Estimation of Resilient Modulus of Unbound Granular Materials from Senegal (West Africa)

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1 Geomaterials, 013, 3, Publishe Online October 013 ( Estimation of Resilient Moulus of Unboun Granular Materials from Senegal (West Africa) Aama Dione 1, Meissa Fall 1, Yves Berthau, Makhaly Bâ 1 1 Laboratoire e Mécanique et Moélisation-UFR Sciences e l Ingénieur, Université e Thiès, Thiès, Sénégal UFR Ingénierie, Université Paris VI Pierre et Marie Curie, Paris, France aama.ione@univ-thies.sn Receive September, 013; revise October, 013; accepte October 9, 013 Copyright 013 Aama Dione et al. This is an open access article istribute uner the Creative Commons Attribution License, which permits unrestricte use, istribution, an reprouction in any meium, provie the original work is properly cite. ABSTRACT The resilient moulus (M r ) is an important parameter which escribes the mechanical behavior of unboun granular materials. However, this parameter can be etermine from physical properties. This paper presents the relationship between resilient moulus an physical properties of Quartzite from Bakel (GB), Basalt from Diack an Bargny an Bania limestones. Simple an multiple regression metho by stepwise are use to establish linear an nonlinear relations to preict the resilient moulus. The results showe no significant correlation for Basalt, a weak estimation of the moulus for GB an goo preiction of resilient moulus for limestone. These results also showe that the moel of Uzan is more suitable to preict the resilient moulus than NCHRP moel an the resilient moulus is better preicte in nonlinear relationship. Keywors: Resilient Moulus; Mechanical Behavior; Correlation; Physical Properties; Unboun Granular Materials 1. Introuction The stiffness of granular materials was characterize in Senegal as in lots of other countries in the worl, by Young s moulus (E). This parameter suppose that the unboun granular materials were elastic linear. Recent stuies have shown that the mechanical behavior of unboun granular materials is nonlinear elastoplastic (Huang, 004) [1]. This behavior le scientists to efine the resilient moulus, which replaces henceforth Young s moulus, in orer to better characterize the real behavior of unboun materials. The resilient moulus is the primary input on materials properties in the NCHRP 1-37 (004) guie. It is very important to calculate the stress, strains an eflections of pavement uner wheel loa. However, the etermination of resilient moulus is time consuming, requires sophisticate equipment which is costly as well as skille personnel for laboratory. It is so important to preict resilient moulus in orer to reuce cost an time in roa project. In aition, the resilient moulus is influence by many factors, the most important of them are stress level an material properties (Lekarp et al., 000 []). This article presents the estimation of resilient moulus of unboun materials from Senegal base on physical properties, since the physical properties are easy to obtain in laboratory an are not expensive.. Backgroun Since 1960, numerous research efforts have been evelope to characterize the resilient behavior of granular materials (Lekarp et al., 000 []). In Senegal, the investigation on mechanical behavior of unboun materials goes up since twenty years. Fall (1993) [3] has announce for the first time, the importance of aequacy input for pavement esign. He unerlines the first avance mechanical properties of lateritic soil from Senegal. Ba (01) [4] also stuie the mechanical behavior uner cyclic wheel loa of granular materials (Diack Basalt, Quartzite from Bakel an limestones from Bargny an Bania) an efine resilient moulus of these materials. This concept of resilient is introuce by See et al. in 1960 (Angelone an Martinez, 000 [5]) an can be efine as the ratio of the repeate axial eviatory stress to the recoverable axial strain (Figure 1). 1 3 M σ σ σ r = = ε ε M r : resilient moulus (kpa), σ 1 : major stress (kpa), σ 3 : minor stress (kpa), σ : eviatoric stress (kpa), ε a : recoverable strain. a a Copyright 013 SciRes.

