Numerical Modeling Of Deformation Research Articles

Laboratory tests and analysis of mathematical models of deformation of crushed salt rocks

Relevance of the work. For a qualitative prediction of the stress-strain state of host rock massifs during the development of potash and salt mines with chamber-pillar mining systems with the backfilling of the excavated space, as well as in other cases of the use of crushed salts as the backfilling masses, it is necessary to take into account the influence of the backfill massive, which determines the relevance of the study devoted to the laboratory tests and analysis of mathematical models of deformation of crushed salt rocks, which usually represent the backfilling massifs used in these cases. The purpose of the work is to analyze situation in the field of mathematical and numerical modeling of deformation of crushed salt rock and investigation of mechanical response of crushed salt rock under hydrostatic conditions. Methods. As the main method of theoretical research, the analysis of modern sources of information related to the subject of the study was used. Laboratory tests were carried out using a standard set of sieves and universal test machine MTS 815. Results. The paper considers the following deformation models used to describe the mechanical response of crushed salt rocks, as well as examples of their use: the Mohr-Coulomb model, the model of double plastic hardening, the S. A. Konstantinova model, the S. Olivella and A. Gens model, and the WIPP Salt model. As part of laboratory studies, data were obtained on the material size modulus, as well as the dependence of the medium pressure on volumetric deformations and volumetric deformations on time, in addition, creep rates for the studied material were obtained at various levels of average stresses under hydrostatic compression conditions. Conclusions. It is proposed to carry out further development of models of crushed salt rocks for mining conditions based on the description of plastic flow surfaces with a hardening/softening area obtained as a result of extensive laboratory and field surveys.

Microstructure-Based Computational Analysis of Deformation Stages of Rock-like Sandy-Cement Samples in Uniaxial Compression

This work presents a new finite-difference continuum damage mechanics approach for assessment of threshold stresses based on the mechanical response of a representative volume element of a sandy-cement rock-like material. An original experimental study allows validating the mathematical model. A new modification of the damage accumulation kinetic equation is proposed. Several approaches based on acoustic emission, instantaneous Poisson's ratio and reversal point method are employed to determine the threshold stresses. Relying on the numerical modeling of deformation and failure of model samples, the threshold stresses and the deformation stages are determined. The model predicts the crack initiation stress threshold with less than 10% error. The model prediction of the crack damage stress threshold corresponds to the upper boundary of the experimental range. The model predicts the peak stress threshold with less than 0.2% error in comparison with the average experimental peak stress. The results of numerical modeling are shown to correlate well with the available experimental and literature data and sufficiently complement them.

Numerical modeling of deformation and fracture of constructions made of concrete composites under non-stationary loading

Numerical modeling of deformation and fracture of constructions made of concrete composites under non-stationary loading

Frequency characteristics of built-in fiber-optic PEL-sensor to diagnose complex harmonic deformations within the polymer composite structure

Fundamentals of operation of an optical fiber piezoelectroluminescent (PEL) sensor inside a polymer composite structure at its cyclic loading are considered. The optical fiber PEL-sensor is considered as part of the composite/sensor electromechanical system taking into account the presence of anisotropy, piezoactivity and Maxwell-Wagner relaxation of the electric fields of the sensor elements. The purpose of the optical fiber PEL-sensor is to diagnose the inhomogeneous complex volumetric deformed state of a long cylindrical area (a neighborhood along the built-in linear sensor) inside a cyclically loaded composite structure. A numerical model has been developed to solve the 3D related boundary value problem of electric elasticity for a representative fragment of the system composite/sensor in the ANSYS package. The numerical modeling of deformation and electric harmonic fields inside the representative fragment was carried out; in particular, distributions of amplitudes of these fields in elements of the structure of the optical fiber PEL sensor were found. The resonant modes are revealed, and the analysis is given of regularities of frequency dependences for the real and imaginary parts of controlling and informative transfer coefficients of the built-in fiber-optic PEL-sensor in the composite/sensor system. Additionally, graphs of frequency dependencies of tangents of mechanical loss angles for various cases of deformation of the composite/sensor system are given. Damping of the composite/sensor system is carried out as a result of the conversion of some part of the mechanical energy (transmitted from the composite to the sensor during their joint deformation) into Joule heat by the fiber-optic PEL sensor with a subsequent dispersion. The latter is caused by the direct piezoelectric effect and Maxwell-Wagner relaxation of electric fields in the sensor elements. The frequency range of deformation of the composite/sensor system is set, in which the passive vibration damping mode is most effectively implemented. It is numerically confirmed that for the extreme high-frequency case of deformation of the composite/sensor system, relaxation processes are not implemented and, as a result, solutions for the controlling and informative transfer coefficients of the PEL-sensor practically coincide with previously obtained numerical solutions that did not take into account the electrical conductivity of the sensor structure elements.

