Nonlinear criteria and the influence of the average principal stress on rocks destruction

Purpose. Consider possible series methods of Mohr-Coulomb nonlinear criterion that takes into account stresses in the plane of fracture. Investigate the influence of the average principal stress on rocks destruction when cylinder modeling under axial and side load conditions. Determine the weakening effect on the internal friction angle in the rocks under study using the examples of sample testing simulation. Methods. To study the processes in rock samples, we used a finite-element method DESTROCK-FE for modeling the deformation of rocks decomposes. The parameters of the deformation and fracture model are determined by comparing the deformation curves obtained by the modeling and experimental approaches. Findings. Modeling of rocks deformation under various loading conditions with a nonlinear criterion of fracture variants, in which destructive stresses can grow limited or unlimited or even decrease with increasing pressure, is performed. The design charts of axial and side deformations of the samples with a good approximation coincide with the experimental ones. The model parameters, including those for triaxial load conditions, are determined with a mathematic method using simulation laboratory tests under axial compression. Modeling with an upgrade fracture criterion showed that the load-bearing strength of salt rock samples under side load is greater than with axial pressure. Internal friction angle reduction with loss of strength reaches 15%. Originality. The Mohr-Coulomb series criterion is proposed, which makes it possible to set the nonlinearity in accordance with experimental data. Mechanical model parameters of rocks can be determined according to the results of single sample testing using the finite-element method DESTROCK-FE of decomposed rocks. The simulation was performed taking into account microdeformation, the influence of which is described by equations for a nonlinear-elastic condition. Practical implications. Cylinder modeling showed that the load-bearing strength of samples under side load is 10% for sylvinite and 20% more for rock salt than at axial loading. The obtained results indicate the ability of the finite-element method DESTROCK-FE of rocks destruction modeling while geomechanics survey conducting. Using this method, based on single sample simulation results, tested at simple compression, the parameters of elasticity, plasticity, viscosity, crisping can be obtained, suitable for deformation and fracture processes studies under various loading conditions.Мета. Розглянути можливі варіанти модифікації нелінійного критерію Кулона-Мора, що враховує напруження в площині руйнування. Дослідити вплив середнього головного напруження на руйнування гірських порід при моделюванні циліндричного зразка в умовах осьового та бічного навантаження. Оцінити вплив ослаблення міцності в досліджуваних гірських породах по поверхнях на кут внутрішнього тертя на прикладах моделювання випробування зразків. Методика. Для дослідження процесів у зразках гірських порід використаний скінчено-елементний метод моделювання деформування гірських порід, що руйнуються, DESTROCK-FE. Параметри моделі деформування і руйнування визначаються при порівнянні кривих деформування, отриманих модельним та експериментальним шляхом. Результати. Виконано моделювання деформування зразків гірських порід у різних умовах навантаження з нелінійним варіантом критерію руйнування, в якому руйнуючі напруження можуть зростати обмежено або необмежено та навіть знижуватися з ростом тиску. Розрахункові графіки осьових і бічних деформацій зразків з достатньою достовірністю збігаються з експериментальними. Параметри моделі, в тому числі для умов об’ємного навантаження, визначаються чисельним методом за допомогою моделювання лабораторних випробувань при осьовому стисненні. Моделювання циліндричних зразків показало, що несуча здатність зразків в умовах бічного навантаження на 10% для сильвініту і на 20% для кам’яної солі більше, ніж при осьовому навантаженні. Зниження кута внутрішнього тертя при втраті міцності по площинах зсуву і відриву для розглянутих соляних порід сягає 15%. Наукова новизна. Запропоновано модифікований критерій Кулона-Мора з урахуванням впливу міцності проміжного головного напруження, що дозволяє задавати нелінійність відповідно до експериментальних даних. Параметри механічної моделі гірських порід можуть визначатися за результатами випробування одного зразка із застосуванням скінчено-елементної моделі гірських порід, що руйнуються, DESTROCK-FE. Моделювання виконано з урахуванням мікродефектів, вплив яких описується рівняннями для нелінійно-пружного середовища. Практична значимість. Отримані результати свідчать про здатність скінчено-елементного методу моделювання руйнування гірських порід DESTROCK-FE вирішувати геомеханічні завдання. За допомогою цього методу за результатами моделювання одного зразка, випробуваного при одноосьовому стисненні, можуть бути отримані параметри пружності, пластичності, в’язкості, крихкості, придатні для застосування у дослідженнях процесів деформування і руйнування в різних умовах навантаження.Цель. Рассмотреть возможные варианты модификации нелинейного критерия Кулона-Мора, учитывающего напряжения в плоскости разрушения. Исследовать влияние среднего главного напряжения на разрушение горных пород при моделировании цилиндрического образца в условиях осевого и бокового нагружения. Оценить влияние ослабления прочности в исследуемых горных породах по поверхностям на угол внутреннего трения на примерах моделирования испытания образцов. Методика. Для исследования процессов в образцах горных пород использован конечно-элементный метод моделирования деформирования разрушающихся горных пород DESTROCK-FE. Параметры модели деформирования и разрушения определяются при сравнении кривых деформирования, полученных модельным и экспериментальным путем. Результаты. Выполнено моделирование деформирования образцов горных пород в различных условиях нагружения с нелинейным вариантом критерия разрушения, в котором разрушающие напряжения могут расти ограниченно или неограниченно, или даже снижаться с ростом давления. Расчетные графики осевых и боковых деформаций образцов с достаточной достоверностью совпадают с экспериментальными. Параметры модели, в том числе для условий объемного нагружения, определяются численным методом с помощью моделирования лабораторных испытаний при осевом сжатии. Моделирование цилиндрических образцов показало, что несущая способность образцов в условиях бокового нагружения на 10% для сильвинита и на 20% для каменной соли больше, чем при осевом нагружении. Снижение угла внутреннего трения при потере прочности по площадкам сдвига и отрыва для рассмотренных соляных пород достигает 15%. Научная новизна. Предложен модифицированный критерий Кулона-Мора c учетом влияния прочности промежуточного главного напряжения, позволяющий задавать нелинейность в соответствии с экспериментальными данными. Параметры механической модели горных пород могут определяться по результатам испытания одного образца с применением конечно-элементной модели разрушающих горных пород DESTROCK-FE. Моделирование выполнено с учетом микродефектов, влияние которых описывается уравнениями для нелинейно-упругой среды. Практическая значимость. Полученные результаты свидетельствуют о способности конечно-элементного метода моделирования разрушения горных пород DESTROCK-FE решать геомеханические задачи. С помощью этого метода по результатам моделирования одного образца, испытанного при одноосном сжатии, могут быть получены параметры упругости, пластичности, вязкости, хрупкости, пригодные для применения в исследованиях процессов деформирования и разрушения в различных условиях нагружения.This study was supported by the Institute of Environmental Geoecology of the Russian Academy of Sciences. Materials with the laboratory rocks tests results were provided by the Research Laboratory of Physico-Mechanical Properties and Rocks Destruction at Saint Petersburg Mining University (Candidate of Technical Sciences M. Il’inov, Candidate of Technical Sciences V. Korshunov, Candidate of Technical Sciences D. Petrov). These studies were made possible by the help of Candidate of Physical and Mathematical Sciences V. Chantsev in the implementation of the author’s ideas in computer programs

