Developing Guidelines for Integrating Safety and Cost-Effectiveness into Resurfacing, Restoration, and Rehabilitation (3R) Projects (2021)

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63 Chapter 7. Application of Benefit–cost Analysis for 3R Projects Benefit–cost analysis enables highway agencies to assess the cost-effectiveness of design alternatives for 3R projects and decide (a) whether geometric design improvements should be made as part of the project and, if so, (b) which geometric design improvements are appropriate for particular projects. This chapter presents how benefit–cost analyses for particular design alternatives should be conducted and shows examples of the computational procedures for benefit–cost analysis. The chapter also illustrates in Section 7.6 that a cost-effectiveness or benefit–cost analysis approach will provide greater crash reduction benefits than any of several alternative sets of dimensional design criteria. 7.1 Elements of Benefit–cost Analysis The elements of a benefit–cost analysis needed for assessment of specific design alternatives are presented here. Examples of the use of these elements in benefit–cost analysis are presented below. While the computations needed for a benefit–cost analysis may appear complex, they can be performed automatically by the benefit–cost analysis spreadsheet tools presented in Chapter 8. 7.1.1 Implementation Cost for Geometric Design Improvements A key element of benefit–cost analysis for a particular geometric design alternative is the cost of implementing that alternative. This cost is referred to as the implementation cost, rather than the construction cost, because it includes not only construction costs, but also the cost of acquiring any right-of-way needed to implement the design alternative. Highway agencies differ in their policies concerning right-of-way acquisition as part of 3R projects. Some agencies almost never consider design alternatives that involve right-of-way acquisition as part of 3R projects; other agencies routinely consider 3R project alternatives that involve right-of-way acquisition. The benefit–cost procedures presented here will support either approach. Utility relocation costs may be incurred in some 3R projects. Such costs are site-specific and difficult to generalize. Therefore, they have not been included in the automated cost estimation procedures incorporated in the spreadsheet tools used with these guidelines. However, users of the procedures may include utility relocation costs in site-specific project implementation costs for benefit–cost analysis, where appropriate. The cost of pavement resurfacing should not be included as part of the implementation cost for benefit–cost analysis of potential geometric design improvements considered in conjunction with 3R projects. For most 3R projects, the pavement will be resurfaced regardless of whether geometric design improvements are made, so the pavement resurfacing cost is not relevant to decisions concerning geometric design improvements and should not be included in the project implementation cost.

64 Every highway agency has established procedures for estimating the cost of geometric design alternatives, both for cost estimates that are sufficiently accurate for planning-level analyses and for detailed cost estimates prepared in final design. It is assumed that, in most cases, highway agencies will prefer to use their own project cost estimation procedures as the basis for 3R project benefit–cost analyses. Cost estimates with planning-level accuracy are appropriate for deciding whether to incorporate geometric design improvements in a 3R project and what geometric design improvements to implement. The elements included in the estimation of 3R project implementation costs have been presented in Chapter 6. A default procedure for estimating the implementation costs of 3R improvements at specific sites is presented in Appendix A. This default cost estimation procedure is intended for application by highway agencies that want to make a quick assessment of the need for geometric improvements in a specific 3R project without the effort needed to apply their own cost estimation procedures. The unit cost values used in the default cost estimation procedure may be easily modified to reflect local conditions. The project implementation cost estimates made with the default procedure can be refined later, if appropriate, using the agency’s own project cost estimation procedures. The implementation cost for geometric design improvements may represent the cost of a single geometric design change or the combined cost of multiple geometric design changes that may potentially be made as part of the same project. The default cost estimation procedure presented in Appendix A can address either single or multiple geometric design improvements. The value of the default cost estimation procedure to highway agencies is that they can quickly determine whether geometric design alternatives should be considered at all and what the general scope of design improvement should be without going to the effort of making detailed cost estimates with their own cost estimation procedures. For example, if a benefit–cost analysis based on the default cost estimation procedure showed that the costs of design alternatives for a particular project far exceed the benefits, the effort required to make more accurate estimates of project implementation cost using the agencies own project cost estimation procedures can be avoided. The decision as to whether to use the default project cost estimation procedure or the agency’s own project cost estimation procedures can be made by each highway agency that uses these guidelines. 7.1.2 3R Project Crash Frequency and Severity Reduction Benefits The benefits of 3R projects are being estimated with a combination of the following elements:  Expected crash frequency by crash severity level for the existing highway if no geometric design improvements are made is estimated based on the HSM Part C predictive methods. The agency may choose to base the benefit–cost analysis on the predicted crash frequency from the HSM Part C predictive method or, when site-specific crash history

65 data are available, to combine the predicted and observed crash frequencies using the Empirical Bayes (EB) procedure presented in the Appendix to HSM Part C.  Expected reduction in crash frequency due to project implementation based on CMFs for specific countermeasures from the HSM and other sources.  Crash cost savings per crash reduced by severity level. Each of these issues is addressed in more detail below. 7.1.3 Expected Crash Frequency by Crash Severity Level If No Geometric Design Improvements are Made This section summarizes the crash prediction methodology from HSM Part C (6), as applied to rural two-lane highways (see HSM Chapter 10), rural multilane highways (see HSM Chapter 11), and urban and suburban arterials (see HSM Chapter 12). Full details of these procedures are provided in the HSM. 7.1.3.1 Roadway Segments on Rural Two-Lane Highways The HSM Chapter 10 crash prediction model for roadway segments on rural two-lane highways has the following functional form (6): 𝑁 AADT L 365 10 e . C CMF CMF … CMF /𝑛 (26) where: Npredicted ravg = predicted annual average crash frequency for a particular road segment averaged over the improvement service life AADTy = annual average daily traffic volume for year y of the improvement service life (veh/day) n = improvement service life (years) L = length of roadway segment (mi) Cr = calibration factor for roadway segments of a particular type developed for a particular jurisdiction or geographical area CMF1r … CMFnr = applicable crash modification factors (see HSM Part C) Equation (26) provides the predicted frequency for total crashes. Values presented in HSM Table 10-3 are used to break this total down for specific severity levels. 7.1.3.2 Roadway Segments on Rural Multilane Highways The HSM Chapter 11 crash prediction model for roadway segments on rural two-lane highways has the following functional form (6):

66 𝑁 𝑒 C CMF CMF … CMF /𝑛 (27) where: a,b = coefficients presented in HSM Chapter 11 In the HSM Chapter 11 procedure, Equation (27) is applied separately for crashes by severity level. The values of coefficients a and b in Equation (27) are presented in Table 11-3 for rural multilane undivided roadway segments and in HSM Table 11-5 for rural multilane divided roadway segments. The CMFs used in Equation (27) also differ between rural multilane undivided and divided roadway segments. 7.1.3.3 Roadway Segments on Urban and Suburban Arterial Roadway Segments The HSM Chapter 12 crash prediction model for roadway segments on urban and suburban arterials is a combination of three terms (6): 𝑁 ∑ 𝑁 𝑁 𝑁 C /𝑛 (28) where: Nbr = predicted average crash frequency for an individual roadway segment averaged over the improvement service life (including multiple-vehicle nondriveway crashes, single-vehicle crashes, and multiple-vehicle driveway crashes) Npedr = predicted average crash frequency of vehicle-pedestrian crashes for an individual roadway segment averaged over the improvement service life Nbiker = predicted average crash frequency of vehicle-bicycle crashes for an individual roadway segment averaged over the improvement service life Equation (28) provides the predicted frequency for crashes separately by severity level. Nbr is a combination of separate models for multiple-vehicle nondriveway crashes, single-vehicle crashes, and multiple-vehicle driveway crashes. The models for multiple-vehicle nondriveway crashes and single-vehicle crashes each incorporate applicable CMFs. The details of the models used for each term in Equation (28) are presented in HSM Chapter 12. 7.1.3.4 At-Grade Intersections The predictive models for at-grade intersections on all facility types have the following general form (6):

