Hydro-mechanical Research Articles

Numerical Investigation of Hydro-Mechanical (HM) Effect on Meso-Failure Properties of Granite Using Improved HM Grain-Based Model

Numerical Investigation of Hydro-Mechanical (HM) Effect on Meso-Failure Properties of Granite Using Improved HM Grain-Based Model

Effects of Glacial Isostatic Adjustment on Fault Reactivation and Its Consequences on Radionuclide Migration in Crystalline Host Rocks

AbstractTo assess the robustness of a safety case for a deep geological repository (DGR), it is necessary to analyze a range of scenarios covering likely, less likely, and hypothetical future developments. Crystalline rock can, under ideal conditions, provide a suitable hydrogeologic barrier due to its extremely low matrix permeability. However, this host rock is often fractured, which can compromise its hydro-mechanical (HM) barrier function. We quantify how faults that are prone to reactivation during glacial events can affect radionuclide migration around a DGR in a crystalline host rock. We extend a previously developed finite element model of coupled fluid flow and radionuclide transport to numerically solve the component transport problem before and after fault reactivation. Assuming that fault reactivation is triggered by changes in mechanical boundary conditions, we derive heterogeneous permeability distributions in the reactivated faults by evaluating the Coulomb failure stress criterion of finite element solutions of a complementary hydro-mechanical problem. Specifically, we evaluate the consequences of glacial isostatic adjustment (GIA) during a glacial cycle. We find that the increased permeability in the reactivated faults accelerates the migration of radionuclides along the fault by channeling the flow, while it is reduced in the direction perpendicular to the fault. The channeling observed is also a result of heterogeneous permeability enhancement, and the flow fields differ from those of the previous model which postulated a homogeneous permeability enhancement. Although the proposed numerical workflow has been applied to the case of GIA, it is adaptable to study hydro-mechanical processes induced by seismic events or by hydrofracking in enhanced geothermal systems.

Exploring different FEM strategies for hydro-mechanical coupled gas injection simulation in clay materials

Over the last few decades, the study of gas injection in porous media, particularly under multi-field coupled conditions, has emerged as a prominent focus within the field of geotechnical engineering. This article presents a comprehensive comparison of three numerical strategies, evaluating their impact on computational efficiency and result accuracy during Hydro-Mechanical (HM) coupled simulations of gas injection in clay-based geomaterials. This comprehensive comparison encompasses three numerical simulation methods for the mechanical sub-problem: The Standard Finite Element Method (SFEM), the Standard Finite Element Method with Selective Integration (SFEM+SI), and the Mixed Finite Element Method (MFEM). The Heat and Gas Fracking model (HGFRAC) is introduced to illustrate the computational characteristics of these methods. The results indicate that the effective application of SFEM is heavily dependent on a high-precision mesh. Convergence issues may arise when dealing with relatively coarse meshes. Nevertheless, these convergence issues can be effectively mitigated by incorporating either the Selective Integration method or the MFEM formulations. In terms of computational efficiency, it is evident that the SFEM+SI method demonstrates higher efficiency than SFEM and MFEM. However, it is noteworthy that the computed gas flow patterns of SFEM and SFEM+SI can be affected by the alignment of the mesh. With MFEM, displacements and strains are calculated as independent unknowns, enhancing result accuracy and achieving mesh independence.

State of the Art of Coupled Thermo–hydro-Mechanical–Chemical Modelling for Frozen Soils

AbstractNumerous studies have investigated the coupled multi-field processes in frozen soils, focusing on the variation in frozen soils and addressing the influences of climate change, hydrological processes, and ecosystems in cold regions. The investigation of coupled multi-physics field processes in frozen soils has emerged as a prominent research area, leading to significant advancements in coupling models and simulation solvers. However, substantial differences remain among various coupled models due to the insufficient observations and in-depth understanding of multi-field coupling processes. Therefore, this study comprehensively reviews the latest research process on multi-field models and numerical simulation methods, including thermo-hydraulic (TH) coupling, thermo-mechanical (TM) coupling, hydro-mechanical (HM) coupling, thermo–hydro-mechanical (THM) coupling, thermo–hydro-chemical (THC) coupling and thermo–hydro-mechanical–chemical (THMC) coupling. Furthermore, the primary simulation methods are summarised, including the continuum mechanics method, discrete or discontinuous mechanics method, and simulators specifically designed for heat and mass transfer modelling. Finally, this study outlines critical findings and proposes future research directions on multi-physical field modelling of frozen soils. This study provides the theoretical basis for in-depth mechanism analyses and practical engineering applications, contributing to the advancement of understanding and management of frozen soils.

