Current Knowledge and Research on the Design of Flexible Pavements in Senegal
Dr Civil Eng., Earth Sciences Institute (IST), Faculty of Sciences and Techniques Fala Paye Dr Civil Eng., Polytechnic School of Thiès (ESP) and Abdoulaye Mbodji Civil Engineer, Jean Lefebvre-Senegal S.A., BP 106 Dakar, Senegal |
ABSTRACT
In previous studies (Fall et al., 2002), we had underlined the importance to have reliable characteristics to allow an optimal design of road structures. The research done in Senegal for the last ten years or so permits to pronounce now amply on the geotechnical reasons of the premature ruin of road structures. The main problem of the weak life span of the road structures is due to an under-estimated design caused by the use of inappropriate characteristics with no control in the numerical codes of road design as Alize III® or Ecoroute® of the LCPC. In situ investigation done since then with complementary experimental works permits to have reliable information on local subgrades, the most common gravel lateritic materials, roadmaking aggregates and finally the laterite-cement. This last material was the object of particular attention, bound to its specificity and especially by the fact that all base or sub-base layers in Senegal is prepared with. Finally, a fine analysis of the interrelationships between these features, their strength parameters and their modulus of elasticity permits to have now tools of choice to do reasonable road design. The done applied boards give satisfaction. It is then question now to define new norms/standards and specifications in road geotechnique. The present article is more amply about results gotten on the laterite-cement, essential element of the road construction in the whole african tropical zone. The results gotten on the surfacing materials as well as a methodology study of the subgrade will also be exposed.
Keywords: Laterite-cement, base, subgrade, gravel lateritic soil, Tropical, road design.
Editor's note. This paper uses the notation of a comma (,) as a decimal point in the figures.
INTRODUCTION
In Senegal, as in a lot of developing countries, the road construction is making without norms and standards. It very often drives always the use of prescriptions contradictory, because the road design is not ever basing on a real knowledge of local material characteristics, the gravel lateritic soil notably. Indeed, the very scattered values of the elastic parameters of the materials, among others the dynamic modulus in the technical reports can constitute an element to convince of it. Besides, the report is made that, on the reinforced roads structures in Senegal, most base layers treated by cement undergo intense deformation or arrive at a premature failure (DTP, 2000). It probably brings us to think on the methods of design utilized in Senegal. Is it that the empiric methods of design as among others the method of the CEBTP (1982) mostly use or the CBR methods are the most suitable for the design of the gravel lateritic bases pavements treated by cement? Is it necessary to incriminate the in situ setting of the laterite-cement? Do the methods say rational otherwise of road design that adopt analytic techniques and use numerical codes of calculation, are very sensitive to the value of the input parameters (FALL and al., 2002) (Ed. note: approximately, 1 bar = 1atm = 103 kPa) If the rational method is adopted, what justifies that it is given of the laterites of CBR lower to 80% and improved at 2.5 or 3%, the very scattered values of elastic modulus of 15000 to 23000 bars (and even sometimes 50000 bars). It can be said therefore that in Senegal, in matters of road studies, doesn't have serious specifications applied like norms to which it must be made reference for the laterite-cement. The research undertook since then in Senegal, in collaboration between the universities, the enterprises and the administration permitted to succeed to a set of results that make largely the object of this article.
PRINCIPAL METHODS OF PAVEMENT DESIGN APPLED IN SENEGAL
2.1. The California Bearing Ratio Method
Known in 1938 (PORTER, 1938 and 1942), it is based on two complementary abacuses that give the total thickness of the pavement. The first gives according to the CBR of the soil support (subgrade), the thickness necessary of the pavement body for a load considered variable of 1 to 10 tons. The second expresses this thickness according to the traffic and the CBR of soil support. This method is used again in Senegal. This method has since been developed and modified in Senegal (REMILLION, 1952). It is recognized today that this technique drives of an overestimate road design, what implies substantial constructional costs.