67 𝑁 ∑ 𝑒 , , 𝐶 𝐶𝑀𝐹 𝐶𝑀𝐹 … 𝐶𝑀𝐹 /𝑛 (29) where: Npredicted iavg = predicted average crash frequency for a particular intersection for a particular year a,b,c = coefficients presented in HSM Chapter 10, 11, and 12 AADTy,maj = annual average daily traffic volume on the major road (veh/day) AADTy,min = annual average daily traffic volume on the minor road (veh/day) Ci = calibration factor for intersections of a particular type developed for a particular jurisdiction or geographical area CMF1i … CMFni = applicable crash modification factors (see HSM Part C) The values for coefficients a, b, and c are presented in the HSM as follows:  in HSM Equations (10-8) through (10-10) for intersections on rural two-lane highways  in HSM Tables 11-7 and 11-8 for intersections on rural multilane highways  in HSM Tables 12-10 and 12-12 for intersections on urban and suburban arterials For intersections on urban and suburban arterials, Equation (29) is applied separately for multiple- and single-vehicle collisions. 7.1.3.5 Combining Predicted and Observed Crash Frequencies Many highway agencies may prefer to take a systemic approach and make risk-based decisions on the need for geometric design improvements in 3R projects based on predicted crash frequencies from the HSM alone. However, observed crash history data can also be considered in analyses for individual sites using the EB procedure presented in the Appendix to HSM Part C (6). This procedure determines a weighted-average crash frequency using the following procedure: 𝑁 𝑤 𝑁 1 𝑤 𝑁 (30)   years studyall predictedNk1 1w (31) where: Nexpected = estimate of expected average crash frequency for the crash data period Npredicted = predictive model estimate of average crash frequency predicted for the crash data period under the given conditions (Npredicted ravg or Npredicted iavg) Nobserved = observed crash frequency at the site over the study period w = weighted adjustment to be placed on the predictive model estimate k = overdispersion parameter of the associated SPF used to estimate Npredicted

68 Values for the overdispersion parameter, k, can be determined from:  HSM Equation (10-7) for roadway segments on rural two-lane highways  Text accompanying HSM Equations (10-8) through (10-10) for intersections on rural two-lane highways  HSM Equation (11-8) and Tables 11-3 and 11-5 for rural multilane highways  HSM Tables 11-7 and 11-8 for intersections on rural multilane highways  HSM Tables 12-3 and 12-5 for roadway segments on urban and suburban arterials  HSM Tables 12-10 and 12-12 for intersections on urban and suburban arterials The EB procedure is implemented by applying the applicable predictive model [i.e. Equation (26), (27), (28), or (29)] to the past period for which observed crash data are available rather than to the future period over which the improvement will be in service. Equations (30) and (31) are then applied to combine the predicted and observed crash frequencies for the crash data period. More detail on application of the EB procedure is presented in Section 7.2.2.2. Finally, the expected crash frequency determined with Equations (30) and (31) is updated to future years as follows: 𝑁 , 𝑁 𝑁 ,𝑁 (32) where: Nexpected,y = expected average crash frequency for year y Npredicted,y = predicted average crash frequency for year y 7.1.4 Expected Reduction in Crash Frequency for Specific Design Alternatives The expected reduction in crash frequency for specific candidate design alternatives can be determined by applying the CMFs presented in Chapter 5 of this report. The expected reduction in crash frequency for specific crash severity level resulting from implementation of a particular design alternative at a particular site can be determined as: 𝐶𝑅 1 𝐶𝑀𝐹 𝑁 (33) where: CRmjk = expected reduction in crash frequency for crash severity level k resulting from implementation of improvement j at site m CMFjk = crash modification factor for crash severity level k from implementing improvement j Nmk = expected annual crash frequency for crash severity level k at site m prior to improvement Nmk represents the value of Npredicted or Nexpected derived in Section 7.1.3.

69 The CMF representing the effectiveness of a single geometric design improvement is determined as: 𝐶𝑀𝐹 𝐶𝑀𝐹 ,𝐶𝑀𝐹 , (34) where: CMFj,after = crash modification factor for improvement j in the condition after improvement CMFj,before = crash modification factor for improvement j in the condition before improvement The CMF representing the combined effectiveness for a design alternative that incorporates several geometric design improvements is determined as: 𝐶𝑀𝐹 𝐶𝑀𝐹 ,𝐶𝑀𝐹 , 𝐶𝑀𝐹 , 𝐶𝑀𝐹 , … 𝐶𝑀𝐹 , 𝐶𝑀𝐹 , (35) 7.1.5 Crash Costs by Crash Severity Level Each highway agency has its own policy concerning the estimated cost savings of reducing crashes of specific severity levels used in benefit–cost analyses. These estimates vary widely based on the assumptions made in developing those estimates. Some agencies rely on estimates of the societal costs of crashes, while others are based on an approach that assesses an individual’s willingness to pay for injury avoidance. Until a national consensus is reached on the appropriate method for estimating crash costs, each highway agency should follow its own policy concerning the appropriate crash cost values for use in benefit–cost analyses. If a highway agency has no specific policy on crash costs for use in benefit–cost analyses, the values in Table 45, which have been updated from those presented in the HSM and represent comprehensive societal costs of crashes, are proposed as default values: Table 45. Comprehensive Societal Costs of Crashes Updated from the Values Presented in the HSM Crash Severity Level Comprehensive Societal Crash Costs Fatal (K) $5,722,300 Disabling Injury (A) 302,900 Evident Injury (B) 110,700 Possible Injury (C) 62,400 Property Damage Only (O) 10,100 NOTE: Updated from HSM Table 7-1 as shown in Appendix C. The methodology used to update the crash cost values presented in Table 45 is documented in Appendix C.

70 7.1.6 Improvement Service Life Pavement resurfacing typically has a service life of 7 to 12 years, depending upon construction and material quality and traffic volume, until resurfacing is needed again. However, the service life for the pavement surface does not typically enter directly into benefit–cost analyses concerning geometric design improvements, because the pavement will require resurfacing at the same interval whether geometric design improvements are incorporated in a 3R project or not. Thus, the interval between pavement resurfacing projects should not typically be a factor in determining the service life for potential geometric design improvements. Geometric design improvements such as widening of the roadway cross section, changing the road alignment, improving the roadside, or improving an intersection are essentially permanent in nature (i.e., they remain in place through future pavement resurfacing). However, they may have a functional life shorter than their physical life because future development or traffic growth may create a need for further improvements. The suggested service life for improvements that involve physical changes to the roadway cross section, the roadway alignment, the roadside, or intersections is 20 years. The suggested improvement service life for rumble strips and striping and delineation improvements (particularly those that use durable pavement markings) is 5 years. However, highway agencies may use other values of improvement service life based on their own policies and experience. 7.1.7 Discount Rate or Minimum Attractive Rate of Return A discount rate or minimum attractive rate of return of 7 percent has been used in benefit–cost analysis, in accordance with the higher value of the discount rates recommended in current Federal guidelines (44). The discount rate or minimum attractive rate of return is used in computing the present value of implementation costs and safety benefits (see below). 7.1.8 Present Value of Implementation Costs and Safety Benefits The present value of the implementation costs and safety benefits must be calculated to obtain a benefit–cost ratio. For implementation costs, the present value must be found only if the improvement is to be repeated in the future (such as striping and delineation which may be repeated several times during the service life of a geometric design improvement). In this case, the present value is computed by multiplying the future implementation cost by the single payment present worth factor:

71 P/F, 𝑖%,𝑛 1 𝑖100 (36) where: (P/F, i%, n) = single payment present worth factor i = discount rate or minimum attractive rate of return (percent) n = number of years into the future when the improvement will be performed The present values for each future improvement are then summed to determine the total present value. Safety benefits are annual crash cost savings. To calculate the present value of safety benefits, the annual crash cost savings are multiplied by the uniform series present worth factor: P/A, 𝑖%,𝑛 1 𝑖 100 1 𝑖/100 1 𝑖100 (37) where: (P/A, i%, n) = uniform series present worth factor i = discount rate or minimum attractive rate of return (percent) n = improvement service life (years) 7.1.9 Benefit–cost Ratio The benefit–cost ratio for a geometric design alternative in a 3R project is computed as: B/C 𝐶𝑅 𝐶 𝑃 𝐴⁄ , 𝑖%,𝑛 / 𝐼𝐶 𝑃 𝐹⁄ , 𝑖%,𝑛 (38) where: B/C = benefit–cost ratio Ck = benefit ($) per crash reduced for crash severity level k ICij = implementation cost ($) for improvement j at site i Only design alternatives with benefit–cost ratios that exceed 1.0 are considered cost-effective. Highway agencies seeking to enhance the effectiveness of the safety improvement investments may choose to seek benefit–cost ratios of 2.0 or higher. 7.1.10 Net Benefit The benefit–cost ratio by itself does not provide a complete picture of the magnitude of difference between the safety benefits and implementation costs for a design alternative in a 3R project. The net benefit (also referred to as net present value) is the difference between the present value of safety benefits and present value of implementation costs.

