# Research on Safety and Static-Dynamic Legibility of Distressed Pavement

Authors: Chengyuan Mao; Yiming Bie; Yulong Pei; Weiwei Qi
Journal: Discrete Dynamics in Nature and Society
 (2015)

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## Abstract

In order to study the impacts of distressed pavement on driving safety, the drivers’ driving behavior and driving characteristics need to be analyzed. By analyzing the drivers’ characteristics, driving behavior’ and braking characteristics of vehicles, relation between static legibility distance of the distressed pavement under different driving conditions and dynamic legibility distance during driving is revealed via statistical analysis. The relation between vehicle speeds, braking performance, and the minimum safety legibility distance is developed. The recommended static legibility distances for different speed limits are proposed, which would be useful to improve the driving safety under adverse road conditions.


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## Body

## 1. Introduction

With the rapid growth of the economy and motorization, road construction has obtained unprecedented development while road mileage and density increase rapidly. In the conditions that facilities and technologies of road maintenance are more and more mature, and the materials are increasingly sophisticated, the road conditions are significantly improved. However, distress in pavement is inevitable due to the limited service life of the pavement, overloading of vehicles, and the quality of pavement. Besides, restricted by practical construction conditions, the distressed pavement cannot be repaired all at once. Therefore, distressed pavements are widespread in the cities with a great quantity beyond imagination. Damage of manhole covers, potholes, and settlement can be seen everywhere in the Chinese cities.In daily life, people may pay more attention to factors which directly trigger traffic accidents since the damage of vehicles, casualties, and economic losses they caused are direct and obvious. Therefore, it is indeed worthy of research and attention [1, 2]. On the other hand there is also another initial factor which may induce traffic accident, reduce traffic capacity, and affect the normal operation of the driver and driving comfort. That is the distress of the pavement widespread in the road. This may not be the most common factors leading to traffic accidents, but their adverse effects cannot be disregarded [3, 4]. The road capacity can be severely reduced by the deceleration or evasion of the vehicles due to the distress of the pavement in a road section with heavy traffic and other damage (such as the increase of the abrasion of tires, energy consumption, and emissions). The physiological and psychological damage to the drivers and the indirect loss (such as drivers’ time loss) may be much more than those of one fatal traffic accident which may be even far beyond our imagination.According to certain analysis, in the traffic accident, the error of observation, misjudgment, error of action, and other errors, respectively, account for 54%, 54%, 36%, and 1%; namely, the accidents resulting from the error of observation account for more than a half of the whole accidents. From this point the study on legibility during driving is the basis of the study on drivers’ characteristics and behaviors [5].Drivers will receive varied stimulations from all kinds of traffic information. The main part of the traffic information which is more than 80% is obtained by vision. Drivers need to sense the traffic condition quickly and accurately, identify initial objectives, predict the development and consequence of the traffic condition, and take proper measures to guarantee the safety of driving under the complex traffic conditions [6, 7]. The psychological mood of the drivers during driving will be influenced by traffic condition and the state of their mind: on the one hand, positive and peaceful mind can remit the driving fatigue while negative mind is more likely to induce anger and tension which will consequently trigger adventure or aggressive driving behaviors; on the other hand, psychological burden of drivers will be increased by bad traffic condition [8].Since distressed pavement will adversely affect the operation of the vehicles, researches on the recognition, classification, and influence of the distress in pavement are conducted by different scholars. Grivas et al. [9, 10] put forward an analysis method based on fuzzy set theory which can be used to determine single index of the pavement damage from several indexes. Different levels of pavement distress are qualitatively described; the value of the distress is expressed through membership function and quantified via the input of road maintenance specialist. Prozzi and Hong [11] established an axle load distribution optimization function, put forward a comprehensive statistical method based on road load, and described the observed axial load by using the mixed lognormal distribution. Khan [12] established an identification manual of the distressed pavement in Pakistan which provided the method to obtain consistent, repeatable, and a large deal of data on pavement distress. It can be an advanced basic reference book on pavement management system which is involved in the deterioration trend analysis and evaluation of motor vehicle traffic, Pakistan, 2006, and at the same time provides quantitative information for the repairing scope of distressed pavement. Karan et al. [13] described the relationship between average speeds of vehicles and the condition of the pavement for two-lane highway: pavement irregularities were chosen to be the evaluation parameters of the pavement condition, 72 of survey sections were selected according to the pavement irregularities, traffic capacity and saturation were calculated, and then comfort index, saturation, and the speed limit were chosen as control index; thus regression model between the average speed of vehicles and the pavement irregularities was established.Scholars have also made some progress on the research in traffic operation and traffic capacity under the condition of distressed pavement. For example, Gallegos López et al. [14] recorded the information of road profile and introduced international roughness index to evaluate the condition of the pavement; the international pavement roughness index was absorbed into the formula of road capacity and LOS (level of service) in HCM2000 as a corrected parameter; thus a new formula considering the influence of both lane width and pavement roughness on road capacity was established; the correction parameters were obtained by fitting to actual statistical data collected in Mexico and tested by actual cases. Chandra [15] analyzed the influence of pavement irregularities on the road capacity and relation model between road capacity and pavement irregularities was established via analyzing the data of pavement irregularities, free stream velocity, and the proportion of middle-sized vehicles. Johnnie and Neil [16] analyzed the traffic stream characteristics when roads were under maintenance and construction: the impact of some lanes under long-term or short-term construction on the traffic flow was investigated; the relation between vehicle speed and density was studied and all the researches indicate that road maintenance and construction have great impact on the parameters of traffic flow [17].In conclusion, the research on the generation of pavement distress and pavement maintenance is numerous. But the research on the relation between static and dynamic legibility of pavement distress and safety which is the base of the research on driving behavior and traffic flow is very few. Therefore, based on experimental investigation, using regression analysis method, by means of theory analysis, the internal relation between pavement distresses, legibility, driving behavior, and driving safety is revealed and the theory of driving behaviors under pavement distress is perfected. The follow-up arrangement of this paper is as follows:(1)
survey on legibility distance of distressed pavement;(2)
relation between static and dynamic legibility of distressed pavement;(3)
analysis on the safety legibility of distressed pavement.


