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54 Discussion of Proposed RDG Occupant Protection Guidelines Appendix B: Proposed RDG Occupant Protection Guide- lines provides a proposal regarding occupant protection for inclusion in a future edition of the RDG. Unlike the AASHTO LRFD Bridge Design Specifications, the RDG does not contain a single section that is applicable only to impacts with bridge piers. The RDG contains guidance applicable to all impacts with roadside objects where the objective is to minimize the risk to a vehicle occupant. In the RDG, a bridge pier is treated like any other fixed object in the clear zone (e.g., utility pole, high-mast light). An objective of NCHRP Project 15-65 (in process) is to âdevelop safety performance-based guidance to address high-priority needs that support quantitative design deci- sions, and that promote consistency in interpretation and implementationâ in anticipation of rewriting a future edi- tion of the RDG [Ray 2017b]. The proposed procedures presented in Appendix B are consistent with the objective of NCHRP Project 15-65 in that they use the risk of a severe or fatal injury crash to quantify the roadside design goal. Further, a workbook approach is anticipated in NCHRP Project 15-65; therefore, the occupant protection guidelines developed under this research are presented using a work- book approach. 4.1 Proposed RDG Guidelines This section presents the development of the procedure for shielding bridge piers for vehicle occupant protection anticipated for inclusion in a future edition of the RDG. Examples and validation with RSAPv3 are provided in Chapter 5. These guidelines are applicable to all bridge pier compo- nents except those that require shielding with a MASH TL-5 rigid barrier in order to protect the pier system according to the AASHTO LRFD Bridge Design Specifications as discussed in the previous chapter. Users are referred to the proposed AASHTO LRFD Bridge Design Specifications, Article 3.6.5, for determining if the bridge pier system requires shield- ing to protect the bridge from collapse due to heavy-vehicle collisions. The general procedure suggested for evaluating bridge piers, as outlined in Table 23, involves finding four values: PVEi = The expected annual number of passenger vehicle encroachments in direction (i) is found using Table 24 knowing the high- way type, traffic volume, and percentage of trucks. Ni = The site-specific adjustment factor is found using Table 15 and the characteristics of the study site. P(C|PVEi) = The probability of a crash given an encroach- ment in direction (i) is found by using Table 25 knowing the pier component offset and size for each direction (i). P(KACUSP|C) = The probability of a severe injury or fatal crash with a bridge pier component given that a crash occurs is found from Table 26 based on the PSL of the roadway. The product of these four values is the estimated annual frequency of severe and fatal injury crashes involving the unshielded pier system. If this value is less than 0.0001 annual fatal and severity injury crashes, the pier system need not be shielded for occupant protection. If this value is greater than or equal to 0.0001 annual fatal and severity injury crashes, the pier system should be shielded with a MASH TL-3 w-beam guardrail. 4.2 Proposed Preliminary RDG Guideline Development As shown in Table 23, estimating the annual number of severe injury and fatal passenger vehicle crashes (AFKA CUSP) involves calculating the following four quantities: C H A P T E R 4
55 1. The annual frequency of passenger vehicle encroachments in each direction (PVEi). 2. The site-specific adjustment factor (Ni). 3. The probability of a crash given a passenger vehicle encroachment [P(C|PVEi)]. 4. The probability of a severe or fatal injury given that a crash with an unshielded pier component has occurred [P(KACUSP|C)]. Once these four values are found, the annual frequency of severe and fatal injury passenger vehicle crashes is found as follows: i i iâ ( ) ( )( )= +ï£®ï£°ï£¯ ï£¹ ï£»ï£º= AF 2 3 PVE PVE KAKA CUSP 1 CUSP n N P C P Ci i m i i The derivation and procedure for calculating each of these quantities is discussed in the following sections. 4.2.1 Annual Frequency of Passenger Vehicle Encroachments: PVEi The procedure for estimating the number of passenger vehicle encroachments for each direction of interest is out- lined in Table 27. The first step in estimating the number of passenger vehicle encroachments is to estimate the base encroachment expected on a typical base segment of the highway. The process of estimating the base encroachments (ENCRBASE) is identical to the process described for heavy vehicles in Section 3.3.1 and summarized in Table 11. The encroachment models given in Table 11 can be used to estimate the number of passenger vehicle encroachments by using the AADT and PT. Also, the encroachment mod- els are based on a 1-mile segment length, but the maximum trajectory length in RSAPv3 based on the collected field tra- jectories in NCHRP Project 17-22 is 300 ft. For fixed-point hazards like bridge piers, only trajectories that depart within 300 ft upstream of the pier are likely to strike the leading component of the pier, so the segment length is 300 ft; the encroachment frequency should therefore be multiplied by 300/5,280 = 0.0568. The encroachment frequencies tabulated in Table 11 are for passenger vehicles at base conditions (i.e., flat, straight sections with 12-ft lanes, no major access points, and 65-mph posted speed limits) for all possible encroachment directions. Each encroachment direction must be evaluated separately, so the total number of encroachments should be divided by four to get one encroachment direction. The Table 23. RDG occupant protection procedure. Find: The annual frequency of severe and fatal passenger vehicle collisions with an unshielded pier system (i.e., AFKA CUSP). This step is not necessary if the LRFD risk-based pier protection procedure determined that a MASH TL-5 rigid barrier is needed. Given: The following traffic and site characteristics for each approach direction where a pier component is exposed to approaching traffic: â¢ The highway type (i.e., divided, undivided, or one-way); â¢ The number of columns in the pier system (n); â¢ Site-specific characteristics like the number of lanes, lane width, major access points, posted speed limit, radius of horizontal curvature, and the grade of the highway; â¢ Total two-way AADT in vehicles/day; â¢ Percentage of trucks (PTi) in each approach direction; â¢ Perpendicular distance in ft from the edge of the travel for each direction of travel to the face of the nearest pier component (Pi); and â¢ Diameter in ft for circular pier columns, the largest cross-sectional dimension for rectangular pier columns or the thickness for pier walls of the pier component (Di) nearest to relative direction of travel, where the offset (Pi) is measured perpendicular to nearest edge of the lane for the travel direction under consideration to the face of the pier. Procedure: Calculate the annual frequency of severe and fatal passenger vehicle collisions with an unshielded pier (AFKA CUSP) as: AF = ( + 2) 3 â â PVE â ( |PVE ) â (KA | ) PVE = ENCR 4 â 300 5,280 â 1 â PT 100 ( |PVE ) = . . . 1 + . . . (KA | ) = 2.3895 â 10â 7 â PSL If AFKA CUSP > 0.0001, Then Shield with a MASH TL-3 guardrail for occupant protection, Else The pier system may remain unshielded.
