# Survival Analysis for Asphalt Pavement Performance and Assessment of Various Factors Affecting Fatigue Cracking Based on LTPP Data

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## Abstract

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## 1. Introduction

^{TM}[39]. The LTPP data is usually collected and uploaded periodically on a six-month cycle by four regional contractors. The information management system, where the LTPP database is stored, consists of 16 general data modulus with 430 tables in a simple row-column format in which the columns are referred to as fields and the rows contains records. The main objective of the LTPP program of collecting and storing performance data is to support analysis and develop usable engineering products relevant to pavement management, construction, maintenance and design. Zhang and Wang [40] developed decision tree models using LTPP data to provide enhanced decision-making information in pavement maintenance and design. Wang et al. [41] developed an AdaBoost regression model to improve the prediction ability of international roughness index (IRI) for roads using records from LTPP program. Another research study was conducted by Rezapour et al. [42] to investigate factors contributing to pavement skid resistance using LTPP data. El Ashwah et al. [43] used the LTPP data to calibrate transfer functions used in developing and implementing a simplified Mechanistic Empirical (M-E) pavement design method.

## 2. Methodology

#### 2.1. Survival Analysis

- Left-censored: data can occur when the pavements section’s true survival time is less than or equal to that pavements section’s observed survival time. In other words, if a pavement is left censored at time “t”, the failure event occurs between time 0 and t before the study began, but the exact time of occurrence is not known.
- Right-censored: most survival data used in this study is right-censored. Data can occur when the event has not occurred during the study or before the termination of data collection. In this case, the true survival time is equal to or greater than the observed survival time.
- Interval-censored: the pavement failed within a certain specified time interval but the exact true failure time is unknown.

#### 2.2. Survival Function:

_{i}is the time of ith pavement failure, d

_{i}is the number of pavement sections that failed at time t

_{i}, and n

_{i}is the number of pavement sections that survived just before time t

_{i}.

#### 2.3. Parametric Survival Analysis

#### 2.4. Model Selection Criterion

_{ci}”, that were reported by Cox and Snell [51] and Hosmer and Lemeshow [52], are formed by using the model-based estimate of the empirical cumulative hazard function $\widehat{H}$(t

_{i}) or the survival empirical hazard function $\widehat{S}$(t

_{i}) where:

#### 2.5. Preparation of Data

- Traffic Loads and Overweighting:

- The annual average daily truck traffic (AADTT), in trucks/day, extracted from LTPP table (TRF_MEPDG_AADTT_LTPP_LN) according to specific state and section ID.
- The annual average cumulative single axle load (KESAL) extracted from two sources. The first table (TRF_HIST_EST_ESAL) contains estimates of 80 KN (18 kips) ESALs for sections with historical traffic data and the second table (TRF_MON_EST_ESAL) contains annual estimate of ESAL during the period when pavement monitoring measurements were conducted.
- The total axle weights (W) for the 13-bin classified vehicles according to FHWA (federal highway administration)The total overweight axles (OW) for the weight of the axles exceed the federal trucks axle weight limit listed in Table 5. The total axle weights and overweight axles are extracted from table (TRF_MEPDG_AX_DIST_ANL), which contains the annual normalized axle distribution by class and axle group and from table (TRF_MONITOR_LTPP_LN), which contains information about the estimated annual volumes of trucks and axles per LTPP lane (LN).
- The total axles volume (V) and the total overweight axles volume (OV) for all the vehicle classes and axle group. These data are also extracted from table (TRF_MONITOR_LTPP_LN).
- The total percentage of overweight axles (%OA) is calculated using the normalized axle distribution by vehicle class and axle group type. The data are extracted from table (TRF_MEPDG_AX_DIST_ANL) and from table (TRF_MEPDG_AX_PER_TRUCK), which contains the annual average number of axles number by vehicle class and axle type per year.

- Environmental Data:

- Pavement Materials:

#### 2.6. Pavement Performance

#### 2.7. Descriptive Analysis

## 3. Results and Analysis

#### 3.1. Non-Parametric Survival Analysis

#### 3.2. Effect of Using RAP in Asphalt Mixes

_{0}) of no difference in survival between using RAP and virgin materials or no difference between the populations in the probability of fatigue failure at any point. The log rank test compares the observed number of events in groups 1 and 2 with what would be expected if the null hypothesis were true.

^{2}statistic. For this test, the chi-square c

^{2}= 0.003 and p-value = 0.956 > 0.05 so the null hypothesis was retained. Therefore, there is no difference in survival curves between using RAP and virgin materials.

#### 3.3. Parametric Survival Analysis

#### 3.3.1. Transverse and Longitudinal Cracking

_{r}) was also found to be statically significant using Weibull and lognormal distributions. As for the transverse cracking, the snowfall and the temperature were found to be the significant variables for all models, and the AADTT was also considered a significant factor when using the Weibull model.

