Numerical Triaxial Tests Research Articles

Numerical modeling of onset and rate of sand production in perforated wells

Shear-type failure at a wellbore or perforation is typically characterized by damage to the formation rock. For example during drilling, wellbore failure may occur with rock fragments breaking off from the wellbore wall, and for producing wells, the applied drawdown pressure can result in sanding. Perforations are more susceptible to such failures because, in general, they become less stable as the reservoir depletes. In this paper, a damage model using the Mohr–Coulomb failure criterion is formulated to better describe the failure of porous granular material. The damage variable is assumed to be related to the increase in porosity resulting from the loss of mass from the formation rock matrix. The comparisons of numerical predictions and triaxial compression tests data show that the model can accurately reproduce the mechanical behavior of sand materials. Numerical simulation of a sand production test on a perforated cylindrical specimen is performed. The proposed model demonstrated its capability to predict the accumulated sand mass and rate produced throughout the entire experiment. A threshold of equivalent plastic shear strain has been quantified to determine the onset of sand production in perforated wells; this threshold can be used for field application of sand production analysis on similar sand material. An application on a vertical well with horizontal perforations has been simulated numerically. The key objectives are to examine the critical drawdown pressure for different reservoir depletions and produced sand volume for different drawdown pressures. The critical drawdown window plot was generated and can be used to estimate the allowable drawdown pressure for different reservoir depletions. In addition, it was shown that the produced sand volume and sand mass rate increase with increase of drawdown pressure.

Discrete modeling of sand–tire mixture considering grain-scale deformability

Mixing sand or soil with small pieces of tire is common practice in civil engineering applications. Although the properties of the soil are changed, it is environmentally friendly and sometimes economical. Nevertheless, the mechanical behavior of such mixtures is still not fully understood and more numerical investigations are required. This paper presents a novel approach for the modeling of sand–tire mixtures based on the discrete element method. The sand grains are represented by rigid agglomerates whereas the tire grains are represented by deformable agglomerates. The approach considers both grain shape and deformability. The micromechanical parameters of the contact law are calibrated based on experimental results from the literature. The effects of tire content and confining pressure on the stress–strain response are investigated in detail by performing numerical triaxial compression tests. The main results indicate that both strength and stiffness of the samples decrease with increasing tire content. A tire contact of 40% is identified as the boundary between rubber-like and sand-like behavior.

Macro-Micromechanical Properties of Sandy Pebble Soil of Different Coarse-Grained Content

Sandy pebble stratum is a typical discrete particle unstable stratum, mainly consisting of sand and pebble. However, the effect of coarse-grained content on the stability of stratum is not clear. This paper defined the sandy pebble soil of different coarse-grained content in Chengdu City, Sichuan Province, China as the research object. Research on macro-mesomechanical properties of sandy pebble soil of different coarse-grained content was carried out using the method combining the indoor large-scale triaxial test of coarse-grained soil with the discrete element numerical triaxial test. The research results showed that the stress-strain curve of sandy pebble soil exhibited strain softening with the increase of coarse-grained content; when the confining pressure was the same, the stress peak increased and the strain when the peak was reached decreased gradually with the increase of coarse-grained content. It revealed the functional relationship between coarse-grained content and mechanical indexes of sandy pebble soil such as internal friction angle and cohesion. The internal friction angle and cohesion of sandy pebble soil linearly increased with the rise of coarse-grained material; it proposed the particle discrete element micro parameters of sandy pebble soil of different coarse-grained content, including contact modulus, friction coefficient, particle stiffness ratio, contact bond strength. The research results provided the theoretical support for the new design and construction of sandy pebble stratum project.

Effects of particle asphericity on the macro- and micro-mechanical behaviors of granular assemblies

Particle shape has been regarded as a key factor affecting mechanical behaviors of granular assemblies. The present work proposes a shape descriptor, i.e., asphericity, to isolate the effect of aspect ratio and angularity. A series of numerical triaxial compression tests are conducted on mono-disperse assemblies with different asphericities using a superball-based discrete element model. The corresponding mechanical behaviors are investigated from both macroscopic and microscopic points of view. Effects of particle asphericity are examined as well. It demonstrates that particle asphericity is able to enhance the particle–particle inter-locking with higher locked-in forces, showing an increasing proportion of sliding contacts, thereby making a granular assembly stiffer and stronger. In addition, weak contacts have a dominant proportion in the overall contact networks, positively correlated with asphericity. However, asphericity has an insignificant effect on the mean coordination number at the critical state. Furthermore, an established analytical stress–force–fabric relationship is verified using the present data. Anisotropy within an assembly is quantified in terms of several measures, i.e., contact normals, normal and tangential branch vectors, and normal and tangential contact forces. It is found that anisotropy of granular fabric is strongly determined by anisotropy sources in strong contact networks, where a larger asphericity results in a more anisotropic granular fabric.