72 NB 𝐶𝑅 𝐶 𝑃 𝐴⁄ , 𝑖%,𝑛 𝐼𝐶 𝑃 𝐹⁄ , 𝑖%,𝑛 (39) where: NB = net benefit The net benefit is often the most useful form of benefit–cost analysis results for identifying the design alternative that will maximize the safety benefits for any given level of expenditure on geometric design improvements in 3R projects. 7.2 Computational Examples of Benefit–cost Analysis This section and Section 7.3 present examples to illustrate the interpretation of benefit–cost analysis results. These examples suggest how benefit–cost analysis can be used in the design guidelines presented in Chapter 6. If improvement costs and crash costs were consistent throughout the U.S., these examples might serve as a basis for 3R design policy. However, since the values used for improvement costs and crash costs vary widely from agency to agency, these examples in their current form should not be used as a basis for policy. Rather, benefit–cost analyses analogous to these examples, but based on site-specific or agency-specific data, should serve as a decision-making tool for choosing among 3R project design alternatives. 7.2.1 Estimating 3R Project Implementation Costs The cost estimation procedure shown in Appendix A is used to calculate the cost of a hypothetical 3R project in which the lane width on a 3-mi section of roadway is widened from 10 to 12 ft. Table 46 in the following section presents roadway geometric information needed to estimate the implementation cost in this example. Unit costs for all elements of the cost estimation are presented in Appendix A. The total cost of the 3R project is determined to be $850,551. This cost however should be modified to exclude costs associated with milling and resurfacing of the existing traveled way. The benefit–cost analysis is only concerned with the costs resulting from the geometric improvement, which is lane widening in this example. The modified total implementation cost is $475,889. 7.2.2 Computational Example of Quantifying Safety Benefits for a 3R Design Alternative Section 7.1 presents the methodology for quantifying safety benefits with and without using observed crash data. In the following example, the annual safety benefit will be calculated for a roadway segment undergoing lane widening as part of a 3R project. Table 46 shows segment characteristics, which will be used in this example.

73 Table 46. Input Data for Safety Benefits Calculation Example Geometric Improvement Lane Widening from 10 to 12 ft Lane Widening Service Life 20 yrs Discount Rate 7% Roadway Type Rural Two-lane Highway Shoulder Width 2 ft Shoulder Type Paved Roadside Slope 1V:3H Centerline Rumble Strip No Shoulder Rumble Strip No Section Length 3 mi AADT (does not change) 1,000 veh/day Terrain Level Percent of Section Length on Curves 20% Typical Curve Radius 2,000 ft Number of Curves on Section 5 Presence of Spiral Transitions Yes Crash History Period 5 yrs Total Fatal and Injury Crashes 2 Total Property-Damage-Only Crashes 5 First, the predicted annual average crash frequency, Npredicted ravg, is calculated using Equation (26) for the existing roadway prior to the 3R project. Since the AADT does not change over time in this example, the equation simplifies to not having a summation. Using HSM Chapter 10 and data from Table 46, CMFs are calculated for use in determining Npredicted ravg. To determine the CMF for a rural two-lane highway with 10-ft lane width, use Table 24 in Chapter 5 of this report. Since the AADT of the roadway section is between 400 and 2,000 veh/day, the following equation is used to calculate the CMFra: 𝐶𝑀𝐹 , , 1.05 2.81 10 𝐴𝐴𝐷𝑇 400 (40) 𝐶𝑀𝐹 , , 1.05 2.81 10 1000 400 1.13 (41) CMFra applies only to single-vehicle run-off-the-road and multiple-vehicle head-on, opposite- direction sideswipe, and same-direction sideswipe crashes. Equation (3) is used to convert CMFra to a CMF for total crashes. For this example pra is 0.574, the default value given in the HSM. 𝐶𝑀𝐹 , , 1.13 1.0 0.574 1.0 1.07 (42) Other CMFs that are calculated for this example are shown in Table 47. Table 47. CMFs for Example Roadway Section Roadway Feature CMF Shoulder Width 1.09 Horizontal Curve 1.01 Roadside Slope 1.00 Centerline Rumble Strip 1.00 Shoulder Rumble Strip 1.00

74 The predicted annual average crash frequency for the roadway prior to the 3R project is 0.942 crashes per year, as shown in Equations (43) through (45). 𝑁 AADT L 365 10 e . C CMF CMF … CMF /𝑛 (43) 𝑁 AADT L 365 10 e . C CMF CMF … CMF (44) 𝑁 1000 3 365 10 e . 1.00 1.07 1.09 1.01 1.00 1.00 1.00 0.942 𝑐𝑟𝑎𝑠ℎ𝑒𝑠/𝑦𝑟 (45) Since the lane width is being modified as part of the 3R project, the CMF for the change in lane widths must be calculated using Equation (34). To do this, the CMF for a lane width of 12 ft must first be calculated using the same procedure shown above for determining the CMF of a 10-ft lane. Table 24 shows that the CMF for 12-ft lanes is 1.00 regardless of AADT. 𝐶𝑀𝐹 , → 𝐶𝑀𝐹 , 𝐶𝑀𝐹 , (46) 𝐶𝑀𝐹 , → 1.001.07 0.934 (47) The CMF for increasing lane width from 10 to 12 ft is 0.93, which is calculated in Equations (46) and (47). At this point in the process of calculating the annual safety benefits, it must be decided whether or not to use observed crash data in the calculation of CRmjk, the expected reduction in crash frequency. For the purpose of this example, both methods (with and without consideration of observed crash history data) will be shown. 7.2.2.1 Observed Crash Data Unavailable If observed crash data are unavailable, or not to be used in the analysis, the expected annual crash reduction is computed, as shown in Equation (48) through (50). 𝐶𝑅 1 𝐶𝑀𝐹 𝑁 (48) 𝐶𝑅 1 𝐶𝑀𝐹 , → 𝑁 (49)