The use of a nonlocal critical state model in modelling triaxial and plane strain tests on overconsolidated clays

When modelling the phenomenon of strain localisation in strain-softening soils with the finite element (FE) method, nonlocal approaches have been commonly employed to avoid mesh dependency and numerical instability. This paper first presents the FE formulation of a critical state model for highly overconsolidated clays incorporating a nonlocal method. The performance of the nonlocal strain regularisation is subsequently assessed through a series of coupled hydro-mechanical (HM) analyses of undrained and drained triaxial compression tests on London clay. The mechanism behind the evolution of strain localisation in triaxial tests is investigated and a comparison with equivalent plane strain analyses is discussed. Finally, a comprehensive sensitivity study is presented, investigating the influence of the two nonlocal parameters, in the adopted nonlocal algorithm, on the predicted stress–strain responses. A key outcome is the derived linear relationship between the two parameters, which enables a unique stress–strain response to be achieved in either axisymmetric or plane strain analyses with multiple combinations of the two parameters. Such a modelling capability is essential in applications of the proposed nonlocal strain regularisation in large scale boundary value problems in which restrictions on element size exist.

Multiscale modeling of gas-induced fracturing in anisotropic clayey rocks

In the context of repositories for nuclear waste, understanding the behavior of gas migration through clayey rocks with inherent anisotropy is crucial for assessing the safety of geological disposal facilities. The primary mechanism for gas breakthrough is the opening of micro-fractures due to high gas pressure. This occurs at gas pressures lower than the combined strength of the rock and its minimum principal stress under external loading conditions. To investigate the mechanism of microscale mode-I ruptures, it is essential to incorporate a multiscale approach that includes subcritical microcracks in the modeling framework. In this contribution, we derive the model from microstructures that contain periodically distributed microcracks within a porous material. The damage evolution law is coupled with the macroscopic poroelastic system by employing the asymptotic homogenization method and considering the inherent hydro-mechanical (HM) anisotropy at the microscale. The resulting permeability change induced by fracture opening is implicitly integrated into the gas flow equation. Verification examples are presented to validate the developed model step by step. An analysis of local macroscopic response is undertaken to underscore the influence of factors such as strain rate, initial damage, and applied stress, on the gas migration process. Numerical examples of direct tension tests are used to demonstrate the model's efficacy in describing localized failure characteristics. Finally, the simulation results for preferential gas flow reveal the robustness of the two-scale model in explicitly depicting gas-induced fracturing in anisotropic clayey rocks. The model successfully captures the common behaviors observed in laboratory experiments, such as a sudden drop in gas injection pressure, rapid build-up of downstream gas pressure, and steady-state gas flow following gas breakthrough.

Effectiveness of injection protocols for hydraulic stimulation in enhanced geothermal systems

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.

Comparative evaluation of hydro-mechanical models in swelling of clay-sulfate rocks: Case study of staufen, Germany

The swelling of clay-sulfate rocks presents a substantial challenge in geotechnical engineering, with the city of Staufen in Germany being a case study, where ground deformations were triggered by water flow into the Triassic Grabfeld Formation. The underlying mechanisms include clay swelling and chemical swelling from the transformation of anhydrite to gypsum, both leading to a volume increase. This research developed two hydro-mechanical (HM) models based on semi-logarithmic and sigmoidal swelling laws to accurately simulate the observed heave in Staufen, and compares them against a previously developed HM model utilizing a linear swelling law. Comparative analysis demonstrates that the proposed models exhibit better capability in replicating the ground heave, with the linear model showing lower performance yet maintaining practical adequacy. Additionally, statistical analyses reveal the impact of geological complexity and spatial heterogeneity of rock properties on swelling behavior, providing crucial insights for engineering geologists and researchers. This study contributes to the development of informed strategies to mitigate risks associated with clay-sulfate rocks, thereby enhancing the stability of affected infrastructure.