## 2. Survey on Legibility Distance of Distressed Pavement

### 2.1. Legibility of Pavement Distress and Its Influencing Factors

In order to study whether pavement distress is easy to be noticed or not or whether it has significant influence on drivers’ operation, the concept of legibility of pavement distress is introduced.Just as the static vision and dynamic visual of the human being, legibility of pavement distress can also be divided into static legibility (Ls) and dynamic legibility (Ld). Ls refers to the complexity for drivers to recognize the pavement distress when the speed of the vehicle is extremely slow or even zero and the distance between the driver and the pavement distress is stable while Ld refers to the complexity for drivers to recognize the pavement distress in the process of driving when the distance between the driver and the pavement distress keeps changing. Ld can be measured by the distance between the eyes of the observer and the pavement distress as Ls. Corresponding with static legibility and dynamic legibility, legibility distance can be divided into static legibility distance (Ds) and dynamic legibility distance (Dd). Existing research indicates that human eyesight will be reduced with the increase of the travelling speed; therefore dynamic legibility is weaker than static legibility and is getting weaker with the speed increasing.According to Yaling Guo et al. studies, the main influencing factors of legibility mainly include the visual angle of the eyes, color contrast surrounding the objects, and the displacement of the object relative to the observer’s eyes. The visual angle of the observer’s eyes on the objects is determined by the size of the objects and the distance between the observer’s eyes and the objects as shown in Figure1; the visual angle on object A is the same to that on object B; then the legibility of them is the same although A is bigger than B [18, 19].Figure 1
The visual angle of the eyes.


### 2.2. Investigation on Legibility Distance of Distressed Pavement

The main factors influencing the legibility distance of distressed pavement are the size of the distress, the location of the distress, drivers’ characteristics and vehicle speed, and so forth. Therefore, the survey is conducted aiming at these factors.Investigation on the size of pavement distress: 20 pavement distresses on expressway, trunk road, secondary road, and branch in Harbin are selected and the extents of the damage (size of the distresses) are measured.Investigation on static legibility distanceDs of distressed pavement: 4 types of drivers including male novice drivers, male skilled drivers, female novice drivers, and female skilled drivers are chosen as respondents and the legibility distances of distressed pavement selected are investigated. CVA (corrected visual acuity) of the respondents ranges from 1.0 to 1.2 and the heights of them range from 1.70 m to 1.74 m. The legibility distances of the whole respondents are recorded and the average legibility distance is chosen to be the static legibility distance of the distressed pavement.Investigation on dynamic legibility distanceDd: the respondents were wearing I view X HED eye tracker which is made in Germany. All respondents have known the position of pavement distress. The investigators are driving a Santana 2000 car in the selected pavement sections, the eye tracker records the drivers’ eyes track, and the vehicle data recorder records vehicle speed and vehicle’s location. Survey with vehicle recorder and eye tracker is shown in Figure 2. The Dd we collected is the average distance between driver’s eyes and distressed pavement, when the driver found distressed pavement.Figure 2
Survey with vehicle recorder and eye tracker.The survey result of legibility distance is shown in Table1. Most legibility distance belongs to 20–100 m, the average Ds is 48.4 m, and average Dd is 65.7 m; obviously,Dsis longer than Dd.Table 1
The investigation results of pavement distress.
Number
Location①
Road level②
Length (10−2 m)
Width (10−2 m)
D
s (m)
D
d (m)
v (km/h)
1
Huang He
b
108
102
94.8
73.7
41.2
2
Huang He
b
122
178
88.0
63.8
41.5
3
Wenchang
b
92
88
94.8
75.4
26.3
4
Wenchang
b
37
32
24.3
18.2
23.6
5
Wenchang
b
163
62
66.3
43.5
35.2
6
Jiaohua
b
125
135
43.6
25.6
18.1
7
Xidazhi
b
145
76
79.5
59.5
36.6
8
Hexing
a
88
98
97.5
75.4
47.6
9
Hexing
a
126
120
106.6
91.1
34.9
10
Jinxiang
b
110
104
71.9
49.2
29.9
11
Jinxiang
b
55
45
33.2
20.5
32.4
12
Gongbin
b
113
96
65.4
51.5
25.1
13
Hanshui
c
88
56
56.4
44.1
18.1
14
Hongxiang
c
106
121
66.2
45.6
34.0
15
Zhongshan
b
114
102
86.1
61.7
38.3
16
Zhongshan
b
90
90
37.6
22.5
32.6
17
Xuan Qiang
d
64
114
43.1
23.3
19.8
18
Lujia
d
210
150
102.9
84.2
24.3
19
Pinggong
d
42
34
30.8
20.3
19.5
20
Pinggong
d
44
30
24.6
18.4
25.8
Notes:①road name.
②a: expressway; b: trunk road; c: secondary road; d: branch.


