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87 where it is acceptable to use a curbguardrail combination as TRIPPING RISK INDEX a function of the lateral offset from the guardrail and the oper- ating speed of the roadway; the shading in the figure marks Development of the Tripping Risk Index the different types of curbs. The information obtained from the full-scale testing and the finite-element parametric analysis performed in this project VALIDATION OF DESIGN GUIDELINES was also used to develop a tripping risk index (TRI) for mount- able curbs. This index indicates the probability of a rollover The foregoing design guidelines and chart were developed based on events observed during the impact. The complexity almost entirely with FEAs so it was necessary to validate the of the problem under analysis makes the identification of the results with some full-scale crash tests. A series of full-scale causes and effects difficult and probably impractical. It is pos- crash tests were performed in this project to validate the sible that two full-scale tests under the same nominal impact design chart, as discussed in Chapter 5. The tests are indi- conditions could lead to dramatically different results (i.e., cated on Figure 44 with square shapes. The purpose of these the vehicle may or may not overturn). tests was to validate the design chart by confirming that test Several events were identified that can be correlated to failures and successes were observed in appropriate regions vehicle rollover during a curb impact: failure of one or two of the chart. tires, rim-curb snagging, and rollover or outrigger engage- E-TECH Test 52-2556-001 was an 85 km/h, 25-degree ment. A TRI value for each test or simulation was generated impact of the guardrail with a 150-mm high B curb located by assigning risk points to each adverse event recorded dur- under the face of the rail. The test was a success and is plotted ing the curb traversal. Points were also added based on the sta- in the acceptable region of the design chart. Test 52-2556-002 bility ranking, a subjective value recorded by the driver that was an 85 km/h, 25-degree impact of the guardrail located indicated the stability of the vehicle during the impact. Ta- 2.5 m behind a 150-mm high B curb. Unfortunately, there ble 40 shows the points assigned to each event and parameter. was an installation error: the guardrail was 100 mm too short. The TRI for each test or simulation was then calculated as The vehicle vaulted over the guardrail, so the test failed. The test conditions are plotted in the unacceptable section of the RiskPts 3600 chart, although the incorrect rail height casts some uncertainty TRI = 100 2 , (1) 33 V on this result. Test 52-2556-005 was a success, using a NY curb 4.5 m in front of the guardrail and impact conditions of 80 km/h and 25 degrees. This test is plotted in the acceptable where region of the chart since the NY curb is a 100-mm high curb. 33 is the maximum number of risk points possible, The objective of Test 52-2556-006 was to validate the cor- 3600 is a normalization factor in kilometers per hour ner of the 2.5-m offset, 150-mm high curb block. The guardrail squared, and was placed 2.5 m behind a 100-mm high NY curb, and the test V is the impact velocity in km/h. was run at 70 km/h and 25 degrees. The test was a success and the impact conditions plotted in the acceptable region of the Note that the TRI can never be equal to zero since there is design chart, validating that portion of the chart. The last test, always the possibility that a curb may act as a tripping mech- 52-2556-007, involved the same installation (i.e., a 100-mm anism due to some parameters or event not explicitly included high NY curb 2.5 m in front of the guardrail), but at a higher in the TRI definition. The TRI is weighted by the inverse of speed of 85 km/h. The FEAs and the design chart suggested the squared impact velocity (proportional to initial kinetic that this test should be a failure, since it plots in the failing energy) to allow comparison of heterogeneous tests con- portion of the design chart. The crash test results, however, ducted at different speeds. indicated it was a success. As mentioned earlier, the NY curb is characterized by a very low tripping risk index, so it seems likely that some very flat-faced, low-height curbs can be used TABLE 40 Risk points 2.5 m in front of a guardrail even on some higher speed road- for definition of the TRI ways. In general, however, guardrails should be placed at Event/parameter Risk pts least 4 m behind the curb on roads with operating speeds Single tire failure 3 between 71 and 85 km/h unless testing or analysis of a spe- Double tire failure 5 cific curb indicates that it will perform satisfactorily. Rim-curb snag 6 Rollover 10 Except when the guardrail was installed with the incorrect Stability Ranking: height, the design chart correctly predicts the results of all the Excellent 3 full-scale tests. This indicates that the design guidelines and Good 6 chart are valid based on a comparison of five full-scale crash Fair 9 Poor 12 tests performed at a variety of locations on the design chart.