Experimental and numerical analysis of flow through a natural rough fracture subject to normal loading

Fractured crystalline rocks have been chosen or are under consideration by several countries as host rock formations for deep geological repositories for spent nuclear fuel. In such geological formations, flow and solute transport are mostly controlled by a network of connected natural fractures, each of them being characterised by internal heterogeneity, also denoted as roughness. Fractures are, in turn, subject to variable load caused by various factors, such as the presence of thick ice sheets formed during glaciation periods. Understanding how coupled hydro-mechanical (HM) processes affect flow and transport at the scale of a single natural fracture is crucial for a robust parameterisation of large-scale discrete fracture network models, which are not only used for nuclear waste disposal applications but are also of interest to problems related to geothermics, oil and gas production or groundwater remediation. In this work, we analyse and model an HM experiment carried out in a single natural fracture and use the results of both, the experimental and the modelling work, to get insights into fundamental questions such as the applicability of local cubic law or the effect of normal load on channeling. The initial fracture aperture was obtained from laser scanning of the two fracture surfaces and an equivalent initial aperture was then defined by moving the two fracture surfaces together and comparing the results obtained using a Navier–Stokes based computational fluid dynamics (CFD) model with the experimental flowrate obtained for unloaded conditions. The mechanical effect of the different loading stages was simulated using a high-resolution contact model. The different computed fracture apertures were then used to run groundwater flow simulations using a modified Reynolds equation. The results show that, without correction, local cubic law largely overestimates flowrates. Instead, we show that by explicitly acknowledging the difference between the mechanical aperture and the hydraulic aperture and setting the latter equal to 1/5 of the former, cubic law provides a very reasonable approximation of the experimental flowrates over the entire loading cycle. A positive correlation between fluid flow channeling and normal load is also found.

Development of CASRock for modeling multi-fracture interactions in rocks under hydro-mechanical conditions

The interaction between multiple fractures is important in the analysis of rock fracture propagation, fracture network evolution and stability and integrity of rocks under hydro-mechanical (HM) coupling conditions. At present, modeling the mechanical behavior of multiple fractures is still challenging. Under the condition of multiple fractures, the opening, closing, sliding, propagation and penetration of fractures become more complicated. In order to simulate the HM coupling behavior of multi-fracture system, the paper presents a novel numerical scheme, including mesh reconstruction and topology generation algorithm, to efficiently and accurately represent fractures and their propagation process, and a potential function-based algorithm to address contact problem. The fracture contact algorithm does not need to set contact pairs and thus is suitable for complex contact situations from small to large deformations induced by HM loading. The topology of fracture interfaces is constructed by the dynamic adding algorithm, which makes the mesh reconstruction more rapid in the modeling of fracturing process, especially in the case of multiple fractures intersections. The numerical scheme is implemented in CASRock, a self-developed numerical code, to simulate the propagation process of rock fractures and the interaction of multiple fractures under the condition of HM coupling. To verify the suitability of the code, a series of tests were performed. The code was then applied to simulate hydraulic fracture propagation and fracture interactions caused by fluid injection. The ability of this method to study fracture propagation, multi-fracture interaction and fracture network evolution under hydro-mechanical coupling conditions is demonstrated.

