Life-cycle failure probability analysis of deteriorated RC bridges under multiple hazards of earthquakes and strong winds

Engineering structures may be exposed to one or more extreme hazards during their life-cycles.Current structural design specifications usually treat multiple hazards separately in designing structures and there is a limited probabilistic basis on extreme load combinations.Additionally,the performance of engineering structures will be deteriorated by the aggressive environments during their service periods,such as chloride attack,concrete carbonation,and wind-induced fatigue.This study presents a probabilistic methodology to assess the time-dependent failure probability of RC bridges with chloride-induced corrosion under the multiple hazards of earthquakes and strong winds.The loss of cross-section area of reinforcements and the reduction in strength of reinforcing steel and concrete cover induced by the chloride attack are considered.Moreover,the Poisson model is employed to obtain the occurrence probabilities of the individual and concurrent earthquake and strong wind events.The convolution integral is used to determine the joint probability distribution of combined load effects under simultaneous earthquakes and strong winds.Numerical results indicate that the structural failure probability under multiple hazards increases significantly during the bridge′s life-cycle due to the chloride corrosion effect.The contribution of each hazard event on the total structural failure probability varies with time.Thus,neglecting the combined influences of multiple hazards and chloride-induced corrosion may bring erroneous predictions in failure probability estimates of RC bridges.

GENERAL FAILURE PROBABILITY SIMULATION AND APPLICATION FOR MULTI-MODE

A general failure probability simulation and deviation evaluation methods were presented for fuzzy safety state and fuzzy failure state. And the corresponding number integral method was simultaneously established. As the distribution of state variable and the membership of the state variable to the fuzzy safety set were normal, the general failure probability of the single failure mode had precise analytic solution, which was used to verify the precision of the presented methods. The results show that the evaluation of the simulation method convergences to the analytic solution with the number increase of the sampling. The above methods for the single failure mode was extended to the multi-mode by the expansion and probability principles. The presented methods were applied to the engineering problem. For the number of significant mode is not too many, the high precision solution can be given by the presented number simulation and number integral methods, which is illustrated by the engineering examples. In addition, the application scope of the methods was discussed.

A Fast Product of Conditional Reduction Method for System Failure Probability Sensitivity Evaluation

Systemreliability sensitivity analysis becomes difficult due to involving the issues of the correlation between failure modes whether using analytic method or numerical simulation methods.A fast conditional reduction method based on conditional probability theory is proposed to solve the sensitivity analysis based on the approximate analytic method.The relevant concepts are introduced to characterize the correlation between failure modes by the reliability index and correlation coefficient,and conditional normal fractile the for the multi-dimensional conditional failure analysis is proposed based on the two-dimensional normal distribution function.Thus the calculation of system failure probability can be represented as a summation of conditional probability terms,which is convenient to be computed by iterative solving sequentially.Further the system sensitivity solution is transformed into the derivation process of the failure probability correlation coefficient of each failure mode.Numerical examples results show that it is feasible to apply the idea of failure mode relevancy to failure probability sensitivity analysis,and it can avoid multi-dimension integral calculation and reduce complexity and difficulty.Compared with the product of conditional marginalmethod,a wider value range of correlation coefficient for reliability analysis is confirmed and an acceptable accuracy can be obtained with less computational cost.

Estimation of failure probability in braced excavation using Bayesian networks with integrated model updating

A probabilistic model is proposed that uses observation data to estimate failure probabilities during excavations.The model integrates a Bayesian network and distanced-based Bayesian model updating.In the network,the movement of a retaining wall is selected as the indicator of failure,and the observed ground surface settlement is used to update the soil parameters.The responses of wall deflection and ground surface settlement are accurately predicted using finite element analysis.An artificial neural network is employed to construct the response surface relationship using the aforementioned input factors.The proposed model effectively estimates the uncertainty of influential factors.A case study of a braced excavation is presented to demonstrate the feasibility of the proposed approach.The update results facilitate accurate estimates according to the target value,from which the corresponding probabilities of failure are obtained.The proposed model enables failure probabilities to be determined with real-time result updating.

Deterministic and probabilistic analysis of great-depth braced excavations:A 32 m excavation case study in Paris

The Fort d’Issy-Vanves-Clamart(FIVC)braced excavation in France is analyzed to provide insights into the geotechnical serviceability assessment of excavations at great depth within deterministic and probabilistic frameworks.The FIVC excavation is excavated at 32 m below the ground surface in Parisian sedimentary basin and a plane-strain finite element analysis is implemented to examine the wall deflections and ground surface settlements.A stochastic finite element method based on the polynomial chaos Kriging metamodel(MSFEM)is then proposed for the probabilistic analyses.Comparisons with field measurements and former studies are carried out.Several academic cases are then conducted to investigate the great-depth excavation stability regarding the maximum horizontal wall deflection and maximum ground surface settlement.The results indicate that the proposed MSFEM is effective for probabilistic analyses and can provide useful insights for the excavation design and construction.A sensitivity analysis for seven considered random parameters is then implemented.The soil friction angle at the excavation bottom layer is the most significant one for design.The soil-wall interaction effects on the excavation stability are also given.

