Equation Method Research Articles

Investigating Ecosystem Service Trade-Offs and Synergies: The Need for Correlations and Driving Factors in the Upper Fen River Basin of Shanxi Province, China

This research provides an overview of the trade-offs and synergies among ecosystem services (ESs) within the upper Fen River Basin (uFRB) that are crucial for informed land management and regional ecological protection. We utilized methodologies, including the dynamic equivalent factor method and spatial autocorrelation analysis, to track ES and driving factors from 1990 to 2020. This study revealed a 13.27% increase in overall ES value, with notable growth in forest land and water areas. Initially, synergies were dominant, but trade-offs became evident over time, particularly with food production. This study identified road proximity and the Normalized Difference Vegetation Index (NDVI) as primary drivers of ES values, with their impact evolving annually. The analysis also highlighted the importance of considering the temporal dynamics in ES relationships and the influence of driving factors on these services. We propose incorporating socio-ecological factors and ES bundles into spatial planning. This is crucial as it will allow us to optimize multi-ES objectives, thus balancing trade-offs and enhancing synergies for sustainable land use.

Performance Evaluation and Optimization of Flux-Regulated Axial-Radial Eddy Current Coupling

Abstract This paper proposes a novel axial-radial permanent magnet eddy-current coupling equipped with a mechanical magnetic adjuster. The innovative design integrates mechanical flux weakening technology with an enhanced magnetic method rooted in axial-radial hybrid flux topology. Concise analytical models for air-gap field and torque are developed, leveraging the magnetic equivalent circuit method and Faraday’s law. These models are subsequently validated using the 3D finite-element method. The results indicate that this device boasts an exceptionally broad torque adjustment range, reaching approximately 93% at a given slip. Furthermore, it exhibits a substantial optimal working area, spanning from 20% to 80% of the mechanical magnetic adjuster's movable distance. To comprehensively analyze the impact of structural parameters on overall performance, three novel metrics are defined. The analysis reveals that the pole pairs of the radial magnetic circuit (RMC) have the most significant influence on the device's comprehensive performance. In the end, a multi-objective optimization method to maximize the global torque regulation capabilities, local torque regulation abilities, and maximum torque potential is developed to enhance the overall performance of this innovative magnetic coupling design.

Experimental Test and Analytical Calculation on Residual Strength of Prestressed Concrete T-Beams After Fire

High temperatures during a fire can lead to the evaporation of moisture and the degradation of hydration products within concrete, consequently compromising its mechanical properties. This paper thoroughly investigates the effect of fire-induced high temperatures on the residual load-bearing capacity of concrete structures, with a focus on prestressed concrete T-beams. By conducting constant temperature tests and residual load-bearing capacity tests, complemented by finite element modeling, this study examines the degradation of mechanical properties in prestressed concrete T-beams due to fire exposure and its impact on post-fire residual load-bearing capacity. Additionally, an equivalent concrete compressive strength method was employed to propose a calculation method for concrete material degradation under high temperatures and a corresponding concrete strength reduction factor. Simplified calculations were also performed for the high-temperature damage to reinforcement and prestressed tendons, leading to the derivation of a simplified formula for the residual load-bearing capacity of post-fire prestressed concrete T-beams. The results indicate that in prestressed concrete T-beams exposed to fire, an increase in holding time results in more severe damage modes, accelerated crack propagation, and wider crack widths during bending failure. Under the same load, a longer holding time corresponds to a more pronounced reduction in deflection. At holding times of 60 min, 120 min, and 180 min, the prestress losses were 48.17%, 85.16%, and 93.26%, respectively. The cracking load decreased by 15%, 27%, and 42%, while the residual load-bearing capacity decreased by 11%, 21%, and 28%. Comparison with experimental data demonstrates that both the finite element model and the simplified calculation formula exhibit high accuracy, offering a reliable reference for the performance evaluation of post-fire prestressed concrete T-beams.