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88 Table 41 shows the TRI values for the studied impact sce- a linear expression was obtained: narios. The TRI for each curb type is the arithmetic average of the TRI values for all the tests and simulations conducted TRI = H a1 + S a2 (7) on that particular curb type. The problem was then solved in transformed space follow- ing the procedure presented for the linear model. Solving Relationship of TRI to Design Variables Equation 5 after the applicable substitution yields The data in Table 41 suggest a correlation between the TRI a1 = 0.8333, TRI = H 0.8333 S 0.7976 (8) and two geometric curb design variables: curb height and curb a2 0.7976 slope. To find an analytical approximate relation between the TRI and these two geometric variables, the method of least The coefficient of determination for this nonlinear model, squares was used. computed in the transformed space, is 0.9912. Figure 48 is a perspective view of the surface described by Equation 8. A linear relation was first assumed of the form Equation 8 was also used to develop the design diagram (2) shown in Figure 49, identifying three areas of tripping risk. TRI = a1 H + a2 S, These areas were determined by tracing the isolevel lines of Equation 8, using a TRI of 20 for the first boundary and TRI where a1 and a2 are regression coefficients, H is the curb of 45 for the second boundary. The diagram shows three height, and S the gross curb slope, computed as the curb rollover tripping risk regions: low risk, moderate risk, and height divided by slope base. For each tested curb type, high risk. The boundaries of the three regions are not defined uniquely since there is a certain degree of arbitrariness in TRI TRIi = [ Hi Si ] 1 a a2 [TRInx1 ] = [ Anx 2 ] [a2 x1 ] (3) threshold values. The threshold values of 20 and 45 were selected after analysis of the data available. Figure 49 can be used as a design tool. For example, if a The problem is overdetermined, but it was solved using the certain road needs a curb height of 120 mm for hydrological least squares method: reasons and the curb must be placed within the clear zone for the roadway, the diagram suggests that the curb slope be less [ a] = ([ A]T [ A]) -1 [ A]T [TRI ] a1 = 0.0432 (4) than 0.3 for a low risk of tripping errant vehicles. a2 50.793 This linear model has a coefficient of determination, R2, Conclusions of 0.793. Figure 47 shows the TRI plane as a function of curb height This section has presented an approximate method to and slope; it was plotted by substituting the correlation coef- numerically evaluate the tripping risk offered by different ficients of Equation 4 into Equation 2. Curbs that are in the types of curbs. The method was used to rank the different lower one-third of the chart are considered the safest. The curbs studied in this research as shown in Table 42. tripping risk increases as the curb slope and height increase. Correlation between the TRI and two geometric curb design The black stars represent the curbs studied in this research. variables allowed the development of an approximate ana- The linear model was not able to correctly compute the TRI lytical relationship of the TRI as a function of the curb height under all circumstances. For a very low curb with a nearly and curb slope, defined in Equation 8. This relationship fits vertical face, the computed TRI indicated an unrealistic pos- the data both visually and statistically with a coefficient of sibility that the curb might trip the vehicle. This is contrary to determination of 0.99, which is exceptionally good for exper- intuition; if the height of the curb approaches zero, there is no imental data. curb to trip the vehicle. Since the linear model was not always Equation 8 was then used to develop the design diagram appropriate, a nonlinear model was sought to better describe shown in Figure 49, which identifies three regions of low, the TRI as a function of the two geometric parameters. moderate, and high risk of vehicle tripping offered by a curb characterized by its height and front face slope. Based on the A relation of the form TRI = H a1 S a2 , (5) tripping risk areas identified in Figure 49, the following can be concluded: was assumed and linearized by taking the natural logarithms of both sides. With a simple transformation of the variables, Curbs with an experimental or estimated (i.e., by Equa- tion 8) TRI above 45 should not be used on higher-speed TRI = ln(TRI), H = ln(H), S = ln(S) (6) roadways.