56 Two-Way AADT Undivided Highways PT veh/day 5 10 15 20 25 30 35 40 1,000 0.0165 0.0157 0.0148 0.0139 0.0130 0.0122 0.0113 0.0104 2,000 0.0268 0.0254 0.0240 0.0226 0.0212 0.0198 0.0183 0.0169 3,000 0.0326 0.0309 0.0292 0.0275 0.0258 0.0240 0.0223 0.0206 4,000 0.0353 0.0334 0.0316 0.0297 0.0279 0.0260 0.0241 0.0223 5,000â41,000 0.0358 0.0339 0.0320 0.0301 0.0282 0.0264 0.0245 0.0226 42,000 0.0371 0.0351 0.0332 0.0312 0.0293 0.0273 0.0254 0.0234 43,000 0.0380 0.0360 0.0340 0.0320 0.0300 0.0280 0.0260 0.0240 44,000 0.0389 0.0368 0.0348 0.0327 0.0307 0.0286 0.0266 0.0245 45,000 0.0397 0.0377 0.0356 0.0335 0.0314 0.0293 0.0272 0.0251 â¥46,000 0.0406 0.0385 0.0364 0.0342 0.0321 0.0299 0.0278 0.0257 Two-Way AADT Divided Highways PT veh/day 5 10 15 20 25 30 35 40 1,000 0.0114 0.0108 0.0102 0.0096 0.0090 0.0084 0.0078 0.0072 5,000 0.0485 0.0459 0.0434 0.0408 0.0383 0.0357 0.0332 0.0306 10,000 0.0789 0.0747 0.0706 0.0664 0.0623 0.0581 0.0540 0.0498 15,000 0.0962 0.0912 0.0861 0.0810 0.0760 0.0709 0.0658 0.0608 20,000 0.1044 0.0989 0.0934 0.0879 0.0824 0.0769 0.0714 0.0659 24,000â47,000 0.1062 0.1006 0.0950 0.0894 0.0838 0.0782 0.0727 0.0671 50,000 0.1143 0.1082 0.1022 0.0962 0.0902 0.0842 0.0782 0.0722 55,000 0.1257 0.1191 0.1125 0.1058 0.0992 0.0926 0.0860 0.0794 60,000 0.1371 0.1299 0.1227 0.1155 0.1082 0.1010 0.0938 0.0866 65,000 0.1485 0.1407 0.1329 0.1251 0.1173 0.1094 0.1016 0.0938 70,000 0.1600 0.1515 0.1431 0.1347 0.1263 0.1179 0.1094 0.1010 75,000 0.1714 0.1624 0.1533 0.1443 0.1353 0.1263 0.1173 0.1082 80,000 0.1828 0.1732 0.1636 0.1540 0.1443 0.1347 0.1251 0.1155 85,000 0.1942 0.1840 0.1738 0.1636 0.1533 0.1431 0.1329 0.1227 â¥ 90,000 0.2057 0.1948 0.1840 0.1732 0.1624 0.1515 0.1407 0.1299 â Encroachment data are not available for one-way roadways.Traditionally, one-way roadways have been evaluated using the encroachment model for divided highways.The one-way AADT value should be multiplied by 2 and used to determine PV ENCRDIV BASE for use in the remaining calculations. Table 24. Base annual passenger vehicle encroachments in direction (i ): PVEi.â Offset (ft) Pier Column Size (ft) 1 2 3 4 6 2 0.1125 0.1242 0.1369 0.1507 0.1818 4 0.1066 0.1178 0.1300 0.1432 0.1730 6 0.1011 0.1117 0.1233 0.1360 0.1646 8 0.0957 0.1059 0.1170 0.1291 0.1565 10 0.0907 0.1004 0.1109 0.1225 0.1487 15 0.0790 0.0876 0.0970 0.1073 0.1307 20 0.0688 0.0763 0.0846 0.0937 0.1146 25 0.0598 0.0664 0.0737 0.0817 0.1002 30 0.0519 0.0577 0.0641 0.0712 0.0875 35 0.0450 0.0501 0.0557 0.0619 0.0762 40 0.0390 0.0434 0.0483 0.0537 0.0663 ( |PVE ) = . . . 1 + . . Pi = Offset to critical pier component in direction (i) in ft where the distance is from the face of the critical pier component to the closest edge of travel lane (i ). Di = Size of the critical component of the pier in direction (i) where size is either the diameter of the critical circular column or the smallest cross-sectional dimension of a rectangular column. Table 25. Probability of a collision given a passenger vehicle encroachment: P(C îºPVEi). Posted Speed Limit (mph) P(KACUSP|C) Posted Speed Limit (mph) P(KACUSP|C) â¥75 0.1008 50 0.0299 70 0.0820 45 0.0218 65 0.0656 40 0.0153 60 0.0516 35 0.0102 55 0.0398 30 0.0065 â¤25 0.0037 Table 26. Probability of a severe or fatal injury given a crash with an unshielded pier component occurs: P(KACUSPîºC).