Numerical modeling of deformation and damage around underground excavation by phase-field method with hydromechanical coupling

In the context of feasibility study for geological disposal of radioactive waste, this work focuses on numerical modeling of hydromechanical response and induced damage zones around an experimental gallery at the underground research laboratory (URL) at Bure in France. A new phase-field method is first proposed by considering two independent damage fields in order to easily describe both tensile and shear cracks. The phase-field method is extended to saturated porous media by incorporating the effect of fluid pressure. The proposed method is implemented in a finite element code and applied to the experimental gallery. The evolutions of hydromechanical responses and induced damaged zones are analyzed in both excavation and post-excavation phases. Numerical results are compared with experimental observations and measurements. It is found that the proposed method is able to well describe the main features of hydromechanical responses and damage processes such as tensile and shear cracked zones.

Numerical Modeling of Deformation at the Baiyun Gold Deposit, Northeastern China: Insights into the Structural Controls on Mineralization

The Qingchengzi ore field is an important gold-polymetallic center of the North China Craton. It has been recognized that the gold deposits in Qingchengzi were controlled by structures like lithological interfaces and fractures along mechanically weak bedding and foliation planes, but it still remains poorly understood how the structures affected the localization of the gold deposits. Finite element based numerical modeling was used to reproduce the deformation process of the Baiyun gold deposit during the mineralization period. Paleoproterozoic schist and marble are widely exposed in Qingchengzi, and a large part of the Baiyun gold ores occurs along the interfaces between the schist and the marble. The modeling results suggest that the mechanical contrast between the schist and the marble may be a major reason why the stress was localized along their lithological interfaces under a compressional stress regime. Two parts of their lithological interfaces were identified to be easily stress-localized and first fractured: the interface between the schist and its underlying marble at shallower levels and the one between the schist and its overlying marble at deeper levels. Stress concentration in these two parts is independent on the dipping angle and direction of the interfaces. Therefore, mineralizing fluids may have been concentrated into these two parts. The first one is consistent with the present ore bodies of the Baiyun gold deposit, and the second one could be considered for deep prospecting. These findings also provide implications for the structural controls of lithological interfaces on the mineralization in other gold deposits of this region.

Numerical modeling of deformation and destruction of NPP containment at impact of falling aircraft engines

Numerical modeling of deformation and destruction of NPP containment at impact of falling aircraft engines

Coupling pore network and finite element methods for rapid modelling of deformation

Numerical modelling of deformation in hydromechanical systems can be time-consuming using fully coupled classical numerical methods for large representative porous media samples. In this paper, we present a new two-way coupled partitioned fluid–solid system. The coupled system is applied for simulating geomechanical processes at the pore-scale. We track the deformation of the solid resulting from the drainage of resident fluids in the pores, as well as the evolution of fluid properties from dynamic loading. The finite element method is responsible for capturing the structural deformation in the coupled system while the dynamic pore network is used for modelling multiphase flow in the fluid subsystem. A fictitious fluid–solid interface is created at each pore network-finite element node junction via convex hulling, followed by data exchange using linear interpolation. The results show good agreement with a pre-existing coupled finite volume model and the computations are completed in much less time.