2.2. The Road Research Laboratory Method
This method uses the following formula, that gives the thickness of the layer (P is the weight of a fictional wheel representing, at a time, the real wheel and the intensity of the traffic). This method doesn't give any value of the parameters for the rational calculation of the pavement structure made of laterite-cement, for example. It use drives at the same findings that for the CBR method. It is used again in Senegal for the design of non-donned pavements.
2.3. The Method of the CEBTP
This method (CEBTP, 1982) is based on the following principles:
- In the case of flexible pavements including any rigidified layers, the CBR and the intensity of the traffic doesn't determine the total thickness of the pavement;
- In the case of pavements including one or several layers, susceptible by their stiffness, of a failure by traction, the design that aimed to avoid the deflexion of the subgrade must be completed by a theoretical analysis whose objective is to verify that the efficient tensile stresses developed at the base of the rigidifies layers are compatible with the probable quality of the materials. The method of the CEBTP proposed in 1982 includes two charts giving, according to the traffic and the allowable bearing pressure on subgrade, the thickness required in layers of foundation, base and surface. It defines the five following classes of traffic expressed in accrued number of passages of an equivalent axle of 13 tons (see Table 1). It also defines the five classes of subgrade (see Table 2). This method takes account of the nature of the materials that should be use. This is how it gives the thickness in centimetres of the pavement body in gravel lateritic soil improved or no. It’s the most common method of road design used in the whole tropical African countries.
Table 1. Traffic classes (CEBTP, 1982)
- | T_{1} | < 5.10^{5} |
5.10^{5}< | T_{2} | < 1.5.10^{6} |
1.5.10^{6}< | T_{3} | <4.10^{6} |
4.10^{6} < | T_{4} | < 10^{7} |
10^{7} < | T_{5} | < 2.10^{7} |
Table 2. Bearing capacity classes (CEBTP, 1982)
S_{1} | CBR | < 5 | |
S_{2} | 5 < | < 10 | |
S_{3} | 10 < | < 15 | |
S_{4} | 15 < | <30 | |
S_{5} | > 30 | ||
2.4. The Rational Methods
They are based on the analysis of the stresses generated by the traffic at different levels of the pavement body and the comparison with the likely performance of the materials of the pavement body. With the development of computer tools, some more complete methods saw the day with the codes of calculation as Alize III^{®} or Ecoroute^{®} distributed by the LCPC, that permit to treat the problem of a multi-layered system completely, in different conditions of the interface state of the layers one on the other. These mathematical models can be used for the design of the reinforced or new pavements structures. They consist to:
- Model a new structure (choice of the number of layers, their thickness and their mechanical characteristics) or to reinforce an old one, in order to calculate the stresses/strain provoked by a unit standard load;
- To search for, with the help of the model, the stress or the maximal deformation susceptible to generate the rupture of a layer with the standard load;
- To compare this stress or deformation at the admissible value ensuing the law of fatigue for the considered materials.
2.5. Discussion
The empiric or semi-theoretical methods of road design have been conceived in particular conditions that don't correspond completely to those of the african tropical countries (AASHOO and WAASHTO Tests, between 1950 to 1962). Their extrapolation in tropical african countries very often entails enormous risks. Indeed, used in the absence of design catalogue, they take in general the thirty superior centimetres of the platform only as a basis and on the expressed traffic class in accrued number of heavy weights. Otherwise, for a material used in the body of the pavement, they don't simulate the real conditions of dynamic and cyclic solicitations (MARTINEZ, 1980 and 1990; FALL, 1993). The complexity of this type of solicitation, with the rotation of the main stresses, requires adequate laboratory tests that reproduce the solicitations the most faithfully in situ. Besides, in the covered pavement design composed of one or several layers of material treaties by hydraulic binders, the CBR method doesn't consider the method of rupture that can be translated following the effect of the tensile stress at the bases of the linked layers. The CBR method and the one of the RRL seem maladjusted for the design of a structure of pavement treated by cement; the mechanical operating mode of these is known like being a flexion. The CBR tests on which are based the empiric methods are tests of penetration, therefore based on one operating mode by compression of the pavement (FALL, 1993). In the pavements treated by hydraulic binders, the materials are supposed linked. Besides, in the CBR method that uses some abacuses and the one of the Road Research Laboratory, the thickness of a layer depends on the value of the CBR of the underlying layer, whereas for the rational methods the thickness of every layer is function of the value of the elastic modulus and the admissible and allowable bearing limit of the material that constitutes it. The rational methods can give satisfactory results if the input parameters, than the Young's modulus and the Poisson's coefficient used correspond precisely to the real characteristics of the materials considered. Their choice appears therefore determinant for the design of the structures of pavements (MARTINEZ, 1980 and 1990 ; FALL, 2002). The rational methods would seem to bring more of precisions than the empiric methods in this sense that they take in account the intrinsic characteristic of the materials of the pavement body.