High‐order models for hydro‐mechanical coupling problems in multiscale porous media

AbstractAn accurate prediction of nonlinear hydro‐mechanical (HM) coupling in subsurface structures with pronounced heterogeneity at multiple spatial scales is still an open topic and crucial for numerous engineering applications, for example, hydraulic fracturing and enhanced geothermal systems. In this study, novel high‐order multi‐scale asymptotic solutions are developed to accurately capture the locally oscillating characteristics of gas flow and solid displacement fields at multiple scales. First, the formal macro‐meso two‐scale asymptotic expansion is performed to establish the homogenized solutions and macro‐meso high‐order models which can predict the HM coupling problems at the macroscale and mesoscale. By directly expanding the cell functions defined at the mesoscale to the microscopic levels, the high‐order two‐scale expansion for the mesoscopic cell functions is built, and the upscaled relations for the flow parameters and constitutive coefficients from the microscale to the mesoscale and macroscale are developed correspondingly. The multi‐scale low/high‐order models are established by combining the high‐order expansion of all cell functions at the mesoscale and the developed macro‐meso two‐scale models. The main contributions are that the present approaches follow the reverse thought processes of reiteration homogenization methods, and offer a very innovative and efficient way to establish high‐accuracy high‐order models for the nonlinear HM coupling problems in the heterogeneous porous medium with any number of spatial scales. The effectiveness and accuracy of the present solution are validated by several representative cases with different constitutive coefficient contrasts. The results demonstrate that the high‐order solutions provide an accurate prediction for gas transport and solid deformation of heterogeneous porous media with multi‐scale configurations.

Research on fracture propagation of hydraulic fracturing in a fractured shale reservoir using a novel CDEM-based coupled HM model

Shale reservoirs are usually buried deep, and contain lots of complex natural fractures (NFs) under the influence of tectonic stress and faults. Previous studies usually focus on small-scale reservoir models and there is also a lack of research that completely focuses on NF characteristics. Using the continuous-discontinuous element method (CDEM), a Hydro-Mechanical (HM) coupling model was constructed to explore the propagation mechanism of hydraulic fracture (HF) and the effects of NF characteristics on HF propagation. The results show that as the HF approaches the NFs, the NFs preferentially tend to undergo shear failure, resulting in a decelerated HF propagation rate and an increased injection pressure. After water enters the NFs, the HF rapidly propagates, so the fracture area swiftly increases and the HF has a more tortuous fracture morphology. The NF orientation (α) and the internal friction angle (φ) exhibit a pronounced and distinct effect on HF propagation. Specifically, when α is 30°∼60°, the HF propagation is more tortuous and complex, so it is easier to form a larger transverse reconstruction range. When the NF density (η) is no less than 0.12, the HF tends to open the NFs and form a more tortuous morphology, but a higher η does not necessarily imply a higher fracture complexity. A longer NF (l > 12 m) benefits to improve the longitudinal reservoir reconstruction scope, but has little impact on the overall reconstruction effect. In the presence of stress shadow effect, it is improbable for the HF to completely open the intersecting NFs; instead, it typically opens only a segment or one of them. Consequently, it may be challenging to establish a fracture network with the simultaneous development of primary and branching fractures. Additionally, some water leakage into the inactive NFs gives rise to a decline in both the fracture length and fracture area. The findings can offer theoretical insights for refining the fracturing design in shale reservoirs with NFs.

Mechanical behaviours of bedded sandstone under hydromechanical coupling

The combination of the dipping effect and hydromechanical (H-M) coupling effect can easily lead to water inrush disasters in water-rich roadways with different dip angles in coal mines. Therefore, H-M coupling tests of bedded sandstones under identical osmotic pressure and various confining pressures were conducted. Then, the evolution curves of stress-strain, permeability and damage, macro- and mesoscopic failure characteristics were obtained. Subsequently, the mechanical behaviour was characterized, and finally the failure mechanism was revealed. The results showed that: (1) The failure of the sandstone with the bedding angle of 45° or 60° was the structure-dominant type, while that with the bedding angle of 0°, 30° or 90° was the force-dominant type. (2) When the bedding angle was in the range of (0°, 30°) or (45°, 90°), the confining pressure played a dominant role in influencing the peak strength. However, within β∈(30°, 45°), the bedding effect played a dominant role in the peak strength. (3) With the increase in bedding angle, the cohesion increased first, then decreased and finally increased, while the internal friction angle was the opposite. (4) When the bedding angle was 0° or 30°, the “water wedging” effect and the “bedding buckling” effect would lead to the forking or converging shear failure. When the bedding angle was 45° or 60°, the sliding friction effect would lead to the shear slipping failure. When the bedding angle was 90°, the combination of the “bedding buckling” effect and shear effect would lead to the mixed tension-shear failure. The above conclusions obtained are helpful for the prevention of water inrush disasters in water-rich roadways with different dips in coal mines.

