Non-symmetric Loading Research Articles

Centrifuge Modelling of Composite Bucket Foundation Breakwater in Clay under Monotonic and Cyclic Loads

This study investigates the monotonic and cyclic performance of composite bucket foundation breakwater in clay through centrifuge modeling. The application of monotonic loads simulates extreme wave conditions, and cyclic load corresponds to long-term serviceability conditions. In centrifuge tests, three typical soil strengths were tested, and two load eccentricities were simulated to check the influence of wave force height. Multiple measurements were conducted, including rotation angle, horizontal displacement, vertical settlement, and pore pressure variation. When soil strength increases in monotonic centrifuge tests, the ultimate bearing capacity of the bucket foundation experiences significant growth, and the foundation failure pattern varies. In responding to the monotonic test, the foundation’s rotation center constantly moved downward during the loading process, indicating that the deeper soil would be activated to resist the horizontal loading. In contrast, the rotation center movement in the symmetric centrifuge test was opposed to the non-symmetric test because the deeper soil was required to provide resistance to balance the more severe load under the non-symmetric loading condition. It should be noted that non-symmetric loading does not impact the bucket foundation as seriously as symmetric loading. The utilization of deep-soil resistance in non-symmetric tests is beneficial in controlling deformation.

Thermally induced mechanical interactions of energy pile groups subjected to cyclic nonsymmetrical thermal loading

Prior to this study, the long-term thermally-induced mechanical interactions of cyclic nonsymmetrical thermally loaded energy pile groups in soft clay have not been systematically elucidated, particularly with a limited understanding of the interactions among operating and non-operating energy piles, soil, and caps. Observing such a challenge, this paper presents a three-dimensional (3D) thermomechanical finite-element model (FEM), which considers the thermal-dependent behavior at the pile-soil interface and is validated using typical centrifuge tests reported in the literature. Special attention is given to the influence of soil-pile thermal expansion coefficient ratio, pile-soil stiffness ratio, and slab-soil stiffness ratio on the abovementioned interaction. The results indicate that a larger soil-pile thermal expansion coefficient ratio intensifies the interaction between energy piles and the surrounding soil, causing cyclic variations in thermally mobilized friction. With increasing pile-soil stiffness ratios, the differential thermomechanical responses among different piles within a group are enhanced because the toe and shaft resistances mobilized by the cap through nonoperating energy piles are weakened in the interaction process among energy piles, nonoperating energy piles, and the cap. Moreover, the increase in the slab-soil stiffness ratio exacerbates this interaction, strengthening the integrity of the pile groups.

Dynamic strain gradient brittle fracture propagation: comparison with experimental evidence

<p>This paper presented a physico-mathematical model for dynamic fracture propagation in brittle materials with a purely continuum mechanics hemi-variational-based strain gradient theory. As for the quasi-static case, the simulation results, obtained by means of finite elements, revealed that strain gradient effects significantly affected the fracture propagation, leading to finite fracture thickness that was independent of the mesh size. It was also observed that nonsymmetric loading rate lead to a deviation from standard mode-Ⅰ crack propagation that cannot be revealed in the quasi-static case. The model results were compared against experimental data from fracture tests on notched specimens taken from the literature. The comparison showed good agreement between the model predictions and the experimental measurements. The presented model and simulation results can be useful in the design and optimization of structural components subjected to dynamic loading conditions.</p>

A DEM Investigation on the Influence of Cyclic and Static Stress Ratios and State Variables on the Pore Water Pressure Generation in Granular Materials

A granular soil may undergo liquefaction failure due to excess pore water pressure (Δu) generation when subjected to cyclic loading such as an earthquake. Several past studies indicated Δu generation may be independent of cyclic stress ratio (CSR), whereas others contradicted this observation. A soil element in its natural state often remains in K0 consolidation state, i.e., subjected to nonzero static shear stress ratio (SSR). Using the discrete element method (DEM), this study performs a large number of cyclic triaxial tests and evaluates various factors influencing the magnitude and rate of Δu generation under symmetric and nonsymmetric cyclic loading conditions. The study also evaluates the capabilities of several existing Δu generation models to predict the development of Δu under different failure scenarios. It was observed that the generation of Δu can be influenced by CSR for specimens subjected to symmetrical cyclic loading and by both CSR and SSR for nonsymmetric cyclic loading conditions. A new prediction model for Δu generation was developed along with an objective framework to estimate its input parameters. The model showed good agreement with the DEM simulation results.

