Pseudo-dynamic Tests Research Articles

One novel block-type brace connector for retrofitting reinforced concrete frames

Buckling-restrained braces are widely utilized for retrofitting existing reinforced concrete frames. However, conventional plate-type brace connectors and joints often suffer damage from the additional forces exerted by buckling-restrained braces during earthquakes. This paper proposes a novel block-type brace connector to address this issue. The seismic performance of this new connector is evaluated through pseudo-dynamic and quasi-static tests. Pseudo-dynamic test results indicate that the reinforced concrete frame retrofitted with the new connectors demonstrates superior seismic performance compared to the frame without retrofitting. During a rare earthquake, the maximum inter-story drift ratios are 1/308 for the frame with new connectors and 1/84 for the frame without retrofitting. Quasi-static test results show that the new connectors shift the potential plastic hinges of the beam away from the gusset plate region by moving the post-installed anchorage position outward. The gusset plate of the conventional connector buckles at an inter-story drift ratio of 1/30, while that of the new connector avoids buckling due to the restraint from the concrete block. Overall, the new connector can mitigate the adverse effects of the additional forces from buckling-restrained braces and improve the seismic performance of the existing reinforced concrete frames.

Seismic capacity evaluation of a reinforced concrete frame infilled with precast modular block wall for enhancing the horizontal load

In this study, we propose a new concept for seismic retrofitting using precast modular block walls (PMBWs) to improve and complement the shortcomings of conventional retrofitting methods for reinforced concrete (RC) frames infilled with shear walls, masonry walls, and precast panels. The PMBW retrofitting method maximizes the advantages of factory-produced modular blocks, innovatively enhancing the constructability and integrity of connections between the existing frame and the infilled PMBW. Additionally, the PMBW reinforcement method improves seismic resistance without significantly increasing structural weight, and the required amount of reinforcement can easily be calculated because the strengthening technique involves typical frame infilling. For RC buildings with non-seismic details dominated by shear failure, the application of this seismic reinforcement method readily ensures sufficient strength. A pseudo-dynamic test was conducted on a full-scale two-story frame, based on an existing RC building with non-seismic details, to evaluate the restoring force characteristics, strength enhancement effects, reinforcement strain, and seismic response control capabilities of the PMBW reinforcement system. Based on the pseudo-dynamic test results, the restoring force characteristics for nonlinear dynamic analysis of the PMBW-reinforced specimen were identified. Finally, nonlinear dynamic analysis was conducted using the proposed restoring force characteristics, and the results were compared with the pseudo-dynamic test results. The unreinforced RC frame experienced shear failure at a design basis earthquake magnitude of 200 cm/s2. However, the frame reinforced with the PMBW sustained only minor damage. Even at higher magnitudes under maximum considered earthquake conditions of 300 cm/s2 and large-scale earthquake conditions of 400 cm/s2, only a slight amount of damage was projected from the analysis. Thus, the newly developed PMBW frame infilling system shows great promise for seismic reinforcement.

Seismic loading assessment of a novel structural column testing equipment

In experimental investigation on seismic performance of structural columns, it is particularly important that the loading device can reproduce a structure’s gravity load and apply a lateral seismic load at the same time, and both should be decoupled. Based on this concept, a two-dimensional multi-usage structural testing equipment (ZJU-MUST) has been developed with the following features: (1) the horizontal loading is ensured perpendicular to the vertical loading, and the loads in different directions are decoupled; (2) horizontal and vertical forces applied to testing specimen can be directly measured without the need to correct the secondary effects due to friction or vertical loading; (3) it is more reliable and suitable for cyclic loading under variable vertical forces. A 2600 mm high steel tubular column was designed for both cyclic loading tests and pseudo-dynamic tests. From the column test, the control system of ZJU-MUST as well as its performance in real-time data transmission and calculation can be verified.