3. BITUMINOUS OR CONCRETE SURFACING
3.1. Choice of the Types of Mineral Aggregates
An important choice of utilized materials for the coatings (bituminous or concrete surfacing) excluded the limestone and the lateritic concretions as aggregates in the confection and the realization of the surfacing layers. These materials don't present any good performance for their use as satisfactory surface (see Table 3). While taking into account these applied observations, a choice is made on the materials as the basalt and the silexite that were the object of important enough works between 1967 and 2002 (see Table 4). Characteristics observed for these two types of material confer them better performance as aggregates for the confection of the bituminous or concrete surfacing test-tubes. The silexite always develops Marshall stabilities of the order of 800 to 900 kg for compressive strengths between 40 and 50 bars. Besides, for what is the simple compressive strength after 7 days of cure in air and after 7 days of immersion, the results give a ratio immersion/compression superior to 1. This phenomenon that is rarely met reveals a good behaviour of the bituminous or concrete samples of silexites in presence of water. This good characteristic consign today the silexites in the same rank than the material of reference that the basalt constitutes in tropical African countries (see Table 4).
Table 3. Traditional aggregates characteristics used in surfacing
Characteristics | Limestone | Laterite |
Los Angeles Abrasion Value, LA (%) | 27.5 – 32.5 | 40.3 – 31 |
Modified Deval Value, MD (%) | 8.9 – 5.4 | 3.09 – 4.08 |
Micro-Deval Value, MDE (%) | 30 – 39 | 44 – 40.5 |
Dry Micro-Deval Value, MDS (%) | 8.9 - 11 | 17.5 - 15 |
Table 4. Basalt and silexite aggregates characteristics (Database of CEREEQ, 1967-2002)
Characteristics | Basalt | Silexite |
Bulk density (kN/m^{3}) | 29.5 – 29.3 | 25.7 – 27 |
Apparent Bulk density (kN/m^{3}) |
15 | 12.9 – 15.3 |
Property (%) |
0.4 – 0.6 | 0.36 - 3 |
Flakiness index, IF (%) | 13 – 18.8 | 13.7 - 20 |
Elongation index, IE (%) | 0.16 | 0.18 |
LA (%) | 9.8 – 10 | 9 – 10 |
Modified Deval (%) | 18.1 | 17.4 |
MDE (%) | 10.4 – 13.5 | 14 |
MDS (%) | 6 – 2.6 | 6.3 – 7 |
3.2. Formulations
The main goal of formulation studies is to determine the best aggregates composition to adopt for a bituminous surfacing that can present some on the one hand properties (permeability, roughness, stability, durability, etc.) and on the other hand to permit controls it ongoing of the constancy of the product of manufacture and facilitate its implementation. An aggregates grain size distribution spindle for bituminous surfacing material has been established. It goes in the setting of a definition of the very local specifications that can really take into account the specificity of the local materials existing in Senegal. By definition a grain-size spindle for aggregates is constituted by the lower and overhead envelopes of a certain number of curves of material mixtures that gave satisfaction in any region. All spindles are built following the same model; that is to say while looking for the envelopes of the maximum of the curves of the mixture. So the definition of a spindle is of an extreme importance because the observations on the limits of those showed here that:
- Clearing the low bottom limit in the zone of the coarse elements can eliminates the manoeuvrability for the in situ setting and in the zone of the fines, increases the permeability.
