Reliability Based Geometric Design of Horizontal Circular Curves

  • Pabitra Rajbongshi
  • Kuldeep Kalita
Original Contribution


Geometric design of horizontal circular curve primarily involves with radius of the curve and stopping sight distance at the curve section. Minimum radius is decided based on lateral thrust exerted on the vehicles and the minimum stopping sight distance is provided to maintain the safety in longitudinal direction of vehicles. Available sight distance at site can be regulated by changing the radius and middle ordinate at the curve section. Both radius and sight distance depend on design speed. Speed of vehicles at any road section is a variable parameter and therefore, normally the 98th percentile speed is taken as the design speed. This work presents a probabilistic approach for evaluating stopping sight distance, considering the variability of all input parameters of sight distance. It is observed that the 98th percentile sight distance value is much lower than the sight distance corresponding to 98th percentile speed. The distribution of sight distance parameter is also studied and found to follow a lognormal distribution. Finally, the reliability based design charts are presented for both plain and hill regions, and considering the effect of lateral thrust.


Horizontal curve Stopping sight distance Reliability 

List of symbols


Available sight distance (m)


Calibrated sight distance (m)


Deceleration of vehicle (m/s2)


Coefficient of variation (%) of random variable X


Distance between centre line of horizontal curve and inner lane


Super-elevation at the horizontal curve (%)


Perception reaction time of driver in s


Lateral coefficient of friction


Probability density function of random variable X


Middle ordinate at the horizontal curve section (m)


Probability of non-compliance


Radius of circular horizontal curve (m)




Stopping sight distance (demand) in metre


Mean speed of vehicular stream (kmph)


Design speed (kmph)


Standard normal deviate


Probability corresponding to standard normal deviate z


SD of random variable X


  1. 1.
    AASHTO, in A policy on geometric design of highways and streets, American Association of State Highway and Transportation Officials (AASHTO), 6th Ed. (Washington, DC, 2011)Google Scholar
  2. 2.
    P. Chakroborty, A. Das, Principles of Transportation Engineering (Prentice Hall of India Pvt. Ltd., New Delhi, 2003)Google Scholar
  3. 3.
    D. Fambro, K. Fitzpatrick, R. Koppa, Determination of stopping sight distance NCHRP Rep. 400 (Transportation Research Board, Washington, DC, 1997)Google Scholar
  4. 4.
    K. Fitzpatrick, M. Wooldridge, Recent geometric design research for improved safety and operation NCHRP Synthesis 299 (Transportation Research Board, Washington, DC, 2001)Google Scholar
  5. 5.
    Y.H. Huang, Pavement Analysis and Design, 2nd edn. (Pearson Prentice Hall, New Jersey, 2004)Google Scholar
  6. 6.
    M. Hussein, T. Sayed, K. Ismail, A.V. Espen, Calibrating road design guides using risk-based reliability analysis. J. Transp. Eng. 140(9), 04014041 (2014)CrossRefGoogle Scholar
  7. 7.
    IRC Geometric Design Standards for Urban Roads in Plains (Indian Roads Congress (IRC), IRC: 86-1983, New Delhi, 1983)Google Scholar
  8. 8.
    IRC Recommendations about the Alignment, Survey and Geometric Design of Hill Roads (Indian Roads Congress (IRC), IRC: 52-1981, New Delhi, 1981)Google Scholar
  9. 9.
    IRC Recommended Practice for Sight Distance on Rural Highways (Indian Roads Congress (IRC), IRC: 66-1976, New Delhi, 1976)Google Scholar
  10. 10.
    S.K. Khanna, C.E.G. Justo, Highway Engineering, 6th edn. (Nem Chand & Bros, Roorkee, 1990)Google Scholar
  11. 11.
    N. Lerner, Age and Driver Perception-Reaction Time for Distance Design Requirements, ITE Compendium of Technical Papers (Institute of Transportation Engineers, Washington, DC, 1995), pp. 624–628Google Scholar
  12. 12.
    L. Richl, T. Sayed, Effect of speed prediction models and perceived radius on design consistency. Can. J. Civil Eng. 32(2), 388–399 (2005)CrossRefGoogle Scholar
  13. 13.
    TRB Managing speed: review of current practice for setting and enforcing speed limits, TRB Special Rep. 254 (Transportation Research Board (TRB), Washington, DC, 1988)Google Scholar

Copyright information

© The Institution of Engineers (India) 2018

Authors and Affiliations

  1. 1.Civil Engineering DepartmentNational Institute of Technology SilcharSilcharIndia

Personalised recommendations