Consideration of Roadside Features in the Highway Safety Manual (2022)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

95 CMFROADSIDE DERIVATION The functional form of the ROR prediction method includes two crash modification functions: CMFROADWAY and a CMFROADSIDE. The severity of an ROR crash is assumed to depend on the object struck off the road and not the geometry of the roadway itself. The companion CMFROADSIDE to SPFEDGE is discussed here. CMFROADSIDE is a crash modification function that adjusts for the features of the roadside. Particular crash modification factors used within CMFROADSIDE are chosen for each particular severity. This function predicts an increase or decrease in the frequency of various severity ROR crashes based on the type, density, and offset of roadside features. The roadside crash modification function (i.e., equation (3)) is shown here for convenience: 𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑂𝑂𝐴𝐴𝐴𝐴𝑆𝑆𝐹𝐹𝐴𝐴𝑆𝑆 = �𝛽𝛽𝑆𝑆𝑅𝑅𝐿𝐿𝐴𝐴 ∙ 𝑋𝑋𝑆𝑆𝑅𝑅𝐿𝐿𝐴𝐴 ∙�𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗 𝑏𝑏1 𝑗𝑗=1 � + �𝛽𝛽𝑈𝑈𝑈𝑈𝑆𝑆𝑅𝑅𝐿𝐿𝐴𝐴 ∙ 𝑋𝑋𝑈𝑈𝑈𝑈𝑆𝑆𝑅𝑅𝐿𝐿𝐴𝐴 ∙�𝐶𝐶𝐶𝐶𝐶𝐶𝑏𝑏 𝑏𝑏2 𝑏𝑏=1 � CMFROADISDE takes an additive form because it considers shielded and unshielded edges independently and these edges must sum to one (i.e.., XSHLD + XUNSHLD=1). CMFs that represent characteristics of the longitudinal barriers (i.e., type, offset, etc.) are multiplied only by the first portion of the function since they would affect only those characteristics. Likewise, characteristics that involve the unshielded roadside edges such as fixed objects and terrain are multiplied only by the second portion of the function since they only affect the proportion of the segment edge with those characteristics. Due to this lack of information on barriers located in the medians, the analysis was only conducted for right edges. Limiting the analysis to right edges eliminated the need to understand the type of barriers located in the median. It is recommended that the findings for the right edges be used for the left edges (i.e., median edges) until better information is available for barriers located within the median. The segments used to develop the SPFs were used again here. These segments represent base conditions for each roadway and area type. Table 66 and Table 67 provide the descriptive statistics for the filtered divided and undivided rural highway datasets. Table 68 and Table 69 provide the descriptive statistics for the filtered divided and undivided urban highway datasets. Each table includes the statistics for segment length in miles (L), annual average daily traffic (AADT), and portion of the primary right edge which is shielded (XSHLD on PRE) at the top of the table. The table then includes descriptive crash frequency statistics for crashes occurring on the primary right edge (PRE) for each severity level. As defined above, any vehicle that runs off the road in any sequence of events is included in the crash dataset (ROR). Longitudinal barrier (LB) crashes are defined as any crash where the longitudinal barrier is the first object struck off the road. Other ROR crashes (OC) is essentially all ROR crashes minus LB crashes for each segment. As with the other analyses, all opposing direction events have been transposed to be primary direction events.

96 Table 66. Descriptive Statistics for Rural Divided Dataset. Table 67. Descriptive Statistics for Rural Undivided Dataset. Table 68. Descriptive Statistics for Urban Divided Dataset. Table 69. Descriptive Statistics for Urban Undivided Dataset. Recall that odds is the ratio of the probability of success to probability of failure. For longitudinal barrier crashes using this model, that equals: 𝑆𝑆(𝐿𝐿𝐿𝐿𝑆𝑆𝑆𝑆𝑆𝑆𝑝𝑝 ≤ 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆) 𝑆𝑆(𝐿𝐿𝐿𝐿𝑆𝑆𝑆𝑆𝑆𝑆𝑝𝑝 > 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆) For other crashes using this model, that equals: 𝑆𝑆(𝑂𝑂𝐶𝐶𝑆𝑆𝑆𝑆𝑆𝑆𝑝𝑝 ≤ 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆) 𝑆𝑆(𝑂𝑂𝐶𝐶𝑆𝑆𝑆𝑆𝑆𝑆𝑝𝑝 > 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆) The natural log of the ratio of these two odds is equal to the slope coefficient (β) reported for every model, as shown here: 𝛽𝛽 = ln [ 𝑆𝑆(𝑂𝑂𝐶𝐶𝑆𝑆𝑆𝑆𝑆𝑆𝑝𝑝 ≤ 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆) 𝑆𝑆(𝑂𝑂𝐶𝐶𝑆𝑆𝑆𝑆𝑆𝑆𝑝𝑝 > 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆)⁄ 𝑆𝑆(𝐿𝐿𝐿𝐿𝑆𝑆𝑆𝑆𝑆𝑆𝑝𝑝 ≤ 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆) 𝑆𝑆(𝐿𝐿𝐿𝐿𝑆𝑆𝑆𝑆𝑆𝑆𝑝𝑝 > 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆)⁄ ] K A B C O Total PRE LB crash 14 56 306 184 1414 1974 PRE OC crash 67 204 846 481 2581 4179 Min. 1st Qu. Median Mean 3rd Qu. Max. XSHLD on PRE 0.0000 0.0000 0.0000 0.1641 0.2344 1.0000 K A B C O Total PRE LB crash 9 27 137 67 467 707 PRE OC crash 114 409 1155 552 2459 4689 Min. 1st Qu. Median Mean 3rd Qu. Max. XSHLD on PRE 0.0000 0.0000 0.0000 0.1299 0.1592 1.0000 K A B C O Total PRE LB crash 19 118 528 372 2479 3516 PRE OC crash 50 257 928 652 3349 5236 Min. 1st Qu. Median Mean 3rd Qu. Max. XSHLD on PRE 0.0000 0.0000 0.0909 0.2279 0.3770 1.0000 K A B C O Total PRE LB crash 4 11 44 23 139 221 PRE OC crash 30 157 415 223 941 1766 Min. 1st Qu. Median Mean 3rd Qu. Max. XSHLD on PRE 0.0000 0.0000 0.0000 0.1268 0.1324 1.0000