- If, on the contrary clearing the overhead limit in the zone of the coarse grains can increases the manoeuvrability but also decreases the stability that is to say the resistance to deformation under loads or traffic. While clearing this curve in the zone of the fine grains, one decreases the richness of binding and it is necessary to compensate this deficit by a growth of dosage while binding.
So a study of composition has been started and this in the worry to work on an optimal formula. The choice of an intermediate formula in the spindle justifies itself by the fact that the previous works in Senegal have reveal that the best performance was gotten with this curve. It could justify itself by a better distribution of the different size fractions. The different formulas are summarized in the Table 5. The particle size data processing permitted us to prepare two types of spindles (Figure 1 and Figure 2).
Figure 1. Spindle of reference for Asphalt 0/16
Figure 2. Spindle of reference for Bituminous concrete 0/8
The comparison of these spindles in relation to the corresponding ones (AASHOO, LCPC and ACE) watch distinctly that the Senegalese formulas enter with difficulty in the other spindles seen the granular class specificity provided by the quarry owners. Local spindles come closer more the LCPC spindles a lot, french standards habitually acted as reference in Senegal. Finally, we will keep that the asphalt 40/50 gives the best performance so much in Marshall test that in Duriez test. It is to bind to the Senegalese climate that is of semi-humid tropical type.
Table 5. Optimal formula for Asphalt and bituminous concrete
Characteristics | Asphalt | Bituminous concrete | |||||||||
Basalt | Silexite | Basalt | Silexite | ||||||||
Composition (%) | 0/3 | 25 | 20 | - | - | ||||||
8/16 | 35 | 30 | 48 | 48 | |||||||
3/8 | 32 | 28 | 40 | 37 | |||||||
Limestone’s filler | 8 | 5 | 6 | 7 | |||||||
Sand | - | 7 | 6 | 8 | |||||||
Specific surface (m^{2}/kg) | 12.88 | 10.73 | 11.78 | 12.86 | |||||||
Module of richness | 3.5 | 3.75 | 4 | 3.5 | 3.75 | 3.5 | 3.75 | 4 | 3.5 | 3.7 | |
Dosage of binding (%) | 5.2 | 5.82 | 6.43 | 5.75 | 6.16 | 5.28 | 5.66 | 6.03 | 5.87 | 6.2 | |
3.3. Modulus of Elasticity and Interrelationships
The compressive strength values for the bituminous concretes of basalt vary between 40 and 60 bars and for the silexite between 30 and 44 bars (Figure 3). Studies of interrelationships done show the difference existing since then between the former values of the utilized modulus of elasticity in Senegal distinctly. The relation found (E_{dyn.} = 436,74.Rc - 9670,6) seems to be enough defer. It expresses a result that permits to have new information concerning the approach of the utilized elastic parameter for the design of the bituminous surface in Senegal (Figure 4). While considering that the bituminous concrete of basalt and silexite develop compressive strengths that turn between 40 and 57 bars, the corresponding modulus turn between 7000 and 14000 bars. The value of 50 bars (that corresponds of a material of good performance) generally allowed in Senegal, as Rc of reference, establishes an estimated modulus of about 12000 bars. These is very distinctly at the present time of the values of 20000, 35000 and 50000 bars, allowed in Senegal, outside of all other information.
Figure 3. Relation between R_{c} and R_{t} for the bituminous mixes
Figure 4. Relation between the dynamic elastic modulus and the simple compressive strength
4. METHODOLOGICAL APPROACHES IN THE CHARACTERIZATION OF SUBGRADE
The parameters kept for the classification of soils arrange themselves in three categories:
- The parameters of nature,
- The parameters of mechanical behaviour;
- The parameters of state.
