Towards establishing practical multi-hazard bridge design limit states

In the U.S., the current Load and Resistance Factor Design （LRFD） Specifications for highway bridges is a reliability-based formulation that considers failure probabilities of bridge components due to the actions of typical dead load and frequent vehicular loads. Various extreme load effects, such as earthquake and vessel collision, are on the same reliability-based platform. Since these extreme loads are time variables, combining them with not considered frequent. non- extreme loads is a significant challenge. The number of design limit state equations based on these failure probabilities can be unrealistically large and unnecessary from the view point of practical applications. Based on the opinion of AASHTO State Bridge Engineers, many load combinations are insignificant in their states. This paper describes the formulation of a criterion to include only the necessary load combinations to establish the design limit states. This criterion is established by examining the total failure probabilities for all possible time-invariant and time varying load combinations and breaking them down into partial terms. Then, important load combinations can be readily determined quantitatively,

Evaluation of the Residual Capacity of a Submarine for Different Limit States with Various Initial Imperfection Models

The current design philosophy for submarine hulls,in the preliminary design stage,generally considers as governing limit states material yielding along with various buckling modes.It is common belief that,beyond the design pressure,material yielding of the shell plating should occur first,eventually followed by local buckling,while global buckling currently retains the highest safety factor.On the other hand,in the aeronautical field,in some cases structural components are designed in such a way that local instability may occur within the design loads,being the phenomena inside the material elastic range and not leading to a significant drop in term of stiffness.This paper is aimed at investigating the structural response beyond a set of selected limit states,using nonlinear FE method adopting different initial imperfection models,to provide the designers with new information useful for calibrating safety factors.It was found that both local and global buckling can be considered as ultimate limit states,with a significant sensitivity towards initial imperfection,while material yielding and tripping buckling of frames show a residual structural capacity.In conclusion,it was found that the occurrence of local buckling leads to similar sudden catastrophic consequences as global buckling,with the ultimate strength capacity highly affected by the initial imperfection shape and amplitude.

Recent Industrial Developments of Marine Composites Limit States and Design Approaches on Strength

To further exploit the potential of marine composites applications in building ship hulls,offshore structures,and marine equipment and components,design approaches should be improved,facing the challenge of a more comprehensive and explicit assessment of appropriately defined limit states.The structure ultimate/limit conditions shall be verified in principle within the whole structural domain and throughout the ship service life.What above calls for extended and reliable materials characterization on the one hand and for accurate and wide-ranging procedures in structural analyses.This paper presents an overview of recent industrial developments of marine composites limit states assessments and design approaches,as available in open literature,focusing on pleasure crafts and yachts as well as navy ships and thus showing a starting point to fill the gap in this respect.After a general introduction about composites characterization techniques,current design practice and rule requirements are briefly summarized.Both inter-ply and intra-ply failure modes and corresponding limit states are then presented along with recently proposed assessment approaches.Three-dimensional aspects in failure modes and manufacturing methods have been identified as the main factors influencing marine composite robustness.Literature review highlighted also fire resistance and hybrid joining techniques as significant issues in the use of marine composites.

Proper interpretation of sectional analysis results

Displacement control algorithms commonly used to evaluate axial force-bending moment(PM)diagrams may lead to incorrect interpretations of the strength envelopes for asymmetric sections.This paper aims to offer valuable insights by comparing existing displacement control algorithms with a newly proposed force control algorithm.The main focus is on the PM diagrams of three example sections that exhibit varying degrees of asymmetry.The comparative study indicates that conventional displacement control algorithms inevitably introduce non-zero out-of-plane bending moments.The reported PM diagram in such cases erroneously neglects the out-of-plane moment and fails to represent the strength envelope accurately.This oversight results in significant and unconservative errors when verifying the strength of asymmetric sections.

Durability design of prestressed concrete structures

Based on the durability characteristics of prestressed concrete structures,the durability limit states of carbonation and chloride ion attack are defined, respectively.Durability predicting models on the basis of reliability mathematics and stochastic processes areconstructed, and the pure theoretical formulae of failure probability of prestressed concretestructures are analyzed. In addition, a simple durability design method for carbonation ofstructures is put forward. According to the analysis, the durability of prestressed concretestructures is superior to that of traditional structures. The research also indicates that theconcrete cover prescribed in the current code (GB 50010-2002) is not adequate. The rational coverthickness should notbe less than 35 or 45 mm according to carbonation or chloride ion attack,respectively.