Simulation of subseismic joint and fault networks using a heuristic mechanical model

Flow simulations of fractured and faulted reservoirs require representation of subseismic structures about which subsurface data are limited. We describe a method for simulating fracture growth that is mechanically based but heuristic, allowing for realistic modelling of fracture networks with reasonable run times. The method takes a triangulated meshed surface as input, together with an initial stress field. Fractures initiate and grow based on the stress field, and the growing fractures relieve the stress in the mesh. We show that a wide range of bedding-plane joint networks can be modelled simply by varying the distribution and anisotropy of the initial stress field. The results are in good qualitative agreement with natural joint patterns. We then apply the method to a set of parallel veins and demonstrate how the variations in thickness of the veins can be represented. Lastly, we apply the method to the simulation of normal fault patterns on salt domes. We derive the stress field on the bedding surface using the horizon curvature. The modelled fault network shows both radial and concentric faults. The new method provides an effective means of modelling joint and fault networks that can be imported to the flow simulator

A fluid flow perspective on the diagenesis of Te Aute limestones

Pliocene cool-water, bioclastic Te Aute limestones in East Coast Basin, New Zealand, accumulated either in shelfal shoal areas or about structurally shallow growth fold structures in the tectonically active accretionary forearc prism. Up to five stages of carbonate cementation are recognised, based on cement sequence-stratigraphic concepts, that formed on the seafloor during exposure of the limestones before burial, during burial, uplift, and deformation. Two principal fluid types are identified--topography-driven meteoric fluids and compaction-driven fluids. We have developed conceptual and quantitative models that attempt to relate the physical characteristics of fluid flow to the cement paragenesis. In particular, we have simulated the effects of uplift of the axial ranges bordering East Coast Basin in terms of the degree of penetration of a meteoric wedge into the basin. The dynamics of meteoric flow changed dramatically during uplift over the last 2 m.y. such that the modelled extent of the meteoric wedge is at least 40 km across the basin, and the penetration depth 1500 m or more corresponding with measured freshwater intersections in some oil wells. Cement-fluid relationships include: (1) true marine cements that precipitated in areas remote from shallow freshwater lenses; (2) pre-compaction cements that formed in shallow freshwater lenses beneath limestone "islands"; (3) post-compaction cements derived from compaction-driven flow during burial; (4) early uplift-related fracture-fill cements formed during deformation of the accretionary prism and uplift of the axial ranges; and (5) late uplift-related cements associated with uplift into a shallow meteoric regime

