakes have emphasized the fact that this phenomenon has signicant practical importance for civil engineering structures (coastal structures, bridge piers, lifelines, etc.), since it imposes considerable lateral loads and may lead to widespread failures. Fortunately, there exist methods today which can be used for the design of such structures against lateral spreading (e.g. P-y analysis). However, their accuracy depends greatly on the ability to estimate the anticipated lateral ground displacements and their variation with depth. In this research, a fully coupled two-dimensional dynamic analysis based on effective stress formulation using saturated porous media considering uid movement has been used to simulate the lateral spreading and evaluate the amount of deformations occurred in liquefiable soils. The governing equations are developed for saturated porous media based on the extension of Biot formulation. The cyclic elastoplastic behavior of soil under earthquake loading is modeled using the generalized plasticity theory composing of a yield surface together with non-associated ow rule proposed by Pastor and Zienkiewicz. A fully explicit dynamic finite element method and a fully coupled (u-w) formulation are employed in a computer code to analyze soil displacements and pore water pressures (Taslimian et al., 2014). In order to ensure the accuracy of numerical analysis results, a centrifuge experiment results has been utilized. The results of numerical analysis compared with experimental measurements indicate that the proposed numerical model has the capability to simulate the lateral spreading phenomenon. The same finite element mesh was used for all numerical simulations, as shown in Figure 1.