Experimental Simulation and Numerical Modeling of Deformation and Damage Evolution of Pre-Holed Sandstones After Heat Treatment

The deformation and damage evolution of sandstone after heat treatment greatly influence the efficient and safe development of deep geothermal energy extraction. To investigate this issue, laboratory confined compression tests and numerical simulations were conducted on pre-holed sandstone specimens after heat treatment. The laboratory test results show that the failure modes are closely related to the heat treatment temperature, with increasing treatment temperature, the failure modes change from mixed and shear modes to a splitting mode. The cracks always initiate from the sidewalls of the hole and then propagate. The failure process inside the hole proceeds as follows: calm period, particle ejection period, rock fragment exfoliation period and rock failure period. The specimens have different final failure features for the entire rock after heat treatment, but have the same failure features inside the hole. These phenomena can be explained by numerical simulations. The numerical simulations reveal that the failure modes in the numerical results agree very well with those observed in the experimental results. The damage zone always occurs at sidewalls of the hole and then propagates to the entire rock affected by shear or tensile damage. From 20°C to 200°C, thermal effect may promote shear damage and restrain tensile damage, while from 200°C to 800°C, thermal effect promotes tensile damage and restrains shear damage. Notably, the damage zone near the sidewalls of the hole has the same distribution range and pattern. Finally, the differences in the mechanisms due to increasing heat temperature are evaluated using scanning electron microscope (SEM) observations.

A probabilistic model of fracture of the composite material of a composite overwrapped pressure vessel

A probabilistic numerical model for fracture of unidirectional composite materials is developed. The algorithm for numerical simulation of the model takes into account the random distribution of carbon fibers, the spread of mechanical properties and the fracture of the structural elements of the material. Multivariate numerical experiments of the composite material of a composite overwrapped pressure vessel under tensile loads were carried out. The analysis of the patterns of deformation and fracture of a composite material is carried out. The physical mechanism of deformation and fracture of a composite material corresponds to a numerical model. The stress-strain curves of a numerical model of a composite material at 70% carbon fiber content are presented. The calculated values of Young’s modulus and tensile strength of the composite material at different percentages are obtained. A comparative analysis of experimental and numerical results showed that the results corresponded to 15%. Using of a numerical model of deformation and fracture of unidirectional composite materials makes it possible to track the mechanics of the processes of fracture of fibers and matrix, to obtain the most accurate analysis of the stress-strain state, and to develop generalized methods for calculating the strength of composite overwrapped pressure vessels

MATHEMATICAL MODELING OF MODERN ANTIFRICTION POLYMERS BEHAVIOR

An physicomechanical properties experimental study of the modern antifriction materials number was performed as part of the work. The 6 polymers and composites based on them having the greatest prospects for use as antifrictional coatings and interlayers in contact nodes are selected. The materials showed a nonlinear deformation behavior model in experimental study of samples. Therefore, the deformation theory of elastic-plasticity for the active loading case is chosen to describe the material behavior model in the framework of the first approximation. A numerical model of deformation of cylindrical samples under constrained compressionan experiment has been constructed. The optimal finite element mesh with a gradient decrease in the element size to the contact area of the cylindrical samples with the press plates has been selected. As part of the numerical experiments series, it was established: samples deformations from modern antifriction composite materials by 25–30 % more than other polymers considered, with one level of contact parameters; the modulus of the maximum contact tangential stress of all the materials examined is on average 25 times lower than the contact pressure.

Ubiquitous lower-mantle anisotropy beneath subduction zones

Seismic anisotropy provides key information to map the trajectories of mantle flow and understand the evolution of our planet. While the presence of anisotropy in the uppermost mantle is well established, the existence and nature of anisotropy in the transition zone and uppermost lower mantle are still debated. Here we use three-dimensional global seismic tomography images based on a large dataset that is sensitive to this region to show the ubiquitous presence of anisotropy in the lower mantle beneath subduction zones. Whereas above the 660 km seismic discontinuity slabs are associated with fast SV anomalies up to about 3%, in the lower mantle fast SH anomalies of about 2% persist near slabs down to about 1,000–1,200 km. These observations are consistent with 3D numerical models of deformation from subducting slabs and the associated lattice-preferred orientation of bridgmanite produced in the dislocation creep regime in areas subjected to high stresses. This study provides evidence that dislocation creep may be active in the Earth’s lower mantle, providing new constraints on the debated nature of deformation in this key, but inaccessible, component of the deep Earth. Lower-mantle anisotropy is present beneath all subduction zones, indicating that dislocation creep is active in the lower mantle, according to analysis of 3D global seismic tomography images.