57 smoothed Cooper data used in the heavy-vehicle portion of the guidelines is also used here for the same reasons. Heavy- vehicle encroachments were already considered in the LRFD portion of the guidelines; therefore, only passenger vehicles are considered in this step. The passenger vehicle encroach- ment frequency in direction i for a highway segment 300 ft upstream of a bridge pier can be written as: i i= ï£® ï£°ï£¯ ï£¹ ï£»ï£º ï£® ï£°ï£¯ ï£¹ ï£»ï£º â ï£® ï£°ï£¯ ï£¹ ï£»ï£º ï£® ï£°ï£¯ ï£¹ ï£»ï£º PVE ENCR 4 300 5,280 1 PT 100 BASE i The values for PVEi in Table 24 were generated using this equation. 4.2.2 Site-Specific Adjustment Factor: Ni The value of PVEi is the expected number of passenger vehicle encroachments under base conditions. Base condi- tions can be adjusted up or down based on the particular characteristics of the site and traffic using the site-specific adjustment factor (Ni). The procedure to calculate Ni for the occupant protection guidelines is exactly the same as was discussed for the LRFD procedures in Section 3.3.2 and outlined in Table 14. Details about the development of the site-specific encroachment adjustment factors used in this step can be found in the RSAPv3 Engineerâs Manual [Ray 2012], the final report for NCHRP Project 22-12(30) [Ray 2014b], and the final report for NCHRP Project 17-54 [Carrigan 2017]. Each site-specific adjustment factor (Ni) should be calcu- lated for each direction of possible encroachment (i) using the values in Table 15. Recall that the direction number (i = 1, 2, 3, etc.) is arbitrary, but the site-specific adjustment must always be matched to the offset (Pi) and traffic characteristics (PTi, PVEi, etc.) that are also associated with that direction of travel in later steps. 4.2.3 Probability of a Crash Given a Passenger Vehicle Encroachment: P(C îºPVEi) Now that the annual frequency of passenger vehicle encroachments (i.e., PVEi, Ni) at the study location is known, the probability of any particular passenger vehicle encroach- ment striking a pier component [P(C|PVEi)] can be esti- mated as outlined in Table 28. A process similar to that described in Section 3.3.2 for esti- mating the conditional probability of heavy vehicles striking a pier component is followed here for passenger vehicles. RSAPv3 simulations were performed with the leading pier column offset distance between the edge of the nearest lane and the face of the nearest pier component varied in 2-ft increments. The objective of this effort was to determine the conditional probability of a crash with a pier component, given an encroachment [P(C |PVEi)] when the size of the pier component and the offset to the pier component are known. It has been assumed that the probability of observing a crash, given an encroachment has occurred, is the same on both the median and roadside. A study design that distinguishes between vehicles that crash and vehicles that do not crash given an encroachment for various pier offsets and sizes is, therefore, desired. A database of simulated passenger vehicle trajectories that encroached onto the roadside within 300 ft of the pier component was generated using RSAPv3 [Ray 2016] for a variety of pier component offsets and diameters. This database is what statisticians refer to as cross-sectional dataset. The predicted probability of a passenger vehicle crash by pier component offset and diameter was then determined. RSAPv3 was used to simulate 549,120 passenger-vehicle encroachment trajectories within 300 ft of a critical pier component where the component of interest was a single pier Find: The base annual frequency of passenger vehicle encroachments for the pier system under consideration. Given: The following traffic and site characteristics for each approach direction where a pier component is exposed to approaching traffic: â¢ The highway type (i.e., divided, undivided, or one-way), â¢ Total two-way AADT in vehicles/day, and â¢ PT. Procedure: Calculate the base annual frequency of passenger vehicle collisions with an unshielded pier component from each direction of travel as follows: PVE = ENCR 4 â 300 5,280 â 1 â PT 100 Repeat this step for each direction of travel where a pier component is exposed to approaching traffic. Table 27. Procedure to find the passenger vehicle encroachments: PVEi.
58 column with a variable diameter. The pier component was studied at a variety of offsets measured from the edge of the travel lane to the pier face. These discrete offsets (4, 6, 8, 10, 15, 20, 25, and 30 ft) were considered for four pier column diameters (1, 2, 3, and 4 ft). The 549,120 passenger-vehicle encroachment trajectory study population is tabulated in Table 29. The trajectory data include two variables of interest for crashes with piers: offset and diameter. The probability of a crash given an encroachment [P(C|PVEi)] with any pier is simply the portion or percentage of the vehicle type of interest that strikes the pier component divided by the total number of the vehicle type of interest that encroaches onto the roadside and does not crash. Proportional data are strictly bounded between 0% and 100%. No less than 0% of the vehicles encroaching will avoid the crash, and no more than 100% of the encroachment vehicles will have a crash. A logistic curve reaches asymptotes of 0 and unity; there- fore, it prevents the model from fitting negative proportions and proportions greater than unity. Log odds provide an appropriate solution for regression, model ing a line fit using the maximum-likelihood method, as shown here: ï£« ï£ï£¬ ï£¶ ï£¸ï£· = +ln C N a bX where C = Number of encroachments that resulted in a crash. N = Number of encroachments where no crash occurred. C N = Odds of a crash. All of the encroachment trajectories in this dataset were considered either crash events (C) or non-crash events (N). These definitions were used to conceptualize the relationships used in this analysis. The statistical analysis and visual inspec- tion of the data were completed using the software program R [R Core Team 2016]. Find: The probability of a collision given a passenger vehicle encroachment with an unshielded pier [P(C|PVEi)] for the pier system under consideration. Given: The following traffic and site characteristics for each approach direction where a pier component is exposed to approaching traffic: â¢ The highway type and layout (i.e., divided, undivided, or one-way); â¢ Perpendicular distance in ft from the edge of the travel lane for each direction of travel to the face of the nearest pier component (Pi); and â¢ Diameter in ft for circular pier columns, the largest cross-sectional dimension for rectangular pier columns, or the thickness for pier walls of the pier component (Di) nearest to relative direction of travel, where the offset (Pi) is measured perpendicular to nearest edge of the lane for the travel direction under consideration to the face of the pier. Procedure: Calculate the probability of a collision given a passenger vehicle encroachment with an unshielded pier [P(C|PVEi)] for the pier system under consideration as follows: ( |PVE ) = . . . 1 + . . . Repeat this step for each direction of travel where a pier component is exposed to approaching traffic. Table 28. Procedure to find the probability of a collision given a passenger vehicle encroachment: P(C |PVEi) Offset (ft) Outcome Diameter (ft) 1 2 3 4 4 Crash 1,850 2,091 2,326 2,560 Non-crash 15,310 15,069 14,834 14,600 6 Crash 1,761 1,981 2,208 2,317 Non-crash 15,399 15,179 14,952 14,843 8 Crash 1,623 1,769 1,978 2,175 Non-crash 15,537 15,391 15,182 14,985 10 Crash 1,510 1,674 1,899 2,051 Non-crash 15,650 15,486 15,261 15,109 15 Crash 1,258 1,429 1,501 1,696 Non-crash 15,902 15,731 15,659 15,464 20 Crash 1,180 1,333 1,496 1,655 Non-crash 15,980 15,827 15,664 15,505 25 Crash 1,102 1,168 1,299 1,430 Non-crash 16,058 15,992 15,861 15,730 30 Crash 879 1,013 1,131 1,227 Non-crash 16,281 16,147 16,029 15,933 Table 29. Simulated passenger-vehicle encroachment trajectory study population.