Hydromechanical characterization of gas transport amidst uncertainty for underground nuclear explosion detection

Given the challenge of definitively discriminating between chemical and nuclear explosions using seismic methods alone, surface detection of signature noble gas radioisotopes is considered a positive identification of underground nuclear explosions (UNEs). However, the migration of signature radionuclide gases between the nuclear cavity and surface is not well understood because complex processes are involved, including the generation of complex fracture networks, reactivation of natural fractures and faults, and thermo-hydro-mechanical-chemical (THMC) coupling of radionuclide gas transport in the subsurface. In this study, we provide an experimental investigation of hydro-mechanical (HM) coupling among gas flow, stress states, rock deformation, and rock damage using a unique multi-physics triaxial direct shear rock testing system. The testing system also features redundant gas pressure and flow rate measurements, well suited for parameter uncertainty quantification. Using porous tuff and tight granite samples that are relevant to historic UNE tests, we measured the Biot effective stress coefficient, rock matrix gas permeability, and fracture gas permeability at a range of pore pressure and stress conditions. The Biot effective stress coefficient varies from 0.69 to 1 for the tuff, whose porosity averages 35.3% ± 0.7%, while this coefficient varies from 0.51 to 0.78 for the tight granite (porosity <1%, perhaps an underestimate). Matrix gas permeability is strongly correlated to effective stress for the granite, but not for the porous tuff. Our experiments reveal the following key engineering implications on transport of radionuclide gases post a UNE event: (1) The porous tuff shows apparent fracture dilation or compression upon stress changes, which does not necessarily change the gas permeability; (2) The granite fracture permeability shows strong stress sensitivity and is positively related to shear displacement; and (3) Hydromechanical coupling among stress states, rock damage, and gas flow appears to be stronger in tight granite than in porous tuff.

A framework for GPR‐based water leakage detection by integrating hydromechanical modelling into electromagnetic modelling

AbstractTimely and accurate detection of water pipe leakage is critical to preventing the loss of freshwater and predicting potential hazards induced by the change in underground water conditions, thereby developing mitigation strategies to improve the resilience of pipeline infrastructure. Ground‐penetrating radar (GPR) has been widely applied to investigating ground conditions and detecting pipe leakage. However, due to uncertainties of complex underground environments and time‐lapse change, a proper interpretation of GPR data has been a challenging task. This paper aims to leverage hydromechanical (HM) modelling to predict electromagnetic (EM) responses of water leakage detection in diverse leakage cases. A high‐fidelity 3D digital model of an actual pipeline network, hosting pipes with various sizes and materials, was reconstructed to represent the complex geometry and various mediums. The interoperability between the digital model and the numerical models utilized in HM and EM simulations was improved to better capture the irregular pipelines. Based on Kriging interpolation and the volumetric complex refractive index model, a linking technique was employed to replicate material heterogeneity caused by water intrusion. Thus, a framework was developed to accommodate the interoperability among digital modelling, HM modelling and finite‐difference time‐domain forward modelling. Moreover, sensitivity studies were conducted to evaluate the influences of different time stages, leak positions and pipe types on GPR responses. In GPR B‐scans, the presence of hyperbolic motion and horizontal reflections serve as indicators to estimate the location and scale of water leakage. Specifically, a downward‐shifting hyperbola indicates that the pipeline is submerged by leaked water, whereas the emergence of horizontal reflection is linked to the wetting front of saturated areas. The developed framework can be expanded for complicated applications, such as unknown locations and unforeseen failure modes of pipelines. It will increase the efficiency and accuracy of traditional interpretations of GPR‐based water leakage detection and thus enable automated interpretations by data‐driven methods.

