N2 Method Research Articles

Assessment of the seismic vulnerability of structures using: the N2 method, taking into account soil-structure interaction

Assessment of the seismic vulnerability of structures using: the N2 method, taking into account soil-structure interaction

Numerical investigation and seismic performance evaluation of an innovative prefabricated structural system

This paper focuses on an innovative structural system with separated gravity and lateral resisting systems (SGLR system), which is suitable for multi-story prefabricated buildings and demonstrates different seismic performance from the traditional rigid frame system (RF system). Elaborate three-dimensional (3D) finite element models for RF and SGLR systems are established and verified by test results. Based on the numerical models, the load-displacement relationship, force mechanism, energy dissipation capacity, local buckling, and stress and strain distribution of SGLR system are investigated in detail in comparison with RF system. In order to conduct the seismic performance evaluation, four groups of RF and SGLR substructures are designed with different lateral stiffness. Pushover analysis and response spectrum analysis are carried out, and safety factors are calculated on the basis of the incremental N2 method. It is indicated that SGLR system has lower loading capacity, smaller safety margin but larger deformation capability than RF system with the same lateral stiffness. Considering that the inter-story drift ratio is a common design index, more stringent design requirements should be proposed for SGLR system to obtain seismic performance equivalent to that of RF system.

The effects of crystal orientation and common coal impurities on electronic conductivity in copper–carbon composites

The electronic conduction properties of copper–graphene composite materials including common coal impurities are studied. Exploring the transport properties for three crystallographic orientations [(111), (110), and (100)] of copper in copper–graphene composites, a strong orientational dependence on electronic conductivity is shown. Graphene exhibits near-ideal registries for (111) and (110) orientations, forming a connected network between grains that enables efficient carrier transport. The influence of non-carbon elements: nitrogen (N), oxygen (O), and sulfur (S) in graphene, representing possible structures in coal-based graphene are investigated. N, O, and S in graphene negatively impact the composite’s electronic conductivity relative to pristine graphene. A new method is introduced for visualizing the spatial distribution of electrical conduction activity in materials using the square of the electronic charge density near the Fermi level, based on the work of Mott. We call this technique the N2 method.

Non-linear response of confined concrete beam-column structures under horizontal loading

In this study, a behavior law for confined concrete is considered with the introduction of transverse reinforcement to increase the compressive strength of concrete, using the model of Mander et al. This model integrates the confinement effects provided by transverse reinforcement, enhancing the load-bearing capacity of concrete under compressive stress. A pushover analysis is carried out on a full-scale, four- levels structure, using the N2 method. This advanced technique combines non-linear static analysis with inelastic response spectra. Using this approach, the structure's seismic performance can be estimated, accounting for its ductility and the non-linear effects at each loading stage. The inelastic response spectra are adjusted using reduction factors based on the structure's capacity to dissipate seismic energy through inelastic deformations. By varying the confinement rate of the concrete sections, different performance points of the structure can be obtained. The confinement ratio is a crucial parameter influencing the ductility and strength of confined concrete. Closer spacing of transverse reinforcement increases the confinement ratio, which improves the concrete's deformation capacity and ultimate strength. The results show the effect of the behavior law used to consider concrete confinement on the performance points of the structure. In particular, it is observed that increasing the confinement leads to significant gains in the strength and ductility of the structure. These results highlight the importance of optimally using transverse reinforcement to design structures that ensure their performance and safety under seismic loads.

Semi-automatic calibration of numerical models for the seismic safety assessment of masonry towers embedded in building aggregates

