CHARACTERIZING ROAD 

SAFETY PERFORMANCE 

USING PAVEMENT 

FRICTION

PUBLICATION NO. FHWA SA-23-006 
i 

Foreword

This report documents the development of safety performance functions (SPFs) that include 

friction and macrotexture on a variety of roadway facility types and categories (i.e., segments, 

intersections, curves, and ramps). The main objectives were: (1) the development of Crash 

Modification Factors (CMFs), or Crash Modification Functions (CMFx) that make it possible to 

evaluate the effect of pavement friction changes on safety performance, which can then inform the 

cost effectiveness of pavement friction improvements; and (2) the establishment of performance 

or investigatory thresholds for friction based on roadway type and category. The analysis 

confirmed a strong statistical association between pavement surface frictional properties (friction 

and macrotexture) and crash rates; lower crash rates were observed with higher friction and 

macrotexture.

The findings from this report support road agency efforts toward the institutionalization of 

Pavement Friction Management, one of the FHWA Proven Safety Countermeasures. The results 

may be used by road agencies to inform safety analyses at both the system/network and site/project 

levels to evaluate the impact and cost-effectiveness of pavement friction enhancement strategies 

and treatments.

Notice

This document is disseminated under the sponsorship of the U.S. Department of Transportation

(USDOT) in the interest of information exchange. The U. S. Government assumes no liability for 

the use of the information contained in this document. The contents of this report reflect the views 

of the contractor, who is responsible for the accuracy of the data presented herein. The contents do 

not necessarily reflect the official policy of the USDOT. This report does not constitute a standard, 

specification, or regulation. 

The U. S. Government does not endorse products or manufacturers named herein. Trademarks or

manufacturers’ names appear in this report only because they are considered essential to the

objective of this report. 

Non-Binding Content

The contents of this document do not have the force and effect of law and are not meant to bind 

the public in any way. This document is intended only to provide clarity to the public regarding 

existing requirements under the law or agency policies. While this is non-binding guidance, you 

must comply with the applicable statutes or regulations. 

Quality Assurance Statement

The Federal Highway Administration (FHWA) provides high-quality information to serve

Government, industry, and the public in a manner that promotes public understanding. Standards

and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its

information. The FHWA periodically reviews quality issues and adjusts its programs and processes 

to ensure continuous quality improvement. 
ii

Technical Report Documentation Page

1. Report No.

FHWA-SA-23-006

2. Government Accession No.

N/A

3. Recipient's Catalog No.

N/A

4. Title and Subtitle

Characterizing Road Safety Performance using Pavement Friction

5. Report Date

February 2023

6. Performing Organization Code

N/A

7. Author(s)

Gerardo Flintsch, Edgar de León Izeppi, Ross McCarthy, Samer 

Katicha, Bhagwant Persaud, Feng Guo, Alejandra Medina, and Priscilla 

Tobias

8. Performing Organization Report No.

N/A

9. Performing Organization Name and Address

Virginia Polytechnic Institute and State University

10. Work Unit No. (TRAIS)

N/A

11. Contract or Grant No.

DTFH61-16-D-00041L

12. Sponsoring Agency Name and Address

Federal Highway Administration

Office of Safety

1200 New Jersey Ave SE

Washington, DC 20590

13. Type of Report and Period Covered

August 2020–February 2023

14. Sponsoring Agency Code

N/A

15. Supplementary Notes

This report was produced under the direction of Jeffrey Shaw (FHWA Office of Safety)

16. Abstract

This report documents the development of safety performance functions (SPFs) that include friction and macrotexture on a 

variety of roadway facility types and categories (i.e., segments, intersections, curves, and ramps). The main objectives 

were: (1) the development of crash modification factors (CMFs), or crash modification functions (CMFx) that make it 

possible to evaluate the effect of pavement friction changes on safety performance, which can then inform the costeffectiveness of pavement friction improvements; and (2) the establishment of performance or investigatory thresholds for 

friction based on roadway type and category. 

The analysis confirmed a strong statistical association between pavement surface frictional properties (friction and 

macrotexture) and crash rates; lower crash rates were observed with higher friction and macrotexture were developed for 

total crashes on different roadway facility types. The Safety Performance Functions (SPFs), which included friction and 

macrotexture measurement, were developed for total crashes using traditional negative binomial models. Friction was 

found to have a statistically significant effect for predicting total crashes on all the roadway facility types; and 

macrotexture was found to have a statistically significant effect for predicting total crashes on all roadway facility types 

except rural two-lane/two-way roads. These SPFs were then used to develop CMF/CMFx for relatively straight segments 

without events (tangents) and with areas of higher friction demand (curves and intersections) on each type of facility. The 

CMFx obtained are reasonable, generally follow the expected trends, and show that potential reduction of up to 30 percent 

of total crashes can be achieved with a 10-point increase in SFN40. Finally, illustrative friction investigatory thresholds 

were also defined for the various roadway facility and site types. As expected, the investigatory levels are higher for higher 

friction demand sites, such as curves, ramp and access points, and intersections.

17. Key Words

Crashes, Friction, Microtexture, Macrotexture, Safety 

Performance Functions (SPF), Crash Modification 

Factors (CMF) and Functions (CMFx)

18. Distribution Statement

No restrictions. 

19. Security Classification (of this report)

Unclassified

20. Security Classification (of this page)

Unclassified

21. No. of Pages

51 

22. Price

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized.
iii

SI* (MODERN METRIC) CONVERSION FACTORS

* SI is the symbol for the International System of Units. Appropriate rounding should be made to comply with 

Section 4 of ASTM E380. (Revised March 2003, Section 508-accessible version September 2009.)
iv

Table of Contents

List of Figures ................................................................................................................................ v

List of Tables ................................................................................................................................ vi

List of Abbreviations .................................................................................................................. vii

CHAPTER 1. Introduction .......................................................................................................... 1

1.1 Previous Research ......................................................................................................... 1

1.2 Current Research .......................................................................................................... 1

1.3 Review of Friction-related SPFS and CMFS .............................................................. 1

1.4 Review of Friction Investigatory Levels ..................................................................... 3

CHAPTER 2. Methodology.......................................................................................................... 5

2.1 SPF Estimation Methods .............................................................................................. 6

2.2 SPF Stratification .......................................................................................................... 8

2.3 Deriving CMFs/CMFx from SPFs ............................................................................... 8

2.4 Identification of Friction Investigatory Thresholds................................................... 8

CHAPTER 3. Data Collection ................................................................................................... 10

3.1 Variables ...................................................................................................................... 10

3.2 Highway Network Mileage ......................................................................................... 11

3.3 Crash Data ................................................................................................................... 13

CHAPTER 4. Results.................................................................................................................. 14

4.1 Hierarchical Standard and Mixed-Effect SPF Regression Modeling .................... 14

4.1.1 All Roadway Types ................................................................................................. 14

4.1.2 Freeways .................................................................................................................. 16

4.1.3 Urban and Suburban Arterials.............................................................................. 16

4.1.4 Rural Multilane Highways ..................................................................................... 16

4.1.5 Rural Two-Lane, Two-Way Roads ....................................................................... 17

4.1.6 Alternative Modeling Approaches......................................................................... 18

4.2 Crash Modification Factors/Functions (CMFs/CMFx) ........................................... 18

4.2.1 CMFs for Friction Improvements ......................................................................... 18

4.2.1.1 CMFx by Roadway Facility Type .................................................................. 20

4.2.1.2 SPF and CMFx by Crash Type...................................................................... 20

4.2.2 CMFs for Macrotexture Improvements ............................................................... 25

4.2.3 Interaction Between Friction and Macrotexture ................................................. 27

4.3 Friction Investigatory Thresholds ............................................................................. 28

CHAPTER 5. Conclusions ......................................................................................................... 38

References .................................................................................................................................... 39
v 

List of Figures 

Figure 1. Illustration. Analysis framework (Source: CSTI/Arora and Associates, P.C.). ..... 5

Figure 2. Graphs. Distribution of friction values and crash rates for interstate tangent 

sites (Source: FHWA). ................................................................................................................ 12

Figure 3. Graph. Comparison of CMFx for friction on different roadway facility types 

(Source: FHWA). ........................................................................................................................ 20

Figure 4. Graph. CMFx for friction on freeway segments by surface condition (Source: 

FHWA). ........................................................................................................................................ 22

Figure 5. Graph. CMFx for friction on urban and suburban arterial highway segments 

by surface condition (Source: FHWA). ..................................................................................... 23

Figure 6. Graph. CMFx for friction on rural multilane highway segments by surface 

condition (Source: FHWA). ....................................................................................................... 24

Figure 7. Graph. CMFx for friction on rural two-lane, two-way road segments by 

surface condition (Source: FHWA). .......................................................................................... 25

Figure 8. Graph. Comparison of CMFx for macrotexture on different roadway facility 

types (Source: FHWA). .............................................................................................................. 27

Figure 9. Chart. Friction distribution, crash rates, and estimated thresholds for freeway 

tangent segments (Source: FHWA). .......................................................................................... 28

Figure 10. Graph. Friction distribution, crash rates, and estimated thresholds for 

freeway curves and ramp access points (Source: FHWA). ..................................................... 30

Figure 11. Graph. Friction distribution, crash rates, and estimated thresholds for urban 

and suburban arterial highway tangents (Source: FHWA). ................................................... 31

