Search results for: nonlinear acoustic NDT&E

Authors: Neda Nabid

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Friction-based supplemental devices have been extensively used for seismic protection and strengthening of structures, however, the conventional use of these dampers may not necessarily lead to an efficient structural performance. Conventionally designed friction dampers follow a uniform height-wise distribution pattern of slip load values for more practical simplicity. This can lead to localizing structural damage in certain story levels, while the other stories accommodate a negligible amount of relative displacement demand. A practical performance-based optimization methodology is developed to tackle with structural damage localization of RC frame buildings with friction energy dissipation devices under severe earthquakes. The proposed methodology is based on the concept of uniform damage distribution theory. According to this theory, the slip load values of the friction dampers redistribute and shift from stories with lower relative displacement demand to the stories with higher inter-story drifts to narrow down the discrepancy between the structural damage levels in different stories. In this study, the efficacy of the proposed design methodology is evaluated through the seismic performance of five different low to high-rise RC frames equipped with friction wall dampers under six real spectrum-compatible design earthquakes. The results indicate that compared to the conventional design, using the suggested methodology to design friction wall systems can lead to, by average, up to 40% reduction of maximum inter-story drift; and incredibly more uniform height-wise distribution of relative displacement demands under the design earthquakes.

Keywords: friction damper, nonlinear dynamic analysis, RC structures, seismic performance, structural damage

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Authors: Hamed K. Esfahani, Bithin Datta

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Transport of reactive chemical contaminant species in groundwater aquifers is a complex and highly non-linear physical and geochemical process especially for real life scenarios. Simulating this transport process involves solving complex nonlinear equations and generally requires huge computational time for a given aquifer study area. Development of optimal remediation strategies in aquifers may require repeated solution of such complex numerical simulation models. To overcome this computational limitation and improve the computational feasibility of large number of repeated simulations, Genetic Programming based trained surrogate models are developed to approximately simulate such complex transport processes. Transport process of acid mine drainage, a hazardous pollutant is first simulated using a numerical simulated model: HYDROGEOCHEM 5.0 for a contaminated aquifer in a historic mine site. Simulation model solution results for an illustrative contaminated aquifer site is then approximated by training and testing a Genetic Programming (GP) based surrogate model. Performance evaluation of the ensemble GP models as surrogate models for the reactive species transport in groundwater demonstrates the feasibility of its use and the associated computational advantages. The results show the efficiency and feasibility of using ensemble GP surrogate models as approximate simulators of complex hydrogeologic and geochemical processes in a contaminated groundwater aquifer incorporating uncertainties in historic mine site.

Keywords: geochemical transport simulation, acid mine drainage, surrogate models, ensemble genetic programming, contaminated aquifers, mine sites

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Authors: Soleen Karim, Meira Yasin, Rezhin Qader

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Children’s books present a colorful life for kids around the world, their current environment or what they could potentially have- a home, two loving parents, a playground, and a safe school within a short walk or bus ride. These images are only pages in a donated book for children displaced by war. The environment they live in is significantly different. Displaced children are faced with a temporary life style filled with fear and uncertainty. Children of war associate various structural institutions with a trauma and cannot enter the space, even if it is for their own future development, such as a school. This paper is a collaborative effort with students of the Kennesaw State University architecture department, architectural designers and a mental health professional to address and link the design challenges and the psychological trauma for children of war. The research process consists of a) interviews with former refugees, b) interviews with current refugee children, c) personal understanding of space through one’s own childhood, d) literature review of tested design methods to address various traumas. Conclusion: In addressing the built environment for children of war, it is necessary to address mental health and well being through the creation of space that is sensitive to the needs of children. This is achieved by understanding critical design cues to evoke normalcy and safe space through program organization, color, and symbiosis of synthetic and natural environments. By involving the children suffering from trauma in the design process, aspects of the design are directly enhanced to serve the occupant. Neglecting to involve the participants creates a nonlinear design outcome and does not serve the needs of the occupant to afford them equal opportunity learning and growth experience as other children around the world.

Keywords: activist architecture, childhood education, childhood psychology, adverse childhood experiences

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Authors: Tuğçe Kiper Elibol, İbrahim Uslan, Mehmet Ali Guler, Murat Buyuk, Uğur Yolum

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According to the FAA report, 142603 bird strikes were reported for a period of 24 years, between 1990 – 2013. Bird strike with aerospace structures not only threaten the flight security but also cause financial loss and puts life in danger. The statistics show that most of the bird strikes are happening with the nose and the leading edge of the wings. Also, a substantial amount of bird strikes is absorbed by the jet engines and causes damage on blades and engine body. Crash proof designs are required to overcome the possibility of catastrophic failure of the airplane. Using computational methods for bird strike analysis during the product development phase has considerable importance in terms of cost saving. Clearly, using simulation techniques to reduce the number of reference tests can dramatically affect the total cost of an aircraft, where for bird strike often full-scale tests are considered. Therefore, development of validated numerical models is required that can replace preliminary tests and accelerate the design cycle. In this study, to verify the simulation parameters for a bird strike analysis, several different numerical options are studied for an impact case against a primitive structure. Then, a representative bird mode is generated with the verified parameters and collided against the leading edge of a training aircraft wing, where each structural member of the wing was explicitly modeled. A nonlinear explicit dynamics finite element code, LS-DYNA was used for the bird impact simulations. SPH methodology was used to model the behavior of the bird. Dynamic behavior of the wing superstructure was observed and will be used for further design optimization purposes.

Keywords: bird impact, bird strike, finite element modeling, smoothed particle hydrodynamics

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Authors: Jakub Zembrzuski, Bartosz Sobczyk, Mikołaj MIśkiewicz

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Besides designing new constructions, engineers all over the world must face another problem – maintenance, repairs, and assessment of the technical condition of existing bridges. To solve more complex issues, it is necessary to be familiar with the theory of finite element method and to have access to the software that provides sufficient tools which to enable create of sometimes significantly advanced numerical models. The paper includes a brief assessment of the technical condition, a description of the in situ non-destructive testing carried out and the FEM models created for global and local analysis. In situ testing was performed using strain gauges and displacement sensors. Numerical models were created using various software and numerical modeling techniques. Particularly noteworthy is the method of modeling riveted joints of the crossbeam of the viaduct. It is a simplified method that consists of the use of only basic numerical tools such as beam and shell finite elements, constraints, and simplified boundary conditions (fixed support and symmetry). The results of the numerical analyses were presented and discussed. It is clearly explained why the structure did not fail, despite the fact that the weld of the deck plate completely failed. A further research problem that was solved was to determine the cause of the rapid increase in values on the stress diagram in the cross-section of the transverse section. The problems were solved using the solely mentioned, simplified method of modeling riveted joints, which demonstrates that it is possible to solve such problems without access to sophisticated software that enables to performance of the advanced nonlinear analysis. Moreover, the obtained results are of great importance in the field of assessing the operation of bridge structures with an orthotropic plate.