Land use change and its impact on ecosystem service value in Xinjiang

Abstract Xinjiang is an important hub connecting China and Eurasia and has an important strategic position in economy, energy, and ecological security. However, due to the fragile ecological environment in Xinjiang, there are substantial challenges in coordinating the relationship between social and economic development and ecological environment construction. To elucidate the relationship between land use changes induced by human activities and the valuation of ecosystem services, this study utilized the value equivalent method to evaluate the ecosystem service value in Xinjiang from 2000 to 2020 while analyzing its spatiotemporal response characteristics related to land use. The results showed that from 2000 to 2020, the value of ecosystem services in Xinjiang showed an upward trend, reaching 182.24 yuan/hm2 in 2020, and the total value of the whole region was 302.584 billion yuan. The value of ecological services in Xinjiang is mainly low-grade (about 50%), and high-grade only accounts for 1.03%~2.19%. There was a significant increase in land use in forested areas and water bodies, while the conversion trend from effective grassland to other land types was relatively limited. Specifically, 4.47% of bare ground and 3.76% of meadows transformed water bodies. Additionally, 2.69% of grassland experienced conversion into woodland. The land use intensity was generally low (more than 85% of the low-grade grades), and 83.71% of the land use intensity increased during the study period. The water area was the main controlling factor of the service value of the state system, with a contribution rate of 78.83%, followed by grassland (11.29%) and woodlands (9.30%), and 54.39% of the land use changes increased the value of ecosystem services.

Experimental and numerical investigation of failure modes in RC frame structures designed using the equivalent linearization method

The codes of many countries currently employ the column-to-beam flexural strength ratio (CBFSR) based on frequent earthquake internal forces to achieve the expected strong-column-weak-beam (SCWB) ductile failure mode. However, real earthquake damage indicates a general failure to achieve SCWB. The design method based on frequent earthquake internal forces struggles to consider factors such as internal force redistribution and variable axial forces under rare earthquakes. Therefore, developing a seismic design method directly based on rare earthquake internal forces is crucial. The equivalent linearization method is a practical approach for obtaining the internal forces of RC frame structures under strong earthquakes without extensive nonlinear computations. In this paper, nonlinear finite element analyses of RC frame structures with expected SCWB failure modes under various structural parameters were conducted to obtain ductility coefficients under rare earthquakes. Using the equivalent linearization method based on secant stiffness, the equivalent stiffness and damping of beams and columns were calculated. Simplified parameters were determined for engineering applications to facilitate seismic design based on rare earthquake internal forces. Two RC frame structures were designed using both the equivalent linearization method and the CBFSR code method, and then subjected to pseudo-static low-cycle reciprocating loading tests. The study investigated failure modes and hysteretic energy dissipation, as well as overall stiffness and bearing capacity under earthquake conditions. Results showed that the equivalent linearization method can effectively direct RC frame structures to achieve the expected strong earthquake failure mode.The dynamic time history analysis was performed on finite element models of different heights, and the results indicated that the equivalent linearization method significantly reduced plastic hinge occurrences and ductility coefficients of column ends, resulting in improved seismic performance compared to the CBFSR code method.

Optimizing Circular MIMO Array Imaging Using Partial Equivalent Method for Sidelobe Suppression

In this paper, we propose a novel approach for circular Multiple-Input Multiple-Output (MIMO) array imaging, termed the Partial Equivalent Method (PEM), aimed at sidelobe suppression. In our method, the imaging process of the circular MIMO array is initially decomposed into bistatic circular synthetic aperture radar (BCSAR) components with different bistatic angles. Components with larger bistatic angles produce equivalent channels whose wavenumber spectra are concentrated near zero frequency, leading to significant broadening of the main lobe in the corresponding point spread function (PSF). In traditional MIMO imaging, each transmit–receive antenna pair is considered an equivalent channel, and all these channels are utilized for imaging. However, components with large bistatic angles, when integrated into the MIMO imaging output, result in increased sidelobe levels. To address this issue, we employ the PEM to restrict the range of equivalent channels. This method selectively retains effective channels generated by components with specific bistatic angles, effectively mitigating the adverse effects of BCSAR components with larger bistatic angles. Through point target simulations, electromagnetic simulations, and practical experiments, we demonstrate that the PEM significantly reduces sidelobes and enhances image quality in circular MIMO array imaging.

Equivalent thickness method of CFRP in chloride ion diffusion equation for CFRP–strengthened RC members and its load capacity assessment method

