An adaptive neuro fuzzy inference system to model the uniaxial compressive strength of cemented hydraulic backfill

Purpose. The purpose of this paper is to develop the models for predicting the uniaxial compressive strength (UCS) of cemented hydraulic backfill (CHB), a widely used technique for filling underground voids created by mining operations as it provides the high strength required for safe and economical working environment and allows the use of waste rock from mining operations as well as tailings from mineral processing plants as ingredients. Methods. In this study, different modelling techniques such as conventional linear, nonlinear multiple regression and one of the evolving soft computing methods, adaptive neuro fuzzy inference system (ANFIS), were used for the prediction of UCS, the main criterion used to design backfill recipe. Findings. Statistical performance indices used to evaluate the efficiency of the developed models indicated that the ANFIS model can effectively be implemented for designing CHB with desired UCS. As proved by the performance indicators ANFIS model gives more compatible results with the expert opinion and current literature than conventional modelling techniques. Originality. In order to construct the models a very large database, containing more than 1600 UCS test results, was used. In addition to widely used conventional regression based modelling techniques, one of the evolving soft computing methods, ANFIS was employed. Numerical examples showing the implementation of constructed models were provided. Practical implementation. As proved by the statistical performance indicators, the developed models can be used for a reliable prediction of the UCS of CHB. However, more accurate results can be achieved by expanding the database and by constructing improved models using the algorithm presented in this paper.Мета. Побудова моделей для прогнозування межі міцності при одноосьовому стисканні цементної гідравлічної закладки для заповнення вироблених просторів шахт. Методика. Для досягнення поставленої мети були використані різні методи моделювання: лінійна та нелінійна множинна регресія, а також порівняно недавно став популярним метод програмування – адаптивне нейронечітке логічне виведення (ANFIS). За їх допомогою було спрогнозовано зміну міцності на одноосьове стискання, що є ключовим показником для визначення складу закладної суміші. Для побудови моделей використана значна база даних, яка включає результати більш ніж 1600 випробувань на одноосьове стискання. Лабораторними дослідженнями також визначалися властивості закладних матеріалів і суміші. Результати. Модель ANFIS дала найкращу продуктивність з урахуванням статистичних показників ефективності, таких як середня абсолютна процентна похибка і змінний обліковий запис. Статистичні показники продуктивності, які використовуються для оцінки ефективності розроблених моделей, свідчать, що моделювання за допомогою ANFIS дозволяє отримати результати, які більше відповідають експертній оцінці та даним з сучасної літератури, ніж інформація, отримана за допомогою традиційного моделювання. Встановлено, що на відміну від регресивного моделювання, ANFIS не вимагає заздалегідь визначених математичних рівнянь для взаємозв’язку між вхідними та вихідними змінними і використовує наданий набір даних для ефективного визначення структури моделі. Наукова новизна. Вперше для прогнозування міцності при одноосьовому стисканні були використані не лише традиційні способи моделювання, засновані на регресії, а й інноваційний метод програмування – адаптивне нейронечітке логічне виведення ANFIS. У статті наведені чисельні приклади впровадження нових побудованих моделей. Практична значимість. Статистичні індикатори продуктивності показали, що розроблені моделі можуть бути використані для надійного прогнозування міцності при одноосьовому стисканні й оптимальної рецептури закладної суміші. Однак, щоб отримати більш точні результати, необхідно мати більш широку базу даних і створити більш досконалі моделі на основі алгоритму, запропонованому в даній статті.Цель. Построение моделей для прогнозирования предела прочности при одноосном сжатии цементной гидравлической закладки для заполнения выработанных пространств шахт. Методика. Для достижения поставленной цели были использованы различные методы моделирования: линейная и нелинейная множественная регрессия, а также сравнительно недавно ставший популярным метод программирования – адаптивный нейронечеткий логический вывод (ANFIS). С их помощью было спрогнозировано изменение прочности на одноосное сжатие, что является ключевым показателем для определения состава закладочной смеси. Для построения моделей использована обширная база данных, которая включает результаты более чем 1600 испытаний на одноосное сжатие. Лабораторными исследованиями также определялись свойства закладочных материалов и смеси. Результаты. Модель ANFIS дала наилучшую производительность с учетом статистических показателей эффективности, таких как средняя абсолютная процентная погрешность и переменная учетная запись. Статистические показатели производительности, используемые для оценки эффективности разработанных моделей, свидетельствуют, что моделирование с помощью ANFIS позволяет получить результаты, которые более соответствуют экспертной оценке и данным из современной литературы, чем информация, полученная при помощи традиционного моделирования. Установлено, что в отличие от регрессионного моделирования, ANFIS не требует заранее определенных математических уравнений для взаимосвязи между входными и выходными переменными и использует предоставленный набор данных для эффективного определения структуры модели. Научная новизна. Впервые для прогнозирования прочности при одноосном сжатии были использованы не только традиционные способы моделирования, основанные на регрессии, но и инновационный метод программирования – адаптивный нейронечеткий логический вывод ANFIS. В статье приведены численные примеры внедрения новых построенных моделей. Практическая значимость. Статистические индикаторы производительности показали, что разработанные модели могут быть использованы для надежного прогнозирования прочности при одноосном сжатии и оптимальной рецептуры закладочной смеси. Однако, чтобы получить более точные результаты, необходимо иметь более широкую базу данных и создать более совершенные модели на основе алгоритма, предложенного в данной статье.The authors thank the staff and the managers of Jinfeng underground gold mine for their helps and cooperation during field and laboratory studies. The company is also acknowledged for the permission to use and publish the data

