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A fuzzy first order and second moment method (FFOSM) is proposed to efficiently estimate time-independent and time-dependent failure credibility in the presence of fuzzy uncertainty. For the time-independent linear performance function with independently, regularly and identically distributed fuzzy inputs, the analytical relationship is firstly derived between the failure credibility and fuzzy safety index, and the relation form is established between fuzzy safety index and fuzzy first two moments of the performance function. Secondly, in the standard space of fuzzy inputs, the minimum infinite norm distance from the coordinate origin to the linear limit state surface is analytically derived, and the point with the smallest infinite norm distance located on the limit state surface is defined as the fuzzy design point. Based on this definition, the geometric and physical meanings are explained for the fuzzy safety index and fuzzy design point, and the fuzzy first order and second moment method for time-independent failure credibility analysis is established for both linear and nonlinear performance function. Thirdly, for time-dependent performance functions, the equivalence is proved between time-dependent fuzzy safety index and the minimum value of transient fuzzy safety indices, on which the iteration steps of fuzzy first order and second moment method is designed for time-dependent fuzzy safety index and failure credibility estimation. Since the proposed fuzzy first order and second moment method is an approximately analytical approach, it has higher efficiency than the fuzzy simulation method and the cut level optimization method. Finally, the effectiveness and applicability of the proposed method are demonstrated by different examples.

Nowadays, the semi-probabilistic design approach using partial safety factors is by far the most widely used technique for the design of new industrial buildings. It is believed that the method delivers a safe design with respect to a minimum degree of reliability as prescribed by EN1990. This paper aims at describing the behaviour of single-bay portal frames at a system level based on analytical reliability approach with dominant failure modes. In the case of extreme loading where cross-sections attain their ultimate resistances, the failure modes of single-bay portal frames can be described using a limited number of critical sections. The limit state or performance function is hence reduced to the assessment of those critical sections. Through the use of the well-known force-based method, an analytical matrix formulation of the problem can be proposed and can be easily implemented. For each variable included in the performance resistance of the system, probability density functions can be calculated (Monte Carlo method) and their influence on the system’s reliability level investigated. Comparison can then be made with the results obtained with the partial safety factor method. As a case-study, the influence of the building shape (height-to-span) and load ratio on the reliability of single-bay portal frames is investigated.

In the field of the system reliability analysis with multiple failure modes, the advances mainly involve only random uncertainty. The upper bound of the system failure probability with multiple failure modes is usually employed to quantify the safety level under Random and Interval Hybrid Uncertainty (RI-HU). At present, there is a lack of an efficient and accurate method for estimating the upper bound of the system failure probability. This paper proposed an efficient Kriging model based on numerical simulation algorithm to solve the system reliability analysis under RI-HU. This method proposes a system learning function to train the system Kriging models of the system limit state surface. The convergent Kriging models are used to replace the limit state functions of the system multi-mode for identifying the state of the random sample. The proposed system learning function can adaptively select the failure mode contributing most to the system failure probability from the system and update its Kriging model. Thus, the efficiency of the Kriging training process can be improved by avoiding updating the Kriging models contributing less to estimating the system failure probability. The presented examples illustrate the superiority of the proposed method.

The serviceability limit state (SLS) design of foundations typically proceeds by limiting the total settlement of individual foundations and thereby attempting to restrict the differential settlement between pairs of foundations. Due to the uncertain nature of the supporting ground, the magnitude of settlement and differential settlement are random. As it is often the differential settlement that governs serviceability, it is desirable to provide design requirements that suitably restrict differential settlements. This paper investigates, by Monte Carlo simulation, the distribution of the maximum differential settlement between pairs of foundations as a function of the spacing between foundations and the number of foundations — groups of four, nine, or 16 foundations, arranged on a grid — are considered. The effects of the correlations between the equivalent stiffness of the ground under each foundation, as well as between the loads applied to the foundations, on the distribution of the maximum differential settlements and angular distortions are investigated. Ratios of resistance factor to resistance bias factor are presented that can be used to calibrate design requirements on the total settlement of individual foundations that also simultaneously achieve acceptable performance with respect to angular distortion.

