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Suggested Citation:"Chapter 4 - Methodology." National Academies of Sciences, Engineering, and Medicine. 2022. Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers. Washington, DC: The National Academies Press. doi: 10.17226/26679.
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Suggested Citation:"Chapter 4 - Methodology." National Academies of Sciences, Engineering, and Medicine. 2022. Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers. Washington, DC: The National Academies Press. doi: 10.17226/26679.
×
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Suggested Citation:"Chapter 4 - Methodology." National Academies of Sciences, Engineering, and Medicine. 2022. Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers. Washington, DC: The National Academies Press. doi: 10.17226/26679.
×
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Page 36
Suggested Citation:"Chapter 4 - Methodology." National Academies of Sciences, Engineering, and Medicine. 2022. Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers. Washington, DC: The National Academies Press. doi: 10.17226/26679.
×
Page 36
Page 37
Suggested Citation:"Chapter 4 - Methodology." National Academies of Sciences, Engineering, and Medicine. 2022. Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers. Washington, DC: The National Academies Press. doi: 10.17226/26679.
×
Page 37
Page 38
Suggested Citation:"Chapter 4 - Methodology." National Academies of Sciences, Engineering, and Medicine. 2022. Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers. Washington, DC: The National Academies Press. doi: 10.17226/26679.
×
Page 38
Page 39
Suggested Citation:"Chapter 4 - Methodology." National Academies of Sciences, Engineering, and Medicine. 2022. Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers. Washington, DC: The National Academies Press. doi: 10.17226/26679.
×
Page 39
Page 40
Suggested Citation:"Chapter 4 - Methodology." National Academies of Sciences, Engineering, and Medicine. 2022. Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers. Washington, DC: The National Academies Press. doi: 10.17226/26679.
×
Page 40

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33   C H A P T E R 4 The statement of work for this research called for using both a risk-based and benefit–cost- based approach in the development of the guidelines. In the very short period since this work commenced, two separate but influential research efforts were completed that caused a shift in the approach to both geometric and roadside design. NCHRP Report 785: Performance-Based Analysis of Geometric Design established a performance-based framework for highway designers to use in the geometric design of highways. (Ray 2014) At about the same time, NCHRP Project 15-65, “Development of Safety Performance Based Guidelines for the Roadside Design Guide,” developed performance-based roadside safety guidance to support quantitative design decisions and promote consistency in interpretation and implementation using a risk-based methodology. (Ray, forthcoming) While NCHRP Project 15-65 has a broader objective to develop quantitative design decisions for the entire RDG, this effort is focused on median barriers (i.e., double-faced) and was extended to include roadside barriers (i.e., single-faced barriers). Ultimately, NCHRP Project 15-65 will result in a framework that all RDG guidance can adopt. The guidelines proposed herein have adopted that risk-based methodological frame- work to coordinate and be consistent with the NCHRP Project 15-65 methodology. This early adoption will result in the products of this research being more easily integrated into the pending update to the RDG. Ray et al. proposed a governing equation to represent the sequence of ROR events and sub- events to develop roadside designs that minimize the OUTCOME (e.g., risk, cost) of a crash, as shown below in Equation 1:(Ray, forthcoming) [ ] [ ] [ ]= • •OUTCOME Number of Encroachments Prob. Interacting Encr Prob. of KA InteractionS ∏( )=    − δ        • • • • • •OUTCOME BEF EAF L 5280 P P 1 THR PSL 65 THR 1j S S S cj SEV j j s 3 3 i i=1 j-1 j where OUTCOMES = The total number of crashes with the specified outcome on the segment involving all features on the segment. OUTCOMEj = The number of crashes with the specified outcome involving feature j (e.g., the number of serious injury or fatal crashes involving impacts with a tree) per edge mile per year. j = Feature number from 1 to n where n is the total number of features evaluated on the segment. BEFS = The expected annual number of encroachments on a segment in edge encroachments/mi/yr assuming base conditions as a function of traffic volume (AADT). Methodology