59 The probability of a crash for each level of offset and diameter was determined as shown in Figure 32. The depen- dent variable [P(C|PVEi)] is shown on the y-axis. The main effects of the independent variables are shown on the x-axis. A two-way interaction between variables is said to be present when the effect of one variable differs depending on the level of another variable. There appears to be little if any interaction between the offset and diameter variables. A regression function from the MASS package available in the R software was used to fit the logit model discussed previously [Venables 2002, R Core Team 2016]. Based on the visual analysis of the data shown in Figure 32, modeling interaction between the variables was not considered neces- sary. On fitting a binomial logit distribution on the propor- tion of crash and non-crash data, both offset and diameter were found to be statistically significant predictors of a crash. The coefficients for the passenger vehicle model are shown in Table 30. These coefficients are in logits. The process for changing from logit x to probabilities was discussed pre- viously. The predicted probability is shown graphically in Figure 33 for the model. The predicted probability of a crash over a range of offsets and diameters is tabulated in Table 25 for the passenger vehicle model. The probability of a crash given a passenger vehicle encroachment [P(C |PVEi)] can now be written by inserting the coefficients found in Table 30 into the equation shown earlier, as follows: ( ) = + = + Î² +Î² +Îµ Î² +Î² +Îµ â + â â + â PVE 1 1 0.0300 0.1122 2.1177 0.0300 0.1122 2.1177 P C e e e e i P D P D P D P D P i D i P i D i i i i i Probabilities of a passenger vehicle colliding with a bridge pier column as function of column diameter and offset from the edge of lane are shown in Table 25 based on this equation. Figure 34 is a plot of the observed probability of a crash for each simulated diameter and offset, with an overlay of the predicted probability of a crash. These predicted probabilities closely track the observed probabilities; therefore, this model is a good representation of the observed data. This model is suggested to be used to represent the probability of a passen- ger vehicle crash, given a passenger vehicle encroachment, for a variety of offsets and diameters. Figure 32. Observed probability of crash by offset and diameter. Estimate Std. Error z Value Pr(>|t|) 2.50% 97.50% (Intercept) -2.1177 0.01 -154.22 <2e - 16 -2.1447 -2.0908 Offset -0.0300 0.00 -53.98 <2e - 16 -0.0311 -0.0289 diameter 0.1122 0.00 27.16 <2e - 16 0.1041 0.1203 Table 30. Passenger-vehicle model coefficients on crash proportion. Figure 33. Predicted probability of crash by offset and diameter.
60 4.2.4 Probability of a Severe or Fatal Crash Given a Collision with an Unshielded Pier Component: P(KACUSP|C) Next a model for the conditional probability of a severe or fatal (KA) crash with a pier component given a collision has occurred [P(KACUSP|C)] is needed. Models for the probability of a vehicle encroaching onto the roadside or median and the conditional probability of a collision given an encroach- ment have been described previously. This section uses the available crash data and extends the equivalent fatal crash cost ratio (EFCCR) procedure used in RSAPv3 to develop the conditional probability [P(KACUSP|C)]. First, the EFCCR procedure and the extension of that procedure are discussed, and then the methodology is applied to the available bridge- pier crash data. Finally, P(KACUSP|C) is documented for use in the proposed guidelines. 18.104.22.168 Methodology The severity model developed and used in RSAPv3, the EFCCR, is based on observed police-reported crashes that are adjusted to account for unreported crashes and scaled to account for speed effects. The process for developing an EFCCR for any hazard was documented by Ray et al., who explained that the process for developing an EFCCR included the following five steps: 1. Isolate a census of police-reported crashes with a particu- lar feature over a range of posted speed limits. 2. Determine the crash severity distribution for crashes that do not have harmful events preceding or following the impact with the hazard under evaluation and do not result in a penetration or rollover. 3. Determine or estimate the percentage of unreported crashes, and add these crashes to the reported crash sever- ity distribution. 4. Calculate the average crash cost of the severity distribution for each posted speed limit and determine the EFCCR, and 5. Adjust for speed effects by determining the EFCCR for a baseline posted speed of 65 mph (i.e., EFCCR65) [Ray 2014a]. The resulting tabulation of data includes the number of crashes by each discrete severity level (i.e., K, A, B, C, and O) as well as the estimated unreported crashes and total crashes across a range of posted speed limits. Including an estimate of unreported crashes ensures that the higher-severity crashes are not overpredicted [Ray 2012]. While RSAPv3 uses the continuous measure of crash severity (i.e., EFCCR) to facilitate benefitâcost analysis, this risk-based procedure requires an estimate of the probability of a KA crash and is not concerned with estimating costs, so the EFCCR procedure was extended to calculate P(KA|C) while maintaining the calculation of unreported crashes and adjustments for speed using a similar five-step process to that shown previously. In this extension of the procedure, rather than calculating an EFCCR for each posted speed limit within each dataset, the conditional probability P(KACUSP|C) is deter- mined for the entire sample. EFCCR Step 5 is carried forward to determine the speed-weighted probability of a KA crash given a collision at a base PSL of 65 mph [P(KACUSP|C)65]. The value for P(KACUSP|C)65 is calculated based on observed crash data using the following five-step process adapted from the EFCCR method: 22.214.171.124 Step 1: Census of Police-Reported Crashes Data from five states were reviewed for bridge pier colli- sions. The states/agencies and data collection years used were: â¢ Ohio Highway Safety Information System (HSIS): 2000â2012 â¢ Washington: 1993â1996 and 1999â2011 â¢ New Jersey Transit Authority: 2001â2013 â¢ North Carolina HSIS: 2003â2012 â¢ Wyoming: 2008â2013 The data for each state were screened in order to identify crashes where a bridge pier collision was the first and only collision in the crash sequence. These types of single-event bridge-pier crashes are referred to as âcleanâ crashes since they only involve a collision with a bridge pier. Each state codes crashes in a slightly different manner. The screening procedure used for each state is listed in the following. Ohio. Any crash records with code â27 â Bridge Pier or Abutmentâ in any of the Events 1â4 were coded as being bridge-pierârelated crashes. Out of these crashes, only those that had â27â in Event 1 and nothing afterward or had Figure 34. Observed and predicted probability of a crash by offset and diameter.