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89 TABLE 41 TRI values by curb type Test name Impact Tire damage Rim-curb Rollover Stability Risk Percentile Tripping speed no. failed snag rating points risk points risk index Curb Type B V1-01_B 60.0 0 1 1 16 76.19 76.19 V1-02_B 60.0 1 1 0 9 42.86 42.86 V1-03_B 60.0 2 0 1 4 27 81.82 81.82 V2-01_B 80.0 0 1 1 4 28 84.85 47.73 V2-02_B 80.0 1 1 1 4 31 93.94 52.84 V2-03_B 80.0 2 0 1 4 27 81.82 46.02 603XB0135A 56.3 0 1 1 4 28 84.85 96.30 603XB0135B 56.3 1 1 0 3 18 54.55 61.91 603XB0235A 56.3 0 0 0 3 9 27.27 30.95 603XB0235B 56.3 0 0 0 3 9 27.27 30.95 Tripping Risk Index for the Curb Type (Average of the tripping risk of each test): 56.76 Curb Type C V1-01_C 60.0 0 0 1 4 22 66.67 66.67 V1-02_C 60.0 1 0 1 4 25 75.76 75.76 V1-03_C 60.0 0 0 1 4 22 66.67 66.67 V2-01_C 80.0 1 0 1 4 25 75.76 42.61 V2-02_C 80.0 1 0 0 2 9 27.27 15.34 V2-03_C 80.0 2 0 1 4 27 81.82 46.02 530XC0135A 56.3 0 0 1 4 22 66.67 75.66 530XC0135B 56.3 0 0 0 3 9 27.27 30.95 530XC0235A 56.3 0 0 0 2 6 18.18 20.64 530XC0235B 56.3 0 0 0 2 6 18.18 20.64 Tripping Risk Index for the Curb Type (Average of the tripping risk of each test): 46.10 Curb Type D 602XD0125A 40.2 0 0 0 1 3 9.09 20.22 602XD0130A 48.3 0 1 0 4 18 54.55 84.26 602XD0130B 48.3 0 1 0 4 18 54.55 84.26 603XD0135A 56.3 1 1 0 3 18 54.55 61.91 603XD0135B 56.3 0 1 0 4 18 54.55 61.91 603XD0135C 56.3 2 1 1 4 33 100.00 113.50 603XD0235A 56.3 0 0 0 2 6 18.18 20.64 603XD0235B 56.3 0 0 0 2 6 18.18 20.64 Tripping Risk Index for the Curb Type (Average of the tripping risk of each test): 58.41 Curb Type G V1-01_G 60.0 2 0 1 4 27 81.82 81.82 V1-02_G 60.0 1 0 0 2 9 27.27 27.27 V1-03_G 60.0 0 0 0 3 9 27.27 27.27 V2-01_G 80.0 1 0 1 4 25 75.76 42.61 V2-02_G 80.0 2 0 0 2 11 33.33 18.75 V2-03_G 80.0 1 0 1 4 25 75.76 42.61 Tripping Risk Index for the Curb Type (Average of the tripping risk of each test): 40.06 Curb Type NY V1-01_NY 60.0 0 0 0 1 3 9.09 9.09 V1-02_NY 60.0 0 0 0 1 3 9.09 9.09 V1-03_NY 60.0 0 0 0 1 3 9.09 9.09 V2-01_NY 80.0 0 0 0 1 3 9.09 5.11 V2-02_NY 80.0 0 0 0 1 3 9.09 5.11 V2-03_NY 80.0 0 0 0 2 6 18.18 10.23 527XN0120A 32.2 0 0 0 1 3 9.09 31.60 529XN0135A 56.3 0 0 0 2 6 18.18 20.64 530XN0135B 56.3 0 0 0 2 6 18.18 20.64 530XN0235A 56.3 0 0 0 1 3 9.09 10.32 530XN0235B 56.3 0 0 0 1 3 9.09 10.32 Tripping Risk Index for the Curb Type (Average of the tripping risk of each test): 12.84

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90 Figure 47. TRI as a linear function of curb height and slope. Figure 48. TRI as a nonlinear function of curb height and slope. Curbs that are located in the moderate risk area of the The use of low-tripping-risk curbs is recommended for diagram should be avoided on higher-speed roadways. roads with 85th percentile speeds above 110 km/h, where Their use may be acceptable where nontracking impacts winter weather conditions (e.g., icing, snow, or mist) are are not probable (e.g., tangent section, warm climate, expected and on poorly paved or drained roads. Low- wide shoulder, or fenced roads) and on roads with 85th tripping-risk curbs should always be used at access ramps percentile speeds below 110 km/h. and curves.

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91 180 Area 3: High Tripping Risk 160 D B 140 Curb height [mm] 120 NY G C 100 80 Area 2: Moderate 60 Tripping Risk Area 1: Low 40 Tripping Risk 20 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Curb Slope Figure 49. Curb geometric design diagram with respect to the tripping risk in nontracking impacts. TABLE 42 Curb safety in nontracking impact scenarios Safety rank Curb type TRI 1 NYDOT NY 12.48 2 AASHTO G 40.06 3 AASHTO C 46.10 4 AASHTO B 56.76 5 AASHTO D 58.41