Energy Dissipation Coefficient Research Articles

Energy evolution and strain localization in fractured sandstone under freeze-thaw cycling and uniaxial loading-unloading

In cold regions, combined cyclic freeze-thaw (F-T) and loading-unloading can cause rock slope instability and sliding. The macro-failure of rock masses originates from the expansion of strain localization areas driven by energy. Therefore, a deep understanding of the energy evolution and strain distribution can reveal the instability process. Along these lines, in this work, intact and intermittently jointed sandstones were subjected to a cyclic F-T environment and subsequently carried out uniaxial graded loading-unloading to obtain their mechanical parameters and X-ray computed tomography images. By investigating the energy density, it was found that the input, elastic, dissipated, and damage energies all increased with loading according to a quadratic polynomial function, with the energies obeying a linear allocation law. Meanwhile, F-T changed the energy storage capacity and energy dissipation coefficient of the rock by causing meso-damage. To measure the meso-scale strain localization characteristics, the advanced digital volume correlation technique was also used to obtain three-dimensional strain fields. In terms of local strain, the failure behavior of intact specimens under the application of low and high numbers of F-T cycles was controlled by potential fracture bands and frost-heave cracks, respectively, while fractured specimens were mainly dependent on the macro-fracture arrangement. However, both frost heaving and thawing transformed sandstone from brittle to ductile. In terms of statistical strain, the equivalent strain (εeq) showed a log-normal distribution and continued to deviate to the right due to loading-unloading. Meanwhile, the normal strain (εxx, εyy, εzz) exhibited a normal distribution, where fractured sandstone mainly developed along with the slip direction. Finally, the intrinsic correlations among the energy parameters, meso-damage, and macro-failure were discussed. From our analysis, three stages of energy allocation and transformation were revealed, namely the uniform allocation of damage energy, banded accumulation of damage energy, and fracture caused by the elastic energy release.

Cyclic behavior and constitutive relations of HRB400E steel under large strain range

To study the differences in material performance between HRB400E steel and conventional strength steel, this paper performed monotonic and cyclic loading tests on HRB400E and Q355B steels under a series of loading protocols. Additionally, the self-designed fixtures were used to achieve large strain rate loading. The ductility, monotonic behavior and hysteretic characteristics of HRB400E and Q355B steels were assessed, along with the energy dissipation capacity evaluated through the energy dissipation coefficients. The cyclic skeleton curves of both steels were fitted using the Ramberg-Osgood model, with further investigation into the influence of kinematic hardening parameters on hysteretic curves. The combined hardening parameters of the Voce-Chaboche model were calibrated based on the experimental results, and the hysteretic curves were simulated under different loading protocols via ANSYS. The analysis results reveal that the energy dissipation coefficients of HRB400E steel are larger than that of Q355B steel, yet smaller than those of Q460D, LYP100, LY100, LY160, and LY225 steels. Both HRB400E and Q355B steels demonstrate significantly improved material strength under cyclic loading. Excellent agreement between simulated and experimental curves is achieved when using four pairs of kinematic hardening parameters. Additionally, the hysteretic performance of HRB400E and Q355B steels under different cyclic loading protocols can be precisely simulated by employing calibrated combined hardening parameters. Through this paper, the cyclic behavior and constitutive relations of HRB400E steel are comprehensively understood, which provides a reliable theoretical basis for engineering design and structural analysis. Furthermore, this research provides a scientific basis for material applications of HRB400E steel.

Fatigue characteristics and energy evolution analysis of red sandstone under the coupling of freeze–thaw and cyclic loading

In order to improve the safety of rock mass engineering in cold regions, this paper discusses the fatigue characteristics and energy evolution of red sandstone under the coupling of freeze–thaw and cyclic loading. Firstly, the correlation between the fatigue life, failure stress, and the number of freeze–thaw cycles of the red sandstone samples was calculated using the Pearson correlation coefficient method. Secondly, the energy evolution of the samples was analyzed using the image integration method and the least squares method. Finally, the damage mechanism of the samples under the coupled effect of freeze–thaw and cyclic loading was discussed using a conceptualized model. The results show that freeze–thaw cycles are negatively correlated with fatigue life and failure stress. The increase in freeze–thaw and fatigue damage leads to an increase in ductility and a decrease in the stiffness of the samples. The total energy density, elastic energy density, and dissipated energy density of the samples all show a quadratic polynomial relationship with the stress level. The energy storage and dissipation coefficients are negatively and positively correlated with the number of freeze–thaw cycles, respectively.