Seismic fragility analysis of highway bridges considering multi-dimensional performance limit state

Fragility analysis for highway bridges has become increasingly important in the risk assessment of highway transportation networks exposed to seismic hazards. This study introduces a methodology to calculate fragility that considers multi-dimensional performance limit state parameters and makes a first attempt to develop fragility curves for a multi-span continuous (MSC) concrete girder bridge considering two performance limit state parameters: column ductility and transverse deformation in the abutments. The main purpose of this paper is to show that the performance limit states, which are compared with the seismic response parameters in the calculation of fragility, should be properly modeled as randomly interdependent variables instead of deterministic quantities. The sensitivity of fragility curves is also investigated when the dependency between the limit states is different. The results indicate that the proposed method can be used to describe the vulnerable behavior of bridges which are sensitive to multiple response parameters and that the fragility information generated by this method will be more reliable and likely to be implemented into transportation network loss estimation.

Limits to foundation displacement of an extra high voltage transmission tower in a mining subsidence area

Given the background of a transmission tower erected on a particular mining subsidence area,we used finite element modeling to analyze the anti-deformation performance of transmission towers under a number of different load conditions,including horizontal foundation displacement,uneven vertical downward displacement,wind loads and icing conditions.The results show that the failure in stability of a single steel angle iron represents the limit of the tower given ground deformation.We calculated the corresponding limits of foundation displacements.The results indicate that compression displacement of the foundation is more dangerous than tension displacement.Under complex foundation displacement conditions,horizontal foundation displacement is a key factor leading to failure in the stability of towers.Under conditions of compression or tension displacement of the foundation,wind load becomes the key factor.Towers do not fail when foundation displacements are smaller than 1% (under tension) or 0.5% (under horizontal compression or single foundation subsidence) of the distance between two supports.

Effects of vertical seismic acceleration on 3D slope stability

The conventional pseudo-static approach often neglects the effect of the vertical＇ seismic acceleration on the stability of a slope, but some analyses under plane-strain （2D） conditions show a significant effect on the slope stability. The purpose of this study is to investigate the effect of the vertical acceleration on the safety of three-dimensional （3D） slopes. In the strict framework of limit analysis, a 3D kinematically admissible rotational failure mechanism is adopted here for 3D homogeneous slopes in frictional/cohesive soils. A set of stability charts is presented in a wide range of parameters for 3D slopes under combined horizontal and vertical seismic loading conditions. Accounting for the effects of the vertical seismic acceleration, the difference in safety factors for 3D slopes can exceed 10%, which will significantly overestimate the safety of the 3D slopes.

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.

A new slope optimization design based on limit curve method

A new method is proposed for slope optimization design based on the limit curve method, where the slope is in the limit equilibrium state when the limit slope curve determined by the slip-line field theory and the slope intersect at the toe of the slope. Compared with the strength reduction (SR) method, finite element limit analysis method, and the SR method based on Davis algorithm, the new method is suitable for determining the slope stability and limit slope angle (LSA). The optimal slope shape is determined based on a series of slope heights and LSA values, which increases the LSA by 2.45°-11.14° and reduces an invalid overburden amount of rocks by 9.15%, compared with the space mechanics theory. The proposed method gives the objective quantification index of instability criterion, and results in a significant engineering economy.

Probabilistic limit state design methodof the axial resistance of post grouting pile

The reliability of post grouting pile axial resistance was studied by proposing a design method for its probabilistic limit state,which is represented by the partial coefficients of load,end,and side resistance.The hyperbolic,modified hyperbolic,and polynomial models were employed to predict the ultimate bearing capacity of test piles that were not loaded to damage in field tests.The results were used for the calculation and calibration of the reliability index.The reliability of the probabilistic limit state design method was verified by an engineering case.The results show that the prediction results obtained from the modified hyperbolic model are closest to those obtained through the static load test.The proposed corresponding values of total,side,and end resistance partial coefficients are 1.84,1.66,and 2.73 when the dead and live load partial coefficients are taken as 1.1 and 1.4,respectively.Meanwhile,the corresponding partial coefficients of total,side,and end resistance are 1.70,1.56,and 2.34 when the dead and live load partial coefficients are taken as 1.2 and 1.4,respectively.

