Thickness Sensitivities for the Surface Course of Pavement based on the Variation of the Poisson Coefficient of Bituminous Concrete

Thickness Sensitivities for the Surface Course of Pavement based on the Variation of the Poisson Coefficient of Bituminous Concrete

Messi A. F., Mamba Mpele, Miyo T. F.

Civil Engineering Department National Advanced School of Engineering

University of Yaounde I Cameroon

Koumbe Mbock., Okpwe Mbarga R. African Center of Excellence in Information and Communication Technologies

University of Yaounde I Cameroon

AbstractThe laboratory tests that allow to evaluate the Poisson coefficient of the pavement materials are costly in tropical countries. In the absence of these tests, a finite number of Poisson coefficient is often prescribed to design the pavements. This paper consists of studying the influence of these prescribed values in the structural design of the pavement, especially, on the thickness of the surface course. For this, we show that the values of Poisson coefficient taken between 0.25 and 0.45 are adapted for the flexible pavements because they do not affect the thickness of the surface course. The usefulness of the variation of the Poisson coefficient is illustrated with local data and the results show that the thickness of the bituminous and semi-rigid pavements can change when the prescribed values change.

KeywordsPavement structures; French method; Poisson coefficient; Bituminous concrete

1. INTRODUCTION

   Several techniques ([1], [3], [5]) have been used to estimate the thickness of the road pavement and some relationship have been established between mechanical parameters and the quality of pavement layer material ([6], [7], [9]). Among these parameters, the Poisson coefficient has been characterized for the lateritic natural grave detailed in [13]. In this work, the behavior of the pavement was studied in laboratory to evaluate the influence of the Poisson coefficient in pavement design. But, this procedure is costly and not always practicable in tropical countries due to the absence of the appropriate infrastructures and the change of material properties.

   In Cameroon, the values 0.25 and 0.35 are recommended in ([14], [15], [16], [17], [18]) and another work [26] had prescribed the value 0.45 while guaranteed values to be used for bituminous concrete has been determined by Messi et al. in [1]. It means that the Poisson coefficient can change for the same type of pavement and this paper consists of studying the thickness sensitivities of the surface course under the change of the prescribed Poisson coefficient of bituminous concrete.

   In this work, we first present the approach which analyzes the thickness sensitivities by applying the French method ([9], [20], [26]) on the local data. By changing the prescribed Poisson coefficient, we then examine this sensitivity, in order to show that the thickness of the surface course remains

   constant for the flexible pavements while it varies for semi- rigid and bituminous pavements. We conclude our study with a short summary and discussion.

2. OUR APPROACH

   1. Input parameters

      For this study, we use the materials to achieve our goal, namely 6 prescribed values of the Poisson coefficient (BC) of the bituminous concrete :

      – 3 recommended values : 0.25, 0.35 and 0.45 ([14],

      [15], [16], [17], [18], [26]) ;

      • 3 calculated values : 0.36, 0.42 and 0.43 [1].

        In addition, 3 types of pavement structures are analyzed :

      • Type 1 : flexible pavement (table I) ;

      • Type 2 : bituminous pavement (table I) ;

      • Type 3 : semi-rigid pavement (table I).

        TABLE I. YOUNG MODULUS AND POISSON COEFFICIENT

        Type of Pavement
        	Surface course	Base course	Subbase
        	Material	Material	Material
        1	BC a	CG/ Ci d	NLG e
        2	BC a	BG b	–
        3	BC a	CeG c	–

        1. BC.: Bituminous concrete.

        2. BG : Bitumen gravel

        3. CeG : Cement grave

        4. CG : Crushed grave 0/31.5 Ci : Cinder

        5. NLG : Natural laterite gravel.

        The design of these pavements is done with the help of the software ALIZE 3 [19] taking into account the recommended values E and of [26] as it is showed in the table II.

        TABLE II. YOUNG MODULUS AND POISSON COEFFICIENT

        Materials
        	BC	BG	CeG	CG/Ci	NLG
        E (MPa)	2 450	3 500	23 000	400	150
        	BC	0.35	0.25	0.35	0.35

        Other parameters used in the French method are important in the pavement design, namely, the traffic and the subgrade parameter. Having the materials defined in the table II above, the additional parameters are showed in the tables III and IV below.

        TABLE III. MECHANICAL CHARACTERISTIC OF THE SUBGRADE [5]

        Layer
        	Category	E (MPa)
        Subgrade	S2	50	0.35
        	S3	75	0.35
        	S4	150	0.35

        In this table, we denote by S2, S3, S4 the subgrade material with given E and .