Carbon fiber reinforced polymer (CFRP)–strengthened reinforced concrete (RC) structures exhibit resistance to chloride ion penetration. However, accurately quantifying this resistance and predicting the load capacity of CFRP–strengthened RC beams subjected to chloride ion erosion requires further investigation. This paper introduces two equivalent thickness methods for non-fully bonded CFRP within the chloride ion diffusion equation: first method assumes CFRP having a fixed equivalent thickness, while the second method allows for CFRP having a linearly decreasing equivalent thickness depending on the depth within the concrete. A model is established between the reduction factor of load capacity in CFRP–strengthened RC beams and the concentration of diffusing chloride ions. Based on experimental results from our research group regarding chloride ion erosion in CFRP–strengthened RC members, both the equivalent thickness method and the load capacity model for CFRP were evaluated. The findings indicate that the chloride ion concentration predicted by the second equivalent thickness method outperforms the first, with an error of 13.1%. Furthermore, this method accurately predicts the chloride ion concentration after 60 days of exposure, exhibiting an error of 7.0%. Additionally, employing the proposed load capacity model, derived from the second equivalent thickness method, the calculated load capacity of CFRP–strengthened RC members subjected to chloride ion erosion shows only a 5.2% deviation from experimental results. This study concludes that the equivalent thickness of non-fully bonded CFRP decreases linearly with depth in concrete and establishes a direct correlation between load capacity and chloride ion concentration, thereby offering more targeted characterization methods.

Advancements to the equivalent compression flange method

AbstractThe simplified method of the equivalent compression flange represents an illustrative and easy‐to‐use engineering model for lateral torsional buckling. The basic concept of the verification procedure has existed since its introduction in the 1950s. It is still frequently used today for preliminary design and application cases where the solution of the ‘correct lateral torsional buckling problem’ is complex and time‐consuming. To adapt the method to the current state of the art, it was further developed in the framework of the Eurocode 3 evolution. This ‘new’ method is part of the second generation of Eurocode 3, Part 1‐1 and is valid for classes 1 to 3 cross sections in major axis bending. The method must be adapted for use in other contexts and for specific applications. Applying the equivalent compression flange verification method to the structural fire design of building structures must consider the temperature‐dependent material properties of steel and their impact on the stability behaviour. Moreover, typical applications for bridge structures, runway beams, and H‐piles in combined walls require additional consideration of class 4 cross sections and various combined loadings, e. g., N–M interaction behaviour. This article presents theoretical studies on extending the simplified method of the equivalent compression flange to meet these demands. Finally, the application of the verification method is demonstrated in working examples.

Simplified assessment of structures with clutching inertia-friction systems by equivalent linearization methods

The innovative Clutching Inertia System (CIS), has garnered increasing recognition for its effectiveness in mitigating structural vibrations. To enhance the efficiency of passive CIS, introducing suitable energy dissipation mechanisms for the rotation inertia component is imperative. This study delves into the dynamic behavior of CIS, augmented with additional friction damping. Initially, the influence of supplementary friction damping within the CIS framework is examined through a dynamic model of a Single-Degree-of-Freedom (SDOF) system, integrated with the CIS and incorporating the Coulomb friction model. Subsequently, to streamline the dynamic analysis of the CIS and optimize the friction force thereby enhancing control efficiency while minimizing inactive durations, the paper introduces two distinct Equivalent Linearization Methods (ELMs). Furthermore, an assessment of the CIS’s dynamic performance, subjected to various external excitations, is presented. The findings highlight the crucial role of supplemental friction damping in reducing the inactivity of CIS and enhancing its overall control effectiveness. The employed ELMs demonstrate commendable accuracy and practicality for both response assessment and CIS performance optimization. In essence, the CIS, when integrated with supplemental friction damping, exhibits superior performance in suppressing structural displacement responses across diverse excitations, particularly in longer-period structures. Conversely, a more pronounced efficacy in managing structural acceleration responses is observed in structures with shorter periods. The study concludes that for specific structural applications, enhancing supplemental friction damping is more advantageous for vibration control than increasing the CIS’s inertia.

Characterizing machine tool spatial stiffness and predicting accuracy

As a typical precision machine, the machine tool has complex structure and changeable working conditions, which leads to huge calculation data and low analysis efficiency when using traditional finite element method to obtain stiffness information. General test methods often have discrete values and cannot obtain stiffness information comprehensively and systematically. In this paper, a method for characterizing the stiffness of machine tool processing space based on multi-body system topology is proposed. Based on the matrix condensation theory, a method for constructing the equivalent condensation model of the stiffness of machine tool components is proposed. The stiffness characterization model of the components is established by using the stiffness equivalent condensation method. Based on the multi-body system theory, the stiffness distribution model of machine tool machining space is established, which can quickly and intuitively characterize the machining stiffness information of machine tool. Finally, based on the stiffness distribution model of the machining space of the machine tool, the machining accuracy of the S-shaped test specimen is predicted. Combined with the experimental analysis, the measurement results are consistent with the prediction results. The accuracy, feasibility, and effectiveness of the stiffness distribution model of machine tool machining space are verified.