Figure 12. Graph. Friction distribution, crash rates, and estimated thresholds for urban 

and suburban arterial highway intersections/ramp access points and horizontal curves 

(Source: FHWA). ........................................................................................................................ 32

Figure 13. Graph. Friction distribution, crash rates, and estimated thresholds for rural 

multilane road tangent segments (Source: FHWA). ................................................................ 33

Figure 14. Graph. Friction distribution, crash rates, and estimated thresholds for rural 

multilane road segments with intersections or horizontal curves (Source: FHWA). ........... 34

Figure 15. Graph. Friction distribution, crash rates, and estimated thresholds for rural 

2-lane, 2-way road tangents (Source: FHWA). ........................................................................ 35

Figure 16. Graph. Friction distribution, crash rates, and estimated thresholds for rural 

2-lane, 2-way (2L2W) road intersections and horizontal curves (Source: FHWA). ............. 36
vi

List of Tables

Table 1. Road classification scheme. ......................................................................................... 11

Table 2. Number of 0.1-mi segments analyzed by State and facility and site type. .............. 12

Table 3. Distribution of crashes by State, Facility and Site type. ........................................... 13

Table 4. Poisson and NB Hierarchical mixed-effect SPF models – all facility and site 

types. ............................................................................................................................................. 14

Table 5. NB SPF model without mixed-effect – All facility and site types – categorical 

variables only. .............................................................................................................................. 15

Table 6. NB model – freeways. ................................................................................................... 16

Table 7. NB model – urban and suburban arterials. ............................................................... 17

Table 8. NB model – rural multilane highways. ....................................................................... 17

Table 9. NB model – rural 2-lane, 2-way roadway. ................................................................. 18

Table 10. CMF and percent crash reduction for a 10-unit increase in SFN40. .................... 19

Table 11. CMF and percent crash reduction by surface condition for a 10-unit increase 

in SFN40. ...................................................................................................................................... 21

Table 12. CMFx and percent crash reduction for a 0.5-mm increase in MPD. .................... 26

Table 13. Summary of the threshold Analysis.......................................................................... 37
vii

List of Abbreviations 

AADT average annual daily traffic

AASHTO American Association of State Highway and Transportation Officials 

AIC Akaike information criterion

CFME continuous friction measuring equipment 

CFR Code of Federal Regulations 

CMF crash modification factor

CMFX crash modification function 

CPFM continuous pavement friction measurement

CSC characteristic skid coefficient

CSTI Center for Sustainable Transportation Infrastructure 

DGAC dense-graded asphalt

DOT Department of Transportation 

EB empirical Bayes

FAA Federal Aviation Administration

FHWA Federal Highway Administration

GAM Generalized Additive Model

GLM/GLPM Generalized Linear Model/Generalized Partial Linear Model

GPF Guide for Pavement Friction 

HFST high friction surface treatment 

HSM Highway Safety Manual

IFI International Friction Index

KABCO Killed, Injury Level A, Injury Level B, Injury Level C, No Injury 

LFC longitudinal friction coefficient 

LRS Linear reference system

LWST locked wheel skid trailer

MPD mean profile depth

MTD mean texture depth

MVMT million vehicle miles traveled

NB negative binomial 

NCHRP National Cooperative Highway Research Program 

NHTSA National Highway Traffic Safety Administration

NZTA New Zealand Transport Agency 

OGFC open-graded friction course 

PFMP pavement friction management program 

RMS root mean square 

SCRIM Sideway-force Coefficient Routine Investigation Machine 

SE standard error 

SFC sideway force coefficient

SFN/SFN40 Sideway Force Number (with speed adjusted to 40 mph 

SMA stone matrix asphalt 

SPF Safety Performance Function

SR SCRIM reading (Skid Resistance)

UK United Kingdom 

US United States
viii

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1 

CHAPTER 1. Introduction

1.1 Previous Research

This current project continues the work documented in “PFM Program Utilizing Continuous 

Friction Measurement Equipment and State-of-the-Practice Safety Analysis Demonstration 

Project – Final Report,” (FHWA-RC-20-0009), which demonstrated a pavement friction 

management plan (PFMP) in four States (Florida, Indiana, Texas, and Washington) using 

pavement friction, texture, and crash data. That project proposed that pavement friction, also 

referred to as skid resistance, is best determined based on continuous measurements that are related 

to road surface microtexture and macrotexture. In each State, the research team:

• Divided the highway networks into groups according to friction needs (friction demand 

categories). 

• Collected friction, texture, crash, traffic, and other data. 

• Analyzed the data to explore investigatory threshold levels for pavement friction and 

texture. 

• Demonstrated proven continuous friction and macrotexture measurement equipment for 

network-level data collection.

1.2 Current Research

This report documents the development of safety performance functions (SPFs) that include 

friction and macrotexture for a variety of roadway facility types and categories (i.e., segments, 

intersections, curves, and ramps) for each category, as applicable. Per the Highway Safety Manual

(HSM), negative binomial (NB) regression modeling is the state-of-the-practice for estimating 

SPFs (AASHTO, 2010). This report also includes the development of Crash Modification Factors 

(CMFs), or Crash Modification Functions (CMFx) implied by the newly developed SPFs 

corresponding to the continuous pavement friction measurement (CPFM) data. 

The objectives of this work were twofold: first, to develop SPFs and CMFs/CMFx that make it 

possible to evaluate the effect of pavement friction changes on safety performance, which can then 

inform the cost-effectiveness of pavement friction improvements; second, to establish 

performance or investigatory thresholds for managing friction based on roadway type and 

category. 

1.3 Review of Friction-related SPFS and CMFS

A search of the available literature related to SPFs and CMFs that links measured skid resistance 

to expected crashes turned up relatively few materials. The limited research available does 

indicate, as expected, that higher skid resistance measurements are associated with lower crash 

rates, particularly wet-road-related collisions. 

Mayora and Pina (2009) studied the relationship between CPFM and injury collisions over two 5-

year periods (1993–1997 and 1998–2002) on two-lane rural road segments of 500-m length in 

Spain. Segments including intersections were not included. Average Sideway-force Coefficient 

Routine Investigation Machine (SCRIM) CPFM data over a 5-year period were included in the 
2 

analysis. Categories of alignment were defined for the analysis (e.g., tangent, radius > 500 m, 

radius 250–500 m, radius < 250 m) as well as categories of skid resistance based on the European 

standard of 50 km/h (e.g., SCRIM Reading (SR) ≤ 40, 40 < SR ≤ 45, 45 < SR ≤ 50, 50 < SR ≤ 55, 

55 < SR ≤ 60, SCRIM > 60). Statistical tests were applied to see whether the mean crash rates 

differed between SCRIM categories for each alignment category tested. A before-after comparison 

group study was conducted to assess the benefits of skid resistance improvements done between 

the two 5-year periods. A group of 419 segments (500-m lengths) with an average SCRIM value 

of less than 50 was treated to improve the SCRIM value to more than 60. The results of crash rate 

analyses showed that both wet- and dry-road crash rates decreased as skid resistance increased. 

Wet-road crash rates were found to be significantly higher in curves than on tangents. For dryroad crashes, no differences were found between curves and tangents. The results of crash rate 

analyses showed that both wet- and dry-road crash rates decreased as skid resistance increased. 

The authors concluded that for tangents and curves with a radius less than 500 m, crash rates are 

significantly lower when the SCRIM value is greater than 55. For curves with a radius less than 

500 m, the SCRIM value cutoff is 60. The before-after study indicates the benefits of increasing 

the skid resistance (measured as SR) from less than 50 to greater than 60 is a 68-percent reduction 

in wet-road crashes. When considering curves only, the reduction was estimated to be 84 percent. 

Ivan et al. (2010) explored the relationship between wet-pavement friction and crashes to identify 

whether wet-pavement friction explains significant variation in crash frequency between similar 

locations, and whether this is particularly significant at high crash locations such as sharp curves 

and intersections. The amount of friction at each location was measured using the locked-wheel 

skid trailer (LWST) with a standard ribbed tire. These tested locations represent discrete 

measurements over a 60-ft length of roadway at 40 mph. NB regression models for K, A, or B 

crashes on the KABCO scale were developed separately for divided and undivided roadways. 

Additional explanatory variables considered included degree of horizontal curvature, rate of 

change of vertical curvature, number of intersections and driveways, pavement width, area type 

(rural, suburban, or urban), and speed limit. Dependent variables considered included total, wetroad, segment-related (sideswipe opposite direction, head-on fixed object, and moving object), and 

intersection-related (turning same direction, turning intersecting paths, sideswipe same direction, 

angle, rear-end, and pedestrian) crashes. The model results indicated that wet-pavement friction is 

most associated with increased crashes under conditions where there would be a demand for 

increased braking — that is, in curves and near driveways. 

Cenek et al. (2011) developed Poisson log-linear regression models for run-off-road crashes on 

curves on rural two-lane roads. These models included the 50th-percentile SCRIM CPFM data

within each curve and confirmed that run-off-road crashes decrease as the CPFM increases.

