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Increasing emission of carbon dioxide from combustion of fossil fuels its effect on the earth’s climate has led to increased research into renewable, clean energy solutions. Wind energy has been used as an alternative energy source for hundreds of years, however current research proposes the deployment of offshore wind farms in the deep waters of the oceans. A major challenge of deploying offshore wind farms is to safely and economically fix the wind turbines by means of anchors in the seabed. The objective of this study is to evaluate whether different anchoring concepts are suitable for securing floating offshore wind turbines in sandy soil conditions. For this purpose, an extensive literature review has been carried out to identify existing anchor capacity prediction models for three different anchor types. A 1-g model laboratory program was then developed and pullout tests using different anchor shapes in sand were performed. The laboratory testing program included pullout tests on shallow, vertically loaded square plate anchors, inclined square plate anchors, and drag embedment anchors in sands. For this purpose a testing facility (1.2 m width, 2.4m length and 0.9m height) was developed and a total of 11 pullout tests were carried out. The sand samples were prepared at a relative density of 22% and the tested depths varied from 0.15 m to 0.45 m. Tests results show an increase in capacity with increasing inclination angles. A comparison of the obtained test results and predicted capacities were used to evaluate the existing models. Best fit models were identified and loads derived from a state-of-the-art wind turbine were used to assess the feasibility of the proposed anchors to secure the 5-MW turbine. The results suggest that the examined anchor types are theoretically capable of mobilizing allowable capacities larger than the acting forces. The feasibility of anchor installation at the required embedment depths has to be proven in future research.

Differing reports regarding the structural features of the mineral stutzite, Ag5–xTe3 (−0.25 ≤ x ≤ 1.44), and the quest for tellurides with low-dimensional fragments stimulated our impetus to review this system by employing experimental as well as quantum-chemical methods. Determination of the crystal structures for three samples with compositions Ag4.72(3)Te3 (I), Ag4.66(1)Te3 (II), and Ag4.96(2)Te3 (III) revealed considerable positional disorders for the Ag and Te sites and previously unknown structure models for I and II, which differ from that of III through the stacking sequences of honeycomb-fashioned Te layers. The crystal structures comprise [Te@Ag9]@Te14 units in the forms of bicapped hexagonal Te antiprisms that enclose Te-centered tricapped trigonal Ag prisms, while each Te atom is encapsulated by Ag atoms assembling diverse types of coordination polyhedra. The vibrational and electronic properties were determined for three models approximating the actual crystal structure of stutzite by means ...

Crime has been plaguing parking garages in the United States. At The Ohio State University, (OSU) crime on campus, in general, has decreased in recent years; however, crime in OSU parking garages has remained stable in spite of campus-wide efforts to reduce crime. When assessing and evaluating parking garages, occupants employ experience-based judgment that is subjective and imprecise, yet extremely useful. When designers employ the principles of crime prevention through environmental design, they also use subjective variables. An approach that captures the imprecise information in noncrisp expressions reflecting subjective and experience-based variables is the fuzzy logic concept. This concept allows the use of mathematical operations to manipulate and operate on imprecise information or knowledge. Variables such as garage illumination and wall height were collected, fuzzified, and treated as the knowledge base of a model presented in this paper. In addition, numerous experience-based implication rules were developed and employed to evaluate subjective variables. A computer program was developed to illustrate implementation of the model.

The Ohio State University ~OSU! initiated this study in response to campus parking garage crime that persisted at an unacceptably high level in spite of campus-wide efforts to reduce crime. The writers combined crime statistics gathered by the OSU Police Department with results of an on-site survey to model parking using Crime Prevention Through Environmental Design ~CPTED! principles. The goal of the study was a group of CPTED-based design changes intended to create an environment that would deter parking garage crime. The analysis included factors such as lighting, visibility, garage color, location of entrances and exits, and design of elevators and stairways. The evaluation showed that lighting was the most significant factors in users' perception of parking garage safety. As a result of this study, OSU implemented the recommended CPTED improvements. In the 2 years following the implementation of CPTED improvements, the average annual incidence of crime in the parking garage where the CPTED improvements had been made fell by more than half of the average annual incidence of crime in that same garage for the four years before the improvements were made.

