Pore Fluid Velocity Research Articles

A finite element analysis of periodontal ligament fluid mechanics response to occlusal loading based on hydro-mechanical coupling model

ObjectiveConsidering fluid stimulation is one of the essential biomechanical signals for periodontal tissues, this study aims to characterizing fluid mechanics response during occlusal loading by a hydro-mechanical coupling model for periodontal ligament. DesignModels simulating periodontium with normal bone height and with intraosseous defects were built with three mechanical modules: tooth, periodontal ligament and alveolar bone. Tooth was modeled as linear elastic, and periodontal ligament and alveolar bone as a hydro-mechanical coupling model. Transient analyses under dynamic occlusal loading were performed. Fluid dynamics within periodontal ligament space was simulated and visualized by post-processing module. ResultsReciprocating oscillatory flow occurred within the periodontal ligament under occlusal loading. Higher pore pressure and fluid velocity were observed in furcation and apical regions compared to mid-root and cervical regions. Intraosseous defects increased pore pressure and fluid velocity within the periodontal ligament, most significantly near the defect. ConclusionBased on the results of the hydro-mechanical coupling model, significant oscillatory fluid motion is observed within the periodontal ligament under occlusal loading. Particularly, higher fluid velocity is evident in the furcation and apical areas. Additionally, Intraosseous defects significantly enhance fluid motion within the periodontal ligament.

Computational simulation of the hydrothermal ore-forming system associated with the Luziyuan Pb-Zn Deposit, Yunnan, China: An example of pore-fluid convection controlled mineralization

The giant Luziyuan Pb-Zn deposit is a typical hydrothermal ore-forming deposit in the southern Baoshan block of SE Tibet. Although extensive studies were conducted to understand the ore-forming system associated with the Luziyuan Pb-Zn deposit through using the traditional geoscience methods, the ore-forming process involved in this deposit has not been justified in a strictly scientific manner to date. In this paper, the hydrothermal ore-forming process of the Luziyuan Pb-Zn deposit is computationally simulated through using the dual length-scale approach associated with the finite element method (FEM). In the dual length-scale approach, the FEM is first used to simulate the regional model of a large length-scale in the geological region where the Luziyuan Pb-Zn deposit is located. Afterward, the FEM is then used to simulate the deposit model of the Luziyuan Pb-Zn deposit. Particularly, the boundary conditions of the deposit model are consistently determined from using the computational simulation results of the regional model. The related numerical results demonstrated that: (1) the pore-fluid convection provides a continuous source of ore-forming fluid and ore-forming material for the Luziyuan Pb-Zn deposit; (2) the convective pore-fluid flow is the main dynamic mechanism, which controls the temperature, pore-fluid velocity and chemical species distribution in the Luziyuan Pb-Zn deposit; (3) the localized structure is the main controlling factor for the localized pore-fluid flow pattern, which further controls the formation and location of the orebody in the Luziyuan Pb-Zn deposit; (4) the dual length-scale approach associated with the FEM is very useful for simulating the hydrothermal ore-forming process of the Luziyuan Pb-Zn deposit.

Computationally simulating the hydrothermal mineralizing system involved in the Laochang Pb-Zn deposit, Gejiu ore district, Yunnan, China: an example of pore-fluid convection controlled mineralization

The Laochang Pb-Zn deposit can be typically considered as a hydrothermal mineralizing deposit in the Gejiu ore district. Although extensive studies were conducted to understand the mineralizing system associated with the Laochang Pb-Zn deposit through using the traditional geoscience methods, the mineralizing process involved in this deposit has not been justified in a strictly scientific manner to date. In this article, the hydrothermal mineralizing mechanism of the Laochang Pb-Zn deposit is computationally simulated through using the dual length-scale approach associated with the finite element method (FEM). The related computationally simulating outcomes have revealed the following understanding: 1) the pore-fluid convection provides a continuous source of mineralizing fluid and material for the Laochang Pb-Zn deposit; 2) the convective flow of pore-fluid is the primary dynamic mechanism, which controls the temperature, chemical species and pore-fluid velocity distributions in the Laochang Pb-Zn deposit; 3) the localized structure plays a key role in controlling the localized pore-fluid flow pattern, which can further control the location and grade of the orebody in the Laochang Pb-Zn deposit; 4) the dual length-scale approach associated with the FEM is very useful for dealing with the computational simulation of the hydrothermal mineralizing mechanism involved in the Laochang Pb-Zn deposit.

