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The prediction of equilibrium paths in the presence of brittle fractures remains a challenge, despite the advances in the fracture modelling techniques. Difficulties arise in the solution of the equilibrium equations in the presence of material and structural instabilities. This work proposes a continuation method with multiple restrictions to solve the nonlinear system of equilibrium equations and overcome global convergence problems owing to the sudden energy release in fracture propagation analyses. The method combines simultaneously the cylindrical arc-length and the dissipation-energy control methods. In addition, this method allows the use of algorithms for the solution of linear systems of equations, which do not require the assembly of the global stiffness matrix. Numerical examples of tensile-mode and mixed-mode fracture propagation are presented and compared with experimental results. A zero-thickness interface element with linear softening damage model simulates mixed-mode fracture. The results show the accuracy, robustness, and effectiveness of the proposed continuation method even for challenging fracture problems.

This paper presents the key aspects of the implementation of an XFEM element for hydraulic fracturing in porous medium in Abaqus. The implemented element has the capability of intersecting fractures inside an element and includes coupled hydro-mechanical behaviour and fluid exchange between fracture and the porous medium. The algorithm has three main steps: fracture geometry pre-processing, local matrix assembling, and post-processing. The first computes all the geometrical parameters of the XFEM. The second computes the jacobian and the right-hand-side matrices for each mesh element. The third checks for fracture propagation and the direction and length for propagating segments. Considering that Abaqus is a commercial software, adaptations were necessary, such as an algorithm for consideration of in-situ stress states, positioning of the degrees of freedom and numerical integration. A discussion on the limitations of the tool and of the use of the User Subroutine feature closes the implementation description. Then, we present the consolidation of a multi-fractured medium, comparing the results with a model with interface elements. In a second example, we simulate an injection in a fracture that propagates and intersects a naturally fractured model. The simulations show that the capabilities of Abaqus were considerably extended with this implementation.

Among the steps in modeling with the Discrete Element Method (DEM), one of the most important is parameter calibration. The commonly used trial-and-error approach brings drawbacks such as user dependence and high computational cost. As an alternative, artificial intelligence methods, such as neural networks and genetic algorithms , have been adopted. In this work, a new methodology based on Genetic Programming (GP) is presented as an alternative to calibrate DEM microparameters. From DEM models, GP provides functions relating microparameters and macro-properties. Given target macro-properties, the microparameters are obtained by an optimization procedure . The calibration procedure was evaluated for a uniaxial compression simulation and showed good accuracy for data sets with a reduced number of models. In addition, GP is less user dependent and less computationally intensive than other calibration methods. The methodology proved to be effective for DEM calibration and can be extended to other multiscale models .

Aiming at accuracy and computational efficiency, integrating discrete fracture and dual porosity-dual permeability models is a viable alternative to simulate flow in naturally fractured reservoirs with discontinuities of multiple lengths. However, previous works focus on the hydraulic problem only and do not take into account geomechanical effects. This study proposes a hydro-mechanical model using the finite element method (FEM) to represent the behavior of fracture networks with fractures of large, medium and small lengths. The methodology integrates the discrete fracture model (DFM) using interface elements, and the dual porosity/dual permeability (DPDP) model. Some synthetic applications compare the results of the models. A case study integrating both approaches is also performed. The results show that fractures of small and medium length enhance the permeability of naturally fractured reservoirs. Their presence within the porous medium results in greater fluid drainage and faster rate of pore pressure dissipation. The fractures contributed significantly to the mechanical behavior with impact on the stiffness of the rock mass system. Aperture variation of the fracture network influences fracture permeability and shows the stress shadowing effect. The results support the application of the proposed large-medium-small length fracture model to represent enhanced permeability of naturally fractured media.

Recent advances, not only in fluid flow but also in soil mechanics, have allowed the understanding and forecasting of common engineering problems such as slope stability, soil shrinkage and soil collapse. However, owing to limited access to data or more sophisticated numerical tools, the modeling of soil behavior is usually carried out considering simpler constitutive models which cannot predict some important features of unsaturated soils. This study is focused on the numerical modeling of unsaturated soils, adopting four constitutive models based on theories of elasticity and plasticity. For each model, a numerical simulation of a circular footing resting over a soil that is subject to drying and wetting processes is analyzed. Through the comparison of results, it is possible to highlight the use of more sophisticated constitutive models for unsaturated soil behavior, particularly forecasting the phenomenon of pore collapse during wetting processes.