Finite element modelling of rate-dependent ratcheting in granular materials

International audienceThe present paper introduces a comprehensive model that is capable of describing the behaviour, under cyclic loading, of the granular materials used in railway tracks and road pavement. Its main thrust is the introduction of the ''Chicago'' law in a continuum approach to account for the ratcheting effects. It also emphasizes rate-dependency as a dissipative mechanism that acts independently or jointly with the ratcheting effect as well as the non-associated plasticity. The numerical procedure is based on the return mapping algorithm, where Newton's method is used to calculate the nonlinear consistency parameter of the flow rule and to obtain a consistent tangent modulus. The model was applied to specific numerical examples including multi-axial and cyclic loading conditions

Modelling glass fibre-reinforced polymer reinforced geopolymer concrete columns

Glass fibre-reinforced polymer (GFRP) bar and stirrup reinforced geopolymer concrete (GPC) is increasingly recognised as a potential replacement to the conventional steel-reinforced ordinary Portland cement (OPC) concrete due to its superior durability. This paper proposed an analytical model to predict the load-displacement relationship of the concentrically and eccentrically loaded GFRP-GPC columns. The cross-section was divided into a number of strips and a strain gradient was assigned to determine the stresses in the cover, core and reinforcement. The theoretical predictions were then validated using experimental results from previous studies on the behaviour of GFRP-GPC, GFRP-OPC concrete and steel-GFRP concrete systems. It was found that the predicted peaks load, displacements at peak load and ductility indices were generally in close agreement with the experimental results of the GFRP-GPC columns. However, the model had a tendency to over-predict the stiffness of GFRP-OPC concrete and steel-OPC concrete columns in the elastic range. Overall, the proposed analytical model is suitable for GFRP-GPC systems and could facilitate the widespread use of this composite material