#### 3.3.2. Fatigue Cracking

_{ac}) and subgrade material resilient modulus (M

_{r}). The AIC values indicated the models in the order of fitness were Weibull, generalized gamma, Gompertz, log-logistic, and log-normal.

_{j}is a vector of covariates, b is a vector of regression coefficients, and p is the shape parameter (also known as the Weibull slope).

_{j}) = exp{−exp (−9.048 + 0.1408 × (%OA) + 0.0012 × (AADTT) + 0.0021 × (KESAL) − 0.0204 × (Total Precip.) − 0.1272 × (h

_{ac}) − 0.00003 × (M

_{r}) − 0.0003 × (FI)) × t

^{3.571}}

#### 3.3.3. Influence of Overweight Axles

## 4. Conclusions

- Non-parametric Kaplan–Meier survival probability curves indicated that the thermal transverse cracking had the highest failure probability followed by the non-wheel path longitudinal cracking, the fatigue cracking, and the wheel path longitudinal cracking.
- To assess the influence of using reclaimed asphalt pavement (RAP) on fatigue service life, the survival curves for the test sections using RAP and virgin materials are separately developed to compare the equality of the two survival curves and the results indicated that there is no difference in fatigue survival life. These results encourage the sustainable use of RAP in pavement construction.
- For fatigue cracking, based on the data extracted from the pavement test sections across the United States, only seven independent variables out of seventeen potential influential factors were found to be statistically significant or marginally significant and the Weibull distribution was found to be an effective description to model the data of concern to our study. A final model for estimating the fatigue survival time, including the potential influential factors, is represented in this paper. This model seems to be more suitable for quantifying the effect of the independent variables (covariates) than predicting the survival time.
- By performing the parametric survival analysis, the median survival time for fatigue failure is 8.07 years. Moreover, the fatigue cracking was found to be sensitive to the percentages of overweight axles but it was difficult to draw a firm conclusion for longitudinal and thermal cracking based on the available extracted data and the selected pavement test sections.
- Percentages of overweight axles, AADTT, ESAL, and thickness of the asphalt layer have significant effects on the hazard rate. The increase of the percentage of overloaded axles from 0% to 20% can reduce the survival time of the fatigue life up to 55%.
- A one-inch increase in asphalt layer thickness can extend the fatigue service life by about half a year when there are no overweight axles and about 0.22 years when the percentage of overweight axles is 20%. Therefore, additional virgin materials and resources are needed to maintain traffic conditions in the road network and to compensate for the reduction in fatigue service life. Therefore, using overweight axles will negatively impact the sustainability of pavement and necessitates new design guides.
- The effect of increasing the overweight axles from 0 to 15% on reducing the fatigue survival life is found to be similar to the effect of increasing the annual average daily truck traffic (AADTT) by ten times.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 4.**Kaplan–Meier Survival Estimates for Asphalt concrete surface with virgin materials versus RAP materials.

**Figure 5.**Graph of the Kaplan–Meier estimate of the cumulative hazard versus the Cox–Snell residuals from the Weibull distribution model.

**Figure 6.**Graph of the Kaplan–Meier estimate of the cumulative hazard versus the Cox–Snell residuals from the generalized gamma distribution model.

**Figure 7.**Graph of the Kaplan-–Meier estimate of the cumulative hazard versus the Cox–Snell residuals from the Gompertz distribution model.

**Figure 10.**Median fatigue survival time vs thickness of asphalt layer with different percentages of over-weight axles.

**Figure 11.**Median survival time Vs equivalent single axle load (KESAL) with various percentages of over-weight axles and under two different traffic scenarios (low and high).

Pavement Condition or Distress Type | Threshold Values for Primary Roads |
---|---|

Alligator cracking | 20% of lane area |

Longitudinal cracking | 132.6 m/km (700 ft/mi) |

Transverse cracking for hot mix asphalt (HMA) | 132.6 m/km (700 ft/mi) |

Pavement Distress Indicator | Percentages of the Complete Cracked Section | Percentages of the Censored Pavement Section |
---|---|---|

Fatigue Cracking | 81% (159) | 19% (37) |

Wheel path Longitudinal Cracks | 62% (108) | 38% (67) |

Non-wheel path Longitudinal Cracks | 55% (84) | 45% (69) |

Transverse Cracks | 64% (112) | 36% (60) |

Category | Variable | Abbreviation | Unit | LTPP Table [39] |
---|---|---|---|---|

Traffic Loads and Overweighting | Annual Average Daily Truck Traffic | AADTT | trucks/day | TRF_MEPDG_AADTT_LTPP_LN |

Annual Average cumulative Single Axle Load (×1000) | KESAL | # | TRF_HIST_EST_ESAL & TRF_MON_EST_ESAL | |