Hydraulic stimulation is a technique in which a mixture of viscous fluids is pumped through an injector well in order to initiate and/or propagate fractures in the rock formation to enhance well-reservoir connectivity. Analytical and numerical methods have been proposed in the literature for predicting the evolution of the induced hydraulic fractures. Most of those studies are limited to some assumptions, such as fracture propagation through intact materials that follow a linear elastic behavior. However, those assumptions do not apply in naturally fractured porous media. The presence of geological discontinuities such as faults, joints, and natural fractures increases the complexity of the hydraulic fracturing treatment, affecting the final configuration of the hydraulic fracture network. This work investigates the effect of natural fractures on hydraulic fracture propagation in two limiting propagation regimes: toughness-fracture storage and viscosity-fracture storage dominated. The model fully couples permeable rock deformation and fluid flow inside and across the fractures. The hydromechanical triple-nodded zero thickness interface element has been combined with a cohesive zone model to simulate hydraulic fracture propagation. Mohr-Coulomb criterion and a contact model represent frictional and closure behavior of natural fractures, respectively. The longitudinal flow within the fracture is governed by Reynold's lubrication theory through smooth narrow parallel plates (i.e., Poiseuille flow). An innovated intrinsic mesh fragmentation technique is used to simulate complex crack patterns during hydraulic crack propagation. The results of the new approach are compared with analytical solutions. Moreover, the influence of parameters such as rock permeability, fluid viscosity, initial stress state, and natural fracture orientation on the hydraulic fracture propagation is analyzed.

A large number of hydrocarbon reservoirs is naturally fractured. When subjected to hydraulic fracturing treatments, the natural fractures may influence the propagation of the hydraulic fracture , which can grow in a complicated manner creating complex fracture networks in the reservoir. In order to better understand and simulate such phenomena, an element based on the eXtended Finite Element Method is proposed. The element formulation comprises fracture intersection and crossing, fracture frictional behaviour , fully coupled behaviour between displacements, pore and fracture fluid pressure, leak-off from the fracture to the surrounding medium and the eventual loss of pressure due to filter cake. The theoretical background and implementation aspects are presented. The results of three practical applications are analysed: percolation of multi-fractured rock in permanent flow regime, laboratory hydraulic fracture tests, and fracture propagation in a multi-fractured medium. The implemented code provides very good predictions of the coupled fluid-rock fracture behaviour and is capable of correctly simulating the interaction between hydraulic and natural fractures. Moreover, the hydraulic behaviour of the models and the intersection between fractures are very sensible to parameters such as differential in-situ stresses , angle between fractures, initial hydraulic aperture and leak-off coefficient.

The double-mechanism creep law (DM model) is an empirical creep constitutive model widely employed in Brazilian salt rock mechanics. This model often presents good performance in steady-state creep prediction. However, transient creep is not accounted for, and whenever early creep estimates are important, the contribution of this phase might be meaningful. This work adds value by presenting two alternatives to account for transient creep in the DM model. The first alternative couples the transient function from Sandia’s multi-mechanism deformation model to the DM model steady-state creep rate (EDMT model). The second alternative couples the DM model response to Norton’s power law when the strain rate given by the latter remains lower than the one from the former (EDMP model). These models can be implemented in numerical simulators at small code extensions of the DM model implementations. Applications from previous works by the authors are revisited to validate the formulations based on experimental data. EDMT and EDMP models differ in the formulation of transient creep and, consequently, in the time of transition between the transient and the steady-state phases. Both methods were successful in treating transient creep and in simulating experimental results.