Cyclic mobility following plastic strain accumulation in sand

Hybrid failure modes/mechanisms under non-symmetrical cyclic loading (partial stress reversal) have received little attention. This paper presents data from cyclic undrained triaxial tests of sand, with initial static shear stress, to investigate a hybrid failure mechanism that controls the behaviour of dilative sand in a narrow range of non-symmetric stress reversal levels. The results indicate that cyclic mobility (Mob) can emerge following significant accumulation of plastic strain. Transition from plastic strain accumulation to Mob can be associated with the instability and phase transformation lines in extension. Two different types of transition and the mechanisms involved are discussed.

Deformability of single layer diamatic space frame Domes under non-symmetrical snow load and earthquake shaking

Earthquakes can significantly affect long-span structures such as Single Layer Diamatic Space Frame Domes, particularly; when exposed to non-symmetric snow loads. The structural system and structure geometry of this lightweight frame structure in combination with non-symmetrical loading conditions may lead to the instability of structural members. There are several relevant effective structural characteristics such as connecting joint systems, member specifications, support conditions and whole structure systematic configuration which can affect the deformability of a structure under earthquake loading. A numerical investigation has been conducted to investigate the earthquake effects on this structure under different loading conditions. Based on the conducted numerical investigation concerning structure deformability, the structure of the system and geometry had lesser influence than parameters such as the structure's natural period, base shear and behaviour coefficient. Six domes with different geometrical form types were considered in the modelling process. It seems that the stability of a dome with non-symmetrical snow loading is more critical while earthquake shaking takes place. The dynamic deformability of most of the dome types was higher when symmetrical snow load under different earthquake acceleration time histories was applied however for a few of the dome types the deformability was higher under non-symmetrical snow loading conditions.

Intrados CFRCM strengthening of masonry arches

This paper describes the preliminary experimental results obtained from destructive cyclic tests on masonry arches strengthened with FRCM (Fiber Reinforced Cementitious Matrix) strengthening system applied onto the arch intrados.The scaled models of the arches used in the tests, reproduce the geometry of the high span ratio bridges typically found in the Italian railway lines. They were tested with a non-symmetrical vertical load that involves a collapse mechanism with 4-hinges similar to the typical seismic collapse mechanism of masonry arches. The experimental campaign made it possible to assess the increase in the arch resistance with the FRCM strengthening system, to simulate the load-displacements curve and to analyze the collapse mechanism of the unstrengthened and strengthened specimens.

Influence of pile head restraint on the performance of floating elevated energy pile groups in soft clay

Thermal elongation of energy piles (EPs) depends on the end restraints to displacement. The EP head is restrained by a working load and non-energy piles (NEPs) within an energy pile group, depending on the cap rigidity. The existence of both EPs and NEPs in non-symmetrical thermally loaded energy pile groups imposes different restraints on EP heads, resulting in different pile elongations. This would induce load redistribution between the piles, thereby influencing the serviceability of energy pile groups in soft soil. In this paper, a 3-D numerical parametric study was conducted after back-analysing a centrifuge test on a floating elevated energy pile group subjected to cyclic non-symmetrical thermal loading in soft clay. Effects of the number of EPs and NEPs in a 2 × 2 group, the flexural stiffness of the cap, and the factor of safety (FS; i.e., working load level) were studied. The non-symmetrical thermally loaded pile group with 3EPs and a rigid cap subjected to the lowest FS showed the maximum settlement due to the largest thermomechanical loading distributed between the piles through the rigid cap. In contrast, a flexible cap over the 2EPs group induced the maximum tilting due to a closer distance between EPs and NEPs in a side tilting. The axial load reduction was significant mainly in the 1EP group during cooling and at a higher FS, resulting in tension along the EP, which should be considered in the design.

Formulation of the critical lateral buckling moment of steel beams under asymmetric loadings

This article investigates the elastic lateral buckling of unrestrained beams. According to the design code, the beam strength is function of the lateral buckling moment. In literature, the buckling moment is function on bending distribution, load height position and the monosymmetry cross section shape. The coefficients C1−C3 are affected to these parameters in the solution. However, no formula or table is available for the case of beams subjected to nonsymmetrical loading. This article proposes an analytical formulation for the critical moment for lateral–torsional buckling of steel beams under asymmetrical loading. The expression of the critical buckling moment, which is based on the Galerkin method, as well as the coefficients (3C) that affect the intensity of the critical moment for asymmetric loading cases, are then proposed. The present method is compared to numerical simulations and available solutions in literature. The results obtained allowed concluding that in the case of asymmetrical loading, the application of the loading cases proposed by the CCM 97 remains unsafe.