## 2.1. Legibility of Pavement Distress and Its Influencing Factors

In order to study whether pavement distress is easy to be noticed or not or whether it has significant influence on drivers’ operation, the concept of legibility of pavement distress is introduced.Just as the static vision and dynamic visual of the human being, legibility of pavement distress can also be divided into static legibility (Ls) and dynamic legibility (Ld). Ls refers to the complexity for drivers to recognize the pavement distress when the speed of the vehicle is extremely slow or even zero and the distance between the driver and the pavement distress is stable while Ld refers to the complexity for drivers to recognize the pavement distress in the process of driving when the distance between the driver and the pavement distress keeps changing. Ld can be measured by the distance between the eyes of the observer and the pavement distress as Ls. Corresponding with static legibility and dynamic legibility, legibility distance can be divided into static legibility distance (Ds) and dynamic legibility distance (Dd). Existing research indicates that human eyesight will be reduced with the increase of the travelling speed; therefore dynamic legibility is weaker than static legibility and is getting weaker with the speed increasing.According to Yaling Guo et al. studies, the main influencing factors of legibility mainly include the visual angle of the eyes, color contrast surrounding the objects, and the displacement of the object relative to the observer’s eyes. The visual angle of the observer’s eyes on the objects is determined by the size of the objects and the distance between the observer’s eyes and the objects as shown in Figure1; the visual angle on object A is the same to that on object B; then the legibility of them is the same although A is bigger than B [18, 19].Figure 1
The visual angle of the eyes.


## 2.2. Investigation on Legibility Distance of Distressed Pavement

The main factors influencing the legibility distance of distressed pavement are the size of the distress, the location of the distress, drivers’ characteristics and vehicle speed, and so forth. Therefore, the survey is conducted aiming at these factors.Investigation on the size of pavement distress: 20 pavement distresses on expressway, trunk road, secondary road, and branch in Harbin are selected and the extents of the damage (size of the distresses) are measured.Investigation on static legibility distanceDs of distressed pavement: 4 types of drivers including male novice drivers, male skilled drivers, female novice drivers, and female skilled drivers are chosen as respondents and the legibility distances of distressed pavement selected are investigated. CVA (corrected visual acuity) of the respondents ranges from 1.0 to 1.2 and the heights of them range from 1.70 m to 1.74 m. The legibility distances of the whole respondents are recorded and the average legibility distance is chosen to be the static legibility distance of the distressed pavement.Investigation on dynamic legibility distanceDd: the respondents were wearing I view X HED eye tracker which is made in Germany. All respondents have known the position of pavement distress. The investigators are driving a Santana 2000 car in the selected pavement sections, the eye tracker records the drivers’ eyes track, and the vehicle data recorder records vehicle speed and vehicle’s location. Survey with vehicle recorder and eye tracker is shown in Figure 2. The Dd we collected is the average distance between driver’s eyes and distressed pavement, when the driver found distressed pavement.Figure 2
Survey with vehicle recorder and eye tracker.The survey result of legibility distance is shown in Table1. Most legibility distance belongs to 20–100 m, the average Ds is 48.4 m, and average Dd is 65.7 m; obviously,Dsis longer than Dd.Table 1
The investigation results of pavement distress.
Number
Location①
Road level②
Length (10−2 m)
Width (10−2 m)
D
s (m)
D
d (m)
v (km/h)
1
Huang He
b
108
102
94.8
73.7
41.2
2
Huang He
b
122
178
88.0
63.8
41.5
3
Wenchang
b
92
88
94.8
75.4
26.3
4
Wenchang
b
37
32
24.3
18.2
23.6
5
Wenchang
b
163
62
66.3
43.5
35.2
6
Jiaohua
b
125
135
43.6
25.6
18.1
7
Xidazhi
b
145
76
79.5
59.5
36.6
8
Hexing
a
88
98
97.5
75.4
47.6
9
Hexing
a
126
120
106.6
91.1
34.9
10
Jinxiang
b
110
104
71.9
49.2
29.9
11
Jinxiang
b
55
45
33.2
20.5
32.4
12
Gongbin
b
113
96
65.4
51.5
25.1
13
Hanshui
c
88
56
56.4
44.1
18.1
14
Hongxiang
c
106
121
66.2
45.6
34.0
15
Zhongshan
b
114
102
86.1
61.7
38.3
16
Zhongshan
b
90
90
37.6
22.5
32.6
17
Xuan Qiang
d
64
114
43.1
23.3
19.8
18
Lujia
d
210
150
102.9
84.2
24.3
19
Pinggong
d
42
34
30.8
20.3
19.5
20
Pinggong
d
44
30
24.6
18.4
25.8
Notes:①road name.
②a: expressway; b: trunk road; c: secondary road; d: branch.