The main oil and gas reserves around the world are found in regions containing evaporitic rocks. Owing to their low porosity and low permeability these rocks provide favorable conditions for hydrocarbon trapping, increasing the probability of success in oil and gas exploration . Salt rocks exhibit time-dependent strain behavior when submitted to deviatoric stresses. This behavior is described by creep constitutive laws based on deformation mechanics. One of the major challenges in modeling stress states in sedimentary basins in the presence of salt structures is to predict the magnitude of stress perturbations around salt bodies. This work presents a geo-mechanical approach to take into account the specific weight variation throughout the lithology and the effects of buoyancy in the resulting forces on the interface salt-body/formation. Modeling is driven by the fact that salt bodies cannot sustain deviatoric stresses. Numerical analyses using the Finite Element Method under plane strain conditions provide the results for the comparison of the methodologies found in the literature with the one proposed by the authors. Two synthetic models with salt dome structures are investigated. The proposed approach provided more realistic stress fields in the vicinity of salt structures.

In recent years, the increasing energy demand has led the oil and gas industry to explore unconventional reservoirs. The hydraulic fracturing technique (fracking) has been adopted in order to increase the reservoir drainage area. Nevertheless, there is an environmental concern about the contamination of aquifers due to this technique. The operation design requires predicting the induced fracture geometry to avoid hazards related to fracking. Hydraulic fracturing changes the state of stress at crack tip leading to more uncertainties in the definition of crack geometry, especially in naturally fractured formations. For such, analytical solutions and numerical simulations have been employed in recent decades. Nevertheless, the numerical models require high computational effort. This paper proposes an artificial neural network (ANN) to predict the interaction between hydraulic fracture and natural fractures. We performed over 800 simulations to build the training database varying the rock mechanical properties and model parameters, such as the approach angle between hydraulic fracture and natural fracture, in-situ stress magnitudes, friction angle, and fracture energy. The ANN results are compared against analytical solutions and numerical models, showing excellent agreement. These results show that the trained neural network can predict fracture interaction accurately. They also suggest that the most sensible parameters were taken into account in the proposed ANN.

In this work, the formation of karstic networks is modeled through the phenomenological stochastic differential Langevin equation. The solution of this equation follows through the application of the lattice-gas cellular automata formalism in terms of spatial and temporal discretization. The flow velocity vector is computed using a stochastic dimensionless equation where permeability, porosity, facies, and fracture persistence are the input parameters. Fluid flow is assumed to follow minimum effort paths in a heterogeneous medium from sinkholes or dolines towards springs. The shortest path search is performed using a fast marching algorithm in which fracture persistence is used as a proxy for a velocity field. Additionally, the Langevin equation's memory effect allows the coupling of the widening of the conduits with the amount of flowing water, taking into account dissolution phenomena. As conduits widen, more particles tend to run through them. This work presents a workflow for the modeling of karst generation in carbonate reservoirs. The workflow is applied to the study of an outcrop from Jandaira Formation, Potiguar Basin, Brazil. High-resolution aerial images of the area, scanlines, and karst facies stacking pattern of an outcrop near this area are the primary data to define the three-dimensional model. Three feasible scenarios of karstification were generated: epigenic, hypogenic, and hybrid karst. As a result, 3D karstic networks form, considering the regional geology, flow conditions, and local heterogeneities.

The work in hand proposes Artificial Neural Networks (ANN) to predict the residual strength of fiber reinforced concrete under bending load. A database containing experimental and synthetic data was constructed with 400 datasets, providing the following input data: fiber aspect ratio, matrix compressive strength, and steel fiber volumetric fraction. The parameter outputs were the flexural strengths fR,1, fR,3, and fR,4 of the composite. This study adopts the Bayesian regularization algorithm to predict the flexural parameters. Five different ANNs were trained and validated to assess the output datasets. The solution presented a particularly good fit for all tested networks, with regression values above 92 %. Once the networks are trained, mean square error analyses and blind tests with different experimental test sets check the solution accuracy, leading to the selection of the best network. Finally, an application regarding fiber-reinforced slabs-on-ground design considering the best ANN response is carried out. The resulting design load is compared to experimental slab tests performed by different authors from the literature and indicates a good agreement. In this sense, applying ANN methodology to slabs-on-ground design becomes an attractive tool for civil engineers.