Indefinite Linear-Quadratic Optimal Control of Mean-Field Stochastic Differential Equation With Jump Diffusion: An Equivalent Cost Functional Method

Indefinite Linear-Quadratic Optimal Control of Mean-Field Stochastic Differential Equation With Jump Diffusion: An Equivalent Cost Functional Method

Environmental behavior and risk of the emerging organic contaminants halogenated carbazoles in chemical industrial park clusters

Polyhalogenated carbazoles (PHCZs) are emerging organic contaminants and have attracted extensive concern because of their widespread occurrence and dioxin-like toxicity. However, the distribution characteristics, environmental behavior, and fate of PHCZs are still poorly understood. In this study, 74 composite environmental samples from 21 Chinese cities were collected around industrial parks in the Yangtze River Delta. The PHCZ concentration ranges in sediment and soil samples were 12.7–5.21 × 103 and 34.6–1.81 × 103 ng/g, respectively, which is equivalent to or higher than those of well-known persistent organic pollutants in the similar areas. The dominant congeners of PHCZs in sediment and soil were 3-chlorocarbazole and 3,6-dichlorocarbazole. Industrial emissions, especially from printing and dyeing textiles, were the main contributors to the high PHCZ environmental concentrations. Potential toxic effects of the PHCZs were evaluated using the toxic equivalent (TEQ) method. The TEQs of PHCZs in sediment and soil were up to 550 and 554 pg TEQ/g dry weight, respectively. The estimated TEQ value of sediment and soil exceeded the corresponding safety guideline, which indicated that PHCZs in the Yangtze River Delta posed high health risks. This study provides an important theoretical basis for controlling and reducing the ecological risks of PHCZs in the chemical industry. At the same time, it also provides reference for the priority control and revision of discharge standards for PHCZs in sewage treatment plants in future.

Analytical Modeling of Short-Circuit Impedance of Square Foil Winding Phase-Shifting Transformer Based on Planar Energy Density Equivalence Method

Analytical Modeling of Short-Circuit Impedance of Square Foil Winding Phase-Shifting Transformer Based on Planar Energy Density Equivalence Method

A Novel Method to Predict Carbohydrate and Energy Expenditure During Endurance Exercise Using Measures of Training Load.

Sports nutrition guidelines recommend carbohydrate (CHO) intake be individualized to the athlete and modulated according to changes in training load. However, there are limited methods to assess CHO utilization during training sessions. We aimed to (1) quantify bivariate relationships between both CHO and overall energy expenditure (EE) during exercise and commonly used, non-invasive measures of training load across sessions of varying duration and intensity and (2) build and evaluate prediction models to estimate CHO utilization and EE with the same training load measures and easily quantified individual factors. This study was undertaken in two parts: a primary study, where participants performed four different laboratory-based cycle training sessions, and a validation study where different participants performed a single laboratory-based training session using one of three exercise modalities (cycling, running, or kayaking). The primary study included 15 cyclists (five female; maximal oxygen consumption [ O2max], 51.9 ± 7.2mL/kg/min), the validation study included 21 cyclists (seven female; O2max 53.5 ± 11.0mL/kg/min), 20 runners (six female; O2max 57.5 ± 7.2mL/kg/min), and 18 kayakers (five female; O2max 45.6 ± 4.8mL/kg/min). Training sessions were quantified using six training load metrics: two using heart rate, three using power, and one using perceived exertion. Carbohydrate use and EE were determined separately for aerobic (gas exchange) and anaerobic (net lactate accumulation, body mass, and O2 lactate equivalent method) energy systems and summed. Repeated-measures correlations were used to examine relationships between training load and both CHO utilization and EE. General estimating equations were used to model CHO utilization and EE, using training load alongside measures of fitness and sex. Models were built in the primary study and tested in the validation study. Model performance is reported as the coefficient of determination (R2) and mean absolute error, with measures of calibration used for model evaluation and for sport-specific model re-calibration. Very-large to near-perfect within-subject correlations (r = 0.76-0.96) were evident between all training load metrics and both CHO utilization and EE. In the primary study, all models explained a large amount of variance (R2 = 0.77-0.96) and displayed good accuracy (mean absolute error; CHO = 16-21g [10-14%], EE = 53-82kcal [7-11%]). In the validation study, the mean absolute error ranged from 16-50g [15-45%] for CHO models to 53-182kcal [9-31%] for EE models. The calibrated mean absolute error ranged from 9-20g [8-18%] for CHO models to 36-72kcal [6-12%] for EE models. At the individual level, there are strong linear relationships between all measures of training load and both CHO utilization and EE during cycling. When combined with other measures of fitness, EE and CHO utilization during cycling can be estimated accurately. These models can be applied in running and kayaking when used with a calibration adjustment.