The concrete-faced rockfill dam (CFRD) is one of the widely constructed dam types, the concrete slab is the key anti-seepage structure of CFRD, and its safety directly affects the safety of the dam. In view of the traditional reliability analysis methods are complicated to calculate and cannot assess concrete slab cracking risk in real-time. In this paper, through the analysis of the response mechanism of slab stress and dam deformation, the coupling relationship between the reliability of concrete slab and monitoring data is revealed. Considering the randomness of the material parameters of CFRD, the limit state functions of concrete slab cracking are established by the response surface method (RSM). The accurate numerical simulation of the construction and operation process of CFRD is realized through the back analysis, then the time-variant reliability calculation of the concrete slab is realized. By analyzing the correlation between concrete slab reliability and some key factors such as dam displacement, water level, and time, a coupled evaluation model of reliability and monitoring data is proposed. Houziyan CFRD is selected as an example, the engineering application shows that the simulation relative error by using this coupled evaluation model is less than 5.0%, this model has the advantages of high efficiency, good precision, and strong applicability. The real-time reliability analysis of the concrete slab is realized and a new method for prediction and early warning of concrete slab cracking of CFRDs is provided.

The proper explicit testing with a rotation impact is wavering parabolical stream antique. It is an incomprehensive, electrical forceful liquid. Isothermal vertical plates are done standardized accelerated abundant lack magneto hydrodynamic described. T’W and the centre equal close to the vessel have been higher near C’w. The value by a plate degree and density grade closer to the plate are step-up constantly. This Logical methodology of the issue addressed the limit state with temperature. Fixations are t. Dimension - less equivalence was assimilated by using the Laplace approach. Velocity outline, climate, absorption shape is developed alternate bodily models corresponding deep (or) mass Grashof value, Schmidt value, prandtl value, rotational boundary, period. The velocity will venture rising appraisal deep Grashof rate. It is furthermore tried that the speed ventures up with diminishing rotational parameters.

Bridges are the essential parts of the transportation facilities and are subjected to various forces depending on the onsite conditions and specific location of the bridge. T-beam bridges are pivotal in commuting from one place to other especially in shorter spans. The major forces acting on the T-beam bridges are static load, moving load and seismic load. Design of the T-beam bridges is conventional and versatile, as the main components are beams and slabs. There are various methods for the design of RC bridges, depending on the safety and serviceability. The earlier bridges were designed based on the working stress method as safety was the only criteria. Nowadays, the design is based on safety and serviceability. Most of the short span bridges in India are constructed as per the design details of standard plans by Ministry of Surface transport, Govt. of India. The complete design details for RCC slab and T-beam bridges (volume II) are available for the span ranging from 10 m to 24 m. The design details are established on the basis of working stress method as per code IRC 21: 1987. Provisions of IRC-6:1985 for seismic loading has also been incorporated in the design details. At present, working stress method of design of RC Road bridges has been outdated and IRC 112: 2011 code is in use. The study is about, to check the suitability of standard design drawings for spans varying from 10 m to 24 m based on limit state guidelines. design details are checked for the suitability at all seismic zones. MIDAS Civil (2019) software has been adopted to conduct this study. Comparative study has been made for the suitability of the design details of all spans in all seismic zones as per the new code.

This paper presents the effect of plasticity and the limit states on the electrical resistivity of bentonite as grounding material. The material used in this study was extracted from Andrassy volcanic formations in Tawau district. The geotechnical properties such as the plasticity characteristic, water content and electrical resistivity of the bentonite were investigated. The electrical resistivity was measured at different limit state of the bentonite using a soil box and a 4-pin resistivity meter. In this study, the Andrassy bentonite showed appropriate composition and technical properties commonly associated in electrical grounding application. Test results indicated that the electrical resistivity is somewhat similar to most bentonites. The resistivity values were found to vary with the bentonite limit state. Water content greatly influences the electrical resistivity of the bentonite. Under dry solid-state, the resistivity is the highest at 11 kΩm. Surprisingly, under liquid state, three distinct resistivity values were observed. Under wet conditions, the resistivity were 4500, 180 and 1.8 Ωm for semi-solid, plastic, and liquid states, respectively. Thus, it is expected that bentonite performance as good grounding enhancement material depends on its wet conditions, mainly when the water content is greater than the plastic limit.

