Abstract
The study of the cyclic behavior of materials has been very successful with the development of increasingly powerful computer tools that allow to limit costly experimental studies in favor of numerical models. This development has led to an increasing demand from the scientific community in terms of accuracy of numerical simulations and in terms of calculation time. The numerical tool allows to simulate the material behavior based on plastic, viscoplastic or elastoplastic behavior models [1]. Our study will focus on the determination of the parameters of three models used for the determination of the reversible moduli (Mr). These models are those of Thom and Brown [2], Uzan [3] and the NCHRP [4] (National Cooperative Highway Research Program) of the MEPDG (Mechanistic-Empirical Pavement Design Guide) which are a function of the loading level (the confining stress (s3), the deviatoric stress (sd), the octahedral stress and the total stress (q)). The research will be carried out on 4 samples of lateritic gravelly soils, 2 of which are from Burkina Faso (the Badnogo and Dédougou sites) and 2 from Senegal (the Sindia and Lam-lam sites). We carried out cyclic triaxial tests with repeated loading (TCR) according to the European standard Nf EN-13286-7 [5]. The tests were performed at variable confining stress to calculate the measured Reversible Modulus (Mrm = sd / e1, r). The materials studied have a maximum diameter of 20 mm and a percentage of fines lower than 20%. The samples are compacted to three water contents (wopm – 2%, wopm and wopm + 2%) and to an optimum dry density (γdopm) equal to 95% and 100%. The methodology used was least squares (Σ(ΔMr)2) and iteration by the “non-linear GRG” solving method used by the Solver calculation engine in Excel software. This allowed us to determine the values of the parameters k1 (in kPa and > 0), k2 (unitless and < 0), k3 (unitless and > 0) of the above numerical models. It is found that the k1, k2, k3 parameters and correlation coefficients are on average equal to 3511.540 kPa, -0.420, 0, and 0.91 for Thom and Brown’s model [2]; 4988.974 kPa, -0.289, 0.536, and 0.97 for Uzan’s model [3]; and 2436.959 kPa, -0.398, 1.864, and 0.91 > 0.90 for NCHRP [4] respectively. The predicted summary reversible modulus (MRSP) by the NCHRP model [4] is on average equal to 377.543 MPa. On the other hand, for the materials Ded/9.93/95.42 and Ded/8.16/95.39 the parameter k1 increases by 37.83% and the modulus MRSP also increases by 39.26%.
Moreover, for Ded/8,16/95,39 and Ded/6,23/95,52 the k1 parameter increases by 65,77% and the MRSP module also increases by 39,11%. This justifies that the parameter k1 tells us about the hardening effect of the material.
Keywords