Total Axle Weights | W | million lb | TRF_MEPDG_AX_DIST_ANL & TRF_MONITOR_LTPP_LN | |

Total Overweight Axles | OW | million lb | TRF_MEPDG_AX_DIST_ANL & TRF_MONITOR_LTPP_LN | |

Total Axles Volume | V | # | TRF_MONITOR_LTPP_LN | |

Total Overweight Axles Volume | OV | # | TRF_MONITOR_LTPP_LN | |

Total Percentage of Overweight Axles | %OA | % | TRF_MEPDG_AX_DIST_ANL & TRF_MEPDG_AX_PER_TRUCK | |

Environmental | Average Annual Precipitation | Total Precip. | in | CLM_VWS_PRECIP_ANNUAL |

Average Freezing Indices (FI) | FI | °F-days | CLM_VWS_TEMP_ANNUAL | |

Average Annual Temperatures | Temp. | °F | CLM_VWS_TEMP_ANNUAL | |

Average Total Annual Snowfall | Total Snow | in | CLM_VWS_PRECIP_ANNUAL | |

Average number of days above 89 °F | Days > 89 °F | # | CLM_VWS_TEMP_ANNUAL | |

Average number of days below 32 °F | Days < 32 °F | # | CLM_VWS_TEMP_ANNUAL | |

Pavement Materials | Total Thickness of Asphalt Layer | h_{ac} | in | SECTION_LAYER_STRUCTURE |

Total Thickness of Base Layer | h_{b} | in | SECTION_LAYER_STRUCTURE | |

Total Thickness of Subbase Layer | h_{sub} | in | SECTION_LAYER_STRUCTURE | |

Subgrade Material Resilient Modulus | M_{r} | psi | TST_UG07_SS07_WKSHT_SUM | |

Asphalt material (1 if RAP, 0 if standard HMA) | RAP | NA | SECTION_LAYER_STRUCTURE |

Category | Variable | Abbreviation | Unit | LTPP Table [39] |
---|---|---|---|---|

Pavement Performance Indicator | Fatigue Cracking | FC | % | MON_DIS_AC_REV |

Non-wheel path Longitudinal Cracks | NWPL | ft/mi | MON_DIS_AC_REV | |

Wheel path Longitudinal Cracks | WPL | ft/mi | MON_DIS_AC_REV | |

Transverse Cracks | TC | ft/mi | MON_DIS_AC_REV |

Axle Group | Limits |
---|---|

Single Axle | 20,000 lbs |

Tandem Axle | 34,000 lbs |

Gross Weight | 80,000 lbs |

Total Precip. | Total Snow | Temp. | Days > 89 °F | Days < 32 °F | FI | |
---|---|---|---|---|---|---|

Total Precip. | 1.0000 | |||||

Total Snow | 0.0497 | 1.0000 | ||||

Temp. | 0.1971 | −0.7628 | 1.0000 | |||

Days > 89 °F | −0.2409 | −0.5136 | 0.8118 | 1.0000 | ||

Days < 32 °F | −0.2538 | 0.7292 | −0.9713 | −0.6531 | 1.0000 | |

FI | −0.1861 | 0.7048 | −0.8004 | −0.5089 | 0.7991 | 1.0000 |

Variables | Mean | Standard Deviation |
---|---|---|

AADTT | 718.336 | 811.192 |

KESAL | 294.112 | 396.653 |

%OA | 14.890 | 6.848 |

Total Precip. | 34.114 | 17.262 |

FI | 602.257 | 703.891 |

Temp. | 55.314 | 11.039 |

Total Snow | 25.926 | 30.935 |

h_{ac} | 7.788 | 3.465 |

h_{b} | 8.906 | 6.211 |

h_{sub} | 5.499 | 7.843 |

M_{r} | 11,661.193 | 5341.987 |

RAP | 0.229 | 0.421 |

95% Confidence Intervals of KMPLE Survival Probability | |||||
---|---|---|---|---|---|

Pavement Distresses | Median Survival Time, in Years | Median Survival Time | 5 Years | 10 Years | 15 Years |

Fatigue Cracking | 8.43 | [0.4009, 0.5889] | [0.7352, 0.8776] | [0.2834, 0.4684] | [0.1050, 0.2664] |

Non-wheel path Longitudinal Cracking | 5.9 | [0.3290, 0.5264] | [0.4229, 0.6094] | [0.151, 0.37545] | [0.0535, 0.2690] |

Wheel path Longitudinal Cracking | 10.6 | [0.3947, 0.6172] | [0.7047, 0.8629] | [0.4321, 0.6483] | [0.2185, 0.4790] |

Transverse Cracking | 1.96 | [0.3639, 0.5659] | [0.0106, 0.2234] | [0.0153, 0.1834] | [0.0112, 0.0425] |

**Table 9.**The selected subset of covariates with the Log-likelihood and AIC values for each estimated model and for various pavement distress type.