97 Exponentiating the slope coefficient, as shown below, provides the odds of an OC crash in the less severe direction when compared to an LB crash. When the exponentiated slope coefficient is less than one, the estimated odds of an OC crash in the lower severity direction is less than the estimated odds of an LB crash. When the value is greater than one, the estimated odds of an OC crash in the lower severity direction is greater than the estimated odds of an LB crash. The models are summarized in Table 70 through Table 73. As would be expected, exponentiating the slope coefficient for each model results in a value of less than one. This shows that the estimated odds of an OC crash in the lower severity direction is about that value times the odds for LB crashes. Restated, if an OC crash is observed, it is more likely to be of higher severity then an observed LB crash. Longitudinal barriers appear to be reducing crash severity. Table 70. Rural Divided Highway Longitudinal Barrier to All Other ROR Crashes Proportional Log Odds Modeling Results. Value Std. Error t value Slope Coefficient OC -0.4524 0.06 -7.79 Intercepts K|A -4.6410 0.12 -38.75 A|B -3.1605 0.07 -44.86 B|C -1.4561 0.05 -28.27 C|O -0.9299 0.05 -18.84 Residual Deviance 12554.25 AIC 12564.25 Log Lik -6277.13 multinomial logit model chi sq p-value 0.3685

98 Table 71. Rural Undivided Highway Longitudinal Barrier to All Other ROR Crashes Proportional Log Odds Modeling Results. Value Std. Error t value Slope Coefficient OC -0.5787 0.08 -7.03 Intercepts K|A -4.2774 0.12 -36.27 A|B -2.6742 0.08 -30.83 B|C -1.1589 0.08 -14.74 C|O -0.6749 0.08 -8.69 Residual Deviance 13027.69 AIC 13037.69 Log Lik -6513.84 multinomial logit model chi sq p-value 0.2172 Table 72. Urban Divided Highway Longitudinal Barrier to All Other ROR Crashes Proportional Log Odds Modeling Results. Value Std. Error t value Slope Coefficient OC -0.2999 0.05 -6.53 Intercepts K|A -5.0247 0.12 -40.36 A|B -3.1176 0.06 -54.64 B|C -1.4679 0.04 -37.66 C|O -0.8727 0.04 -23.86 Residual Deviance 17344.21 AIC 17354.21 Log Lik -8672.11 multinomial logit model chi sq p-value 0.3876

99 Table 73. Urban Undivided Highway Longitudinal Barrier to All Other ROR Crashes Proportional Log Odds Modeling Results. Value Std. Error t value Slope Coefficient OC -0.3894 0.14 -2.73 Intercepts K|A -4.4048 0.22 -20.33 A|B -2.5305 0.15 -16.92 B|C -1.0451 0.14 -7.62 C|O -0.5220 0.14 -3.85 Residual Deviance 4788.84 AIC 4798.84 Log Lik -2394.42 multinomial logit model chi sq p-value 0.6659 CMFROADSIDE RESULTS The logit models can be used to estimate the probable severity level of LB and OC crashes using the model form: 𝑖𝑖𝑙𝑙𝑙𝑙𝑖𝑖𝑙𝑙[𝑆𝑆(𝐿𝐿𝐿𝐿𝑆𝑆𝑆𝑆𝑆𝑆𝑝𝑝 ≤ 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆)] = ε𝑆𝑆𝑆𝑆𝑆𝑆𝑗𝑗 + βx, where X=0 for LB and X=1 for OC. The resulting estimates are shown in Table 74 through Table 77. Table 74. Rural Divided Highway Estimated Probability of Crashes by Severity and Type. Table 75. Rural Undivided Highway Estimated Probability of Crashes by Severity and Type. Table 76. Urban Divided Highway Estimated Probability of Crashes by Severity and Type. K A B C O KABCO P(LB) 0.0096 0.0311 0.1484 0.0939 0.7170 1.0000 P(OC) 0.0149 0.0476 0.2057 0.1146 0.6171 1.0000 K A B C O KABCO P(LB) 0.0137 0.0508 0.1744 0.0985 0.6626 1.0000 P(OC) 0.0242 0.0854 0.2494 0.1171 0.5240 1.0000 K A B C O KABCO P(LB) 0.0065 0.0359 0.1449 0.1074 0.7053 1.0000 P(OC) 0.0088 0.0476 0.1808 0.1234 0.6394 1.0000