Cross‐laminated timber for seismic retrofitting of RC buildings: Substructured pseudodynamic tests on a full‐scale prototype

AbstractThis paper presents an experimental study on an innovative timber‐based retrofit solution for reinforced concrete (RC) framed buildings, with or without masonry infills. The intervention aims to enhance seismic resistance through a light, cost‐effective, sustainable, and reversible approach integrating energy efficiency upgrades. The method employs cross‐laminated timber (CLT) panels as infills or external retrofitting elements, mechanically connected to the RC frame through steel fasteners. The system is combined with thermal insulation for improved energy efficiency. The seismic performance of the proposed retrofit technique was assessed experimentally on a full‐scale building model at the European Laboratory for Structural Assessment (ELSA). The experiments included tests on two five‐story building configurations: a masonry‐infilled RC building as a reference and the same structure strengthened with CLT panels. Each building was subjected to unidirectional earthquake simulations of increasing intensity using the pseudodynamic (PsD) testing method with substructuring. The physical substructure of the hybrid model consisted of the first story of a two‐story mockup built and retrofitted in the laboratory, while stories two to five were simulated numerically. The paper discusses major observations from the tests, comparing the damage evolution and hysteretic responses of the two configurations. The experiments yielded promising results, showing that the suggested retrofit solution significantly increased displacement and energy dissipation capacity. The retrofitted building survived earthquake intensities up to 50% higher than the non‐retrofitted counterpart, exhibiting only slight structural damage. These pioneering experiments provide compelling data on the high effectiveness of the proposed CLT‐based retrofit system in enhancing the seismic performance of full‐scale RC buildings.

Adaptive sliding-mode delay compensation for real-time hybrid simulations with multiple actuators

Real-time hybrid simulation (RTHS) is a widely applied test method in structural engineering, which is developed from pseudo-dynamic test. Much of the past work has been centered on one-dimensional RTHS using a single hydraulic actuator. When the complexity of the problem demands to increase the number of degrees of freedom to be enforced on the boundary conditions, more than one hydraulic actuator must be used. Multiple-actuator or multi-axial RTHS (maRTHS) requires that more than one hydraulic actuator exerts the required motion on experimental substructures demanding the implementation of multiple-input multiple-output (MIMO) control strategies. A new maRTHS benchmark control problem has been developed, focusing on a frame subjected to seismic load at the base, substantially transforming and intensifying the complexity of the problem. The time delay generated by the dynamic characteristics of the loading system and the transmission process as well as the high coupling between the hydraulic actuators and the nonlinear kinematics escalates the complexity of the actuator control tracking. A sliding mode adaptive delay compensation method suitable for maRTHS is proposed, which utilizes a MIMO sliding mode method to reduce the coupling effects of actuators and the adaptive compensation method to compensate the residual delay. The effectiveness of the method is verified by numerical simulating different working conditions in the Benchmark Problem Platform.

Biaxial seismic response of base-column connections in sub-standard steel buildings: dataset.

Existing steel frames not complying with modern seismic codes are often vulnerable to earthquakes due to inadequate seismic detailing. These types of framed structures typically feature semi-rigid and partial strength column-base connections; the behaviour of such connections may significantly affect their seismic performance. However, current code provisions offer limited guidance for the assessment and retrofit of column-base connections To fill the knowledge gap, the H2020 EU-funded Earthquake Assessment of Base-Column Connections in Existing Steel Frames (HITBASE) project experimentally investigated, the response of exposed column-base plate connections. Bi-directional Pseudo-Dynamic tests were carried out at the Structures Laboratory (STRULAB) of the University of Patras within the framework of Engineering Research Infrastructures for European Synergies (ERIES). The case-study steel frame featured two types of column-base plate connections, i.e., stiffened and unstiffened, representing respectively the base connections of an external moment-resisting frame and an internal gravity frame. The experimental programme comprised free vibration tests to identify the modal properties of the sample steel frame. A set of quasi-static cyclic tests and Pseudo-Dynamic tests were then carried out to investigate the performance of the steel frame under bi-directional earthquake sequences. The response of each component constituting the column-base plate connections was monitored during the tests to fully capture the behaviour of the connections. Such experimental results allow model calibration and further parametric investigation on column base plate connections.