How Small Strain Stiffness and Yield Surface Affect Undrained Excavation Predictions

This paper discusses how small-strain stiffness and some aspects of the yield surface affect the finite-element predictions of excavation responses, including wall and ground deformations. By using the in-house-developed constitutive model SC1SS, it is possible to isolate and quantify impacts brought about by selected aspects of the soil behavior. This soil model has been validated to reasonably model Taipei silty clay and deep excavations in such soil. This study shows that ignoring small-strain stiffness can overestimate deformations by as much as 80%, leading to conservative and costly design. Inclined yield surface and Lode-angle dependency (on deviatoric planes) have lesser effects on the prediction results. In addition, the mechanisms behind these impacts are investigated through numerical triaxial tests.

A hybrid approach for modeling of breakable granular materials using combined finite-discrete element method

It is well known that particle breakage plays a critical role in the mechanical behavior of granular materials and has been a topic subject to intensive studies. This paper presents a three dimensional fracture model in the context of combined finite-discrete element method (FDEM) to simulate the breakage of irregular shaped granular materials, e.g., sands, gravels, and rockfills. In this method, each particle is discretized into a finite element mesh. The potential fracture paths are represented by pre-inserted non-thickness cohesive interface elements with a progressive damage model. The Mohr–Coulomb model with tension cut-off is employed as the damage initiation criterion to rupture the predominant failure mode at the particle scale. The particle breakage modeling using combined FDEM is validated by the qualitative agreement between the results of simulated single particle crushing tests and those obtained from laboratory tests and prior DEM simulations. A comprehensive numerical triaxial tests are carried out on both the unbreakable and breakable particle assemblies with varied confining pressure and particle crushability. The simulated stress–strain–dilation responses of breakable granular assembly are qualitatively in good agreement with the experimental observations. The effects of particle breakage on the compressibility, shear strength, volumetric response of the fairly dense breakable granular assembly are thoroughly investigated through a variety of mechanism demonstrations and micromechanical analysis. This paper also reports the energy input and dissipation behavior and its relation to the mechanical response.

Simulation of triaxial response of granular materials by modified DEM

A modified discrete element method (DEM) with rolling effect taken into consideration is developed to examine macroscopic behavior of granular materials in this study. Dimensional analysis is firstly performed to establish the relationship between macroscopic mechanical behavior, mesoscale contact parameters at particle level and external loading rate. It is found that only four dimensionless parameters may govern the macroscopic mechanical behavior in bulk. The numerical triaxial apparatus was used to study their influence on the mechanical behavior of granular materials. The parametric study indicates that Poisson’s ratio only varies with stiffness ratio, while Young’s modulus is proportional to contact modulus and grows with stiffness ratio, both of which agree with the micromechanical model. The peak friction angle is dependent on both inter-particle friction angle and rolling resistance. The dilatancy angle relies on inter-particle friction angle if rolling stiffness coefficient is sufficiently large. Finally, we have recommended a calibration procedure for cohesionless soil, which was at once applied to the simulation of Chende sand using a series of triaxial compression tests. The responses of DEM model are shown in quantitative agreement with experiments. In addition, stress-strain response of triaxial extension was also obtained by numerical triaxial extension tests.

Prediction of Transport Properties of Deformed Natural Fracture Through Micro-scale Hydro-mechanical Modeling

To study the effect of fracture properties on mechanical and fluid flow behavior of fractured rocks, we developed a micro-scale hydro-mechanical model. Modeling grains and studying their interactions are used to predict the mechanical response of digital rock samples. Fluid flow behavior is obtained through a realistic network model of the pore space in the compacted assembly. As a result of grain deformation and micro-crack development in a rock sample, the geometric description of the complex pore structure is regenerated to predict fluid flow performance of the rock sample using a dynamic pore network model. In our numerical model, the first step consisted of constructing a Berea sandstone sample. Then, fractures with different properties such as orientation, dilation angle, roughness, and cementing materials are introduced. Mechanical properties of the fractured sample are measured as functions of deformation by performing numerical triaxial tests. Applying a dynamic pore network provides a tool to investigate the important role of fracture parameters on transport behavior. Our results show that shearing along the fracture dilates the sample, and increases its permeability, which is a complex function of fracture mechanical properties.