100 Table 77. Urban Undivided Highway Estimated Probability of Crashes by Severity and Type. The roadside conditions were not measured and modeled in the development of the SPF. There are, therefore, a certain amount of roadside conditions “built” into SPFEDGE and its coefficients. In essence, βSHLD and βUNSHLD represent the “typical” roadsides associated with the straight, flat roads in Ohio and Washington. The objective of this modeling was to determine βSHLD and βUNSHLD for base conditions at each severity level. CMFj and CMFk have been set to unity for this part of the analysis because this modeling was conducted using base segments: 𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑂𝑂𝐴𝐴𝐴𝐴𝑆𝑆𝐹𝐹𝐴𝐴𝑆𝑆|𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑅𝑅𝐹𝐹𝐴𝐴𝑆𝑆 = �𝛽𝛽𝑆𝑆𝑅𝑅𝐿𝐿𝐴𝐴 ∙ 𝑋𝑋𝑆𝑆𝑅𝑅𝐿𝐿𝐴𝐴 ∙�𝐶𝐶𝐶𝐶𝐶𝐶𝑗𝑗 𝑏𝑏1 𝑗𝑗=1 � + �𝛽𝛽𝑈𝑈𝑈𝑈𝑆𝑆𝑅𝑅𝐿𝐿𝐴𝐴 ∙ 𝑋𝑋𝑈𝑈𝑈𝑈𝑆𝑆𝑅𝑅𝐿𝐿𝐴𝐴 ∙�𝐶𝐶𝐶𝐶𝐶𝐶𝑏𝑏 𝑏𝑏2 𝑏𝑏=1 � 𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑂𝑂𝐴𝐴𝐴𝐴𝑆𝑆𝐹𝐹𝐴𝐴𝑆𝑆|𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑅𝑅𝐹𝐹𝐴𝐴𝑆𝑆 = [𝛽𝛽𝑆𝑆𝑅𝑅𝐿𝐿𝐴𝐴 ∙ 𝑋𝑋𝑆𝑆𝑅𝑅𝐿𝐿𝐴𝐴] + [𝛽𝛽𝑈𝑈𝑈𝑈𝑆𝑆𝑅𝑅𝐿𝐿𝐴𝐴 ∙ 𝑋𝑋𝑈𝑈𝑈𝑈𝑆𝑆𝑅𝑅𝐿𝐿𝐴𝐴] for CMFj=CMFk=1 XSHLD and XUNSHLD are the proportion of the segment which is shielded and unshielded respectfully. These values for XSHLD range from 0 to 1 for no shielding to completely shielded. The values for XUNSHLD = 1-XSHLD. It is assumed, based on the definitions used to develop the datasets for LB and OC crashes, that an LB crash can only occur when longitudinal barrier is present. Similarly, an OC crash can only occur when longitudinal barrier is not present. Therefore, the modeled probabilities above will be applied to the CMFROADSIDE model using the proportion of shielded and unshielded segments. The models developed and documented above provide the probability of a longitudinal barrier (LB) crash or a crash of any other ROR type (OC) at each severity level. The probabilities are cumulative, therefore, the values shown for K+A+B+C+O=KABCO. Determining βSHLD and βUNSHLD simply requires adding the values shown in Table 74 through Table 77. The resulting CMFROADSIDE coefficients are shown in Table 78. Table 78. CMFROADSIDE Coefficients. Area Type Highway type Coefficient K KA KAB F+I PDO KABCO Rural Divided βSHLD 0.0096 0.0407 0.1891 0.2830 0.7170 1.0000 βUNSHLD 0.0149 0.0625 0.2682 0.3829 0.6171 1.0000 Undivided βSHLD 0.0137 0.0645 0.2389 0.3374 0.6626 1.0000 βUNSHLD 0.0242 0.1095 0.3589 0.4760 0.5240 1.0000 Urban Divided βSHLD 0.0065 0.0424 0.1873 0.2947 0.7053 1.0000 βUNSHLD 0.0088 0.0564 0.2372 0.3606 0.6394 1.0000 Undivided βSHLD 0.0121 0.0737 0.2602 0.3724 0.6276 1.0000 βUNSHLD 0.0177 0.1052 0.3417 0.4669 0.5331 1.0000 K A B C O KABCO P(LB) 0.0121 0.0617 0.1864 0.1122 0.6276 1.0000 P(OC) 0.0177 0.0875 0.2365 0.1252 0.5331 1.0000

101 CMFROADSIDE is represented graphically in Figure 34 through Figure 37 to allow for a visual assessment. Notice that for each highway type and area type, as the shielding on the x- axis increases, the PDO crashes are expected to increase whereas the injury crashes (F+I) are expected to decrease. This relationship is most prevalent for the undivided roads in both urban and rural areas, which likely is a representation of more stringent implementation of design standards for divided roadways. Figure 34. Rural Divided CMFROADSIDE for the Each Severity Distribution. Figure 35. Rural Undivided CMFROADSIDE for the Each Severity Distribution. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0 0.2 0.4 0.6 0.8 1 C M F R O A D SI D E XSHLD K KA KAB F+I PDO 0.00 0.20 0.40 0.60 0.80 0 0.2 0.4 0.6 0.8 1 C M F R O A D SI D E XSHLD K KA KAB F+I PDO

102 Figure 36. Urban Divided CMFROADSIDE for the Each Severity Distribution. Figure 37. Urban Undivided CMFROADSIDE for the Each Severity Distribution. Longitudinal barriers are intended to reduce the severity of ROR crashes, this effort confirms that longitudinal barriers are preforming as intended. While PDO crashes increase as shielding increases, the number of injury crashes is predicted to decrease for all highway and area types. In summary, the coefficients shown in Table 78 to accompany CMFROADSIDE were developed from well fit models with minimal error. It is recommended that CMFROADSIDE be included in the HSM as a function with CMFj and CMFk as companions. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0 0.2 0.4 0.6 0.8 1 C M F R O A D SI D E XSHLD K KA KAB F+I PDO 0.00 0.20 0.40 0.60 0.80 0 0.2 0.4 0.6 0.8 1 C M F R O A D SI D E XSHLD K KA KAB F+I PDO

103 CMFJ AND CMFK DEVELOPMENT Recall CMFj is a collection of countermeasures which impact the frequency or severity of longitudinal barrier crashes (e.g., offset, barrier type, etc.) and will be applied to the first half of CMFROADSIDE. CMFk is a collection of countermeasures which impact the frequency or severity of crashes on unshielded sections of the roadway. These collections of CMFs were generated using a number of data sources, both collected and simulated. The data itself was assessed using state of the practice techniques for CMF development and discussed above. Each section below discuses the origin and analysis of the data as well as the result. CMFJ for Change to Barrier Type The objective of this CMF is to account for changes to barrier type. A large amount of crash data has been assembled recently for use in developing the RSAPv3 severity measure known as the equivalent fatal crash cost ratio (EFCCR). The EFCCR is developed base on crash data then adjusted for unreported crashes for use in the encroachment probability model employed by RSAPv3. RSAPv3 predicts both reported and unreported crashes, therefore capturing low-severity unreported crashes in the modeling of the EFCCR is essential for the encroachment probability model. The SPFs developed for the HSM are modeled from a database of reported crashes. Thus, the SPFs do not account for low-severity, unreported crashes. The crash data collected for the development of EFCCRs can be used in its unadjusted form, however, to create CMFs which account for changes to barrier type. The crashes coded as a single vehicle (SV) first and only harmful event (FOHE) longitudinal barrier (LB) crashes were isolated from each data set for EFCCR development. SV FOHE were used to ensure the crash severity outcome reflects the crash with the barrier and not interaction with an obstacle prior to or following interaction with the barriers under evaluation. This filtering strategy is appropriate for this CMF development as well. The data assembled originally for EFCCR development, the CMF analysis methodology, and the resulting CMFs are discussed below. Crash Data Barrier inventories and accompanying crash data were made available by the states of Ohio and Pennsylvania for use in NCHRP 22-31, “Selection and Placement Guidelines for Test Level 2 Through Test Level 5 Median Barriers.” The crash database and the longitudinal barrier inventory for Ohio and Pennsylvania were linked to allow for the identification of barrier types involved in the crash. [Carrigan18] NCHRP 22-12(03), “Selection Guidelines for Test Level 2 through Test Level 2 Bridge Railings” assembled crash data for crashes with median barriers and bridge rails then identified the rails involved using photologs. [Ray14] NCHRP 22-27, “Update to the Roadside Safety Analysis Program” conducted a search of the literature to identify in- service performance evaluation studies where the full crash severity distribution and the barrier type was identified by the conducting agency. [Ray12] All of these data have been assembled in Table 79 through Table 86 by barrier type for use in this effort. Please reference the original project reports for details on the data collection and identification of barriers. The project reports have been noted in each table.