Mechanical property of bolted-assembled reinforced concrete column-steel composite joints

Herein, a new type of bolted-assembled reinforced-concrete column-steel (RCS) beam composite joint is proposed by analysing the force and force transmission process of RCS beam composite joints. The practicality and uniqueness of the structure apply to beam–column joints in large shopping malls, mid- to high-rise office buildings, factories, garages and other building structures. By the finite-element software modelling, a numerical simulation is established and used to analyse the variation of stress and equivalent plastic deformation, hysteresis curve, skeleton curve, stiffness degradation and energy dissipation coefficient under monotonic displacement–load and cyclic displacement–load. Results elaborate that the RCS composite connection has good ductility under monotonic displacement–load. Besides, under the cyclic displacement–load capacity, the hysteresis curve is full, the stiffness degradation is not obvious and the ductility and energy dissipation are good. This study is expected to promote the engineering application and guide follow-up research of the new nodes.

Experimental study and numerical analysis on the failure mode of staggered truss framing system

To investigate the seismic performance of staggered truss framing system under different failure modes, two trusses were designed according to the capacity design method. Then, two models with a scale of 1/2.5 were made and subjected to quasi-static tests. The hysteresis curve, stiffness, energy dissipation, and ductility coefficient of the two models were analyzed. The test results show that the specimen designed for chord failure has better seismic performance than that designed for diagonal web failure. The ultimate drift ratios of the two specimens are both less than 1.5%, indicating that the deformation ability of the staggered truss is insufficient. By analyzing the relationship between the plastic hinge rotation and the drift ratio of the truss, it is suggested that the limit value of the drift ratio of the staggered truss framing system should not exceed 1.5%. The yield-bearing capacity calculated by considering the composite effect of the chord and floor slab is closer to the test results than that calculated without considering the composite effect, indicating that the composite effect of the chord and floor slab should be considered when designing the trusses. Through the numerical analysis, it is recommended to take a minimum amplification factor of 1.3 for the internal force of web members to realize the purpose of chord failure.

Seismic performance of joints of prefabricated corrugated steel utility tunnels Part(I)–Experimental analysis

This paper presents the seismic performance of a corrugated steel plate utility tunnel, based on an engineering prototype. The research combines quasi-static testing and numerical simulation to investigate the behavior of the structure under cyclic loads in different directions. Specifically, six loading scenarios were considered: the quasi-static test was conducted for transverse tension and compression, transverse bending and shear, vertical shear test (Conditions (1–3)), while numerical simulations were performed for longitudinal tension and compression, transverse shear, and vertical bending shear test (Condition (4–6)) in Part(II). The results reveal comprehensive hysteresis curves for the plate under diverse loading directions, with an extended yield platform section that underscores its significant plastic deformation capacity. However, the “pinch” phenomenon of the hysteresis curve is obvious. The existence of rounded corners not only makes the hysteresis curve of the plate asymmetrical but also makes a great difference to the bearing capacity of the structure in the direction of positive and negative loading. The component exhibits superior bearing capacity and stiffness along the longitudinal direction compared to other orientations. Additionally, the structure demonstrates remarkable energy dissipation capabilities because of the inherent “accordion effect” of the corrugated steel plate. Moreover, the maximum energy dissipation coefficient in three directions is more than 1.0, illustrating its excellent energy dissipation capacity. The results provided valuable insight into the seismic performance of joints and contributed to the safe design of prefabricated corrugated steel utility tunnels.