Rapid growth of the construction industry in the United Arab Emirates is often accompanied by frequent occurrences of construction accidents. A survey to determine how safe construction companies operate their site activities was conducted through questionnaires and site interviews. Over 120 construction companies in the two largest cities in the country have participated in this survey. The types of accidents that have frequently occurred are falls from higher/same elevation, struck by equipment/objects, natural causes (primarily illness), electrocution, caught by equipment/material, and drowning and fire-related accidents. The findings of this study suggest that several companies are deficient in providing worker's benefits, site orientation, personal protective equipment, accident prevention, and health and hygiene. To a certain extent, violations by foreign workers contribute to the occurrence of these accidents. Lack of regulations and codes required for safe construction operations exacerbate the pr...

A total of 225 building failures in the United States from 1989 to 2000 were recorded in this study. The result shows that failures of low-rise buildings constitute about 63% of all cases, followed by multistory buildings as a distant second. In terms of their functions, apartments are the most frequent to fail. External events and construction and maintenance deficiencies have been identified as the most frequent principal causes. External events include rain, wind, snow, vehicular impact, and collision. Construction deficiencies encompass improper renovation, unplanned demolition, poor workmanship, and unsafe excavation operations. Maintenance deficiencies are associated with building deterioration that was overlooked and improperly maintained. A comparative analysis conducted between this study and two previous studies indicates an inclined trend of relative failure occurrences of low-rise and multistory buildings. The study also suggests that, despite the recent enhancement of information technology, current sources of information are still incomplete. The creation of new complete databases, further improvement of information sources, and their dissemination through the Internet are deemed essential to prevent building failures from recurring.

Over 500 failures of bridge structures in the United States between 1989 and 2000 were studied. The age of the failed bridges ranged from 1 year (during construction) to 157 years, with an average of 52.5 years. The most frequent causes of bridge failures were attributed to floods and collisions. Flood and scour, with the major flood disaster in 1993, contributed to the frequency peak of bridge failures (almost 53% of all failures). Bridge overload and lateral impact forces from trucks, barges/ships, and trains constitute 20% of the total bridge failures. Other frequent principal causes are design, detailing, construction, material, and maintenance. Comparison made among three periods of similar studies (1977–1981, 1982–1988, and 1989–2000) revealed almost similar trends, with most failures occurring during the bridge’s service life. Also, human-induced external events occurred frequently in all three periods, but were most dominant in the first and third periods. Technological advances in information sys...

This work presents a project overview and recent research results for the MEMS Rotary Engine Power System project at the Berkeley Sensor & Actuator Center of the University of California at Berkeley. The research motivation for the project is the high specific energy density of hydrocarbon fuels. When compared with the energy density of batteries, hydrocarbon fuels may have as much as 20x more energy. However, the technical challenge is the conversion of hydrocarbon fuel to electricity in an efficient and clean micro engine. A 12.9 mm diameter Wankel engine will be shown that has already generated 4 Watts of power at 9300rpm. In addition, the 1mm and 2.4 mm Wankel engines that BSAC is developing for power generation at the microscale will be discussed. The project goal is to develop electrical power output of 90milliwatts from the 2.4 mm engine. Prototype engine components have already been fabricated and these will be described. The integrated generator design concept utilizes a nickel-iron alloy electroplated in the engine rotor poles, so that the engine rotor also serves as the generator rotor.

An interactive training model called SAVR was developed to train construction students, novice engineers, and construction workers to prevent falls from form scaffolding. The model was implemented in a workstation, an ONYX Reality Engine2. The SAVR model provides trainees with an immersive, interactive virtual environment to perform "on the job" safety training without physically being in a real construction site. This model includes two major training modules: erection, which teaches trainees the correct procedure to erect a commonly used metal bracket form scaffolding; and inspection, which introduces several hazardous conditions in an existing platform and requires trainees to visually identify them. The modular design of the SAVR model enables future expansion of the model to include additional types of scaffolding platforms, helps avoid significant frame rate decreases, and simplifies the debugging process during application development. Evaluation by independent experts of SAVR's inspection...

This paper describes the testing stage of the knowledge base of the expert system EXACT (EXpert system of Actuated control for Traffic at isolated intersections). In Tests by two parties (our expert and external experts), more than eighty percent agreement was found between EXACT's solutions and the two parties’ solutions. EXACT was developed to assist traffic engineers in selecting the appropriate type of traffic-actuated controller and its associated features, the type of detector and its configuration, and time settings at a particular intersection. The development of EXACT, including the identification of variables, shell selection, knowledge acquisition, knowledge representation, and knowledgebase development, was presented in earlier papers.