34 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers EAFS = Highway and traffic characteristic encroachment adjustment factors for the highway segment of interest. LS = Segment length in miles. Pcj = The conditional probability of a vehicle striking an object given an encroach- ment occurs. The length ratios are the probability of leaving the roadway in the given proportion of the roadway under the assumption that encroach- ments are equally likely anywhere on the segment. The form of Pcj depends on the type of object, as shown below: Continuous Features (e.g., guardrails, median barriers, terrain) Discrete Features (e.g., trees, poles, bridge piers, water bodies) PSEVj = The conditional probability of observing the severity of interest given that there is an interaction with roadside feature j. THRj = The conditional probability of passing through feature j given the vehicle inter- acts with feature j. δj = δ = 1 if all interactions with the feature do not lead to an increase in harm (e.g., terrain). δ = 0 if all interactions with the feature lead to an increase in harm (e.g., longitu- dinal barrier). PSLs = The posted speed limit on the segment in mi/hr. Lj = The effective length of an individual feature j along the segment in feet. (See Figure 21.) Continuous Features (e.g., longitudinal barriers, terrain, medians) The length of a continuous feature is measured parallel to the roadway. Single Discrete Features For single discrete features such as trees or utility poles, this is equal to the diameter of the feature. For rectangular features, this is the length parallel to the roadway. Add VW sin(θ85) to the length or diameter. Multiple Discrete Features For features like a line of poles or series of bridge piers, the effective length is the length in feet from the upstream traffic face of the first feature to the Figure 21. Roadside geometry of discrete features and continuous shielding features. (Ray 2021, forthcoming)

Methodology 35   downstream face of the last feature plus VW sin(θ85) as long as the spacing between features is less than WB/tan θ15. If the spacing between features is greater than WB/tan θ15 then treat the individual feature as a single isolated feature. Pyj = The cumulative probability density function of the lateral extent of encroach- ment when lateral offset y = Y. Px(Xj) = Sum of the cumulative probability density function of the maximum longitu- dinal extent of encroachment. WBj = The distance in feet from the edge of the traveled way measured laterally to the farthest point of feature j plus VW cos(θ15). WFj = The distance in feet from the edge of the traveled way to the closest face (i.e., traffic side) of feature j. For foreslopes, the distance is measured to the bottom of the foreslope. LTMax = The length in ft of the longest trajectory in the database of trajectories used to calculate Px(Xj) and Pyj (i.e., 1,000 ft). Vw = Typical passenger vehicle width in feet (e.g., 6.5 ft). θ15 = The 15th percentile encroachment angle in degrees (e.g., 5 degrees (Gabler, forthcoming-a)). θ85 = The 85th percentile encroachment angle in degrees (e.g., 22 degrees (Gabler, forthcoming-a)). More details on the derivation of Equation 1 can be found in the NCHRP Project 15-65 final report. (Ray, forthcoming) For terrain features such as slopes, the area of concern is generally the entire length of the segment. Similarly, the area of concern when assessing the need for median barriers is also the entire length of the segment. Conversely, fixed objects such as trees, poles, or bridge piers are not equal to the length of the segment because striking the fixed object is only a concern in the portion of the segment where the fixed objects are located. The guidelines developed in this research use a relative-risk approach: The risk of a fatal or serious injury crash with the roadside feature shielded by a roadside or median barrier is divided by the risk of a fatal or serious injury crash with the unshielded feature. For example, the risk of a median crossover crash with a median barrier installed is divided by the risk when no median barrier is installed. =RR OUTCOME OUTCOME 2SHIELDED/UNSHIELDED SHIELDED UNSHIELDED Referring to Equation 1, using the relative risk simplifies the process since the BEFs, EAFs, and Ls all cancel out when the same road segment is being evaluated in the numerator and the denominator. Guidelines for median barrier need and the need for shielding fixed objects and terrain in the median are all developed using this relative risk approach. This research included the conduct of and assemblage of the underlying research and sub- sequent development of many of the variables that comprise the governing equation proposed by Ray et al. under NCHRP Project 15-65. Restated, fundamental components of the governing equation proposed by Ray et al. were developed under this effort and are therefore presented in this final report. The background and new research conducted to develop and assemble each of these variables for the selection and placement of MASH double-faced barriers within the median and MASH single-faced barriers within the median or on the roadside are discussed in this section. Each