61 â8 â Ran off road right,â â9 â Ran off road left,â â10 â Cross median/centerline,â or â11 â Downhill runawayâ in Event 1 followed by â27â in Event 2 and a blank in Event 3 were con- sidered clean bridge-pier crashes. Washington. Any crash records with code â12 â Bridge Column, Pier, or Pillarâ in either the Object 1 or Object 2 fields were coded as being bridge-pierârelated crashes. (The Events 1â4 fields are used differently in Washington than in most states.) Out of these crashes, only those that had â12â in Object 1 followed by a blank in Object 2 were considered to be clean bridge-pier crashes. New Jersey. Any crash records with code â43 â Bridge Pier or Supportâ in any of Events 1â4 were coded as being bridge-pierârelated crashes. Out of these crashes, only those that had â43â in Event 1 followed by nothing or had codes â05 â Ran Off Road â Right,â â06 â Ran Off Road â Left,â â07 â Crossed Median/Centerline,â or â08 â Downhill Runawayâ followed by â43â and nothing after were considered clean bridge-pier crashes. North Carolina. Any crash records with code â52 â Pier on Shoulderâ or â53 â Pier on Medianâ in any of Events 1â4 were coded as being bridge-pierârelated crashes. Out of these crashes, only those that had â52â or â53â in Event 1 fol- lowed by nothing, or had codes â01 â Ran Off Road â Right,â â02 â Ran Off Road â Left,â â03 â Ran Off Road â Straight,â â06 â Crossed Median/Centerline,â or â07 â Downhill Run- awayâ followed by â43â and nothing after were considered clean bridge-pier crashes. Wyoming. These crash records were provided by the Wyoming DOT based on the assumption that they repre- sented clean bridge-pier crashes, as defined previously. Initial examination of the data revealed that there were numerous miscoded crash locations. In order to isolate the crash severity of just the bridge pier, it was necessary to verify (1) that there was a bridge pier at the crash locations and (2) the bridge pier was not shielded by longitudinal barriers of any type. The crash data include the route and milepost of each clean bridge-pier crash. Using this information, the corresponding stateâs photologs for the nearest year were viewed to determine if there was, in fact, an unshielded bridge pier at that location. The top row in Figure 35 shows several typical examples of bridge pier collision locations from the Washington State photologs. Figure 35(A) shows what was intended for bridge pier crash locations to be used in the analysis; the pier is exposed and unprotected. These types of pier locations accounted for only 20% of the cases in Washington State. Figure 35(B) and Figure 35(C) show several other locations where the pier was protected by a barrier: a w-beam guardrail in the case of Figure 35(B) and a cable median barrier in the case of Figure 35(C). Even though the vehicle would have had to strike and penetrate or vault over the barrier, the reporting police officer coded the cases such that the only object struck was a bridge pier. In other words, the police officer neglected to include the collision with the protecting guardrail. Unfortu- nately, 39% of the single-event cases in Washington appeared to have an unrecorded collision with a barrier prior to the pier collision and had to be excluded. Another 40% did not appear to involve bridge piers at all but were miscoded bridge railings or bridge abutments. The situation for the Ohio data was even more discourag- ing, as shown by the examples in the second row of Figure 35. More than 70% of the collision locations in Ohio were similar to Figure 35(D), where there was no apparent bridge pier at the site. In these cases, it appears that the reporting police officer miscoded bridge railings or abutments as bridge piers. Figure 35(E) and Figure 35(F) show that, like in Washington, the protecting barrier was often not included in the sequence of eventâs codes. Another 20% appeared to be bridge piers protected by some type of longitudinal barrier. Only 10% of the cases in Ohio were truly unprotected pier locations with a single crash event involving a bridge pier. An updated dataset of crash cases where the location was verified to be either an unprotected pier or a pier protected by a barrier was assembled for New Jersey, North Carolina, Ohio, Wyoming, and Washington State. Table 31 shows the results for the calculated EFCCR65 based on the verified crash locations. Washington State yielded the highest EFCCR65 value (0.3303) for unprotected piers, and New Jersey yielded the lowest (0.0075). Data from all five states were combined and re-analyzed as shown in Table 31. For bridge piers that were unprotected and were the only object struck, the EFCCR65 was found to be 0.0784. 126.96.36.199 Step 2: Severity Distribution The datasets developed in Step 1 for each state are sum- marized by crash severity level in Table 32 through Table 36 for first and only harmful events (FOHEs) with unshielded bridge piers. As earlier, crash severity is represented in these datasets using the KABCO scale, where the maximum injury of a crash is reported. K is taken to equal a fatal crash, A is an incapacitating injury crash, B is a non-incapacitating injury crash, C is a possible injury crash, and O is a property- damageâonly crash. Not surprisingly, the distributions are different for different speeds, partly due to exposure and partly due to speed. For example, the higher speed limits (e.g., 55 mph and above) would be representative of controlled- access facilities where one might expect more bridges, larger offsets, and wider clear zones.