75 𝐶𝑅 1 0.934 0.942 0.062 𝑐𝑟𝑎𝑠ℎ𝑒𝑠 𝑟𝑒𝑑𝑢𝑐𝑒𝑑 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟 (50) 7.2.2.2 Using Observed Crash Data The EB methodology, described in Section 7.1.3.5 is used to incorporate observed crash data into the calculation of the expected reduction in crash frequency. The overdispersion factor, k, is 0.236 divided by the section length, which correlates with the safety performance function for predicting crash frequency on rural two-lane roadways. Using the equations shown in Section 7.1.3.5 the expected crash frequency is calculated in Equations (51) through (54). The total crash reduction per year is calculated in Equations (55) through (57). 𝑤 11 𝑘 ∑ 𝑁 (51) 𝑤 1 1 0.2363 0.942𝑐𝑟𝑎𝑠ℎ𝑒𝑠 𝑦𝑟 5𝑦𝑟𝑠 0.730 (52) 𝑁 𝑤 𝑁 1 𝑤 𝑁 (53) 𝑁 0.730 0.942 5𝑦𝑟𝑠 1 0.730 5 2 5.33 𝑐𝑟𝑎𝑠ℎ𝑒𝑠 𝑝𝑒𝑟 5 𝑦𝑟 𝑜𝑟 1.065 𝑐𝑟𝑎𝑠ℎ𝑒𝑠/𝑦𝑟 (54) 𝐶𝑅 1 𝐶𝑀𝐹 𝑁 (55) 𝐶𝑅 1 𝐶𝑀𝐹 , → 𝑁 (56) 𝐶𝑅 1 0.934 1.065 0.071 𝑐𝑟𝑎𝑠ℎ𝑒𝑠 𝑟𝑒𝑑𝑢𝑐𝑒𝑑 𝑝𝑒𝑟 𝑦𝑒𝑎𝑟 (57) 7.2.2.3 Calculate Present Value of Safety Benefit So far in the example, the total crash reduction per year has been calculated with and without the use of observed crash history. The present value of the safety benefit in this example is calculated using Equation (58). Equation (58) is the numerator of Equation (21). B 𝐶𝑅 𝐶 𝑃 𝐴⁄ , 𝑖%,𝑛 (58) Equation (58) can be broken into three components: (a) CRmjk, crash reduction by severity level; (b) Ck, crash cost by severity level; and (c) the uniform series present worth factor. Default crash

76 severity distributions from HSM Chapter 10 are used to transform total annual crash reduction into annual crash reduction by severity level in Table 48. Table 48. Calculation of Annual Crash Reduction by Severity Level Crash Severity Level Proportion of Total Crashes CRtotal per year, Observed Crash History Known CRtotal per year, Observed Crash History Unknown CRk, Observed Crash History Known CRk, Observed Crash History Unknown K 0.013 0.071 0.062 0.000923 0.000806 A 0.054 0.071 0.062 0.00383 0.00335 B 0.109 0.071 0.062 0.00774 0.00676 C 0.145 0.071 0.062 0.0103 0.00899 O 0.679 0.071 0.062 0.0482 0.0421 The crash cost by severity level is shown in Table 45. The uniform series present worth factor is needed to transform the annual crash reduction benefit into present crash reduction benefit over the entire service life of the improvement. This is calculated in Equations (59) and (60). P/A, 𝑖%,𝑛 1 𝑖 100 1 𝑖/100 1 𝑖100 (59) P/A, 𝑖%,𝑛 1 7 100 1 7/100 1 7100 10.5940 (60) Equations (61) and (62) shows the computation of the present value of the safety benefit. For the purposes of this example, only the expected crash reduction by severity level where the observed crash history is unknown is used in the calculation of the present value of the safety benefit. B 𝐶𝑅 𝐶 𝑃 𝐴⁄ , 𝑖%,𝑛 (61) B 0.000806 ∗ 4008900 0.00335 ∗ 216000 0.00676 ∗ 79000 0.00899 ∗ 44900 0.0421 ∗ 7400 10.5940 $56,041 (62) 7.2.3 Computational Example of Benefit–cost Analysis The implementation cost of widening the roadway section in this example is $475,889, which was discussed in Section 7.2.1. There is no need to convert this implementation cost to a present value, because the cost of the 3R project occurs in the present. No future improvements will be made during the 20-yr service life. The present value of the safety benefit is $56,041, which was

77 calculated in Section 7.2.2. The benefit–cost ratio of widening the example roadway section can now be computed, which is shown in Equation (63): 𝐵/𝐶 , → $56,041$475,889 0.12 (63) 7.3 Interpreting Benefit–cost Analysis Results Further examples of benefit–cost analysis results are presented here to illustrate how analyses to assess design alternatives can be conducted and how the results of such analyses should be interpreted. 7.3.1 Example of Benefit–cost Analysis for a Specific Project Alternative This example of a benefit–cost analysis uses the results derived in Section 7.2 to address the cost-effectiveness of widening lanes from 10 to 12 ft for a rural two-lane highway in level terrain with 2-ft paved shoulders, 1V:3H roadside foreslopes, and flexible pavement. The section of roadway considered in this example is 3 mi in length with an AADT of 1,000 veh/day. The roadway section contains modest horizontal curvature (20 percent of section length consists of horizontal curves with a typical curve radius of 2,000 ft). The safety performance of the roadway before and after widening is estimated using the HSM Chapter 10 procedures and the implementation cost for widening is based on the cost estimation procedures contained in Spreadsheet Tool 1 which is presented in Section 8.1. The present value of the net implementation cost for this example is $475,889 (see Section 7.2.1). The net implementation cost does not include the milling and resurfacing costs for the existing traveled way with 10-ft lanes, since these costs would be incurred by the highway agency regardless of whether the lanes are widened. The annual safety benefit of widening the lanes from 10 to 12 ft for a rural two-lane highway in this example is $5,290 (see Section 7.2.2). Assuming a discount rate of 7 percent and a service life of 20 years, the present value of the safety benefit is calculated using Equations (61) and (62), as $56,041. The benefit– cost ratio is then calculated as follows: 𝐵/𝐶 → , $56,041$475,889 0.12 (64) The benefit–cost ratio is 0.12, meaning that the lane widening is not economically justifiable for this roadway section. Widening the lanes from 10 to 12 ft in this 3R project would not be a desirable investment of scarce resources, unless the roadway had an existing crash pattern that is potentially correctable by widening or the level of service (LOS) was less than the highway agency’s target LOS for this roadway and widening the lanes would help to meet that target. Absent these concerns, the funds that would be needed to widen the lanes on this roadway ($475,889) would be better invested on another roadway where the safety benefits would be higher.

78 Consider, for example, a similar site, identical in most respects to the previous example, but with an AADT of 4,000 veh/day. In this case, the net implementation cost remains the same at $475,889. However, the annual safety benefit would increase to $54,641, resulting in a present value of safety benefits equal to $578,871. The benefit–cost ratio for widening lanes from 10 to 12 ft would be: 𝐵/𝐶 → , $578,871$475,889 1.22 (65) This example illustrates that the difference in AADT between 1,000 to 4,000 veh/day results in lane widening being economically justifiable. Lane widening for the roadway with the AADT of 4,000 veh/day would be a much better investment in safety improvement than lane widening for the roadway with an AADT of 1,000 veh/day. 7.3.2 Example of Benefit–cost Analysis to Establish Minimum Traffic Volume Levels for Improvement Alternatives As the examples in Section 7.3.1 demonstrate, benefit–cost analysis can serve as a tool for assessing the cost-effectiveness of geometric design improvements for specific projects. These examples also suggest that benefit–cost analysis can serve as a tool to establish minimum AADT threshold for specific improvement types. Site-specific benefit–cost analyses are the more desirable approach, because they can consider both site-specific cost and benefit estimates. However, where site-specific benefit–cost analyses are not feasible, development of minimum AADT thresholds for specific improvement types may provide useful guidance to highway agencies in making 3R project design decisions. Such minimum AADT thresholds are most applicable to sites that represent average implementation costs for a particular highway agency and terrain type. Because unit construction costs, typical right-of-way costs, and crash cost values vary from agency to agency, the following tables should be considered as examples and not as a basis for design policy. Table 49 presents the results of benefit–cost calculations for widening lanes from 10 to 12 ft in level terrain on a rural two-lane highway. This example is based on the same assumptions as the examples presented in Section 7.3.1 Indeed, the lines in the table for AADTs of 1,000 and 4,000 veh/day are the results of the two computational examples shown in the previous section. Table 49 shows that the minimum AADT levels that would provide benefit–cost ratios of at least 1.0 and 2.0 for widening lanes from 10 to 12 ft are 4,000 and 7,000 veh/day respectively.