        EN a
        	Traffic class	Equivalent number of vehicle per day
        < 5×105	T1	< 300
        From 5×105 to 1.5×106	T2	300 to 1 000
        From 1.5×106 to 4×106	T3	1 000 to 3 000
        From 4×106 to 107	T4	3 000 to 6 000

        EN a
        	Traffic class	Equivalent number of vehicle per day
        < 5×105	T1	< 300
        From 5×105 to 1.5×106	T2	300 to 1 000
        From 1.5×106 to 4×106	T3	1 000 to 3 000
        From 4×106 to 107	T4	3 000 to 6 000

        TABLE IV. TRAFFIC CLASSES DEFINED IN TROPICAL COUNTRIES [5]

        The calculus made with the software ALIZE 3 provides all the information related to the stress and strain tensors for each pavement structure. From these informations, the following values are chosen and compared to admissible values in order to design the pavement structure.

        TABLE V. MAXIMUM STRESS OR STRAIN TO CONSIDERATE [5]

        Material
        	Stress or strain (max)
        Hydrocarbon materials	t
        Concrete and hydraulic binder treated materials	t
        Untreated soil and materials	z

        We note hat the admissible values are found in [5].

        TABLE VI. ADMISSIBLE DEFLECTION IN FUNCTION OF TRAFFIC CLASS

        [5]

        Traffic class
        	Admissible deflections (in 1/100 mm)
        T1	125
        T2	90
        T3	65
        T4	40

   2. States of stress and strain

      a. EN: Equivalent number of axles.

   3. Description of the procedure

      To study the thickness sensitivities of the surface course

      In continuum mechanics, the states of stress and strain at a point in cylindrical coordinates are determined by :

      • r, t, z : normal stresses ;

      • tz, rz, rt : shear stresses ;

      • r, t, z : linear strains ;

      • tz, rz, rt : angular strains.

        With known Young modulus and Poisson coefficient given by the formulas:

        Ei = µi.(3.i + µi)/(i + µi) (1)

        And

        i = i/(2.(i + µi)) (2)

        We determine the Lame coefficients µ and . According to the model prescribed by Burmister [19], we have the following graphic :

        Fig. 1. State of stress at a point in cylindric coordinates

        under the change of the Poisson coefficient of the bituminous concrete, we follow the steps below :

      • The pavement is designed firstly with the recommended values E and ;

      • The Poisson coefficient of the bituminous concrete is modified subject to keep the thicknesses of the base course and subbase constant.

3. PRESENTATION OF THE RESULTS

   1. Case study of the pavement n°1

      In this case, we have the input data :

      • Traffic class T1 ;

      • Pavement materials and parameters (E and ) (Table

        VII) ;

      • Subgrade (soil) mechanical characteristics (E and ) (Table VII).

        TABLE VII. MECHANICAL CHARACTERISTICS OF THE PAVEMENT N°1

        Layer
        	Material/ Category	E (MPa)
        Surface course	BC	2 450	BC
        Base course	CG/ Ci	400	0.35
        Subgrade	S2	50	0.35

        With these entries, the software ALIZE 3 gives us different thicknesses of the surface course as shown in the table VIII and the figure 2.

        	15	BC	BG
        	16	BC	BG
        	17	BC	BG
        	18	BC	BG
        	19	BC	BG
        	20	BC	BG
        	21	BC	BG
        	22	BC	BG
        	23	BC	BG
        	24	BC	BG
        3	25	BC	CeG
        	26	BC	CeG
        	27	BC	CeG
        	28	BC	CeG
        	29	BC	CeG
        	30	BC	CeG
        	31	BC	CeG
        	32	BC	CeG
        	33	BC	CeG
        	34	BC	CeG
        	35	BC	CeG
        	36	BC	CeG

        	15	BC	BG
        	16	BC	BG
        	17	BC	BG
        	18	BC	BG
        	19	BC	BG
        	20	BC	BG
        	21	BC	BG
        	22	BC	BG
        	23	BC	BG
        	24	BC	BG
        3	25	BC	CeG
        	26	BC	CeG
        	27	BC	CeG
        	28	BC	CeG
        	29	BC	CeG
        	30	BC	CeG
        	31	BC	CeG
        	32	BC	CeG
        	33	BC	CeG
        	34	BC	CeG
        	35	BC	CeG
        	36	BC	CeG

        TABLE VIII. THICKNESS OF THE SURFACE COURSE IN FUNCTION OF THE POISSON COEFFICIENT OF THE BITUMINOUS CONCRETE

        BC
        	Thickness (cm)
        0.25	3
        0.35	3
        0.36	3
        0.42	3
        0.43	3
        0.45	3