Effect of Particle Size on Mechanical and Material Behaviors of Sand under Triaxial Shear

This study examines the effect of particle size on the behaviors of triaxial sand specimens. In order to investigate the material behaviors (i.e., local void ratios and inter-particle contacts) as well as the mechanical behaviors, three numerical triaxial tests assigned with different particle size ranges were performed. The results showed that the specimen with uniform particle sizes exhibited higher strength, larger local void ratios and more inter-particle contacts than the specimen of wider size ranges.

Coulomb-Cam Model for Dilatancy and Work-Softening of Sand

Cambridge model gets the extensive application, which has advantages of rigorous theoretical derivation and model parameters which can entirely be obtained by triaxial tests, while it has deficiencies of the narrow applicative scope and describing the dilatancy hardly. As the most widely used strength theory, Mohr-Coulomb model can directly represent shear strength of soil material simply, without consideration for compression deformation yet. On account of the critical state of dilatancy defined comprehensively, this paper based on the description of dilatancy combines the advantage of Cambridge model and Mohr-Coulomb strength theory, applying to compression deformation and conciseness of Mohr-coulomb model, reflecting shear deformation and puts forward an elastic-plastic model—Coulomb-Cam model. At last, this constitutive model, proved by the contrast of numerical simulation and GDS triaxial tests is of the priority in representing the dilatancy and work-softening rationally.

Effect of Particle Grading on the Response of an Idealized Granular Assemblage

The effects of particle-size distribution on a granular assemblage’s mechanical response were studied through a series of numerical triaxial tests using the three-dimensional (3D) discrete-element ...

Micromechanical modelling of erosion due to evaporation in a partially wet granular slope

SUMMARYSmall quantities of water in a granular slope increase the overall stability and justify the large slope angle which is sometime observable in nature. However, the evaporation usually changes the water content of soil, especially in very shallow layers, leading to a soil strength reduction and the trigger of erosion processes. This work presents some numerical tests simulating a small slope physical model constituted of monosized glass ballotini in a pendular state. After a brief review of the different theories describing the capillary bridge which forms between two spheres and its effects on inter‐particle forces, this paper deals with the implementation of the minimum energy approach within a discrete element model (DEM). Some numerical triaxial tests with different water contents and confinement stresses were performed: the analyses permitted to emphasize the shear strength increase occurring at low water content. Moreover, moving from the observations performed in the physical model, a law relating the evaporation rate with depth and air–water interface was also included in the DEM. Finally, the improved DEM was successfully adopted in the simulation of the erosion process occurring in the physical model: it very well captures the formation of a talus slope profile, typical of the long‐term evolution of granular slopes. The monitoring of soil displacements and suction distribution during the numerical test also allows for the evaluation of erosion mechanisms: for instance, both in experimental and numerical tests, it was observed a rigid displacement at the slope toe after the initial phase of shallow erosion. Copyright © 2011 John Wiley & Sons, Ltd.

Shear behaviour in numerical triaxial compression tests by 3D fluid-coupled DEM: a fundamental study on mechanisms of landslide initiation

Shear behaviour in triaxial compression tests was numerically examined by 3D fluid-coupled DEM in a fundamental study on the mechanisms of landslide initiation. Changes in pore-water pressure because of undrained compression were calculated by introducing a measurement sphere surrounding a ball which represented the soil particles. The pore-water pressure was assigned to the measurement sphere as the product of the changes in volumetric strain and modulus of compressibility of water, and resulting flow due to the pressure differences among neighbouring measurement spheres was given on the basis of Darcy's law. Specimens for the numerical triaxial compression tests were prepared with wide ranges of initial void ratio by use of samples with three different grain-size distributions. In the loose specimens, positive pore-water pressure build-up and subsequent liquefaction were numerically reproduced. In contrast, in the dense specimens, negative pore-water pressure was observed, showing upgrade of soil structure. For the medium specimens, phase transformation, which is a typical characteristic of granular soils, was successfully reproduced. Although steady-state lines were found for each sample on a diagram, there was a gap at a specific initial void ratio. Although the angles of internal friction were inversely proportional to the initial void ratio in both the undrained and drained tests in the medium to dense specimens, the observed angles of internal friction were smaller than the particle-to-particle friction angle. This result may be attributable to the fact that the balls could not form the complicated soil structures created in reality by particles with complex shapes.