VIV analysis of pipelines under complex span conditions

Spans occur when a pipeline is laid on a rough undulating seabed or when upheaval buckling occurs due to constrained thermal expansion. This not only results in static and dynamic loads on the flowline at span sections,but also generates vortex induced vibration (VIV),which can lead to fatigue issues. The phenomenon,if not predicted and controlled properly,will negatively affect pipeline integrity,leading to expensive remediation and intervention work. Span analysis can be complicated by:long span lengths,a large number of spans caused by a rough seabed,and multi-span interactions. In addition,the complexity can be more onerous and challenging when soil uncertainty,concrete degradation and unknown residual lay tension are considered in the analysis. This paper describes the latest developments and a'state-of-the-art' finite element analysis program that has been developed to simulate the span response of a flowline under complex boundary and loading conditions. Both VIV and direct wave loading are captured in the analysis and the results are sequentially used for the ultimate limit state (ULS) check and fatigue life calculation.

Damage mechanism of single-layer reticulated domes under severe earthquakes

To study the damage mechanism of single-layer reticulated domes subject to severe earthquakes, three limit states of single-layer reticulated domes under earthquakes are defined firstly in this paper. Then, two failure modes are presented by analyzing damage behaviors, and their characteristics are pointed out respectively. Furthermore, the damage process is analyzed and the causes of structural damage in different levels are studied. Finally, by comparing deformation and vibration status of domes with different failure modes, the principles of different failures are revealed and an integrated frame of damage mechanism is set up.

Target reliability index for serviceability limit state of single piles

The objective is to develop an approach for the determination of the target reliability index for serviceability limit state(SLS) of single piles. This contributes to conducting the SLS reliability-based design(RBD) of piles. Based on a two-parameter,hyperbolic curve-fitting equation describing the load-settlement relation of piles, the SLS model factor is defined. Then, taking into account the uncertainties of load-settlement model, load and bearing capacity of piles, the formula for computing the SLS reliability index(βsls) is obtained using the mean value first order second moment(MVFOSM) method. Meanwhile, the limit state function for conducting the SLS reliability analysis by the Monte Carlo simulation(MCS) method is established. These two methods are finally applied to determine the SLS target reliability index. Herein, the limiting tolerable settlement(slt) is treated as a random variable. For illustration, four load test databases from South Africa are compiled again to conduct reliability analysis and present the recommended target reliability indices. The results indicate that the MVFOSM method overestimates βsls compared to that computed by the MCS method. Besides, both factor of safety(FS) and slt are key factors influencing βsls, so the combination of FS and βsls is welcome to be used for the SLS reliability analysis of piles when slt is determined. For smaller slt, pile types and soils conditions have significant influence on the SLS target reliability indices; for larger slt, slt is the major factor having influence on the SLS target reliability indices. This proves that slt is the most key parameter for the determination of the SLS target reliability index.

New algorithm of mine slope reliability based on limiting state hyper-plane and its engineering application

Due to the influence of joint fissure, mining intensity, designed slope angle, underground water and rainfall, the failure process of mine slope project is extremely complicated. The current safety factor calculation method has certain limitations, and it would be difficult to obtain the reliability index when the performance function of reliability analysis is implicit or has high order terms. Therefore, with the help of the logistic equation of chaos theory, a new algorithm of mine slope reliability based on limiting state hyper-plane is proposed. It is shown that by using this new reliability algorithm the calculation of partial derivative of performance function is avoided, and it has the advantages of being simple and easy to program. The new algorithm is suitable for calculating the reliability index of complex performance function containing high order terms. Furthermore, the limiting state hyper-plane models of both simplified Bishop's and Janbu's method adaptive to slope project are obtained, and have achieved satisfactory effect in the study of mine slope stability in Dexing copper open pit.

