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The disorders caused by the swelling of the soil on the structures have been observed for several years in the city of Rufisque. This article presents the results of the study of swelling kinetics of expansive soils in Rufisque and their prediction based on the hyperbolic rule. The odometer is used as an instrument for measuring swelling and the tests are carried out on some intact samples at their sampling water content. The present study shows that in Rufisque the most swelling layer is marl. The results show two phases of development. The first phase is very fast and represents 77% of the final deformation and the second one is slower. The prediction of the issue by the hyperbolic rule shows that it underestimates the first phase but gives a good prediction of the second phase of the swelling rate. There is a good correlation between the final swelling rates. However, the model gives a bad approximation of the half-swelling time.

The swelling of natural soils is specific to materials containing clayey minerals capable of interacting with water. These soils shrink and expand depending on their water content and environmental factors. These volume variations result in changes in the physical characteristics of the soil and in disturbances which are sometimes responsible for serious damage. The expansive soils are located in geographical areas which show large seasonal moisture deficits, where evapo- transpiration superior to precipitations favors their formation. They have been described in Central Europe, Australia, Asia, the southern United States, and in African countries of the tropical belt. The damages caused by this phenomenon are estimated in the United States at $2.3 billion in 1973 and then from $7 billion to $9 billion in 1986 and they exceed all natural risks [

In the city of Rufisque, the disorders caused by the swelling of soils on light buildings have been observed for several years. Around the 1980s, following an expertise of the degraded buildings, it was realized that they were swelling soils. Since 1983, these expansive soils have been the subject of many researches. Authors such as [

The original swelling mechanisms of soils have been widely studied, but it is still difficult to establish a relationship between the progression of the issue and the time. Indeed, the changes caused by the swelling of expansive soils are the result of a long process, involving the chemical, mineralogical proprieties and water. It often takes 5 to 10 years to see stabilized movements in the center of a building [

The study of the kinetics of swelling arouses many interests [

The objective of this article is to study the swelling kinetics of the expansive soils of Rufisque and to predict their behavior based on the hyperbolic rule.

The sedimentary province of Rufisque is located at about 25 km south-east of the peninsula of Dakar, in the immediate vicinity of the Atlantic Ocean. It lies between the meridians 17˚15'W and 17˚20'W and the parallels 14˚41'00''N and 14˚46'30''N, at the western extremity of the large Senegalo-Mauritanian Meso- Cenozoic sedimentary basin [^{2}. In this zone, the climate tropical and characterized by the alternation of a dry season, that lasts nine (9) months, and a rainy season that lasts three (3) months. The annual rainfall average from 1921 to 2004 is 500 mm at the Rufisque station. The monthly maximum temperatures average can reach 30.9˚C in October and the minimum exceed 17˚C in February.

The geology of Rufisque belongs to that of the peninsula of Cape Verde which is in the western extremity of the Senegalo-Mauritanian basin. The structure of the Senegal-Mauritanian basin is complicated in western Senegal by some brittle tectonics marked by the appearance of a network of faults. Those breaks, whose main system is oriented from N-S to NE-SW, delimited rising blocks such as the Ndiass and Dakar horsts and collapsed blocks like the Rufisque graben. The different outcrops encountered in the area of Rufisque-Bargny are formed by a volcanic group and a sedimentary group of tertiary to quaternary age.

・ The entire sedimentary to which is dated the inferior Eocene (Ypresien) to the medium (Lutetien), includes the Member of Cap des Biches and the Member of Rufisque [

・ The whole volcanic is composed to a big nephelinit flow set in as 20.9 ± 0.6 et 13.5 ± 0.2 Ma [^{3}, intimately associated to the lava, and probably resulting from phreato-magmatic eruption.

・ The flushing quaternaries are composed by beach rocks, azoïque sand deposits or rich littoral fauna [

The studied soils are taken from two sites in Rufisque: Cap des Biches and Arafat. The map below (

Analysis of the sampling profiles carried out in this sector reveals a great heterogeneity with a strong presence of soils susceptible to swelling (

Site | Ech. | Depth(m) | W_{n} (%) | γ (kN/m^{2}) | γ_{d} (kN/m^{2}) | γ_{sat} (kN/m^{2}) | γ_{s} (kN/m^{2}) | W_{L} (%) | PI (%) | VB | % < 2 µm | A_{c} |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Arafat | ACM31 | 0.44 à 1.36 | 11 | 17.7 | 15.9 | 20.0 | 27 | 44 | 31 | 6.5 | 15 | 0.43 |

ACM32 | 1.36 à 2.20 | 14 | 16.9 | 15.1 | 19.5 | 26.9 | 52 | 33 | 7.1 | 24 | 0.30 | |

ACM33 | 2.20 à 2.60 | 37 | 16.0 | 11.8 | 17.5 | 27.1 | 158 | 115 | 10.6 | 32 | 0.33 | |

ACM34 | 2.60 à 3.00 | 46 | 14.2 | 9.8 | 16.0 | 26.1 | 158 | 86 | 13.4 | 25 | 0.54 |

Site | Ech. | Depth(m) | W_{n} (%) | γ (kN/m^{2}) | γ_{d} (kN/m^{2}) | γ_{sat} (kN/m^{2}) | γ_{s} (kN/m^{2}) | W_{L} (%) | PI (%) | VB | % < 2 µm | A_{c} |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Cap des Biches | CB11 | 0 à 0.27 | 22 | 17.7 | 14.3 | 19.1 | 27 | 153 | 98 | 4.5 | 44 | 0.10 |

CB12 | 0.27 à 2.00 | 12 | 17.4 | 14.9 | 19.5 | 27.2 | 139 | 87 | 2.9 | 34 | 0.09 |

Arafat; there is a succession of clayey sands to very clayey in depth, followed by marl clay then marl that rests on a clay, whereas at Cap des Biches, it is made up of marl clay on the surface and becomes very compact to calcareous in depth.