Pavement Distress Indicator | Model | The Most Significant Subset of Covariates (Significant or Marginally Significant at 5%) | Log-Likelihood (LL) | AIC |
---|---|---|---|---|

Fatigue Cracking | Gompertz | %OA, AADTT, KESAL, Total Precip., FI, h_{ac}, M_{r} | −50.902038 | 119.8041 |

Generalized Gamma | %OA, AADTT, KESAL, Total Precip., FI, h_{ac}, M_{r} | −47.825837 | 115.6517 | |

Weibull | %OA, AADTT, KESAL, Total Precip., FI, h_{ac}, M_{r} | −47.682033 | 113.3641 | |

Log-logistic | %OA, AADTT, KESAL, Total Precip., FI, h_{ac}, M_{r} | −53.071456 | 124.1429 | |

Log normal | %OA, AADTT, KESAL, Total Precip., FI, h_{ac}, M_{r} | −56.657391 | 131.3148 | |

Non-wheelpath Longitudinal Cracks | Gompertz | Temp. | −95.414942 | 196.8299 |

Generalized Gamma | - | - | - | |

Weibull | Temp. | −92.772062 | 191.5441 | |

Log-logistic | - | - | - | |

Log normal | - | - | - | |

Wheelpath Longitudinal Cracks | Gompertz | AADTT, FI | −141.98669 | 291.9734 |

Generalized Gamma | AADTT, FI | −138.18737 | 286.3747 | |

Weibull | AADTT, FI, M_{r} | −139.47333 | 288.9467 | |

Log-logistic | AADTT, FI | −139.39759 | 286.7952 | |

Log normal | AADTT, FI, M_{r} | −138.19604 | 284.3921 | |

Transverse Cracks | Gompertz | Snowfall, Temp. | −126.30721 | 260.6144 |

Generalized Gamma | Snowfall, Temp. | −115.62259 | 241.2452 | |

Weibull | Snowfall, Temp., AADTT | −120.67733 | 251.3547 | |

Log-logistic | Snowfall, Temp. | −112.28529 | 232.5706 | |

Log normal | Snowfall, Temp. | −116.30418 | 240.6084 |

Weibull Distribution Model | |||
---|---|---|---|

Metric | Survivor Function S(t) | Parametrization | Ancillary Parameters |

PH | exp(−l_{j}t^{p}_{j}) (1) | l_{j} = exp(x_{j}b) | p |

AFT | exp(−l_{j}t^{p}_{j}) (2) | l_{j} = exp(−px_{j}b) | p |

Variable | Coefficient | Std. Error | Z Score | p-Value (Two-Tailed) | Hazard Ratio |
---|---|---|---|---|---|

%OA | 0.1408651 | 0.0216452 | 6.51 | p < 0.001 | 1.151269 |

AADTT | 0.0012121 | 0.0001983 | 6.11 | p < 0.001 | 1.001213 |

KESAL | 0.0021101 | 0.0004219 | 5 | p < 0.001 | 1.002112 |

Total Precip. | −0.0204645 | 0.0064971 | −3.15 | 0.002 | 0.9797434 |

h_{ac} | −0.1272957 | 0.0373627 | −3.41 | 0.001 | 0.8804733 |

M_{r} | −0.0000395 | 0.0000215 | −1.84 | 0.066 | 0.9999605 |

FI | −0.0003363 | 0.0001371 | −2.45 | 0.014 | 0.9996638 |

_cons | −9.048324 | 0.9245831 | −9.79 | p < 0.001 | 0.0001176 |

/ln_p | 1.273013 | 0.0818707 | 15.55 | p < 0.001 | |

p | 3.571599 | 0.2924095 | |||

1/p | 0.2799866 | 0.0229227 |

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**MDPI and ACS Style**

Hatoum, A.A.; Khatib, J.M.; Barraj, F.; Elkordi, A.
Survival Analysis for Asphalt Pavement Performance and Assessment of Various Factors Affecting Fatigue Cracking Based on LTPP Data. *Sustainability* **2022**, *14*, 12408.
https://doi.org/10.3390/su141912408

**AMA Style**

Hatoum AA, Khatib JM, Barraj F, Elkordi A.
Survival Analysis for Asphalt Pavement Performance and Assessment of Various Factors Affecting Fatigue Cracking Based on LTPP Data. *Sustainability*. 2022; 14(19):12408.
https://doi.org/10.3390/su141912408

**Chicago/Turabian Style**

Hatoum, Ali A., Jamal M. Khatib, Firas Barraj, and Adel Elkordi.
2022. "Survival Analysis for Asphalt Pavement Performance and Assessment of Various Factors Affecting Fatigue Cracking Based on LTPP Data" *Sustainability* 14, no. 19: 12408.
https://doi.org/10.3390/su141912408