A New Model of Equivalent Modulus Derived from Repeated Load CBR Test

Document Type : Original Article


1 Structural and Material Mechanics team, National High School of Electricity and Mechanics, Hassan II University of Casablanca, Casablanca, Morocco

2 Research Team in Construction Engineering, LaGCHEC Laboratory, Hassania School of Public Works, Casablanca, Morocco


This paper presents a new model of equivalent modulus derived from the Repeated Load CBR (RL-CBR) test without strain gauge. This model is an updated version of Araya et al. model (2011), the update consists of using the vertical strain as weighting factor instead of vertical displacement in the mean vertical and horizontal stresses calculation. The accuracy of equivalent modulus was improved by decreasing the relative error from 25% to 3%. The extra-large mold adopted by Araya et al. is used with a thickness of 8 mm instead of 14.5 mm. In experimental investigations, equivalent modulus may be calculated from experimental data and model parameters estimated by finite element (EF) simulation. There are five model parameters when the RL-CBR test is used, and three parameters when the strain gauge is not used. Model parameters are determined in two steps. First, the FE simulation of the RL-CBR test is conducted using various loading conditions (i.e., plunger penetration) and various quality ranges of unbound granular materials (UGM). In the second step, the non-linear multidimensional regression is accomplished to fit the equivalent modulus to Young’s modulus. The influence of FE analysis inputs is investigated to find the optimal inputs set that make the best compromise between the model accuracy and the calculation time consumption. The calculation of model parameters is carried out based on the optimal set data. Results from the new model and those from Araya et al. model are compared and have shown the improved accuracy of the developed model.


1. Mendoza C., Caicedo B. “Elastoplastic framework of relationships between CBR and Young’s modulus for granular material”. Road Materials and Pavement Design. Vol. 19, No. 8, (2017). DOI:10.1080/14680629.2017.13475 17.
2. Araya A.A. “Characterization of unbound granular materials for pavements”, PhD thesis, Delft University of Technology, (2011).
3. Araya A.A., Huurman M., Molenaar A.A.A. “Integrating traditional characterization techniques in mechanistic pavement design approaches”. In 1st Congress of Transportation and Development Institute, Chicago, Illinois,United States, March 13-16 2011, American Society of Civil Engineers, (2011), 596-606, DOI: 10.1061/41167 (398)57
4. Molenaar A.A.A. “Repeated load cbr testing, a simple but effective tool for the characterization of fine soils and unbound materials”. In Transportation Research Board 87th Annual Meeting, January 13-17 2008, Washington, United States, (2008).
5. Molenaar A.A.A. “Characterization of Some Tropical Soils for Road Pavements”. Transportation Research Record: Journal of the Transportation Research Board, 2007, Vol. 1989-2, No. 1, 186-193. DOI: 10.3141/1989-63
6. AFNOR. NF P 98-086- “Dimensionnement structurel des chaussées routières- application aux chaussées neuves”. 2011.
7. Araya A.A, Huurman M, Molenaar A.A.A, Houben LJM. “Investigation of the resilient behavior of granular base materials with simple test apparatus”, Materials and Structures, (2012), Vol. 45, No. 5, 695–705. DOI:10.1617/ s11527-011-9790-1
8. Han Z., Vanapalli S.K. “State of the art: prediction of resilient modulus of unsaturated subgrade soils”. International Journal of Geomechanics, (2016), Vol. 16, No.4, 1–15. DOI:10.1061/(ASCE)GM.1943-5622.0000631.
9. Fredrick L., Ulf I., Andrew D. “State of the art. I: resilient response of unbound aggregates”, Journal of Transportation Engineering, (2000), Vol. 126, No. 1, 66–75. DOI: 10.1061/(ASCE)0733-947X(2000)126:1(66)
10. Saada A., Townsend F., “State of the art: laboratory strength testing of soils”, in Laboratory Shear Strength of Soil, ed. R. Yong and F. Townsend (West Conshohocken, PA: ASTM International), (1981), 7-77. DOI:10.1520/STP28744S
11. Minassian G.H. “Behavior of granular materials under cyclic and repeated loading”, Ph.D thesis, University of Alaska Fairbanks, United States, (2003).
12. Gidel G. “Comportement et valorisation des graves non traitées calcaires utilisées pour les assises des chaussées souples”, Thèse de doctorat, Université Bordeaux I, France, (2001).
13. Semmelink C.J. “The use of DRTT K-mould to determine the elastic and shear properties of pavement materials”, Report No. 89/149, Department of Transport, South Africa, (1991).
14. Edwards P., Thom N., Fleming P.R., Williams J. “Testing of unbound materials in the nottingham asphalt tester springbox”, Transportation Research Record: Journal of the Transportation Research Board, (2005), Vol. 1913, No. 1, 32-40. DOI: 10.1177/0361198105191300104
15. Jalili M, Ghasemi M.R., Pifloush A.R., “Stiffness and strength of granular soils improved by biological treatment bacteria microbial cements”. Emerging Science Journal, (2018), Vol. 2, No. 4, 219-227, DOI: 10.28991/esj-2018-01146
16. Ogundipe O.M., Adekanmi J.S., Akinkurolere O.O., Ale P.O., “Effect of compactive efforts on strength of laterites stabilized with sawdust ash”. Civil Engineering Journal, (2019), Vol. 5, No. 11, 2502–25014, DOI: 10.28991/cej-2019-03091428
17. CEN. “EN 13286-7- Unbound and hydraulically bound mixtures - Part 7 : Cyclic load triaxial test for unbound mixtures”, European committee for standardization, (2004).
18. Albayati A.H, Al-Mosawe H, Fadhil A.T., Allawi A.A. “Equivalent Modulus of Asphalt Concrete Layers”, Vol. 4, No. 10, Civil Engineering Journal, (2018), 2264-2274. DOI:10.28991/cej-03091156
19. Timoshenko S, Goodier J.N. “Theory of elasticity”, ed. McGraw-Hill, (1951), 532.
20 J. Shen et X. Zhou, “Least Squares Support Vector Machine for Constitutive Modeling of Clay“, International Journal of Engineering Transactions B: Applications, Vol. 28, No. 11, (2015), 1571-1578.
21. Haghighi H., Arulrajah A., Mohammadinia A., Horpibulsuk S. “A new approach for determining resilient moduli of marginal pavement base materials using the staged repeated load CBR test