钱营孜矿3<sub>2</sub>煤层开采顶底板变形破坏的数值模拟分析

钱营孜矿3<sub>2</sub>煤层开采顶底板变形破坏的数值模拟分析

Numerical simulation of strain localization and its relationship to formation of the Sue unconformity-related uranium deposits, eastern Athabasca Basin, Canada

Unconformity-related uranium deposits in the Athabasca Basin (Canada) are spatially associated with reactivated basement faults that cut the unconformity surface between Archean to Paleoproterozoic basement and Paleoproterozoic to Mesoproterozoic sedimentary rocks of the Athabasca Group. The Sue deposits (Sue A, B, C, D, and E) are located in the eastern Athabasca Basin along a 2-km-long north-northeast-trending structural corridor and have both sandstone-hosted (Sue A and Sue B; to the north) and basement-hosted (Sue C, Sue D, and Sue E; to the south) orebodies. All the deposits are structurally controlled by north-northeast-trending basement faults that demonstrate different degrees of reverse displacements of the unconformity surface. However, it is not clear why the mineralization is distributed in such a pattern along the corridor. In this study, both 2-dimensional (2D) and 3-dimensional (3D) numerical modeling of deformation were conducted to examine the relationship between the distribution of strain and uranium mineralization. The modeling shows that dilation (positive volumetric strain), thought to correlate with the development of extensional fracture systems and dilational jogs that represent potential mineralization sites, is primarily controlled by the rheological contrasts in basement rocks and the degree of deformation. The presence of faulted graphitic pelitic gneiss associated with the sandstone-hosted Sue A and Sue B deposits favours dilation localized within the sandstone at low degrees of deformation mainly due to the overlying competent hangingwall granitic gneiss. In contrast, the basement-hosted Sue C, Sue D and Sue E deposits are associated with dilation zones localized along the contact between the faulted graphitic pelitic gneiss and competent footwall silicified gneiss at higher degrees of deformation. The modeling results highlight the importance of both graphitic basement structures and strong rheological contrasts between basement rocks in uranium exploration in the Athabasca Basin.

A thermo-poro-mechanical constitutive and numerical model for deformation in sedimentary basins

Comprehensive modeling of sedimentary basins should integrate the coupled nature of different phenomena such as sediment compaction, pore-fluid flow and heat transport. In this context, the thermal evolution of the basin plays an important role in the mechanical and chemo-mechanical deformation processes as heat modifies fluids viscosity and minerals physicochemical properties, thus affecting pore fluid expulsion and mineral stability. The present paper describes a three-dimensional constitutive and numerical model specifically devised for dealing with thermo-poromechanical deformation processes during diagenesis. The sedimentary basin is modeled as a fully saturated thermo-poro-elastoplastic-viscoplastic medium undergoing large strains. A key feature of the model is related to the evolution of the sediment material properties associated with temperature and large irreversible porosity changes. The computational model, which integrates both poroplastic and poroviscoplastic components of deformation at large strains, relies upon a parallel implementation of the finite element method with a shared memory multiprocessing interface. Numerical simulations of gravitational compaction during the sediment accretion phase as well as along geological period of pore pressure dissipation are performed in the context of oedometric setting. Special emphasis is given to temperature effects on the deformation history of the basin.

Geomechanical conditions of the Tien Shan and Altai Orogeny

The results of numerical modelling of deformation of the Earth’s crust along the Tarim–Altai profile caused by the force of gravity and lateral compression using the approximate two-dimensional model of the elastoplastic transition are presented. The conditions of the formation of mountains and their roots were determined taking into account some geological and geophysical parameters.