62 (A) WA Case (B) WA Case (C) WA Case (D) OH Case (E) OH Case (F) OH Case Figure 35. Typical bridge-pier crash locations in Washington State and Ohio.
63 State/Years Number Reported Cases Number Estimated Unreported EFCCR65 Bridge Pier First and Only Object Struck NJ 2001â2013 25 72 0.0075 NC 2003â2012 52 72 0.0889 OH 2000â2012 86 203 0.0623 WA 1993â1996 and 1999â2011 46 60 0.3303 WY 2008â2013 30 113 0.0473 Combined 239 520 0.0784 Table 31. Summary of bridge pier EFCCRs. PSL K A B C O Unknown Row Totals 65 1 2 3 1 6 0 13 55 0 5 7 2 11 0 25 50 0 0 1 1 0 0 2 45 0 0 0 2 1 0 3 40 0 1 1 1 1 0 4 35 2 3 3 3 7 0 18 25 0 3 6 2 10 0 21 Column Totals 3 14 21 12 36 0 86 Table 32. Ohio FOHE bridge pier: 2000â2012. PSL K A B C O Unknown Row Totals 70 2 0 1 1 0 0 4 60 4 1 2 1 4 0 12 55 1 0 1 1 3 2 8 35 0 1 4 1 2 0 8 30 0 0 0 1 4 0 5 25 1 0 2 1 5 0 9 Column Totals 8 2 10 6 18 2 46 Table 33. Washington FOHE bridge pier: 1993â1996 and 1999â2011. PSL K A B C O Unknown Row Totals 65 0 0 1 1 2 0 4 55 0 0 1 0 0 0 1 50 0 0 1 0 0 0 1 40 0 0 0 0 1 0 1 35 0 0 0 0 3 0 3 30 0 0 0 0 1 0 1 25 0 0 1 5 8 0 14 20 0 0 0 0 0 0 0 Column Totals 0 0 4 6 15 0 25 Table 34. New Jersey FOHE Bridge Pier: 2001â2013.
64 188.8.131.52 Step 3: Estimate Unreported Crashes Step 3 of the EFCCR procedure includes the determination or estimation of the percentage of unreported crashes. These values are added to the field-observed crashes to obtain the full distribution of both reported and unreported crashes. Crash reporting thresholds vary by state, with some states only requir- ing reports when there is an injury. It has long been recognized that police-reported crash data underreport lower-severity crashes. âThese low-severity crashes represent roadside design successes since the vehicle was able to encroach onto the road- side or median without causing an injuryâ [Ray 2014a]. When the EFCCR approach was developed, it included a step for esti- mating unreported crashes to account for this bias. The same estimating procedure is used here for the same reasons. Unreported crashes have been addressed in several research studies, including the FHWA Pole Study [Mak 1980], NCHRP Report 490 [Ray 2003] and NCHRP Report 638 [Sicking 2009]. Blincoe estimated that, for all types of highway crashes, nearly half (48%) of all property-damageâonly (PDO) crashes and a little over 20% (21.42%) of injury crashes were not reported [Blincoe 2002]. It has been found that the unreported rate is different for different types of roadside objects. For example, 77% of con- crete barrier crashes were unreported [Fitzpatrick 1999], while 34% of low-tension cable barrier crashes were unreported [Hammond 2008]. Building on a model developed by Nilsson [Nilsson 1981], Ray et al. estimated the percentage of noninjury crashes (PNIC) by comparing crashes at two speeds [Ray 2014a], as follows: ( )= â â ï£® ï£°ï£¯ ï£¹ ï£»ï£º = â ï£® ï£°ï£¯ ï£¹ ï£»ï£º 1 1 1NI2 NI1 2 1 2 1 2 1 2 P P V V P V V I This expression allows the unobservable percentage of non injury crashes to be estimated based on the number of observed injury crashes. Next, the percentage of unreported and PDO crashes, which is either known or assumed at the base speed of 65 mph, is used to extrapolate to all other speeds. When the estimate produces no negative crash esti- mates, the estimate is balanced and has reached the maxi- mum-likelihood estimate of total crashes for the dataset [Ray 2014a]. A summary of the total number of reported FOHE unshielded bridge-pier crashes from each dataset is shown in Table 37. The maximum-likelihood estimate of unreported crashes for each dataset resulted in assumed percentage of injury (PI) crashes to total crashes at the 65-mph PSL. PI crashes within each dataset are also shown in Table 37. These values are used to estimate the unreported crashes by comparing the observed PI to the estimated PI and extrapolating to find the corrected percentage of non- injury crashes that include the unreported crashes. The unreported crash counts by dataset and PSL are shown in PSL K A B C O Unknown Row Totals 70 1 1 0 4 1 0 7 65 2 1 1 3 8 0 15 60 0 0 0 1 0 0 1 55 0 0 0 0 3 0 3 45 0 1 4 1 6 0 12 40 0 0 1 0 0 0 1 35 0 0 5 3 4 1 13 Column Totals 3 3 11 12 22 1 52 Table 35. North Carolina FOHE bridge pier: 2003â2012. PSL K A B C O Unknown Row Totals 75 1 0 1 0 2 0 4 65 0 0 3 0 6 0 9 40 0 0 0 0 4 1 5 35 0 0 0 0 2 1 3 30 0 0 5 0 2 0 7 20 0 0 1 0 1 0 2 Column Totals 1 0 10 0 17 2 30 Table 36. Wyoming FOHE bridge pier: 2008â2013.