## 3. Relation Analysis onDs and Dd

### 3.1. Analysis on Data Investigated

As the data investigated from 20 pavement distresses show,(1)
the range of static legibility distance is from 24.3 m to 106.6 m and the average is 65.7 m;(2)
the range of dynamic legibility distance is from 18.2 m to 91.1 m and the average is 48.4 m;(3)
the static legibility distance is much longer than the dynamic legibility distance in one distressed pavement which indicates that dynamic vision is weaker than static vision once again.


### 3.2. Relation Analysis on Static Legibility Distance (Ds) and Dynamic Legibility Distance (Dd)

Existing research shows that dynamic legibility distance (Dd) of the object is related to static legibility distance (Ds) and the speed of the object v. Taking Dd as the dependent variable and taking Ds and v as the independent variable, then
(1)Dd=0.9004·Ds-0.1968·v-4.7645,
where Dd is the pavement distress’s dynamic legibility, m; Ds is the pavement distress’s static legibility, m; v is the vehicle’s speed, m/s.The relationship betweenDd and Ds is shown in Figure 3. We can see a linear relationship between Dd, Ds, and v (the correlation coefficient was 0.9851; the standard error was 3.8120).Figure 3
Analysis of relationship betweenDdandDs.IfDs∈(0,100), v∈(0,100), then we can get the relationship between Dd, Ds, and v, shown in Figure 4. The results indicated that Dd increased with the raising of Ds and diminishes with v. So, if we want to increase Dd, we could set a speed limit and increase the value of Ds.Figure 4
Relation analysis onDd, Ds, and v.


## 3.1. Analysis on Data Investigated

As the data investigated from 20 pavement distresses show,(1)
the range of static legibility distance is from 24.3 m to 106.6 m and the average is 65.7 m;(2)
the range of dynamic legibility distance is from 18.2 m to 91.1 m and the average is 48.4 m;(3)
the static legibility distance is much longer than the dynamic legibility distance in one distressed pavement which indicates that dynamic vision is weaker than static vision once again.


## 3.2. Relation Analysis on Static Legibility Distance (Ds) and Dynamic Legibility Distance (Dd)

Existing research shows that dynamic legibility distance (Dd) of the object is related to static legibility distance (Ds) and the speed of the object v. Taking Dd as the dependent variable and taking Ds and v as the independent variable, then
(1)Dd=0.9004·Ds-0.1968·v-4.7645,
where Dd is the pavement distress’s dynamic legibility, m; Ds is the pavement distress’s static legibility, m; v is the vehicle’s speed, m/s.The relationship betweenDd and Ds is shown in Figure 3. We can see a linear relationship between Dd, Ds, and v (the correlation coefficient was 0.9851; the standard error was 3.8120).Figure 3
Analysis of relationship betweenDdandDs.IfDs∈(0,100), v∈(0,100), then we can get the relationship between Dd, Ds, and v, shown in Figure 4. The results indicated that Dd increased with the raising of Ds and diminishes with v. So, if we want to increase Dd, we could set a speed limit and increase the value of Ds.Figure 4
Relation analysis onDd, Ds, and v.