Numerical investigations on constitutive model parameters of HRB400 and HTRB600 steel bars based on tensile and fatigue tests

Abstract In recent years, HRB400 and HTRB600 steel bars have become the mainstream standard reinforcing steel used in concrete structures in China. However, significant controversy still exists regarding the selection of material constitutive models and the determination of model parameters for buckling, fatigue, hysteresis, and other material characteristics. In this article, an automated process of multi-parameter calculation of the constitutive model for reinforcing steel – simulation accuracy evaluation of the constitutive model – selection of the constitutive model of reinforcing steel is established based on the hybrid programming method using MATLAB and OpenSees software. First, tensile and low-cycle fatigue tests were carried out on HRB400 and HTRB600 steel bars. Second, based on the constitutive model in OpenSees software and the skeleton curve and characteristics such as yielding, fatigue, and hysteresis, the constitutive model parameters of HRB400 and HTRB600 steel bars are determined using indirect and direct fitting methods. Finally, the five similarity parameters of the simulated normalized cumulative hysteretic energy dissipation coefficient are compared with the test results. The results indicate that the simulation accuracy of the Reinforcing Steel model exceeds 72%, which is higher than other four models, making it the best choice for reinforcing steel in numerical simulation.

Investigating the wave attenuation capabilities of rectangular pile head breakwater: A physical modelling approach

The study provides a comprehensive examination of single row Rectangular Pile Head Breakwaters (RPHB), encompassing both non-perforated and perforated variations. In the non-perforated RPHB category, the investigation delves into the effects of pile head height and width, and wave climate. For perforated RPHB structures, the study analyses the influence of percentage of perforations, perforation size, and depth of water. Further, the research includes a comparative assessment between non-perforated and perforated RPHB structures. Additionally, the research conducts a comparative analysis with similar structures. In the case of non-perforated RPHB, the configuration with relative pile head diameter (D/d) of 2.4 and relative pile head height (Y/Hmax) of 1.5 stood out as the most effective model. Similarly, the perforated RPHB demonstrated its maximum wave attenuation potential with percentage of perforations (P) of 24% with relative size of perforations (S/D) of 0.25. This optimal configuration achieved a minimal wave transmission coefficient (Kt) of 0.53, reflection coefficient (Kr) of 0.33, and energy dissipation coefficient (Kd) of 0.79 at a relative water depth (h/H) 0.865. Notably, the introduction of perforations on the RPHB structure led to an improvement in wave attenuation performance by 4–8%, resulting in lower reflection and higher energy dissipation. Comparatively, the RPHB structure outperformed the Enlarged (cylindrical) Pile Head Breakwater (EPHB) and Conical Pile Head Breakwater (CPHB) structures in terms of wave attenuation, exhibiting higher reflection and superior energy dissipation characteristics. The consistent outcome of these investigations reveals that the RPHB exhibits superior hydrodynamic performance characteristics and design suitability, making it a promising choice for breakwater applications.

Classical and local similarity in problems of turbulent convection: Extension of Prandtl semi-empirical theory for horizontal layers of water and air mediums

A variant of the local similarity theory is considered, assuming a priori specification of two basic dimensional parameters: the second moment of vertical velocity and the “spectral” Prandtl mixing length. Such selection of basic parameters lets us interpret the algebraic formulas of Prandtl's semiempirical turbulence theory for the coefficients of turbulent heat transfer and kinetic energy dissipation as relationships of the local similarity theory. A priori approximations of the basic parameters are based on known relationships and consider the upper boundary of the convective layer as a solid wall. Within the framework of local similarity theory, approximations for the turbulent moments of buoyancy and vertical velocity of arbitrary order are also proposed. The correspondence of these approximations to experimental data has been established in both air and water mediums, as well as in the results of numerical modeling. Such correspondence allows us to conclude that a wide class of vertical profiles of turbulent moments in a windless convective layer depends only on two basic parameters: the second moment of vertical velocity and the “spectral” Prandtl mixing length. The obtained result indicates the universal nature of the theory of local similarity and is a significant addition to the semiempirical Prandtl theory.

Upgrading seismic performance of beam-column joints using steel-polypropylene hybrid fiber: Experiment and numerical simulation