This paper presents a novel sequential-explicit coupling technique to solve hydromechanical problems in poroelastic media. The proposed approach combines appropriate coupling terms defined in a rate form and an automatic time-stepping scheme that controls the temporal discretization error through a single parameter. Such technique has been implemented in a framework that manages sequential simulations, exchanges of information between models and adapts the time marching in a multirate approach. We present several numerical tests in which we evaluate the new scheme’s stability, accuracy, and performance through comparisons with the fully implicit solution. We observe that the proposed technique is stable, robust and accurate, and can be used in engineering applications for large scale and long time durations.

Production of fluids in reservoirs, such as oil, gas and water, leads to changes in the stress and strain fields, generating compaction in the reservoir and subsidence of the ground surface. Some of the severe consequences of these displacements are rock fracture, induced seismicity, fault reactivation, wellbore failure, and reduction in the storage capacity of aquifer systems. Analytic methods based on the nucleus of strain approach with simplifying assumptions can be useful to estimate compaction and subsidence, and to indicate when more detailed analyses are required. However, these methods may present problems by the evaluation of the displacement response inside and in the vicinity of the reservoir due to the presence of singularities in the solution. In this work, an analytical displacement solution is obtained for reservoirs of arbitrary shape in a linear elastic semi-infinite medium under arbitrary distribution of pressure changes. For this, the reservoir is discretized in parallelepiped cells. A three-dimensional integration of the solution is carried out over each cell for an infinitesimal reservoir based on the nucleus of strain approach. The final displacement field is given by the superposition of the solutions of individual cells. The three-dimensional integration eliminates the singularities and allows the evaluation of displacements throughout the entire model, including the reservoir. The solutions presented can be easily implemented in a computational procedure, maintaining the low effort of similar methods. Finite element models are employed to verify the accuracy of the proposed solution.

The development of new and complex models is typically required to gain an understanding of advanced materials and structures. The accuracy of a structural response obtained from finite element analysis is highly dependent on the extent to which a material model represents actual material behavior. This study proposes the application of rational surfaces to provide a smooth response surface for membrane material behavior. Constitutive material tensor is calculated by using the derivatives of rational surfaces. The surfaces possess two axes of strain and an axis of stress. The methodology is validated based on classical hyperelastic models. A set of results from an aluminum testing program illustrates the response surface construction procedure from the test results. The results indicate that it is easy to implement an extension of finite element codes to include the response surface approach based on NURBS.

In structural engineering, many problems present nonlinear behavior associated to a large number of sources, ranging from the presence of large displacements and large strains to the constitutive material behavior. The simulation of such complex structural systems with the finite element method often requires the use of analysis control schemes, called continuation methods. These schemes aim at depicting equilibrium paths, associated with system stiffness loss and to the occurrence of load and displacement limit points. Among them, the arc length and the strain control methods are very popular. However, under certain conditions, these methods either fail to provide the full system response or require a large number of iterations for convergence. In the present work, a continuation method with combined restrictions is proposed to provide the full system response in the presence of both geometric nonlinearities and material elasto-plastic softening. Two or more restrictions are combined resulting in a more robust scheme for the solution of the nonlinear system of equilibrium equations. Consistency of the extended system is reached through the least squares method. The efficiency of the combined control is compared to the application of the restrictions individually in a Newton-Raphson solution scheme. An automatic increment adaptation strategy for the control parameters is introduced which helps stabilize the incremental process with multiple restrictions. In the analysis of the highly non-linear problems studied in this paper, the proposed method with combined restrictions proves to be more robust than the standard procedure with single restrictions. In the cases where the single restrictions failed, the combined restriction was able to provide the full solution. A continuation method with multiple combined restrictions is proposedThe combination of methods results in a more robust controlThe proposed method helps stabilize the incremental process.The proposed method with an automatic control size adaptation reduces the need for user intervention in the analysis.