It is necessary to have a good foundation so that the pavement must be placed in good conditions (CEBTP, 1984). The value to carry on is the CBR of the 30 cm superior of the subgrade. The thickness of soil, processed to define the bearing capacity of the subgrade is justified by the climatic conditions that are those of the hot countries in which the problems of frost don't exist. The attenuation of the surface stresses is sufficient considering the thickness of the pavement so that the settlement of the subgrade is thus avoided. The CBR is determined according to the conditions of density and most unfavourable moisture content undergone long-term by the subgrade. There is place to distinguish, from that point of view, for what concerns the tropical countries three big major climatic categories and three big types of soils.
- Desert and Sub-Saharan Zone with very weak rainfall (<300 mm per year). Soils are there fine and permeable rarely saturated; the natural moisture content is there the most often lower of the one of the optimum modified Proctor (OPM).
- Tropical Zone with dry season well labelled (> 300 mm per year). It is the zone of the savannas in which the natural moisture content exceeds of some points in humid season, the optimum Proctor modified (OPM).
- Guinean Zone of very strong rainfall (> 1 m per year). It is the forest zone in which the precipitations yearly excess 4.2 m. soils remain moistened a big part of the year. The moisture content is very distinctly overhead of the optimum Proctor modified. Soils are there thin and little permeable.
Five classes of soils are kept in the different classifications based on the CBR indication. One distinguishes according to the CEBTP (1984), the following classes (Table 6). It is well sensible, the realization of the pavements on problematic soils (S_{1} class) that poses the major inconvenience. The swelling terrain has a very particular behaviour. It agrees to treat them according to methods resulting from specific studies. It will always be necessary, anyway, to look for to have the best soil of subgrade possible. One will have interest to select the material, in order to have at the head of embankment good soils on at least a thick meter. The bad quality of soils is generally due to excessive moisture content. For the design of the pavement structures, the long-term quality performance of the subgrade is determined from the couple PST-Subgrade (PST: upper part of embankment). One distinguishes 4 classes of quality of the subgrade defined by valuable beaches of reversible elastic modulus (Table 7). The problems are less important for the classes S_{3} to S_{5}. The methodology setting up currently in Senegal is rather turned toward the soils of platform of difficult behaviours (swelling, withdrawal, fissuring, settling) (Chart 1).
Table 6. Bearing capacity classes of subgrade (CEBTP, 1984)
Classes | S_{1} | S_{2} | S_{3} | S_{4} | S_{5} |
CBR (%) | < 5 | 5 - 10 | 10 - 15 | 15 - 30 | >30 |
Table 7. Subgrade classes according to the elastic modulus (LCPC, 1992)
Elastic modulus (Mpa) | 20 | 50 | 120 | 200 | |
Subgrade classes | PF_{1} | PF_{2} | PF_{3} | PF_{4} | |
Chart 1. Methodology of characterization of subgrade’s soil
5. RESULTS ON LATERITE-CEMENT
Among the objectives aimed by this work, face in good place the determination of the Young's modulus of gravel lateritic materials improved by cement and of their tensile and compression strengths expressed at 7, 28 and 90 days of cure (sometimes at 365 days). These different laterites have a maximal diameter understood between 25 and 40 mm and a percentage of fines ( < 80 µm) lower to 35%, with however a middle plasticity (Ip </= 22%). Besides the increase of the percentage of fines after compaction is the order of 2% for the set of the materials. The laterite is mixed with 2, 2.5 and 3% of cement. The utilized cement is of type CEM II or CPA 325. A stage important of the studies of the laterite-cement mix is its formulation. This one must succeed to the determination of dosage made of cement permitting to reach the sought-after resistance level. The only retained criterion is the CBR to conform itself to the usually taken arrangements (CBR ≥ 160% for the laterite-cement mixtures). With regard to the determination of the optimal dosage made of cement, the CBR test has been preferred to the simple compression test, because by definition, the optimal dosage made of cement is the one that permits to get on mixture prepared in the laboratory a CBR at least equal to 160%. The choice of a CBR indication at least equal to 160% for the laterite-cement mixes are based on the fact that a base layer must have after its setting a CBR at least equal to 80% (REMILLION, 1952). The mixtures being often achieved in conditions better controlled in the laboratory that at the field, it agrees therefore to affect the results gotten in the laboratory of a margin of safety. While taking 2 for this coefficient, one hopes to get in situ a CBR of 80% (LIAUTAUD, 1975). After formulation, the tests for the mechanical performance determination have been done. The successive stress/strain curve has been treated in view of the determination of the elastic modulus. Besides, the measure of the tensile stresses of the laterite-cement constitutes complementary information in this sense that it is processed for rational design of the treated layer. In this study, the utilized method consists to take the moisture content corresponding of optimum Proctor modified (OPM) to conform itself to the in situ conditions of compaction. In this case, the moisture content to adopt varies according to the laterites; what represents some differences more or less important of a quarry owner to the other.