MINING OF BIOMECHANICAL AND GEOMETRY DATA OF INTERVERTEBRAL DISC FINITE ELEMENT SIMULATIONS

This study investigates the relationships between Intervertebral Disc (IVD) morphology and biomechanics using patient-specific (PS) finite element (FE) models and poromechanical simulations.169 3D lumbar IVD shapes from the European project MySpine (FP7-269909), spanning healthy to Pfirrmann grade 4 degeneration, were obtained from MRIs. A Bayesian Coherent Point Drift algorithm aligned meshes to a previously validated structural FE mesh of the IVD. After mesh quality analyses and Hausdorff distance measurements, mechanical simulations were performed: 8 and 16 hours of sleep and daytime, respectively, applying 0.11 and 0.54 MPa of pressure on the upper cartilage endplate (CEP). Simulation results were extracted from the anterior (ATZ) and posterior regions (PTZ) and the center of the nucleus pulposus (CNP). Data mining was performed using Linear Regression, Support Vector Machine, and eXtreme Gradient Boosting techniques. Mechanical variables of interest in DD, such as pore fluid velocity (FLVEL), water content, and swelling pressure, were examined. The morphological variables of the simulated discs were used as input features.Local morphological variables significantly impacted the local mechanical response. The local disc heights, respectively in the mid (mh), anterior (ah), and posterior (ph) regions, were key factors in general. Additionally, fluid transport, reflected by FLVEL, was greatly influenced (r2 0.69) by the shape of the upper and lower cartilage endplates (CEPs).This study suggests that disc morphology affects Mechanical variables of interest in DD. Attention should be paid to the antero-posterior distribution and local effects of disc heights. Surprisingly, the CEP morphology remotely affected the fluid transport in NP volumes around mid-height, and mechanobiological implications shall be explored. In conclusion, patient-specific IVD modeling has strong potential to unravel important correlations between IVD phenotypes and local tissue regulation.Acknowledgments: European Commission: Disc4All-MSCA-2020-ITN-ETN GA: 955735; O-Health-ERC-CoG-2021-101044828

Gas hydrate saturation from NGHP 02 LWD data in the Mahanadi Basin

During the Indian National Gas Hydrate Program (NGHP) Expedition 02, Logging-while-drilling (LWD) logs were acquired at three sites (NGHP-02-11, NGHP-02-12, and NGHP-02-13) across the Mahanadi Basin in area A. We applied rock physics theory to available sonic velocity logs to know the distribution of gas hydrate at site NGHP-02-11 and NGHP-02-13. Rock physics modeling using sonic velocity at well location shows that gas hydrate is distributed mainly within the depth intervals of 150–265 m and 100–215 mbsf at site NGHP-02-11 and NGHP-02-13, respectively, with an average saturation of about 4% of the pore space and the maximum concentration of about 40% of the pore space at 250 m depth at site NGHP-02-11, and at site NGHP-02-13 an average saturation of about 2% of the pore space and the maximum concentration of about 20% of the pore space at 246 m depth, as gas hydrate is distributed mainly within 100–246 mbsf at this site. Saturation of gas hydrate estimated from the electrical resistivity method using density derived porosity and electrical resistivity logs from Archie's empirical formula shows high saturation compared to that from the sonic log. However, estimates of hydrate saturation based on sonic P-wave velocity may differ significantly from that based on resistivity, because gas and hydrate have higher resistivity than conductive pore fluid and sonic P-wave velocity shows strong effect on gas hydrate as a small amount of gas reduces the velocity significantly while increasing velocity due to the presence of hydrate. At site NGHP-02-11, gas hydrate saturation is in the range of 15%–30%, in two zones between 150-180 and 245–265 mbsf. Site NGHP-02-012 shows a gas hydrate saturation of 20%–30% in the zone between 100 and 207 mbsf. Site NGHP-02-13 shows a gas hydrate saturation up to 30% in the zone between 215 and 246 mbsf. Combined observations from rock physics modeling and Archie’s approximation show the gas hydrate concentrations are relatively low (<4% of the pore space) at the sites of the Mahanadi Basin in the turbidite channel system.