Keywords: bridge, diagnostics, FEM simulations, failure, NDT, in situ testing

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Authors: Niroshan K. Walgama Wellalage, Tieling Zhang, Richard Dwight

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State-based Markov deterioration models (SMDM) sometimes fail to find accurate transition probability matrix (TPM) values, and hence lead to invalid future condition prediction or incorrect average deterioration rates mainly due to drawbacks of existing nonlinear optimization-based algorithms and/or subjective function types used for regression analysis. Furthermore, a set of separate functions for each condition state with age cannot be directly derived by using Markov model for a given bridge element group, which however is of interest to industrial partners. This paper presents a new approach for generating Homogeneous SMDM model output, namely, the Modified Weibull approach, which consists of a set of appropriate functions to describe the percentage condition prediction of bridge elements in each state. These functions are combined with Bayesian approach and Metropolis Hasting Algorithm (MHA) based Markov Chain Monte Carlo (MCMC) simulation technique for quantifying the uncertainty in model parameter estimates. In this study, factors contributing to rail bridge deterioration were identified. The inspection data for 1,000 Australian railway bridges over 15 years were reviewed and filtered accordingly based on the real operational experience. Network level deterioration model for a typical bridge element group was developed using the proposed Modified Weibull approach. The condition state predictions obtained from this method were validated using statistical hypothesis tests with a test data set. Results show that the proposed model is able to not only predict the conditions in network-level accurately but also capture the model uncertainties with given confidence interval.

Keywords: bridge deterioration modelling, modified weibull approach, MCMC, metropolis-hasting algorithm, bayesian approach, Markov deterioration models

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Authors: Mohamed Elghorab, Vendra C. Madhav Rao, Jennifer X. Wen

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Turbulence modelling is still evolving, and efforts are on to improve and develop numerical methods to simulate the real turbulence structures by using the empirical and experimental information. The monotonically integrated large eddy simulation (MILES) is an attractive approach for modelling turbulence in high Re flows, which is based on the solving of the unfiltered flow equations with no explicit sub-grid scale (SGS) model. In the current work, this approach has been used, and the action of the SGS model has been included implicitly by intrinsic nonlinear high-frequency filters built into the convection discretization schemes. The MILES solver is developed using the opensource CFD OpenFOAM libraries. The role of flux limiters schemes namely, Gamma, superBee, van-Albada and van-Leer, is studied in predicting turbulent statistical quantities for a fully developed channel flow with a friction Reynolds number, Re_T = 180, and compared the numerical predictions with the well-established Direct Numerical Simulation (DNS) results for studying the wall generated turbulence. It is inferred from the numerical predictions that Gamma, van-Leer and van-Albada limiters produced more diffusion and overpredicted the velocity profiles, while superBee scheme reproduced velocity profiles and turbulence statistical quantities in good agreement with the reference DNS data in the streamwise direction although it deviated slightly in the spanwise and normal to the wall directions. The simulation results are further discussed in terms of the turbulence intensities and Reynolds stresses averaged in time and space to draw conclusion on the flux limiter schemes performance in OpenFOAM context.

Keywords: flux limiters, implicit SGS, MILES, OpenFOAM, turbulence statistics

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Authors: Sajjad Izadpanah, Seyed Hadi Ghaderi, Morteza Sayah Irani, Mahdi Gerdooei

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In this research work, a sophisticated yield criterion known as BBC2003, capable of describing planar anisotropic behaviors of aluminum alloy sheets, was integrated into the commercial finite element code ABAQUS/Standard via a user subroutine. The complete formulation of the implementation process using a fully implicit integration scheme, i.e., the classic backward Euler method, is presented, and relevant aspects of the yield criterion are introduced. In order to solve nonlinear differential and algebraic equations, the line-search algorithm was adopted in the user-defined material subroutine (UMAT) to expand the convergence domain of the iterative Newton-Raphson method. The developed subroutine was used to simulate a challenging computational problem with complex stress states, i.e., deep drawing of an anisotropic aluminum alloy AA3105. The accuracy and stability of the developed subroutine were confirmed by comparing the numerically predicted earing and thickness variation profiles with the experimental results, which showed an excellent agreement between numerical and experimental earing and thickness profiles. The integration of the BBC2003 yield criterion into ABAQUS/Standard represents a significant contribution to the field of computational mechanics and provides a useful tool for analyzing the mechanical behavior of anisotropic materials subjected to complex loading conditions.

Keywords: BBC2003 yield function, plastic anisotropy, fully implicit integration scheme, line search algorithm, explicit and implicit integration schemes

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Authors: S. Fominow, C. Dobert

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The present article describes the research that deals with the development of equivalent geometric imperfections for the stability design of steel members considering lateral-torsional buckling. The application of these equivalent imperfections takes into account the stiffness-reducing effects due to inelasticity and residual stresses, which lead to a reduction of the load carrying capacity of slender members and structures. This allows the application of a simplified design method, that is performed in three steps. Application of equivalent geometric imperfections, determination of internal forces using geometrical non-linear analysis (GNIA) and verification of the cross-section resistance at the most unfavourable location. All three verification steps are closely related and influence the results. The derivation of the equivalent imperfections was carried out in several steps. First, reference lateral-torsional buckling resistances for various rolled I-sections, slenderness grades, load shapes and steel grades were determined. This was done either with geometric and material non-linear analysis with geometrical imperfections and residual stresses (GMNIA) or for standard cases based on the equivalent member method. With the aim of obtaining identical lateral-torsional buckling resistances as the reference resistances from the application of the design method, the required sizes for equivalent imperfections were derived. For this purpose, a program based on the FEM method has been developed. Based on these results, several proposals for the specification of equivalent geometric imperfections have been developed. These differ in the shape of the applied equivalent geometric imperfection, the model of the cross-sectional resistance and the steel grade. The proposed design methods allow a wide range of applications and a reliable calculation of the lateral-torsional buckling resistances, as comparisons between the calculated resistances and the reference resistances have shown.