36 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers heading represents a variable of the governing equation that will be used for MASH median and roadside barrier selection and placement guideline development. Detailed statistical modeling is provided, when necessary, in the appendices to support these variable summaries, as outlined below. 4.1 Probability of Reaching the Lateral Offset of Feature j—PY(Yj) NCHRP Project 15-65 defines “PY(Yj)” as the “cumulative probability density function of the lateral extent of encroachment when lateral offset y = Y.” (Ray, forthcoming) Further, WBj is “the distance in feet from the edge of the traveled way measured laterally to the farthest point of feature . . .” and WFj is “the distance in feet from the edge of the traveled way to the clos- est face of feature j.” Considerable effort was expended to obtain and model the maximum lateral extent of passenger vehicles on median and roadside terrain for this research project. Details of this modeling effort are documented in Probability of Reaching the Lateral Offset of Feature j—PY(Yj). The NTSB recommendations to AASHTO and the FHWA regarding median barrier selection and placement guidelines explicitly target heavy vehicles. Little is directly known about heavy vehicle trajectories. Ideally, heavy vehicle trajectory data would have been gathered, however, that endeavor would be extremely costly and was outside the scope of this research. The model developed for passenger vehicles was used for heavy vehicles. It is believed this approach, while not ideal, is conservative. Trajectory simulations obtained from the recently completed NCHRP Project 17-55 in com- bination with the encroachment conditions determined in NCHRP Project 17-43 were used to develop the probability distribution for the lateral extent of encroachment, PY(Yj). (Gabler, forthcoming; Sheikh 2019) There is ongoing research to model ditches under NCHRP Project 16-05, “Guidelines for Cost-Effective Safety Treatments of Roadside Ditches” that could be used to further extend this research. (Sheikh 2021) Probability of Reaching the Lateral Offset of Feature j—PY(Yj) also addresses how to integrate the results of the NCHRP Project 16-05 research into these guidelines. A summary of the maximum lateral extent (i.e., PY(Yj)) used in these guidelines is shown in Figure 22. Details about the development of this figure, the data and the statistical method used, and background are provided in Probability of Reaching the Lateral Offset of Feature j— PY(Yj). 4.2 Probability of Crash Severity (PSEVj) NCHRP Project 15-65 defines PSEVj as “the conditional probability of observing the severity of interest given that there is an interaction with roadside feature j.” (Ray, forthcoming)The outcome of interest, when considering the median design and the possible need for installing a median barrier or a roadside barrier, includes barrier type, terrain features, fixed objects, and other roadway users (i.e., vehicle occupants in the opposing lanes in a CMC). Many different sources of crash data were used to develop these relationships for various longitudinal barriers, rolling over on the terrain, fixed objects, and CMCs. These data sources and the analysis of the data are documented in PROBABILITY OF CRASH SEVERITY (PSEVJ). The outcome of interest for guidelines development is shown in Table 8.

Methodology 37   Yj (ft) PY(Yj) 0 1.0000 1 0.9761 2 0.9431 3 0.9090 4 0.8844 5 0.8650 10 0.7737 15 0.7191 20 0.6741 25 0.6238 26 0.6120 27 0.6014 28 0.5908 29 0.5815 30 0.5699 35 0.5082 40 0.4603 45 0.4063 50 0.3622 55 0.3254 60 0.2887 65 0.2531 70 0.2307 75 0.2115 80 0.1918 85 0.1752 90 0.1624 95 0.1515 100 0.1416 Figure 22. Probability of an encroachment reaching a feature offset Y, PY(Yj). Feature K65 KA65 KAB65 KABC65 Longitudinal Barriers Cable Barrier 0.0009 0.0050 0.0297 0.0849 Metal-Beam Barrier 0.0013 0.0084 0.0369 0.0895 Concrete Barrier 0.0021 0.0159 0.0810 0.1667 Fixed Objects and Rollover 0.0142 0.0589 0.3138 0.4836 Enter Opposing Lanes 0.0098 0.0451 0.1290 0.1938 Table 8. Outcomes for selected roadside and median features (PSEVj).