The present work addresses the topic of automated calibration of numerical models starting from the experimental characterization of the structure’s dynamic behaviour. The importance of the topic is well known in the literature, especially in cases where it is necessary to have at disposal validated numerical models, necessary for the correct evaluation of the safety of existing buildings. Generally, the calibration problem is developed with a manual approach (manual tuning), with a positive outcome whenever there is a good knowledge of the boundary and internal constraint conditions and the elastic mechanical properties of the construction’s constituent materials. Conversely, the positive outcome is particularly difficult to achieve manually when there are non-homogeneous and/or complex structures, as in the cases of historic masonry structures, which are often the result of constructions carried out at different times, organized in aggregates whose interaction between the portions is not simple to understand. For this purpose, the present work, using commercial software and specially prepared routines, illustrates a semi-automatic procedure, which employs genetic algorithms, suitable for the optimized identification of the numerical model that best represents the structure’s experimental dynamic behaviour. The procedure is presented with reference to two case studies: the Gabbia Tower historic masonry aggregate in Mantua and the bell tower of the Monastery of the Ursuline nuns in Capriolo, Brescia. In the first case, in addition to the experimental dynamic characterization, a good instrumental characterization of the tower’s masonry mechanical properties is available. In the second case, alongside a good experimental dynamic characterization, only a qualitative estimate of the masonry mechanical properties, based on visual inspections, is available. The two case studies allow for testing the validity of the numerical models’ calibration procedure, necessary for their application in the field of safety checks. Finally, for the case studies analysed the work presents an assessment of seismic vulnerability starting from the models identified with the semi-automatic procedure. The seismic vulnerability assessment was obtained using non-linear static analysis following the N2 method.

Test of three-storey confined masonry structure built from clay blocks and PU glue

The paper presents an experimental test of a nearly full-scale three-storey model of a confined masonry structure. The walls were constructed using newly developed clay masonry blocks, with large holes filled with thermal insulation and polyurethane glue instead of mortar. In the construction,relatively thick 38 cm walls and large tie-columns with 25 cm × 25 cm plan dimensions. The test model was built as confined masonry according to Eurocode 8. The innovative materials and construction were developed for thermal efficiency and the test was intended to verify the structural response. The model, test setup, and test procedures are described, and the results of the tests are analysed. The building responded primarily in shear, and ultimately failed in the ground floor in a storey mechanism, but there was also substantial damage on the floor above. Due to the non-standard dimensions of the tie-columns and because masonry was thicker than the tie-columns, the in-plane loaded walls developed an interesting response mechanism in which protruding masonry sheared off. Although this did not significantly impact the overall response, it led to the earlier onset of the significant damage limit state of the structure. The model responded well with wide hysteretic loops and distributed damage, which indicated large energy dissipation capacity, and the response envelopes showed gradual strength deterioration after peak load. The response of the model was quantitatively estimated using the N2 method. Calculations showed that the tested model could withstand a design seismic load corresponding to a 0.21 g peak ground acceleration with significant damage and almost 0.52 g before collapsing. The overstrength was estimated at 1.71.

Evaluating Seismic Performance in Reinforced Concrete Buildings with Complex Shear Walls: A Focus on a Residential Case in Chile

This study employs a non-linear static analysis, known as pushover analysis, to explore the flexural-compressive behavior of complex shear walls within a reinforced concrete (R.C.) structure, adhering to contemporary design standards in Chile. The primary objective is to assess the initiation of damage as the building approaches the limit states outlined in Achisina’s seminal “Performance Based Seismic Design” framework. To achieve this, a sophisticated fiber model, accounting for the confined behavior of concrete derived from the structural elements’ detailing, has been uniformly integrated across the building’s entire height. Furthermore, the analysis incorporates a rigid diaphragm to simulate the R.C. slab’s response accurately. The study implements the N2 method, adjusting for seismic demands in an acceleration-displacement format, which leverages the displacement spectrum defined by Supreme Decree 61, a legislative response to the 8.8 Mw Maule earthquake in 2010. The findings reveal that the analyzed structure meets the immediate occupancy performance level with drifts nearing 5‰ in the symmetrical Y direction. This outcome aligns with prior assessments of Chilean R.C. wall buildings. However, in the asymmetric X direction, the structure exhibits a higher degree of structural damage, aligning with a life safety performance level. This differentiation underscores the critical need for nuanced understanding and modeling of structural behavior under seismic loads, contributing to the ongoing refinement of seismic design practices and standards.