A hybrid equivalent circuit model and plane wave spectrum method for decoupling surface designs in multi‐band shared‐aperture antenna arrays

AbstractShared‐aperture antenna arrays are attractive for 5G base stations, owing to their compact size and multi‐band frequency coverage. Decoupling surfaces are effective for suppressing crossband mutual coupling. However, their designs typically rely on full‐wave simulations of scattering parameters, which may not ensure a good radiation performance and is time‐consuming. A systematic methodology based on the hybrid equivalent circuit model and plane wave spectrum method is proposed for decoupling surface designs. The decoupling surface is represented by its equivalent circuit and the spectral expression converts the electromagnetic field into a circuit problem. Both the scattering parameter and radiation pattern can be solved with the circuit, offering an efficient design method that ensures consistent radiation patterns between the model and full‐wave simulations. A double‐layer decoupling surface with wide stopbands, high transmission property, and sharp roll‐off transition was realised. Furthermore, to reduce the overall profile height, the reflection phase of the decoupling surface was tuned. A triple‐band shared‐aperture base station antenna array was developed. Simulated and measured results demonstrate the array works properly in the 0.69–0.96 GHz, 1.7–2.7 GHz, and 3.3–3.8 GHz frequency bands with stable radiation patterns, and crossband mutual coupling is well suppressed, validating the effectiveness of the proposed methodology.

Residual Effects of Pig Slurry Fertilization in a Mediterranean Rainfed Cereal System

An increase in nitrogen (N) use efficiency (NUE) in agriculture is a requirement for sustainable development. The reduction in nitrogen inputs might benefit from the residual N of former organic fertilization procedures. A 10 year experiment was established in a rainfed Mediterranean system (barley–wheat rotation). The objective of this experiment was to quantify the N residual effects of a single pig slurry (PS) application at sowing (20, 40, and 80 m3 ha−1) and up to three years later. The mineral N equivalence method was used to compare the grain yield (GY) and the whole-plant N uptake (WPNU) between the slurry fertilized plots (slurries applied in previous years) and annual mineral N fertilized ones (30, 60, 90, 120, and 150 kg N ha−1). From the total N applied with PS, a fraction of, ca., 21% accounted for the residual equivalent mineral N for a total period of three years after the PS application. For the 20 m3 ha−1 rate, the relative residual N based on the GY and WPNU equaled to 89–90% of the applied organic N, respectively. This rate also allowed for an increase in NUE values to above 33%. In semiarid areas, the introduction of residual N when scheduling fertilization is important to reduce N inputs and to increase NUE.

Spatiotemporal Change Analysis and Multi-Scenario Modeling of Ecosystem Service Values: A Case Study of the Beijing-Tianjin-Hebei Urban Agglomeration, China

Ecosystem service value (ESV) assessment is a crucial indicator of regional ecological quality and ecological management effectiveness. Ecosystem services (ES) provide the environmental foundation for human existence and social advancement. However, the future course of land use change (LUC) in urban agglomerations and its implications for human society remains uncertain, which presents a challenge to maintaining a balance between ecological service functions and regional socioeconomic growth. This paper took the Beijing-Tianjin-Hebei (BTH) urban agglomeration as an example and used the future land use simulation (FLUS) model to project the spatial distribution of land use under the natural development scenario (NDS), food security scenario (FSS), and ecological priority scenario (EPS) of BTH in 2030, 2040, and 2050. Next, the changes to ESV under various scenarios were investigated through the equivalent coefficient method. In order to make more targeted recommendations for regional development, the study also used hotspot analyses to explore the impacts of LUCs on ESV. The results showed that: (1) from 2000 to 2020, the LUC in the BTH was dramatic and mainly focused on the interconversions among the three land use categories of cropland, grassland, and built-up land. The total ESV demonstrated the tendency to decrease from CNY 386,859.89 × 106 in 2000 to CNY 371,968.78 × 106 in 2020. (2) Compared with 2020, the ESV in BTH in 2050 under the FSS loses 16,568.78 × 106 CNY, followed by the NDS (CNY 10,960.84 × 106), while the ESV under the EPS increases by CNY 9373.74 × 106. The results of the scenario simulation showed that there was significant variability in ESV under different political orientations. (3) Hotspot analysis indicated that the ESV changes were clustered in the northeastern part and the eastern coastal region of the BTH. On this basis, we identified Chengde, Beijing, Tianjin, and Zhangjiakou as the key cities to focus on and made meaningful suggestions for their future regional environmental protection and sustainable development. This research can serve as a guide in creating sustainable BTH development policies and offer fresh perspectives for investigating how land use patterns affect the ecological environment’s regional quality under various policy trajectories.

