Keywords: construction risk, fuzzy set, fuzzy logic, diaphragm wall, linguistic evaluation, construction safety, fuzzy function, translational model, angular model, modus ponens deduction, MPD.

This paper describes development of software that utilizes the concept of fuzzy sets to overcome problems encountered in diaphragm wall construction. A diaphragm wall system is commonly used as a temporary or permanent earth retaining system. Construction of a diaphragm wall system often requires a complicated procedure and involves a lot of heavy work, often resulting in a high-risk operation. To guarantee a safe work environment and a successful project, it is very important to know the factors that govern the amount of risk embedded in the diaphragm wall construction, to evaluate each of these factors correctly, and to integrate the results from these evaluations. However, most of the time in field operations, it is difficult to evaluate the governing factors numerically, since so many aspects cannot be precisely determined and are related to each other.

A computer program is developed and presented that allows users to input linguistic expressions of factors governing the diaphragm wall construction and produces a numerical index that shows the evaluation of the overall diaphragm wall construction. This program allows users to input linguistic expressions, instead of numerical values, of the factors governing the diaphragm wall construction, and then produces a numerical index that shows the evaluation of the overall diaphragm wall construction. The output of this evaluation can be used in the stages of pre, during, and post construction for a variety of purposes.

Factors that govern the diaphragm wall construction are obtained based on the authors' knowledge and experience. These factors are size, site condition, ground condition, ground water condition, design, contractor, price, and schedule.

Each factor can be evaluated by linguistic values, which are very appropriate, appropriate, moderate, inappropriate, and very inappropriate. Users are able to input their choice of linguistic expression for each factor along with the weight of the factor. The weight is the user's assessment of the importance of each factor in the overall evaluation, ranging from 0 to 100. Users are allowed to input production rules, one production rule for each factor, which enables the program to incorporate the expert's opinion. To maintain consistency in comparing indices of different projects, the program will keep the default values for these production rules, even though the user can input new values. When the user inputs the values of factor evaluations, their weights and production rules, these linguistic values are converted into fuzzy sets that can be expressed as fuzzy functions in the form of a translational triangular model. This model was selected, instead of rotational model or angular model, due to its ability to produce the ranking index and the overall rating.

The user's input with regard to level of performance is compared with the production rules to determine the influence of each factor on the entire diaphragm wall construction. This phase is performed by a fuzzy logic operation process, which is called modus ponens deduction (MPD) technique. The authors also employ the operation formulae that are used for angular model, where only simple tangent functions are used to produce the result of evaluating each factor in the form of a translational model.

The results from the evaluations of the above factors are integrated into the overall rating, by using the weight of each rating. Fuzzy algebraic operations as described in Zadeh's extension principle are used in this overall rating formula. The final index is calculated by comparing the area to the right of the overall rating fuzzy function and the area to the left of it. This index has a value ranging from 0 to 10, with a rating of 10 represents the construction of diaphragm wall best performance. This process is coded in the program, so that the overall fuzzy rating indicates when the index is 0, and when the index is 10.

For example, by having an index output closer to 0 at the pre-construction stage, a construction party, such as a contractor or a municipal authority, knows that improvement is required to guarantee a safe work environment and a successful project. In contrast, an index value close to 10 indicates that the diaphragm wall construction is considered safe. During construction, the user can assess the impact of any changes made in the individual performance factor on the overall evaluation by monitoring the index change. Another benefit of this model is for a construction company to keep records of performance indices and their corresponding project performance, as such, enabling the company to set meaningful standard indices for use as a guideline in future projects.

The future work following this study will expand the fault tree so that it can accommodate more general cases. It is also expected that the planned extension will accommodate the use of additional evaluation factors.

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