The evaluation of target displacement in structural systems using damage-based N2 (DN2) method under far-field ground motions for performance-based design theory

The evaluation of target displacement in structural systems using damage-based N2 (DN2) method under far-field ground motions for performance-based design theory

Photogrammetry-aided numerical seismic assessment of historical structures composed of adobe, stone and brick masonry. Application to the San Juan Bautista Church built on the Inca temple of Huaytará, Peru

This research presents a cost-effective surveying methodology to assist the seismic assessment of complex heritage buildings, based on terrestrial structure-from-motion (SfM) photogrammetry. The method was applied to the study of the seismic performance of the church of San Juan Bautista – Inca temple of Huaytará, Peru, an emblematic case study due to its complex architecture and coexistence of different construction materials. The geometrical model for the seismic assessment was developed with an error of less than 2 % using SfM photogrammetry. Non-linear static pushover analyses were performed on 3D FEM models of the nave and the towers to evaluate their individual response under seismic loading. Mechanical properties of different structural materials of the church were evaluated based on laboratory experimental tests on mortar and adobe, contemporary and ancient fired brick, Inca stone, colonial stone and rubble stone units. Non-linear pushover analyses were conducted in four directions perpendicular to the perimeter walls, and the response of the structure was compared with the seismic demand specified in Peruvian Standards. The simulations show that damage-prone areas are the western and eastern facades, with cracking at the connections between orthogonal walls, as well as at the interface of adobe masonry with Inca stone masonry. The towers exhibit similar seismic response, with lower strength capacities compared to the main nave. In this case, flexural overturning mechanisms and cracking at the interface between stone and adobe masonry were observed. The displacement-based seismic assessment using the N2 method shows that a peak ground acceleration of 0.21 g could lead to the collapse of the north and south facades of the main nave. The towers showed a much smaller capacity with PGA leading to collapse of approximately 0.09 g. Overall, this study contributes to the understanding of the seismic performance of the Huaytará-Huancavelica church, highlighting vulnerabilities and providing valuable information for its preservation and future interventions. Future investigations should focus on on-site tests that will allow the estimation of the effect of existing damage on the structural response and their incorporation in the numerical model.

Effects of the extended N2 method on non-linear static procedures of reinforced concrete frame structures

This paper intends to contribute to the validation of the extended N2 nonlinear static method of seismic analysis through the study of two existing reinforced concrete frames. The scope is to further investigate the limitations of the original N2 method in predicting the seismic response of plan asymmetric buildings and to assess the higher accuracy of the extended N2 method. The two case study buildings are representative of the Italian construction between the ’70s and ’90s. One is designed for gravity loads only, the other is designed according to an old seismic code. Two modelling strategies are used, one with distributed and the other with lumped plastic hinges. Three eccentricities eCM between centre of mass and plan geometric centre are considered (eCM = 0%, 5% and 15%). The pushover analyses are carried out following the N2 method, the N2 method plus the 100:30 directional combination rule and the extended N2 method. The results are compared with those obtained from nonlinear history analyses. For each building the seismic demand is assessed for three hazard levels. The results indicate that the application of the extended N2 method significantly enhances the shape of the demand prediction, particularly for buildings with higher plan eccentricities. On the other hand, the directional combination does not significantly change the results and should be neglected.

Performance based probabilistic seismic risk assessment for urban heritage. An example in Pla del Remei Area (Valencia)

The assessment of the seismic behaviour of historic residential buildings and the estimation of their possible losses in the event of an earthquake, is a must for defining strategic mitigation plans to prevent irreplaceable heritage losses. In this study an integrated performance based probabilistic risk assessment methodology is developed. An archival study and a field survey allow to identify architectural and construction characteristics of heritage residential buildings in urban areas and determine realistic structural models. These are analysed by using a limit state approach, coded in the FaMIVE method, considering different construction hypotheses, to produce capacity curves which support the identification of a discrete number of typologies representative of the entire building stock in the area. Their fragility functions are then derived using the modified N2 method. Because of the difficulty in quantifying the expected probable losses in purely economic terms, given the heritage value of these assets, losses are computed in terms of damaged floor surface area and mean damage ratio. These have been obtained through the earthquake loss estimation platform SELENA, considering different possible seismic scenarios. The procedure is applied to masonry residential buildings in Pla del Remei area of Valencia, Spain, built between the end of the 19th Century and the end of the Spanish War (1939). This neighbourhood embodies the cultural values, construction techniques and historic legacy of a new and brief era of modernity, inspired by the new urban theories and architectural styles of Eclecticism and Modernism. Despite Valencia being located in an area of low to moderate seismicity, the results show that the maximum percentage of built damaged area ranges from 5.8 to 11.6% for 475 years return period, increasing to 33.59–51.59% for 975 years return period. The high level of resolution of the study allows mapping and identifying the structures at higher risk and is therefore a valuable tool to support sensitive and targeted retrofitting policies.