Twin earth pressure balance tunnelling – monitoring and numerical study of an urban case

In recent decades, numerical calculations have often been used to optimise, from a technical and economical perspective, the design of underground works. Using these tools allows efficient and affordable designs to be obtained. Simulation of the tunnelling procedure when using a tunnel-boring machine and in urban areas is a complex soil–structure interaction problem. Here, a three-dimensional (3D) code using finite differences is used. The reference case of this study is Lyon metro line D project in France, where a non-symmetric load is present at the surface due to the presence of a retaining wall. An accurate on-site monitoring system was set up to assess ground movements during the mechanised excavation of twin tunnels. The collected data are used as a reference to show the validity and accuracy of the developed 3D model. Two constitutive models were used to simulate the soil behaviour: plastic hardening (PH) and linear elasticity with perfect plasticity (Mohr–Coulomb shear failure criterion). The Mohr–Coulomb constitutive model shows some drawbacks, which can be eliminated by using PH. The existence of a retaining wall induces a non-symmetric load condition; however, the settlement trough predicted by advanced numerical models shows good agreement with that obtained by monitoring data.

Measurement of Circulating Currents in Split-Winding Transformer and Comparison with Numerical Calculation

Split-winding transformer is a one of the common transformer types with one low-voltage winding placed above the other low-voltage winding and with the jointly high-voltage and regulation winding. The paper investigates circulating currents that occur in high-voltage and regulation windings in case of nonsymmetric load. In addition, measurement of circulating currents for a case of 240MVA, 220 kV transformer is presented along with a numerical calculation of circulating currents and compared with the measurement.

Development of a loading protocol for long links in eccentrically braced frames

Loading protocols are generally used for qualification testing of structural members. In eccentrically braced frames (EBFs), the connections of short links attached to columns are evaluated based on the loading protocol given in the AISC Seismic Provisions for Structural Steel Buildings (AISC 341–16). Behavior of many short links without column attachments was also investigated by making use of this loading protocol. The AISC341 loading protocol is suitable for only short links and does not take into account the one-sided nature of link rotation angle (LRA) demands due to mean effects. Long link behavior differs from short link behavior in a sense that long links are subjected to strength and stiffness degradation due to local buckling effects. A nonsymmetrical loading protocol for long links was developed as a part of this study. Twenty-four long link EBF archetypes with variable floor plans, bay widths, number of stories and link length to bay width (e/L) ratios were designed according to the US standards. The responses of EBFs under maximum considered earthquake (MCE) and collapse level earthquake (CLE) were obtained by making use of numerical analysis employing degrading link models. The link rotation angle time histories were reduced and converted into a series of cycles and the peaks of the LRA response were identified by using the rainflow counting algorithm. The nonsymmetrical loading protocol was represented as a function of maximum rotation range, which depends on the seismic hazard and e/L ratio.

A genetic algorithm of optimal design of beam at restricted sagging

A genetic algorithm for solving the problem of optimal beam material distribution along length at a given restriction on maximum sagging value is suggested. A review of literature sources is conducted and it was shown that existing solutions cover partial cases only in which the position of the point with maximum sagging was defined previously. In the paper presented I-section beam with constant proportions is considered, i.e., beam width, caps, and web thickness are proportional to beam height in the current cross-section. A statically determined beam is being considered. The load applied to a beam can be arbitrary, including cases of non-symmetrical loads and differently oriented ones. The position of point(s) at which beam sagging is maximum are unknown at the beginning of optimization and are found in the process solution. The problem is solved in the linear definition. Beam mass was assumed to be an optimization criterion. The method of finite differences is used for beam sagging finding, i.e., for the solution of the differential equation of the bending beam with a variable cross-section. Discretization allows transforming the problem of design into the problem of beam height determination at a system of reference points. At this stage, found values of beam height must satisfy restrictions on reference point displacements. The suggested technique allows controlling beam displacement quite flexibly because restrictions on point displacement are considered separately and do not depend on each other. The suggested objective function is the linear superposition of beam mass and the possible penalty in case of beam maximum sagging over exceeding predefined values. The application of a genetic algorithm allows getting sets of beam thicknesses those, which guaranty reaching the minimum of the objective function. The model problem is solved. It is shown that the suggested algorithm allows effectively solves problems of optimal design of beams with restrictions on the maximum sagging value. The suggested approach can be developed for strength restrictions, statically undetermined structures, etc.