        Type of Pavement	Numbered pavement
        		Subbase	Subgrade	Traffic class
        		Material	Category
        1	1	NLG	S2	T1
        	2	NLG	S3	T1
        	3	NLG	S4	T1
        	4	NLG	S2	T2
        	5	NLG	S3	T2
        	6	NLG	S4	T2
        	7	NLG	S2	T3
        	8	NLG	S3	T3
        	9	NLG	S4	T3
        	10	NLG	S2	T4
        	11	NLG	S3	T4
        	12	NLG	S4	T4
        2	13	–	S2	T1
        	14	–	S3	T1
        	15	–	S4	T1
        	16	–	S2	T2
        	17	–	S3	T2
        	18	–	S4	T2
        	19	–	S2	T3
        	20	–	S3	T3
        	21	–	S4	T3
        	22	–	S2	T4
        	23	–	S3	T4
        	24	–	S4	T4
        3	25	–	S2	T1
        	26	–	S3	T1
        	27	–	S4	T1
        	28	–	S2	T2
        	29	–	S3	T2
        	30	–	S4	T2
        	31	–	S2	T3
        	32	–	S3	T3
        	33	–	S4	T3
        	34	–	S2	T4
        	35	–	S3	T4
        	36	–	S4	T4

        Type of Pavement	Numbered pavement
        		Subbase	Subgrade	Traffic class
        		Material	Category
        1	1	NLG	S2	T1
        	2	NLG	S3	T1
        	3	NLG	S4	T1
        	4	NLG	S2	T2
        	5	NLG	S3	T2
        	6	NLG	S4	T2
        	7	NLG	S2	T3
        	8	NLG	S3	T3
        	9	NLG	S4	T3
        	10	NLG	S2	T4
        	11	NLG	S3	T4
        	12	NLG	S4	T4
        2	13	–	S2	T1
        	14	–	S3	T1
        	15	–	S4	T1
        	16	–	S2	T2
        	17	–	S3	T2
        	18	–	S4	T2
        	19	–	S2	T3
        	20	–	S3	T3
        	21	–	S4	T3
        	22	–	S2	T4
        	23	–	S3	T4
        	24	–	S4	T4
        3	25	–	S2	T1
        	26	–	S3	T1
        	27	–	S4	T1
        	28	–	S2	T2
        	29	–	S3	T2
        	30	–	S4	T2
        	31	–	S2	T3
        	32	–	S3	T3
        	33	–	S4	T3
        	34	–	S2	T4
        	35	–	S3	T4
        	36	–	S4	T4

        Fig. 2. Thickness of the surface course in function of the Poisson coefficient of the bituminous concrete for the pavement n°1

        In the figure 2, we can see that the thickness of the surface course remains constant under the change of the prescribed Poisson coefficient of the bituminous concrete.

   2. Application on a finite number of pavement structures

   We applied the procedure described in the previous section to determine the thickness of the surface course under the change of the Poisson coefficient of the bituminous concrete for 36 pavement structures.

   These pavement structures are presented in the table IX.

   TABLE IX. DESCRIPTION OF THE PAVEMENT STRUCTURES

   Type of Pavement	Numbered pavement
   		Surface course	Base course
   		Material	Material
   1	1	BC	CG/ Ci
   	2	BC	CG/ Ci
   	3	BC	CG/ Ci
   	4	BC	CG/ Ci
   	5	BC	CG/ Ci
   	6	BC	CG/ Ci
   	7	BC	CG/ Ci
   	8	BC	CG/ Ci
   	9	BC	CG/ Ci
   	10	BC	CG/ Ci
   	11	BC	CG/ Ci
   	12	BC	CG/ Ci
   2	13	BC	BG
   	14	BC	BG

   The next tables and figures show that the thickness of surface course can vary when the prescribed Poisson coefficient of the bituminous concrete changes.

   TABLE X. THICKNESS OF THE SURFACE COURSE IN FUNCTION OF THE POISSON COEFFICIENT OF THE BITUMINOUS CONCRETE FOR THE FLEXIBLE PAVEMENTS

   Numbered pavement
   	Thickness of the surface course (cm)
   	BC = 0.25	BC = 0.35	BC = 0.36	BC = 0.42	BC = 0.43	BC = 0.45
   1	3	3	3	3	3	3
   2	3	3	3	3	3	3
   3	3	3	3	3	3	3
   4	3	3	3	3	3	3
   5	3	3	3	3	3	3
   6	3	3	3	3	3	3
   7	4	4	4	4	4	4
   8	4	4	4	4	4/p>	4
   9	4	4	4	4	4	4
   10	4	4	4	4	4	4
   11	4	4	4	4	4	4
   12	4	4	4	4	4	4

   Fig. 3. Thickness of the surface course in function of the Poisson coefficient of the bituminous concrete for flexible pavements

   In the figure 3, we can see that the thickness of the surface course of the bituminous pavement does not change under the prescribed Poisson coefficient of the bituminous concrete.