Keywords: equivalent geometric imperfections, GMNIA, lateral-torsional buckling, non-linear finite element analysis

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Authors: J. Novak, A. Kohoutkova, V. Kristek, J. Vodicka, M. Sramek

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While the use of cast-in-place concrete for an airfield and highway pavement overlay is very common, the application of precast concrete elements is very limited today. The main reasons consist of high production costs and complex structural behavior. Despite that, several precast concrete systems have been developed and tested with the aim to provide a system with rapid construction. The contribution deals with the reinforcement design of a hexagonal element developed for a proposed airfield pavement system. The sub-base course of the system is composed of compacted recycled concrete aggregates and fiber reinforced concrete with recycled aggregates place on top of it. The selected element belongs to a group of precast concrete elements which are being considered for the construction of a surface course. Both high costs of full-scale experiments and the need to investigate various elements force to simulate their behavior in a numerical analysis software by using finite element method instead of performing expensive experiments. The simulation of the selected element was conducted on a nonlinear model in order to obtain such results which could fully compensate results from experiments. The main objective was to design reinforcement of the precast concrete element subject to quasi-static loading from airplanes with respect to geometrical imperfections, manufacturing imperfections, tensile stress in reinforcement, compressive stress in concrete and crack width. The obtained findings demonstrate that the position and the presence of imperfection in a pavement highly affect the stress distribution in the precast concrete element. The precast concrete element should be heavily reinforced to fulfill all the demands. Using under-reinforced concrete elements would lead to the formation of wide cracks and cracks permanently open.

Keywords: imperfection, numerical simulation, pavement, precast concrete element, reinforcement design, stress analysis

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Authors: Gelacio JuáRez-Luna, Daniel Enrique GonzáLez-RamíRez, Enrique Tenorio-Montero

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Frame elements coupled with springs elements are used for modelling the development of hinges in segmented tunnels, the spring elements modelled the rotational, transversal and axial failure. These spring elements are equipped with constitutive models to include independently the moment, shear force and axial force, respectively. These constitutive models are formulated based on damage mechanics and experimental test reported in the literature review. The mesh of the segmented tunnels was discretized in the software GID, and the nonlinear analyses were carried out in the finite element software ANSYS. These analyses provide the capacity curve of the primary and secondary lining of a segmented tunnel. Two numerical examples of segmented tunnels show the capability of the spring elements to release energy by the development of hinges. The first example is a segmental concrete lining discretized with frame elements loaded until hinges occurred in the lining. The second example is a tunnel with primary and secondary lining, discretized with a double ring frame model. The outer ring simulates the segmental concrete lining and the inner ring simulates the secondary cast-in-place concrete lining. Spring elements also modelled the joints between the segments in the circumferential direction and the ring joints, which connect parallel adjacent rings. The computed load vs displacement curves are congruent with numerical and experimental results reported in the literature review. It is shown that the modelling of a tunnel with primary and secondary lining with frame elements and springs provides reasonable results and save computational cost, comparing with 2D or 3D models equipped with smeared crack models.

Keywords: damage, hinges, lining, tunnel

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Authors: Yanling Li, Linying Ji, Zita Oravecz, Timothy R. Brick, Michael D. Hunter, Sy-Miin Chow

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Assessing several individuals intensively over time yields intensive longitudinal data (ILD). Even though ILD provide rich information, they also bring other data analytic challenges. One of these is the increased occurrence of missingness with increased study length, possibly under non-ignorable missingness scenarios. Multiple imputation (MI) handles missing data by creating several imputed data sets, and pooling the estimation results across imputed data sets to yield final estimates for inferential purposes. In this article, we introduce dynr.mi(), a function in the R package, Dynamic Modeling in R (dynr). The package dynr provides a suite of fast and accessible functions for estimating and visualizing the results from fitting linear and nonlinear dynamic systems models in discrete as well as continuous time. By integrating the estimation functions in dynr and the MI procedures available from the R package, Multivariate Imputation by Chained Equations (MICE), the dynr.mi() routine is designed to handle possibly non-ignorable missingness in the dependent variables and/or covariates in a user-specified dynamic systems model via MI, with convergence diagnostic check. We utilized dynr.mi() to examine, in the context of a vector autoregressive model, the relationships among individuals’ ambulatory physiological measures, and self-report affect valence and arousal. The results from MI were compared to those from listwise deletion of entries with missingness in the covariates. When we determined the number of iterations based on the convergence diagnostics available from dynr.mi(), differences in the statistical significance of the covariate parameters were observed between the listwise deletion and MI approaches. These results underscore the importance of considering diagnostic information in the implementation of MI procedures.

Keywords: dynamic modeling, missing data, mobility, multiple imputation

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Authors: Regina Rekuviene, Vykintas Samaitis, Liudas Mažeika, Audrius Jankauskas, Virginija Jankauskaitė, Laura Gegeckienė, Abdolali Sadaghiani, Shaghayegh Saeidiharzand

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Icing brings significant damage to aviation and renewable energy installations. Air-conditioning, refrigeration, wind turbine blades, airplane and helicopter blades often suffer from icing phenomena, which cause severe energy losses and impair aerodynamic performance. The icing process is a complex phenomenon with many different causes and types. Icing mechanisms, distributions, and patterns are still relevant to research topics. The adhesion strength between ice and surfaces differs in different icing environments. This makes the task of anti-icing very challenging. The techniques for various icing environments must satisfy different demands and requirements (e.g., efficient, lightweight, low power consumption, low maintenance and manufacturing costs, reliable operation). It is noticeable that most methods are oriented toward a particular sector and adapting them to or suggesting them for other areas is quite problematic. These methods often use various technologies and have different specifications, sometimes with no clear indication of their efficiency. There are two major groups of anti-icing methods: passive and active. Active techniques have high efficiency but, at the same time, quite high energy consumption and require intervention in the structure’s design. It’s noticeable that vast majority of these methods require specific knowledge and personnel skills. The main effect of passive methods (ice-phobic, superhydrophobic surfaces) is to delay ice formation and growth or reduce the adhesion strength between the ice and the surface. These methods are time-consuming and depend on forecasting. They can be applied on small surfaces only for specific targets, and most are non-biodegradable (except for anti-freezing proteins). There is some quite promising information on ultrasonic ice mitigation methods that employ UGW (Ultrasonic Guided Wave). These methods are have the characteristics of low energy consumption, low cost, lightweight, and easy replacement and maintenance. However, fundamental knowledge of ultrasonic de-icing methodology is still limited. The objective of this work was to identify the ice formation processes and its progress by employing ultrasonic guided wave technique. Throughout this research, the universal set-up for acoustic measurement of ice formation in a real condition (temperature range from +240 C to -230 C) was developed. Ultrasonic measurements were performed by using high frequency 5 MHz transducers in a pitch-catch configuration. The selection of wave modes suitable for detection of ice formation phenomenon on copper metal surface was performed. Interaction between the selected wave modes and ice formation processes was investigated. It was found that selected wave modes are sensitive to temperature changes. It was demonstrated that proposed ultrasonic technique could be successfully used for the detection of ice layer formation on a metal surface.