This paper presents a new method to estimate the duration of construction activities. A model, Activity Duration Decision Support System (ADDSS), was developed. This model employs the fuzzy modus ponens deduction (FMPD) technique to evaluate the impact of different factors on activity duration. The linguistic values of these factors are represented by angular fuzzy set models. The technique described in this paper allows a scheduler to partially match an evidence with a rule. The use of angular models demonstrates the use of a single and relatively simple fuzzy logic formula. The technique we developed does not require the scheduler to understand the underlying concept of fuzzy logic. In fact, one needs only to input an assessment of factors that may affect the completion of an activity. At this stage, ADDSS interfaces with the CA‐SuperProject scheduling package. ADDSS was also developed to export and import data to and from the CA‐SuperProject. Both the logic operations and angular models of ADDSS are el...

This paper describes the application of expert systems in traffic-actuated control at isolated signalized intersections. The expert system EXACT (EXpert system of ACtuated control for Traffic at isolated intersections) was developed to assist traffic engineers in selecting the appropriate type of traffic-actuated controller and its associated features, the type of detector and its configuration, and time settings at a particular intersection. EXACT was structured to handle both design and operational problems. The first steps of EXACT's development, including variable identification, shell selection, knowledge acquisition, and knowledge representation, are presented in detail in this paper.

A construction worker was seriously injured after falling from a roof to a concrete floor. He was working on a plank while placing insulation material when the accident occurred. The plank broke into three pieces. Visual observation of the plank indicated a relatively new plank. Further investigation of the plank revealed a grade of structural plank no. 2. A common practice is for a construction worker to use scaffold grade plank, which has twice the capacity of a structural grade plank. This represents the most probable procedural cause of the plank's failure. The most probable enabling cause (internal cause) of the failure is a local split at the midspan, whereas the most probable triggering cause (external cause) is the impact loads produced by the weight of the worker and the insulation material he carried while walking on the plank. The study also concluded a failure mechanism that was initiated by a longitudinal split at the midspan of the plank. The split weakened the plank and led to a transverse ...

When a construction‐fall investigation is undertaken, the success of arriving at a conclusion depends on the available information and the expert's judgment to establish the possible and probable causes of the fall. In the first of a two‐part study, fault‐tree models are developed to explain the etiology of construction falls. These models represent the frame of knowledge concerning causal relationships of reasonable and possible causes of falls. Causes are classified as the enabling, triggering, and support‐related causes. Each cause is expanded to reach the basic and conditional causes that contribute to the fall. The analysis is limited to fault‐tree qualitative modeling for construction falls from elevated floor openings. The study resulted in 17 basic causes, four conditional causes, and 28 sets of combined basic and conditional causes that have the potential to contribute to a construction fall. Our study concludes the usefulness of fault‐tree models to systematically and logically represent an expe...

In this study, a fault‐tree expert system for construction fall (FTES‐FALL) was developed to simulate and investigate unintentional construction falls from floor openings. Fault‐tree models constructed in an earlier study were used as the knowledge representation for FTES‐FALL. The knowledge base accommodates expertise obtained from experts and literature. A step‐by‐step process in developing the knowledge base was presented. Prompts were designed to lead the user to finding information/evidence needed to reach a conclusion. Parameters were identified and classified, leading to the establishment of frame‐subframe relations. Each frame contains production rules that represent the expert knowledge. In addition, abundant help statements were provided to guide the user through the consultation process. FTES‐FALL was tested by the knowledge engineer for its accuracy, completeness, efficiency, and user‐friendliness. Although FTES‐FALL is still in its development stage, it has demonstrated its capability to assi...

The study in this paper introduces the development of a knowledge-based expert system that helps to determine the suitability of FGD by-product in embankment construction. The expert system shell Personal Consultant Plus was used for this purpose. The knowledge base in the Embankment Construction Expert System (ECES) consists of a root frame and four subframes, and accommodates the production rules obtained from laboratory tests as well as an extensive literature review. An external program to calculate the embankment settlement was integrated into the system. A case study is presented to demonstrate the use of ECES. This study provides the embankment designer with a useful tool for making decisions on FGD by-product application as an embankment material.