Near-surface-mounted retrofitting of adobe walls using different materials: Evaluation of seismic performance

This study focuses on the seismic strengthening of adobe walls using different reinforcement materials and different reinforcement schemes through the near-surface-mounted (NSM) technique. Six adobe wall panels (1900 × 1200 × 200 mm) were quasi-statically tested and comprised one unreinforced wall and five specimens reinforced with reinforced mortar strip, bamboo plywood and wood, respectively. The strengthening procedure involved insertion of the reinforcing materials into the grooves cut symmetrically on both sides of the walls. The results were described in terms of energy dissipation, lateral resistance, ultimate displacement, stiffness degradation, ductility, and tolerate maximum peak ground accelerations. The tolerate maximum peak ground accelerations (PGA) of the specimens were analyzed using the N2 method. The test results indicated that the tensile strength, elastic modulus and scheme of reinforcement materials had a significant impact on the seismic performance and failure mode of specimens. The reinforced mortar strips significantly improved the seismic performance of adobe walls, particularly when using horizontal and vertical reinforcement schemes. The reinforcement of adobe walls with bamboo plywood and wood had achieved satisfactory results in terms of ductility, energy dissipation, and PGA. Finally, the masonry calculation formula was modified to establish the formula for estimating lateral resistance of adobe wall.

Multi-factorial investigation of the effect of biochar of the secondary medicinal residue of snow lotus on the adsorption of two azo dyes,methyl red and methyl orange.

Azo dye residues pollute water, which are difficult to decompose, and posing a major threat to the ecological environment. The residues of Chinese medicine still have many possibilities for use after its medicinal value has been brought into play. In this study, secondary residue biochar activation (Na2 CO3 -modified, SBA) and secondary residue biochar (unmodified, SBC) were prepared from the secondary residue of snow lotus at 200-600°C. Surface features were obtained by Brunauer-Emmett-Teller N2 method and combined with scanning electron microscopy, and their structures were analyzed by x-ray diffraction spectroscopy, Fourier infrared and near-infrared spectroscopy. The effects of five factors, including initial concentration, contact time and adsorption temperature and so forth, on the adsorption of methyl red (MR) and methyl orange (MO) solutions were investigated. Results showed that the biochar yield, specific surface area, and pore size increased after modification. modification promoted the formation of the internal structure aromatization and oxygen-containing functional groups. Adsorption experiments showed that the surroundings pH = 8, the dyes adsorption concentration of 8 mg/L, adsorption temperature of 20-40°C and time of about 1 h were more stable. Under the condition, the removal of MO by SBA could reach approximately 60%-80% (480-640 mg/g), while the removal of MR could reach more than 90% (>720 mg/g).The charcoal prepared and modified under high temperature conditions was more effective for MO adsorption, while MR relied on low temperature effectively. This study provides a new choice of adsorbent for MR and MO and finds a new direction for the utilization of snow lotus residues.

