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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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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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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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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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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