Keywords: ice formation processes, ultrasonic GW, detection of ice formation, ultrasonic testing

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Authors: E. Faizan, Wahab Abdul Ghafar, Tao Zhong

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Steel plate shear walls (SPSWs) are a robust lateral load resistance structure because of their high flexibility and efficient energy dissipation when subjected to seismic loads. This research investigates the seismic performance of an innovative infill web strip (IWS-SPSW) and a typical unstiffened steel plate shear wall (USPSW). As a result, two 1:3 scale specimens of an IWS-SPSW and USPSW with a single story and a single bay were built and subjected to a cyclic lateral loading methodology. In the prototype, the beam-to-column connections were accomplished with the assistance of semi-rigid end-plate connectors. IWS-SPSW demonstrated exceptional ductility and shear load-bearing capacity during the testing process, with no cracks or other damage occurring. In addition, the IWS-SPSW could effectively dissipate energy without causing a significant amount of beam-column connection distortion. The shear load-bearing capacity of the USPSW was exceptional. However, it exhibited low ductility, severe infill plate corner ripping, and huge infill web plate cracks. The FE models were created and then confirmed using the experimental data. It has been demonstrated that the infill web strips of an SPSW system can affect the system's high performance and total energy dissipation. In addition, a parametric analysis was carried out to evaluate the material qualities of the IWS, which can considerably improve the system's seismic performances. These properties include the steel's strength as well as its thickness.

Keywords: steel shear walls, seismic performance, failure mode, hysteresis response, nonlinear finite element analysis, parametric study

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Authors: Arwin Malabanan, Carl Chester Ragudo, Jerome Tadiosa, John Dee Mangoba, Eric Augustus Tingatinga, Romeo Eliezer Longalong

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Concrete hollow blocks (CHB) are the most commonly used masonry block for walls in residential houses, school buildings and public buildings in the Philippines. During the recent 2013 Bohol earthquake (Mw 7.2), it has been proven that CHB walls are very vulnerable to severe external action like strong ground motion. In this paper, a numerical model of CHB structures is proposed, and seismic behavior of CHB houses is presented. In modeling, the Rigid Body Spring-Discrete Element method (RBS-DEM)) is used wherein masonry blocks are discretized into rigid elements and connected by nonlinear springs at preselected contact points. The shear and normal stiffness of springs are derived from the material properties of CHB unit incorporating the grout and mortar fillings through the volumetric transformation of the dimension using material ratio. Numerical models of reinforced and unreinforced walls are first subjected to linearly-increasing in plane loading to observe the different failure mechanisms. These wall models are then assembled to form typical model masonry houses and then subjected to the El Centro and Pacoima earthquake records. Numerical simulations show that the elastic, failure and collapse behavior of the model houses agree well with shaking table tests results. The effectiveness of the method in replicating failure patterns will serve as a basis for the improvement of the design and provides a good basis of strengthening the structure.

Keywords: concrete hollow blocks, discrete element method, earthquake, rigid body spring model

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Authors: Mohammadreza Salek Faramarzi, Touraj Taghikhany

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In this paper, seismic fragility assessment of a recently developed hybrid structural system, known as the strongback system (SBS) is investigated. In this system, to mitigate the occurrence of the soft-story mechanism and improve the distribution of story drifts over the height of the structure, an elastic vertical truss is formed. The strengthened members of the braced span are designed to remain substantially elastic during levels of excitation where soft-story mechanisms are likely to occur and impose a nearly uniform story drift distribution. Due to the distinctive characteristics of near-field ground motions, it seems to be necessary to study the effect of these records on seismic performance of the SBS. To this end, a set of 56 near-field ground motion records suggested by FEMA P695 methodology is used. For fragility assessment, nonlinear dynamic analyses are carried out in OpenSEES based on the recommended procedure in HAZUS technical manual. Four damage states including slight, moderate, extensive, and complete damage (collapse) are considered. To evaluate each damage state, inter-story drift ratio and floor acceleration are implemented as engineering demand parameters. Further, to extend the evaluation of the collapse state of the system, a different collapse criterion suggested in FEMA P695 is applied. It is concluded that SBS can significantly increase the collapse capacity and consequently decrease the collapse risk of the structure during its life time. Comparing the observing mean annual frequency (MAF) of exceedance of each damage state against the allowable values presented in performance-based design methods, it is found that using the elastic vertical truss, improves the structural response effectively.

Keywords: IDA, near-fault, probabilistic performance assessment, seismic fragility, strongback system, uncertainty

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Authors: Majid Hejazian, Nam-Trung Nguyen

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Over the past few years, microfluidic devices have generated significant attention from industry and academia due to advantages such as small sample volume, low cost and high efficiency. Microfluidic devices have applications in chemical, biological and industry analysis and can facilitate assay of bio-materials and chemical reactions, separation, and sensing. Micromixers are one of the important microfluidic concepts. Micromixers can work as stand-alone devices or be integrated in a more complex microfluidic system such as a lab on a chip (LOC). Micromixers are categorized as passive and active types. Passive micromixers rely only on the arrangement of the phases to be mixed and contain no moving parts and require no energy. Active micromixers require external fields such as pressure, temperature, electric and acoustic fields. Rapid and efficient mixing is important for many applications such as biological, chemical and biochemical analysis. Achieving fast and homogenous mixing of multiple samples in the microfluidic devices has been studied and discussed in the literature recently. Improvement in mixing rely on effective mass transport in microscale, but are currently limited to molecular diffusion due to the predominant laminar flow in this size scale. Using magnetic field to elevate mass transport is an effective solution for mixing enhancement in microfluidics. The use of a non-uniform magnetic field to improve mass transfer performance in a microfluidic device is demonstrated in this work. The phenomenon of mixing ferrofluid and DI-water streams has been reported before, but mass transfer enhancement for other non-magnetic species through magnetic field have not been studied and evaluated extensively. In the present work, permanent magnets were used in a simple microfluidic device to create a non-uniform magnetic field. Two streams are introduced into the microchannel: one contains fluorescent dye mixed with diluted ferrofluid to induce enhanced mass transport of the dye, and the other one is a non-magnetic DI-water stream. Mass transport enhancement of fluorescent dye is evaluated using fluorescent measurement techniques. The concentration field is measured for different flow rates. Due to effect of magnetic field, a body force is exerted on the paramagnetic stream and expands the ferrofluid stream into non-magnetic DI-water flow. The experimental results demonstrate that without a magnetic field, both magnetic nanoparticles of the ferrofluid and the fluorescent dye solely rely on molecular diffusion to spread. The non-uniform magnetic field, created by the permanent magnets around the microchannel, and diluted ferrofluid can improve mass transport of non-magnetic solutes in a microfluidic device. The susceptibility mismatch between the fluids results in a magnetoconvective secondary flow towards the magnets and subsequently the mass transport of the non-magnetic fluorescent dye. A significant enhancement in mass transport of the fluorescent dye was observed. The platform presented here could be used as a microfluidics-based micromixer for chemical and biological applications.