Whether UnReinforced Masonry (URM) infills should be employed as structural members in frame structures is a debatable subject in performance-based earthquake engineering. This paper presents a detailed assessment of the seismic response of infilled moment-resisting steel frames. A recently proposed multi-strut model is applied here to consider both the local and global effects of URM infills. The capability of the employed model in predicting the local and global effects of URM panels has previously been verified by the authors of this study. Two structures, a four-story building and a two-story building, were designed using seismic design codes, and one of the outer frames of each structure was selected for the numerical models. Based on the conventional layouts of URM panels in buildings, three different configurations are considered: the bare frame (model in which the URM panels are isolated from the surrounding frame), the infilled frame, and the soft-first story frame. Fifteen ground motion records have been used to perform nonlinear Incremental Dynamic Analyses (IDA), which were then employed to derive the fragility curves of the studied structures for the Immediate Occupancy (IO), Life Safety (LS), and Collapse Prevention (CP) limit states. The results show that in lower limit states, the masonry infill leads to some beneficial effects. However, at more severe limit states, these beneficial effects diminish and at some point, revert to adverse effects. This is evident in the CP limit state, wherein the masonry infill weakens the seismic performance of the structure.

The dynamic response of modern slender footbridges is usually sensitive to both the pedestrian actions and the uncertainties associated with their inherent structural behavior. Thus, tuned mass dampers have been widely integrated in the design of these structures to guarantee the fulfillment of the vibration serviceability limit state during their overall life cycle. Three different techniques of tuned mass dampers (active, semi-active and passive) are usually considered for this purpose. Although there are algorithms for the robust design of each particular technique, however, this specificity makes difficult the implementation of all these techniques in practical engineering applications. Herein, the motion-based design method under uncertainty conditions is proposed and further implemented to create a common framework for the robust design of all these techniques when they are employed to mitigate pedestrian-induced vibrations in slender footbridges. According to this method, the design problem may be transformed into the combination of two sequential sub-problems: (i) a reliability multi-objective optimization sub-problem; and (ii) a decision-making sub-problem. Subsequently, the performance of this proposal has been validated through a numerical case study in which the dynamic response of a steel footbridge has been controlled by three different tuned mass damper techniques designed according to the proposed common framework.

Reliability-based design (RBD) can overcome some limitations and ambiguities in the partial factor design approach found in Eurocode 7 (EC7) and the load and resistance factor design (LRFD) method used in North America. The aim of this study is to show how RBD via the first-order reliability method (FORM) can complement LRFD and EC7 codes. Three geotechnical engineering examples are used to demonstrate that RBD-via-FORM can provide guidance to the partial factor design approach in situations with load-resistance duality, shear strength parameters with context-dependent sensitivities, parameters not covered in design codes, cross-correlated parameters, and designs aimed at a target reliability or failure probability. Insights from RBD-via-FORM are presented. The differences and similarities between the design points in RBD, partial factor, and LRFD methods are explained. Comparisons are made with Monte Carlo simulations, the mean-value first-order second-moment method, and the Bathurst–Javankhoshdel closed-form reliability index solution which is restricted to simple linear limit state performance functions with lognormally distributed load and resistance terms and bias factors. It is suggested that RBD-via-FORM can be conducted in tandem with EC7 and LRFD methods in order to overcome limitations and ambiguities which sometimes arise using these methods.

Bridges are a critical part of transport infrastructure networks for social activities and economics of human life. Dynamic analysis of bridge is very important to perform in order to ensure the ability of the bridge to withstand loads and maintain the sustainability of transport infrastructure. This paper presents a methodological framework for monitoring dynamic behavior of the bridge (e.g., natural frequencies, displacement time history) by using civil engineering micro-tremor technique and numerical modeling. The study was conducted at the Alue Raya Bridge located in Lhokseumawe City, Aceh Province, Indonesia. To capture the dynamic behavior of the bridge under traffic loading, the micro-tremor techniques, e.g., Short Period Seismograph (SPS) sensor was placed underneath the bridge at the mid span of the bridge girder. The obtained vibration data were processed using Geopsy software. A three dimensional (3D) model of the bridge was then developed by using CSI Bridge software. The modal analysis was conducted to obtain the modal natural frequencies of the bridge due to traffic loads. The natural frequency measurements using SPS were compared with the simulation results. Through analyzing the measured results, it was found that the natural frequency of the bridge is around 4,3275 Hz which is very close to those obtained from numerical modeling using CSI bridge software. The measured maximum vertical displacement of the bridge girders is below 5mm under normal traffic condition which is under the allowable serviceability limit state requirements of the bridge. The outcomes of this study could have the potential to enable maintenance and capital works decisions which are an important component of the sustainability of transport infrastructure.