Simulating dual solutions of coupled pore-fluid flow and chemical dissolution problems in fluid-saturated heterogeneous porous media

PurposeThe objective of this paper is to establish a solution strategy for obtaining dual solutions, namely trivial (conventional) and nontrivial (unconventional) solutions, of coupled pore-fluid flow and chemical dissolution problems in heterogeneous porous media.Design/methodology/approachThrough applying a perturbation to the pore-fluid velocity, original governing partial differential equations of a coupled pore-fluid flow and chemical dissolution problem in heterogeneous porous media are transformed into perturbed ones, which are then solved by using the semi-analytical finite element method. Through switching off and on the applied perturbation terms in the resulting perturbed governing partial differential equations, both the trivial and nontrivial solutions can be obtained for the original governing partial differential equations of the coupled pore-fluid flow and chemical dissolution problem in fluid-saturated heterogeneous porous media.FindingsWhen a coupled pore-fluid flow and chemical dissolution system is in a stable state, the trivial and nontrivial solutions of the system are identical. However, if a coupled pore-fluid flow and chemical dissolution system is in an unstable state, then the trivial and nontrivial solutions of the system are totally different. This recognition can be equally used to judge whether a coupled pore-fluid flow and chemical dissolution system involving heterogeneous porous media is in a stable state or in an unstable state. The proposed solution strategy can produce dual solutions for simulating coupled pore-fluid flow and chemical dissolution problems in fluid-saturated heterogeneous porous media.Originality/valueA solution strategy is proposed to obtain the nontrivial solution, which is often overlooked in the computational simulation of coupled pore-fluid flow and chemical dissolution problems in fluid-saturated heterogeneous porous media. The proposed solution strategy provides a useful way for understanding the underlying dynamic mechanisms of the chemical damage effect associated with the stability of structures that are built on soil foundations.

A New Explicit Sequentially Coupled Technique for Chemo-Thermo-Poromechanical Modelling and Simulation in Shale Formations

A new explicit sequentially coupled technique for chemo-thermo-poromechanical problems in shale formations is developed. Simultaneously solving the flow and geomechanics equations in a single step is computationally expensive with consequent limitations on the computations involving well or reservoir-scale geometries. The newly developed solution sequence involves solving the temperature field within the porous system. This is followed by the computation of the chemical activity constrained by the previously computed temperature field. The pore pressure is then computed by coupling the pore thermal and chemical effects but without consideration of the volumetric strains. The geomechanical effect of the volumetric strain, stress tensors, and associated displacement vectors on the pore fluid is subsequently computed explicitly in a single-step post-processing operation. By increasing the borehole pressure to 20 MPa, it is observed that the rock displacement and velocities concurrently increase by 50%. However, increasing the wellbore temperature and chemical activities shows only a slight effect on the rock and pore fluid. In the chemo-thermo-poroelasticity steady-state simulation, the maximum displacements recorded in the Hmin and Hmax are 0.00633 m and 0.0035 m, respectively, for 2D and 0.21 for the 3D simulation. In the transient simulation, the displacement values are observed to increase gradually over time with a corresponding decrease in the maximum pore-fluid velocity. A comparison of this work and the partial two-way coupling scheme in a commercial simulator for the 2D test cases was carried out. The maximum differences between the computed temperatures, displacement values, and fluid velocities are 0.33%, 0.7%, and 0%, respectively. The analysed results, therefore, indicate that this technique is comparatively accurate and more computationally efficient than running a full or partial two-way coupling scheme.