Evaluating Indoor Air Quality in Residential Environments: A Study of PM2.5 and CO2 Dynamics Using Low-Cost Sensors

Indoor air quality (IAQ) poses a significant public health concern, and exposures to high levels of fine particulate matter (PM2.5) and carbon dioxide (CO2) could have detrimental health impacts. This study focused on assessing the indoor air pollutants in a residential house located in the town of Mission, Hidalgo County, South Texas, USA. The PM2.5 and CO2 were monitored indoors: the kitchen and the bedroom. This investigation also aimed to elucidate the effects of household activities such as cooking and human occupancy on these pollutants. Low-cost sensors (LCSs) from TSI AirAssure™ were used in this study. They were deployed within the breathing zone at approximately 1.5 m above the ground. Calibration of the low-cost sensors against Federal Equivalent Method (FEM) instruments was undertaken using a multiple linear regression method (MLR) model to improve the data accuracy. The indoor PM2.5 levels were significantly influenced by cooking activities, with the peak PM2.5 concentrations reaching up to 118.45 μg/m3. The CO2 levels in the bedroom increased during the occupant’s sleeping period, reaching as high as 1149.73 ppm. The health risk assessment was assessed through toxicity potential (TP) calculations for the PM2.5 concentrations. TP values of 0.21 and 0.20 were obtained in the kitchen and bedroom, respectively. The TP values were below the health hazard threshold (i.e., TP < 1). These low TP values could be attributed to the use of electric stoves and efficient ventilation systems. This research highlights the effectiveness of low-cost sensors for continuous IAQ monitoring and helps promote better awareness of and necessary interventions for salubrious indoor microenvironments.

Evaluation of the flexural stiffness of a lattice girder composite slab at the construction stage according to the lattice girder shape

Lattice girder composite slabs (LGCS) for use in construction stages are structures in which part of the lattice girder is embedded in precast concrete panels with a thickness of less than 100 mm. they serve as a permanent formwork supporting the casting loads of on-site concrete while constituting a portion of the RC slab. In this study, analytical research was conducted to evaluate the flexural stiffness of LGCS effectively and simply considering a range of variables. Based on the results, an Euler-Bernoulli beam-theory-based equivalent sectional analysis method is proposed. To achieve this, the study extracted the second moments of area (Iexp) from the experimental results of previous researchers and compared them with the second moments of area (Ibeam) calculated using the Euler-Bernoulli beam-theory-based sectional analysis, analyzing how the ratio (Ibeam/Iexp) varies according to the design parameters. Variable analyses over a wide range were conducted by expanding the types and ranges of variables, and the effects of different variables and ranges were analyzed by comparing the second moments of area based on an FE analysis of LGCS (IFEM) with those based on a beam analysis (Ibeam). Furthermore, to apply the equivalent sectional analysis method to LGCS, equivalent second-moment-of-area formulas were proposed through the equivalent neutral axis and equivalent arm length for each sectional element.

Shaking table test and numerical simulation of rocking wall frame structure considering dynamic soil-structure interaction

This study investigates the seismic response of a rocking wall frame structure considering dynamic soil-structure interaction (DSSI) through shaking table tests. A comparison with conventional frame structures and structures with fixed-base foundations is made to examine the influence of DSSI effects on various aspects including structural damage distribution, dynamic characteristics, and floor responses. Test results indicate that the presence of a rocking wall reduces structural responses across different site conditions, although the reduction is less significant under soft soil conditions compared to fixed-base foundation conditions. Overall, DSSI diminishes the mitigating effect of the rocking wall on the maximum structural response. Furthermore, a three-dimensional finite element model of the shaking table test is established. The numerical model employs the equivalent linear method to simulate the soil's nonlinear behavior and incorporates the concept of the rocking wall. Comparative analysis between experimental and simulated results demonstrates that the model effectively predicts the dynamic response of the rocking wall frame structure in DSSI systems.