Due to the exceptional resistance to concrete cracking, appropriate incorporation of steel-polypropylene hybrid fiber is anticipated to enhance the mechanical properties of beam-column joints that are crucial for ensuring the integrity of frame structures under earthquake excitations. In this study, twenty-eight steel-polypropylene hybrid fiber reinforced concrete beam-column joints (HFRC-BCJs) were tested under cyclic loading to investigate their seismic performance, in which the effects of fiber types, concrete strength, axial compression ratio, and characteristic parameters of hybrid fiber are taken into account. The results indicated that the incorporation of steel-polypropylene hybrid fiber can exert a beneficial synergetic effect on improving the seismic responses of beam-column joints in multiple aspects. Specifically, hybrid fiber not only alleviated the concrete damage within the core region significantly, but also augmented the initial cracking load, displacement ductility coefficient, and energy dissipation coefficient of the beam-column joints by an average of 40.5 %, 31.4 %, and 37.3 %, respectively. Moreover, with the purpose of enabling a reasonable prediction of the seismic responses of HFRC-BCJs, a modified super degree-of-freedom (DOF) element was adopted for the numerical simulation, in which a user-defined UMAT subroutine was developed to more accurately reflect the enhancements of fiber inclusion on the tensile and compressive stress-strain behaviors of HFRC, as well as the associated damage evolution.

Application and Performance Evaluation of Superelastic Shape Memory Alloys in Building Vibration Isolation Systems

Abstract In this study, the intrinsic model of Shape Memory Alloys (SMA) is employed to facilitate a comprehensive analysis of the phase transition process, encapsulating the evolution of stress and strain across varying temperatures. The martensite volume fraction is quantitatively described using a cosine function, culminating in the formulation of a cosine-type SMA phase transition equation. This model enables the simulation of superelasticity, shape memory effects, and the elastic-thermal behavior of SMA by varying the loading conditions. This approach allows for an assessment of how different material parameters influence SMA properties. Notably, the results highlight that the heating temperature significantly affects the hyperelastic energy dissipation properties of SMA. The energy dissipation coefficient increased by 15.3% when the temperature was increased from 350 to 550 and decreased by 36.3% when the temperature was increased from 550 to 650. The peak values of top acceleration and interstorey displacement of the SMA-isolated structure were 0.826 m/s² and 0.641 mm for EL-centro waves at 7+ seismic intensities. The values of non-isolated were 1.151 m/s², 0.856 mm. 10 ground shaking, the SMA braced structure relative to the steel frame structure on the maximum peak inter-story displacement angle and the structure of the top layer of the permanent displacement, have different degrees of reduction. Therefore, the SMA material possesses good damping performance in the seismic isolation system.

Simulation Analysis of the Influence of Amplitude on Deformation and Fracture Characteristics of Hard Rock under Ultrasonic Vibration Load

The utilization of auxiliary tools employing ultrasonic high-frequency vibration to enhance rock breaking efficiency holds significant potential for application in underground hard rock excavation engineering. To investigate the failure mechanism of rocks under high frequency ultrasonic vibration load, this study employs particle flow software PFC2D for numerical simulation. By incorporating boundary conditions from actual ultrasonic vibration rock breaking experiments and utilizing a parallel bond model to construct the rock, we analyze the deformation, damage, fracture, and energy evolution process of hard rocks subjected to vibrational loads. The results demonstrate that the maximum displacement in hard rocks increases nearly linearly with vibrations until reaching 5.0199 × 10−3 m, after which it plateaus. Additionally, macroscopic fissures formed during rock failure exhibit an X-shaped pattern. Furthermore, based on our model, we examine the impact of amplitude variation on hard rocks with an equal number of cycles (5,000,000 cycles). Under ultrasonic vibration loads, amplitude influences the total input energy within the rock system. While increasing amplitude does not alter maximum deformation in rocks, it enhances fragmentation degree, fracture degree and energy dissipation coefficient—thereby improving rock breaking efficiency.

Seismic performance of cold-formed thin-walled C-shaped steel composite wall with fireproof straw boards cladding

ABSTRACT In order to study the seismic performance of cold-formed, thin-walled C-shaped steel composite wall, a set of cold-formed thin-walled C-shaped steel skeleton structure and a set of composite wall covered with fireproof straw boards on both sides were tested with a low cyclic alternative load. The seismic performance indexes, such as bearing capacity characteristic value, lateral stiffness, ductility coefficient, energy dissipation coefficient and stiffness degradation, were analysed by obtaining the backbone curves of each group of specimens. The effects of fireproof straw boards on the seismic performance of the composite wall were compared, and a mechanical analysis model of the cold-formed thin-walled C-shaped steel composite wall was established by using ANSYS/structural finite element software. The results show that the damage patterns, backbone curves and capacity characteristic values of the finite element model are in general agreement with the tests. The bearing capacity and lateral stiffness of the light steel skeleton structure without boards is very low, while the bearing capacity of the composite wall with straw boards on both sides is significantly increased. The lateral stiffness increased by 10.76%, the ductility coefficient increased by 27.34% and the energy dissipation coefficient decreased by 45.8%.