5.1. Interrelationships
The analysis of the interrelationship rights shows that the modulus doesn't evolve in a proportional manner with the compressive strength and the age with notably of the weaker slopes at the end of 90 days. It should give coefficients of correspondence at 90 days more important for the compressive strengths than for the modulus. Otherwise, the registered results permitted us to pull the E_{dyn.} relation according to Rc. The interrelationships between modules and resistances are given on Figures 5 and Figure 6. The evolution of the dynamic modulus according to the resistance and the age is not quite linear (Figures 7 and Figure 8). Slopes that regress at the end of 90 days materialize it. Thus, one should have coefficients of correspondence of 90 days weaker for the modulus than the tensile strengths. The E_{dyn.} relation according to R_{tb} [E_{dyn. }= 2925.6xR_{tb} + 3396.9] is well substantial for tensile strengths of the order of 1 to 2 bars. We established some relations between the mechanical strengths. Figures 9 and 10 represent the evolution of the compressive strength according to the tensile stress at the different ages of cure. According to these interrelationships, the ratio between R_{tb} and R_{c} is around 0.1, or 10%.
Figure 5. Relation E_{dyn}. = K.R_{c}
Figure 6. Correlation E_{dyn.} = K.R_{c}
Figure 7. Evolution of E_{dyn.} with R_{tb} and the age
Figure 8. Evolution of E_{dyn.} with R_{c} and the age
Figure 9. Relation R_{tb} = K.R_{c}
Figure 10. Correlation R_{tb} = K.R_{c}
5.2. Coefficient of Correspondence
The coefficients have been proposed while regrouping the set of the measures made at the periods of cure considered. The value of the coefficients for the different laterites meets in the fashions of the histograms. However the affinities between the gravel and binder is own for every gravel lateritic material.
5.2.1. Coefficient between Mechanical Strength
The different coefficient distributions between mechanical strengths are represented on Figures 11 and 12, and Table 8. The coefficients of correspondence, that it is for the tensile and the compressive strength, distribute themselves better in the intervals ]1.24-1.30] and ]1.46-1.52] with equal to middle reports 1.27 between 28 and 7 days and 149 between 90 and 7 days. So one has:
Table 8. Coefficient of correspondence
Rc_{28} = 1.27xRc_{7} | Rc_{90} = 1.49xRc_{7} |
Rt_{28} = 1.27xRt_{7} | Rt_{90} = 1.49xRt_{7} |
Figure 11. Distribution of coefficients Rc_{28}/Rc_{7 }et Rt_{28}/Rt_{7}
Fig. 12. Distribution of coefficients Rc_{90}/Rc_{7} et Rt_{90}/Rt_{7}
5.2.2. COEFFICIENT BETWEEN MODULUS AT DIFFERENT AGE
The results are represented on the Figure 13 and Table 9. It shows that the coefficients of correspondence E_{28}/E_{7} and E_{90}/E_{7} distribute themselves better in the respective intervals ]1.14 - 1.20] and ]1.32 - 1.38] with on average shown in the table 9:
Table 9. Coefficient between modulus at different age
E_{28} = 1.17xE_{7} | E_{90} = 1.35xE_{7} |
Table 10 sums up the results and compares them with those proposed by AUTRET (1983) for gravel lateritic soils treaties with 3.5% of cement and with the values proposed by the directive SETRA/LCPC of 1994 for a gravel-cement and even utilized by some local offices. This comparison is founded by the LCPC (2001) that finds that the coefficients of correspondence are independent of the percentage of binder of the mixture. In relation to a gravel-cement, one notes that the gains of resistance are weaker for lateritic gravel-cement. Otherwise, the results confirm the results proposed by Autret.