Investigation on physical exercise-induced interstitial fluid flow in bone tissue to mitigate osteoporosis and disuse bone loss

Osteoporosis and disuse bone loss in elderly individuals, bed-ridden patients, and astronauts are serious health issues. Severe bone loss increases bone porosity and thus decreases bone strength which further promotes bone fractures. Prophylactic exercise is beneficial in preventing bone loss as mechanical loading enhances bone modeling and remodeling activities. Loading-induced fluid flow within the bone tissue is considered as stimulus of excitation of mechanosensory bone cells, i.e., osteocytes, which regulate the osteoactivities related to bone remodeling. In vivo and in silico studies observed that bone loss adversely influences the bone microarchitecture, such as porosity and permeability, which reduces interstitial fluid flow required for the bone remodeling process. Physical exercise-induced mechanical loads on bone may enhance interstitial fluid flow above the osteogenic threshold. Nevertheless, how physiological loading associated with exercise influences interstitial fluid flow in osteoporotic/disused bone tissue is not well established. Thus, the present study computes the interstitial fluid flow in healthy and osteoporotic/disused cortical bone tissue as a function of gait loading waveforms of physical exercise using a poromechanical finite element model. The outcomes indicate that osteoporotic and disused cortical bone tissue with greater porosity and less permeability experience comparatively lower pore pressure and fluid velocity than healthy tissue. Moreover, physiological loading exercise enhances fluid flow in diseased tissue, which is helpful in exciting bone cells for improvement in bone remodeling. Overall, the findings of the present investigation may be beneficial in the design of potential physiological exercises to prevent osteoporotic and disuse bone loss.

Relationship between pore fluid velocity distribution and pore size distribution

AbstractThis study investigated the normalized velocity magnitude distribution and normalized pore volume distribution in different porous media with porosity between 13.5% and 85%, including sandstones, carbonates, synthetic silica, sphere packings and fiber scaffolds. It was found that both velocity magnitude and pore size follow the same distribution. These results allow the prediction of the velocity distribution in a porous medium when its pore structure is known or tuning the velocity by controlling the pore structure.

Biomechanical analysis of a lacunar-canalicular system under different cyclic displacement loading

The objective of this study is to use the finite element (FE) method to predict the mechanical signals (interstitial fluid velocity, strain, pore pressure, and pore fluid velocity) produced by osteocyte during physiological activities. The model predicts that the amplitude and distribution of the mechanical signals are mainly affected by the loading rate. The magnitude of mechanical signals in the lacunar-canalicular system increases as the amplitude, frequency and amount of direction of load increase. Collagen hillocks can effectively amplify strain signals at the process. The established model can be used for studying the mechanism of bone mechanotransduction at the micro-level.

Investigating porosity structure effects on hydrothermal mineralization patterns within permeable horizontal layers of fluid-saturated rocks: Semi-analytical approach through generic models