Conformal mapping methods for interfacial dynamics

The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the article begins with an overview of continuous conformal-map dynamics. This includes problems of interfacial motion driven by harmonic fields (such as viscous fingering and void electromigration), bi-harmonic fields (such as viscous sintering and elastic pore evolution), and non-harmonic, conformally invariant fields (such as growth by advection-diffusion and electro-deposition). The second part of the article is devoted to iterated conformal maps for analogous problems in stochastic interfacial dynamics (such as diffusion-limited aggregation, dielectric breakdown, brittle fracture, and advection-diffusion-limited aggregation). The third part notes that all of these models can be extended to curved surfaces by an auxilliary conformal mapping from the complex plane, such as stereographic projection to a sphere. The article concludes with an outlook for further research.Comment: 37 pages, 12 (mostly color) figure

Scaling of interfaces in brittle fracture and perfect plasticity

The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a linear size L=350 it is found that in the cases studied the fracture surfaces exhibit self-affine scaling with a roughness exponent close to 2/3, which is asymptotically exactly true for plasticity though finite-size effects are evident for both. The overlap of yield or minimum energy and fracture surfaces with exactly the same disorder configuration is shown to be a decreasing function of the system size and to be of a rather large magnitude for all cases studied. The typical ``overlap cluster'' length between pairs of such interfaces converges to a constant with $L$ increasing.Comment: Accepted for publication in Phys. Rev.

Estimating Terminal Velocity of Rough Cracks in the Framework of Discrete Fractal Fracture Mechanics

In this paper we first obtain the order of stress singularity for a dynamically propagating self-affine fractal crack. We then show that there is always an upper bound to roughness, i.e. a propagating fractal crack reaches a terminal roughness. We then study the phenomenon of reaching a terminal velocity. Assuming that propagation of a fractal crack is discrete, we predict its terminal velocity using an asymptotic energy balance argument. In particular, we show that the limiting crack speed is a material-dependent fraction of the corresponding Rayleigh wave speed

From fracture to fragmentation: discrete element modeling -- Complexity of crackling noise and fragmentation phenomena revealed by discrete element simulations

Discrete element modelling (DEM) is one of the most efficient computational approaches to the fracture processes of heterogeneous materials on mesoscopic scales. From the dynamics of single crack propagation through the statistics of crack ensembles to the rapid fragmentation of materials DEM had a substantial contribution to our understanding over the past decades. Recently, the combination of DEM with other simulation techniques like Finite Element Modelling further extended the field of applicability. In this paper we briefly review the motivations and basic idea behind the DEM approach to cohesive particulate matter and then we give an overview of on-going developments and applications of the method focusing on two fields where recent success has been achieved. We discuss current challenges of this rapidly evolving field and outline possible future perspectives and debates

An embedded FE model for modelling reinforced concrete slabs in fire

This is the post-print version of the final paper published in Engineering Structures. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2008 Elsevier B.V.It is evident from a series of tests on simply supported reinforced concrete slabs that the failure of the slabs at large deflections is due to the formation of individual large cracks. This failure mode was also observed in the Cardington full-scale fire tests. Previous research indicates that the global behaviour of concrete slabs subject to large deflections can be well predicted by the smeared cracking model; however, the model cannot quantitatively predict the openings of individual cracks within the slabs at large deflections. For the discrete approach it is usually assumed that the cracks are formed along element edges, therefore continuous re-meshing is required during the analysis. Consequently, the results are mesh-dependent and the computing cost is high. In recent years, mesh independent finite element procedures, such as embedded (EFEM) and extended (XFEM) approaches, were widely used for modelling of the crack initiation and growth in structural members. However, most of the meshless models developed are either based on in-plane loading conditions or confined to thin shells with assumed full-depth cracks, which form apparent displacement jumps within an element. For a reinforced concrete slab, an out-of-plane load causes coupled stretching and bending of the slab, cracks are usually initiated at discrete positions and then propagated, until at last some individual full-depth cracks are formed. Pure stretching or assumed full-depth cracking is inadequate for modelling this kind of failure. Therefore, in this research, a non-linear layered procedure with embedded weak discontinuity is developed to quantitatively model the progressive tensile failure of reinforced concrete slabs subjected to large deflections. The current model inherits the advantage of the smeared approach, and at the same time, introduces the opening width of crack explicitly by taking the advantage of the better description of the kinematic characteristics of the EFEM approach. A series of validations have been conducted against test data at both ambient and elevated temperatures, and the research shows that the model developed in this paper is not sensitive to the FE mesh size and the aspect ratio of the slab. The results predicted by the model developed agreed well with the test data in terms of deflection and crack open width, also agreeing well with those modelled by the smeared model. Hence, this new approach provides a numerical method to predict the load capacity as well as identifying the occurrence and severity of crack failure in reinforced concrete slabs subjected to extreme loading conditions, such as fire