## 4. Analysis on Safety Legibility of Distressed Pavement

### 4.1. Basic Legibility Rules

When the driver notices the pavement distress, he/she would judge if or not the pavement distress has a negative effect, and then he/she will decide how to drive, for example, gazing at the pavement distress and paying attention to the position of the vehicle. The worse the legibility of pavement distress is and the greater the distress is, the longer the fixation time can be.In order to judge the probable damage caused by the pavement distress, the drivers still need to constantly collect driving information by watching, listening, and touching. When the vehicle is approaching the pavement distress, the driver will pay more and more attention to it; in particular when the vehicle is 5–20 meters away from the pavement distress, the driver will always gaze at it till pass the distressed pavement as shown in Figure5.Figure 5
The drivers’ observation process of pavement distress.


### 4.2. Safety Legibility Distance Analysis

#### 4.2.1. The Minimum Safety Distance

The minimum safety distance (Dmin⁡1) refers to the safe distance to front vehicle or obstacle when vehicle suddenly brakes from 100 km/h to 0 in an emergency, which can be expressed as follows:
(2)Dmin⁡1=-0.5·v2a+d,
where Dmin⁡1 is the minimum safety distance, m; a is acceleration of the vehicle, acceleration a>0, deceleration a<0, emergency braking a belongs to −7.5 m/s2~−10 m/s2, and a=-7.5 m/s2 in this paper. d is safe stopping distance, at most d = 2~5 m in general, and d=5 m in this paper.According to formula2, we can see that the better the vehicle braking performance is, the shorter the Dmin⁡1 is. Thus we can get Dmin⁡1 in all speed conditions, as shown in Table 2.Table 2
D
min
⁡
1 in different speed conditions.
Number
v (Km/h)
v (m/s)
Brake time (s)
Brake distance (m)
D
min
⁡
1 (m)
1
20
5.56
0.74
2.06
7.06
2
30
8.33
1.11
4.63
9.63
3
40
11.11
1.48
8.23
13.23
4
50
13.89
1.85
12.86
17.86
5
60
16.67
2.22
18.52
23.52
6
70
19.44
2.59
25.21
30.21
7
80
22.22
2.96
32.92
37.92
8
90
25.00
3.33
41.67
46.67
9
100
27.78
3.70
51.44
56.44The legal requirement of automobile (nonload) braking distance in China is as follows.(1)
The braking distance of a passenger service vehicle with no more than 9 seats must be shorter than 19 m when its initial velocity is 50 km/h.(2)
The braking distance of a truck with a total mass less than 4.5 t must be shorter than 21 m when its initial velocity is 50 km/h.(3)
The braking distance of the other cars must be shorter than 9 m when its initial velocity is 30 km/h.So, in the first case, the maximumDmin⁡1 is 19+5=24 m; in the second case, the maximum Dmin⁡1 is 21+5=26 m and in the third case the maximum Dmin⁡1is 9+5=14 m.


#### 4.2.2. Theoretical Minimum Safety Legibility Distance

The theoretical minimum safety legibility distance refers to the safe braking distance when the driver fully concentrates on driving, finds the distress at the first time, and decelerates immediately fromvto 0 km/h.According to normal driving behaviors,Dmin⁡0equals the sum of the distance vehicle runs during the drivers’ perception-reaction time trand the safe distance between vehicles d. Perception-reaction time of the driver tr is as follows:
(3)tr=t1+t2,
where t1 is perception reaction time, 0.3–0.5 s, and t2 is driving behavior operation time, 0.3–0.5 s:
(4)tb=-va.d
r is the traveling distances of the vehicle when the driver responses to the pavement distress:
(5)dr=t1+t2·v.And the traveling distance of the vehicle during the brake can be shown in formula5:
(6)db=-0.5·a·tb2.Put formula4 into formula 6:
(7)db=-0.5·v2a.Then(8)Dmin⁡0=dr+db+d=t1+t2·v-0.5·v2a+d.


#### 4.2.3. Actual Minimum Safety Legibility Distance

Influenced by the driving condition, the drivers’ psychological and physiological state, the drivers’ attention, and the drivers’ dynamic vision, the actualDd is larger than Dmin⁡0.IfDd<Dmin⁡0, it is danger; while Dd≥Dmin⁡0, it is safe. Then the safety condition can be concluded as follows:
(9)0.9004Ds-0.1968v-4.7645≥v·tr-0.5v2a+d.Take sedan car as an example, when, in emergency,tr=1.0s,  a=-7.5 m/s2, and d=5 m. Put these parameters into formula 9; then we can get
(10)Ds≥0.074v2+1.3292v+10.8446.When the equal sign is tenable in formula10Ds becomes the actual minimum safe static legibility distance Dmin⁡s:
(11)Dmin⁡s=0.074v2+1.3292v+10.8446.