Labi (2011) developed a CMF for crashes on rural two-lane roads through regression modeling 

that included the pavement friction measured with a LWST with a standard smooth tire at discrete 

60-ft length pavement sections at 40 mph. The CMF is determined using the friction number before 

treatment, X, and the friction number after treatment, Y, for various classes of severity. As an 

example, the CMF for ABC crashes on the KABCO scale is: 

(1)
3 

Pratt et al. (2014) similarly developed a CMF for the skid number reading (LWST with a smooth 

tire at discrete 60-ft length of roadway sections at 40 mph) using regression modeling. The CMF

applies to horizontal curves on rural two-lane roads and all crash types. As an example, the CMF 

for KABCO crashes on the KABCO scale is:

(2)

A report from the Scottish Road Research Board (2020) examined the relationship between wetroad crashes per million kilometers traveled and the SCRIM-measured characteristic skid 

coefficient (CSC). Piecewise linear regression models were fit to the data, which for some road 

types showed no discernible pattern, but for others did show an increased crash risk at low skid 

coefficient values.

Wallbank et al. (2016) developed generalized linear regression models with an NB error 

distribution to predict all crashes and wet-condition crashes on several categories of rural 

roadways. The models indicated that crash risk is reduced as SCRIM CPFM increases, particularly 

on segments with curves and grades. It was found that for wet-condition crashes skid resistance is 

more predictive of crashes, while for all crash types a measurement of texture depth was more 

predictive. As an example, the model for wet-condition crashes on motorways is: 

(3)

De Leόn Izeppi et al. (2019) collected and analyzed approximately 4,000 miles of SCRIM CPFM 

data and recommended a methodology for identifying sections of roadway with high rates of 

friction-related crashes using SPFs and an empirical Bayes (EB) methodology that considered 

friction, macrotexture, geometric data, traffic, and crash counts. The report showed that the high 

resolution of CPFM (10-m data for network-level analysis) is sensitive to identifying potential 

friction problems on road sections with a high friction demand, such as curves and intersections. 

Finally, in an evaluation by Merritt et al. (2020) of the safety effects of high-friction surface 

treatments, univariate categorical analysis and CMF/CMFx development indicated that there was 

a logical and consistent relationship between CMFs and three variables: friction improvement as 

measured by the percentage of high-friction surface treatment (HFST) friction increase, average 

annual daily traffic (AADT), and the expected crash frequency before treatment. It was found that 

the greater the percentage increase in friction, the greater was the observed decrease in crash 

frequency.

1.4 Review of Friction Investigatory Levels 

The investigatory level for friction is the value below which crash risk increases significantly. This 

level can be used to identify sites where the skid resistance of pavement may be inadequate for the 

given road type, context, and expected traffic maneuvers. Pavement friction values lower than this 

threshold indicate the potential need for site review and possible consideration of treatments to 

improve friction. 
4 

In Australia, New Zealand, and the United Kingdom (UK), investigatory levels of friction are 

routinely monitored to ensure adequate pavement-friction properties and potentially reduce 

friction-related crash risk (Highways England, 2019; NZTA, 2013; Pratt and Neaylon, 2011). The 

UK introduced the first set of friction investigatory levels in 1988 and updated over time (Roe and 

Caudwell, 2008; Highways England, 2019). The friction management policy is found in CS 228

Pavement Inspection and Assessment. Other countries, such as Australia and the New Zealand, 

establish standards and specifications that provide recommendations and guidelines for local 

agencies to adopt/adapt to their local districts. 

The standards for friction management in Australia and New Zealand were originally designed 

based on those from the UK and later adapted to the environment and roadway conditions in the 

two respective countries (Owen, 2014; Pratt and Neaylon, 2011). The first standard of the New 

Zealand policy, known as the T10 specification, was published in 1997 (NZTA, 2013). The final 

version of the T10 specification was published in 2013. The latest version of the recommended 

standards for motorway safety in Australia were published in a 2011 report, known as AP-R374-

11 (Pratt and Neaylon, 2011). 
5 

CHAPTER 2. Methodology 

The overall analysis framework is presented in Figure 1. This framework illustrates that there are 

many factors that influence the outcome variables (crashes) and that all these factors and outcomes 

are considered in developing SPFs. The SPFs are mathematical equations that predict the outcome 

variable (crashes) using the known values of the predictor variables. From these SPFs, 

CMFs/CMFx can be derived.

Figure 1. Illustration. Analysis framework (Source: CSTI/Arora and Associates, P.C.). 

Relationship 

between 

CPFM and 

Safety

Crashes

Crash Type

KABCO

Dry/wet weather

Pavement Surface 

Characteristic 

Friction 

(Microtexture)

Macrotexture

Facility Type and 

Elements

Segments

Curves 

Intersections/

Ramp Access Points

Facility Type

Freeway

Arterial

Rural multilane

Rural 2L2W

Safety Performance 

Function

Study design

Cross-sectional 

Models 

Poisson 

– Negative binomial

– Mixed-effect negative 

binomial

CMF/CMFunctions

– Change in crash risk by oneunit increase in CPFM

– CMF for typical CPFM 

The cross-sectional approach is based on a prescribed time period under the assumption that the 

CMF/CMFx can be estimated as the ratio of the average crash frequency for sites with different 

values of a variable, assuming the values of all other variables remain constant. The reduction in 

crashes can be based on the increase of CPFM, based on the measurements of microtexture and 

macrotexture in accordance with AASHTO TP-143. 

When estimating CMFs/CMFx from regression models, it is important to consider potential errors 

that may arise for several reasons, including inappropriate functional form, omitted variable bias, 

or correlation of variables. It is common practice to use generalized linear modeling (GLM) 

techniques, assuming an NB error structure, to estimate multivariable crash prediction models

(AASHTO, 2010). However, it is difficult to account for all factors that affect safety using such 

modeling techniques. 

For example, intersections with left-turn lanes also tend to have illumination. If a crash prediction 

model is used to estimate a CMF for left-turn lanes, and the presence of illumination is not 
6 

accounted for in the model, the difference in model predictions with and without left-turn lanes 

could be partly due to illumination differences. Ironically, it is precisely because a variable is found 

to be correlated with another variable that it may be omitted during the model fitting exercise. 

Including correlated variables could, in fact, lead to effects that are counterintuitive (e.g., 

illumination increases nighttime crashes). In this report, the illumination analogy is equivalent to 

obtaining friction measurements without collection of pavement macrotexture. 

Another reason the effect of an element that may affect safety cannot be captured in a model is 

because the sample used to develop the model is too small, or there is little or no variation in the 

element. For example, the effect of illumination cannot be captured if all locations in a sample are 

illuminated. Again, in this report, the effect of pavement friction levels cannot be captured if there 

is little or no variation of microtexture and macrotexture. These two variables are interrelated, 

which occasionally results in confounding effects in the model coefficients (collinearity). 

In evaluating CMFs derived from a cross-sectional study, Gross et al. (2010) identified the 

following questions for consideration: 

• Does the direction of effect (i.e., expected decrease or increase) in crashes meet 

expectations?

• Does the magnitude of the effect seem reasonable?

• Are the parameters of the model estimated with statistical significance?

These challenges may be mitigated by undertaking a rigorous before-after study, but this was not 

possible because of the unavailability of appropriate data. Thus, this study employed a crosssectional approach to develop CMFs/CMFx. 

2.1 SPF Estimation Methods

For this study, the research team tried (a) Poisson regression with mixed-effect, (b) NB regression 

with mixed-effect, and (c) NB regression without mixed-effect, to develop the SPFs that link the 

crash frequency with exposure and risk factors, including friction. When applying NB regression

over time, it is assumed that the observed crashes for a site will follow a Poisson process around a 

long-term mean (the SPF estimate) that varies between similar locations in accordance with a 

gamma distribution. Crash counts in each period for sites with the same estimated long-term mean 

will follow an NB distribution. 

To estimate the models, the crash, geometric, and friction data were organized by 0.1-mi sections, 

which accounted for crash data location accuracy and consistency with the segmentation typically

used within many pavement management systems, where CPFM is collected every 10 m, and then

a representative unit value is obtained from the lowest three-point moving average in a 0.1-mi 

section. 

The NB SPF estimation theory is as follows. Let Yij denote the crash counts on the j

th segment of 

a road section i. The distribution assumption is shown in equation (4): 

(4)
7 

Where E[Yij] = λij is the expected number of crashes and γ is the overdispersion parameter of the 

NB model to accommodate extra-Poisson variation. As it happens, this overdispersion parameter 

is fundamental to the EB methodology for before-after evaluations and is one of several SPF 

goodness-of-fit parameters. 

The functional form of the SPF establishes the relationship between the explanatory and dependent 

variables. As noted earlier, an incorrect functional form can result in biased and inconsistent 

parameter estimates, so it makes sense that the selection of a functional form is critical to 

developing a reliable CMF/CMFx. 

Most SPFs apply a GLM functional form as shown in equation (5). In this equation, the expected 

number of crashes is linked with the traffic volume, road characteristics, and friction number 

through a log-link function: 

(5)

where βs are the regression coefficients, Xfriction,ij is the friction number for segment ij, and the 

logarithm of traffic volume is included as an exposure term. Other factors are included as 

exponential terms (X3,ij to Xp,ij).

While the shape of the exponential curve is somewhat flexible, it does not permit relationships that 

have turning points (inflections or clear changes in slopes). In some cases, this may give rise to 

misleading conclusions about the effects of safety treatments (Hauer, 2004). For this research, the 

most appropriate model forms were investigated using the Akaike’s information criterion (AIC). 