Anisotropic characteristics of layered backfill: Mechanical properties and energy dissipation

Layered backfill is commonly used in mining operations, and its mechanical behavior is strongly influenced by delamination parameters. In this study, 13 specimens with different numbers of delamination and delamination angle were prepared to investigate the anisotropic mechanical behavior, energy dissipation characteristics and crack development of backfill. P-wave velocity, uniaxial compression, scanning electron microscope (SEM), and acoustic emission (AE) experiments were conducted. The results indicate that: (1) The P-wave velocity has linear and elliptical relationships with the number of delamination surface and delamination angle, respectively; the strength, delamination parameters and P-wave velocity show a high degree of coincidence in terms of their function relationship, which can realize the rapid prediction of strength. (2) The microstructure of the delaminated surface is looser than that of the matrix, leading to a decrease in strength and an increase at the pore-fissure compaction stage. The number and angle of delamination increase linearly with the anisotropy coefficient. (3) The energy evolution in angle-cut backfill can be divided into four stages, with a decrease in the proportion of elastic energy at the initiation stress and peak stress with increasing number of delamination planes and delamination angle. (4) Crack development increases with the number of delamination surface and delamination angle, resulting in a decrease in energy dissipation coefficient and peak AE energy. These findings provide valuable insights for the design of filling materials and processes in mining operations.

Numerical and Theoretical Analyses of Friction-Oval Section Mild Steel Rod Composite Dampers

In order to improve the seismic and energy dissipation capacity of the whole structure, a friction-oval section mild steel rod composite damper (FOSRCD) was proposed, and its working principle was clarified. The finite element analysis of FOSRCD was carried out, and the effects of friction, frequency and displacement on the damper performance were studied. Considering the structural characteristics of FOSRCD and the mechanical models of friction dampers and mild steel rod dampers, the restoring force model of the composite dampers was proposed and compared with the numerical simulation results. The results showed that the FOSRCDs had good performance and could provide stable energy dissipation capacities in both directions, with the energy dissipation coefficient exceeding 2.3 and the equivalent damping ratio exceeding 0.37. The theoretical analysis results were in good agreement with the numerical simulation results, which verified the theoretical restoring force model; the FOSRCDs make full use of the friction energy dissipation and the shear and bending energy dissipations of the mild steel rod. It enables the two dampers to work together to achieve the purpose of multi-stage energy dissipation. FOSRCD’s structure allows it to dissipate energy in both the X- and Y-directions. The composite dampers have a variety of restoring force models and can be utilized in a wide range of practical applications.

Experiment study on seismic performance and size effect in BFRP-RC squat shear walls with different horizontal reinforcement ratios

Focusing on the combined effects of the horizontal reinforcement ratio and the structural size on the seismic performance of BFRP reinforced concrete (BFRP-RC) shear walls, the present study experimented on six shear walls with different structural sizes up to 1800 mm × 1800 mm × 240 mm (length × height × thickness) having various horizontal reinforcement ratios of 0.25% and 0.50%. From the experiment, it is concluded that: (1) the failure modes of the specimens with horizontal reinforcement ratios of 0.25% and 0.50% are mainly shear failure and compressive-shear failure, respectively. (2) When the length of the specimen increases from 600 mm to 1800 mm, the nominal cracking, elastic and shear strength of shear walls with the horizontal reinforcement ratio of 0.25% (resp. 0.50%) decreases by 66% (resp. 59%), 30% (resp. 29%) and 28% (resp. 24%), respectively. The results demonstrate that the size effect on the BFRP-RC shear wall is significant. Meanwhile, the ductility coefficients decreased by 19% (resp. 22%), and energy dissipation coefficients decreased by 39% (resp. 18%). (3) When the horizontal reinforcement ratio increases from 0.25% to 0.50%, the nominal shear strength of specimens with lengths of 600 mm, 1200 mm and 1800 mm increases by 14%, 15% and 19%. It is worth noting that the size effect is significantly suppressed with the increase of horizontal reinforcement ratios. Besides, the good consistency found between the experiments and the size effect law proposed by Jin et al. allows the validation of the accuracy and rationality of the size effect law.