104 Table 79. Summary of Crash Severity Distribution Data for Strong Post W-beam. State Reference Barrier Type K A B C O Unk OH 22-31 W-beam 9 46 306 242 2449 WA 22-27 W-beam 15 92 384 535 2754 175 NE 22-12-03 W-beam 2 6 18 17 119 NC 22-27 W-beam 3 5 20 29 132 PA 22-31 W-beam (Strong Post with offset bracket) 12 63 163 506 1788 205 PA 22-31 W-beam (Strong Post with rub rail and offset bracket) 0 5 12 49 182 39 PA 22-31 W-beam (Strong Post) 0 0 1 6 36 4 PA 22-31 W-beam (Strong Post, Double Faced) 0 2 5 16 42 9 Table 80. Summary of Crash Severity Distribution Data for Weak Post W-beam. State Reference Barrier Type K A B C O Unk PA 22-31 W-beam (weak post) 1 14 38 137 857 54 PA 22-31 W-beam (weak post, Double Faced) 0 0 0 6 53 8 Table 81. Summary of Crash Severity Distribution Data for High Tension Cable. State Reference Barrier Type K A B C O Unk WA 22-27 HT Cable 2 1 25 34 474 5 IA 22-27 HT Cable 0 1 0 2 17 0 PA 22-31 HT Cable 0 1 2 14 60 5 Table 82. Summary of Crash Severity Distribution Data for Low Tension Cable. State Reference Barrier Type K A B C O Unk WA 22-27 LT Cable 0 0 1 4 11 4 NC 22-27 LT Cable 0 2 9 28 88 OR 22-27 LT Cable 0 0 0 5 15 6 PA 22-31 LT Cable 0 0 1 1 27 0

105 Table 83. Summary of Crash Severity Distribution Data for New Jersey Shape Barrier. State Reference Barrier Type K A B C O Unk IA 22-12-03 NJ BR 2 28 105 122 475 0 NE 22-12-03 42" NJ BR 2 1 7 18 39 NE 22-12-03 32" NJ BR 1 6 14 14 134 NJ 22-12-03 NJ TL5 MB 0 12 115 342 1198 390 OH 22-31 NJ Slope Short 0 6 27 22 140 OH 22-31 NJ Slope Tall 0 1 7 4 42 OH 22-12-03 36" NJ BR 2 18 109 96 510 9 OH 22-12-03 42" NJ BR 1 19 71 64 324 5 TX 22-27 32" NJ MB 8 115 456 209 890 0 WA 22-12-03 32" NJ MB 2 4 62 112 362 7 Table 84. Summary of Crash Severity Distribution Data for Vertical Rail Barrier. State Reference Barrier Type K A B C O Unk IA 22-12-03 Vertical BR 6 33 85 114 521 0 NE 22-12-03 34" Vertical BR 7 20 43 54 347 Table 85. Summary of Crash Severity Distribution Data for F-shape Barrier. State Reference Barrier Type K A B C O Unk MA 22-12-03 32" F-shape MB 3 4 40 21 77 9 MA 22-12-03 42" F-shape MB 0 0 6 4 23 1 Table 86. Summary of Crash Severity Distribution Data for Single-Slope Barrier. State Reference Barrier Type K A B C O Unk OH 22-12-03 42" SS BR 1 3 29 18 139 3 WA 22-12-03 34" SS MB 0 3 20 28 124 3 These data represent data where the type of barrier involved in the crash can be confirmed using the state inventory or was visually confirmed using the state photologs. Companion CMFs for use with CMFROADSIDE were developed using these data to adjust for the expected change in crash severity if an alternative to w-beam is considered. Methodology The CMF for change to barrier type developed from crash data will use a case-control study. A case-control study is a study in which existing groups with differing outcomes are identified and compared on the basis of some supposed causal attribute. The WHO says “…the choice of controls and cases must not be influenced by exposure status, which should be

106 determined in the same manner for both.”[Bonita06] Lewallen and Courtright (1998) offer additional advice on selecting controls, stating “[c]ontrols should be chosen who are similar in many ways to the cases.” “The selected control group must be at similar risk of developing the outcome.…” [Lewallen98] The WHO suggestion for the design of a case-control study is shown graphically in Figure 38. Figure 38. WHO Suggested Design of a Case-Control Study. [Bonita06] Gross, Persaud, and Lyon (2010), with respect to highway safety studies specifically, indicate “[c]ase-control studies are based on cross-sectional data.” [Gross10] Sites and controls are identified by outcome (e.g., crash or no crash; A+K crash or BCO crash, etc.). The treatment at each site is then determined. The WHO suggestion for the design of a case-control study shown in Figure 38 has been adapted for a study of barrier type where the investigator wishes to study the odds of a crash of a particular severity (e.g., fatal and severe) on a comparison barrier to a crash of that severity on w-beam. This is shown in Figure 38a. Notice that the choice of cases and controls was not influenced by which barrier was involved. This process ensures that the cases and controls were determined using the same approach and that the identification of controls was not influenced by the barrier type, as the WHO warns against. Figure 38a. WHO Suggest Design of Case-Control Study Applied to Barrier Type. Crash Database Cases (KA) Controls (BCO) Other barrier w-beam Other barrier w-beam Direction of Inquiry Time