In this work, the odometer is used as an instrument for measuring the swelling kinetics. The swelling tests were carried out on intact samples at their sampling water content. Cylindrical specimens were made while avoiding to disturb them. The samples were placed in greased odometrer cells to reduce the effect of lateral friction. The test samples are then immersed in distilled water, allowed to swell freely under a small normal stress. The movement is read at increasing steps of time during the first hours, then every 24 hours until the total stabilization of the swelling. The latter is considered stable when no movement is recorded during 6 consecutive readings days. The swelling potential (ε) is given by the following relation:

with: ΔH the vertical displacement and H the initial height of the sample.

Experimentally, swelling kinetics, as a general rule, can be approximated by a

hyperbolic relation [

with t: time elapsed, β and α: constants determined graphically and correspond

respectively to the slope of the line (t,

The validity of the model can be demonstrated if the curve of the inverse of

the swelling speed (

relation which is of the form (3).

The hyperbolic relation also predicts the maximum value of the swelling at an

infinite time. The maximum swelling is always equal to (

to the inverse of the slope of the regression line of the experimental points ex-

pressed in the diagram (t,

Vayssade (1978) proposes a hyperbolic rule of the following form:

ε_{inf} represents the final swelling rate obtained for an infinite time and t_{0.5} the half-swelling time (relative to the final swelling). This model can be written as an

equation of a straight line in the coordinate system (t,_{0.5} can

be determined graphically.

The numerical simulation of the hyperbolic rule was performed with the Matlab R2013 software. The results of the numerical simulation were compared to the experimental data.

The experimental results of the swelling kinetics of the expansive soils of Arafat and Cap des Biches are shown in

In order to evaluate the validity of the hyperbolic rule on the swelling soils of

Rufisque,

according to time (t) and then the parameters of the model can be deduced.

Analysis of the swelling layer by layer shows that the amplitude of swelling according to depth increases at Arafat while it decreases at Cap des Biches. In Arafat, the most swelling layer is between 2.20 and 2.60 m with swelling amplitude of 0.94 mm whereas at Cap des Biches, the surface layer is the most swelling

with amplitude of swelling of 1.80 mm. For both sites, the swelling is relatively slow and may exceed 30 days.

The study of the swelling kinetics of the expansive soils of Arafat and Cap des Biches highlights two phases; primary swelling and secondary swelling. The primary swelling takes place in less than 48 hours and represents more than 77% of the final swelling. For Rufisque soils, swell speeds reached 0.0034 to 0.013 mm∙min^{−1} for samples from Arafat and 0.084 to 0.116 mm∙min^{−1} for samples from Cap des Biches at the end of the primary phase. The primary swelling is carried out in two stages. The first step would correspond to the filling of the intervals of

the non-swelling fraction. It does not reflect a real swelling of the material, but an overall contraction due to the penetration of water into the pores, it depends on the void index and the swelling and non-swelling fraction of the material [

The secondary swelling was slower with velocities ranging from 1.068 × 10^{−5} to 2.78 × 10^{−5} mm∙min^{-1} for the Arafat samples and from 1.2 × 10^{−4} to 2.84 × 10^{−5} mm∙min^{−1} for the Cap des Biches samples. This phase is related to the percentage of clayey minerals and their nature. It reveals the hydration of clayey minerals and the beginning of the physicochemical properties of expansive soils [

The comparison of the experimental curves with the curves predicted by the model shows a good agreement of the appearances. The predicted curves (Figures 8-13) make it possible to account for the different phases of the swelling kinetics. However, there is an offset between the two curves which is all the more important as the sample is swelling. The estimation of the relative deviation between the experimental measurements and the predicted measurements shows that the hyperbolic law underestimates the first phase of swelling kinetics. This underestimate is maximal at the beginning of swelling with 94% error for Arafat samples and 99% for Cap des Biches samples. This is due to the fact that the first variations in volume do not really correspond to the swelling of the sample but to a filling of the voids in the material. There is a good correspondence between the two curves from the second phase of the swelling. The model provides a good approximation of the final swelling rate with deviations of less than 1.5%.

predicted final swelling rate. However, this correlation is almost absent between the observed and predicted half-swelling time (

This article highlighted the swelling of the soils of Rufisque according to time. This study shows that swelling is a very slow multi-phase process that can last several weeks before its stabilization. In this area, the behavior of soils differs from one sector to another. The shape of the kinetic curves of the soils of Rufisque corroborates that obtained in the literature. Its prediction based on

the hyperbolic rule reveals that the model underestimates the kinetics of the primary swelling as well as the half-swelling time. However, it gives a good approximation of the final swelling rate. Yet, for a more reliable representation of the swelling kinetics of the expansive soils of Rufisque, it will be necessary to consider an improvement of the model by integrating the primary phase characterized by mechanical activities.

Our special and sincere thanks to the Director of SIPRES for his technical and financial support.

Faye, P.S., Ndoye, I., Ndiaye, M., Tall, A., Cissé, I.K. and Mag- nan, J.P. (2017) Prediction of Swelling Ki- netics of Expansive Soils of Rufisque (Senegal, West Africa). Open Journal of Civil Engineering, 7, 267-281. https://doi.org/10.4236/ojce.2017.72017