   TABLE XI. THICKNESS OF THE SURFACE COURSE IN FUNCTION OF THE POISSON COEFFICIENT OF THE BITUMINOUS CONCRETE FOR THE BITUMINOUS PAVEMENTS

   20	7	6	6	6	6	5
   21	7	7	6	6	6	6
   22	8	7	7	6	6	6
   23	8	7	7	7	7	6
   24	8	7	7	6	6	6

   Fig. 4. Thickness of the surface course in function of the Poisson coefficient of the bituminous concrete for bituminous pavements

   In the figure 4, the thickness of the surface course of the bituminous pavement changes under the prescribed Poisson coefficient of the bituminous concrete for the pavements numbered from 18 to 23 in contrary to those numbered from 13 to 17.

   Numbered pavement
   	Thickness of the surface course (cm)
   	BC = 0.25	BC = 0.35	BC = 0.36	BC = 0.42	BC = 0.43	BC = 0.45
   25	4	3	3	3	3	3
   26	6	5	5	4	4	4
   27	4	3	3	3	3	3
   28	6	5	5	4	4	4
   29	5	4	4	3	3	3
   30	8	7	7	6	6	6
   31	7	6	6	5	5	5
   32	6	5	5	4	4	4
   33	9	8	7	7	6	6
   34	8	7	7	6	6	6
   35	7	6	6	5	5	5
   36	7	6	6	5	5	5

   Numbered pavement
   	Thickness of the surface course (cm)
   	BC = 0.25	BC = 0.35	BC = 0.36	BC = 0.42	BC = 0.43	BC = 0.45
   25	4	3	3	3	3	3
   26	6	5	5	4	4	4
   27	4	3	3	3	3	3
   28	6	5	5	4	4	4
   29	5	4	4	3	3	3
   30	8	7	7	6	6	6
   31	7	6	6	5	5	5
   32	6	5	5	4	4	4
   33	9	8	7	7	6	6
   34	8	7	7	6	6	6
   35	7	6	6	5	5	5
   36	7	6	6	5	5	5

   TABLE XII. THICKNESS OF THE SURFACE COURSE IN FUNCTION OF THE POISSON COEFFICIENT OF THE BITUMINOUS CONCRETE FOR THE SEMI-RIGID PAVEMENTS

   Numbered pavement
   	Thickness of the surface course (cm)
   	BC = 0.25	BC = 0.35	BC = 0.36	BC = 0.42	BC = 0.43	BC = 0.45
   13	3	3	3	3	3	3
   14	3	3	3	3	3	3
   15	3	3	3	3	3	3
   16	4	4	4	4	4	4
   17	4	4	4	4	4	4
   18	5	5	5	4	4	4
   19	7	7	7	6	6	6

   Fig. 5. Thickness of the surface course in function of the Poisson coefficient of the bituminous concrete for semi-rigid pavements

   In the figure 5, we observe that the thickness of the surface course of the semi-rigid pavement changes under the prescribed Poisson coefficient of the bituminous concrete for the corresponding pavements.

4. CONCLUSION

In this paper, the French method has been applied to study the thickness sensitivities of the surface course under the variation of the Poisson coefficient of the bituminous concrete. The case study of flexible pavements has shown that the prescribed values taken between 0.25 and 0.45 do not change the thickness of the surface course. In opposition, the analysis of the semi-rigid and bituminous pavements has shown that the change in Poisson coefficient can modify the thickness of the surface course considerably. We conclue that this second case study is sensitive under the variation of the Poisson coefficient than the flexible pavements. It is important to take into account the influence of the variation of the Poisson coefficient before recommending the mechanical values for these pavements design in tropical countries.

ACKNOWLEDGMENT

We would like to thank the Center of Excellence in Information of Communication Technologies at the University of Yaounde I for their support and collaboration.

REFERENCES

1. A. F. Messi, F. Sikali, B. C. Toh, "Proposal of minimum and maximum values for the poissons ratio of asphaltic concrete", International Journal of Lastest Research in Science and Technology, 2014, pp 25-29.