#### 4.2.4. Case Study

The range of design speed of the urban road in China is 20~80 km/h; and then, the values ofDmin⁡s in different speeds can be calculated by formula 11, and the results are shown in Table 3.Table 3
D
min
⁡
s in different speed conditions.
Number
v (km/h)
v (m/s)
AcademicDs (m)
RecommendedDs (m)
1
20
5.56
20.51
25
2
30
8.33
27.06
30
3
40
11.11
34.75
35
4
50
13.89
43.58
45
5
60
16.67
53.55
55
6
70
19.44
64.67
65
7
80
22.22
76.93
80
8
90
25.00
90.32
95
9
100
27.78
104.87
105
Note: the mantissa of recommendedDs takes an integer multiple of 5.It can be found that the value ofDs gradually increases as the speed increases when compared with Tables 2 to 3. When the value ofvreaches 100 km/h, Ds reaches 105 m, which is much longer than normal braking distance when v=100 km/h (50 m). The two main reasons are (1) the driver failed to detect the pavement distress in time; (2) there is a delay between the drivers’ identification, reaction, and the operation.Driving safety is not only associated with vehicles but also associated with the drivers’ reaction characteristics and operation skills. Therefore, we need to be aware of the possibility that the driver may not be able to find the distress in time and certain observation time and space are necessary.Data in Table3 shows that, in a road section where limit speed is 60 km/h, if the static legibility distance Ds is less than 55 m, it will be susceptible to accidents.In addition, according to the inquiring survey on drivers in the condition that there is no need to brake when pavement distress is noticed, whent<3s, drivers will react to the pavement distress in haste and it is prone to accidents, when t>4s, drivers can deal with the information better, and when t>5s, drivers can take the information in stride.


## 4.1. Basic Legibility Rules

When the driver notices the pavement distress, he/she would judge if or not the pavement distress has a negative effect, and then he/she will decide how to drive, for example, gazing at the pavement distress and paying attention to the position of the vehicle. The worse the legibility of pavement distress is and the greater the distress is, the longer the fixation time can be.In order to judge the probable damage caused by the pavement distress, the drivers still need to constantly collect driving information by watching, listening, and touching. When the vehicle is approaching the pavement distress, the driver will pay more and more attention to it; in particular when the vehicle is 5–20 meters away from the pavement distress, the driver will always gaze at it till pass the distressed pavement as shown in Figure5.Figure 5
The drivers’ observation process of pavement distress.


## 4.2. Safety Legibility Distance Analysis

### 4.2.1. The Minimum Safety Distance

The minimum safety distance (Dmin⁡1) refers to the safe distance to front vehicle or obstacle when vehicle suddenly brakes from 100 km/h to 0 in an emergency, which can be expressed as follows:
(2)Dmin⁡1=-0.5·v2a+d,
where Dmin⁡1 is the minimum safety distance, m; a is acceleration of the vehicle, acceleration a>0, deceleration a<0, emergency braking a belongs to −7.5 m/s2~−10 m/s2, and a=-7.5 m/s2 in this paper. d is safe stopping distance, at most d = 2~5 m in general, and d=5 m in this paper.According to formula2, we can see that the better the vehicle braking performance is, the shorter the Dmin⁡1 is. Thus we can get Dmin⁡1 in all speed conditions, as shown in Table 2.Table 2
D
min
⁡
1 in different speed conditions.
Number
v (Km/h)
v (m/s)
Brake time (s)
Brake distance (m)
D
min
⁡
1 (m)
1
20
5.56
0.74
2.06
7.06
2
30
8.33
1.11
4.63
9.63
3
40
11.11
1.48
8.23
13.23
4
50
13.89
1.85
12.86
17.86
5
60
16.67
2.22
18.52
23.52
6
70
19.44
2.59
25.21
30.21
7
80
22.22
2.96
32.92
37.92
8
90
25.00
3.33
41.67
46.67
9
100
27.78
3.70
51.44
56.44The legal requirement of automobile (nonload) braking distance in China is as follows.(1)
The braking distance of a passenger service vehicle with no more than 9 seats must be shorter than 19 m when its initial velocity is 50 km/h.(2)
The braking distance of a truck with a total mass less than 4.5 t must be shorter than 21 m when its initial velocity is 50 km/h.(3)
The braking distance of the other cars must be shorter than 9 m when its initial velocity is 30 km/h.So, in the first case, the maximumDmin⁡1 is 19+5=24 m; in the second case, the maximum Dmin⁡1 is 21+5=26 m and in the third case the maximum Dmin⁡1is 9+5=14 m.


### 4.2.2. Theoretical Minimum Safety Legibility Distance

The theoretical minimum safety legibility distance refers to the safe braking distance when the driver fully concentrates on driving, finds the distress at the first time, and decelerates immediately fromvto 0 km/h.According to normal driving behaviors,Dmin⁡0equals the sum of the distance vehicle runs during the drivers’ perception-reaction time trand the safe distance between vehicles d. Perception-reaction time of the driver tr is as follows:
(3)tr=t1+t2,
where t1 is perception reaction time, 0.3–0.5 s, and t2 is driving behavior operation time, 0.3–0.5 s:
(4)tb=-va.d
r is the traveling distances of the vehicle when the driver responses to the pavement distress:
(5)dr=t1+t2·v.And the traveling distance of the vehicle during the brake can be shown in formula5:
(6)db=-0.5·a·tb2.Put formula4 into formula 6:
(7)db=-0.5·v2a.Then(8)Dmin⁡0=dr+db+d=t1+t2·v-0.5·v2a+d.