Slope reliability analysis can effectively account for uncertainties involved in a slope system. However, commonly used slope reliability analysis methods often require huge computational cost, especially in large-scale problems, which hinders its wide application to engineering practice. This paper proposes an efficient slope reliability analysis method based on the active learning support vector machine (SVM) and Monte Carlo simulation (MCS). The proposed method makes use of an active learning function and cross-validation techniques to select the most suitable training samples to update the SVM model. The selected training samples are associated with a small distance to the limit state surface of the slope stability model and a large local uncertainty, which are more informative to gradually tune the SVM model to approximate the actual slope performance function. As a result, the proposed method can estimate the slope reliability with a small number of evaluations of the slope performance function, thus improving the efficiency significantly. Four slope examples are employed to demonstrate the effectiveness of the proposed method. The presented approach is also compared with some other commonly used surrogate models in slope reliability analysis. It is shown that the proposed method performs better in terms of computational efficiency to obtain similar estimation accuracy of the failure probability for the investigated examples.

Based on the first-order second-moment method, a comparative study on seismic fragility analysis with consideration of modeling uncertainty is carried out for a 12-story reinforced concrete frame structure under excitation with far-field and pulse-like near-field ground motions by using the multiple stripes analysis method. The sensitivity of the median fragility capacity of the building to fourteen parameters in the cases of three limit states (i.e., immediate occupancy, life safety, and collapse prevention) is analysed, and the effect of the selection of ground motion intensity measures on the determination of modeling uncertainty is investigated. Finally, the annual probabilities of exceeding each limit state with different confidence levels are calculated, and two methods, the mean estimates approach and the confidence interval method, are used to incorporate uncertainties. The results show that the characteristics of ground motions affect the sensitivity of the median capacity to the disturbance of structural parameters. The modeling uncertainty estimated in the near-field records is meaningfully less than that in the far-field records. Judging from this limited case study, the modeling uncertainty estimated may be underestimated by using an inefficient IM. The influence of the modeling uncertainty in the fragility analysis for each limit state cannot be ignored when using the confidence interval method.

Multiframe PC box-girder bridge with intermediate hinges is a kind of bridge having complex structural characters, which is very quintessential in California. In this study, a typical bridge was adopted to establish a nonlinear dynamic model through OpenSees platform. Intermediate hinge and inhibiting devices in it were elaborately simulated. Meanwhile, pushover analysis was used to reinstate a specimen of column test, which has the similar ratio of reinforcement to the typical bridge, and the hysteretic model parameters of the longitudinal steels inside columns were obtained. The damage indexes of column and hinge, which are primary components, under different limit states were acquired by moment-curvature analysis. Taking into account the uncertainty, nonlinear time-history analysis of the bridge was carried out through a suite of synthetic ground motions. Subsequently, a probabilistic seismic demand model was developed, and fragility curves were further focused on. According to fragility assessment, the conclusion shows that columns and hinge restrainers exhibit high fragility, and bridge system fragility is gradually determined by column fragility along with aggravating of the damage state. Unseating of girder can hardly occur at abutments and intermediate hinges. Moderate limit state could be exceeded in the positions of plug-type concrete structures in intermediate hinges, which tends to create transverse and vertical cracks, furthermore causing reinforcements yield. It indicates that it would severely underestimate the seismic fragility of intermediate hinges without considering the elaborate simulation of hinges.