107 Gross, Persaud, and Lyon (2010) provide a table to capture both the cases and controls. This table is reproduced here as Table 87. This table is accompanied by an equation to determine the odds ratio which references the table, as shown here: Odds Ratio (OR)=CMF= 𝐴𝐴 𝐵𝐵� 𝐶𝐶 𝐴𝐴� = 𝐴𝐴𝐴𝐴 𝐵𝐵𝐶𝐶 Table 87. Tabulation for Simple Case-Control Analysis. [Gross10] Number of Cases Number of Controls With Treatment A B Without Treatment C D After determining the CMFs, the 95% confidence intervals were determined as follows: Results Using the methodology described by Lewallen and Courtright (1998) and by Gross, Persaud, and Lyon (2010), the CMFs were generated along with the 95% confidence intervals. It was decided to combine the crash data available within each group or shape of barrier. For example, the strong post w-beam was considered to be a single group. The weak post w-beam was considered a single group. The high tension cable, low tension cable, f-shape concrete, new jersey shape concrete, etc. were all considered individually, however, a distinction was not made by test level. This allowed for the same shape and materials to be combined and provide more robust results, but does not allow for distinctions between test level barriers. This approach was chosen for many reasons including these data are mostly limited to NCHRP Report 350 barriers and AASHTO is currently implemented barriers developed under MASH. Distinguishing between test levels would provide results inconsistent with the current implementation of MASH. [Ross93; AASHTO09] Further, this study methodology does not consider vehicle types; assessing barrier test level absent of vehicle types is inappropriate. The resulting CMFs are shown in Table 88. W-beam barrier is the base alternative, therefore, every other barrier is compared to w-beam. The results are shown for expected changes to fatal and injury (i.e., F+I or KABC) crashes, changes to KAB, and changes to KA for use with CMFROADSIDE. When the 95% confidence interval includes 1.0, then the results are said to be statistically insignificant. Insignificant results can be used to interpret a trend in behavior, but are not considered robust. The low tension cable, for example, was found to generally be less severe than w-beam, however these results are shown in italic font thus the findings are not statistically significant.

108 Table 88. CMFj for Changes to Barrier Type. Barrier Type KABC CMF (95% C.I.) KAB CMF (95% C.I.) KA CMF (95% C.I.) W-beam 1.00 1.00 1.00 W-beam (weak post) 0.62 (0.53, 0.73) 0.38 (0.29, 0.50) 0.51 (0.30, 0.87) High Tension Cable 0.45 (0.36, 0.57) 0.42 (0.29, 0.60) 0.31 (0.13, 0.75) Low Tension Cable 1.04 (0.76, 1.44) 0.55 (0.31, 0.97) 0.39 (0.10, 1.59) New Jersey Shape 1.50 (1.41, 1.61) 1.73 (1.59, 1.89) 1.38 (1.15, 1.66) Vertical Wall Barrier 1.29 (1.13, 1.47) 1.50 (1.27, 1.76) 2.23 (1.69, 2.95) F-shape Barrier 2.19 (1.63, 2.94) 3.13 (2.27, 4.33) 1.52 (0.71, 3.27) Single-Slope Barrier 1.17 (0.93, 1.48) 1.42 (1.06, 1.90) 0.76 (0.36, 1.62) *CMFs in Italic are not statistically significant. The results of this study show that weak post and high tension cable barriers are generally less severe than w-beam barriers. Concrete barriers, however, are generally more severe than w- beam barriers. These results are consistent with the conventional wisdom on barrier severity. It is critical, however, that these results are interpreted along with the appropriate use and structural limitations of each of these types of barriers. One would not, for example, choose to install a cable barrier in place of a concrete bridge rail to reduce crash severity because the cable barrier is designed to reduce severity by deflecting whereas the concrete is designed to be rigid. A cable barrier could not deflect if used as a bridge rail, therefore, is not appropriate in that situation. While these results are statistically robust, the implementation of these results should be made with caution and a note should be included referencing the user to the AASHTO Roadside Design Guide for the appropriate selection and placement of barriers. CMFK for Change to Roadside Slope The objective of CMF is to account for changes to roadside or median slopes. It was assumed that the probability of rollover on a slope is the same on both the median and roadside slopes (i.e., left and right edges). A study design which distinguishes between vehicles that rollover and vehicles that do not rollover on various slopes is, therefore, desired. Ideally crash data collected on a variety of known sloped terrain which is free of other roadside obstacles (e.g., longitudinal barriers, trees, poles, ledge, etc.) would be used. This ideal situation, however, is not realistic. Steep slopes have routinely been protected by longitudinal barrier for more than forty years leaving only traversable terrain on unprotected roadside. For this reason, simulated trajectory data were favored to allow for the CMF to be independent from other CMFs for roadside features developed in this research or future research. Simulated trajectories generated under previous research for a range of slopes at different encroachment angles and speeds were used. While simulated, this data can be considered cross- sectional in nature. Predicted probabilities of rollover by slope were developed considering those vehicles which rolled over compared to those vehicles which did not roll over by slope. Simulated Trajectory Data The Texas Transportation Institute (TTI) conducted computer simulations for MASH test vehicles to identify the limits of recoverable, traversable, and critical slopes. These simulations

109 were conducted under several ongoing NCHRP projects, including NCHRP 16-05, 17-55, and 22-22(02). The objective of NCHRP 16-05 is to develop guidelines for cost-effective treatments of roadside ditches and appurtenances in order to reduce the severity of ditch crashes. [Bullard16] The objective NCHRP 17-55 is to develop guidelines for what constitutes recoverable, traversable, and critical sideslope conditions considering the characteristics of today’s passenger vehicle fleet. [Sheikh16] The objective of NCHRP 22-22(02) is to produce comprehensive recommendations for placement of barriers on roadside and median slopes. [Bligh16] Toward these objectives, TTI simulated 1,440 MASH small car trajectories which interacted with foreslopes. Foreslope ratios (FS) studied included -10H:1V, -6H:1V, -4H:1V, - 3H:1V, and -2H:1V on foreslope widths (FSW) of either eight or sixteen feet. These trajectories were simulated for a variety of encroachment speeds (i.e., 25, 30, 35, and 40 mph) and angles (i.e., 10, 20, and 30 degrees). TTI graciously provided these simulated trajectories for use in the development of slope CMF. The 1,440 MASH small car trajectories which interacted with the slopes are the study “population.” The rollover and non-rollover events within the population are tabulated for each FS and width in Table 89. These data are shown aggregated across encroachment speed and angle for simplicity. Table 89. Simulated Trajectory Study Population. FSW FS ___H:1V -10 -6 -4 -3 -2 8’ Rollover 26 69 136 181 272 Non-rollover 1,414 1,371 1,304 1,259 1,168 16’ Rollover 88 157 301 466 778 Non-rollover 1,352 1,283 1,139 974 662 Methodology The objective of this study was to develop a CMF for change to the roadside slope. The trajectory data include four categorical variables of interest for predicting rollovers on slopes: foreslope (FS), foreslope width (FSW), encroachment speed, and encroachment angle. FS has five levels, FSW has two levels, encroachment speed has four levels, and encroachments angles have three levels. A factorial study of these factors can therefore be described as FS(5) x FSW(2) x Speed(4) x Angle(3), including 120 groups of rollover and non-rollover outcomes. All of the simulated trajectories in the dataset which interacted with the foreslope were considered either rollover (R) events or non-rollover (NR) events and used to find the log odds. These definitions were used to conceptualize the relationships used in this analysis. The statistical analysis and visual inspection of the data was completed using R. [R16] A visual inspection of the data was conducted and there was an apparent interaction between FS and FSW. The significance of this interaction was explored in the statistical analysis. Other possible interactions appear less obvious under visual inspection, but there was some evidence that the interactions may exist and should be explored. Statistical Analysis A factorial study of both the main effect of these four variables and the replication of the combination of factor levels was conducted. A negative binomial regression function from the