The porosity structures of a permeable rock can have remarkable effects on pore-fluid flow within the rock. According to the modern mineralization theory, the mineralization pattern in a hydrothermal ore-forming system is strongly dependent on the pore-fluid flow velocity, so that different porosity structures of a permeable rock can affect significantly hydrothermal mineralization patterns within the permeable layers consisting of fluid-saturated porous rocks. This paper presents a semi-analytical approach, in which pore-fluid velocity is directly used as fundamental primary variables in the governing equations of the problem and the property matrices of finite elements are analytically evaluated in a purely mathematical manner, to ensure the high accuracy of the obtained pore-fluid velocity, which is involved in controlling mineralization patterns in hydrothermal ore-forming systems. After the proposed semi-analytical approach is verified through comparing the numerical solution with the analytical solution for a benchmark problem, it has been used to investigate how different porosity structures can affect the hydrothermal mineralization patterns within permeable horizontal layers consisting of fluid-saturated porous rocks through using a generic model, which can be viewed as the representation of a generalized and simplified geological model. Main outcomes of this study have demonstrated that: (1) the proposed semi-analytical approach can produce highly-accurate numerical solutions for solving coupled pore-fluid flow and heat transfer problems in fluid-saturated porous rocks with different porosity structures; (2) the different porosity structure within a permeable horizontal layer consisting of fluid-saturated porous rocks can have a significant effect on the hydrothermal mineralization pattern of the permeable horizontal layer; (3) layered pore-fluid vertical velocity focusing may take place within a permeable horizontal layer involving a heterogeneous porosity structure.

Semi-analytical finite element method for simulating chemical dissolution-front instability problems in fluid-saturated porous media

PurposeThe objective of this paper is to develop a semi-analytical finite element method for solving chemical dissolution-front instability problems in fluid-saturated porous media.Design/methodology/approachThe porosity, horizontal and vertical components of the pore-fluid velocity and solute concentration are selected as four fundamental unknown variables for describing chemical dissolution-front instability problems in fluid-saturated porous media. To avoid the use of numerical integration, analytical solutions for the property matrices of a rectangular element are precisely derived in a purely mathematical manner. This means that the proposed finite element method is a kind of semi-analytical method. The column pivot element solver is used to solve the resulting finite element equations of the chemical dissolution-front instability problem.FindingsThe direct use of horizontal and vertical components of the pore-fluid velocity as fundamental unknown variables can improve the accuracy of the related numerical solution. The column pivot element solver is useful for solving the finite element equations of a chemical dissolution-front instability problem. The proposed semi-analytical finite element method can produce highly accurate numerical solutions for simulating chemical dissolution-front instability problems in fluid-saturated porous media.Originality/valueAnalytical solutions for the property matrices of a rectangular element are precisely derived for solving chemical dissolution-front instability problems in fluid-saturated porous media. The proposed semi-analytical finite element method provides a useful way for understanding the underlying dynamic mechanisms of the washing land method involved in the contaminated land remediation.

A novel mechanistic anion exclusion model to investigate partially water‐saturated transport in soils and shales: A case study of nitrate solution flow

AbstractAnion exclusion is an important phenomenon in agricultural, environmental and engineering fields which still needs suitable quantitative models. In this work, a novel model is proposed which considers the porous media as parallel capillaries with negatively charged walls that cause total anion exclusion at a distance from the walls. By defining the ‘anion velocity coefficient’, , as the ratio of anion velocity to pore fluid velocity, equations to estimate the value of at the injection inlet have been derived by three different methods, namely from the profiles' data, , from the concentration ratio at the inlet, , and from the electrical double layer thickness model, . Finally, a simple sensitivity analysis for the third method has been presented. The estimates of presented in this paper were examined versus 22 data points for nitrate solution flow in initially dry soil columns for various soil and salt types and solution concentrations. The coefficient of determination between and for the whole dataset was 0.7755. Also, the estimate could predict the value estimated from the breakthrough anion concentration curve for available data of an advective injection test in a clayey rock. As a result, when anion exclusion dominates, the anion flux decreases but the anion velocity increases. In the case of using nitrate fertilisers, this point may be used to regulate the amount of optimal irrigation and also to explain the extent of contamination of a distant groundwater body.Highlights Modelling the anion exclusion phenomena in soils and shales. A mechanistic capillary model is developed to extract the anion velocity coefficient from data. Anion exclusion explains the anion concentration peaks in the unsaturated soil column test results. The derived estimates for anion velocity coefficient are shown to be reliable and promising.