Table 10. Comparison between correspondence coefficients
R_{c28}/R_{c7} | Rc_{90}/Rc_{7} | E_{28}/E_{7} | E_{90}/E_{7} | ||
This study | Laterite-cement | 1.27 | 1.49 | 1.17 | 1.35 |
Autret | 1.27 | 1.46 | No value | ||
SETRA/LCPC | Gravel-cement | 1.75 | 2.38 | ||
Figure 13. Distribution of coefficients E_{28}/E_{7} et E_{90}/E_{7}
5.2.3. Comments on Test Results
The experimental tests have been made in order to better characterize the laterite-cement mixes and especially to verify, for the mixtures having a CBR of 160%, the traditionally allowed values [for the elastic modulus (15000, 23000 and very often 50000 bars) and the tensile strength (9 bars)] up to here utilized in the pavement design in Senegal. It will have shown that the experimental values are extensively lower to those that have been very often used. Indeed, one notes that for the best mixtures, the indirect tensile strength is about of 2 bars at 90 days of cure, either by the relation R_{f }= 1.6x R_{tb} a resistance of 3.2 bars very lower than 9 bars. Besides, the dynamic modulus means at 90 days are of 9591 bars, value that doesn't attain 15000 bars, even below 23000 and 50000 bars.
5.2.4. Application
It will be in application about valuing the influence of the modulus of the laterite-cement in the Pavement Design Code Ecoroute^{®} or Alize III^{®} of the LCPC (France). Figure 14 shows an example of results with these DOS codes of calculations. Thus, the modules of 23000, 15000 and 9500 bars will be used in our different hypotheses.
Figure 14. An example of results of a simulation with Alize III^{®} of the LCPC
5.2.4.1. SECTION ROAD SEO-DIOURBEL
It'sa reinforced road maintenance project on a linear of about 35 km (FALL, 2002). The object of the road design consists to put a base layer in laterite-cement and a surfacing made of bituminous concrete, the former pavement being considered like the new road foundation. The pavement is large of 7 m with shoulders of 1.5 m. The traffic is of T_{4} type with N = 4.3´10^{6} axles of 13 tons. The Young's modulus of the platform is deducted of the relation E = 50.CBR (CEBTP, 1982). The values of modulus of the old structure have been determined from the measures of deflection. The three values of modules of the new reinforced subbase follows will be used so as to follow their influence on its thickness:
- 1^{st} case: E = 9500 bars
- 2^{nd} case: E = 15000 bars
- 3^{rd} case: E = 23000 bars
Figure 15. Evolution of σ_{z adm. }et de ε_{z adm. }at the top of the subgrade on section road Séo-Diourbel
The module of the surfacing is taken equal to 13000 bars at 30°C. Its Poisson’s coefficient is taken also equal to n = 0.35, equal to 0.25 for the other layers. The life span is fixed at 15 years. The vertical stress and admissible deformation at the top of the subgrade presents the following evolution according to the PK (Figure 15). The thickness of the bituminous surfacing is fixed at 5 cm. The thickness of determined in the three cases and are exposed in the Figure 16. One notes once again that the thickness to foresee is distinctly more important in the hypothesis of E = 9500 bars in comparison with E = 15000 bars or E = 23000 bars for the laterite-cement.