Seismic Analysis of a Self-Centering Braced Frame in Pseudodynamic Tests: Response Characteristics, Brace Contribution, and Damage Evolution

Seismic Analysis of a Self-Centering Braced Frame in Pseudodynamic Tests: Response Characteristics, Brace Contribution, and Damage Evolution

Pseudo-dynamic tests of steel frame with disc spring self-centering energy dissipation braces under doublet earthquake and mainshock-aftershock sequence

To provide valuable insights into the seismic performance and self-centering behavior of self-centering braced systems, a 1/2-scale 3-story 1-bay steel frame equipped with disc spring self-centering energy dissipation braces (DS-SCBs) was designed, fabricated, and subjected to pseudo-dynamic testing. This testing encompassed various earthquake hazard levels, a doublet earthquake, and a mainshock-aftershock sequence. The experimental findings revealed the stable hysteretic response of the DS-SCB, with no observed degradation in stiffness or activation forces. Additionally, the test frame exhibited outstanding seismic performance, sustaining only confined damage under very rare earthquakes. Due to the presence of the DS-SCBs, the test frame performed commendable self-centering behavior, characterized by minimal residual deformations. Peak story drifts and floor accelerations under two earthquakes of the same hazard level were regarded as equivalent. Furthermore, the subsequent aftershocks exhibited no discernible impact on the seismic performance of the test frame. Floor acceleration spikes were observed at locations where the brace stiffness underwent changes or where adjacent stories moved in opposite directions. The steel frame equipped with DS-SCBs proved to be an attractive, low-damage alternative to conventional steel systems for the development of resilient urban areas.

Seismic protection provided by a new diamond-shaped bracing system with a horizontally layered friction damper

We present a new diamond-shaped bracing system with a horizontally layered friction damper (HLFD) that remedies the drawbacks of existing vibration control systems and is applicable to existing reinforced concrete (R/C) buildings. We investigated the material properties and energy dissipation of the HLFD. Pseudo-dynamic testing was performed on two-story full-size frame specimens based on an existing R/C building lacking seismic protection. We studied the hysteretic characteristics, energy dissipation, and ability to control the seismic response. The hysteretic characteristics were subjected to non-linear dynamic analysis, and the results were compared to those of the pseudo-dynamic test. Next, the effects of the new system on an existing R/C building lacking seismic protection were evaluated in terms of the non-linear dynamics. We derived the seismic response force, displacement characteristics, energy dissipation, and damper forces and displacements before and after seismic strengthening. Without protection, the building exhibited shear collapse at an earthquake ground acceleration of 200 cm/s2. However, damage was minimal when the new protective system was installed. At a maximum earthquake acceleration of 300 cm/s2, seismic damage remained low.

Pseudo‐dynamic testing, repairability, and resilience assessment of a large‐scale steel structure equipped with self‐centering column bases

AbstractRecent destructive seismic events have underlined the need for increasing research efforts devoted to the development of innovative seismic‐resilient structures able to reduce seismic‐induced direct and indirect losses. Regarding steel Moment Resisting Frames (MRFs), the inclusion of Friction Devices (FDs) in Beam‐to‐Column Joints (BCJs) has emerged as an effective solution to dissipate the seismic input energy while ensuring a damage‐free behavior. Additionally, recent studies have demonstrated the benefits of implementing similar damage‐free solutions for Column Bases (CBs). In this context, the authors have recently experimentally investigated a Self‐Centering CB (SC‐CB) aimed at residual drift reduction. Previous experimental tests only focused on the response of isolated SC‐CBs under cyclic loads. Conversely, the present paper advances the research through an experimental campaign on a large‐scale steel structure equipped with the proposed SC‐CBs, providing valuable insights into the global structural response and improved repairability. A set of eight Pseudo‐Dynamic (PsD) tests were conducted considering different records and configurations of the structure. The experimental results highlighted the effectiveness of the SC‐CBs in minimizing the residual interstory drifts and protecting the first‐story columns from damage, thus enhancing the structure's resilience. Moreover, the consecutive PsD tests allowed investigating the effectiveness of the reparation process in restoring the seismic performance of the ‘undamaged’ structure. An advanced numerical model was developed in OpenSees and validated against the global and component‐level experimental results. Incremental Dynamic Analyses were finally performed to investigate the influence of the SC‐CBs on the structure's seismic response while accounting for the record‐to‐record variability.

Pseudo-Dynamic Tests on Frame–Shear Wall Structure with Precast Concrete Diaphragm

In order to study how to improve the spatial action of precast monolithic composite floor slabs, and examine replacing the cast-in-place surface layer for reducing the weight of structure, we used pseudo-dynamic tests on one-quarter scale models of two-span and three-story frame structures. The lateral load tests compared the stresses and displacements with a cast-in-place floor frame–shear wall structure (SJ1) and a precast monolithic floor frame–shear wall structure with X horizontal braces at the bottom of the floor (SJ2). The results show the X horizontal braces can improve the spatial action. Structural integrity (SJ2) as well as the effective transmission of the horizontal force can be ensured by additional X bracing at the bottom of the rigidity of the floor without a cast-in-place concrete topping. The results show that X horizontal braces more effectively transfer horizontal stress, which provides a beneficial reference for similar research.