### 4.2.3. Actual Minimum Safety Legibility Distance

Influenced by the driving condition, the drivers’ psychological and physiological state, the drivers’ attention, and the drivers’ dynamic vision, the actualDd is larger than Dmin⁡0.IfDd<Dmin⁡0, it is danger; while Dd≥Dmin⁡0, it is safe. Then the safety condition can be concluded as follows:
(9)0.9004Ds-0.1968v-4.7645≥v·tr-0.5v2a+d.Take sedan car as an example, when, in emergency,tr=1.0s,  a=-7.5 m/s2, and d=5 m. Put these parameters into formula 9; then we can get
(10)Ds≥0.074v2+1.3292v+10.8446.When the equal sign is tenable in formula10Ds becomes the actual minimum safe static legibility distance Dmin⁡s:
(11)Dmin⁡s=0.074v2+1.3292v+10.8446.


### 4.2.4. Case Study

The range of design speed of the urban road in China is 20~80 km/h; and then, the values ofDmin⁡s in different speeds can be calculated by formula 11, and the results are shown in Table 3.Table 3
D
min
⁡
s in different speed conditions.
Number
v (km/h)
v (m/s)
AcademicDs (m)
RecommendedDs (m)
1
20
5.56
20.51
25
2
30
8.33
27.06
30
3
40
11.11
34.75
35
4
50
13.89
43.58
45
5
60
16.67
53.55
55
6
70
19.44
64.67
65
7
80
22.22
76.93
80
8
90
25.00
90.32
95
9
100
27.78
104.87
105
Note: the mantissa of recommendedDs takes an integer multiple of 5.It can be found that the value ofDs gradually increases as the speed increases when compared with Tables 2 to 3. When the value ofvreaches 100 km/h, Ds reaches 105 m, which is much longer than normal braking distance when v=100 km/h (50 m). The two main reasons are (1) the driver failed to detect the pavement distress in time; (2) there is a delay between the drivers’ identification, reaction, and the operation.Driving safety is not only associated with vehicles but also associated with the drivers’ reaction characteristics and operation skills. Therefore, we need to be aware of the possibility that the driver may not be able to find the distress in time and certain observation time and space are necessary.Data in Table3 shows that, in a road section where limit speed is 60 km/h, if the static legibility distance Ds is less than 55 m, it will be susceptible to accidents.In addition, according to the inquiring survey on drivers in the condition that there is no need to brake when pavement distress is noticed, whent<3s, drivers will react to the pavement distress in haste and it is prone to accidents, when t>4s, drivers can deal with the information better, and when t>5s, drivers can take the information in stride.


## 4.2.1. The Minimum Safety Distance

The minimum safety distance (Dmin⁡1) refers to the safe distance to front vehicle or obstacle when vehicle suddenly brakes from 100 km/h to 0 in an emergency, which can be expressed as follows:
(2)Dmin⁡1=-0.5·v2a+d,
where Dmin⁡1 is the minimum safety distance, m; a is acceleration of the vehicle, acceleration a>0, deceleration a<0, emergency braking a belongs to −7.5 m/s2~−10 m/s2, and a=-7.5 m/s2 in this paper. d is safe stopping distance, at most d = 2~5 m in general, and d=5 m in this paper.According to formula2, we can see that the better the vehicle braking performance is, the shorter the Dmin⁡1 is. Thus we can get Dmin⁡1 in all speed conditions, as shown in Table 2.Table 2
D
min
⁡
1 in different speed conditions.
Number
v (Km/h)
v (m/s)
Brake time (s)
Brake distance (m)
D
min
⁡
1 (m)
1
20
5.56
0.74
2.06
7.06
2
30
8.33
1.11
4.63
9.63
3
40
11.11
1.48
8.23
13.23
4
50
13.89
1.85
12.86
17.86
5
60
16.67
2.22
18.52
23.52
6
70
19.44
2.59
25.21
30.21
7
80
22.22
2.96
32.92
37.92
8
90
25.00
3.33
41.67
46.67
9
100
27.78
3.70
51.44
56.44The legal requirement of automobile (nonload) braking distance in China is as follows.(1)
The braking distance of a passenger service vehicle with no more than 9 seats must be shorter than 19 m when its initial velocity is 50 km/h.(2)
The braking distance of a truck with a total mass less than 4.5 t must be shorter than 21 m when its initial velocity is 50 km/h.(3)
The braking distance of the other cars must be shorter than 9 m when its initial velocity is 30 km/h.So, in the first case, the maximumDmin⁡1 is 19+5=24 m; in the second case, the maximum Dmin⁡1 is 21+5=26 m and in the third case the maximum Dmin⁡1is 9+5=14 m.