This paper addresses problems in deep foundation construction in Taiwan. Some of these problems are unique to Taiwan, but several others are universal. Four areas of concern are presented here: inadequate dewatering procedure, inadequate lateral bracings, poor workmanship in slurry wall construction, and inadequate consideration of soil pressures. Lack of monitoring the water table during dewatering attributed to collapses of several foundations. Inadequate connection or spacing of walings and struts contributed to the failure of lateral bracings. Poor workmanship in reinforcement placement occurred during slurry wall construction. Failure to understand soil characteristics had caused frequent excessive soil pressure. In this paper, we present illustrations of such problems in Taiwan and suggest preventive methods. Several of the deficiencies explained in each problem area could easily have been avoided simply by adopting stricter quality control measures and by enforcing the specifications in field practice. Prequalified foundation contractors should have adequate knowledge of soil conditions and behavior and should be safety-conscious.

Three case studies of bridge-pier-related problems are presented. The first two concern problems during the construction of new bridge piers, while the third examines the reconstruction of an existing bridge. The first case is associated with an error in a construction drawing, the second involves inadequate pier survey, and the third is related to poor judgment in the inspection of the bridge-pier base. The enabling causes of these problems were poor planning and supervision prior to and during construction stages. As design and construction of bridges becomes more and more complex, component details can be easily overlooked without adequate planning and supervision. Despite their significance for pier performance, such problems are generally unreported, and even if they are investigated, the results are seldom publicized. These problems, which cause project cost overruns and delays, can be avoided by emphasizing stricter quality-control measures.

Design, modeling, and analysis of a novel in-plane cantilever apex seal for maintaining high compression ratios in a MEMS-based rotary internal combustion engine are presented. This work is part of an effort to create a portable, MEMS-based Rotary Engine Power System (MEMS REPS) capable of producing power on the order of tens of milliwatts and with an energy density better than that of a conventional battery. A Wankel-type rotary engine is advantageous for a MEMS-based internal combustion engine due to its planar geometry, self-valving operation, and few moving parts. Large scale rotary engines typically incorporate a complex apex and face sealing system composed of many parts and involved assembly. A MEMS-based apex seal system can be incorporated as part of the rotor in order to eliminate manual assembly. The seal system must also have a minimal footprint and closely follow the epitrochoid profile in order to effectively integrate with the other engine systems. Based on these objectives, an integrated in-plane cantilever apex seal system can be integrated into the rotor with a small footprint. The first step in the development of the MEMS REPS is an air-powered expander which can be used to demonstrate electrical generator operation, engine rotation, and apex seal operation. The apex seals discussed here are optimized for use in an air-powered expander. A performance analysis of this flexure apex seal design is performed which examines 4 major performance constraints: resonant frequency, strain, pressure, and power dissipation. In addition, the seal design also accounts for fabrication tolerances of thick deep reactive ion etching (DRIE). During operation, dynamic effects due to combustion process and mechanical translation may drive the flexures into resonance, leading to galloping of the cantilever tips. Galloping will result in large leakage paths, thereby, reducing the compression ratio. A 0.25% strain limit is imposed to minimize the effect of fatigue on seal performance. Pre-compressed apex seals are used to counteract forces generated on the apex seal due to a pressure differential. The apex seal is also designed to minimize the power dissipated due to frictional losses. To model the cantilever apex seal, two different loading conditions are examined. One condition is distinguished by point loading at the tip, when contact is made between the seal and housing wall. Another condition is characterized by a distributed loading, due to the changing pressure by both the compression and the combustion events. Analytical models in addition to a finite element analysis were performed.

A research project is currently underway to develop small-scale internal combustion engines fueled by liquid hydrocarbons. The ultimate goal of the MEMS Rotary Internal Combustion Engine Project is to develop a liquid hydrocarbon fueled MEMS-size rotary internal combustion micro-engine capable of delivering power on the order of milli-watts. This research is part of a larger effort to develop a portable, autonomous power generation system with an order of magnitude improvement in energy density over alkaline or lithium-ion batteries. The rotary (Wankel-type) engine is well suited for the fabrication techniques developed in the integrated chip (IC) community and refined by the MicroElectroMechanical Systems (MEMS) field. Features of the rotary engine that lend itself to MEMS fabrication are its planar construction, high specific power, and self-valving operation. The project aims at developing a “micro-rotary” engine with an epitrochoidal-shaped housing under 1 mm3 in size and with a rotor swept volume of 0.08 mm3. To investigate engine behavior and design issues, larger-scale “mini-rotary” engines have been fabricated from steel. Mini-rotary engine chambers are approximately 1000 mm3 to 1700 mm3 in size and their displacements range from 78 mm3 to 348 mm3. A test bench for the mini-rotary engine has been developed and experiments have been conducted with gaseous-fueled mini-rotary engines to examine the effects of sealing, ignition, design, and thermal management on efficiency. Preliminary testing has shown net power output of up to 2.7 W at 9300 RPM. Testing has been performed using hydrogen-air mixtures and a range of spark and glow plug designs as the ignition source. Iterative design and testing of the mini-engine has lead to improved sealing designs. These particular designs are such that they can be incorporated into the fabrication of the micro-engine. Design and fabrication of a first generation meso-scale rotary engine has been completed using a SiC molding process developed at Case Western Reserve University. The fabrication of the micro-rotary engine is being conducted in U.C. Berkeley’s Microfabrication Laboratory. Testing of the mini-engine has lead to the conclusion that there are no fundamental phenomena that would prevent the operation of the micro-engine. However, heat loss and sealing issues are key for efficient operation of the micro-engine, and they must be taken into account in the design and fabrication of the micro-rotary engine. The mini-rotary engine design, testing, results and applications will be discussed in this paper.