Seismic behaviour of a steel moment resisting frame structure featuring hourglass double split tee joints

The occurrence of brittle fractures in welds of full-strength joints of steel moment-resisting frames (MRFs) during earthquakes in Northridge (1994) and Kobe (1995) marked a turning point in seismic design philosophies for steel structures. This led to the development of new strategies focusing on enhancing structural resilience and energy dissipation. While Reduced Beam Sections (RBS) were traditionally favoured, recent approaches include partial-strength joints and replaceable dissipative fuses, in some cases also equipped with self-centring components. These systems often employ friction or yielding dampers, ensuring that the weakest joint component comprises well-designed dampers for optimal ductility and energy dissipation.In this context, the present study evaluates the performance of a large-scale structure featuring MRFs with partial-strength double-split tee (DST) joints and hourglass dampers. These joints are conceptually similar to ADAS dampers and the Simpson Strong Tie moment connection prequalified by AISC 358–16. The research involves conducting a pseudo-dynamic test campaign on a two-storey steel structure designed according to EC8 provisions. Findings from experiments and a numerical model developed using OpenSees are discussed. Incremental Dynamic Analyses (IDAs) compare structures with hourglass DST joints to those with full-strength joints, showing enhanced self-centring capacity in DST-equipped structures despite lacking dedicated self-centring components. Additionally, structures with hourglass DST joints demonstrate significant low-cycle fatigue life, potentially reducing the need to replace dissipative components after severe seismic events.

Seismic Performance Evaluation of Reinforced Concrete Buildings Retrofitted with a New Concrete Filled Tube Composite Strengthening System

This study proposes a concrete-filled tube composite strengthening system (CCSS), which is a new concept that can improve and supplement the vulnerability of existing CFT seismic strengthening methods. The CCSS seismic reinforcement method is easy to construct and integrates with the existing frame and reinforcement. It is one of the seismic strengthening methods that allows the simple calculation of the required amount of seismic reinforcement and can efficiently increase the strength when applied to existing reinforced concrete (R/C) buildings with non-seismic details dominated by shear failure. To examine the seismic safety of the proposed CCSS, two framework specimens were prepared based on an existing R/C building with non-seismic details. A pseudo-dynamic test was conducted on the unreinforced framework specimen and the framework specimen reinforced with CCSS to verify the seismic strengthening effect of applying CCSS to the existing R/C framework, i.e., in terms of the load–displacement characteristics and seismic response control capability. Based on the pseudo-dynamic test results, restoration of the force characteristics was proposed for the nonlinear dynamic analysis of the building reinforced with CCSS. Nonlinear dynamic analysis was conducted based on the proposed restoration of the force characteristics, and the results were compared with the pseudo-dynamic test results. Finally, for the commercialization of CCSS, nonlinear dynamic analysis was conducted on the existing whole R/C building with non-seismic details that was reinforced with CCSS. The seismic strengthening effect was then verified by examining the seismic response load, displacement characteristics, and the degree of seismic damage to the members based on the ductility ratio before and after seismic strengthening. The study results show that under a design basis earthquake with a magnitude of 200 cm/s2, the unreinforced R/C building exhibits shear failure, and light seismic damage is expected on the CCSS-reinforced building.

Seismic Capacity of R/C Buildings Retrofitted with a V-Bracing System Equipped with a Novel Laterally Layered Friction Damper