Seismic Performance Assessment of a Moment-Resisting Frame Steel Warehouse Provided with Overhead Crane

The purpose of this study is to analyze the nonlinear behavior of a steel warehouse structured by moment-resistant frames, which utilizes an overhead crane on its interior brackets and as an external load of the weight of the lining panels. The analysis methods used are (i) pushover analysis, which consists of applying an incremental force in the transverse and longitudinal direction to obtain the capacity curve of the structure; (ii) time-history analysis, in which different records of destructive earthquakes that occurred in Chile are used in order to analyze the response of the structure to these loads. The results indicate that the transverse direction is more ductile than the Y direction of the structure within the pushover and time-history methods but not using the N2 method. It is also found that most of the columns are within the life safety and collapse prevention criteria. It is concluded that most of the analyses agree with each other and with what is expected, except for the N2 method, which contradicts the results of the time-history analysis, so the N2 method would not be suitable for this type of structure. In addition, it has been determined that the overhead crane loads do not substantially affect the seismic performance of the warehouse.

Seismic evaluation of vertically irregular RC frames subjected to mainshock-aftershock sequences of near-fault and far-fault ground motions

Sequential ground motions can significantly affect the seismic demands of reinforced concrete (RC) frames with irregularity along the height. In this paper, the effect of sequential near-fault and far-fault ground motion records with strong and weak aftershocks on the seismic demands of vertically irregular 10-story RC building frames is investigated. The vertically irregular frames with stiffness and mass irregularities were created by applying a modification factor of MF = 2 in three different locations along the height of the reference regular frame. Eigenvalue analysis was performed to evaluate the dynamic characteristics of the structures (i.e. the period and the effective modal participating mass ratio for different modes of vibration). In order to study the seismic demands of these structures, the non-linear response history analysis (NL-RHA), which is the most accurate method of seismic evaluation of structures, was carried out. The floor displacements, story drifts, plastic hinge rotations and residual story drifts obtained from the NL-RHAs were exhaustively studied, and the effect of seismic sequences on the seismic responses was investigated. Furthermore, the enhanced pushover analyses, including the modal pushover analysis (MPA), consecutive modal pushover (CMP) procedure, extended N2 (EN2) method, single-run multi-mode pushover (SMP) method and non-adaptive displacement-based pushover (NADP) procedure were implemented to consider the effect of higher modes in computing the seismic demands of the structures subjected to sequential near-fault and far-fault records as well as mainshocks. The results accentuate that the maximum seismic demands and damage of the structure for sequential near-fault and far-fault records with strong aftershocks are much greater than those for the corresponding mainshocks. Moreover, the enhanced pushover analyses in the case of sequential records have usually less accuracy in estimating the seismic demands in comparison with mainshocks only.

Comparative analysis of code-compliant seismic assessment methods through nonlinear static analyses and demand spectrum: N2 Method vs. Capacity Spectrum Method

This paper investigates the main differences in evaluating the seismic performance of buildings through nonlinear static procedures according to different code-compliant approaches, with a specific focus on the two alternative methods reported in the Italian Building Code, namely “Method A” and “Method B”, referring to the N2 Method and the Capacity Spectrum Method, respectively. An extensive parametric analysis is carried out by performing several nonlinear static analyses on Multi-Degree-of-Freedom (MDoF) models of different Reinforced Concrete (RC) frame structures. Seismic assessment is then performed by applying the two spectrum-based methods, and results are compared in terms of safety evaluation and loss assessment. Results of the comparison highlight that the ductility capacity of the structure strongly affects the seismic assessment, leading to larger differences when more ductile structures are considered. This work could be considered as a preliminary step toward the development of specific guidelines including provisions on the recommended simplified approach to be adopted for seismic assessment of buildings (also based on the observed/expected seismic behavior) in practical applications.

A new genetic algorithm framework based on Expected Annual Loss for optimizing seismic retrofitting in reinforced concrete frame structures

The design of seismic retrofitting for existing reinforced concrete frame structures concerns the determination of the position and the arrangement of reinforcements. Currently, this design practice is mainly based on trial-and-error attempts and engineers’ experience, without a formal implementation of cost/performance optimization. Though, the implementation of this intervention is associated with significant costs, noticeable downtimes, and elevated invasiveness. This paper presents a new genetic algorithm-based framework for the optimization of two different retrofitting techniques (FRP column wrapping and concentric steel braces) that aims at minimizing costs considering indirectly the lessening of expected annual values. The feasibility of each tentative solution is controlled by the outcomes of static pushover analyses in the framework of the N2 method, achieved by a 3D fiber-section model implemented in OpenSees. Application of the framework in a realistic case study structure will show that the sustainability of retrofitting intervention is achievable by employing artificial intelligence aided structural design.