Centrifuge Modeling of Cyclic Nonsymmetrical Thermally Loaded Energy Pile Groups in Clay

Heat transfer from/to energy piles can cause plastic contraction of soft clay with a low overconsolidation ratio (OCR) during heating and cooling. This can lead to thermally induced excess pore water pressure and changes in the lateral stress acting on a pile. These thermally induced phenomena cause additional plastic settlement of the soil and pile. Irreversible settlement may cause serviceability or ultimate limit state problems for floating energy piles whose capacity is mainly derived from shaft resistance. Due to intended operational needs or by accident, cyclic nonsymmetrical thermal loads may be applied to floating energy pile groups and piled rafts. The thermomechanical interaction among nonsymmetrical loaded piles is not well understood. In this study, a series of cyclic nonsymmetrical thermally loaded centrifuge model tests were conducted on floating pile groups and piled rafts in soft kaolin clay with an OCR of 1.7 at the pile toe. The performance of floating 2×2 elevated energy pile groups and energy piled rafts was investigated. Three piles in each group were subjected to 15 cycles of ±14°C in temperature change. The thermally induced irreversible settlement and tilting of the elevated pile groups exceeded serviceability and ultimate criteria. The piled rafts similarly settled but to a smaller extent than the elevated group. Their tilting, however, did not exceed the serviceability criterion. It is recommended that energy piled rafts be used in soft clay instead of elevated energy piles.

A Method for Designing and Optimizing the Electrical Parameters of Dynamic Tuning Passive Filter

Power electronics-based apparatuses absorb non-sinusoidal currents. These are considered non-linear and non-symmetrical loads for the power grid, and they generate a harmonic current. The dynamic tuning passive filter (DTPF) is one of the best solutions for improving power quality and filtering out harmonic currents to get a symmetrical current waveform. The electrical parameters of DTPF can influence its absorbing harmonic current, tuning performance, and cost. In this paper, a method for designing and optimizing the electrical parameters of dynamic tuning passive filter is proposed in order to improve the effectiveness of DTPF and the symmetry level of the power source. First, according to the characteristics of the harmonic source, the design technical indicators of DTPF, and its topology, the design procedure for the electrical parameters of DTPF is proposed. Second, based on detailed analysis of the test results, the range of the harmonic current absorption coefficient is determined. Third, the range of the relationship coefficient is determined by analyzing the impact of the filter capacitor’s capacity on the filter performance. Fourth, the calculation method for the electrical parameters of DTPF is devised. Finally, the validity of this method is verified by several engineering cases, and the electrical parameters of the filter capacitor and electromagnetic coupling reactance converter (ECRC) under the lowest total cost are simulated and optimized. Our approach can optimize the electrical parameters of DTPF and improve the harmonic suppression effectiveness, thus leading to a more symmetrical waveform and successfully avoiding power grid problems. The research results of this study not only provide a basis for the design of ECRC, but also lay a foundation for the machining DTPF.

Performance of elevated energy pile groups with different pile spacing in clay subjected to cyclic non-symmetrical thermal loading

There is an increasing interest and use of energy foundation worldwide. Full-scale tests, physical model tests at one Earth’s gravity and at elevated gravity in a geotechnical centrifuge and numerical simulations have been widely reported in the literature. Almost all studies have focused on single energy piles (EPs) and pile groups subjected to symmetrical thermal loads, although it is not unusual to have energy pile groups stressed by non-symmetrical thermal loads. In this study, a series of non-symmetrical thermal loading centrifuge model tests were conducted in saturated soft clay (OCR = 1.7), which is much vulnerable to temperature changes. The tests aim to investigate the effects of pile spacing on the serviceability of floating energy pile groups. Fifteen cycles of non-symmetrical thermal loading are applied to three EPs in 2 x 2 elevated energy pile groups with 3D and 5D (D denotes pile diameter) pile spacing. The thermally induced irreversible settlement and tilting in the 3D-pile group are 200% and 300% larger than those in the 5D one, respectively. Contrary to the 5D-pile group where the serviceability criteria (EN 1997-1:2004) are satisfied, the settlement and tilting are 30% and 200% larger than the criteria in the 3D one, respectively.

Efficient semi-analytical simulation of elastic guided waves in cylinders subject to arbitrary non-symmetric loads

In this paper, we present an approach to model the propagation of high-frequency elastic guided waves in solid or hollow cylinders. This formulation requires only discretization of the radial direction, whereas the circumferential direction is approximated via a truncated Fourier series, and the axial direction is described analytically. The model is extended to allow applying arbitrary non-symmetric loads f(r,θ) on the flat cylinder surface. Efficiency is increased by a proposed methodology to limit the number of Fourier coefficients and by the implementation of hierarchical shape functions to dynamically adjust discretization with respect to frequency. Results are validated against conventional finite element applications, demonstrating the accuracy of the model and a reduction of the computing time by three orders of magnitude. Additionally, we apply a matrix function solution for the scaled boundary finite element method leading to a linear solution in the static case.