Keywords: ferrofluid, mass transfer, micromixer, microfluidics, magnetic

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Authors: Mansoor Soomro

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The evolution of power electronic equipment has been pivotal in making industrial processes productive, efficient and safe. Despite its attractive features, it has been due to nonlinear loads which make it vulnerable to power quality conditions. Harmonics is one of the power quality problem in which the harmonic frequency is integral multiple of supply frequency. Therefore, the supply voltage and supply frequency do not last within their tolerable limits. As a result, distorted current and voltage waveform may appear. Attributes of low power quality confirm that an electrical device or equipment is likely to malfunction, fail promptly or unable to operate under all applied conditions. The electrical power system is designed for delivering power reliably, namely maximizing power availability to customers. However, power quality events are largely untracked, and as a result, can take out a process as many as 20 to 30 times a year, costing utilities, customers and suppliers of load equipment, a loss of millions of dollars. The ill effects of current harmonics reduce system efficiency, cause overheating of connected equipment, result increase in electrical power and air conditioning costs. With the passage of time and the rapid growth of power electronic converters has highlighted the damages of current harmonics in the electrical power system. Therefore, it has become essential to address the bad influence of current harmonics while planning any suitable changes in the electrical installations. In this paper, an effort has been made to mitigate the effects of dominant 3rd order current harmonics. Passive filtering technique with six pulse multiplication converter has been employed to mitigate them. Since, the standards of power quality are to maintain the supply voltage and supply current within certain prescribed standard limits. For this purpose, the obtained results are validated as per specifications of IEEE 519-1992 and IEEE 519-2014 performance standards.

Keywords: current harmonics, power quality, passive filters, power electronic converters

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Authors: K. S. Sivakumaran, T. Thanga, B. Halabieh

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The end panels of a large rectangular industrial duct, which experience significant internal pressures, also experience considerable transverse shear due to transfer of gravity loads to the supports. The current design practice of such thin plate panels for shear load is based on methods used for the design of plate girder webs. The structural arrangements, the loadings and the resulting behavior associated with the industrial duct end panels are, however, significantly different than those of the web of a plate girder. The large aspect ratio of the end panels gives rise to multiple bands of tension fields, whereas the plate girder web design is based on one tension field. In addition to shear, the industrial end panels are subjected to internal pressure which in turn produces significant membrane action. This paper reports a study which was undertaken to review the current industrial analysis and design methods and to propose a comprehensive method of designing industrial duct end panels for shear resistance. In this investigation, a nonlinear finite element model was developed to simulate the behavior of industrial duct end panel subjected to transverse shear and internal pressures. The model considered the geometric imperfections and constitutive relations for steels. Six scale independent dimensionless parameters that govern the behavior of such end panel were identified and were then used in an extensive parametric study. It was concluded that the plate slenderness dominates the shear strength of stockier end panels, and whereas, the aspect ratio and plate slenderness influence the shear strength of slender end panels. Based on these studies, this paper proposes design aids for estimating the shear strength of rectangular duct end panels.

Keywords: thin plate, transverse shear, tension field, finite element analysis, parametric study, design

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Authors: Deginet Aklilu, Tianqi Wang, Endwoke Amsalu, Wei Feng, Zhiwei Li, Xia Li, Lixin Tao, Yanxia Luo, Moning Guo, Xiangtong Liu, Xiuhua Guo

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Extreme temperature-related cardiovascular diseases (CVDs) have become a growing public health concern. However, the impact of temperature on the cause of specific CVDs has not been well studied in the study area. The objective of this study was to assess the impact of temperature on cause-specific cardiovascular hospital admissions in Beijing, China. We obtained data from 172 large general hospitals from the Beijing Public Health Information Center Cardiovascular Case Database and China. Meteorological Administration covering 16 districts in Beijing from 2013 to 2017. We used a time-stratified case crossover design with a distributed lag nonlinear model (DLNM) to derive the impact of temperature on CVD in hospitals back to 27 days on CVD admissions. The temperature data were stratified as cold (extreme and moderate ) and hot (moderate and extreme ). Within five years (January 2013-December 2017), a total of 460,938 (male 54.9% and female 45.1%) CVD admission cases were reported. The exposure-response relationship for hospitalization was described by a "J" shape for the total and cause-specific. An increase in the six-day moving average temperature from moderate hot (30.2 °C) to extreme hot (36.9 °C) resulted in a significant increase in CVD admissions of 16.1%(95% CI = 12.8%-28.9%). However, the effect of cold temperature exposure on CVD admissions over a lag time of 0-27 days was found to be non significant, with a relative risk of 0.45 (95% CI = 0.378-0.55) for extreme cold (-8.5 °C)and 0.53 (95% CI = 0.47-0.60) for moderate cold (-5.6 °C). The results of this study indicate that exposure to extremely high temperatures is highly associated with an increase in cause-specific CVD admissions. These finding may guide to create and raise awareness of the general population, government and private sectors regarding on the effects of current weather conditions on CVD.