2 A. DIONE ET AL. 173 Figure 1. Definition of resilient moulus (Hopkins et al., 004 [6]). However, since the laboratory etermination of resilient moulus is complex, costly an time consuming, resilient moulus can be estimate base on correlation with physical properties. In Senegal no stuies for estimating resilient moulus were performe. But in the worl there are many stuies for preicting resilient moulus from physical proprieties. Jones an Witczak (1977) [7] evelope two correlation equations for A-7-6 subgrae soil in California, combining the water content an the egree of saturation. The results show a coefficient of 0.96 for compacte soil an 0.45 for unisturbe soil. Carmichael an Stuart (1985) [8] evelope two relations result from tests conucte on 50 soils. Yau an Von Quintus (00) [9] propose an equation for preicting resilient moulus. They foun that the equation i not fit all situations. George (004) [10] foun linear an nonlinear relationships for estimating resilient moulus for fine an coarse graine soils from physical properties. Kim et al. (007) [11] establishe relationships to estimate moels parameters of resilient moulus. Van Aswegen an Steyn (013) [1] also stuy the statistical moeling of the resilient behavior of unboun granular material of South Africa soils. These stuies are very important for estimating resilient moulus of unboun granular materials. 3. Characteristics of Materials an Testing Proceure 3.1. Characteristics of Materials The materials use in this stuy are unboun aggregates coming from various geological formations of Senegal. They are amongst others like the Bakel Quartzite, the Diack Basalt an Bargny an Bania Limestones (Figure ). These materials were use in base course as alternative materials to the lateritic soils. Figure. Various materials of the stuy (Ba, 01) [4]. The atabase is collecte from Ba (01) [4] in orer to obtain material characteristics. The sizes use are 0/0 an 0/31.5 for Bakel Quartzite an limestones an only 0/31.5 for Diack Basalt. Grain size istributions (Figure 3) an conitions of compaction for the materials are performe respectively accoring to stanar ASTM C an ASTM D Testing Proceure Specimens were subjecte to the resilient moulus test proceure. A MTS close-loop servo-electro-hyraulic testing system was use to apply the cyclic loaing in a haversine waveform, with 0.1 secon of loaing uration an 0.9 secon of rest perio. Displacements were measure internally using Linear Variable Displacement Transucer ( LVDT ) mounte aroun the specimen insie the cell. The specimens have been teste using the NCHRP Protocol 1-8. Each specimen was conitione with kpa confining pressure, an 1000 cycles of 07 kpa eviator stress. The cycles are repeate 100 times for 30 loaing sequences with ifferent combinations of confining pressures an eviator stresses. The last five cycles of each sequence are use to calculate the resilient moulus (Ba, 011) [13]. 4. Statistical Analysis The resilient moulus test results an physical properties of materials collecte from Ba (01) [4] were analyze using statistica software. The ata base is not large, so it is not aequate to perform suitable statistical analysis. But it is important to efine basic knowlege for correlating resilient moulus of unboun granular materials of Senegal Description of Variables The variables use in this analysis are resilient moulus Copyright 013 SciRes.