79 Table 49. Example of Benefit–cost Calculations for Lane Widening from 10 to 12 ft in Level Terrain on a Rural Two-Lane Highway Lane Width (ft) AADT (veh/day) Net Implementation Cost ($) Present Value of Safety Benefits ($) Benefit–cost Ratio Before After 10 12 1,000 475,889 56,041 0.17 10 12 2,000 475,889 289,265 0.61 10 12 3,000 475,889 434,153 0.91 10 12 4,000 475,889 578,871 1.22 10 12 5,000 475,889 723,589 1.52 10 12 6,000 475,889 868,306 1.82 10 12 7,000 475,889 1,013,024 2.13 10 12 8,000 475,889 1,157,742 2.43 10 12 9,000 475,889 1,302,459 2.74 10 12 10,000 475,889 1,447,177 3.04 NOTE: Assumed conditions – 2-ft paved shoulders; 1V:3H roadside foreslopes; flexible pavement. This analysis can be repeated for determining minimum traffic volume levels in which lane widening of other intervals becomes economically feasible. Using the same roadway section characteristics as the previous examples, benefit–cost ratios for widening lanes of different widths can be calculated at several AADT levels using the same procedures. Tables 50 through 54 show the results. Table 50. Example of Benefit–cost Calculations for Lane Widening from 9 to 10 ft in Level Terrain on a Rural Two-Lane Highway Lane Width (ft) AADT (veh/day) Net Implementation Cost ($) Present Value of Safety Benefits ($) Benefit–cost Ratio Before After 9 10 1,000 380,941 41,964 0.11 9 10 2,000 380,941 192,458 0.50 9 10 3,000 380,941 289,435 0.76 9 10 4,000 380,941 385,914 1.01 9 10 5,000 380,941 482,392 1.27 9 10 6,000 380,941 578,871 1.52 9 10 7,000 380,941 675,349 1.77 9 10 8,000 380,941 771,828 2.03 9 10 9,000 380,941 868,306 2.28 9 10 10,000 380,941 964,785 2.53 NOTE: Assumed conditions – 2-ft paved shoulder; 1V:3H roadside foreslopes; flexible pavement.

80 Table 51. Example of Benefit–cost Calculations for Lane Widening from 9 to 11 ft in Level Terrain on a Rural Two-Lane Highway Lane Width (ft) AADT (veh/day) Net Implementation Cost ($) Present Value of Safety Benefits ($) Benefit–cost Ratio Before After 9 11 1,000 475,889 86,797 0.18 9 11 2,000 475,889 433,512 0.91 9 11 3,000 475,889 651,230 1.37 9 11 4,000 475,889 868,306 1.82 9 11 5,000 475,889 1,085,383 2.28 9 11 6,000 475,889 1,302,459 2.74 9 11 7,000 475,889 1,519,536 3.19 9 11 8,000 475,889 1,736,613 3.65 9 11 9,000 475,889 1,953,689 4.10 9 11 10,000 475,889 2,170,766 4.56 NOTE: Assumed conditions – 2-ft paved shoulders; 1V:3H roadside foreslopes; flexible pavement. Table 52. Example of Benefit–cost Calculations for Lane Widening from 9 to 12 ft in Level Terrain on a Rural Two-Lane Highway Lane Width (ft) AADT (veh/day) Net Implementation Cost ($) Present Value of Safety Benefits ($) Benefit–cost Ratio Before After 9 12 1,000 570,837 98,005 0.17 9 12 2,000 570,837 481,723 0.84 9 12 3,000 570,837 723,589 1.27 9 12 4,000 570,837 964,785 1.69 9 12 5,000 570,837 1,205,981 2.11 9 12 6,000 570,837 1,447,177 2.54 9 12 7,000 570,837 1,688,373 2.96 9 12 8,000 570,837 1,929,570 3.38 9 12 9,000 570,837 2,170,766 3.80 9 12 10,000 570,837 2,411,962 4.22 NOTE: Assumed conditions – 2-ft paved shoulders; 1V:3H roadside foreslopes; flexible pavement. Table 53. Example of Benefit–cost Calculations for Lane Widening from 10 to 11 ft in Level Terrain on a Rural Two-Lane Highway Lane Width (ft) AADT (veh/day) Net Implementation Cost ($) Present Value of Safety Benefits ($) Benefit–cost Ratio Before After 10 11 1,000 380,941 44,833 0.12 10 11 2,000 380,941 241,054 0.63 10 11 3,000 380,941 361,794 0.95 10 11 4,000 380,941 482,392 1.27 10 11 5,000 380,941 602,990 1.58 10 11 6,000 380,941 723,589 1.90 10 11 7,000 380,941 844,187 2.22 10 11 8,000 380,941 964,785 2.53 10 11 9,000 380,941 1,085,682 2.85 10 11 10,000 380,941 1,205,981 3.17 NOTE: Assumed conditions – 2-ft paved shoulders; 1V:3H roadside foreslopes; flexible pavement.

81 Table 54. Example of Benefit–cost Calculations for Lane Widening from 11 to 12 ft in Level Terrain on a Rural Two-Lane Highway Lane Width (ft) AADT (veh/day) Net Implementation Cost ($) Present Value of Safety Benefits ($) Benefit–cost Ratio Before After 11 12 1,000 380,941 11,208 0.03 11 12 2,000 380,941 48,211 0.13 11 12 3,000 380,941 72,359 0.19 11 12 4,000 380,941 96,478 0.25 11 12 5,000 380,941 120,598 0.32 11 12 6,000 380,941 144,718 0.38 11 12 7,000 380,941 168,837 0.44 11 12 8,000 380,941 192,957 0.51 11 12 9,000 380,941 217,077 0.57 11 12 10,000 380,941 241,196 0.63 11 12 11,000 380,941 265,316 0.70 11 12 12,000 380,941 289,435 0.76 11 12 13,000 380,941 313,555 0.82 11 12 14,000 380,941 337,675 0.89 11 12 15,000 380,941 361,794 0.95 11 12 16,000 380,941 385,914 1.01 11 12 17,000 380,941 410,034 1.08 11 12 18,000 380,941 434,153 1.14 11 12 19,000 380,941 458,273 1.20 11 12 20,000 380,941 482,392 1.27 NOTE: Assumed conditions – 2-ft paved shoulders; 1V:3H roadside foreslopes; flexible pavement. 7.4 Using Benefit–cost Analysis to Establish Minimum AADT Guidelines for 3R Improvements The cost-effectiveness of any specific design alternative for a 3R project can be assessed in a benefit–cost analysis analogous to that shown in any line of Tables 49 through 54. However, benefit–cost analysis has a further advantage in that it can be used to identify which of multiple design alternatives for a 3R project would be most cost-effective. This type of analysis is referred to as incremental benefit–cost analysis. Incremental benefit–cost analysis assesses whether each additional expenditure in implementation cost provides an added net benefit. The simplest method for performing an incremental benefit–cost analysis is to determine the net benefit (present value of safety benefits minus implementation cost) for each design alternative and select the design alternative with the highest net benefit, as long as that highest net benefit is also greater than zero. The example in Table 55 shows an incremental benefit–cost analysis for lane widening for an existing rural two-lane highway with 9-ft lanes in level terrain. The implementation cost, safety benefit, and benefit–cost ratio shown in Table 55 for lane widening from 9 to 10 ft, 9 to 11 ft, and 9 to 12 ft are those shown in Tables 50, 51, and 52, respectively. In each case, the net benefit has also been added. Table 55 shows the following results for roadways with existing 9-ft lanes:

82 Table 55. Example of Incremental Analysis to Determine Net Benefits of Lane Widening for Existing Rural Two-Lane Highways with 9-ft Lanes in Level Terrain AADT (veh/day) Lane Widening from 9 to 10 ft Lane Widening from 9 to 11 ft Lane Widening from 9 to 12 ft Implementation Cost ($) Crash Reduction Benefit ($) B-C Ratio Net Benefit ($) Implementation Cost ($) Crash Reduction Benefit ($) B-C Ratio Net Benefit ($) Implementation Cost ($) Crash Reduction Benefit ($) B-C Ratio Net Benefit ($) 1,000 380,941 41,964 0.11 -338,977 475,889 86,797 0.18 -389,092 570,837 98,005 0.17 -472,832 2,000 380,941 192,458 0.50 -188,483 475,889 433,512 0.91 -42,377 570,837 481,723 0.84 -89,114 3,000 380,941 289,435 0.76 -91,506 475,889 651,230 1.37 175,341 570,837 723,589 1.27 152,752 4,000 380,941 385,914 1.01 4,973 475,889 868,306 1.82 392,417 570,837 964,785 1.69 393,948 5,000 380,941 482,392 1.27 101,451 475,889 1,085,383 2.28 609,494 570,837 1,205,981 2.11 635,144 6,000 380,941 578,871 1.52 197,930 475,889 1,302,459 2.74 826,570 570,837 1,447,177 2.54 876,340 7,000 380,941 675,349 1.77 294,408 475,889 1,519,536 3.19 1,043,647 570,837 1,688,373 2.96 1,117,536 8,000 380,941 771,828 2.03 390,887 475,889 1,736,613 3.65 1,260,724 570,837 1,929,570 3.38 1,358,733 9,000 380,941 868,306 2.28 487,365 475,889 1,953,689 4.10 1,477,800 570,837 2,170,766 3.80 1,599,929 10,000 380,941 964,785 2.53 583,844 475,889 2,170,766 4.56 1,694,877 570,837 2,411,962 4.22 1,841,125 NOTE: Based on conditions evaluated in Tables 49 through 54.

83  For a roadway with an AADT of 1,000 veh/day, none of the lane widening alternatives are cost-effective.  For a roadway with an AADT of 2,000 or 3,000 veh/day, lane widening from 9 to 11 ft has the maximum net benefit. While lane widening from 9 to 12 ft is cost-effective, its net benefit is less than the net benefit of widening from 9 to 11 ft, and therefore the additional increment of investment to widen to 12-ft lanes is not cost-effective.  For a roadway with an AADT of 4,000 veh/day or more, widening from 9 to 12 ft has the highest net benefit in all cases. Table 56 shows a similar analysis for lane widening for an existing two-lane highway with 10-ft lanes in level terrain which indicates that:  For a roadway with an AADT of 3,000 veh/day or less, none of the lane widening alternatives are cost-effective.  For a roadway with an AADT of 4,000 veh/day, the alternatives of lane widening from 10 to 11 ft and from 10 to 12 ft are nearly equal in net benefits, although widening from 10 to 12 ft is slightly higher.  For a roadway with an AADT of 5,000 veh/day or more, widening from 10 to 12 ft has the highest net benefit in all cases. For an existing two-lane highway with 11-ft lanes in level terrain, there is only one alternative to be considered (lane widening from 11 to 12 ft), so no incremental analysis is needed. Table 54 addresses this situation, indicating that lane widening from 11 to 12 ft only becomes cost- effective for roadways with AADT of 16,000 veh/day or more. Thus, lane widening in 3R projects on most existing rural two-lane highways with 11-ft lanes is not a desirable safety investment. The reason for this result is that the HSM Chapter 10 procedures show very little difference in crash frequency between 11- and 12-ft lanes on rural two-lane highways. The results of the incremental benefit–cost analyses presented above show that benefit–cost analyses can be used to create guidelines on the minimum AADT levels for which lane widening or other geometric design improvements may be cost-effective in 3R projects. Further examples of using benefit–cost analysis to establish 3R design guidelines using minimum AADT levels are presented in the next section. Tables 49 to 54 show that the minimum AADT levels that would provide benefit–cost ratios of at least 1.0 and 2.0 for each widening scenarios are as follows: Lane Widening Scenario Minimum AADT (veh/day) for B/C=1.0 B/C=2.0 Widen from 9 to 10 ft 4,000 8,000 Widen from 9 to 11 ft 3,000 5,000 Widen from 9 to 12 ft 3,000 5,000 Widen from 10 to 11 ft 4,000 7,000 Widen from 10 to 12 ft 4,000 7,000 Widen from 11 to 12 ft 16,000 32,000

84 Table 56. Examples of Incremental Analysis to Determine Net Benefits of Lane Widening for Existing Rural Two-Lane Highways with 10-ft Lanes in Level Terrain AADT (veh/day) Lane Widening from 10 to 11 ft Lane Widening from 10 to 12 ft Implementation Cost ($) Crash Reduction Benefit ($) B-C Ratio Net Benefit ($) Implementation Cost ($) Crash Reduction Benefit ($) B-C Ratio Net Benefit ($) 1,000 380,941 44,833 0.12 -336,108 475,889 56,041 0.17 -419,848 2,000 380,941 241,054 0.63 -139,887 475,889 289,265 0.61 -186,624 3,000 380,941 361,794 0.95 -19,147 475,889 434,153 0.91 -41,736 4,000 380,941 482,392 1.27 101,451 475,889 578,871 1.22 102,982 5,000 380,941 602,990 1.58 222,049 475,889 723,589 1.52 247,700 6,000 380,941 723,589 1.90 342,648 475,889 868,306 1.82 392,417 7,000 380,941 844,187 2.22 463,246 475,889 1,013,024 2.13 537,135 8,000 380,941 964,785 2.53 583,844 475,889 1,157,742 2.43 681,853 9,000 380,941 1,085,682 2.85 704,741 475,889 1,302,459 2.74 826,570 10,000 380,941 1,205,981 3.17 825,040 475,889 1,447,177 3.04 971,288 NOTE: Based on conditions evaluated in Tables 49 through 54.

85 The minimum AADT levels for lane widening can be expanded to include rolling and mountainous terrain types, as shown in Table 57. Minimum AADT levels can be established for shoulder widening using the same procedure described above, as shown in Table 58. 7.5 Specific Benefit–cost Analysis Applications for 3R Project Design Descriptions Three specific benefit–cost analysis applications have a role in 3R project design decisions. These are:  benefit–cost analysis for a single design alternative for a specific site  benefit–cost analysis to choose among several design alternatives for a specific site  benefit–cost analysis to develop agency-specific minimum AADT guidelines for application in design decisions Each of these benefit–cost applications is discussed below. 7.5.1 Benefit–cost Analysis for a Single Design Alternative for a Specific Site A single design alternative for a specific site can be evaluated by determining the benefit–cost ratio for the alternative using Equation (21). If the computed benefit–cost ratio equals or exceeds 1.0, the design alternative is cost-effective and implementation of the geometric design improvement deserves consideration as part of the 3R project. If the benefit–cost ratio is less than 1.0, the design alternative is not cost-effective and should not typically be considered as part of the 3R project unless the crash history shows a specific crash pattern that is potentially correctable by the geometric design improvement in question, or the geometric design improvement is essential to achieving the traffic operational LOS for the project. An equivalent analysis can be performed by determining whether the net benefits determined with Equation (39) exceed zero. Highway agencies may prefer to seek minimum benefit–cost ratios greater than 1.0 to assure that limited funds available for safety improvements are invested productively. Benefit–cost analysis for a single design alternative can be performed with Spreadsheet Tool 1 presented in Section 8.1.