Natural gas has become a global energy consumption hotspot because of its large reserves and clean combustion. Due to soil corrosion, construction damage, and natural disasters, leakage accidents of buried natural gas pipelines often occur. In this paper, the steady simulation method was used to study the methane invasion limit state (MILS) and the methane invasion limit distance (MILD) under the conditions of hardened surface ground (HSG), unhardened surface ground (UHSG), and semihardened surface ground (SHSG), and the transient simulation of methane invasion distance (MID) under the condition of HSG with the largest MILD was carried out. The results showed that regardless of ground conditions, with the increase of leakage time, the diffusion range of methane in soil will not increase all the time, and there was a limit state (MILS). The distribution range and concentration of methane in the soil under HSG condition were the largest, followed by the SHSG condition, and the UHSG condition was the smallest. When the ground condition changed from UHSG to HSG, the MILD increased from 3.41 to 9.32 m. The HSG condition will increase the MILD and the range of dangerous areas. The buried depth of the pipeline had a serious impact on the MILD. When the buried depth of the pipeline increased from 0.3 to 1.5 m, the MILD increased from 1.75 to 3.49 m under the condition of UHSG and exceeded 10 m under the condition of HSG. The average error of the MID prediction model was 2.37% under the condition of HSG, which can accurately predict the leakage of buried pipeline. The MID provides a reference for the layout of urban underground gas leakage monitoring points. The MILD can provide guidance for the safe distance between natural gas pipeline and structures in the design code of natural gas pipeline.

Evaluation of seismic retrofitting costs, a key issue in the risk mitigation strategies, requires the estimation of the building performance and the forecast of the site response. In addition, a target building performance should be a priori defined. In this study, a procedure to provide seismic retrofitting costs is suggested with reference to a case study, based on what following: i) the building performance is described by fragility curves obtain via recorded data on the building itself (Seismic Model from Ambient Vibration - SMAV), ii) the local seismic site response is estimated by means of numerical one-dimensional simulation based on site-specific data or by means of simplified technical code approach, iii) the building performance and the site response are combined in order to obtained an Annual Frequency of Failure for each damage limit state, iv) this frequency is compared to the target allowable reliability level according to the classes of use and limit states of building in order to obtained a Vulnerability index, v) seismic retrofitting costs, depending on the Vulnerability index values, are evaluated from literature suggestions (caterino et alii, 2018). Finally, with reference to the case study of the “San Benedetto” school of Norcia (Central Italy), the proposed methodology is satisfactorily verified by comparing the forecast with real costs. The innovative aspect of the proposed methodology lies in the use of the recorded data and SMAV model and in the procedure for defining the local seismic response which considers the building- specific characteristics and the site-specific conditions

The mega-sub controlled structural system (MSCSS) is a new structural system that combines structural response control theory with the construction principle of mega frame structure (MFS), and has significant response control effects. It is of practical significance to study the method which accurately evaluate the seismic vulnerability of structures. In this paper, Multiple Stripes Analysis (MSA) and Incremental Dynamic Analysis (IDA) are used to evaluate the vulnerability of MSCSS structure. The comparison between these two methods certify the accuracy of MSCSS vulnerability evaluation along with the impact of the number of stripes used in MSA method. In addition, through the comparative analysis of structural vulnerability analysis results, it is found that under limit state LS4, the failure probability of MSCSS is 30% lower than that of MFS, and the exceeding probability of megastructure is 50% lower than that of substructure, indicating that MSCSS structure has advanced disaster prevention design concept. Afterward, by introducing the seismic damage index used for regional structural seismic damage assessment into the vulnerability assessment, an intuitive seismic risk assessment method for buildings is anticipated by combining the seismic damage index and the beta distribution function, which can provide a reference for the risk assessment of super high-rise buildings.

Lateral responses of a pile are governed by its mutual interaction with the supporting soil, known as the Pile-Soil Interaction (PSI), which in turn influences its structural limit states. The present study evaluates the seismic limit states for bridge pile in sand, while incorporating the parametric influences of pile and soil assessed through PSI. Such influences have not been dealt with in the past, except for the p (soil-pile reaction) – y (pile deflection) responses (though with only few pile parameters). Pile cross sectional size, grades of concrete and reinforcement, longitudinal and transverse reinforcement ratios, axial load ratio and the sand effective friction angle are observed to affect the PSI and consequently the limit states. Thus, limit states are proposed as parameterised expressions, generated through regression on the limit state data obtained by analysing the damage model (developed herein) for the pile-soil system samples generated over wide ranges of the influential parameters. These expressions, validated through the compliance with the expected trends and a fair agreement with a test result, can be readily used to obtain the expected values of the limit states over a broad range of parametric combinations and without requiring analysis repetition. These, in turn, can contribute to reliable estimation of fragility of a bridge system with the given properties for its pile foundation.