Numerical Investigation of Damage Evolution and Localized Fracturing of Brittle Rock in Compression

In the present paper, a numerical model for deformation and fracturing of brittle rocks is used to study the damage evolution and localized fracturing of brittle rocks based on statistical mesoscopic damage mechanics. In the model, material heterogeneity and the mesoscopic renormalization concept are introduced to consider the interaction among microcracks in rock. The temporal and spatial evolution of acoustic emissions in the stressed rock are also described. Correspondingly, numerical tests on rock specimens with different heterogeneities, porosities, and scales are performed to investigate the damage evolution and localized fracturing of brittle rocks. The localized damage and fracturing of brittle rocks induced by microstructural damage is investigated. The study shows that heterogeneity, porosities, and scales of rock specimen have significant impact on damage evolution and localized fracturing mode. In addition, the study reveals that the postpeak response of stress-strain curve is due to the deformation of the structural elements, and localization means that the descending branch of the stress-strain curve of the rock specimen is size dependent, and the stress-strain curve can therefore not be regarded as a pure material property.

A sensitivity study on the numerical model of displacement and deformation of embedded brittle rock bodies in extension environment during salt tectonics

Many salt bodies contain large rock inclusions (called stringers) such as carbonate or anhydrite bodies. Mostly, large rock inclusions embedded in salt bodies have different ways of movement and deformation, including displacement, folding and fracturing. A finite element model with adaptive remeshing has been built for downbuilding simulation. The standard model set-up is constrained by observations from the South Oman Salt Basin. Based on the generic model in the previous research which shows the fracture, overtrusting or folding deformation during downbuilding process, a sensitivity study has been conducted on the numerical model of the deformation and displacement of brittle rock bodies, including the parameters such as the initial depth and the distance between them. The results of simulation are analyzed based on the data from SOSB and Zechstein salt basin. The study shows that the frequency of the break and the size of stringer fragments are strongly affected by the initial depth and thickness of stringers and the basement configuration.

Numerical modeling of deformation and vibrations in the construction of large-size fiberglass cooling tower fan

This paper presents the results of numerical modeling of deformation processes and the analysis of the fundamental frequencies of the construction of large-size fiberglass cooling tower fan. Obtain the components of the stress-strain state structure based on imported gas dynamic and thermal loads and the form of fundamental vibrations. The analysis of fundamental frequencies, the results of which have been proposed constructive solutions to reduce the probability of failure of the action of aeroelastic forces.

Contrasted continental rifting via plume-craton interaction: Applications to Central East African Rift

The East African Rift system (EARS) provides a unique system with the juxtaposition of two contrasting yet simultaneously formed rift branches, the eastern, magma-rich, and the western, magma-poor, on either sides of the old thick Tanzanian craton embedded in a younger lithosphere. Data on the pre-rift, syn-rift and post-rift far-field volcanic and tectonic activity show that the EARS formed in the context of the interaction between a deep mantle plume and a horizontally and vertically heterogeneous lithosphere under far-field tectonic extension. We bring quantitative insights into this evolution by implementing high-resolution 3D thermo-mechanical numerical deformation models of a lithosphere of realistic rheology. The models focus on the central part of the EARS. We explore scenarios of plume-lithosphere interaction with plumes of various size and initial position rising beneath a tectonically pre-stretched lithosphere. We test the impact of the inherited rheological discontinuities (suture zones) along the craton borders, of the rheological structure, of lithosphere plate thickness variations, and of physical and mechanical contrasts between the craton and the embedding lithosphere. Our experiments indicate that the ascending plume material is deflected by the cratonic keel and preferentially channeled along one of its sides, leading to the formation of a large rift zone along the eastern side of the craton, with significant magmatic activity and substantial melt amount derived from the mantle plume material. We show that the observed asymmetry of the central EARS, with coeval amagmatic (western) and magmatic (eastern) branches, can be explained by the splitting of warm material rising from a broad plume head whose initial position is slightly shifted to the eastern side of the craton. In that case, neither a mechanical weakness of the contact between the craton and the embedding lithosphere nor the presence of second plume are required to produce simulations that match observations. This result reconciles the passive and active rift models and demonstrates the possibility of development of both magmatic and amagmatic rifts in identical geotectonic environments.