86 Table 57. Example of AADT Levels at which Lane Widening Becomes Cost-Effective Rural Two-Lane Highway Segments Assuming 2-ft Paved Shoulders, 1V:3H Roadside Foreslopes, and Moderate Horizontal Curvature Proposed Improvement Minimum AADT level (veh/day) for benefit–cost ratio = 1.0 Minimum AADT level (veh/day) for benefit–cost ratio = 2.0 Level Rolling Mountainous Level Rolling Mountainous Widen from 9 to 10 ft 4,000 5,000 7,000 8,000 10,000 14,000 Widen from 9 to 11 ft 3,000 3,000 4,000 5,000 5,000 8,000 Widen from 9 to 12 ft 3,000 3,000 4,000 5,000 6,000 8,000 Widen from 10 to 11 ft 4,000 4,000 6,000 7,000 8,000 11,000 Widen from 10 to 12 ft 4,000 4,000 6,000 7,000 8,000 11,000 Widen from 11 to 12 ft 16,000 19,000 28,000 32,000 37,000 55,000 Table 58. Example of AADT Levels at which Shoulder Widening Becomes Cost-Effective Rural Two-Lane Highway Segments Assuming 10-ft Lanes, Paved Shoulders, 1V:3H Roadside Foreslopes, and Moderate Horizontal Curvature Proposed Improvement Minimum AADT level (veh/day) for benefit–cost ratio = 1.0 Minimum AADT level (veh/day) for benefit–cost ratio = 2.0 Level Rolling Mountainous Level Rolling Mountainous Widen from 0 to 2 ft 3,000 4,000 6,000 6,000 8,000 12,000 Widen from 0 to 4 ft 3,000 4,000 5,000 6,000 7,000 10,000 Widen from 0 to 6 ft 3,000 4,000 5,000 6,000 7,000 9,000 Widen from 0 to 8 ft 3,000 4,000 5,000 6,000 7,000 9,000 Widen from 2 to 4 ft 5,000 6,000 9,000 10,000 12,000 17,000 Widen from 2 to 6 ft 4,000 5,000 6,000 8,000 9,000 12,000 Widen from 2 to 8 ft 4,000 4,000 6,000 8,000 8,000 11,000 Widen from 4 to 6 ft 6,000 7,000 10,000 12,000 13,000 19,000 Widen from 4 to 8 ft 5,000 5,000 7,000 9,000 10,000 14,000 Widen from 6 to 8 ft 8,000 9,000 12,000 16,000 17,000 24,000 7.5.2 Benefit–cost Analysis to Choose Among Several Design Alternatives for a Specific Site Multiple design alternatives for a specific site can be evaluated by comparing their net benefits determined with Equation (39) and selecting for consideration the alternative that has the largest positive value of net benefits. If all of the design alternatives considered have net benefits less than zero, none of the alternatives are cost-effective and none deserve consideration as part of the 3R project unless the crash history shows a specific crash pattern that is potentially correctable by one or more of the design alternatives or that one or more of the design alternatives is essential to achieving the traffic operational LOS for the project. Highway agencies should consider budget constraints in choosing among multiple alternatives, and may also consider the magnitude of the benefit–cost ratio for the selected design alternative, computed with Equation (38), as focusing the expenditure of limited funds on design alternatives with benefit–cost ratios substantially greater than 1.0 helps assure that the funds available for safety improvements are invested productively.

87 Benefit–cost analysis for multiple design alternatives can be performed with Spreadsheet Tool 2 presented below in Section 8.2. 7.5.3 Benefit–cost Analysis to Develop Agency-Specific Minimum AADT Guidelines for Application in Design Decisions Highway agencies can develop minimum AADT guidelines for application in 3R project design decisions, analogous to those shown in Tables 57 and 58. Such guidelines can be developed through repeated application of Spreadsheet Tool 1, presented in Section 8.1. Each entry in Tables 49 through 54 is obtained from a single application of Spreadsheet Tool 1. The results are then summarized in a form like Tables 55 and 56. The results like those in Tables 56 and 57 can then be expressed as minimum AADT guidelines like those presented in Tables 57 and 58. Benefit–cost analyses to establish minimum AADT guidelines should be based on generic site characteristics representative of a specific agency’s facilities. Separate minimum AADT guidelines are needed for each facility type and terrain category. All assumptions in the benefit– cost analysis, including implementation costs and crash costs, should be based on the policies and experience of an individual highway agency. Policies based on agency-specific minimum AADT guidelines are an acceptable method for making 3R project design decisions, but will not provide results as reliable as the site-specific benefit–cost analyses discussed in Sections 7.5.1 and 7.5.2. 7.6 Alternative Approaches to Presenting Design Guidelines Several alternative approaches to presenting design guidelines have been identified and are being considered in the research. These include:  Dimensional design criteria  Minimum AADT levels to initiate consideration of specific improvement types  Crash history reviews of candidate improvement sites  Site-specific benefit–cost analyses The final design guidance will likely include a mix of these approaches. Each of these approaches is discussed below, followed by a comparison of their application to a typical rural state highway system. 7.6.1 Dimensional Design Criteria The AASHTO Green Book (1) contains extensive dimensional design criteria for use in the project development process. Tables 20 to 22 show examples of the dimensional design criteria used in the Green Book for traveled way width (and therefore, by implication, for lane width) on rural two-lane arterials.

88 Similarly, TRB Special Report 214 (4) presents the dimensional design criteria for lane and shoulder width shown in Table 19, which are, in some cases, less than the Green Book criteria for new construction or reconstruction. It should be noted that both the Green Book and the TRB Special Report 214 criteria include the design volume as a factor in determining the dimensional criteria. Dimensional design criteria of this type can be developed from benefit–cost analysis results like those presented in Section 7.2 of this report. However, since dimensional design criteria are shown in the analysis presented below in Section 7.7 to provide suboptimal results, they are not proposed for use in the new guidelines. 7.6.2 Minimum AADT Levels to Initiate Consideration of Specific Improvement Types Tables 55 to 58 in Section 7.4 of this report illustrate how minimum AADT levels can be used initiating consideration of specific improvement types. Use of minimum AADT levels in this way serves a systemic safety approach in which improvement needs at sites that meet particular criteria are considered regardless of crash history. This may be an acceptable method for the development of design guidelines, but the analyses in Section 7.7 suggest that site-specific benefit–cost analyses (see Section 7.6.4) are likely to result in greater overall crash reductions. 7.6.3 Crash History Reviews of Candidate Improvement Sites It appears that a crash history review of each 3R project site should be part of the design guidelines. Such reviews can serve several purposes. First, for sites with AADT levels below values like those specified in Tables 57 and 58, a crash history review may identify crash patterns that indicate an improvement need, even though traffic volume by itself does not. Second, for sites with AADT levels above levels like those specified in Tables 57 and 58, the crash history review can serve as part of the design process to assure that the appropriate improvement for the site is chosen. Finally, once crash history for a given site is available, a benefit–cost analysis like that discussed in Section 7.1 can be based on an Empirical Bayes (EB) estimate of expected crash frequency, rather than on just the HSM predicted crash frequency. This can increase the accuracy of the crash frequency and severity estimates on which the benefit–cost analysis will be based. Thus, crash history are desirable as part of the design guidelines for 3R projects. 7.6.4 Site-Specific Benefit–cost Analyses Section 7.1 of this report has illustrated procedures for benefit–cost analyses. Benefit–cost analyses can be applied as a tool for helping to develop design guidelines, as discussed in Section 7.6.2. However, benefit–cost analyses can also be applied as a site-specific tool to support in project-level decision-making. A benefit–cost approach would be applied as follows:

89  The expected crash frequency by crash severity level for the existing conditions at the site is determined using the applicable HSM predictive method together, where crash history data are available, with the EB method presented in the Appendix to HSM Part C.  Candidate improvements to be considered for implementation in the 3R project are identified; dimensional elements like lane width this would include a range of potential dimensions; for example, for an existing site with 9-ft lanes, potential lane widening to 10-ft, 11-ft, and 12-ft lanes would be considered.  The cost for each improvement alternative is estimated using the procedures in Appendix A of this report or the highway agency’s own procedures.  The expected annual crash reduction by severity level is estimated for each alternative using appropriate CMFs, such as those presented in Chapter 5 of this report.  The annual crash reduction is converted to dollar terms using appropriate crash costs by severity level and the annual benefit is converted to a present value using the uniform series present worth factor, as shown in Equation (38) in Section 7.1.9 of this report.  The benefit–cost ratio and net benefits are then computed for each alternative. Where dimensional elements like lane width are considered, benefit–cost analysis should be performed for each increment of widening. For example, for an existing roadway with 9-ft lanes, widening to 10-, 11-, and 12-ft lanes should be considered. This can be done with incremental benefit–cost analysis as described below. Equation (66) illustrates a traditional benefit–cost ratio for widening a lane from 9 to 10 ft: BC → N 1 C → 𝑃/𝐴, 𝑖%,𝑛 /IC → (66) while Equation (67) illustrates an incremental benefit–cost ratio for further widening from 10 to 11 ft at a site with existing 9-ft lanes where widening from 9 to 10 ft has already been found to be cost effective: Incremental BC → N 1 C → N 1 C → 𝑃/𝐴, 𝑖%,𝑛 / IC → IC → (67) Where widening to 11-ft lanes has already been found to be cost-effective, the analysis should then determine the incremental benefit–cost ratios for widening from 11- to 12-ft lanes. The logic for incremental analysis of benefit–cost ratios seems complex to most engineers. Fortunately, a much simpler computational approach using the net benefit, rather than the benefit–cost ratio, is available. Benefit–cost analysis is applied to each potential alternative, such as:  Widening lanes from 9 to 10 ft  Widening lanes from 9 to 11 ft  Widening lanes from 9 to 12 ft