Contribution to the Characterization of Vibration Isolators Based on Metal Mesh

The prediction of the behavior of vibration isolators is essential for effective and efficient design of these devices, as well as for accurately characterizing the isolator behavior. In this work, an experimental study was performed to characterize the behavior of metal-mesh isolators. Although these elements’ performance is of great interest because of their usage in several applications, their characterization is complex due to their nonlinear nature, among other factors. This study’s aim was to obtain the quasi-static behavior of these isolators, although dynamic tests are required for their complete characterization. These quasi-static tests allowed for the highlighting of some characteristics in a simpler and faster manner and also provided a starting point for designing future dynamic tests. The quasi-static tests performed resulted in the calculation of the hysteresis cycle under different operating conditions and manufacturing parameters. The study of different insulator characteristics, such as the energy dissipation coefficient and stiffness, led to interesting conclusions about the isolator performance. From the results, it was observed that the relative density affected most the nonlinear behavior of the insulator. Moreover, to correctly characterize their behavior, not only the Coulomb’s damping but also the viscous damping had to be considered.

Sill Role Effect on the Flow Characteristics (Experimental and Regression Model Analytical)

This study investigates the effects of gate openings and different sill widths on the sluice gate’s energy dissipation and discharge coefficient (Cd). The physical model of the sills includes rectangular sills of different dimensions. The results show that the gate opening size is inversely related to the Cd for a gate without a sill. In addition, increasing the gate opening size for a given discharge decreases the relative energy dissipation, and increasing the Froude number increases the relative energy dissipation. The results also show that the Cd and relative energy dissipation decrease when the width of the sill is decreased, thus increasing the total area of the flux flowing through the sluice gate and vice versa. According to the experimental results, the relative energy dissipation and the Cd of the sluice gate are larger for all sill widths than without the sill. Finally, non-linear polynomial relationships are presented based on dimensionless parameters for predicting the relative energy dissipation and outflow coefficient.

Experimental and Numerical Study of the Nonlinear Evolution of Regular Waves over a Permeable Submerged Breakwater

The permeable submerged breakwater has gained popularity in recent days due to its merits of reducing incident wave energy without negatively impacting the aesthetics of the ocean view and allowing for water exchange. However, the effect of porosity on wave nonlinearity and turbulence motion close to the water/structure interface is not well resolved in the literature. This paper presents an experimental and numerical study of regular wave propagation over a permeable submerged breakwater with a wide top width. The laboratory experiments were conducted in a wave flume and included 45 test cases. The numerical simulations were performed utilizing validated olaFoam. The results show that the nonlinearity of the waves on the permeable submerged breakwater is weak, which can effectively suppress and reduce the second harmonic waves. A large amount of turbulent kinetic energy exists at the interface between the permeable submerged breakwater and the water body, which helps to dissipate wave energy. For the wider permeable submerged breakwater in this paper, the wave dissipation capacity is greatest when the porosity is between 0.2 and 0.3, and as the length of the breakwater increases, the energy transmission coefficient decreases, and the energy dissipation coefficient increases. Better wave attenuation is achieved when the permeable submerged breakwater has a certain porosity and a large width.

Tensile behavior of CFRP-Steel composite laminates

Carbon-fiber/epoxy steel composite laminate (CSL) is a type of fiber metal laminate formed by stacking thin layers of carbon-fiber/epoxy and steel sheet. To investigate the stress–strain relationship under monotonic tensile and cyclic tensile, comprehensive experiments were conducted on five groups, including four groups of CSL specimens with different steel volume fractions (SVF) and one group of control steel plate specimens. Furthermore, stable post-yield modules and comparatively small residual deformation could be observed from CSLs curves. Based on the experimental failure mode, the theoretical models were proposed, and the numerical simulation was established, and verified by the test results. Theoretical calculations and numerical analysis were performed to estimate the effect of varying the SVF on the mechanical performance of the CSL, particularly in the absorption and energy dissipation coefficients.