Ultimate State of Samples of Ellipsoids under Different Stress Paths

The ultimate state of granular material was investigated by the discrete element method. This paper discusses a series of numerical triaxial tests on samples of two kinds of ellipsoids. Samples of three different densities were loaded along various stress paths. The ellipsoids were mixed in the proportions 50:50 by weight. The longer particles have an aspect ratio (major length/minor length) of 1.5 and the other particles have an aspect ratio of 1.2. The samples were generated by deposition under gravity to simulate the air-pluviation sample preparation technique. Then they were consolidated isotropically. Fourteen stress-path controlled triaxial tests were conducted numerically for each sample. They are sheared to the ultimate state to determine the friction angle and void ratio at the ultimate state. When samples of different densities were sheared along the same loading path, a unique ultimate state was observed. The initial density does not affect the ultimate state. However, when different loading paths are applied to the same numerical specimen, they do not always arrive at the same critical state in the void-mean stress space.

Numerical simulation of drained triaxial test using 3D discrete element modeling

A discrete element modeling of granular material was carried out using a 3D spherical discrete model with a rolling resistance, in order to take into account the roughness of grains. The numerical model of Labenne sand was generated, and the desired porosity was obtained by a radius expansion method. Using numerical triaxial tests the micro-mechanical properties of the numerical material were calibrated in order to match the macroscopic response of the real material. Numerical simulations were carried out under the same conditions as the physical experiments (porosity, boundary conditions and loading). The pre-peak, peak and post-peak behavior of the numerical material was studied. The calibration procedure revealed that the peak stress of the sand sample does not only depend on local friction parameters but also on the rolling resistance. The larger the value of the applied rolling resistance, the higher the resulting stress peak. Furthermore, the deformational response depends strongly on local friction. The numerical results are quantitatively in agreement with the laboratory test results.

Coupling pore-water pressure with distinct element method and steady state strengths in numerical triaxial compression tests under undrained conditions

The undrained shear behaviour of sands has been a key topic after the devastating geo-disasters during the 1964 Niigata Earthquake in Japan. Extensive geo-technical soil tests, especially undrained triaxial compression tests, have revealed that the liquefaction phenomenon was the major cause for the disaster expansions. To numerically reproduce the liquefaction phenomenon, the pore-water pressure was coupled with a distinct element method. In this model, the dynamic changes in pore-water pressure were taken into consideration by the changes in volumetric strain and modulus of compressibility of water in the respective measurement spheres. Fluid-flows among the measurement spheres were controlled by Darcy’s law. The effective stress paths and steady state strengths in undrained triaxial compression tests associated with the wide ranges of initial void ratio were investigated. The effective mean stresses of medium-dense to dense numerical specimens at the steady state were negatively proportional to the initial void ratio. Loose numerical specimens reproduced quasi-liquefaction with the effective mean stresses that were less than 25% of the initial value. The medium-dense numerical specimens reproduced the phase transformation that was a typical characteristic of granular materials. The rolling restraints did not much influence of the effective angle of internal friction but strongly affected pore-water pressure behaviour within a certain range of initial void ratio.

Three-dimensional constitutive relations for granular materials based on the dilatant double shearing mechanism and the concept of fabric

An extension of a three-dimensional model proposed by Anand and Gu (2000) for amorphous granular materials to include the effects of initial and induced anisotropy is presented in this paper. The proposed model can also be considered as a three-dimensional generalization of a model recently developed by Zhu et al. (2005) for the planar deformation of granular materials. The main ingredients of the model include the dilatant double shearing mechanism ( Spencer, 1964; Mehrabadi and Cowin, 1978), the concept of fabric ( Oda, 1972), and an extension of the Mohr–Coulomb yield criterion ( Shield, 1955; Spencer, 1982) to three dimensions. The constitutive equations are implemented in the finite element program ABAQUS/Explicit ( ABAQUS, 2001) by developing a user-material subroutine to conduct numerical triaxial compression tests for samples of granular materials with different initial anisotropy. The numerical results agree with the observed behavior and show that the extended constitutive model is capable of capturing the strength anisotropy of granular materials. Employing the anisotropic model developed here, we have also repeated the numerical simulation of the stress state in a static conical sand pile conducted earlier by Anand and Gu (2000). We find that fabric has little or no influence on the vertical stress distribution except at the base of the sand pile where the peak value of this stress is slightly higher than that predicted by the model of Anand and Gu (2000) which does not include the effects of fabric. We also find that the direction of the principal compressive stress changes from vertical at points away from the center of the pile to almost horizontal at points close to the center of the pile. This result provides a possible explanation for the observed dip in the vertical stress distribution in sand piles.