2. A. F. Messi, K. Mbock, R. P. M. Okpwe, J. Madjadoumbaye, T. F. Miyo, "New approach for determining Young modulus and Poisson coefficient in the structural design of the pavement", International Journal of Engineering Research & Technology, 2016, pp. 616-621.

3. Association of State Highway, Official AASHTO guide for design of pavement structures. Association of State Highway, American, Washington, D. C., 1993.

4. Austroads, Pavement design. Sydney, 2004.

5. CEBTP, Guide pratique de dimensionnement des chaussées pour les pays tropicaux. Ministère des relations extérieures, Coopération et Développement, République Française, 1984.

6. Department of the Environment, RN-29, A guide to the structural design for new roads. Department of the Environment, HMSO, London, 1970.

7. E. E. Putri, N. S. V. K. Rao, M. A. Mannan, "Evaluation of the modulus of elasticity and resilient modulus for hightway subgrades," EJGE, University of Malaysia Sabah, Kota Kinabaly, Malaysia, 2010.

8. F. A. Miyo Tchatchouang, Influence de linexactitude des valeurs des paramètres mécaniques (E et ) des matériaux constitutifs des chaussées sur le dimensionnement de celles-ci, simulation par le logiciel Alizé 3. Master in Engineering thesis, National Advanced School of Engineering, Cameroon, 2015.

9. H. Goacolu et Al. "La méthode française de dimensionnement," LCPC, p. 15, 2003.

10. H. L. Theyse, M. Beer, F. C. Rust, Overview of the South African mechanistic pavement design analysis method, Transportation Research Record, 1539, TRB, National Research Council, Washington, D.C., 1996, pp.6-17.

11. IRC, Guidelines for the design of flexible pavements, 2nd revision. IRC, 2001.

12. Japan Road Association, Manual for asphalt pavement. Japan Road Association, Japan, 1989.

13. J. Madjadoumbaye, S. M. Lezin, P. Mangoua, S. F. Takoukam, T. T. Tamo, "Poissons ratio in the choice of thicknesses of layers of pavement structure in lateritic natural grave", International Journal of Latest Research in Science and Technology, 2012.

14. LABOGENIE, Etudes géotechniques routières en vue de la construction de certaines routes du réseau national-lot 9 : Tronçon (RP19) Dschang-Fontem-Bakebe, Cameroon,. 2012.

15. LABOGENIE, Etudes géotechniques routières en vue de la construction de certaines routes du réseau national-lot 9 : Road Ring Carrefour Nyos-Weh. LABOGENIE, Cameroon, 2012.

16. LABOGENIE, Etudes géotechniques routières en vue de la construction de certaines routes du réseau national-lot 9 : Road Ring (RN11) Kumbo-Nkambe-Misaje-Mungong-Kimbi-Nyos-Weh-Wum. LABOGENIE, Cameroon, 2012.

17. LABOGENIE, Recommandation pour lutilisation des assises de chaussées en graveleux latéritiques. LABOGENIE, Cameroon, 1983.

18. LABOGENIE, Recommandation pour lutilisation des assises de chaussées en graves concassées. LABOGENIE, Cameroon, 1983.

19. LCPC, Manuel d'utilisation du logiciel ALIZE- LCPC version 1.3. LCPC, 2010.

20. LCPC and SETRA, French design manual for pavement structures. Guide Technique, Union Des Synducates, De L'industrie Routiere, 1997.

21. M. Kassogue, G. Hebert, M. Massiera, Contrôle de la qualité sur les matériaux des couches de chaussée (revêtement exclu). Faculté dIngénierie (Génie Civil), Université de Moncton, Canada, 2002.

22. M. Karray, G. Lefebre, "Significance and evaluation of Poissons ratio in Rayleigh wave testing", Canadian Geotechnical Journal, 2008.

23. NCHRP, Mechanistic-empirical design of new & rehabilitated pavement structures, 2011.

24. N. T. TRAN, Valorisation de sédiments marins et fluviaux en technique routière. PhD Thesis, Université dArtois, France, 2009.

25. RstO 2000, Richtlinien für die Standardisierung des Oberbaues von Verkehrsflächen, Entwurf, September 1999.

26. SETRA-LCPC. Conception et dimensionnement des structures de chaussées. Guide technique, LCPC, 1994.

27. Shell International Petroleum Company Limited, Shell pavement design manual asphalt pavements and overlays for road traffic, Shell International Petroleum Company Limited, London, 1978.

28. S. Triaw, Dimensionnement mécaniste-empirique des structures de chaussées: application au tronçon Séo-Diourbel. Master in Engineering thesis. Ecole Supérieure Polytechnique Centre, Senegal, 2006.