3 174 A. DIONE ET AL. Figure 3. Particles size istribution for the 4 materials (Ba, 01) [4]. which is the epenent variable an physical properties of unboun granular materials represent the inepenent variables. There are water content (W), optimum water content (W opt ), ry ensity (γ ), maximum ry ensity (γ max ), the percentage of fine particles (% fine), the percent passing on sieve mm (P ), the maximum size of particle (D max ), the coefficient of uniformity (Cu) an the coefficient of curvature (Cc). The resilient moulus was calculate using Uzan an NCHRP moels, because they are more suitable to preict the resilient moulus (Ba, 011) [13]. They are etermine from states of stresses usually foun in base course efine by NCHRP (004) [14]. There is summary resilient moulus which is use to perform correlations. The following equations show the moels as well as the states of stresses use. k θ σ M r k1pa Pa Pa k θ τ oct r 1 = Uzan moel k3 M = k Pa + 1 NCHRP moel Pa Pa M r : resilient moulus (MPa), θ: bulk stress = 08 kpa, τ oct : octaeral shear stess = kpa, Pa: atmospheric pressure = kpa, σ : eviatoric stress 103 kpa, k i : moel parameters (kpa). k3 4.. Relationships between Variables After escribing the variables, we will carry out a Principal Component Analysis (PCA) to look for relationships between variables. This analysis allowe the etection of the relationships between variables an helpe to choose the best type of regression, Figures 4-6 represent the PCA performe with GB, Diack Basalt an limestones. The result shows for GB (Figure 4) that the resilient moulus is explaine at 67.64%, an is posi- Figure 4. Principal Component Analysis performe on GB. Figure 5. Principal Component Analysis performe on the basalt. tively epenent on γ, γ max an D max an negatively epenent on W opt, P W an % fines. For the Diack Basalt (Figure 5), the resilient moulus is positively epenent on γ an negatively epenent on W, it is explaine at 80.88%. For limestones (Figure 6) the resilient moulus is explaine at 81.1% an is positively epenent on γ an negatively on W. These PCA o not justify a real connection with resilient moulus. They give just an overall vision on the touchiness of possible relations with the moulus. There are also other methos such as the examination of the matrix of correlation an the stepwise metho which guie the selection of the best variables in the moels. Copyright 013 SciRes.

4 A. DIONE ET AL. 175 Figure 6. Principal Component Analysis performe on limestones Correlation Analysis In this analysis, regression metho by stepwise is use. It is base on the coefficient of etermination R an the tests of Stuent an Fischer. Only the variables most correlate an satisfactory with tests are selecte in the moel. These tests are associate at the p-level, an all variables inferior at threshol (0.05) are significant. However, linear an nonlinear relationships are etermine for all materials. Inee, multicolinearity test is performe between inepenent variables, in orer to prevent bias relations. For the majority of our relations, the following general equation is use. Y = β + β X + β X + β X + ε p p Y: epenent variable (resilient moulus), β 0 : intercept, β i : moel parameters, X i : inepenent variables (physical properties), ε: error. The results show no correlation for Diack Basalt because there is a lack of ata. They also show that the resilient moulus is weakly explaine for GB with R of 0.34 an 0.3 for Uzan an NCHRP (004) moels. For limestones, there are a R of 0.96 for Uzan moel an a R of 0.94 for NCHRP moel. The summary of the relations establishe in linear regression accoring to the moels of Uzan an NCHRP (004) gave the following equations: GB for UZAN moel SRM = ( γ ) R = 0.34 GB for NCHRP moel SRM = ( γ ) R = 0.3 Limestone for UZAN moel ( ) 4 ( ) SRM = W γ R = 0.96 Limestone for NCHRP moel ( ) 1 ( ) SRM = W γ R = 0.94 SRM: Summury Resilient Moulus (MPa), W: water content (%), γ : ry ensity (kn/m 3 ). Figures 7-11 show the scatter between measure an preicte resilient moulus for several materials in linear moels. They show a scatter plot wiely isperse for Basalt, moerately isperse for GB an a scatter plot showing a goo correlation for limestones. There are also nonlinear relationships evelope in this paper. They showe as in linear relations that the resilient is weakly explaine for GB with R of 0.38 an Figure 7. Relation between actual an preicte resilient moulus for GB of the moel of Uzan in linear moel. Figure 8. Relation between actual an preicte resilient moulus for GB of the moel of NCHRP in linear moel. Copyright 013 SciRes.