38 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers 4.3 Probability of Passing Through a Feature (THRj) THRj is “the conditional probability of passing through feature j given the vehicle interacts with feature j.” (Ray, forthcoming) For example, a vehicle may travel on a median slope, interact with and penetrate a median barrier, and enter the opposing lanes where it may be struck by another vehicle. The proportion that passes through for each category of roadside feature (i.e., the first slope and the median barrier) is dependent on characteristics unique to the specific type of feature. This effort derived values for THRj across a wide range of features including various barriers, terrain, crossing into opposing lanes, and fixed objects. The background information and derivation of each of these groups are discussed below. 4.3.1 Probability of Passing Through, Under, or Over a Barrier (THRBAR) Vehicle type, barrier material (e.g., cable, metal beam, and concrete) and TL, and barrier placement were evaluated as explanatory variables for THRBAR. Both mechanistic and crash- data-based empirical calculations were employed to model THRBAR due to a lack of empirical data. The objective of the modeling effort was to represent the probability of getting through various barrier types, materials, and TLs (i.e., penetration, rolling over the barrier, vaulting the barrier). It was found that there is not a significant difference between barrier material within a particular TL group. It was further found that while area type (i.e., urban or rural) does influ- ence the mix of the traffic, it does not have a significant influence on the value of THRBAR. It is recommended, therefore, that the values for THRBAR are a function only of barrier TL and PT. Probability of Passing Through, Over, or Under a Barrier (THRBAR) provides details on the modeling effort. It should be recognized that there are no assurances that all crashes of any type will be contained or not be contained. Table 9 shows values of THRBAR with consideration of traffic mix where PT is expressed as a number, not a decimal. 4.3.2 Probability of Passing Through a Terrain Feature (THRTERRAIN) For terrain features like foreslope, backslope, and ditch bottom, the proportion of vehicles that pass through the feature is determined by predicting the proportions of rollover crashes that occur between when the encroachment enters the slope and departs the slope. THRTERRAIN, for example, is the proportion of vehicles that travel across the slope feature without rolling over, stopping, or returning to the roadway. Recall the maximum lateral extent of passenger vehicles on median and roadside terrain was modeled during this research effort, which included the competing risk of rolling over on the terrain. This modeling effort, including the competing risk of rolling over, is documented in Probability of Reaching the Lateral Offset of Feature j—PY(Yj). The proportion of vehicles that rolled over on the slope is not included in THR. The probability of rollover (i.e., do not pass THR) was modeled. Table 10 shows values of THRTERRAIN, which are one minus the proportion rolling over on each type of foreslope. Tables like this are needed for backslopes and ditch type and width but have not yet been developed. The study of ditches is underway in NCHRP Project 16-05, “Guidelines for Cost-Effective Safety Treatments of Roadside Ditches.” (Sheikh 2021) When implementing these findings, it is recommended that slopes of flatter than −10:1 use the −10:1 finding. 4.3.3 Probability of Passing Across the Opposing Lanes (THREOL) A model that considered lane volume in vehicles per day was developed to represent the probability of passing across opposing lanes for these guidelines. The model development and THRBAR 2 PT/100 3 PT/100 4 0.75PT/100 5 0 Test Level Table 9. Values for THRBAR for guideline development.