Assessment of the Soil Structure Inertial Interaction Effect on the Behavior Coefficient Using Simplified Methods

This study aims to assess the effect of the Soil Structure inertial Interaction (SSI) on the behavior coefficient (R). For this purpose, R was estimated with and without SSI. The pushover N2 method and its extension SSI-N2 method were applied to the plain Reinforced Concrete (RC) frame structures. For calculating the SSI effect on R, four shear wave velocities Vs, representing rocky soil, firm soil, loose soil, and very loose soil, with three soil damping ratios ζg% for each soil type were considered. The estimated values of R using the N2 method were 4.1, 4.97, 5.75, and 6.96 for rocky soil, firm soil, loose soil, and very loose soil respectively. For the SSI-N2 method, R values were in the range of 3.67-3.97 for rocky soil, 4-4.69 for firm soil, 4.01-5.09 for loose soil, and 4.14-5.81 for very loose soil. In the Algerian code, R was kept constant for each soil type, and its value is 3.5 and 5 with and without infill masonry respectively. Soil shear wave velocity and the soil damping ratio must be taken into account in calculating R. The redundancy, overstrength, and ductility reduction coefficients were determined by taking into account the SSI. The SSI effect can change the values of R, so it must be taken into account when calculating R.

Nonlinear Static Seismic Analysis and Its Application to Shallow Founded Buildings with Soil-Structure Interaction

This paper presents new research in the field of nonlinear static seismic analysis and the N2 method for soil-structure systems. The rationale for this study stems from the inclusion of soil-structure systems in simplified displacement-based design methods. The conducted research comprises three parts, including original experimental investigations, the development of numerical models and the validation of results. A new methodology is presented that provides a step-by-step procedure for the implementation of the N2 method on soil-structure systems. Results of a dynamic shake-table test on a simplified scaled structural model founded on compacted dry sand are presented, and a numerical model of the experiment is developed and calibrated with the inclusion of soil-structure interaction effects. This indicates one main significance of this paper, which is the variation between the experimental and the analytical model and how they can be compared. Lastly, a case study was conducted on a numerical model of a 3D steel building. The building was analysed using pushover analysis for a fixed base-case and by considering soil-structure interaction effects. The results of both observed cases were mutually compared and further examined by validating them with nonlinear dynamic analyses. A comparison was conducted considering the inter-story drifts, calculated according to the N2 method and time-history analyses. The results show good agreement when the N2 method is used for buildings on compliant soils. Overall, it was observed that a decrease in the inter-story drifts appears at ground level of the building. This research also provides a framework for future research in the examined field, for instance, on different types of buildings, building typologies and irregularities of the structural system.

IMPA versus Cloud Analysis and IDA: Different Methods to Evaluate Structural Seismic Fragility

Well-known methods for seismic performance assessment, such as incremental dynamic analysis (IDA), multi-stripes analysis (MSA) and the cloud method, involve nonlinear response time-history analyses to characterize the relationship between the chosen damage measure versus intensity measure. Over the past two decades, many authors have proposed simplified procedures or nonlinear static approaches to develop fragility. In these procedures, the capacity of the system is evaluated by nonlinear static procedures (i.e., the capacity spectrum method (CSM), the N2 method, modal pushover analysis (MPA)) and the demand is derived by response spectra. In addition to the familiar ones, incremental modal pushover analysis (IMPA) is a novel nonlinear static procedure proposed in recent years, and it is used in this research to present an IM-based fragility estimation. The accuracy and effectiveness of different methods to assess vulnerability are investigated by comparing fragility curves derived by MPA-based cloud analysis, IMPA and cloud analysis against IDA. The comparison gives valuable insights on the influence of scaling on different sets of records; however, a more extended validation is needed to confirm the obtained results and draw more general conclusions. Results arise from two relatively small bins of record motions differing by ranges of Joyner-Boore distance and scattered in a range of magnitude are presented.