Keywords: admission, Beijing, cardiovascular diseases, distributed lag non linear model, temperature

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Authors: Oluwaseun K. Oyebode, Josiah A. Adeyemo

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Hydrological modelling plays a crucial role in the planning and management of water resources, most especially in water stressed regions where the need to effectively manage the available water resources is of critical importance. However, due to the complex, nonlinear and dynamic behaviour of hydro-climatic interactions, achieving reliable modelling of water resource systems and accurate projection of hydrological parameters are extremely challenging. Although a significant number of modelling techniques (process-based and data-driven) have been developed and adopted in that regard, the field of hydrological modelling is still considered as one that has sluggishly progressed over the past decades. This is majorly as a result of the identification of some degree of uncertainty in the methodologies and results of techniques adopted. In recent times, evolutionary computation (EC) techniques have been developed and introduced in response to the search for efficient and reliable means of providing accurate solutions to hydrological related problems. This paper presents a comprehensive review of the underlying principles, methodological needs and applications of a promising evolutionary computation modelling technique – genetic programming (GP). It examines the specific characteristics of the technique which makes it suitable to solving hydrological modelling problems. It discusses the opportunities inherent in the application of GP in water related-studies such as rainfall estimation, rainfall-runoff modelling, streamflow forecasting, sediment transport modelling, water quality modelling and groundwater modelling among others. Furthermore, the means by which such opportunities could be harnessed in the near future are discussed. In all, a case for total embracement of GP and its variants in hydrological modelling studies is made so as to put in place strategies that would translate into achieving meaningful progress as it relates to modelling of water resource systems, and also positively influence decision-making by relevant stakeholders.

Keywords: computational modelling, evolutionary algorithms, genetic programming, hydrological modelling

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Authors: Daniel Dahis, Haim Azhari

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Noninvasive image-guided intracranial treatments using high intensity focused ultrasound (HIFU) are on the course of translation into clinical applications. They include, among others, tumor ablation, hyperthermia, and blood-brain-barrier (BBB) penetration. Since many of these procedures are associated with local temperature elevation, thermal monitoring is essential. MRI constitutes an imaging method with high spatial resolution and thermal mapping capacity. It is the currently leading modality for temperature guidance, commonly under the name MRgHIFU (magnetic-resonance guided HIFU). Nevertheless, MRI is a very expensive non-portable modality which jeopardizes its accessibility. Ultrasonic thermal monitoring, on the other hand, could provide a modular, cost-effective alternative with higher temporal resolution and accessibility. In order to assess the feasibility of ultrasonic brain thermal monitoring, this study investigated the usage of brain tissue attenuation coefficient (AC) temporal changes as potential estimators of thermal changes. Newton's law of cooling describes a temporal exponential decay behavior for the temperature of a heated object immersed in a relatively cold surrounding. Similarly, in the case of cerebral HIFU treatments, the temperature in the region of interest, i.e., focal zone, is suggested to follow the same law. Thus, it was hypothesized that the AC of the irradiated tissue may follow a temporal exponential behavior during cool down regime. Three ex-vivo bovine brain tissue specimens were inserted into plastic containers along with four thermocouple probes in each sample. The containers were placed inside a specially built ultrasonic tomograph and scanned at room temperature. The corresponding pixel-averaged AC was acquired for each specimen and used as a reference. Subsequently, the containers were placed in a beaker containing hot water and gradually heated to about 45ᵒC. They were then repeatedly rescanned during cool down using ultrasonic through-transmission raster trajectory until reaching about 30ᵒC. From the obtained images, the normalized AC and its temporal derivative as a function of temperature and time were registered. The results have demonstrated high correlation (R² > 0.92) between both the brain AC and its temporal derivative to temperature. This indicates the validity of the hypothesis and the possibility of obtaining brain tissue temperature estimation from the temporal AC thermal changes. It is important to note that each brain yielded different AC values and slopes. This implies that a calibration step is required for each specimen. Thus, for a practical acoustic monitoring of the brain, two steps are suggested. The first step consists of simply measuring the AC at normal body temperature. The second step entails measuring the AC after small temperature elevation. In face of the urging need for a more accessible thermal monitoring technique for brain treatments, the proposed methodology enables a cost-effective high temporal resolution acoustical temperature estimation during HIFU treatments.

Keywords: attenuation coefficient, brain, HIFU, image-guidance, temperature

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Authors: Emmanuel O. Ezim, Idowu A. Olayinka, Michael Oladunjoye, Izuchukwu I. Obiadi

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Monitoring of reservoir properties prior to well placements and production is a requirement for optimisation and efficient oil and gas production. This is usually done using well log analyses and 3-D seismic, which are often prone to errors. However, 4-D (Time-lapse) seismic, incorporating numerous 3-D seismic surveys of the same field with the same acquisition parameters, which portrays the transient changes in the reservoir due to production effects over time, could be utilised because it generates better resolution. There is, however dearth of information on the applicability of this approach in the Niger Delta. This study was therefore designed to apply 4-D seismic, well-log and geologic data in monitoring of reservoirs in the EK field of the Niger Delta. It aimed at locating bypassed accumulations and ensuring effective reservoir management. The Field (EK) covers an area of about 1200km2 belonging to the early (18ma) Miocene. Data covering two 4-D vintages acquired over a fifteen-year interval were obtained from oil companies operating in the field. The data were analysed to determine the seismic structures, horizons, Well-to-Seismic Tie (WST), and wavelets. Well, logs and production history data from fifteen selected wells were also collected from the Oil companies. Formation evaluation, petrophysical analysis and inversion alongside geological data were undertaken using Petrel, Shell-nDi, Techlog and Jason Software. Well-to-seismic tie, formation evaluation and saturation monitoring using petrophysical and geological data and software were used to find bypassed hydrocarbon prospects. The seismic vintages were interpreted, and the amounts of change in the reservoir were defined by the differences in Acoustic Impedance (AI) inversions of the base and the monitor seismic. AI rock properties were estimated from all the seismic amplitudes using controlled sparse-spike inversion. The estimated rock properties were used to produce AI maps. The structural analysis showed the dominance of NW-SE trending rollover collapsed-crest anticlines in EK with hydrocarbons trapped northwards. There were good ties in wells EK 27, 39. Analysed wavelets revealed consistent amplitude and phase for the WST; hence, a good match between the inverted impedance and the good data. Evidence of large pay thickness, ranging from 2875ms (11420 TVDSS-ft) to about 2965ms, were found around EK 39 well with good yield properties. The comparison between the base of the AI and the current monitor and the generated AI maps revealed zones of untapped hydrocarbons as well as assisted in determining fluids movement. The inverted sections through EK 27, 39 (within 3101 m - 3695 m), indicated depletion in the reservoirs. The extent of the present non-uniform gas-oil contact and oil-water contact movements were from 3554 to 3575 m. The 4-D seismic approach led to better reservoir characterization, well development and the location of deeper and bypassed hydrocarbon reservoirs.