Hierarchical model forms were also considered. In a hierarchical modeling framework, as applied 

in road safety context by Chen and Persaud (2014), the parameter estimate for an explanatory 

variable may vary by group, for example, for sites from different States, or vary in a more complex 

way by being a function of other explanatory variables. Hierarchical models are used for analyzing 

data that are characterized by correlated responses within hierarchical clusters. Not considering 

the potential hierarchical structure of the data (the potential of a complex correlation structure) 

may lead to poorly estimated coefficients and associated standard errors, particularly when they 

are modeled using a traditional count-data modeling approach. For this reason, specific SPFs were 

developed for different road categories. 

As segments on the same road section share many similar characteristics that are not easily 

quantified, it is likely that crash counts along these segments are correlated with each other. Spatial 

correlation is explored using a random-effect term, αij, to incorporate such correlation. The 

random-effect term can take many different forms, from the simple, within-section correlation to 

spatial correlation over larger distance. The within-section correlation takes the form of αij = αi ~ 

Normal (0,σ), such that all segments on the same section share the same normally distributed 

random terms. In the context of this study, the research team considers spatial correlation between 

segments (see Lord and Mannering, 2010).

Multi-state, multi-corridor, high-resolution data leads to a complicated correlation structure and 

heterogeneity. A hierarchical, mixed-effect model is recommended with several levels of 

correlation structure for the macro-State-level, corridor-level (i.e., routes), to micro-level spatial 
8 

correlation (segments close to each other). The correlation is mainly attributed to the shared 

characteristics at various levels. For example, all roads in the same State share a similar design 

standard, management, maintenance route, and State-level traffic management and regulation. At 

the micro level, segments close to each other share similar characteristics due to their similar 

spatial locations. The multi-level model can accommodate such correlations by either a Bayesian 

or frequentist approach. The basic model structure, however, is based on the formulation discussed 

above. 

2.2 SPF Stratification

Many factors can contribute to crash risk, including functional class, facility types and elements, 

and pavement surface characteristics. The confounding and interacting effects caused by these 

factors can lead to biased estimations. In developing the cross-sectional regression models, it is 

ideal to develop separate models so that each group is as identical as possible, except for the

treatment under consideration. However, this can be challenging when sample sizes are too small, 

which can necessitate combining groups, e.g., site types. Where this happens, such that a group is 

not homogeneous, a group classification categorical variable(s) may be considered for inclusion 

in the SPF as a multiplier or as an interaction term, if found to be statistically significant. As noted 

earlier, the quality of fit for the functional form of the SPFs proposed in this study was investigated 

with the AIC method.

2.3 Deriving CMFs/CMFx from SPFs

The CMFs/CMFx were derived from the estimated SPFs. The effects on safety from the friction 

measurements were used to estimate the reduction in crashes for every 10-unit increase in the 

CPFM. Equation (6) shows an example of a CMF-derived model form in equation (5), where β1 is 

the regression coefficient for the friction or macrotexture measurements. Equation (7) shows the 

corresponding calculation for the standard error of the CMF based on the delta methodology 

presented in Park et al. (2016) and applied by Anarkooli et al. (2021). Depending on the coding 

method for the friction variable, Xfriction, the CMF can be interpreted differently. For the continuous 

CPFM, the CMF represents the change to crash risk when friction increases by 10-units of sideway 

force number with speed adjusted to 40 mph according to AASHTO TP 143 (SFN40). For 

dichotomized, Xfriction, the CMF represents the crash frequency between two levels of CPFM.

(6)

(7)

2.4 Identification of Friction Investigatory Thresholds

The research team employed two approaches to identify the investigatory level, including the 

change point-based method and a more practical graphical assessment based on observation of 

crash rates for different friction levels. 

The model-based method assumes a nonlinear functional form of the SPF and friction number 

relationship. The investigatory level is the point at which the slope of the curve changes and below 
9 

which decreasing friction is associated with a rapid increase in crash risk. This approach provided 

a wide range of thresholds, especially for roadway facility types with relatively small sample sizes, 

which was not considered acceptable. Thus, only the results from the graphical assessment are 

included in this report. 
10

CHAPTER 3. Data Collection 

The friction, macrotexture, and roadway geometry data were collected with SCRIM CPFM 

equipment (de Leόn Izeppi et al. 2019). Multiple databases were used to collect the following data:

crashes, traffic volume, geospatial referencing (linear reference system [LRS] roadway points and 

GPS), etc. The CPFM data were collected every 10 m with a sideway-force friction device 

(AASHTO TP 143, 2021), and summarized into homogeneous 0.1-mi road segments, curves, and 

intersections, to match the common pavement management systems used in the United States(US). 

All the CPFM data were collected with the same device, which was calibrated in 2015 and 2019.

These small segments are the basic analysis unit for SPF and CMF development. 

3.1 Variables

The CMFs were developed by the research team using 3 years of collected crash data, including 

information on KABCO severity and wet/dry pavement condition, which were used to specify the 

dependent variables for modeling. The team also accounted for any surface changes applied to 

each section during the time-period of the collected crash and CPFM data. Sections that received 

interventions in the 3 years before testing were eliminated from the analysis. 

The variables directly or indirectly relevant to safety that were considered in the SPF development 

are listed below: 

1. Average annual daily traffic (AADT). 

2. Roadway classification (Table 1). 

3. Pavement surface mix:

a. Asphalt: Dense Graded, Open Graded (or Porous) Friction Course, Stone Matrix 

Asphalt (SMA), Microsurfacing, Chip Seal. 

b. Concrete: Tined, Ground, Grooved, Other (burlap, etc.). 

c. The age of the road surface type (years). 

4. Available continuously collected data: 

a. Friction (SFN40): Minimum SR adjusted for speed to 40 mph from a 90-ft moving 

average on a 0.1-mi. segment.

b. Macrotexture (mean profile depth, MPD): Average MPD for each 0.1-mi. segment. 

c. Cross-slope and/or superelevation (%: Average of the absolute value of percentage for 

a 0.1-mi segment). 

d. Vertical Grade (%): Average percentage for a 0.1-mi segment. 

e. Curvature (1/R): The inverse of the average of the absolute value of the curve radius 

(R) for a 0.1-mi segment. 

5. Crashes

a. Total crashes. 

b. Dry crashes: crashes when the pavement condition specified is dry. 

c. Wet crashes: crashes when the pavement condition specified is wet. 

d. Fatal and Injury Crashes. 
11

Table 1. Road classification scheme.

1

Roadway 

Facility Type Site Type Description

Freeways and 

Ramps

Roadway Segment 

(Urban and Rural) Tangents with R > 2,000 ft

Ramp Access Points Roadway access to on-/off-ramps

Curves R < 2,000 ft

Urban and 

Suburban 

Arterial

Roadway Segment Divided tangents with R > 2,000 ft

Undivided tangents with R > 2,000 ft

Intersections Signalized and unsignalized stop-controlled, including ramp 

access points.

Curves R < 2,000 ft

Rural 

Multilane 

Highway

Roadway Segment Divided, tangent with 4+ lanes and R > 2,000 ft

Undivided, tangent with 4+ lanes and R > 2,000 ft

Intersections Signalized and unsignalized stop-controlled

Curves R < 2,000 ft

Rural 2-lane 2-

way Roads 

Roadway Segment Undivided, 2-lane tangent roadway with R > 2,000 ft

Intersections Signalized and unsignalized stop-controlled

Curves R< 2,000 ft

3.2 Highway Network Mileage 

Table 2 shows the mileage of the highway network based on 0.1-mi road segments (tangent, ramp 

access points, curves, and intersections) with CPFM and crash data for each facility and site type

that were considered. The network in this study includes 55,677 0.1-mi roadway segments in five 

States separated into the 14 facility and site types from Table 1. For illustration purposes, Figure 

2 shows the trend of crash rates per 100 million vehicle miles traveled (100 MVMT) for interstate 

tangent sites. The figure shows that the rate increases for lower friction values. 

The international community that has extensive experience with continuous friction data collection 

and analysis recognizes that seasonal variations occur that impact the friction measurements. There 

are procedures to adjust friction test results for analysis. The data in this study does not have a 

seasonal adjustment, but it is recognized that a seasonal adjustment would have enhanced the data 

analysis. It is expected that as the US gains experience with CPFM data collection, seasonal 

adjustment will become a standard practice.

1 Curves have been added to the site types to account for the additional demand for friction while driving on curves. They represent segments 

of roadway with a horizontal radius lower than 2,000 ft. The rationale for this classification was taken from the recommendations of Friction 

Demand Site Categories in the UK (Highways England, Design Manual for Roads and Bridges, Volume 7, Section 3, CS 228, Revision 1, 

Pavement, Inspection and Assessment. Skidding Resistance (formerly HD 28/15 – Withdrawn), Crown, United Kingdom, 2020). In this 

recommendation, curves were segments of roads with a radius lower than 500 m; the interpretation in this report was that 2,000 ft provides a 

more conservative estimate for use in the United States.
12

Table 2. Number of 0.1-mi segments analyzed by State and facility and site type. 