ПРИМЕНЕНИЕ БЫСТРЫХ РАЗЛОЖЕНИЙ ДЛЯ ПОСТРОЕНИЯ ТОЧНЫХ РЕШЕНИЙ ЗАДАЧИ О ПРОГИБЕ ПРЯМОУГОЛЬНОЙ МЕМБРАНЫ ПОД ДЕЙСТВИЕМ ПЕРЕМЕННОЙ НАГРУЗКИ

The problem of rectangular membrane deflection under alternating loads is solved in general terms by means of the method of fast expansions. The exact solution is represented by the finite expression borrowed from the theory of fast expansions as a sum of the boundary function and Fourier sine series with two Fourier coefficients taken into account. The obtained exact solution includes free parameters. Changing the values of these parameters, one can derive many new exact solutions. Obtaining of exact solutions to a problem of the rigidly fixed membrane under two types of loads (dome-shaped and sinusoidal) is shown as an example. Graphs of the dome-shaped and sinusoidal loads on the membrane and the curves of the corresponding deflections and stress components are presented in the paper. From the analysis of the exact solutions, it is obvious that only when a symmetrical alternating load is used, the membrane maximum deflection is attained in the center of the membrane, and the stresses reach the highest values in the middle of both long sides. In the case of a non-symmetrical load, the maximum stress occurs in the middle of either one of two long sides of the rectangular membrane, and the maximum deflection is found in the central region.

Improving the Structural Behavior of Tied-Arch Bridges by Doubling the Set of Hangers

In tied-arch bridges with a single arch, the deck is usually suspended from the arch by means of a single set of cables, pinned at both ends and anchored to the centerline, using either vertical or Nielsen-type hanger arrangements. When properly designed, this layout can significantly reduce forces and deflections under loads that are symmetrical with respect to the plane of the arch. However, it does not contribute to the support of nonsymmetrical loads, such as eccentric loads distributions or wind loading, and does not reduce the sensibility of the arch to out-of-plane buckling. Thus, this paper studies how a cable arrangement composed of two sets of lateral hangers, attached to both edges of a deck, can be very suitable to address these problems. Firstly, it is demonstrated that the structural behavior under symmetrical loads improves with respect to the bridge with centered hangers. Secondly, it is shown how nonsymmetric loads are partially carried by structural systems (such as the transversal stiffness both of the arch and the deck) that would remain inactive for tied-arch bridges with centered hangers, leading to a general reduction in the forces and the deflections of the bridge and in the critical buckling load of the arch.

Experimental and Numerical Investigation on the Influence of Thermally Induced Stress Gradients on Fatigue Life of the Nickel-Base Alloy Mar-M247

Abstract Today's and future parameters of stationary gas turbines and aircraft engines require intensive and highly efficient cooling of hot gas path components. High temperature and thermally induced stress gradients with impact on fatigue life are the consequence. Thermally induced stress gradients differ from geometrically induced stress gradients with respect to stress mechanics by the independence from external loads and material mechanics by the influence of temperature on material properties and strength. Regarding the contribution and evaluation on damage, the latter characteristic feature in turbomachinery is currently not fully understood. Therefore, a test facility has been designed, setup, and reported in GTP-18-1482 for the investigation of the influence of stationary temperature, and thus thermally induced stress gradients, on the damage evolution of cooled high-temperature components. To achieve high temperature and thermally induced stress gradients, large heat fluxes are required. A unique radiation heating has been developed allowing very high heat fluxes of q˙ ≥ 1.5 MW/m2 for testing of hollow cylindrical specimens. The conventional cast nickel-base alloy Mar-M247 has been chosen to study the influence of thermally induced stress gradients on fatigue life. The low-cycle fatigue testing of the hollow cylindrical specimens has been conducted both with and without superimposed stationary temperature gradients. In addition, complex low-cycle fatigue (CLCF) tests with symmetric and nonsymmetric loading conditions have been performed to provide the necessary database for the adaptation of a viscoplastic deformation model. To calculate the local stress–strain field and service life of the test specimens, linear elastic and viscoplastic finite element studies have been performed and were assessed by means of a fracture mechanics-based lifetime model. The test results show the considerable influence of the temperature gradient on the low-cycle fatigue life for the investigated material. Both the radial temperature variation over the specimen wall with a hot outer surface and a cooled inner surface as well as the thermally induced stresses are stated to be the main drivers for the change in low-cycle fatigue life. The test results enhance the understanding of fatigue-damage mechanisms under local unsteady conditions and can be used as a basis for improved service life predictions.