Towards multiple hazard resilient bridges:a methodology for modeling frequent and infrequent time-varying loads Part I,Comprehensive reliability and partial failure probabilities

The current AASHTO load and resistance factor design （LRFD） guidelines are formulated based on bridge reliability, which interprets traditional design safety factors into more rigorously deduced factors based on the theory of probability. This is a major advancement in bridge design specifications. However, LRFD is only calibrated for dead and live loads. In cases when extreme loads are significant, they need to be individually assessed. Combining regular loads with extreme loads has been a major challenge, mainly because the extreme loads are time variables and cannot be directly combined with time invariant loads to formulate the probability of structural failure. To overcome these difficulties, this paper suggests a methodology of comprehensive reliability, by introducing the concept of partial failure probability to separate the loads so that each individual load combination under a certain condition can be approximated as time invariant. Based on these conditions, the extreme loads （also referred to as multiple hazard or MH loads） can be broken down into single effects. In Part II of this paper, a further breakdown of these conditional occurrence probabilities into pure conditions is discussed by using a live truck and earthquake loads on a bridge as an example. There are three major steps in establishing load factors from MH load distributions： （1） formulate the failure probabilities; （2） normalize various load distributions; and （3） establish design limit state equations. This paper describes the formulation of the failure probabilities of single and combined loads.

Processing for Zero-Failure Data of the Products

In this paper, an estimation method for reliability parameter in the case of zero-failuare data-synthetic estimation method is given. For zero-failure data of double-parameter exponential distribution, a hierarchical Bayesian estimation of the failure probability is presented. After failure information is introduced, hierarchical Bayesian estimation and synthetic estimation of the failure probability, as well as synthetic estimation of reliability are given. Calculation and analysis are performed regarding practical problems in case that life distribution of an engine obeys double-parameter exponential distribution.

Application of Importance Sampling Method in Sliding Failure Simulation of Caisson Breakwaters

It is assumed that the storm wave takes place once a year during the design period, and Nhistories of storm waves are generated on the basis of wave spectrum corresponding to the N-year design period. The responses of the breakwater to the N histories of storm waves in the N-year design period are calculated by mass-spring-dashpot mode and taken as a set of samples. The failure probability of caisson breakwaters during the design period of N years is obtained by the statistical analysis of many sets of samples. It is the key issue to improve the efficiency of the common Monte Carlo simulation method in the failure probability estimation of caisson breakwaters in the complete life cycle. In this paper, the kernel method of importance sampling, which can greatly increase the efficiency of failure probability calculation of caisson breakwaters, is proposed to estimate the failure probability of caisson breakwaters in the complete life cycle. The effectiveness of the kernel method is investigated by an example. It is indicated that the calculation efficiency of the kernel method is over 10 times the common Monte Carlo simulation method.

Moment-independence global sensitivity analysis for the system with fuzzy failure state and its Kriging method

For the system with the fuzzy failure state, the effects of the input random variables and the fuzzy failure state on the fuzzy probability of failure for the structural system are studied, and the moment-independence global sensitivity analysis（GSA） model is proposed to quantitatively measure these effects. According to the fuzzy random theory, the fuzzy failure state is transformed into an equivalent new random variable for the system, and the complementary function of the membership function of the fuzzy failure state is defined as the cumulative distribution function（CDF） of the new random variable. After introducing the new random variable, the equivalent performance function of the original problem is built. The difference between the unconditional fuzzy probability of failure and conditional fuzzy probability of failure is defined as the moment-independent GSA index. In order to solve the proposed GSA index efficiently, the Kriging-based algorithm is developed to estimate the defined moment-independence GSA index. Two engineering examples are employed to verify the feasibility and rationality of the presented GSA model, and the advantages of the developed Kriging method are also illustrated.

Gorilla Troops Optimizer Based Fault Tolerant Aware Scheduling Scheme for Cloud Environment

In cloud computing(CC),resources are allocated and offered to the cli-ents transparently in an on-demand way.Failures can happen in CC environment and the cloud resources are adaptable tofluctuations in the performance delivery.Task execution failure becomes common in the CC environment.Therefore,fault-tolerant scheduling techniques in CC environment are essential for handling performance differences,resourcefluxes,and failures.Recently,several intelli-gent scheduling approaches have been developed for scheduling tasks in CC with no consideration of fault tolerant characteristics.With this motivation,this study focuses on the design of Gorilla Troops Optimizer Based Fault Tolerant Aware Scheduling Scheme(GTO-FTASS)in CC environment.The proposed GTO-FTASS model aims to schedule the tasks and allocate resources by considering fault tolerance into account.The GTO-FTASS algorithm is based on the social intelligence nature of gorilla troops.Besides,the GTO-FTASS model derives afitness function involving two parameters such as expected time of completion(ETC)and failure probability of executing a task.In addition,the presented fault detector can trace the failed tasks or VMs and then schedule heal submodule in sequence with a remedial or retrieval scheduling model.The experimental vali-dation of the GTO-FTASS model has been performed and the results are inspected under several aspects.Extensive comparative analysis reported the better outcomes of the GTO-FTASS model over the recent approaches.