A strain-based failure criterion for pillar stability analysis

Strain-based failure criteria have several advantages over stress-based failure criteria: they can account for elastic and inelastic strains, they utilise direct, observables effects instead of inferred effects (strain gauges vs. stress estimates), and model complete stress-strain curves including pre-peak, non-linear elasticity and post-peak strain weakening. In this study, a strain-based failure criterion derived from thermodynamic first principles utilising the concepts of continuum damage mechanics is presented. Furthermore, implementation of this failure criterion into a finite-element simulation is demonstrated and applied to the stability of underground mining coal pillars. In numerical studies, pillar strength is usually expressed in terms of critical stresses or stress-based failure criteria where scaling with pillar width and height is common. Previous publications have employed the finite-element method for pillar stability analysis using stress-based failure criterion such as Mohr-Coulomb and Hoek-Brown or stress-based scalar damage models. A novel constitutive material model, which takes into consideration anisotropy as well as elastic strain and damage as state variables has been developed and is presented in this paper. The damage threshold and its evolution are strain-controlled, and coupling of the state variables is achieved through the damage-induced degradation of the elasticity tensor. This material model is implemented into the finite-element software ABAQUS and can be applied to 3D problems. Initial results show that this new material model is capable of describing the non-linear behaviour of geomaterials commonly observed before peak strength is reached as well as post-peak strain softening. Furthermore, it is demonstrated that the model can account for directional dependency of failure behaviour (i.e. anisotropy) and has the potential to be expanded to environmental controls like temperature or moisture

Interaction Diagram of Rubberised Concrete Filled Circular Hollow Sections

Concrete filled steel tube (CFST) is increasingly used in engineering construction as columns and beams. CFST is known to absorb large amounts of energy as a result of the composite effect. Internationally, there are increasing amounts of waste rubber. In this study recycled rubber is used as aggregate supplement in concrete. Rubberised concrete is known to be more ductile than conventional concrete however has a lower compressive strength. This study investigated the performance of thirty rubberised concrete-filled single-skin steel tubes under combined loading conditions and compared the results against six steel hollow tubular members. Three rubber replacement ratios, 0%, 15% and 30%, three load eccentricities and four tube sections with section slenderness (b/t, width/thickness) of 18 to 36 were examined. The results have shown that the composite section had greatly improved load carrying capacity. The ductile rubberised concrete was more effective in delaying the premature buckling failure of the steel tube compared to the normal concrete. The interaction diagrams were constructed from the experiments and theoretical calculations. It was found that the behaviours of the rubberised concrete filled steel tubes could be accurately predicted using existing design guidelines. This study demonstrated the potential of using rubberised concrete as a cost-effective solution to safe roadside barriers and structural members in buildings located in seismic active zones

Interaction Diagram of Rubberised Concrete Filled Square Hollow Sections

Rubberised concrete utilises waste material, prevents resource extraction and improves concrete ductility, however at the cost of reduced strength and stiffness. The performance of thirty rubberised concrete-filled single-skin steel tubes under combined loading conditions were systematically investigated and comparisons against six steel hollow tubular columns and beams were made. The experimental program consisted of three rubber replacement ratios, 0%, 15% and 30%, three load eccentricities and four tube sections with section slenderness (b/t, width/thickness) of 18 to 50. The results showed that the confined rubberised concrete and the restrained steel tube improved strength and ductility of the composite section. The rubberised concrete was more effective in delaying the premature buckling failure of the steel tube compared to the more brittle normal concrete. The rubberised concrete with 15% rubber replacement ratio showed a good balance of strength and ductility. The interaction diagrams obtained from the experiments and theoretical calculations were constructed and compared. The behaviours of the rubberised concrete filled steel tubes could be accurately predicted using existing design guidelines and safe designs can be produced. This study demonstrated the possibility of using rubberised concrete as a cost-effective solution to problems that require high moment and deformation capacity, such as the roadside barriers and columns in buildings located in seismic active zones

A discrete element study of settlement in vibrated granular layers: role of contact loss and acceleration

This paper deals with the vibration of granular materials due to cyclic external excitation. It highlights the effect of the acceleration on the settlement speed and proves the existence of a relationship between settlement and loss of contacts in partially confined granular materials under vibration. The numerical simulations are carried out using the Molecular Dynamics method, where the discrete elements consist of polygonal grains. The data analyses are conducted based on multivariate autoregressive models to describe the settlement and permanent contacts number with respect to the number of loading cycles