In this paper the complex nature of Signal Processing (SP) is highlighted. Some basic architectural considerations for Knowledge-Based (KB) signal processing systems are discussed. A “multi-task” KB system called SPES (Signal Processing Expert System) is proposed to provide solutions for multiple SP task that employ common SP functions in their solution. Some features of the system to deal with multiplicity of tasks are discussed in detail.

The durability and service life of concrete pipe culverts are discussed. The study reported includes the analysis of important enabling and triggering events that have caused or have the potential to cause the deterioration of concrete pipes. Regression analyses were used to produce prediction equations for the expected service life of culverts. The findings reveal an expected service life of 86 years. The service life reported herein may be of value to cost engineers performing life-cycle cost studies of these types of culverts. However, the prediction equations given should not be used to predict the service life of a particular culvert.

The frequent complex construction procedures of constructed facilities have led to the inevitable use of linguistic expression in the specificationre generated based on the specifier’s subjective judgment, while those commonly encountered during and following construction are often used for assessing the performance of the facilities. The use of such expressions has often caused their misinterpretation. This, in turn, results in inadequate performance and subsequently in the failure of the constructed facilities. To overcome these problems, the use of fuzzy set concept is suggested. This concept quantifies the linguistic values and translates them into graphical models. The use of a fuzzy average rule and fuzzy algebra are introduced for integrating subjective judgments of the assessors, leading to the overall performance rating. An example using graphical display is demonstrated. Despite the innovativeness of the concept introduced for assessing the performance of constructed facilities, the method demonstrated herein is relatively simple to follow and easy to understand.

This paper demonstrates the use of a rule-based weighted rating system (RWRS) developed for improving the rating of concrete culverts. RWRS combines the qualitative rating based on a guideline commonly used by the Department of Transportation, the quantitative rating based on a regression model, and the inspector's own judgment on the culvert's rating. Weight on each rating is provided by the supervisor. A case study is presented to demonstrate the use of RWRS.

A study of nearly 150 recent major collapses and distresses of structures around the world discloses that external events and deficiencies in the areas of construction and design were the principal sources of failures. More than one-third of the surveyed structures were bridges, and the remaining were low-rise, multi-story, plant-industrial, and long-span buildings. The major incidents in the category of external events were the lateral impact forces and other unexpected live loads on bridges, and explosion impact loads in concrete silos. Construction deficiencies included falsework and concreting faults in several concrete structures and inadequate welding operations in steel bridges. Design deficiency related events were found to vary with the type of the observed structures, but a significant number of failures were attributed to lack of knowledge in long-term creep and shrinkage effects on prestressed concrete members. These findings suggest that attention should be directed to three areas: (1) Identification of potential deficiencies from past failure data; (2) enhancement in procedural methods during design and construction operations; and (3) incorporation of risk analyses of structures during their service life and construction phases.

This paper presents case studies of ceiling collapses and identifies causes of failures. These ceilings were designed to accommodate dead loads only. In most cases, these collapses were preceded by ceiling distress in the form of sagging or bowing out of the ceiling. Despite such warning no immediate preventive measures were provided, and hence, the distress progressed to become a collapse. This study reveals that in all cases poor workmanship experienced by the hanger connections enabled the failure while the load of workers on the ceiling triggered the collapse. These enabling events, which were common among several hangers, caused progressive ceiling failures.