Keywords: reservoir monitoring, 4-D seismic, well placements, petrophysical analysis, Niger delta basin

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Authors: Nikolaos Papadimas, Joanna Bennett, Amir Sakhaei, Timothy Dodwell

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Composite modeling of consolidation processes is playing an important role in the process and part design by indicating the formation of possible unwanted prior to expensive experimental iterative trial and development programs. Composite materials in their uncured state display complex constitutive behavior, which has received much academic interest, and this with different models proposed. Errors from modeling and statistical which arise from this fitting will propagate through any simulation in which the material model is used. A general hyperelastic polynomial representation was proposed, which can be readily implemented in various nonlinear finite element packages. In our case, FEniCS was chosen. The coefficients are assumed uncertain, and therefore the distribution of parameters learned using Markov Chain Monte Carlo (MCMC) methods. In engineering, the approach often followed is to select a single set of model parameters, which on average, best fits a set of experiments. There are good statistical reasons why this is not a rigorous approach to take. To overcome these challenges, A hierarchical Bayesian framework was proposed in which population distribution of model parameters is inferred from an ensemble of experiments tests. The resulting sampled distribution of hyperparameters is approximated using Maximum Entropy methods so that the distribution of samples can be readily sampled when embedded within a stochastic finite element simulation. The methodology is validated and demonstrated on a set of consolidation experiments of AS4/8852 with various stacking sequences. The resulting distributions are then applied to stochastic finite element simulations of the consolidation of curved parts, leading to a distribution of possible model outputs. With this, the paper, as far as the authors are aware, represents the first stochastic finite element implementation in composite process modelling.

Keywords: data-driven , material consolidation, stochastic finite elements, surrogate models

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Authors: Habib Muhammetoglu, I. Ethem Karadirek, Selami Kara, Ayse Muhammetoglu

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The problem of non-revenue water (NRW) from municipal water distribution networks is common in many countries such as Turkey, where the average yearly water losses are around 50% . Water losses can be divided into two major types namely: 1) Real or physical water losses, and 2) Apparent or commercial water losses. Total water losses in Antalya city, Turkey is around 45%. Methods: A research study was conducted to develop appropriate methodologies to reduce NRW. A pilot study area of about 60 thousands inhabitants was chosen to apply the study. The pilot study area has a supervisory control and data acquisition (SCADA) system for the monitoring and control of many water quantity and quality parameters at the groundwater drinking wells, pumping stations, distribution reservoirs, and along the water mains. The pilot study area was divided into 18 District Metered Areas (DMAs) with different number of service connections that ranged between a few connections to less than 3000 connections. The flow rate and water pressure to each DMA were on-line continuously measured by an accurate flow meter and water pressure meter that were connected to the SCADA system. Customer water meters were installed to all billed and unbilled water users. The monthly water consumption as given by the water meters were recorded regularly. Water balance was carried out for each DMA using the well-know standard IWA approach. There were considerable variations in the water losses percentages and the components of the water losses among the DMAs of the pilot study area. Old Class B customer water meters at one DMA were replaced by more accurate new Class C water meters. Hydraulic modelling using the US-EPA EPANET model was carried out in the pilot study area for the prediction of water pressure variations at each DMA. The data sets required to calibrate and verify the hydraulic model were supplied by the SCADA system. It was noticed that a number of the DMAs exhibited high water pressure values. Therefore, pressure reducing valves (PRV) with constant head were installed to reduce the pressure up to a suitable level that was determined by the hydraulic model. On the other hand, the hydraulic model revealed that the water pressure at the other DMAs cannot be reduced when complying with the minimum pressure requirement (3 bars) as stated by the related standards. Results: Physical water losses were reduced considerably as a result of just reducing water pressure. Further physical water losses reduction was achieved by applying acoustic methods. The results of the water balances helped in identifying the DMAs that have considerable physical losses. Many bursts were detected especially in the DMAs that have high physical water losses. The SCADA system was very useful to assess the efficiency level of this method and to check the quality of repairs. Regarding apparent water losses reduction, changing the customer water meters resulted in increasing water revenue by more than 20%. Conclusions: DMA, SCADA, modelling, pressure management, leakage detection and accurate customer water meters are efficient for NRW.

Keywords: NRW, water losses, pressure management, SCADA, apparent water losses, urban water distribution networks

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Authors: Dawei Shen, Ming Xu, Pengfei Liu

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The joints between simply supported bridge decks and abutments need to be regularly repaired, which would greatly increase the cost during the service life of the bridge. Simply supported girder bridges suffered the most severe damage during earthquakes. Another type of bridge, the integral bridge, of which the superstructure and abutment are rigidly connected, was also used in some European countries. Because no bearings or joints exit in the integral bridge, this type of bridge could significantly reduce maintenance requirements and costs. However, conventional integral bridge usually result in high earth pressure on the abutment and surface settlement in the backfill. To solve these problems, a new type of integral bridge, geosynthetic-reinforced soil (GRS) integral bridge, was come up in recent years. This newly invented bridge has not been used in engineering practices. There was a lack of research on the seismic behavior of the conventional and new type of integral abutments. In addition, no common design code could be found for the calculation of seismic pressure of soil behind the abutment. This paper developed a dynamic constitutive model, which can consider the soil behaviors under cyclic loading. Numerical analyses of the seismic response of a full height integral bridge and GRS integral bridge were carried out using the two-dimensional numerical code, FLAC. A parametric study was also performed to investigate the soil-structure interaction. The results are presented below. The seismic responses of GRS integral bridge together with conventional simply supported bridge, GRS conventional bridge and conventional integral bridge were investigated. The results show that the GRS integral bridge holds the highest seismic stability, followed by conventional integral bridge, GRS simply supported bridge and conventional simply supported bridge. Compared with the integral bridge with 1 m thick abutments, the GRS integral bridge with 0.4 m thick abutments is subjected to a smaller bending moment, and the natural frequency and horizontal displacement remains almost the same. Geosynthetic-reinforcement will be more effective when the abutment becomes thinner or the abutment is higher.