Methodology 39   analysis of the simulated data are documented in Appendix E Probability of Passing Across the Opposing Lanes (THREOL). The opposing lanes of traffic are another median-related feature with which vehicles may interact. In this case, the probability of passing through the feature (i.e., getting across the oppos- ing lanes without striking another vehicle) is a function of the traffic volume in the opposing lanes. If there is little traffic, a vehicle that enters the opposing lanes is unlikely to interact with another vehicle whereas if there is a high volume, it is more likely a vehicle will be present that the encroaching vehicle may strike. A CMC model has long been a missing part of the encroachment probability model for modeling CMCs. This effort provided valuable insight into the probability of these events. The proportions of the vehicles passing through, rather than having a crash (i.e., THREOL), are shown in Table 11 as a function of lane volume and land use. These values have been tabulated by lane volume in vehicles per day in the opposing lane adjacent to the median. If the lane volume is not known, the bi-directional AADT may be divided by the total number of lanes. Survived the Terrain Lateral Extent THRTERRAIN ft –10:1 or flatter –6:1 –4:1 –3:1 –2:1 0 1.0000 1.0000 1.0000 1.0000 1.0000 1 1.0000 1.0000 1.0000 1.0000 1.0000 2 1.0000 1.0000 1.0000 1.0000 1.0000 3 1.0000 1.0000 1.0000 1.0000 1.0000 4 1.0000 1.0000 1.0000 1.0000 1.0000 5 1.0000 1.0000 1.0000 1.0000 1.0000 10 1.0000 1.0000 1.0000 1.0000 0.9995 15 0.9992 0.9993 0.9998 0.9997 0.9985 20 0.9963 0.9962 0.9957 0.9966 0.9948 25 0.9921 0.9911 0.9885 0.9887 0.9835 26 0.9900 0.9896 0.9867 0.9869 0.9802 27 0.9892 0.9887 0.9851 0.9840 0.9762 28 0.9890 0.9876 0.9847 0.9815 0.9736 29 0.9884 0.9867 0.9831 0.9803 0.9696 30 0.9876 0.9851 0.9811 0.9782 0.9659 35 0.9804 0.9784 0.9712 0.9643 0.9356 40 0.9755 0.9731 0.9640 0.9516 0.9092 45 0.9687 0.9639 0.9557 0.9381 0.8813 50 0.9638 0.9567 0.9446 0.9252 0.8577 55 0.9579 0.9507 0.9382 0.9139 0.8320 60 0.9543 0.9451 0.9298 0.9018 0.8073 65 0.9487 0.9384 0.9181 0.8852 0.7832 70 0.9428 0.9330 0.9113 0.8757 0.7670 75 0.9416 0.9296 0.9058 0.8638 0.7514 80 0.9393 0.9264 0.8976 0.8550 0.7392 85 0.9340 0.9227 0.8903 0.8453 0.7267 90 0.9307 0.9168 0.8846 0.8377 0.7186 95 0.9295 0.9139 0.8805 0.8323 0.7068 100 0.9266 0.9104 0.8756 0.8275 0.7001 Table 10. Encroachments passing all the way through terrain (THRTERRAIN).

40 Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers Lane Volume (veh/day) THREOL Rural THREOL Urban Lane Volume (veh/day) THREOL Rural THREOL Urban 500 0.8861 0.9254 12,000 0.7859 0.7971 1,000 0.8893 0.9214 13,000 0.7693 0.7793 2,000 0.8878 0.9137 14,000 0.7513 0.7600 3,000 0.8830 0.9056 15,000 0.7318 0.7391 4,000 0.8765 0.8970 16,000 0.7106 0.7163 5,000 0.8689 0.8877 17,000 0.6876 0.6916 6,000 0.8602 0.8777 18,000 0.6626 0.6648 7,000 0.8504 0.8669 19,000 0.6356 0.6356 8,000 0.8397 0.8551 19,500 0.6212 0.6201 8,500 0.8340 0.8488 20,000 0.6062 0.6039 9,000 0.8280 0.8423 21,000 0.5744 0.5695 10,000 0.8151 0.8285 22,000 0.5400 0.5321 11,000 0.8011 0.8134 ≥23,000 0.5026 0.4914 Table 11. Proportion of vehicles passing across the opposing lanes without striking an opposing vehicle when the vehicle enters the opposing lanes (THREOL).

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The variety of median widths and terrains combined with evolving testing specifications and lack of conclusive data on median crossover crashes have been obstacles to developing median barrier guidance.

The TRB National Cooperative Highway Research Program's NCHRP Research Report 996: Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers develops, in a format suitable for consideration and possible adoption by AASHTO, proposed guidelines for the selection and placement of Manual for Assessing Safety Hardware (MASH) Test Levels 2 through 5 (TL2-TL5) median barriers.

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