This study proposed a novel V-bracing system equipped with a laterally layered friction damper (LLFD), which can supplement the shortcomings of conventional vibration control systems and is applicable to existing reinforced concrete (R/C) buildings. A material test was used to evaluate the material performance and energy dissipation capacity of this LLFD. Pseudo-dynamic testing was conducted on two-story frame specimens based on an existing R/C building with non-seismic details to verify the seismic retrofitting effects of applying the LLFD V-bracing system to existing R/C frames, i.e., the restoring force characteristics, energy dissipation capacity, and seismic response control capacity. Based on the results of the material and pseudo-dynamic tests, restoring characteristics were proposed for the non-linear dynamic analysis of a building (frame specimen) retrofitted with the LLFD V-bracing system. A non-linear dynamic analysis was conducted based on the proposed restoring force characteristics, and the results obtained were compared with the pseudo-dynamic test results. Finally, for evaluating the commercialization potential of the LLFD V-bracing system, a non-linear dynamic analysis was conducted on an existing R/C building with non-seismic details retrofitted with the system. The seismic retrofitting effect was verified by examining the seismic response load and displacement characteristics, energy dissipation capacity, and damper load and displacement response before and after seismic retrofitting. The study results showed that the R/C frame (building) with non-seismic details exhibited shear failure at a design basis earthquake scale of 200 cm/s2; however, light seismic damage could be expected for a frame (building) retrofitted with the LLFD V-bracing system. At a maximum considered earthquake scale of 300 cm/s2, insignificant seismic damage was also anticipated, thereby verifying the validity of the newly developed LLFD V-bracing system.

Seismic capacity evaluation of existing reinforced concrete buildings strengthened with a novel prestressing steel frame system for increasing lateral strength

In this study, a new concept of seismic retrofit, the Prestressing Steel Frame (PSF) system, is proposed to improve and compensate for the weaknesses of the existing strength-enhancing seismic retrofit method. The PSF system, a construction method that maximizes the advantages of the H-shaped steel frame, innovatively improves the constructability and integrity of existing reinforced concrete (R/C) frames and reinforcement joints. This method is a type of typical strength-increasing reinforcement method that facilitates calculation of the required seismic reinforcement amount, and easily enhances the horizontal strength of shear collapse-type R/C buildings with non-seismic detailing. To review the seismic performance of the proposed PSF method, pseudo-dynamic tests were conducted on a real two-story frame based on an existing R/C building without seismic detailing, and seismic performance was evaluated in terms of load and displacement characteristics, seismic damage level, strength enhancement effect, and displacement control. In addition, based on the results of pseudo-dynamic testing, a hysteresis model was proposed to perform non-linear dynamic analysis of the seismically reinforced structure (two-story frame) with the PSF method. Non-linear dynamic analysis was performed based on the proposed hysteresis model, and the results were compared against that of pseudo-dynamic testing. For the commercialization of the method, non-linear dynamic analysis was conducted on the entire R/C building reinforced with PSF, and the effectiveness of seismic reinforcement was verified by comparing the seismic response load and displacement response before and after reinforcement. In the event of an earthquake with a maximum ground acceleration of 200 cm/s2, which is 2/3 of major earthquakes with a 2400-year recurrence interval stipulated in Korea Design Standard (KDS) 41, shear failure is expected for R/C buildings with non-seismic detailing, while small-scale damage is predicted for buildings reinforced with the PSF method. This shows that the PSF strengthening method is effective in minimizing earthquake damage.

Improved seismic response prediction of isolated structures using hardening correction in a novel LRB model

This study aimed to accurately characterize the large deformation and hardening behavior of lead rubber bearings (LRBs) subjected to seismic loadings. Specifically, both pseudo-static and pseudo-dynamic tests were conducted on LRB600 and LRB400 to investigate the LRB’ mechanical characteristics subjected to large deformation loading. Results indicated that the loading and unloading stiffness and hysteretic behavior can be effectively modeled by a novel mechanical model considering hardening correction. The proposed mechanical model demonstrated a better performance to predict the seismic response of isolated structures compared to other models that tend to overestimate the superstructure's performance state. Therefore, the mechanical model based on hardening correction provides a more accurate assessment of the seismic response of isolated structures than existing models.

Seismic performance of a full‐scale five‐story masonry‐infilled RC building subjected to substructured pseudodynamic tests