Time-step constraints in coupled hydro-mechanical finite element analysis of unsaturated soils

In the finite element (FE) modelling of transient coupled problems for soils, the associated equations need to be integrated numerically over a time interval during the solution process. A minimum time-step size has been observed to exist, below which spatial oscillations in the obtained solutions can occur. These oscillations might lead to an accumulation of the resultant errors, eventually leading to invalid final predictions. This paper presents an analytical approach for deriving the time-step constraints for FE modelling of the transient behaviour of unsaturated soils with a fully coupled hydro-mechanical (HM) formulation. The effects of both element type and nonlinear soil properties are accounted for in the derivation. The proposed time-step constraints were subsequently verified through a series of coupled HM FE analyses of unsaturated soils, showing an excellent agreement. The present work shows that, when dealing with unsaturated soils, the minimum time-step size depends on the suction range investigated. This dependency derives from the nonlinear variation of water content and permeability with suction, as demonstrated through a set of comparative studies with three different types of unsaturated clays.

Properties of Bentonite-Based Sealing Materials during Hydration

A typical deep geological repository (DGR) design consists of a multi-barrier system, including the natural host rock and the engineered barrier system. Understanding the swelling behavior of bentonite-based sealing materials (BBSM), as a candidate material for the engineered barrier system, is crucial for DGR’s long-term safety. In this study, a hydromechanical (HM) column-type test was designed to model the hydration of BBSM from the underground water and determine the resulting swelling pressure in vertical and radial directions. Five hydration tests were carried out on identical compacted samples of 70% bentonite and 30% sand (70-30 bentonite-sand) mixtures with a dry density of 1.65 g/cm3 for varied durations of hydration, between 1 day and 120 days. The experiments were performed parallel to the compaction direction. Following each HM column-type test, the advancement of the wetting front was determined for each test. After 120 days, 56,339 mm3 of water infiltrated the sample and the wetting front reached over 50% of the sample height. The evolution of axial swelling pressure revealed an initial increase in swelling pressure with time in all tests, followed by a reduction in the rate at later times. After early stages of swelling, radial sensors showed an increase in swelling pressure. After 120 days, the radial pressure sensor closest to the hydration front showed 52% more radial pressure than the axial swelling pressure.

The importance of the microstructure on hydro-mechanical behaviour of compacted granular bentonite

Granular bentonite (GB) with extended grain size distribution, a candidate material to construct engineered barriers, has low water permeability, high swelling potential and self-sealing capacity and is desirable in portability and workability. However, few systematic data combining microstructural descriptions and hydro-mechanical (HM) behavioural features are available. The present work investigates the HM performance of Wyoming (MX80)-type GB samples compacted at different initial water contents and at a fixed dry density of 1550 kg/m3. The samples' microstructure and its evolution along stress paths were studied using X-ray micro-computed tomography and mercury intrusion porosimetry. The results highlighted that the compacted GB presented local density heterogeneity and a multi-porosity network. Compaction at low initial water content increased the proportion of macropores and contributed to the enhancement of the compressibility and collapse on wetting under high stresses. During isochoric saturation, two stages of swelling development were identified. First, the flooding of macropores and matric suction reduction was related to the initial increase in swelling pressure. The secondary swelling was due to the water absorption of clay sheets in micropores and the expansion of micropores within granules and aggregates, during which the density of pore water increased. A decrease in the compaction water content can result in a higher pore water density after isochoric saturation and a lower water permeability. Finally, the water retention behaviour of the compacted sample within drying/wetting cycles was less sensitive to the initial pore size distribution. The current outcomes underline the critical role of the microstructure on the HM behaviour of compacted GB.

Hydro-mechanical modelling of swell behaviour of bentonite buffer

Hydro-mechanical modelling of swell behaviour of bentonite buffer

Numerical modelling of a large-diameter sealing structure in a deep radioactive waste repository

Numerical modelling of a large-diameter sealing structure in a deep radioactive waste repository