110 MASS package available in R was used to fit the logit model discussed above. [Venables02, R16] The main effects of each factor (i.e., FS, FSW, Speed, and Angle) averaged over the levels of the other factors addressed these questions: 1. FS: Does a change in foreslope impact the probability of rollover? 2. FSW: Does a change in foreslope width impact the probability of rollover? 3. Speed: Does a change in encroachment speed impact the probability of rollover? 4. Angle: Does a change in encroachment angle impact the probability of rollover? Based on the visual analysis of the data, some interaction of factors was anticipated. Three or four-way interactions are also plausible and were also reviewed. Interaction Analysis Starting with the most complex model which included the four-way interactions, the model perfectly separated the probability of rollover into zeros and ones (i.e., rollover or no rollover). While this might sound ideal, in fact it was a reflection of at least one zero in any case in each category of the constructed contingency table. In the simplest case of a 2X2 table, if there is a zero in the 2X2 table an estimate for the regression coefficient does not exist. Imagine a much larger 4X4 table. The four-way interactions were removed from the model. The same phenomenon was observed for the three-way interactions, therefore, the three-way interactions were removed from the model as well. The two-way interactions of FSxFSW, FSxSpeed, and FSxAngle were found to only be significant at the FS level of -2H:1V. It was found that when the FS is equal to -2H:1V and the width increased from eight to sixteen, the probability of a rollover increase by approximately twice (p< 2.53e-09). This is likely reflective of the increased exposure of the vehicle to the slope (i.e., more time on the slope). This analysis showed for the two-way interaction of FSxSpeed that as the encroachment speed increased and all factors are held constant, the probability of a rollover on a -2H:1V slope decreased. This interaction was only significant for the -2H:1V slope. The results showed a variable trend for the other FSxSpeed interactions. Specifically, as the encroachment speed increased, the probability of a rollover varied up and down by speed for different foreslopes. The two-way interactions of FSWxSpeed and FSWxAngle were also found to be significant at limited levels. The two-way interaction of Speed x Angle, however, was not significant at any level. Each of the interactions were removed from the model due to lack of statistical significance. Future analysis may find these interactions are statistically significant, however, that conclusion is not supported by these data. The main effects of each factor (i.e., FS, FSW, Speed, and Angle) remained in the model and were each highly significant while the interactions were not. Main Effects Upon fitting a binomial logit distribution for the main effects on the proportion of rollover and non-rollover data, the error was not binomial as assumed, the model was overdispersed. A quasibinomial model was fit to account for the overdispersion. After correcting for overdispersion, each of the model coefficients remained statistically significant. The coefficients for the minimal adequate model are shown in Table 90. These coefficients are in logits. Changing from logit x to probability were discussed above. The predicted probability of each of these factors is shown in Figure 39.

111 Table 90. Model Coefficients on Rollover Proportion. Estimate Std. Error t value Pr(>|t|) (Intercept) -6.5665 0.462 -14.203 < 2e-16 -6H:1V 0.7809 0.385 2.027 0.0451 -4H:1V 1.6256 0.358 4.544 1.43E-05 -3H:1V 2.2074 0.349 6.324 5.76E-09 -2H:1V 3.0758 0.346 8.894 1.42E-14 FSW=16’ 1.4471 0.175 8.287 3.30E-13 Speed = 30mph 0.6186 0.266 2.326 0.0219 Speed = 35 mph 1.2463 0.255 4.896 3.41E-06 Speed = 40 mph 1.6584 0.251 6.604 1.51E-09 Angle = 20 deg 1.9154 0.235 8.163 6.25E-13 Angle = 30 deg 1.4916 0.237 6.290 6.76E-09

112 a) F or es lo pe F ac to r b) Fo re sl op e W id th F ac to r c) E nc ro ac hm en t S pe ed F ac to r d) En cr oa ch m en t A ng le F ac to r Figure 39. Predicted Probability of Rollover for Population Factors.

113 Summary The probability of rollover has long been exclusively explained by the foreslope alone. This analysis captured the effect of FS and studied how variations in FSW, encroachment speed and encroachment angle also effect the probability of rollover. Only two levels of FSW were available in the data. These two levels show width has a highly significant effect and the effect size is quite large. Sweeping conclusions relative to effect of FSW from this two level factor, however, are not justified, but insight into the future direction of slope-based research was provided. The effect of width increasing from eight to sixteen approximately doubles the probability of a rollover. The interaction of FSW and FS was not found significant, however, the increase in width has a significant effect on slopes of -2H:1V. Future research should be considered to provide guidance on limiting the width of slopes, particularly steep slopes. Encroachment speed and encroachment angle were included at their respective levels and the effect assessed herein. This analysis showed this interaction between encroachment speed and angle is not significant except on steep slopes (i.e., 2:1). Individually, however, these factors were highly significant and the results reported above. As the angle increases from 10 to 20 degrees, the probability of rollover increases. Most interestingly, however, this relationship does not continue as the angle increases from 20 to 30 degrees. Much of the Roadside Design Guide uses guidance based on the encroachment probability model, therefore, encroachment speed and angle are directly considered in that model. These findings show that more analysis of a larger dataset may provide significant interactions of these factors at levels other than -2H:1V. These findings for the main effects are highly significant and have large effect sizes. These findings should be considered useful toward the understanding of slopes. Until such time as it is shown that crash severity varies by slope, it is recommended that the CMF simply account for frequency of crashes of all severity. The unprotected roadsides in Ohio and Washington were found to be traversable, essentially flat slopes, thus the base condition for this CMF was set to -10H:1V or flatter. Exponentiating the model coefficients provides an odds ratio which would traditionally be used a CMF, but that would be incorrect in this case. If the ratio of the probabilities is taken (i.e., a risk ratio), then the CMF could be applied to the entire unprotected roadside without farther adjustment for ROR crash type distribution. Odd ratios are the comparison of events that happen to events which do not happen under two different conditions. If one assumes that the roadside slope does not impact the number of vehicles which leave the road, but is limited in influence to the vehicles which either rollover or not, then risk is appropriate. In this case, the probability of a rollover on a slope is equal to the number of vehicles which rolled over verses all the vehicle which interacted with the slope. When comparing the probability of rollover on a 10:1 and a 2:1, for example, the same number of vehicles interacted with the slope under the same conditions in this simulated study. For these reasons, risk ratios (i.e., probability) were favored over odds ratios. The CMF recommended for inclusion in the HSM for slopes is shown in Table 91. Furthermore, the CMF doubles as an EAF for use in RSAPv3.