Keywords: geosynthetic-reinforced soil integral bridge, nonlinear hysteretic model, numerical analysis, seismic response

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Authors: Ariungerel Jargal

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: Cave mining is a bulk underground mining method, which allows large low-grade deposits to be mined underground. This method involves undermining the orebody to make it collapse under its own weight into a series of chambers from which the ore extracted. It is a useful technique to extend the life of large deposits previously mined by open pits, and it is a method increasingly proposed for new mines around the world. We plan to conduct a feasibility study using Electrical impedance tomography (EIT) technology to show how much subsidence there is at the intersection with the cave mining surface. EIT is an imaging technique which uses electrical measurements at electrodes attached on the body surface to yield a cross-sectional image of conductivity changes within the object. EIT has been developed in several different applications areas as a simpler, cheaper alternative to many other imaging methods. A low frequency current is injected between pairs of electrodes while voltage measurements are collected at all other electrode pairs. In the difference EIT, images are reconstructed of the change in conductivity distribution (σ) between the acquisition of the two sets of measurements. Image reconstruction in EIT requires the solution of an ill-conditioned nonlinear inverse problem on noisy data, typically requiring make simpler assumptions or regularization. It is noted that the ratio of current to voltage represents a complex value according to Ohm’s law, and that it is theoretically possible to re-express EIT. The results of the experiment were presented on the simulation, and it was concluded that it is possible to conduct further real experiments. Drill a certain number of holes in the top wall of the cave to attach the electrodes, flow a current through them, and measure and acquire the potential through these electrodes. Appropriate values should be selected depending on the distance between the holes, the frequency and duration of the measurements, the surface characteristics and the size of the study area using an EIT device.

Keywords: impedance tomography, cave mining, soil, EIT device

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Authors: Khanyisile Mnguni, Muthukrishnavellaisamy Kumarasamy, Jeff C. Smithers

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Umgeni Water is a water board that supplies most parts of KwaZulu Natal with bulk portable water. Currently, Umgeni Water is running its distribution system based on required reservoir levels and demands and does not consider the energy cost at different times of the day, number of pump switches, and background leakages. Including these constraints can reduce operational cost, energy usage, leakages, and increase performance. Optimising pump schedules can reduce energy usage and costs while adhering to hydraulic and operational constraints. Umgeni Water has installed an online hydraulic software, WaterNet Advisor, that allows running different operational scenarios prior to implementation in order to optimise the distribution system. This study will investigate operation scenarios using optimisation techniques and WaterNet Advisor for a local water distribution system. Based on studies reported in the literature, introducing pump scheduling optimisation can reduce energy usage by approximately 30% without any change in infrastructure. Including tariff structures in an optimisation problem can reduce pumping costs by 15%, while including leakages decreases cost by 10%, and pressure drop in the system can be up to 12 m. Genetical optimisation algorithms are widely used due to their ability to solve nonlinear, non-convex, and mixed-integer problems. Other methods such as branch and bound linear programming have also been successfully used. A suitable optimisation method will be chosen based on its efficiency. The objective of the study is to reduce energy usage, operational cost, and leakages, and the feasibility of optimal solution will be checked using the Waternet Advisor. This study will provide an overview of the optimisation of hydraulic networks and progress made to date in multi-objective optimisation for a selected sub-system operated by Umgeni Water.

Keywords: energy usage, pump scheduling, WaterNet Advisor, leakages

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Authors: Anthony Quansah, Tresor Ntaryamira, Shula Mushota

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Models for geotechnical centrifuge testing are usually made from re-formed soil, allowing for comparisons with naturally occurring soil deposits. However, there is a fundamental omission in this process because the natural soil is deposited in layers creating a unique structure. Nonlinear dynamics of clay material deposit is an essential part of changing the attributes of ground movements when subjected to solid seismic loading, particularly when diverse intensification conduct of speeding up and relocation are considered. The paper portrays a review of axis shaking table tests and numerical recreations to explore the offshore clay deposits subjected to seismic loadings. These perceptions are accurately reenacted by DEEPSOIL with appropriate soil models and parameters reviewed from noteworthy centrifuge modeling researches. At that point, precise 1-D site reaction investigations are performed on both time and recurrence spaces. The outcomes uncover that for profound delicate clay is subjected to expansive quakes, noteworthy increasing speed lessening may happen close to the highest point of store because of soil nonlinearity and even neighborhood shear disappointment; nonetheless, huge enhancement of removal at low frequencies are normal in any case the forces of base movements, which proposes that for dislodging touchy seaward establishments and structures, such intensified low-recurrence relocation reaction will assume an essential part in seismic outline. This research shows centrifuge as a tool for creating a layered sample important for modelling true soil behaviour (such as permeability) which is not identical in all directions. Currently, there are limited methods for creating layered soil samples.

Keywords: seismic analysis, layered modeling, terotechnology, finite element modeling

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Authors: Abhilash Sahu, Amit Priyadarshi

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In this paper, we will discuss the existence of weak solutions of the Kirchhoff type boundary value problem on the Sierpinski gasket. Where S denotes the Sierpinski gasket in R² and S₀ is the intrinsic boundary of the Sierpinski gasket. M: R → R is a positive function and h: S × R → R is a suitable function which is a part of our main equation. ∆p denotes the p-Laplacian, where p > 1. First of all, we will define a weak solution for our problem and then we will show the existence of at least two solutions for the above problem under suitable conditions. There is no well-known concept of a generalized derivative of a function on a fractal domain. Recently, the notion of differential operators such as the Laplacian and the p-Laplacian on fractal domains has been defined. We recall the result first then we will address the above problem. In view of literature, Laplacian and p-Laplacian equations are studied extensively on regular domains (open connected domains) in contrast to fractal domains. In fractal domains, people have studied Laplacian equations more than p-Laplacian probably because in that case, the corresponding function space is reflexive and many minimax theorems which work for regular domains is applicable there which is not the case for the p-Laplacian. This motivates us to study equations involving p-Laplacian on the Sierpinski gasket. Problems on fractal domains lead to nonlinear models such as reaction-diffusion equations on fractals, problems on elastic fractal media and fluid flow through fractal regions etc. We have studied the above p-Laplacian equations on the Sierpinski gasket using fibering map technique on the Nehari manifold. Many authors have studied the Laplacian and p-Laplacian equations on regular domains using this Nehari manifold technique. In general Euler functional associated with such a problem is Frechet or Gateaux differentiable. So, a critical point becomes a solution to the problem. Also, the function space they consider is reflexive and hence we can extract a weakly convergent subsequence from a bounded sequence. But in our case neither the Euler functional is differentiable nor the function space is known to be reflexive. Overcoming these issues we are still able to prove the existence of at least two solutions of the given equation.

Keywords: Euler functional, p-Laplacian, p-energy, Sierpinski gasket, weak solution

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