5 176 A. DIONE ET AL for Uzan an NCHRP (004) moels. For limestones, there are a R of 0.98 for Uzan moel an a R of 0.98 for NCHRP moel. The result also showe that the R is increasing in nonlinear moels. Inee; the use of nonlinear moels are the best for preicting resilient moulus. The moels in nonlinear relationships are represente by the following equations: GB for UZAN moel Figure 9. Relation between actual an preicte resilient moulus for basalt of the moel in linear moel. Figure 10. Relation between actual an preicte resilient moulus for limestones of the moel of Uzan in linear moel. log R ( SRM ) = GB for NCHRP moel log R ( SRM ) = Limestone for UZAN moel = γ = γ log ( SRM ) = ( W ) γ R = 0.98 Limestone for NCHRP moel ( SRM) = ( W) + ( γ ) log R = 0.98 SRM: Summary Resilient Moulus (MPa), W: water content (%), γ : ry ensity (kn/m 3 ). In nonlinear moel, Figures 1 an 13 show a ba istribution of points resulting from low correlation with GB. However, a goo estimation was note for limestones Figures 14 an 15 show a goo istribution of points resulting from goo estimation of resilient moulus of limestones from physical properties. Figure 11. Relation between actual an preicte resilient moulus for limestones of the moel of NCHRP in linear moel. Figure 1. Relation between actual an preicte resilient moulus for GB of the moel of Uzan in nonlinear moel. Copyright 013 SciRes.

6 A. DIONE ET AL Conclusion The estimation of the resilient moulus of GNT from Senegal, shows that the Uzan moel is more suitable for preicting the materials. However, there is no correlation for the basalt ue to the eficiency of significant variables, a weak correlation for GB an a goo relationship for limestones which have a strong affinity with water. The results also show that the resilient is better preicte in nonlinear moels. This stuy is important to get a way to estimate suitability of the resilient moulus, but the relations cannot be use for all situations, because of the small size of ata base. Figure 13. Relation between actual an preicte resilient moulus for GB of the moel of NCHRP in nonlinear moel. 6. Acknowlegements We woul like to acknowlege Dr. Makhaly Ba to have place at our isposal the unit of its experimental results, which were useful for this article. We also thank the French cooperation for the granting for a research grant in Paris VI. Figure 14. Relation between actual an preicte resilient moulus for limestones of the moel of Uzan in nonlinear moel. Figure 15. Relation between actual an preicte resilient moulus for limestones of the moel of NCHRP in nonlinear moel. REFERENCES [1] Y. Huang, Pavement Analysis an Design, n Eition, Prentice-Hall, Inc., Upper Sale River, New Jersey, 004. [] F. Lekarp, U. Isacsson an A. Dawson, State of the Art. I: Resilient Response of Unboun Aggregates, Journal of Transportation Engineering, Vol. 16, No. 1, 000, pp [3] M. Fall, Ientification et Caractérisation Mécanique e Graveleux Latéritiques u Sénégal: Application au Domaine Routier, Thèse e Doctorat INPL, 1993, 40 p. [4] M. Ba, Comportement Mécanique sous Sollicitations Cycliques e Granulats Quartzitiques e Backel-Comparaison avec es Matériaux e Référence u Sénégal et Amérique (USA): Application au Dimensionnement Mécanistique es Chaussées Souples, Thèse e Doctorat Université Cheikh Anta Diop e Dakar, 01, p. 39. [5] S. Angelone an F. Martinez, Analysis of Non-Linear Moels Describing the Resilient Behavior for Soils an Unboun Materials, 000. [6] T. C. Hopkins, T. L. Beckham an C. Sun, Resilient Moulus of Compacte Crushe Stone Aggregate Bases, Research Report KTC-05-7/SPR F, Kentucky Transportation Center, College of Engineering, University of Kentucky, 007, p. 89. [7] M. P. Jones an M. W. Witczak, Subgrae Moulus on the San Diego Test Roa, Transportation Research Recor 641, TBR, National Research Council, Washington, 1977, pp [8] R. F. Carmichael an E. Stuart, Preicting Resilient Moulus: A Stuy to Determine the Mechanical Properties of Subgrae Soils, Transportation Research Recor 1043, TBR, National Research Council, Washington, D.C., pp Copyright 013 SciRes.

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