114 Table 91. Slope CMF Recommended for the HSM and EAF for use in RSAPv3. xH:1V CMF -10 or flatter 1.00 -6 1.98 -4 3.83 -3 5.68 -2 9.21 CMFJ and CMFK Developed from Simulated Before/After Study Hauer described a before-after approach to the development of CMFs where data was gathered under two conditions and the expected number of crashes for each condition compared. [Hauer97] This before-after approach has been adopted here. The data used in the analysis, however, were simulated using the third version of the Roadside Safety Analysis Program (RSAPv3). [Ray12] A simulated data collection technique is favored here for many reasons, including data collection by states of roadside conditions and assets is only now starting to gain momentum (e.g., many states lack guardrail inventory) so existing inventory data is limited at present. The use of RSAPv3 will allow states to continually apply this procedure to develop additional CMFs as desired. RSAPv3 was the chosen simulation tool because it is used by the AASHTO Technical Committee on Roadside Safety (TCRS) to develop roadside design guidance. The objective of this study was to understand the change in frequency of observed crashes for variations in the roadside conditions. This study design does not consider variations in AADT, but distinguishes between vehicles that crash and vehicles that do not crash given an encroachment for various roadside features. A database of simulated passenger vehicle which encroached onto the roadside were generated using RSAPv3 for a variety of roadside features. The simulated data and a tabulation of the crash and non-crash events within the population provided for future reference in Appendix D: RSAPv3 Simulations. A logistic regression modeling estimated using the maximum likelihood method was assumed to take this form: 𝑦𝑦 = 𝑖𝑖𝑙𝑙 � Crash TRAJ − Crash � = a + bX These definitions were used to conceptualize the relationships used in this analysis. The logit is the log of the odds, thus the ratio of the odds (i.e., odds ratio) for some change in offset, for example, in relation to the base condition for offset is 𝑒𝑒𝛽𝛽𝑖𝑖(𝑋𝑋𝑝𝑝𝑝𝑝𝑜𝑜𝑝𝑝𝑜𝑜𝑝𝑝𝑝𝑝𝑝𝑝−𝑋𝑋𝑏𝑏𝑎𝑎𝑝𝑝𝑝𝑝) . The statistical Where: Crash+Non-Crash=TRAJ = Total vehicle trajectories (TRAJ) per edge are equal to all crash events (C) plus non-crash (NC) events. 𝐶𝐶 𝐴𝐴𝑇𝑇𝐴𝐴𝑇𝑇 − 𝐶𝐶 = Odds of a crash. 𝑁𝑁𝐶𝐶 𝐴𝐴𝑇𝑇𝐴𝐴𝑇𝑇 − 𝑁𝑁𝐶𝐶 = Odds of a non-crash.

115 analysis and visual inspection of the data was completed using the software program R. A regression function from the MASS package available in the R software was used to fit the logit models. [Venables02, R16] CMFJ for Offset to Barriers The coefficients for the model are shown in Table 92. These coefficients are in logits. Table 92. Longitudinal Barrier Model Coefficients on Crash Proportion. Estimate Std. Error z value Pr(>|t|) 2.50% 97.50% (Intercept) 3.2728852 0.01 296.4 <2e-16 3.25128367 3.29456670 Offset -0.0726526 0.00 -230.0 <2e-16 -0.07327262 -0.07203413 CMFK for Narrow Fixed Objects A visual inspection was done and there was not an interaction between offset and density visually apparent. Upon fitting a binomial logit distribution on the proportion of crash and non- crash data, both offset and density were found to be statistically significant predictors of a crash. The coefficients for the model are shown in Table 90. These coefficients are in logits. Table 93. NFO Model Coefficients on Crash Proportion. Estimate Std. Error z value Pr(>|t|) 2.50% 97.50% (Intercept) -2.202E+00 0.00 -1481.50 <2e-16 -2.205E+00 -2.200E+00 Offset -2.814E-02 0.00 -468.90 <2e-16 -2.826E-02 -2.803E-02 Density 4.705E-03 0.00 1295.80 <2e-16 4.698E-03 4.712E-03 CMFK for Miscellaneous Obstacles The interaction between offset and density was not visually apparent. Upon fitting a binomial logit distribution on the proportion of crash and non-crash data, both offset and density were found to be statistically significant predictors of a crash. The coefficients for the model are shown in Table 94. These coefficients are in logits. Table 94. Misc. Model Coefficients on Crash Proportion. Estimate Std. Error z value Pr(>|t|) 2.50% 97.50% (Intercept) -3.107E+00 0.00 -1148.60 <2e-16 -3.113E+00 -3.102E+00 Offset -2.143E-02 0.00 -239.80 <2e-16 -2.161E-02 -2.126E-02 Density 7.728E-04 0.00 1101.30 <2e-16 7.714E-04 7.742E-04