Thermal-stress induced phenomena in two-component material:part I

The paper deals with analytical fracture mechanics to consider elastic thermal stresses acting in an isotropic multi-particle-matrix system. The multi-particle-matrix system consists of periodically distributed spherical particles in an infinite matrix. The thermal stresses originate during a cooling process as a consequence of the difference αm - αp in thermal expansion coefficients between the matrix and the particle, αm and αp, respectively. The multi-particle-matrix system thus represents a model system applicable to a real two-component material of a precipitation-matrix type. The infinite matrix is imaginarily divided into identical cubic cells. Each of the cubic cells with the dimension d contains a central spherical particle with the radius R, where d thus corresponds to inter-particle distance. The parameters R, d along with the particle volume fraction v = v（R, d） as a function of R, d represent microstructural characteristics of a twocomponent material. The thermal stresses are investigated within the cubic cell, and accordingly are functions of the microstructural characteristics. The analytical fracture mechanics includes an analytical analysis of the crack initiation and consequently the crack propagation both considered for the spherical particle （q = p） and the cell matrix （q = m）. The analytical analysis is based on the determination of the curve integral Wcq of the thermal-stress induced elastic energy density Wq. The crack initiation is represented by the determination of the critical particle radius Rqc = Rqc（V）. Formulae for Rqc are valid for any two-component mate- rial of a precipitate-matrix type. The crack propagation for R 〉 Rqc is represented by the determination of the function fq describing a shape of the crack in a plane perpendicular

An Explicit Iteration Algorithm for Structural Reliability and its Realization by MATLAB

Based on the improved first order second moment method of the structural reliability, an explicit iteration algorithm is proposed, which can avoid solving structural performance function to obtain reliability index β and have simple calculation forms. Finally, the validity of the explicit iteration algorithm is illustrated through two examples by MATLAB programming.

Probabilistic Failure Analysis of Composite Beams for Optimum Ply Arrangements under Ballistic Impact

The probabilistic analysis takes into consideration an effect of scatter in elastic and strength properties of composite beam, and velocity of impactor. The damage model is implemented in the FE （finite element） code by a VUMAT （user-defined subroutine）. The inter ply failure is modeled using cohesive surfaces between the plies. Dynamic response is obtained using explicit time domain integration approach. SFEA （stochastic finite element analysis） is used to study the initiation of fiber failure analysis due to ballistic impact. SFEA provided the critical stress input in the limit state which is computationally solved using reliability software. The random variation in these properties is used for determining statistics of stress in the lamina. These are compared to the random strengths in the limit state function and probability failure surface is obtained by using GPRSM （Gaussian process response surface method）. GPRSM is used to predict the Pf （probability of failure） for different ply lay-ups arrangement. The Pf of Chang-Chang initiation of fiber failure for simply supported composite beams with symmetric cross ply lay-ups are （88.9%, 1.47% and 58.1%） greater than the anti-symmetric cross ply, symmetric angle ply and anti-symmetric angle ply, respectively. Sensitivity analysis is also carried out for symmetric cross ply arrangements.

Degradation process assessment of prestressed concrete continuous bridges in life-cycle

To accurately evaluate the degradation process of prestressed concrete continuous bridges exposed to aggressive environments in life-cycle,a finite element-based approach with respect to the lifetime performance assessment of concrete bridges was proposed.The existing assessment methods were firstly introduced and compared.Some essential mechanics problems involved in the degradation process,such as the deterioration of materials properties,the reduction of sectional areas and the variation of overall structural performance caused by the first two problems,were investigated and solved.A computer program named CBDAS(Concrete Bridge Durability Analysis System) was written to perform the above-metioned approach.Finally,the degradation process of a prestressed concrete continuous bridge under chloride penetration was discussed.The results show that the concrete normal stress for serviceability limit state exceeds the threshold value after 60 a,but the various performance indicators at ultimate limit state are consistently in the allowable level during service life.Therefore,in the case of prestressed concrete bridges,the serviceability limit state is more possible to have durability problems in life-cycle;however,the performance indicators at ultimate limit state can satisfy the requirements.

Critical Slope and Plasticity

Limit analysis based on upper bound theorem into slope stability is presented. A rotational failure mechanism (log spiral) passing through the toe in an inclined slope is assumed for getting the critical height. The proposed limit analysis, although on the kinematical admissible velocity field, always satisfies the equilibrium of forces acting on sliced rigid blocks. And the most critical slip surface can be searched by random technique. A new solution scheme is also developed for rapid searching critical slip surface. It is also applicable to a variety of slope models. The method is shown having a high accuracy compared with limit solution for simple slope.