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WWRC 93-20
Least Total Expected Cost (LTEC) Analysis for Selecting a Defensible Design Flood Frequency for Highway Drainage Structure in Wyoming

Scope, Objectives, and Tasks of the Study

The main thrust of this study is to develop a scientifically and technically defensible procedure for quickly and easily estimating the design flood frequency associated with the least total expected cost for almost all highway drainage structures in Wyoming by considering the important tangible and intangible factors. The results of the study would provide a mechanism, when coupled with WDT design practice and policy, for selecting a design frequency for various roadway crossing structures in Wyoming. As such these research findings will complement current WDT Design and Operating Policy 18-6. Types of highway drainage structures considered are bridges as well as box and pipe culverts. Storm drains and other unique drainage facilities are not addressed by this research. However, the methodological framework developed in this study can equally be applied to other types of highway drainage facilities. The LTEC analysis adopted in this study considers only the inherent hydrologic randomness of floods without incorporating uncertainties from other aspects such as hydraulic uncertainties. Furthermore, the cost associated with the loss of highway drainage structures during their expected service life is not considered in the LTEC analysis.

The original goal of the study was to develop empirical working equations that relate LTEC design frequency to relevant economic, social, and drainage basin characteristics. Later, it was felt that the goal could be extended to bring both tangible and intangible factors into the overall decision-making process for determining a more appropriate design frequency for highway drainage structures. Such multi-dimensional decision-making framework would result in a balanced decision between the tangible technical quantities, and the intangible items such as available funds, public convenience, future maintenance budget, and legal liability of the WDT. This balanced design framework would provide a finding to be tempered by judgement in selecting a design flood frequency to be considered.

To address the issues and problems considered in this research, it appears practical to perform the task of determining the appropriate design frequency for highway drainage structures in the following three phases:

Phase 1 Determine the LTEC design frequency solely based on tangible physical and economic characteristics of the sites typical to Wyoming.

Phase 2 For each site typical to Wyoming, develop a mechanism for determining the extended-LTEC design frequency by incorporating relevant intangible factors.

Phase 3 Based on all relevant sites typical to Wyoming, develop working relationships between the LTEC /extended-LTEC design frequencies and various site conditions, tangible and intangible factors.

Based on the above outline, the approach adopted in this research was to first develop algorithms for estimating the significant tangible factors and costs necessary for reliably applying LTEC practices to WDT road-crossing drainage facilities such as culverts and bridges. Next, efforts were directed at identifying and quantifying the various intangible factors commonly considered important in highway drainage structure designs. Following this rather unique investigation a vast data base was assembled which is representative of wide range of watershed and drainage site characteristics found in Wyoming and perhaps other states. This data base was then analyzed and equations formulated to allow a hydraulics engineer or designer to quickly, and with known accuracy limits, identify an LTEC design frequency for comparison with the design frequency set by WDT policy. The findings from the aforementioned analysis of intangible factors affecting a drainage design were then analyzed and guidance formulated so they could be objectively considered by the hydraulics engineer or designer in selecting a scientifically defensible design flood frequency.

More specifically, the major tasks performed to accomplish the study objectives involves:

  1. Identification, definition, and collection of social, economical, and physical parameters and variables relevant to the design of highway drainage structures;
  2. Determination of a flood frequency associated with the LTEC design practice;
  3. Determination of an extended-LTEC frequency by considering, in addition to the economic aspect, certain intangible factors that affect the selection of design frequency;
  4. Development of a mechanism to relate LTEC design frequency and/or extended-LTEC design frequency to economic, social, hydrologic/hydraulic characteristics of drainage basins which are typical to Wyoming and perhaps other states.

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