90 Then, the most cost-effective alternative is simply the alternative with the largest net benefit, as determined with Equation (39). A budget constraint can also be applied. The preferred alternative can be chosen as the alternative with the largest net benefit that is within the agency’s available budget for the project. 7.7 Investing Available 3R Funds for Maximum Reduction of Crash Frequency and Severity Since funds available for highway infrastructure improvements are limited, it is important that those funds, including funds for 3R projects, be invested to accomplish the project objectives, including preserving the pavement and extending the pavement service life, improving traffic operations, and, to the extent practical, maximizing the potential reduction in crash frequency and severity. Maximizing the reduction in crash frequency and severity requires that the available funds be invested in a logical priority fashion, focusing on those projects where the maximum crash reduction benefit can be obtained for the least cost. Investing available funds in safety improvement without careful planning can lead to suboptimal results. This is illustrated by the following example. 7.7.1 Example of Optimal and Suboptimal Strategies for Investing Available Funds in Design Improvements to Reduce Crash Frequency and Severity Highway agency users who apply the 3R design guidelines will apply them to one site at a time, but their appropriateness can be tested by applying them systemwide to rural highway systems and reviewing the results. As an example, four potential strategies for lane widening to the rural two-lane highway system of an actual state using data from the FHWA Highway Safety Information System (HSIS) were tested in recent research. This rural two-lane highway system consists of 4,630.71 mi of road with AADTs up to 25,000 veh/day. The current lane width distribution for this road system is: Lane Width (ft) Total Length (mi) 9 18.29 10 251.74 11 2,087.38 12 2,273.30 TOTAL 4,630.71 The following improvement strategies were considered and were applied as if the entire road system were a candidate for resurfacing in a single year:  Widen all lanes with widths less than 12 ft to 12 ft  Widen lanes where a need is indicated by the TRB Special Report 214 (4) lane width criteria presented in Table 19

91  Widen lanes on roadways where the AADT exceeds the minimum AADT criteria presented in Table 57  Widen lanes where the net present benefits of the project exceeds zero (i.e., where the benefits exceed the costs) based on the benefit–cost analysis procedure presented in Chapter 5 The benefits and cost of lane widening in this example are based on assumptions concerning crash costs, unit construction costs, project service life, and minimum attractive rate of return presented in Section 7.1. These values vary widely in current practice, but the assumptions used here are typical of the middle range of values currently used by highway agencies. 7.7.1.1 Lane Widening Strategy—Widen All Lanes to 12 ft This strategy would select for widening the 2,357.41 mi of roadway with existing lane widths less than 12 ft. This would change the lane-width distribution on the roadway system as shown below: Lane Width (ft) Total Length (mi) Before After 9 18.29 0.00 10 251.74 0.00 11 2,087.38 0.00 12 2,273.30 4,630.71 TOTAL 4,630.71 4,630.71 This improvement program would provide benefits of $68,911,192 at a cost of $516,336,773, equivalent to a benefit–cost ratio of 0.13. Of the 2,357.41 mi of roadway improved, 97 percent consisted of projects with benefit–cost ratios less than 1.0. This high proportion of projects that were not cost-effective occurred because most of the extensive mileage of two-lane roadways consisted of 11-ft lanes, where lane widening provides only a limited benefit (see Section 5.4.1) 7.7.1.2 Lane Widening Strategy—Widen Lanes Based on TRB Special Report 214 Criteria This strategy would select for widening the 832.28 mi of roadway that do not meet the TRB Special Report 214 lane width criteria shown in Table 19. This would change the lane-width distribution on the roadway system as shown below: Total Length (mi) Lane Width (ft) Before After 9 18.29 0.00 10 251.74 175.20 11 2,087.38 1,432.58 12 2,273.30 3,022.93 TOTAL 4,630.71 4,630.71

92 This improvement program would provide benefits of $57,180,686 at a cost of $200,107,835, equivalent to a benefit–cost ratio of 0.29. Of the 832.28 mi of roadway improved, 96 percent consisted of projects with benefit–cost ratios less than 1.0. This strategy does a better job at focusing on the best projects and avoided many of the projects included in the 12-ft lane strategy that were not cost-effective, but not all of them. 7.7.1.3 Lane Widening Strategy—Minimum AADT Levels This strategy would select for widening the 54.88 mi of roadway that meet the minimum AADT criteria presented in Table 57. This would change the lane-width distribution on the roadway system as shown below: Total Length (mi) Lane Width (ft) Before After 9 18.29 18.29 10 251.74 231.25 11 2,087.38 2,052.99 12 2,273.30 2,328.18 TOTAL 4,630.71 4,630.71 This improvement program would provide benefits of $12,391,936 at a cost of $14,824,774, equivalent to a benefit–cost ratio of 0.84. Of the 54.88 mi of roadway improved, 60 percent consisted of projects with benefit–cost ratios less than 1.0. This strategy does a better job at focusing on the best projects and avoided many of the projects that are not cost-effective. 7.7.1.4 Lane Widening Strategy—Benefit–cost Analysis for Individual Projects This strategy would select for widening 35.34 mi of roadway for which a need for lane widening was identified by a benefit–cost analysis using the benefit–cost analysis procedure presented in Section 7.2.2. This would change the lane-width distribution on the roadway system as shown below: Total Length (mi) Lane Width (ft) Before After 9 18.29 18.29 10 251.74 219.36 11 2,087.38 2,076.96 12 2,273.30 2,301.32 TOTAL 4,630.71 4,630.71 This improvement program would provide benefits of $7,817,183 at a cost of $5,603,567, equivalent to a benefit–cost ratio of 1.40. Every portion of the 35.34 mi of roadway improved in this program was a cost-effective project, and the benefits for the program as a whole exceed the

93 costs. This strategy does the best job at focusing on the best projects and avoids many of the projects that are not cost-effective. 7.7.1.5 Summary of Findings from the Example of Lane Widening Strategies The example of lane widening strategies for a statewide system of rural two-lane highways shows that an improvement program based on benefit–cost analysis for individual projects would provide the greatest net present benefits and the greatest return per dollar spent and would avoid improvements that are not cost-effective. However, benefit–cost analysis results are not necessarily exact, and not every highway agency will have the data available and in a suitable form for a benefit–cost analysis. Minimum AADT criteria developed through a benefit–cost analysis come the closest of the other alternatives to providing optimal results. Both blanket lane widening to a minimum 12-ft lane width and lane widening based on the design criteria from TRB Special Report 214 (4) result in many lane widening investments that would not be cost- effective. The primary drawback of strategies developed before publication of the HSM is likely to be a focus on widening 11 ft lanes to 12 ft, which is unlikely to be cost-effective except at very high volumes, particularly for rural two-lane and multilane highways. Finally, it should be noted that in actual practice some roadways might be found to have experienced patterns of single-vehicle run-off-road, head-on, opposite-direction sideswipe, or same-direction sideswipe crashes that could indicate a need for lane widening regardless of the results of the benefit–cost analysis.