Major collapses of falsework during construction processes were attributed to the triggering, enabling, and procedural causes. The effects of impact and vibration during concrete pouring have often triggered the failures. Several design and construction deficiencies which existed in the components of temporary structures enabled the failures. This study shows that several procedural causes initiated the triggering and enabling causes. The survey are tabulated to serve as a guide for performance control of falsework erection in the future.

This paper introduces the development of knowledge bases, by using factors that affect international construction projects, for decision support purposes. These factors are categorized as the areas of site office, home office, and construction business environment. These knowledge bases can be used to assess the performance of construction projects as time progresses, for comparing the performance of several projects at a certain moment of time, and for determining the causes of problems so that preventive measures can be suggested. The results can be presented with graphs that represent the performance of a project in relation to each affecting factor. The system can be used as a support for making decisions with respect to construction performance.

A modified fault tree analysis for structural systems is introduced to determine potential structural problems. The analysis incorporates the development of fault tree models and qualitative evaluation of the models, producing the minimal cut sets that will guarantee the occurrence of a predetermined top event. Structural dependencies and modes of failure are also included in the analysis. The study indicates the enabling, triggering and conditional fault events as the basic events that contribute to component failures. Examples and a case study are presented.

A study of 85 major falsework collapses of bridges and buildings in the past 23 yrs has documented the types of collapsed falseworks and failed permanent structures, the construction stages at the time of collapse, and the causes of failures. Three causes of failure were identified: triggering; enabling; and procedural causes. Most failures occurred because of the interaction of the triggering and enabling events that were, in many cases, produced by inadequacies in the procedural methods. Impact forces resulting from concreting operations have repeatedly triggered falsework failures that were enabled by deficiencies in the falsework bracings, components, connections, foundations, and design. Inadequate review of falsework design and monitoring procedures were frequent problems that facilitated the occurrernce of these events. The findings emphasize the importance of proper delineation of responsibility of each party in the building process in order to reduce falsework failures in the future.

In this study, a method based on the fuzzy set concept is employed to assess the urgency measure to prevent further damage of concrete components. Two assessments are considered. One is a constraint; and therefore, the inverse composite fuzzy relation operations are incorporated. A case study is also presented in which three concrete components are assessed for their prevention urgency measures.

Performance in concrete construction in developing countries such as the Far East and Southeast Asian countries is frequently identified by poor workmanship and inadequate quality control measures. These problems often occur during the erection of falsework and formwork, and during the mixing and handling of the concrete. Some of these problems are peculiar to concrete practices in developing countries; others are more universal problems. Several examples are provided in this paper. Understanding of these problems is needed to prevent their recurrence. The fact that the related facilities and quality control measures are frequently lacking has promoted such problems. Testing of concrete is often limited to the existing facilities, and inspection procedures are minimally or inadequately performed. This paper suggests that more specific quality control and quality assurance can be enforced by establishing a team for quality control and quality assurance, developing a specific quality control and quality assurance program conducive to the local conditions, providing with good quality inspectors, and providing the quality team with the authority to mediate between the designer/engineer and the contractor in order to avoid any problems.

This paper introduces a new technique in construction networking. A modified fault tree analysis was employed to determine the critical paths, sequence of activities, and the basic events that have the potential to induce the delays of any activity in the network. This method can be used for both deterministic and non-deterministic approaches. It also incorporates the provision of minimal cut sets that guarantee the occurrence of a delay. The cut sets can be evaluated qualitatively, quantitatively, or both, in order to determine their rank of importance.

In this study, we examined the enabling and triggering events that caused failures in temporary structures. Using event tree analysis, we then analyzed the propagation of component failures. The concept of fuzzy sets is used to manipulate human‐based subjective judgments, which are abundant during the construction of temporary structures, and to minimize the complexities of conditional events in the trees. Ranking of critical paths, based on the highest probability of failure, is also presented for quality control purposes.

Damage of highway bridges has become a serious problem nationwide. In this study, bridge damage is related to deterioration and/or distress which progress incrementally in stages. We use models that incorporate the Markov Chain concept to describe the cumulative damage of a bridge. Unfortunately, statistical data required for the damage increment are seldom available in most offices of the State Department of Transportation. However, bridge inspection reports are abundant. In these reports, bridge inspectors assess the conditions of the bridge components such as the bridge deck, superstructure, and substructure. They frequently use subjective notions in their ratings and descriptions of the component conditions. The concept of fuzzy set is used in this study to take advantage of these subjective judgements. The fuzzy operations result in fuzzy probability of component failures which is used to assess the cumulative damage of the bridge. A case study is presented to demonstrate the use of this method.