Facility and Site Types Florida North 

Dakota Texas Virginia Washington Total 

Freeway Segments 2,742 4,677 2,108 11,924 2,571 24,022 

Freeway Ramp Access Points 410 281 560 1,291 541 3,083 

Freeway Curves 15 0 25 186 71 297 

Divided Urban Arterial Segments 1,076 97 542 1,793 28 3,536 

Undivided Urban Arterial Segments 318 27 757 392 82 1,576 

Urban Arterial Intersections 1,582 27 983 1,848 87 4,527 

Urban Arterial Curves 35 9 50 116 2 212 

Divided Rural Multilane Segments 0 1,930 170 6,416 27 8,543 

Undivided Rural Multilane Segments 0 0 902 643 52 1,597 

Rural Multilane Highway Intersections 6 140 338 2,009 6 2,499 

Rural Multilane Highway Curves 0 12 51 244 19 326 

Rural 2-lane, 2-way Segments 214 2,181 1,926 1,482 970 6,773 

Rural 2-lane, 2-way Intersections 35 68 363 445 168 1,079 

Rural 2-lane, 2-way Curves 4 82 127 252 225 690 

Total 6,027 9,250 8,342 27,750 4,308 55,677

Figure 2. Graphs. Distribution of friction values and crash rates for interstate tangent sites

(Source: FHWA). 

0

50

100

150

200

250

300

0

500

1000

1500

2000

2500

3000

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Average Crash Rate per 100M VMT

Number of Sections

Friction (SFN40)

Freeway Roadway Segments Friction Histogram

Total Crash Rate

Smoothed Crash Rate
13

3.3 Crash Data

Table 3 shows the distribution of crashes for each facility and site type and State. Some site types 

have a relatively small number of crashes. 

Table 3. Distribution of crashes by State, facility, and site type. 

Facility and Site Types Florida North 

Dakota Texas Virginia Washington Total 

Freeway Segments 6,278 923 26,537 27,995 19,949 81,682

Freeway Ramp Access Points 2,523 152 8,511 6,093 9,292 26,571

Freeway Curves 50 0 272 590 914 1,826

Divided Urban Arterial 

Segments 2,375 53 2,759 3,846 14 9,047

Undivided Urban Arterial 

Segments 105 9 1,341 850 115 2,420

Urban Arterial Intersections 10,930 195 6,463 10,328 552 28,468

Urban Arterial Curves 30 8 94 165 1 298

Divided Rural Multilane 

Highway Segments 0 173 115 2,652 9 2,949

Undivided Rural Multilane 

Highway Segments 0 0 343 465 6 814

Rural Multilane Highway 

Intersections 7 92 427 2,448 3 2,977

Rural Multilane Highway 

Curves 0 2 39 190 9 240

Rural 2-lane, 2-way Segments 51 100 547 467 430 1,595

Rural 2-lane, 2-way 

Intersections 46 19 275 479 193 1,012

Rural 2-lane, 2-way Curves 9 12 47 75 74 217

Total 22,404 1,738 47,770 56,643 31,561 160,116
14

CHAPTER 4. Results

This chapter presents the results for the hierarchical mixed-effect and fixed-effect crash models. 

Analysis was performed using all the crash data, for fatal and serious-injury crashes, and for each 

surface condition (dry/wet). 

4.1 Hierarchical Standard and Mixed-Effect SPF Regression Modeling

This section uses the data from all five States to develop three different SPF regression model 

types: (a) Poisson mixed-effect, (b) NB mixed-effect, and (c) NB without mixed-effect. The 

analysis is presented for the three model types for all roadway site types combined. This is 

followed by the analysis for each individual roadway site type using only the NB without mixedeffect model type. 

4.1.1 All Roadway Types

The three models in this section were developed for all roadway functional classifications. Table

4 lists the estimated regression coefficients (β) and p-value the variables in each model, in addition 

to the AIC and overdispersion parameters. The full set of regression coefficients and p-values for 

State and functional classification in the NB model without mixed-effect is shown Table 5. Both 

the friction and macrotexture are significant (p < 0.05) for all three models. 

Table 4. Poisson and NB hierarchical mixed-effect SPF models – all facility and site types. 

Parameters

Poisson with

Mixed -Effect

NB with

Mixed -Effect

NB without

Mixed- Effect

β p-value β p-value β p-value

Intercept, β0 -11.2038 <0.0001 -10.6554 <0.0001 -10.9950 <0.0001

ln (AADT) 1.2950 <0.0001 1.2260 <0.0001 1.2263 <0.0001

Friction (SFN40) -0.0139 <0.0001 -0.0105 <0.0001 -0.0105 <0.0001

Texture (MPD-mm) -0.1622 <0.0001 -0.2401 <0.0001 -0.2400 <0.0001

Grade (%) 0.0095 <0.0001 - - - -

Curvature (1/m) 107.9594 <0.0001 175.0743 <0.0001 175.3708 <0.0001

Overdispersion n/a 1.1616 1.1609 

AIC 300,108 177,997 177,907 

The AIC is similar for both fixed-effect and mixed-effect NB models. The AIC is significantly 

lower than for the Poisson mixed-effect. Based on AIC, the NB models are better than Poisson

mixed-effect for modeling crash counts for all facility and site types. Furthermore, the regression 

coefficients for friction and macrotexture are the same for both NB models; therefore, the fixedeffect NB was selected for modeling all facility and site types. 
15

Table 5. NB SPF model without mixed-effect – all facility and site types – categorical 

variables only. 

Parameters β p-value

Intercept, β0 -10.9950 <0.0001

ln (AADT) 1.2263 <0.0001

Friction (SFN40) -0.0105 <0.0001

Texture (MPD-mm) -0.2400 <0.0001

Curvature (1/m) 175.3708 <0.0001

State 1 -0.5334 <0.0001

State 2 -0.8369 <0.0001

State 3 Reference Variable

State 4 0.3549 <0.0001

State 5 0.5515 <0.0001

Freeway Segment Reference Variable

Freeway Ramp 0.3878 <0.0001

Freeway Curve 0.1658 0.0308

Divided Urban Arterial Segment 0.6481 <0.0001

Undivided Urban Arterial Segment 0.3066 <0.0001

Urban Arterial Intersection 1.7696 <0.0001

Urban Arterial Curve 0.1242 0.2365

Divided Rural Multilane Highway Segment 0.3541 <0.0001

Undivided Rural Multilane Highway Segment -0.0281 0.5710

Rural Multilane Highway Intersection 1.1440 <0.0001

Rural Multilane Highway Curve 0.6511 <0.0001

Rural 2-lane, 2-way Road Segment 0.4116 <0.0001

Rural 2-lane, 2-way Road Intersection 1.3876 <0.0001

Rural 2-lane, 2-way Road Curve 0.6410 <0.0001

In both plots, the models tend to overestimate the number of crashes for the locations with a low 

predicted crash frequency, probably due to the considerable number of segments with zero 

observed crashes. However, the plots show that both models are better when predicting sites with 

higher crash frequencies. 

The NB without mixed-effect and mixed-effect NB models have similar AICs (much better than 

the Poisson) and produce very similar or identical regression coefficients for friction and 

macrotexture. Equivalent results were observed after stratification. Therefore, only the results for 

the NB regression model without mixed-effect are reported for the remaining roadway functional 

classifications. Furthermore, the regression coefficients for both friction and macrotexture are 

statistically significant at a 95-percent confidence level (p-values < 0.05). 
16

4.1.2 Freeways 

Table 6 lists the NB without mixed-effect coefficients (β and p-value), overdispersion, and AIC 

for the freeway fixed-effect NB model. This table shows that both friction and macrotexture are 

statistically significant at the 95-percent confidence level.

Table 6. NB model – freeways.

Parameters β Standard 

Error

95% CI 

Lower

95% CI 

Upper p-value 

Intercept, β0 -13.2201 0.1618 -13.5372 -12.9029 <0.0001

ln (AADT) 1.4180 0.0128 1.3930 1.4431 <0.0001

Friction (SFN40) -0.0031 0.0010 -0.0050 -0.0012 0.0013

Texture (MPD-mm) -0.1175 0.0299 -0.1760 -0.0590 0.0001

Curvature (1/m) 312.1713 26.3390 260.5468 363.7957 <0.0001

State 1 -1.0801 0.0328 -1.1444 -1.0158 <0.0001

State 2 -0.8676 0.0517 -0.9690 -0.7662 <0.0001

State 3 Reference Variable

State 4 -0.6636 0.0251 -0.7128 -0.6144 <0.0001

State 5 0.3187 0.0330 0.2539 0.3835 <0.0001

Segments Reference Variable

Ramp Access Points 0.3362 0.0235 0.0235 0.3823 <0.0001

Curves -0.0170 0.0870 0.0870 0.1536 0.8449

Overdispersion 1.0146 

AIC 98,441 

4.1.3 Urban and Suburban Arterials

Table 7 lists the fixed-effects (β and p-value), overdispersion, and AIC for the fixed-effect NB

model for urban and suburban arterials. In this case again, both the friction and the macrotexture 

are statistically significant at the 95-percent confidence level. 

4.1.4 Rural Multilane Highways

Table 8 lists the fixed-effects (β and p-value), the overdispersion, and the AIC for the fixed-effect 

NB model for rural multilane highways. In this case, friction is statistically significant at the 95-

percent confidence level but not macrotexture, which is significant at the 90-percent level, with a 

direction of effect that is consistent with that for freeways and urban and suburban arterials. 
17

Table 7. NB model – urban and suburban arterials. 