Evaluating force distributions within virtual uncemented mine backfill using discrete element method

This paper investigates the distribution of intergranular forces within uncemented mine backfills using the discrete element method (DEM) and compares it with the existing analytical method. The virtual backfilling is modeled via the DEM to simulate the underground mining stopes backfilling with uncemented granular materials. Normal and shear forces of all particle contacts within the model backfill are tracked and analyzed with particular attention to the effect of sidewall friction. The DEM evaluates normal force chains and reveals a concentration of high forces within the model backfill. The DEM shows profiles of forces that are distinctly different from those obtained from analytical solutions. Quantitative analyses of the spatial distribution of forces, number of contact points, and changes in the orientation of forces are presented. The DEM demonstrates its capacity as a good tool for looking closely into the backfill on a particle scale. It highlights potential force distribution and concentration within a backfill and shows the limitations of analytical solutions, which helps engineers in the mining industry to better understand the possible mechanisms within backfill

Experimental and numerical characterization of a mechanical expansion process for thin-walled tubes

Air heat exchangers are made with tubes joined to finned pack. The connection between tubes and fins can be obtained through a mechanical process where an ogive is pushed inside the tube with smaller internal diameter causing its expansion. Residual plastic deformation provides the assembly with the fins. Accurate connection over the whole contact area of the tubes and fins is essential for maximum heat exchange efficiency. The goal of this work is to study and develop a finite element model able to effectively simulate expansion forming, allowing process analysis and, eventually, process optimization. The paper is divided into a first experimental part, where the materials used for the heat exchangers are characterized, and a second numerical part where models have been developed on the basis of the experimental data. The developed models are used to identify the material properties with an inverse method, and then to study the technological process of tube expansion by using a simplified but sufficiently accurate description. The model has proved to be an effective design tool, as it can evaluate the influence of the main parameters on the process and so optimize production according to technological variations

Creep Fractures in the Mantle and their role for Deep Fluid Transfer

When hot and ductile rocks fail they do so with an astonishing variety. Observations from crustal deformation show that when the fluid content is low (less than a few per cent) they form the cores of anastomosing mylonitic shear zones, which feature strong gradients in grain size towards their metamorphic fluid rich centre (Fusseis et al., 2009). In circumstances where the fluid/melt content is high they form macroscopically visible ductile fractures (Weinberg and Regenauer-Lieb, 2010) which allow melt transfer into the shallower crust forming the feeder zone of granites. We show here that all of the above phenomena are new types of instabilities well known from high temperature deformation of ceramics, i.e. materials that otherwise show brittle cleavage at cold laboratory conditions. The new failure modes boil down to a series of microscopic processes, where upon increasing temperature and decreasing applied stress failure modes transition from brittle cleavage to transgranular and intergranular “creep fractures”, summarized by Ashby’s classical deformation mechanism maps (Ghandi and Ashby, 1979). Although Material Scientists are well aware of these creep enhanced fracture modes we have been lacking concise evidence in the laboratory and field proving the existence of these failure transitions. As creep fracture processes are happening on relatively slow geodynamic time scales they have been argued to provide the critical mechanism linking plate tectonic processes and deep fluid transfer processes (Regenauer-Lieb, 1999). In these considerations fluids are viewed as creating their own pathways through facilitating shear localization by creep fractures, rather than being a passive constituent simply following brittle fractures that are generated inside a shear zone caused by other localization mechanisms. Recently, the missing laboratory (Rybacki et al., 2008) and field evidence for creep fractures have been found (Fusseis et al., 2009). Ghost images of both creep fractures and brittle fractures can also be seen in OH diffusion profiles on grain boundaries (Sommer et al., 2008) and fully embedded intragranular cracks in mantle xenoliths (Sommer et al., 2012). In order to illustrate the fundamental implications for deep fluid transfer we extend classical solutions of material sciences to geodynamic conditions and incorporate melting reactions into the numerical formulation. We will show the implications to a number of applied field studies