The stiffness of the stiffener plate of a tube-gusset plate joint (TGPJ) with a multi-ring stiffener plate is much larger than that in the chord wall. The load on the gusset plate will be concentrated in the area where the stiffener plate is located, and the joint will eventually fail in this area as a result of the ultimate state of the ring stiffener plate. This study investigated the stiffness and ultimate strength of a ring stiffener plate under an axial load. First, an experimental study was carried out on X-shaped TGPJs with double-ring stiffener plates. The failure mode of the joints was clarified, the variation law of the joint stiffness was revealed, and the rationality of using a 3% chord wall deformation as the criterion for determining the ultimate state of joints was verified. Then, based on the test results, finite element models (FEMs) of the X-type joint and ring stiffener plate were established, and their accuracy was verified. Numerical analysis results clarified the synergistic mechanism of the double-ring stiffener plate of an X-type joint, and the equivalence between the joint failure and the single-ring stiffener plate failure was revealed. Different nominal yield strength parameters (345 and 420 MPa), different dimensions (D/t = 32.3–55.9 and R/tr = 6–33.3), and different load conditions (tension and compression) for ring stiffener plates were analysed, and the accuracy of the calculation methods for the limit state of the ring stiffener plates proposed in this paper was verified. A comparison showed that the ‘four-hinged ring beam model’ proposed in this paper did not consider the changes in the curvature of the ring beam between plastic hinges. Thus, the calculation results of the model were obviously conservative, and the ‘deformation stiffness model’ was more accurate than the calculation results of other methods mentioned in this paper.

Introduction. The work is devoted to one of the main issues of structural mechanics - the determination of the elements in which the limiting state occurs first. At first glance, the task has an infinite number of results, meaning an infinite number of options for loading the system. The problem becomes solvable if one examines the structure of a building (structure) for possible variations in displacements (forces) in the nodes of the structure. For this approach, it becomes possible to determine the main values and vectors of displacement of the system, which correspond to the maximum (minimum) values of deformations (forces) in the rods of the system. As close approaches to the formulation of the problem, one should indicate the theory of the limiting equilibrium of structures under the assumption of the work of the material under flow conditions, where the equality of the work of external forces and internal forces is considered (kinematic method), or possible static stress states of the system for maximum limiting loads (static method). The theory of protecting buildings and structures from progressive collapse seeks to solve similar problems, focusing on options for design solutions that prevent destruction from non-design loads. Materials and methods. To determine the options for the distribution of extreme values of internal forces (deformations) in the system, the problem is formulated in the form of an eigenvalue problem. The latter turns out to be the most convenient mathematical model of the problem, since, in addition to extreme values (as in the optimization problem), it allows one to take into account the values of the problem on the upper and lower bounds. The theoretical basis for the formulation of the problem is the criterion of the critical levels of the internal potential energy of the system, which makes it possible to find the self-stress states of the structure corresponding to the limiting states of the structural elements. Results. The methodology for solving the problem is illustrated by the example of a statically indeterminate five-rod truss, which was also considered by other authors. The matrix formulation of the problem and a detailed algorithm for its solution are given. It is shown that the values of the internal forces in the rods, obtained using the traditional method, are in the interval between the maximum and minimum main values of the self-stress state of the system. Solutions are given at each of the critical energy levels corresponding to the disconnection of bonds from work.

Cost optimization of Geogrid-Reinforced Pile-Supported Foundation (GRPSF) requires the minimum construction cost among all design alternatives within both ultimate limit state (ULS) and serviceability limit state (SLS) criteria. Usually, the optimization is conducted by selecting a limited number of design alternatives based on experience and then comparing them, which often does not lead to the real optimal design. This paper presents a novel optimization framework to systematically determine the design parameters to achieve the minimum construction cost for GRPSF, considering both ULS and SLS constraints that are relevant to post-construction performance and constructability. This framework is a hybrid of surrogate modeling and Finite Element Method (FEM) to calculate the post-construction settlement of GRPSF and search for the optimal design. Genetic Algorithm improved Black Hole Algorithm (BH-GA) was developed to determine the optimal values of design variables, including pile length and spacing, pile cap geometry, and geogrid layers and layout. The proposed approach can quickly identify the optimal design by exhausting all possible combinations of design parameters. Two well-documented case histories of GRPSF were redesigned using this framework, which validated its applicability and effectiveness in optimizing the design of GRPSF.