65 Table 38. Counts are not estimated when there are no data at a PSL level; therefore, some cells in Table 38 contain no values. 184.108.40.206 Revised Step 4: Determine Probability of a Crash In this extension of the procedure, rather than calculat- ing an EFCCR in Step 4 for each PSL level within each data- set, P(KACUSP|C) is determined. Carrigan and Ray discuss the transformation of crash severity to a probability and conclude, based on a review of available literature, that the ârisk of an incapacitating or fatal crash (%KA) involving roadside hard- ware is simply the portion or percentage of all crashes involving that hardware type that result in fatal or severe injuries. The absolute risk when defined this way is also the probability of observing a KA crash given all crash severitiesâ [Carrigan 2016]. P(KACUSP|C) can therefore be found by summing the total num- ber of KA crashes in the data and dividing by the total num- ber of all crashes of all severities plus the estimated unreported crashes from Step 3, as shown here: â â ( ) ( ) = + KA KA KABCO UR CUSP PSL=25 PSL=75 PSL=25 PSL=75 P C Where KA = Number of police-reported severe and fatal injury crashes in each posted speed limit cate- gory (PSLi), KABCO = Number of police-reported crashes of all severi- ties in each PSLi, and UR = Estimated number of unreported crashes in each PSLi. The results of this calculation for each posted speed limit level within each dataset and within the combined dataset are shown in Table 39. In some cases, there were no observed crashes at a posted speed limit level; therefore, the calcula- tion could not be performed. In these cases, the cells in the table have no values. In other cases, there are no observed severe or fatal crashes; however, crashes of other severities are observed. In these cases, the probability calculation results in a value of 0, so a 0 is reported in these cells. 220.127.116.11 Revised Step 5: Adjust Probability for Speed In the EFCCR procedure, the individual EFCCRs are combined into a case-weighted, single, dimensionless value at a baseline speed that can be adjusted up or down for each site-specific analysis. In this extension of the proce- dure, the speed-weighted probability of a KA crash given a collision at a base PSL of 65 mph [P(KACUSP|C)65] is determined. This is calculated using the case-weighted average P(KACUSP|C) for each level of PSL in each dataset as follows: KA KA 65 PSL CUSP 65 CUSP 3 3P C P C i ( ) ( ) ( )= State and Hardware Type Years Total Reported Crashes PI Ohio 2000â2012 86 53 Washington 1993â1996 and 1999â2011 46 52 New Jersey 2001â2013 25 50 North Carolina 2003â2012 52 46 Wyoming 2008â2013 30 33 Combine all datasets 239 37 Table 37. Total report crashes and estimated injury percentage for each dataset. PSL OH WA NJ NC WY Combined Data Analysis 75 â â â â 0.55 0.06 70 â 2.63 â 4.25 â 9.64 65 0.21 0.00 0.22 0.09 10.35 60 â 6.06 â 1.55 â 11.03 55 11.89 0.06 1.79 0.00 â 28.17 50 4.38 â 2.38 â 10.70 45 4.87 â â 15.21 â 30.11 40 10.95 â 0.00 4.74 0.00 17.55 35 53.58 31.80 0.00 46.98 0.00 189.04 30 â 4.03 0.00 â 64.13 65.13 25 119.30 43.00 67.12 â â 322.41 20 â â â â 30.01 26.55 Column Totals 205.18 87.58 71.29 72.95 94.78 720.74 Table 38. Unreported crash count estimates by dataset.
66 The resulting value can be used in the guidelines and adjusted using the site-specific PSL, as follows: KA KA 65 PSLPSL CUSP 65 3 3P C P C ii ( ) ( )= ï£® ï£°ï£¯ ï£¹ ï£»ï£º The probability of a severe or fatal crash with a bridge pier at a baseline speed of 65 mph, for each dataset, is as follows: â¢ Ohio: 0.1435 â¢ Washington: 0.1599 â¢ New Jersey: 0 (no observed KA crashes in this dataset) â¢ North Carolina: 0.0766 â¢ Wyoming: 0.0137 â¢ Combined analysis: 0.0656 Washington State yielded the highest probability (0.1599) for unshielded piers, and (excepting New Jersey) Wyoming yielded the lowest (0.0137). Data from all five states were combined, resulting in a probability of a severe or fatal crash severity of 0.0656 for bridge piers that are unshielded at a base condition speed of 65 mph. It is suggested that the value obtained from the combined analysis be used in the guide- lines. Substituting the suggested value of 0.0656 into the formula and simplifying provides this model for use in the guidelines: KA 0.0656 65 PSL 2.3895 10 PSLCUSP PSL 3 3 7 3P C i ii i i( ) = ï£® ï£°ï£¯ ï£¹ ï£»ï£º = â i i( ) = âKA 2.3895 10 PSLCUSP 7 3P C i 18.104.22.168 Results As will be shown later in the examples, these procedures estimate the number of crashes with the lead column of a pier system, so impacts with the interior columns must be added to the estimate since fatal and severe injury crashes can occur with these columns as well. RSAPv3 runs show that col- umns downstream of the leading column experience about one-third the number of collisions as the leading column, so the estimate of total passenger vehicle crashes can be deter- mined from the leading-edge collisions as follows, where n is the number of columns in the pier system: i iï£® ï£°ï£¯ ï£¹ ï£»ï£º + ï£® ï£°ï£¯ ï£¹ ï£»ï£º = +ï£® ï£°ï£¯ ï£¹ ï£»ï£º AF 3 2 AF 3 AF 2 3 PV CUSP PV CUSP PV CUSP n n The annual frequency of severe or fatal passenger vehicle collisions with the unshielded pier component can now be found as follows: i i iâ ( ) ( )( )= +ï£®ï£°ï£¯ ï£¹ ï£»ï£º= AF 2 3 PVE PVE KAPV CUSP 1 CUSP n N P C P C i m i i i The objective of roadside design is to minimize the conse- quences of vehicles leaving the road. This has generally been interpreted as attempting to minimize the occurrence of severe and fatal crashes (i.e., KA crashes). NCHRP Project 22-12(03) used a risk of 0.01 of a severe injury or fatal crash occurring during the 30-year design life on a 1,000-ft length of bridge railing as an acceptance value for selecting bridge railings [Ray 2014b]. Converted to an annual per-mile risk, the value used in NCHRP Project 22-12(03) would be a risk of 0.0018 KA PSL OH WA NJâ NC WY Combined data analysis 75 â â â â 0.2197 0.2463 70 â 0.3015 â 0.1778 â 0.173 65 0.2271 â 0 0.1971 0 0.1168 60 â 0.2769 â 0 â 0.1051 55 0.1355 0.1241 0 0 â 0.0935 50 0 â 0 â â 0 45 0 â â 0.0367 â 0.0222 40 0.0669 â 0 0 0 0.0350 35 0.0698 0.0251 0 0 0 0.0257 30 â 0 0 â 0 0 25 0.0214 0.0192 0 â â 0.0109 20 â â â â 0 0 P(KACUSP|C)65 0.1435 0.1599 0 0.0766 0.0137 0.0656 â No severe or fatal crashes in the data. Table 39. Probability of KA crashes [P(KACUSP|C)] by dataset and speed.