Advances in statistical mechanics of rock masses and its engineering applications

To efficiently link the continuum mechanics for rocks with the structural statistics of rock masses,a theoretical and methodological system called the statistical mechanics of rock masses(SMRM)was developed in the past three decades.In SMRM,equivalent continuum models of stressestrain relationship,strength and failure probability for jointed rock masses were established,which were based on the geometric probability models characterising the rock mass structure.This follows the statistical physics,the continuum mechanics,the fracture mechanics and the weakest link hypothesis.A general constitutive model and complete stressestrain models under compressive and shear conditions were also developed as the derivatives of the SMRM theory.An SMRM calculation system was then developed to provide fast and precise solutions for parameter estimations of rock masses,such as full-direction rock quality designation(RQD),elastic modulus,Coulomb compressive strength,rock mass quality rating,and Poisson’s ratio and shear strength.The constitutive equations involved in SMRM were integrated into a FLAC3D based numerical module to apply for engineering rock masses.It is also capable of analysing the complete deformation of rock masses and active reinforcement of engineering rock masses.Examples of engineering applications of SMRM were presented,including a rock mass at QBT hydropower station in northwestern China,a dam slope of Zongo II hydropower station in D.R.Congo,an open-pit mine in Dexing,China,an underground powerhouse of Jinping I hydropower station in southwestern China,and a typical circular tunnel in Lanzhou-Chongqing railway,China.These applications verified the reliability of the SMRM and demonstrated its applicability to broad engineering issues associated with jointed rock masses.

Towards multiple hazard resilient bridges:a methodology for modeling frequent and infrequent time-varying loads Part Ⅱ,Examples for live and earthquake load effects

The current AASHTO load and resistance factor design （LRFD） guidelines are formulated based on bridge reliability, which interprets traditional design safety factors into more rigorously deduced factors based on the theory of probability. This is a major advancement in bridge design specifications. However, LRFD is only calibrated for dead and live loads. In cases when extreme loads are significant, they need to be individually assessed. Combining regular loads with extreme loads has been a major challenge, mainly because the extreme loads are time variable and cannot be directly combined with time invariant loads to formulate the probability of structural failure.To overcome these difficulties, this paper suggests a methodology of comprehensive reliability, by introducing the concept of partial failure probability to separate the loads so that each individual load combination under a certain condition can be approximated a,; time invariant. Based on these conditions, the extreme loads （also referred to as multiple hazard or MH loads） can be broken down into single effects. In this paper, a further breakdown of these conditional occurrence probabilities into pure conditions is discussed by using a live truck and earthquake loads on a bridge as an example.

Importance Sampling Method in V-Space

Based on the observation of importance sampling and second order information about the failure surface of a structure, an importance sampling region is defined in V-space which is obtained by rotating a U-space at the point of maximum likelihood. The sampling region is a hyper-ellipsoid that consists of the sampling ellipse on each plane of main curvature in V-space. Thus, the sampling probability density function can be constructed by the sampling region center and ellipsoid axes. Several examples have shown the efficiency and generality of this method.

Advanced response surface method for mechanical reliability analysis

Based on the classical response surface method （RSM）, a novel RSM using improved experimental points （EPs） is presented for reliability analysis. Two novel points are included in the presented method. One is the use of linear interpolation, from which the total EPs for determining the RS are selected to be closer to the actual failure surface; the other is the application of sequential linear interpolation to control the distance be- tween the surrounding EPs and the center EP, by which the presented method can ensure that the RS fits the actual failure surface in the region of maximum likelihood as the center EPs converge to the actual most probable point （MPP）. Since the fitting precision of the RS to the actual failure surface in the vicinity of the MPP, which has significant contribution to the probability of the failure surface being exceeded, is increased by the presented method, the precision of the failure probability calculated by RS is increased as well. Numerical examples illustrate the accuracy and efficiency of the presented method.