116 Results The base conditions are also summarized here in Table 95. Recalling the relationship for the CMF development, 𝑒𝑒𝛽𝛽𝑖𝑖(𝑋𝑋𝑝𝑝𝑝𝑝𝑜𝑜𝑝𝑝𝑜𝑜𝑝𝑝𝑝𝑝𝑝𝑝−𝑋𝑋𝑏𝑏𝑎𝑎𝑝𝑝𝑝𝑝) and referencing the models developed and documented above, CMFk and CMFj can be completed to account for variations in offset or density from the base conditions. Table 95. Measured Roadside Base Conditions. Area Type Highway Type LB Offset (feet) LB (feet/ mile) NFO Density (#/mile) NFO Offset (feet) Misc. Density (feet/ mile) Mics Offset (feet) Rural Undivided 8.34 558 33 37.56 465 42.25 Divided 10.23 1,645 33 31.34 605 43.99 Urban Undivided 3.89 760 44 16.83 508 15.73 Divided 12.53 630 28 6.98 311 6.76 Calculating the influence any changed offset or density has for use with CMFROADSIDE is accomplished using the relationship 𝑒𝑒𝛽𝛽𝑖𝑖(𝑋𝑋𝑝𝑝𝑝𝑝𝑜𝑜𝑝𝑝𝑜𝑜𝑝𝑝𝑝𝑝𝑝𝑝−𝑋𝑋𝑏𝑏𝑎𝑎𝑝𝑝𝑝𝑝) . Table 96 compiles the coefficients generated above which represent βi. Table 95 is the measured base conditions, a rational number, however, was used for each roadway type to represent xbase. The results for changes to offsets of longitudinal barriers have been summarized in Table 97. The results for changes to offsets in NFOs have been summarized in Table 98 and NFO density in Table 99. Likewise, the results across change to offset or density for miscellaneous obstacles are shown in Table 100 and Table 101. Table 96. Summary of βi for Calculating CMFs. βi 2.50% 97.50% LB Offset -7.265e-02 -7.327e-02 -7.203e-02 NFO Offset -2.814E-02 -2.826E-02 -2.803E-02 NFO Density 4.705E-03 4.698E-03 4.712E-03 Misc. Offset -2.143E-02 -2.161E-02 -2.126E-02 Misc. Density 7.728E-04 7.714E-04 7.742E-04

117 Table 97. Resulting Modifiers for Changes to Offset of Longitudinal Barriers. Offset Rural Xbase Urban Xbase Undiv Div Undiv Div 8 10 4 12 4 1.34 1.55 1.00 1.79 6 1.16 1.34 0.86 1.55 8 1.00 1.16 0.75 1.34 10 0.86 1.00 0.65 1.16 15 0.60 0.70 0.45 0.80 20 0.42 0.48 0.31 0.56 25 0.29 0.34 0.22 0.39 30 0.20 0.23 0.15 0.27 35 0.14 0.16 0.11 0.19 40 0.10 0.11 0.07 0.13 45 0.07 0.08 0.05 0.09 50 0.05 0.05 0.04 0.06 Table 98. Resulting Modifiers for Changes to Offset of NFOs. Offset Rural Xbase Urban Xbase Undiv Div Undiv Div 38 30 17 7 4 2.60 2.08 1.44 1.09 6 2.46 1.96 1.36 1.03 8 2.33 1.86 1.29 0.97 10 2.20 1.76 1.22 0.92 15 1.91 1.53 1.06 0.80 20 1.66 1.32 0.92 0.69 25 1.44 1.15 0.80 0.60 30 1.25 1.00 0.69 0.52 35 1.09 0.87 0.60 0.45 40 0.95 0.75 0.52 0.40 45 0.82 0.66 0.45 0.34 50 0.71 0.57 0.40 0.30

118 Table 99. Resulting Modifiers for Changes to Density of NFOs. Density Rural Xbase Urban Xbase Undiv Div Undiv Div 33 33 44 28 1 0.86 0.86 0.82 0.88 5 0.88 0.88 0.83 0.90 10 0.90 0.90 0.85 0.92 20 0.94 0.94 0.89 0.96 30 0.99 0.99 0.94 1.01 40 1.03 1.03 0.98 1.06 50 1.08 1.08 1.03 1.11 60 1.14 1.14 1.08 1.16 70 1.19 1.19 1.13 1.22 80 1.25 1.25 1.18 1.28 90 1.31 1.31 1.24 1.34 100 1.37 1.37 1.30 1.40 200 2.19 2.19 2.08 2.25 250 2.78 2.78 2.64 2.84 300 3.51 3.51 3.34 3.60 400 5.62 5.62 5.34 5.76 500 9.00 9.00 8.55 9.21 Table 100. Resulting Modifiers for Changes to Offset of Misc. Obstacles. Offset Rural Xbase Urban Xbase Undiv Div Undiv Div 45 45 15 7 4 2.41 2.41 1.27 1.07 6 2.31 2.31 1.21 1.02 8 2.21 2.21 1.16 0.98 10 2.12 2.12 1.11 0.94 15 1.90 1.90 1.00 0.84 20 1.71 1.71 0.90 0.76 25 1.54 1.54 0.81 0.68 30 1.38 1.38 0.73 0.61 35 1.24 1.24 0.65 0.55 40 1.11 1.11 0.59 0.49 45 1.00 1.00 0.53 0.44 50 0.90 0.90 0.47 0.40

119 Table 101. Resulting Modifiers for Changes to Density of Misc. Obstacles. Density Rural Xbase Urban Xbase Undiv Div Undiv Div 450 600 500 300 50 0.73 0.65 0.71 0.82 100 0.76 0.68 0.73 0.86 200 0.82 0.73 0.79 0.93 300 0.89 0.79 0.86 1.00 400 0.96 0.86 0.93 1.08 450 1.00 0.89 0.96 1.12 500 1.04 0.93 1.00 1.17 600 1.12 1.00 1.08 1.26 700 1.21 1.08 1.17 1.36 800 1.31 1.17 1.26 1.47 1000 1.53 1.36 1.47 1.72 2000 3.31 2.95 3.19 3.72 3000 7.18 6.39 6.90 8.06 4000 15.54 13.84 14.95 17.45 5000 33.66 29.97 32.38 37.79 Summary The tables provided above are modifications to the crash frequency. The tables or the functions can be used in conjunction with CMFROADSIDE. As users implement these findings, new RSAPv3 analysis need not be run, but an understanding of either the base conditions or the “before” condition for a particular road can be measured and these analyses used in the same manner.