67 crashes/edge-mile/year. AASHTO SCOBS T7 and the AASHTO Technical Committee on Roadside Safety (TCRS) have been considering the suggestions of NCHRP Project 22-12(03), so there is also some history of support for an annual risk of fatal or severe injury in the range 0.0018 KA crashes/edge-mile/year. Bridge piers are essentially point hazards, whereas the risk value of 0.0018 KA crashes/edge-mile/year involves a length (e.g., 1 mile). Trajectories in RSAPv3 are generally less than 300 ft, so it could be argued that a point hazard like a bridge pier is actually exposed to traffic 300 ft upstream of the hazard; encroachments that start more than 300 ft upstream of a pier are very unlikely to reach the pier. Using the NCHRP Project 22-12(03) recommendation, this would equate to an annual risk of a fatal or severe crash of 0.01 KA crashes/ 30 years/1,000 ft of bridge edge = (0.01 â¢ 300)/(30 â¢ 1,000) = 0.0001. Interestingly and coincidentally, this value is exactly the value used for the annual risk of bridge collapse in Arti- cles 3.14 and 3.6.5 of the LRFD Bridge Design Specifications for critical bridges. It is encouraging that these two entirely independent criteria are the same since that indicates that these two different areas of bridge design have selected con- sistent thresholds of risk with respect to the possibility of the loss of life in a catastrophic event. The risk criterion suggested for the passenger-vehicle occupant protection procedures is that the annual risk of a fatal or severe injury crash (AFKA CUSP) must be less than or equal to 0.0001 KA crashes involving an unshielded bridge pier per year. 4.2.5 Shielding Barrier Layout Occupant Protection Recommendations for barrier placement and layout are provided in Sections 5.6.4 of the RDG [AASHTO 2011]. The suggestions for placement and layout of barriers used for passenger-vehicle occupant protection generally conform to the RDG guidance, with some variations as discussed in the following sections. 22.214.171.124 Shielding Barrier Type The barrier options for shielding bridge piers to minimize the chance of passenger vehicle occupants being severely or fatally injured in a collision with a bridge pier will only include barriers that meet the MASH crash-testing guidelines [AASHTO 2016]. The FHWA has encouraged states to adopt MASH TL-3 31-in.-tall w-beam guardrails [FHWA 2014b]. A w-beam guardrail is the most commonly used barrier sys- tem for occupant protection, and it is the default test level for the National Highway System, so it has been included in this research as the most likely occupant protection alternative, whereas TL-5 concrete barriers were included for pier protec- tion from heavy-vehicle impacts. 126.96.36.199 Shielding Barrier Layout for Occupant Protection If the annual frequency of severe or fatal injury passenger vehicle collisions is greater than or equal to 0.0001 for the unshielded pier system, the pier system should be shielded for passenger-vehicle occupant protection. The placement of a shielding barrier for passenger-vehicle occupant protection from pier component impacts should follow the recommen- dations of Section 5.6.4 of the RDG [AASHTO 2011]. The layout requires determination or selection of the following six dimensions, as shown in RDG Figure 5â39: 1. The shy-line offset distance (LS) (RDG Table 5â7). 2. The run-out length (LR) (RDG Table 5â10). 3. The flare rate (a/b), if desired (RDG Table 5â8). 4. The tangent length (L1), if desired. 5. The barrier offset from the edge of lane (L2). 6. The lateral extent of the area of concern (LA). The user first determines the shy-line offset distance from RDG Table 5â7. Next, the expected barrier deflection dis- tance for a MASH TL-3 barrier should be determined from Table 5â6. The barrier should be placed at least far enough away from the face of the closest pier component to provide the deflection distance in RDG Table 5â6, and ideally this should be beyond the shy-line distance in RDG Table 5â7. If there is insufficient room for both, the deflection distance should be maintained, and the barrier can be placed inside the shy line. This barrier offset distance from edge of the travel lane to the face of the w-beam guardrail is L2. Next, the user should determine if a flared or tangent installation is desired. If the terrain is relatively flat and tra- versable, a flared installation is often most desirable, but if a flared installation would require extensive site work to make the approach and run-out areas traversable, a tangent instal- lation can be used. The maximum flare rates (a/b) are found in RDG Table 5â8. If the guardrail is inside the shy distance, the column headed âFlare Rate for Barrier Inside Shy Lineâ should be used, and if it is beyond the shy-line distance, the column headed âBâ can be used. The tangent distance (L1) is the distance upstream that the guardrail will extend before the start of the flare. The run-out length needed for the particular speed limit and traffic volume is then determined from RDG Table 5â10. Once these values are found or selected, RDG Equation 5-1 (flared) or Equation 5-2 (tangent) can be used to find the length-of-need X shown in RDG Figure 5â39.