Parameters β Standard

Error

95% CI 

Lower

95% CI 

Upper p-value 

Intercept, β0 -6.3395 0.2369 -6.8038 -5.8752 <0.0001

ln (AADT) 0.8893 0.0216 0.8469 0.9316 <0.0001

Friction (SFN40) -0.0282 0.0016 -0.0313 -0.0251 <0.0001

Texture (MPD-mm) -0.2363 0.0368 -0.3085 -0.1641 <0.0001

Grade (%) -0.0256 0.0097 -0.0446 -0.0067 0.0079

State 1 -0.1650 0.0367 -0.2370 -0.0930 <0.0001

State 2 -0.1012 0.1318 -0.3596 0.1572 0.4429

State 3 Reference Variable

State 4 -0.1289 0.0360 -0.1995 -0.0583 0.0003

State 5 0.5295 0.0984 0.3367 0.7224 <0.0001

Divided Segments Reference Variable

Undivided Segments -0.3111 0.0457 -0.4008 -0.2215 <0.0001

Intersections 0.9898 0.0291 0.9327 1.0469 <0.0001

Curves -0.2807 0.1045 -0.4855 -0.0758 0.0072

Overdispersion 1.2318 

AIC 44,402 

Table 8. NB model – rural multilane highways. 

Parameters β Standard

Error

95% CI 

Lower

95% CI 

Upper p-value

Intercept, β0 -7.3199 0.3211 -7.9493 -6.6905 <0.0001

ln (AADT) 0.8878 0.0299 0.8291 0.9464 <0.0001

Friction (SFN40) -0.0265 0.0018 -0.0301 -0.0229 <0.0001

Texture (MPD-mm) -0.1645 0.0764 -0.3142 -0.0147 0.0313

Curvature (1/m) 315.3585 27.1809 262.0838 368.6332 <0.0001

State 1 1.2137 0.5675 0.1014 2.3261 0.0325

State 2 -0.4364 0.0933 -0.6192 -0.2536 <0.0001

State 3 Reference Variable

State 4 0.3902 0.0547 0.2830 0.4975 <0.0001

State 5 0.3524 0.2363 -0.1107 0.8155 0.1358

Overdispersion 1.0225 

AIC 23,148 

4.1.5 Rural Two-Lane, Two-Way Roads 

Table 9 shows the fixed-effects (β and p-value), the overdispersion, and AIC for the fixed-effect 

NB model for rural two-lane, two-way roadways. The friction is statistically significant at the 95-

percent confidence level. The results show that the p-value for macrotexture is not statistically
18

significance at the 95-percent confidence level. Furthermore, the positive sign for the regression 

coefficient contradicts the expectation that higher macrotexture results in lower crashes. 

Table 9. NB model – rural 2-lane, 2-way roadway. 

Parameters β Standard

Error

95% CI 

Lower

95% CI 

Upper p-value 

Intercept, β0 -7.3174 0.3595 -8.0220 -6.6129 <0.0001

ln (AADT) 0.8246 0.0380 0.7501 0.8991 <0.0001

Friction (SFN40) -0.0202 0.0024 -0.0249 -0.0155 <0.0001

State 1 0.4842 0.1387 0.2123 0.7560 0.0005

State 2 -0.4451 0.1147 -0.6700 -0.2202 0.0001

State 3 Reference Variable

State 4 0.5962 0.0703 0.4584 0.7340 <0.0001

State 5 1.1315 0.0852 0.9644 1.2985 <0.0001

Segments Reference Variable

Intersections 0.9125 0.0621 0.7908 1.0342 <0.0001

Curves 0.3566 0.0953 0.1698 0.5434 0.0002

Overdispersion 1.4116 

AIC 10,572 

4.1.6 Alternative Modeling Approaches

Two alternative modeling approaches were also tested. The first approach consisted of using a 

generalized partial linear model (GPLM), a special case of a generalized additive model (GAM). 

This approach was not adopted as the CMF estimations for different values of SFN40 lie within 

the GLM standard errors, which implies that the non-linearity in the safety effects is not 

statistically meaningful. The second approach explores the use of alternative SPFs that allow the 

development of CMFs for a change in friction to vary depending on the level of friction before the 

change. This approach was not adopted as the friction coefficients obtained are considerably higher 

than those obtained using the traditional approach and are not recommended for implementation. 

4.2 Crash Modification Factors/Functions (CMFs/CMFx) 

Estimating CMFs and CMFx that capture the variability inherent in CMFs using cross-sectional 

models is akin to developing SPFs and observing how the predicted crash frequency differs by a 

variation in the feature of interest. This section reports the CMFx computed using equation (6) and 

the NB model coefficients for each roadway facility and site type (segments, junctions, curves, 

and others). Functions are included only when the measurement of interest is statistically 

significant at a 95-percent level of confidence for that facility type/category. For example, if 

friction is significant, but macrotexture is not, then only the CMFx for friction is included. 

4.2.1 CMFs for Friction Improvements 

Table 10 presents the friction improvement regression coefficient (β1) for each CMFx for each 

roadway facility and site type, the resulting CMFs for a 10-unit increase in friction (SFN40), and 
19

the estimated percentage crash reductions using equation (6). For some site types, the friction 

coefficients were not statistically significant in the NB analysis, and they were omitted. The 

standard error for the 10-unit increase CMF was calculated using equation (7). 

Table 10. CMF and percent crash reduction for a 10-unit increase in SFN40.

1,2

Roadway 

Facility Site Type CMFx regression 

coefficient (β1) 

CMF for 10-

Unit SFN40 

Increase

Standard 

Error

(CMF)

% Crash 

Reduction

All Facilities All Site Types -0.0105 0.901 0.0064 9.9 

Freeways 

All Freeways Site 

Types -0.0031 0.969 0.0093 3.1 

Tangent 

Segments -0.0023 0.977 0.0103 2.3 

Ramp Access 

Points -0.0135 0.874 0.0219 12.6 

Curves -0.0169 0.844 0.0611 15.6 

Urban Arterials

All Urban 

Arterials Site 

Types 

-0.0282 0.754 0.0118 24.6 

Divided Tangent 

Segments -0.0288 0.754 0.0221 25.0 

Undivided 

Tangent 

Segments 

-0.0230 0.794 0.0286 20.6 

Intersections -0.0357 0.700 0.0161 30.1 

Curves -0.0281 0.755 0.0625 24.5 

Rural Multilane 

Highways 

All Rural 

Multilane 

Highways Site 

Types 

-0.0265 0.767 0.0142 23.3 

Divided Tangent 

Segments -0.0168 0.846 0.0238 15.4 

Undivided 

Tangent 

Segments 

-0.0094 0.910 0.0318 9.0 

Intersections -0.0344 0.709 0.0218 29.1 

Curves -0.0187 0.829 0.0731 17.1 

Rural – 2-Lane

2-Way Road 

All R2L-2W 

Roads Site Types -0.0202 0.817 0.0196 18.3 

Tangent 

Segments -0.0096 0.909 0.0243 9.1 

Intersections -0.0188 0.829 0.0386 17.1 

Curves -0.0188 0.829 0.0593 17.1 

1 The CMF values were obtained using equation (6), with the corresponding regression coefficients for β1 provided in this table, and assuming 

a 10-point increase in SFN40 value. 2 The CMFx and CMF corresponding to the Curve site types were developed based on a relatively small number of segments. 
20

4.2.1.1 CMFx by Roadway Facility Type 

Figure 3 compares the crash modification functions for the various roadway facility types. The 

impact of friction on crashes is relatively small on freeways but quite significant on urban arterials 

and rural multilane highways. In these types of facilities, a 10-point increase in SFN40 can result 

in a 23- to 25-percent reduction in crashes.

Figure 3. Graph. Comparison of CMFx for friction on different roadway facility types

(Source: FHWA). 

4.2.1.2 SPF and CMFx by Crash Type 

A similar approach was conducted by breaking down the analysis by crash type and developing 

separate SPFs for wet and dry crashes, as well as fatal (K) and fatal and serious injury (K+A)

crashes. This analysis used data from four States, as the detailed crash breakdown was not readily 

available for Texas. The effect of friction on fatal (K) and fatal and serious injury (K+A) crashes 

observed is highly variable and thus these results are not reported. The variability in the estimated 

model coefficients for the different facility types can probably be attributed to the smaller sample 

size. The resulting CMFx regression coefficients (β1) and CMF for 10-unit increase in friction 

(SFN40) using equation (6), and the estimated percentage crash reductions by surface condition 

are presented in Table 11, and Figure 4 through Figure 7. As expected, the figures show that in all 

cases friction has a higher impact on wet crashes than on dry crashes. 

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0 2 4 6 8 10 12 14

CMF

SFN40 Improvement

All

Freeways

Urban Arterials

Rural MLH

Rural 2L2W
21

Table 11. CMF and percent crash reduction by surface condition for a 10-unit increase in 

SFN40.1

Roadway 

Facility

Surface 

Condition 

CMFx regression 

coefficient (β1) 

CMF for 10-

unit SFN40 

increase (1)

Standard 

Error

CMF 

% Crash 

reduction

Expressways

Total Wet -0.0270 0.763 0.0109 23.7 

Total Dry -0.0135 0.873 0.0078 12.6 

Freeways

Total Wet -0.0088 0.916 0.0152 8.4 

Total Dry -0.0023 0.977 0.0106 2.3 

Urban 

Arterials

Total Wet -0.0479 0.619 0.0198 38.1 

Total Dry -0.0348 0.706 0.0150 29.4 

Rural 

Multilane 

Highways

Total Wet -0.0251 0.778 0.0179 22.2 

Total Dry -0.0251 0.778 0.0178 22.2 

Rural 2-lane, 2-

way Road

Total Wet -0.0467 0.627 0.0575 37.3 

Total Dry -0.0354 0.702 0.0343 29.8 

1 The CMF values were obtained using equation (6), with the corresponding regression coefficients for β1 provided in this table, and assuming 

a 10-point increase in SFN40 value. 
22

Figure 4. Graph. CMFx for friction on freeway segments by surface condition (Source: 

FHWA). 