Study on the poroelastic behaviors of the defected articular cartilage

This article presented the possible mechanism of arthritis damaged changes in cartilage’s interstitial fluid flowing behavior. Firstly, the analytical solutions for the pore fluid pressure and velocity in the idealized cartilage defect model were obtained, which are employed to validate the finite element (FE) method. Then according to the MRI data, an articular cartilage FE model was developed to study the effects of defect characteristics on its poroelastic behaviors. The results showed the interstitial fluid pressure and velocity in defected articular cartilage is diminished, moreover, this trend is even more severe as the defect radius or thickness increased. As the development of osteoarthritis goes, the fluid velocity is decreased and cause the even serious nutrients loss.

A non-Darcy flow model for a non-cohesive seabed involving wave-induced instantaneous liquefaction

Prediction of wave-induced instantaneous (oscillatory or momentary) liquefaction is particularly important for the design of offshore foundations. Most previous studies applied the linear Darcy model to characterize the porous flow in a seabed. This treatment was found to cause fallacious tensile stresses in a non-cohesive seabed. In this study, to overcome such shortcomings of previous models, a non-Darcy flow model is proposed based on a Karush–Kuhn–Tucker (KKT) condition. In the KKT condition, the primal constraint arises from the fact that the tensile behavior does not exist in a non-cohesive seabed, while the dual condition arises from the physical evidences that the pore-fluid velocity increases during liquefaction. The non-linearity of the present model is handled by the Newton–Raphson method within the standard finite element framework, without coding constrained variational principle. This highlights the convenience for numerical implementation. The difficulties in treating the nonlinearity by previous dynamic permeability model are also eliminated by the non-Darcy flow model. The merits of the proposed model are validated by examining four numerical treatments and two liquefaction criteria. The liquefaction depth by the present model is found to be roughly 0.73 times of the value by the linear Darcy model.

Analytical solutions for excess pore water pressures generated by TBM tunnelling in a semi-confined aquifer

Tunnel-boring machine (TBM) tunnelling through an aquifer will generate excess pore water pressures in the soil around the tunnel face. Accurately predicting the magnitude of the excess pore water pressures is significant because it directly determines the effective face support pressure. In this study, an analytical solution for transient cylindrical flow caused by TBM tunnelling considering the elastic storage of the aquifer is developed. Furthermore, a quasi-static solution to couple the effect of slurry infiltration with the elastic storage is presented. It is shown that the pore water pressures derived from the analytical solution match quite well with the measurements obtained in proximity to as well as far away from the TBM. The coupled quasi-static solution also agrees with the measurements for the places close to the tunnel face, but underestimates the observations far away from the tunnel face. The results also show that a larger infiltration distance leads to a slower dissipation of excess pore water pressures, which does not make a difference during excavation (when excavation velocity is faster than the pore fluid velocity).

A physics-informed and hierarchically regularized data-driven model for predicting fluid flow through porous media

This paper presents a new deep learning data-driven model for predicting structure dependent pore-fluid velocity fields in rock. The model is based on a Convolutional Auto-Encoder (CAE) artificial neural network capable of learning from image data generated by direct numerical simulations of fluid flow through pore-structures, such as by Lattice Boltzmann or molecular dynamics methods. The main novelty of the model in comparison to previous CAE-based data-driven approaches consists of three parts. The first is a methodology for decomposing the full-domain of the porous media into sub-regions, or “sub-domains”, in order to reduce the overall size of the CAE, batch process the sub-domains in parallel, and enable the CAE to learn local and generalizable nonlinear mappings of pore-fluid velocities. The second consists of embedding the finite difference solutions of the incompressible Navier-Stokes and continuity equations into convolutional layers prior to the CAE in order to provide the CAE with knowledge of fluid dynamics physics (PhyFlow). The third main novelty is that the training of the CAE is regularized with a hierarchical loss function that encourages the learning of fluid flow patterns (in a way similar to ranked modes in principal component analysis), ranking from most to least important. This is shown to increase the stability in learning, reduce over-fitting, and promote interpretability of the CAE neural network layers (HierCAE). The comprehensive new data-driven model, which we call the PhyFlow-HierCAE model, is shown to exhibit improved accuracy and generalizability of flow field predictions over conventional CAE models, attributable to the embedded physical knowledge and the hierarchical regularization, as well as realize orders of magnitude speed-ups in computation times as a surrogate for the direct numerical simulations. Examples of training and forward predictions on unseen pore-structures are provided and evaluated for data from Lattice Boltzmann and molecular dynamics simulations of pore-fluid flow. The model is shown to be a fast and accurate emulator (or “surrogate”) for predicting effective permeability of unseen pore-structures based on learning from relatively small direct numerical simulation datasets.