Stochastic seismic slope stability assessment using polynomial chaos expansions combined with relevance vector machine

This paper presents probabilistic assessment of seismically-induced slope displacements considering uncertainties of seismic ground motions and soil properties.A stochastic ground motion model representing both the temporal and spectral non-stationarity of earthquake shakings and a three-dimensional rotational failure mechanism are integrated to assess Newmark-type slope displacements.A new probabilistic approach that incorporates machine learning in metamodeling technique is proposed,by combining relevance vector machine with polynomial chaos expansions(RVM-PCE).Compared with other PCE methods,the proposed RVM-PCE is shown to be more effective in estimating failure probabilities.The sensitivity and relative influence of each random input parameter to the slope displacements are discussed.Finally,the fragility curves for slope displacements are established for sitespecific soil conditions and earthquake hazard levels.The results indicate that the slope displacement is more sensitive to the intensities and strong shaking durations of seismic ground motions than the frequency contents,and a critical Arias intensity that leads to the maximum annual failure probabilities can be identified by the proposed approach.

Application of saddlepoint approximation in reliability analysis of dynamic systems

The application of the saddlepoint approximation to reliability analysis of dynamic systems is investigated. The failure event in reliability problems is formulated as the exceedance of a single performance variable over a prescribed threshold level. The saddlepoint approximation technique provides a choice to estimate the cumulative distribution function （CDF） of the performance variable. The failure probability is obtained as the value of the complement CDF at a specified threshold. The method requires computing the saddlepoint from a simple algebraic equation that depends on the cumulant generating function （CGF） of the performance variable. A method for calculating the saddlepoint using random samples of the performance variable is presented. The applicable region of the saddlepoint approximation is discussed in detail. A 10-story shear building model with white noise excitation illustrates the accuracy and efficiency of the proposed methodology.

Inspection interval optimization for aircraft composite structures with dent and delamination damage

The optimization of inspection intervals for composite structures has been proposed,but only one damage type,dent damage,has been addressed so far.The present study focuses on the two main damage types of dent and delamination,and a model for optimizing the inspection interval of composite structures is proposed to minimize the total maintenance cost on the premise that the probability of structure failure will not exceed the acceptable level.In order to analyze the damage characteristics and the residual strength of the composite structure,the frequency,energy,size,and depth of the damage are studied,and the situation of missing detection during the inspection is considered.The structural residual strength and total maintenance cost are quantified corresponding to different inspection intervals.The proposed optimization method relieves the constraints in previous simulation methods,and is more consistent with the actual situation.Finally,the outer wing of aircraft is taken as an example,and with the historical cases and experimental data,the optimization method is verified.The optimal inspection interval is shorter than the actually implemented inspection interval,and the corresponding maintenance cost is reduced by 23.3%.The result shows the feasibility and effectiveness of the proposed optimization method.

Risk Analysis of Breakwater Caisson Under Wave Attack Using Load Surface Approximation

A new load surface based approach to the reliability analysis of caisson-type breakwater is proposed. Uncertainties of the horizontal and vertical wave loads acting on breakwater are considered by using the so-called load surfaces, which can be estimated as functions of wave height, water level, and so on. Then, the first-order reliability method（FORM） can be applied to determine the probability of failure under the wave action. In this way, the reliability analysis of breakwaters with uncertainties both in wave height and in water level is possible. Moreover, the uncertainty in wave breaking can be taken into account by considering a random variable for wave height ratio which relates the significant wave height to the maximum wave height. The proposed approach is applied numerically to the reliability analysis of caisson breakwater under wave attack that may undergo partial or full wave breaking.

Probabilistic Assessment of Wave Overtopping of Nampo Dikein the West Coast of Korea

The Nampo dike, which is located at the west coast of Korea, was destroyed by wave overtopping during the storms on 30 August and 17 September in 1959. In this paper, is performed the probabilistic assessment of wave overtopping of Nampo dike by use of Owen model, Van der Meer ＆ Janssen model and Hedges ＆ Reis model for wave overtopping of seawall. Based on the available tidal and wave data for storm surges in 1989, the risk assessment of wave overtopping of the Nampo dike has been carried out by both Level Ⅱ and Level Ⅲ reliability methods. The calculated resuhs show the general agreement of failure probability between the two methods. By utilizing the rehabilitated cross section of Nampo dike, the failure probability of wave overtopping for the Nampo dike after rehabilitation will be rapidly reduced to that of initial design at crest level of 9.0 m with the improved slope from 1 ： 2 to 1 ： 4 at seaside. Since the sea level may only rise 1.0 m in the next few decades, the failure probability of Nampo dike will be still in the safe range.

Reliability Analysis of Flexure Hinge Based on Kriging Method

The uncertainty widely exists in the engineering practice.Therefore,it is necessary to research the effect of uncertainty on the structural system. In this paper,the reliability and sensitivity of the flexure hinge, which is the key component of the compliant mechanisms,are investigated. The results of the reliability analysis can effectively guide the engineer to design and optimize the flexure hinge. In order to improve the calculating efficiency,the kriging method is introduced to estimate the failure probability and reliability sensitivity.