All the samples that we studied here come from Senegal in West Africa “Figure 1”. It is about two lateritic careers in two localities: The lateritic career of Sindia and the lateritic career of Keur Samba Kane. The choice of these two careers is justified by the fact that we want to study examples of tropical soils. And those two lateric careers of Sindia and Keur Samba Kane participated in the realization of the biggest works of the country.

The preliminary analyses showed that these clays are low plastic lateritic gravels with the following characteristics “Table 1”.

We used a square shear-box (60 mm) to make the whole set of tests on our samples. Our samples have all been compacted to the middle energy of Proctor (theoretically) in Proctor moulds as specimen of more or less 70 mm in height. These specimens were realized in several copies at the same time and then packed in tight films. Before the compaction of our samples in the Proctor moulds, we made them pass to the sifter of the module 44 (20 mm) in accordance with the norm French Industrial Standards Authority (AFNOR) to knead to the contents in water of the Proctor modified then found for every sample.

After this modus operandi, we realised the tests in three phases of respective loads, corresponding to initial normal constraints of 196 kPa, 392 kPa and 784 kPa with the speed fixed to 0.3 mm/min for all the tests. The characteristics of shearing that we have found are summarized in the “Table 2” and on the “Figure 2”. “Figure 3” and “Figure 4” are the corresponding figures for the sample of Sindia and the “Table 3” and the “Figure 5”, “Figure 6” and “Figure 7” for the sample of Keur Samba Kane.

The lateritic soil of Sindia presents a strong cohesion due to the fact that the effect of compaction cements the sol. The evolution of the tangential stress is monotonic and becomes rather constant when the resistance to the maximal shearing is reached. It is due to the fact that the compactness does not reach 95%

of the OPM [4] [5] [6] . This lateritic material of Sindia has a behaviour therefore called “ductile”. For a maximal resistance of 175 kPa during the first loading, the maximal value of this resistance to the shearing is 436 kPa with a 784 kPa initial normal stress. The vertical displacement versus to the horizontal displacement curve is characteristic of a contracting material [7] . This shape shows a reduction of the volume of the sample during the test. Like previously, the results of the shearing test to the shear-box of the lateritic soil of Keur Samba Kane are inserted in the “Table 3” and “Figure 5”. The value of the cohesion is also high. The effect of the compaction is therefore visible with the material that is cemented itself.

For a normal initial stress of 196 kPa, the resistance to the maximal shearing is of 228 kPa, whereas for a normal initial constraint of 784 kPa, the resistance to the maximal shearing developed by the lateritic material of Keur Samba Kane in a compacted state is of 535 kPa. The curves of the vertical displacement versus the horizontal displacement all show a contracting behaviour of the material all along the test. This reduction in the volume is mainly caused by the presence of water at the time of the test that favours the settling [8] .

Usually we observe for lateritic soil a dilating (resp. contracting) behaviour for low (resp. large) constraints. This transition between dilation and contraction is also observed when water content of compaction varies [9] . This is not case for our materials.

The effect of the compaction is noticed well for the two samples compacted lateritic gravels at the time of the loadings to the oedometer. We do not observe an elastic slope at the beginning of the loading; the void ratio decreases after a certain level of stress “Figure 8”. Before the beginning the test, we let the piston of the device react on the sample during several hours and we recorded the variation of the void ratio. Two samples exhibited a classical behaviour (one dimensional consolidation) after unloading-reloading process [10] . After these tests of

oedometer loading-unloading, we got the following set of parameters (Table 4).

The yield surface in the plane (p, q) of modified Cam Clay model is given by this expression:

f = q 2 + M 2 ( p 2 − p p c r ) = 0. (8)

The Critical Line State is given by this equation:

q = M p . (9)

While applying these expressions to the results of our tests on the two compacted lateritic materials, we obtain the “Figure 9” and “Figure 10”. In these figures of the Cam Clay’s modified model, we observe yield surfaces in the shape of ellipses centred on Pcr, the critical pressure that is the projection on the axis of the spherical pressure of the intersection between the critical state Line and the loading surface. The parameter of hardening is given by this critical pressure Pcr equal to Pc0/2. These two figures correspond to the two yield surfaces of the lateritic samples in the plane (p, q). Each of the figures watch two surfaces elasto-plastic limit with two pressures of pre-consolidation giving two critical pressures in accordance with the results of the oedometers tests.

The projection of these curves of the plane (q, p) onto the plane (e, p) permits us to pass to the plane (e, lnp) to see the isotropic virgin curve and the critical state line defined by the equations:

e = e λ − λ ln p , (10)

e = Γ − λ ln p , (11)

with

Γ = e λ − λ + k . (12)

This projection is made in the same system of axis and permits to really describe the loading path for the oedometer test.

The isotropic virgin curve (named as virgin consolidation curve) is the curve of loading that would be obtained during the isotropic triaxial test. Soil is normally consolidated all along this curve and is in a plastic state “Figure 11” and “Figure 12”.

The results of the consolidation tests “Table 6” give the constraints of pre-con- solidation from which we calculated the pressures of pre-consolidation while considering that the materials are normally consolidated. In the same Table are given the values of the friction angle that permit to calculate the slope of the Critical State Line.

The results of the following triaxial tests for various pressures of confinement gave the values of p and q “Table 7” for every one of the three materials studied by [11] . We have used them to draw the loading surfaces corresponding to the first and to the last pressure of confinement (two surfaces) for every material.

We proceeded thus to a possible comparison with the surfaces given from consolidation tests and shear box. This triaxial tests also give the slope of the critical state line η = q/p for the set of confinement constraints “Table 8”.

We have results of shearing, oedometer and triaxial tests for three samples made

of compacted lateritic gravels of Ndienne, Sebikhotane and Yenne. These results permit us verification while drawing the yield surfaces and respective CSL “Figures 13-15”. That is to say, for a couple of results shear-box, oedometer test, we draw the loading surface and the CSL; for results given by the triaxial tests on the same material we draw the yield surface also and the CSL. For every material, we put the two loading surfaces on the same figure and at the same scale to compare the results.

The remark is that with the means of simple tests (shear-box and oedometer tests) we succeeded to describe the behaviour in the critical state but with less precision compared to the identification of the results given by triaxial tests.

For the samples of Ndienne and Yenne, we see that the spherical pressure is very lower (difference of 400 kPa) than the one of the triaxial test. It can be a consequence of the method of calculation of the pressure in the case of the oedometer test. Indeed in this case the lateral stresses is unknown and very often one uses the empirical law k₀ = 1 − sinφ (k₀ is the coefficient of earth pressure at- rest) while considering that the materials are normally consolidated. If we observe the sample of Sebikhotane, we even see that the spherical mean pressure is larger in the case of the method of the simple tests. This sample of Sebikhotane presents the weakest angle of friction (biggest value of the empiric constant k₀).