AbstractThis paper discusses the results of a series of hybrid earthquake tests on a full‐scale reinforced concrete (RC) building with masonry infills. The prototype was a five‐story structure representing the vulnerable part of a typical RC building in Southern Europe, with beams stronger than the columns and masonry infill walls weaker than the surrounding frame elements. The specimen was subjected to a sequence of unidirectional earthquake simulations of increasing intensity up to conditions of significant damage to the infills, using the pseudodynamic (PsD) testing method with substructuring. The input ground motion was a real earthquake recording, slightly modified in amplitude and frequency to match the elastic design code spectrum. The physical substructure of the hybrid model consisted of the first story of a two‐story mock‐up structure built in the European Laboratory for Structural Assessment (ELSA); the second story ensured realistic boundary conditions at the top of the first one. The characteristics of stories two to five were simulated by a numerical finite‐element model developed in OpenSEES and updated throughout the test sequence using data obtained from preceding tests. The experiments were terminated with the onset of a soft‐story mechanism at the first story of the physical substructure for an earthquake with a peak ground acceleration of 0.3 g. The paper summarizes the key characteristics of the specimen and the major observations from the hybrid tests, illustrating the evolution of structural/nonstructural damage and the cyclic hysteretic building response. The attainment of significant damage limit states is correlated with experimentally defined engineering demand parameters and ground‐motion intensity measures for the performance‐based seismic assessment of buildings. Data and observations from these experiments add substantially to our understanding of the effects of masonry infills on the seismic behavior of RC‐framed structures.

Substructure Pseudo-Dynamic Test Study for a Structure Including Soil–Pile–Structure Dynamic Interaction

An improved Penzien model is proposed in this paper as a simplified model of soil–pile–structure interaction. The dynamic nonlinearity of soil under earthquake excitation is simulated by ANSYS in a free-field model and added to the original Penzien model. The improved Penzien model uses the finite element software ANSYS 2021 to simulate the dynamic nonlinearity of soil. The improved Penzien model is then used as a simplified calculation model of the numerical substructure. A substructure pseudo-dynamic test based on the improved Penzien model is carried out. The realization of the substructure pseudo-dynamic test verifies the feasibility and effectiveness of this method, which provides a convenient test method for the study of soil–pile–structure interaction in general laboratories. Soil and structure interaction reduces the acceleration of the structure, and the response exhibited a hysteresis phenomenon because of the nonlinear characteristics of the soil. The influences of soil–pile–structure interaction on velocity and displacement are very complex. The conclusions are reasonable, which proves that the substructure pseudo-dynamic test method of soil–pile–structure dynamic interaction using the improved Penzien model is feasible.

Flat slab response for seismic and cyclic actions prediction with numerical models

As an outcome of a recent European research project, the modelling of the response of flat slab structures for seismic and cyclic loading was the object of a blind competition. No other blind tests are available in the literature on this topic. The test results concern a full-scale, two-storey, three-by two bay reinforced concrete flat slab frame. The seismic tests were carried out using a hybrid pseudo-dynamic test up to the ULS design excitation. The cyclic test reached a drift capacity of 2.5% and 6% in two concatenated tests. A synthesis of the models of three participants is provided, with one 3D NLFE (Nonlinear finite element) models and two slab and frame models. The CSCT (Critical Shear Crack Theory) model included in the fib MC2010 was adopted in the two latter to predict punching failure. The results are presented and discussed. Conclusions are drawn on research developments and practical approaches.

A stability-based energy-dissipation design method of viscoelastic dampers

Viscoelastic damper (VED) is one of the most effective velocity dampers, which can provide equivalent stiffness and damping for structures. The stability of the damper is an important factor affecting the control performance of dampers. However, most research works on the stability are focused on metal dampers, few research works on the stability of velocity dampers have been carried out. To solve the stability problem of VED, an energy-dissipation design method considering the stability of VED is proposed in this paper. Through parametric analysis, relationships between height-thickness ratios, loading frequency and stability-bearing capacity of VEDs are established. Then, the concepts of stability coefficient and frequency coefficient of VED are added into the mechanical model of VED. Subsequently, pseudo-dynamic tests and variable frequency loading tests are carried out for two groups of full-scale VEDs to verify the reliability of the stability coefficient and frequency coefficient. Here, a stability-based energy-dissipation design method of VEDs is proposed. Based on an actual project, nonlinear time-history analyses are carried out for the original structure and the controlled structure ignoring/considering the stability respectively. Results indicate that control effects considering stability are lower than control effects ignoring stability. In other words, it is shown that ignoring stability of VED will result in not meeting energy-dissipation expectations, which may bring potential safety hazards to the structure. Finally, to improve its stability, a new VED with improved out-of-plane stiffness is proposed. It can be concluded that it is necessary to take the VED stability into account in the design and performance evaluation of VE structures using the proposed method.