In the present work, a finite element based methodology was developed to assess the deformations and stresses during the construction of a vertical oil well drilled into Brazilian Halite. The impact of each construction stage is addressed focusing on the investigation of the early age creep of the cement slurry and its effects on the well integrity. The cement slurry was considered as an aging viscoelastic material and a parametric case study was addressed using the solidification theory. The rock salt constitutive model accounted for the primary and secondary creep through a combination of a power law and the double mechanism law. It was observed that if the cement slurry time-dependent behavior is neglected, the development of deviatoric stresses in cement slurry and hazard phenomena may be overlooked.

Dynamic fracturing of rock masses simulated by the conventional FEM, XFEM and the element deletion method.XFEM analysis of dynamic fracturing with and without pre-existing cracks.FEM and XFEM analysis of dynamic fracturing with and without impenetrability constraint.Cohesive fractures modeled by the method of phantom nodes. This paper presents a numerical analysis based on the finite element method to simulate blast-induced hard rock fracture propagation. Three different approaches are compared: the extended finite element method, with a cohesive zone model to represent the growth of fractures; the conventional finite element method using a remeshing technique and based on the linear fracture mechanics; the element deletion method to simulate a rock fragmentation process. The rock mass is a sound granite that remains linear elastic right up the breakage. Two numerical examples are presented in order to discuss the advantages and limitations of each approach.

A wellbore analysis presents several challenges regarding the drilling, construction and production phases. Owing to that, the cement and casing stress states during the wellbore lifespan are also difficult to predict. Nevertheless, analytical solutions can reach good results. Additionally, once analytical approaches are exhibited as mathematical expressions, they facilitate the assessment of the interaction between variables and the impact on results. On the other hand, wellbore analytical solutions do not usually consider all the phases involved. In this work, an analytical solution is developed to assess the stresses during the drilling, construction and production phases. Three models are adopted to be compared with a numerical approach. Thus, single and double casing configurations are analyzed. In both approaches, the initial stress states in the formation and in the cement, as well as the drilling operation, the casing run, the pressure changes, and the pore pressure variations are considered. The solutions consider plane strain conditions, continuous homogeneous isotropic media and linear elastic materials. In addition to the casing integrity, radial and tangential stresses for casing, cement and formation are presented. In conclusion, this analytical solution reaches excellent results when compared to the numerical model, therefore, becoming an alternative for the stress evaluation for everyday scenarios. Capable of simulating different scenarios regarding the wellbore stresses and integrity, this analytical solution is a good tool for a preliminary design.

In recent years, operational issues during the exploration of Pre-salt reservoirs have aroused the interest of the Brazilian oil and gas industry in studying karstification and its effect on carbonate reservoirs. Since then, a massive research effort was dedicated to the geology of the Brazilian onshore karstified carbonate formations; however, geomechanical modeling of reservoirs with karstic cavities remains unexplored in the literature. This work analyzes the mechanical behavior of karstified carbonate reservoirs during the hydrocarbon production period. A synthetic case study based on real geologic horizons of a Brazilian basin is carried out to predict the mechanical response of the reservoir and surroundings. The presence of a preexistent cavity developing around the reservoir symmetry axis is postulated. Different scenarios of karstic geometry and filling material are considered. Results focus on reservoir compaction, surface subsidence, and stress paths in regions of interest of the reservoir, caprocks, and cavity wall. Comparative results show that the horizontal extension of the cavity and the compressibility of the filling material play an important role in reservoir integrity. The qualitative results are useful for the oil and gas industry in terms of identifying problematic regions for wells and establishing loading limits. The findings and the preliminary results of this innovative work shall guide further advanced analyses, especially in the area of dolines generation from karstic cavities.

This paper proposes a new numerical model for simulating cement composite materials' mechanical behavior in tensile and bending in a mesoscale approach. A new finite element is developed in which the fiber is embedded in the cementitious matrix element, taking into account fiber orientation, stiffness, and strength. The novel formulation consists of the coupling of uniaxial fiber finite elements with continuum cementitious elements through cinematic constraint equations. The fiber degrees of freedom are eliminated at the element level. One of the significant advantages of this methodology is that mesh generation does not depend on fiber dispersion. Furthermore, the implementation allows multiple fibers crossing an element and can be applied for any fiber type. A new cohesive interface element completes the description of fiber-reinforced concrete (FRC) behavior. In addition to describing the cementitious matrix's degradation and fracture, the interface element includes the effect of the cross fracture fiber reinforcement. Finally, direct tensile and bending tests presented in the literature are simulated. Fibers are distributed randomly in the model according to the volumetric fiber fractions of the experiments. The numerical results show close agreement with the experiments and illustrate the proposed model's efficiency and robustness.