 0.4

 0.5

 0.6

 0.7

 0.8

 0.9

 1.0

 1.1

0 2 4 6 8 10 12 14

CMF

SFN40 Improvement

All Crashes

Wet

Dry
23

Figure 5. Graph. CMFx for friction on urban and suburban arterial highway segments by 

surface condition (Source: FHWA). 

 0.4

 0.5

 0.6

 0.7

 0.8

 0.9

 1.0

0 2 4 6 8 10 12 14

CMF

SFN40 Improvement

All Crashes

Wet

Dry
24

Figure 6. Graph. CMFx for friction on rural multilane highway segments by surface 

condition (Source: FHWA). 

 0.4

 0.5

 0.6

 0.7

 0.8

 0.9

 1.0

0 2 4 6 8 10 12 14

CMF

SFN40 Improvement

All Crashes

Wet

Dry
25

Figure 7. Graph. CMFx for friction on rural two-lane, two-way road segments by surface 

condition (Source: FHWA).

4.2.2 CMFs for Macrotexture Improvements 

Table 12 presents the macrotexture improvement CMFx regression coefficient (β1) in terms of 

MPD for each roadway facility and site type in which macrotexture has a statistically significant 

effect on crashes. It lists the corresponding CMFs for a 0.5-mm increase in macrotexture (MPD) 

using equation (8) and the predicted percent crash reduction in each case. 

(8)

 0.4

 0.5

 0.6

 0.7

 0.8

 0.9

 1.0

0 2 4 6 8 10 12 14

CMF

SR40 Improvement

All

Wet

Dry

CMF=exp(β1ΔMPD)
26

Table 12. CMFx and percent crash reduction for a 0.5-mm increase in MPD.1

Roadway 

Facility Site Type CMFx regression 

coefficient (β1) 

CMF for 

0.5-mm 

Increase in 

MPD (1)

Standard 

Error 

(CMF)

% Crash 

Reduction

All Road 

Facilities All Site Types -0.2400 0.89 0.0064 11.3 

Freeways

All Site Types 0.1175 0.94 0.0141 5.7 

Tangent 

Segments -0.0982 0.95 0.0159 4.8 

Ramp Access 

Points -0.2159 0.90 0.0317 10.2 

Curves N/A

Urban 

Arterials

All Site Types -0.2363 0.89 0.0164 11.1 

Divided 

Tangent 

Segments

-0.2608 0.88 0.0299 12.2 

Undivided 

Tangent 

Segments

N/A

Intersections -0.2207 0.90 0.0214 10.4

Curves N/A

Rural 

Multilane 

Highways

All Site Types -0.1645 0.92 0.0352 7.9 

Divided 

Tangent 

Segments

N/A

Undivided 

Tangent 

Segments

N/A

Intersections -0.2885 0.87 0.0533 13.4

Curves N/A

Rural 2-lane, 

2-way Road 

All Site Types N/A

Tangent 

Segments N/A

Intersections N/A

Curves N/A

1 The CMF values were obtained using equation (8), with the corresponding regression coefficients for β1 provided in this table, and assuming 

a 0.5-mm increase in MPD value. 
27

Figure 8. Graph. Comparison of CMFx for macrotexture on different roadway facility 

types (Source: FHWA). 

4.2.3 Interaction Between Friction and Macrotexture 

Pavement friction is measured as the combination of two main components: microtexture and 

macrotexture. In this report, microtexture is represented by AASHTO TP 143 sideway-force 

friction (SFN40), and macrotexture is characterized by the mean profile depth, or “MPD.” 

The values of SFN40 generally vary from 10 to 90 and are affected by the polishing caused by the 

tires of the vehicles traveling on the individual aggregate particles in the pavement surface. The 

MPD values of the macrotexture are reported in millimeters and generally vary between 0.1 and 3 

mm. MPD values are representative of the level of openness in the pavement surface that allows 

water to travel out of the path of a tire. Pavement surface friction characteristics (i.e., microtexture 

and macrotexture) need to meet the friction demand for the given pavement section. Friction 

demand is the level of friction needed to safely perform braking, steering, and acceleration 

maneuvers. Friction demand varies with location and time due to changing geometrics, site and 

environmental conditions, traffic characteristics, and driver/vehicle characteristics. The interplay 

between microtexture and macrotexture to develop the needed friction forces to meet the friction 

demand is complex and varies. For example, macrotexture becomes more critical for meeting the 

friction demand as speed increases. Thus, the interaction of the two must be kept in mind when 

using the CMFs presented in the previous section. Research on pavement surface characteristics to 

develop a single parameter to describe friction has not yet succeeded. Several indices have been 

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0 0.2 0.4 0.6 0.8 1 1.2 1.4

CMF

MPD Improvement (mm)

All

Freeways

Urban Arterials

Rural MLH
28

proposed, like the International Friction Index (IFI) and other variants, but they consistently have 

been proven unreliable in resolving this problem (Jackson, 2008).

4.3 Friction Investigatory Thresholds

As previously discussed, the research team employed two approaches to identify the investigatory 

level, including the model-based method, and a more practical, graphical assessment using 

observed crash rates per 100 MVMT for different friction levels. The investigatory levels 

presented in this report reflect the graphical assessment of the dataset investigated. It is expected 

that larger datasets will improve the basis of investigatory thresholds. 

Figure 9 presents the investigatory threshold results for freeways. In general, for freeway tangent 

segments there is a trend of higher crash rates at lower friction values; however, the crash risk 

clearly increases when the friction value is lower than 36–38. Specifically, the difference in 

average crash rate is maximized when the friction threshold is set to that level. Therefore, in this 

example, the friction investigatory level would be between 36 and 38 SFN40, which corresponds 

to an approximate average risk of 80 crashes per 100 MVMT. The distribution of friction values 

for this roadway category is superimposed on the plot to provide an indication of what percentage 

of sections would fall below the investigatory level. 

Figure 9. Chart. Friction distribution, crash rates, and estimated thresholds for freeway

tangent segments (Source: FHWA). 

Figure 10 through Figure 16 present the graphical assessment results for investigatory threshold 

levels for the other roadway facility types. For these plots, the crash rates were calculated using 

0

50

100

150

200

250

300

0

500

1,000

1,500

2,000

2,500

3,000

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Average Crash Rate per 100 MVMT

Number of Sections

Friction (SFN40)

Freeway Roadway Segments

Friction Histogram

Total Crash Rate

Smoothed Crash Rate
29

the smoothing methodology from McCarthy et al. (2021a). Where n is the number of roadway 

segments, the smoothing methodology uses an adjusted, sliding window with (n ÷ 4) – 1 raw data 

points to flatten the curve produced using the observed crash counts. Using a smoothed curve, an 

inflection point, also the investigatory level, is easier to identify. 

Figure 10 shows that freeway ramp access points and horizontal curves present slightly higher 

thresholds than tangent segments (SFN40 of 42–44 and 44–46, respectively). Furthermore, the 

distribution of friction values shows a higher percentage of segments with friction lower than the 

thresholds, possibly due to the additional surface wear on these high demand friction areas. 

Figure 11 for urban and suburban arterial divided and undivided tangents and Figure 12 for urban 

and suburban arterial segments with intersections/ramp access points and horizontal curves have 

higher thresholds than other facility and site types, possibly due to factors other than friction. A 

friction level of 48–50 SFN40 corresponds to a transition in the crash rate curve for both divided 

and undivided, tangent segments thus adopted as the investigatory level range for the tangent 

segments. These values correspond to a risk of approximately 80–120 total crashes per 100 

MVMT. A similar value also seems to be applicable to curves, although the sample size was small

in this case. Finally, the last plot of the figure shows that crash rates are significantly higher for 

intersections (note the different scale) and a higher threshold of 54–58 seems to be appropriate. 

Figure 13 shows that for rural multilane roadway divided and undivided tangents, the crash rates 

increase as friction decreases, but the threshold determination is not as clear as in the case of 

freeway tangents. The figure also shows that a threshold range as high as 64–66 may be selected. 

However, given the distribution of friction values, a threshold of 48–50, which corresponds to an 

approximate average risk of 60 crashes per 100 MVMT in both divided and undivided rural 

multilane roadways, seems more appropriate. An interesting find for this example is that the 

friction investigatory level for this type of facility is higher than for freeways, possibly due to more 

potential vehicle maneuvers and conflicts. Although they show more variability, the plots for high 

demand segments (curves and intersections) in this type of facility indicate that higher thresholds 

(54–56 SFN40) may be appropriate in these locations. 