Oscillatory interstitial fluid pressure and velocity in a solid tumor with partial surface fluid leakage

This work investigates the interstitial fluid flow characteristics in a solid tumor with partial fluid leakage at the tumor surface subjected to oscillatory microvascular pressure. Solutions of the pore fluid pressure and velocity in a spherical tumor are obtained using the poroelasticity theory for small strains. It is found that partial fluid leakage at the tumor surface reduces the pore pressure drop and decreases the fluid velocity near the surface compared with those in a tumor with a fully leaking surface. Both the pore pressure and the fluid velocity decrease dramatically with an increase in the vascular frequency. The pore pressure at a vascular frequency of 1 Hz is two orders of magnitude smaller than the amplitude of the vascular pressure, and the fluid velocity at the same frequency is one order of magnitude smaller than that produced by the steady constant vascular pressure. The pore pressure amplitude may reach that of the vascular pressure under the steady state vascular pressure condition.

Modeling of reactive acid transport in fractured porous media with the Extended–FEM based on Darcy-Brinkman-Forchheimer framework

In this paper, a fully coupled numerical model is developed based on the X-FEM technique to simulate the reactive acid transport in fractured porous media. The porous medium consists of the solid and fluid phases, in which the fluid phase includes water and acid components, and chemical reactions can be occurred between acid component and solid phase at the solid–fluid interfaces. The governing equations include the mass and momentum conservation laws for fluid phase, and the advective–diffusive transport of acid component that must be solved to obtain the primary unknowns, including the pore fluid pressure, acid concentration, and fluid velocity vector. Applying the Darcy-Brinkman-Forchheimer framework, the velocity field is obtained accurately compared to the Darcy framework. The mass and momentum exchange between the fracture and surrounding porous matrix are incorporated in the weak form of governing equations using the extended finite element method (X-FEM). The X-FEM is applied by employing appropriate enrichment functions to model fractures in porous media. Finally, several numerical examples of acid injection inside both homogenous and heterogeneous fractured porous media are modeled to validate the accuracy and versatility of the proposed model. Moreover, the effects of fracture properties, such as the orientation and aperture, and the matrix properties, such as the diffusion and permeability, together with the injection velocity are investigated on the dissolution patterns. In addition, the wormhole patterns are compared in the DBF and Darcy frameworks.

Numerical Analysis of Unsaturated Soil Slopes under Rainfall Infiltration Based on the Modified Glasgow Coupled Model

An ABAQUS UMAT subroutine was used for the secondary development of the established coupled hydromechanical constitutive model of unsaturated soil considering the effect of the microscopic pore structure. Combined with Euler’s backward implicit integration algorithm, a numerical program was established for simulating the proposed model. The developed numerical program was used to simulate the rainfall infiltration process of an actual slope engineering example, and the effects of rainfall intensity and rainfall duration on the pore pressure, fluid velocity, and displacement of the unsaturated soil slope were analyzed. The results show that the developed numerical program can reasonably analyze the changes in the seepage field and displacement field of unsaturated soil slopes under rainfall infiltration.