In the last decades, the study of fluid flow through discontinuities such as fractures has received significant attention from the petroleum industry owing to the discovery of highly productive naturally fractured reservoirs. Several approaches based on an explicit or implicit representation of fractures have been adopted for modeling fluid migration in fractured rocks. The explicit approach is the most accurate for such a purpose; however, it is computationally expensive. Alternatively, the implicit representation is very attractive because fracture properties, such as stiffness and permeability can be introduced in the model through dual continuum models. Therefore, the modeling of fluid flow through fractured porous media has been performed through conceptual models, while the modelling of more realistic scenarios is still an open question. This paper proposes a new embedded fracture approach for fluid flow in highly fractured porous media. This approach includes the fracture contribution into the continuum element using a condensation technique based on the multi-constrain method. The main advantage of this approach is the guarantee of compatibility between fracture and porous matrix within a standard finite element mesh. Several fractured rock reservoir cells are analyzed to demonstrate the robustness of the proposed approach and its applicability to highly fractured rocks with random fracture orientation. The pore pressure field obtained with the proposed embedded approach is very close to the predictions provided by the explicit approach with zero-thickness interface elements. Despite the simplicity of the method, the results are promising.

This paper focuses on the development of alternative coupling strategies for hydromechanical applications considering highly nonlinear constitutive models to represent the behavior of porous media. We present a novel consistent iterative coupling formulation based on fixed stress rates to define the coupling terms between mass balance and equilibrium equations. We show that controlling stress rates allows the application of an adaptive iterative coupling scheme with single or multi-rate solutions. The proposed methodology has been implemented in a framework that manages sequential simulations, exchanges of information between models, and checks the convergence of the iterative process. We present several numerical tests in which we evaluate the stability, accuracy, and performance of the proposed coupling technique. From the results, we confirm that the rate form of the fixed stress split guarantees solution stability and yields results as accurate as those obtained through fully implicit solutions, even for highly nonlinear constitutive behavior.

Hydraulic fracturing is a technique in which pressurized fluid is pumped into the well to induce fracture propagation in the rock formation. The treatment aims at enhancing permeability and well-reservoir connectivity. However, the presence of natural fractures can impact the hydraulic fracture propagation, increasing the complexity of the hydraulic fracturing treatment, and affect the final configuration of the fracture network. Furthermore, different propagation regimes can develop depending on field conditions, properties of the porous matrix, fractures, the injection fluid, and time. This work introduces a robust fully coupled hydro-mechanical approach to investigate the impacts of natural fractures on hydraulic fracturing in four limiting propagation regimes: toughness-storage, toughness-leak-off, viscosity-storage, and viscosity-leak-off dominated. The proposed approach is based on the finite element method and incorporates the coupling of pore pressure/stress within the permeable rock formation and fracture propagation. An innovative mesh fragmentation technique with an intrinsic pore-cohesive zone approach is implemented in the in-house multiphysics framework to simulate fracture propagation with complex crack patterns. Cohesive Zone Model (CZM) represents the initiation and propagation of hydraulic fractures while a contact model with the Mohr–Coulomb criterion is used to represent the normal closure/opening and friction/shear dilation of natural fractures. The results of the new approach are compared against analytical and numerical solutions. Moreover, the influence of parameters such as rock permeability, fluid viscosity, initial stress state, and intercepting angle on the hydraulic and natural fracture is also investigated. The robustness of the presented methodology is demonstrated by simulating crossing with an offset, branching, fracture propagation from the tip of a natural crack, and interaction of multiple cracks. These results can provide guidance for a better understanding of the complex process of hydraulic fracturing.