Figure 15 shows the results for rural 2-lane, 2-way tangent segments, and Figure 16 presents the 

results for rural 2-lane, 2-way with intersections or curves. In this case, the trend seems to suggest 

that a threshold range as high as 68–78 SFN40 may be appropriate for tangent segments; however, 

a lower range is recommended (54–56 SFN40) based on the distribution of friction values 

measured. As in the previous case, the plots for high demand segments (curves and intersections) 

in this type of facility indicate that higher thresholds may be appropriate for these locations.
30

(a) Ramp Access Points

(b) Freeway Curves

Figure 10. Graph. Friction distribution, crash rates, and estimated thresholds for freeway 

curves and ramp access points (Source: FHWA). 

0

50

100

150

200

250

300

0

50

100

150

200

250

300

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Average Crash Rate per 100 MVMT

Number of Sections

Friction (SFN40)

Freeway Ramp Access Points

Friction Histogram

Total Crash Rate

Smoothed Crash Rate

0

50

100

150

200

250

300

0

50

100

150

200

250

300

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Average Crash Rate per 100 MVMT

Number of Sections

Friction (SFN40)

Freeway Curves

Friction Histogram

Total Crash Rate

Smoothed Crash Rate
31

(a) Divided

(b) Undivided 

Figure 11. Graph. Friction distribution, crash rates, and estimated thresholds for urban 

and suburban arterial highway tangents (Source: FHWA). 

0

50

100

150

200

250

300

0

50

100

150

200

250

300

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Average Crash Rate per 100 MVMT

Number of Sections

Friction (SFN40)

Divided Urban Arterial Tangents

Friction Histogram

Total Crash Rate

Smoothed Crash Rate

0

50

100

150

200

250

300

0

50

100

150

200

250

300

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Average Crash Rate per 100 MVMT

Number of Sections

Friction (SFN40)

Undivided Urban Arterial Tangents

Friction Histogram

Total Crash Rate

Smoothed Crash Rate
32

(a) Intersections

(b) Curves

Figure 12. Graph. Friction distribution, crash rates, and estimated thresholds for urban 

and suburban arterial highway intersections/ramp access points and horizontal curves

(Source: FHWA). 

0

50

100

150

200

250

300

350

400

450

500

550

600

0

100

200

300

400

500

600

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Average Crash Rate per 100 MVMT

Number of Sections

Friction (SFN40)

Urban Arterial Intersections

Friction Histogram

Total Crash Rate

Smoothed Crash Rate

0

50

100

150

200

250

300

0

50

100

150

200

250

300

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Average Crash Rate per 100 MVMT

Number of Sections

Friction (SFN40)

Urban Arterial Curves

Friction Histogram

Total Crash Rate

Smoothed Crash Rate
33

(a) Divided

(b) Undivided 

Figure 13. Graph. Friction distribution, crash rates, and estimated thresholds for rural 

multilane road tangent segments (Source: FHWA). 

0

50

100

150

200

250

300

0

200

400

600

800

1000

1200

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Average Crash Rate per 100 MVMT

Number of Sections

Friction (SFN40)

Divided Rural Multilane Tangents

Friction Histogram

Total Crash Rate

Smoothed Crash Rate

0

50

100

150

200

250

300

0

50

100

150

200

250

300

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Average Crash Rate per 100 MVMT

Number of Sections

Friction (SFN40)

Undivided Rural Multilane Tangents

Friction Histogram

Total Crash Rate

Smoothed Crash Rate
34

(a) Intersections

(b) Curves

Figure 14. Graph. Friction distribution, crash rates, and estimated thresholds for rural 

multilane road segments with intersections or horizontal curves (Source: FHWA). 

0

50

100

150

200

250

300

0

50

100

150

200

250

300

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Average Crash Rate per 100 MVMT

Number of Sections

Friction (SFN40)

Rural Multilane Intersections

Friction Histogram

Total Crash Rate

Smoothed Crash Rate

0

50

100

150

200

250

300

0

50

100

150

200

250

300

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Average Crash Rate per 100 MVMT

Number of Sections

Friction (SFN40)

Rural Multilane Curves

Friction Histogram

Total Crash Rate

Smoothed Crash Rate
35

Figure 15. Graph. Friction distribution, crash rates, and estimated thresholds for rural 2-

lane, 2-way road tangents (Source: FHWA). 

0

50

100

150

200

250

300

0

100

200

300

400

500

600

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Average Crash Rate per 100 MVMT

Number of Sections

Friction (SFN40)

Rural 2L2W Tangents Friction Histogram

Total Crash Rate

Smoothed Crash Rate
36

(a) Intersections

(b) Curves

Figure 16. Graph. Friction distribution, crash rates, and estimated thresholds for rural 2-

lane, 2-way (2L2W) road intersections and horizontal curves (Source: FHWA). 

0

50

100

150

200

250

300

0

50

100

150

200

250

300

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Average Crash Rate per 100 MVMT

Number of Sections

Friction (SFN40)

Rural 2L2W Intersections

Friction Histogram

Total Crash Rate

Smoothed Crash Rate

0

50

100

150

200

250

300

0

50

100

150

200

250

300

0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96

Average Crash Rate per 100 MVMT

Number of Sections

Friction (SFN40)

Rural 2L2W Curves

Friction Histogram

Total Crash Rate

Smoothed Crash Rate
37

Table 13 summarizes the values obtained by the graphical assessment for all roadway site types 

investigated. The table also includes an approximate conversion to the side-force coefficient of 

friction measured in the UK at 30 mph (50 km/h), or “UK CSC,” and the friction investigatory 

levels adopted in the UK for similar roadway types with regular or standard risk areas (ST) and 

lower-risk areas (LR) (CS 228; Highways England, 2019). The UK equivalent is obtained by 

removing the adjustment that is used in the UK to account for a change in the rubber characteristics 

of the tire (0.78), adjusting for speed (40 mph versus 30 mph in the UK), and dividing by 100 to 

convert the friction number to a coefficient of friction. These are provided as baseline references

only, but it is interesting to note that the values are relatively consistent. Furthermore, the CS 228 

does not include a separate category for urban and suburban arterial roadways. 

Table 13. Summary of the threshold analysis

Roadway 

Facility 

Type

Site Type Suggested Graphic 

Threshold

Approximate 

UK CSC Eq.

CS 228 ST CS 228 LR

Freeways 

Tangents 40 36 – 38 0.29 - 0.31 0.35 0.30

Curves 45 42 – 44 0.34 - 0.36 0.45 - 0.50

Ramp Access 45 44 – 46 0.36 - 0.37

Rural 

Multilane 

Roadways

Divided Tangents 50 48 – 50 0.39 - 0.41 0.35 - 0.40 0.30

Undivided 

Tangents 50 48 – 50 0.39 - 0.41 0.40 - 0.45 0.35 

Curves 55 54 – 56 0.44 - 0.46 0.45 - 0.50

Intersections 55 54 - 56 0.44 - 0.46 0.45 - 0.55 0.40

Rural 2-

lane, 2-

way

Roadways

Tangents 50 48 - 50 0.39 - 0.41 0.40 - 0.45 0.35 

Curves 55 54 - 56 0.44 - 0.46 0.50- 0.55 0.45 

Intersections 60 54 - 56 0.44 - 0.46 0.45 - 0.55 0.40 

Urban and 

Suburban 

Arterials 

Divided Tangents 50 48 - 50 0.39 - 0.41

Undivided 

Tangents 50 48 - 50 0.39 - 0.41 

Curves 50 48 - 50 0.39 - 0.41

Intersections 55 54 - 56 0.44 - 0.46
38

CHAPTER 5. Conclusions

The following conclusions can be drawn from the analysis of the relationship between crash rates 

and frictional properties using the five-State data set described in this report: 

• The analysis confirmed a strong statistical association between pavement surface frictional 

properties (friction and macrotexture) and crash rates. Lower crash rates were observed 

with higher friction (SFN40) and macrotexture (MPD) on all roadway types. 

• The data supported development of SPFs for total crashes on different roadway facility 

types that included friction and macrotexture measurement using traditional NB models. 

o Friction was found to have a statistically significant effect for predicting total 

crashes on all the roadway facility types. 

o Macrotexture was found to have a statistically significant effect for predicting total 

crashes on all roadway facility types except rural two-lane/two-way roads.

However, thisis likely due to data limitations, and should not be interpreted to mean

that macrotexture is not important on these roads. 

• These SPFs were then used to develop CMFs and CMFx for relatively straight segments 

without events (tangents) and with areas of higher friction demand (curves and 

intersections) on each type of facility. 

o The CMFx and corresponding crash reduction percentages for 10-unit increases in 

SFN40 are presented in Tables 10 and 12. They are reasonable and generally follow 

the expected trends. 

o The results in Table 10 indicated potential reductions of up to 30 percent of total 

crashes can be achieved with a 10-unit increase in SFN40 (on urban arterial 

intersections). 

• Illustrative friction investigatory thresholds were also defined for the various roadway 

facility and site types. They were developed based mostly on the graphical interpretation

of the crash rates for different friction levels. As expected, the investigatory levels are 

higher for higher friction demand sites, such as curves, ramp access points, and 

intersections. 

The following research is recommended for further improving the models and resulting 

CMF/CMFx: 

• Some categories have a relatively small number of observations and further work should 

include incorporating data from other States that is becoming available (Kentucky, Illinois, 

etc.). It would be particularly useful to assemble larger data sets to get more robust results 

for fatal and serious injuries crash and crash types. 

• The interaction between microtexture and macrotexture needs further investigation. 

• As the US gains experience with continuous friction measurement data collection, seasonal 

adjustments can be applied, in accordance with international practice, to enhance the 

analysis.
39

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