## 4.2.2. Theoretical Minimum Safety Legibility Distance

The theoretical minimum safety legibility distance refers to the safe braking distance when the driver fully concentrates on driving, finds the distress at the first time, and decelerates immediately fromvto 0 km/h.According to normal driving behaviors,Dmin⁡0equals the sum of the distance vehicle runs during the drivers’ perception-reaction time trand the safe distance between vehicles d. Perception-reaction time of the driver tr is as follows:
(3)tr=t1+t2,
where t1 is perception reaction time, 0.3–0.5 s, and t2 is driving behavior operation time, 0.3–0.5 s:
(4)tb=-va.d
r is the traveling distances of the vehicle when the driver responses to the pavement distress:
(5)dr=t1+t2·v.And the traveling distance of the vehicle during the brake can be shown in formula5:
(6)db=-0.5·a·tb2.Put formula4 into formula 6:
(7)db=-0.5·v2a.Then(8)Dmin⁡0=dr+db+d=t1+t2·v-0.5·v2a+d.


## 4.2.3. Actual Minimum Safety Legibility Distance

Influenced by the driving condition, the drivers’ psychological and physiological state, the drivers’ attention, and the drivers’ dynamic vision, the actualDd is larger than Dmin⁡0.IfDd<Dmin⁡0, it is danger; while Dd≥Dmin⁡0, it is safe. Then the safety condition can be concluded as follows:
(9)0.9004Ds-0.1968v-4.7645≥v·tr-0.5v2a+d.Take sedan car as an example, when, in emergency,tr=1.0s,  a=-7.5 m/s2, and d=5 m. Put these parameters into formula 9; then we can get
(10)Ds≥0.074v2+1.3292v+10.8446.When the equal sign is tenable in formula10Ds becomes the actual minimum safe static legibility distance Dmin⁡s:
(11)Dmin⁡s=0.074v2+1.3292v+10.8446.


## 4.2.4. Case Study

The range of design speed of the urban road in China is 20~80 km/h; and then, the values ofDmin⁡s in different speeds can be calculated by formula 11, and the results are shown in Table 3.Table 3
D
min
⁡
s in different speed conditions.
Number
v (km/h)
v (m/s)
AcademicDs (m)
RecommendedDs (m)
1
20
5.56
20.51
25
2
30
8.33
27.06
30
3
40
11.11
34.75
35
4
50
13.89
43.58
45
5
60
16.67
53.55
55
6
70
19.44
64.67
65
7
80
22.22
76.93
80
8
90
25.00
90.32
95
9
100
27.78
104.87
105
Note: the mantissa of recommendedDs takes an integer multiple of 5.It can be found that the value ofDs gradually increases as the speed increases when compared with Tables 2 to 3. When the value ofvreaches 100 km/h, Ds reaches 105 m, which is much longer than normal braking distance when v=100 km/h (50 m). The two main reasons are (1) the driver failed to detect the pavement distress in time; (2) there is a delay between the drivers’ identification, reaction, and the operation.Driving safety is not only associated with vehicles but also associated with the drivers’ reaction characteristics and operation skills. Therefore, we need to be aware of the possibility that the driver may not be able to find the distress in time and certain observation time and space are necessary.Data in Table3 shows that, in a road section where limit speed is 60 km/h, if the static legibility distance Ds is less than 55 m, it will be susceptible to accidents.In addition, according to the inquiring survey on drivers in the condition that there is no need to brake when pavement distress is noticed, whent<3s, drivers will react to the pavement distress in haste and it is prone to accidents, when t>4s, drivers can deal with the information better, and when t>5s, drivers can take the information in stride.


## 5. Conclusions

Identification of road information is the premise of the driving safety. Pavement distress is taken as research object in this paper and legibility distances in different conditions are studied; the main conclusions are as follows.(1)
Concepts of static legibility distance (Ds) and dynamic legibility distance (Dd) of pavement distress are put forward to describe the legibility of the pavement distress. And the relation betweenDsand Ddis revealed.(2)
Safety legibility distance is analyzed from the aspects of minimum safety distance, theoretical minimum safety legibility distance, and actual minimum safety legibility distance. Relation between speeds, braking performance, and the minimum safety legibility distance is confirmed. And the recommend static legibility distances in different speed conditions are put forward.One of the shortcomings of this paper is that the basic data in this paper is collected in urban road where the driving condition differs significantly from the highway; therefore the application in highway still needs to be verified.



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*Source: 235974-2015-03-25.xml*