Figure 16. Evolution of the reinforced base thickness in the 3 cases
5.2.4.2 Comparison with the Previous Results and Technical Choices Made
The results of the study are compared here with other technical choices on the section road from the PK 15 to the PK 17.5. The hypotheses for the different technical choices are summarized in the Table 11. The comparison is summarized in the Table 12. Table 13 compares the costs of implementation for the different technical choices. One notes that the costs of execution of our technical choice and the one of the choice II are nearly identical. The difference is of 0.84%, therefore weak. For these two technical choices the costs increase otherwise, of about 23% in comparison with the definitive technical. It is justify respectively by the use of the modules of 35000 bars and 15000 bars for the bitumen surface and the base layer made of laterite-cement. In the setting of this work the values of modules of 13000 bars and 9500 bars are assigned respectively to the bituminous surfacing and to the base layer made of laterite-cement. In summary, the use of elevated modules decreases the thickness considerably and correlatively the costs of execution in a project.
Table 11. The different technical choices
Technical choices of the Project | This study | ||
Surface modulus (bars) | 35000 | 35000 | 13000 |
Base modulus (bars) | 15000 | 32xCBR | 9500 |
Subgrade modulus (bars) | 50xCBR | 50xCBR | |
Table 12. Comparison with the previous technical choices
Definitive technical choice of the Project (I) | |||
From Pk 15 + 000 to Pk 17 + 500 | Base | Sub-base | Surfacing |
15 cm laterite-cement | 15 cm laterite | 5 cm asphalt | |
Definitive technical choice of the Project (II) | |||
From Pk 15 + 000 to Pk 17 + 500 |
Base | Sub-base | Surfacing |
Only one layer over of the former pavement (45 cm of raw laterite) |
5 cm asphalt | ||
This study | |||
From Pk 15 + 000 to Pk 17 + 500 |
Base | Sub-base | Surfacing |
Only one layer over of the former pavement (28 cm of raw laterite) |
5 cm bituminous concrete |
Table 13. Comparison of the execution costs for the different technical choices
Designation | Unit | Quantity | Unit price (F. CFA) | Total price (F. CFA) | |
Choice (I) | Total supplying in laterite | m^{3} | 10500 | 6 400 | 67 720 000 |
Total supplying in cement | T | 187.5 | 76 000 | 14 250 000 | |
Total | 81 450 000 | ||||
choice (II) | Total supplying in laterite | m^{3} | 15750 | 6 400 | 100 800 000 |
This study | Total supplying in laterite | m^{3} | 9800 | 6 400 | 62 720 000 |
Total supplying in cement | T | 490 | 76 000 | 37 240 000 | |
Total | 99 960 000 | ||||
6400 et 76000 F CFA: price kept by the project [1 US Dollar ( $ ) = 700 F CFA] |
6. CONCLUSION
The interrelationships permitted to appreciate the values of modules in relation to the compressive and tensile strengths. Thus, one will keep that the elevated or over-valued different parameter values studied and defined for the laterite-cement especially corresponds to stabilization. The premature deformation can be explained by one under-estimate design of the reinforced roads for which the modulus of the laterite-cement was supposed equal or superior to 15000 or 23000 bars (or 50000 bars). The overestimate of the modulus entails some weak thickness of pavement, therefore one under-estimate the road design. Thus, the choice of the module of the laterite improved by cement and of its resistance in bending is determinant in the application of the analytic method of road structures design; it puts the necessity to define them in the best way in order to avoid a bad design and to cause the anticipated lengths of road service. The works exposed in this article simply show the difficulties that the actors of the construction meet in Senegal. The non-existence of norms as well as serious specifications for the road design permit each one the use without no reserves methods and techniques of no control.
7. ACKNOWLEDGEMENTS
The authors hold to thank the CEREEQ (Experimental Centre of Research and Studies for the Equipment-Ministry of the Equipment of Senegal) to have put again our disposition it extraordinary database. Our acknowledgments also address to the GIC’s Research Department (Design Agency) that wanted to really put our disposition the confidential information of roadwork. The JEAN LEFEBVRE-Senegal s.a. assured at the same time as the laboratories of the CEREEQ, and also the University of Dakar the realization of the geotechnical tests. The credits-research has been financed entirely by the JEAN LEFEBVRE-Senegal s.a.
8. REFERENCES
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