# Pavement dimensioning with and on lateritic materials of the Mbu–Baforchu area

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## Abstract

The present study was conducted on lateritic sub-grade soils with the pavement structure built using lateritic materials. The objective of this work was to characterize the lateritic materials and obtain a correlation between the modulus of elasticity (E_{dyn}) and the Californian bearing ratio (CBR) around the Mbu–Baforchu area in a bid to dimension a second access highway to the city of Bamenda. Identification tests (water content, particle size analysis, Atterberg limits) and mechanical characteristics tests (Modified Proctor, CBR and simple compression) were carried out on soil samples taken from the field. The CBR results were variable with values between 32 and 49 for burrow materials, while those for sub-grade vary between 6.5 and 14.4. A regression equation between the E_{dyn} and CBR for the burrow material gave E_{dyn} = 155.8exp (0.0541CBR) with a regression coefficient of 0.9599 while that for the sub-grade material was E_{dyn} = 69.064exp (0.0706CBR) with a regression coefficient of 0.9295. The burrow and sub-grade soils fall within the S3 and S5 soil classes respectively. The HRB classification pits the burrow materials in the A-2 class with a group indices varying between 0 and 6, which describes them as a clayey loamy soils with (compressible nodular silty sands), while the sub-grade soils falls in the A-7-5 class and having variable group indices (12–20), thereby characterizing them as inorganic clays of high plasticity. The pavement structure designed for consists of a bituminous cover of 5 cm, a base course of 20 cm and a sub-base course of 20 cm. The pavement structure can carry a traffic loading of up to 3000 vehicles per day, inducing stresses and deflections within the pavement structure which are lower than their required permissible values. With ε_{t }= − 14.5 μdef, ε_{t, perm }= 62.8 μdef for the riding surface; σ_{t} = − 0.118 MPa with σ_{t, perm} = 0.427 MPa representing the permissible value for the base layer and ε_{z} = 103.8 μdef, ε_{z, perm} = 487.3 μdef for the sub-base layer; which reassures us that the pavement structure is durable.

## Keywords

Laterite Identification tests California bearing ratio Modulus of elasticity Pavement Regression equation Stresses and deflections## 1 Introduction

The road network can be taken as an indicator of development of any society since it facilitates the movement of goods and services, therefore having a direct impact on economic growth. For developing countries the major challenge is to provide such a facility at an affordable cost as well as meeting the maintenance exigencies of such an infrastructure. So far in Francophone West Africa, the lifespan of most newly constructed roads ranges from 15 to 20 years. Therefore, the choice of the design parameters is very important at the onset of the design process. Also control during the construction of the pavement layers is an essential part of the construction process performed to ensure that the final product meets design specifications as well as in-service performance of the pavement [2]. The pavement dimensioning procedure can be effected with the CEBTP [4] approach or using softwares such as Ecoroute and and Alizé, which compares the pavement material characteristics to the traffic demands. Consequently obtaining these characteristics have been the subject of debate among various stakeholders. The objective of this work is to characterize the lateritic materials and obtain a correlation between the modulus of elasticity and the Californian bearing ratio around the Mbu–Baforchu area in a bid to dimension a second access highway to the city of Bamenda.

## 2 Geotechnical properties

Average monthly precipitation and temperature of the Santa district.

*Source*: Regional delegation of Northwest Transportation in Amawa et al. [1]

Month | January | February | March | April | May | June | July | August | September | October | November | December |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Rainfall (mm) | 10 | 20 | 90 | 21 | 192 | 310 | 402 | 440 | 415 | 230 | 17 | 50 |

Temperature (°C) | 22.1 | 22.7 | 23.0 | 22.6 | 21.8 | 20.9 | 20.1 | 20.1 | 20.5 | 20.8 | 21.5 | 21.7 |

## 3 Materials and methods

### 3.1 Field and laboratory work

Remolded samples were collected from burrow pits as well as from the sub-grade. Three of the burrow pits were located close to the road, while subgrade materials were collected along the road stretch. Seven (07) representative samples were taken from the burrow pits while nine (09) samples were collected from the subgrade over a distance of 10 km each. These were packaged in plastic bags of approximately 40 kg each and transported by a pick-up vehicle for the purpose of determining geotechnical characteristics in the laboratory. The laboratory analysis carried out were particle size analysis done in accordance with the NFP 94-056 [15]; the Atterberg limits done in accordance with the NFP 94-051 [14] and mechanical characteristics. The mechanical characteristics tests consists of the modified Proctor test carried out in accordance with the NFP 94-093 [16], CBR test carried out in accordance with the NFP 94 078 [13] and finally simple compression test. The compression test was performed on the CBR equipment with the specimen sandwiched between two metal discs of similar circumference. The plunger transmits a vertical load through a steel ball onto the top disc and the specimen is sheared along the vertical axis at the same rate of shearing as in the CBR testing. The static elastic modulus obtained allows us to find the modulus elasticity (Edyn). This parameter is calculated by the expression E_{dyn} = 3E_{stat}, with E_{stat} = R × L/ΔL where E_{stat} is the static modulus of elasticity, R the compressive strength of the material, ΔL the variation of the specimen length.

### 3.2 CEBTP method for tropical countries

CBR values as a function of subgrade soil classes

Soil classes | CBR values |
---|---|

S1 | CBR < 5 |

S2 | 5 < CBR < 10 |

S3 | 10 < CBR < 15 |

S4 | 15 < CBR < 30 |

S5 | CBR > 30 |

The different classes of traffic (CEBTP, 1984)

Equivalent number of trucks | Traffic classes | Equivalent number of vehicles per day |
---|---|---|

< 5 × 10 | T1 | < 300 |

From 5 × 10 | T2 | 300–1000 |

From 1.5 × 10 | T3 | 1000–3000 |

From 4 × 10 | T4 | 3000–6000 |

From 10 | T5 | 6000–12,000 |

### 3.3 French pavement design method: use of Alizée-LCPC software

The Alizé software (also called ALIZE-LCPC) was developed in 1965 by LCPC and SETRA. This was put in place to facilitate as much as possible the implementation of the rational design method. This software enables the determination of stresses resulting from various traffic loadings in the different pavement layers as well as the deflection on the riding course, in principle it makes use of the Burmister model. The various pavement properties enables the software to provide permissible parameters as well as determines the stresses and deflections of the structure thanks to the theoretical model chosen. The permissible stresses and deflections were obtained from the Alize software by inputting the results of the laboratory tests carried out, the traffic loadings, risk value involved and observational data from similar pavements.

_{6}: strain due to one million loads, E: Elasticity at a temperature of 10 °C, NE: Number of equivalent axles = 13 T, b: slope of the fatigue line, S

_{h}: standard deviation on the thickness of the layer, K

_{C}: Calibration coefficient, K

_{S}: Coefficient taking into account the heterogeneity of the bearing pressure of the support, r: risk, Kr: Risk coefficient, C: Coefficient linking the variation of deflection to the variation of the roadway, δ: Standard deviation thickness/fatigue.

Parameters used to determine the allowable deflection of bituminous materials

ε (µdéf) | E (MPa) | − 1/b | S | S | K | r (%) | K | |
---|---|---|---|---|---|---|---|---|

Bituminous materials | 100 | 7200 | 5 | 1 | 0.25 | 1.1 | 10 | 1 |

Parameters used for the determination of the permissible stress of stabilized materials

σ | −1/b | S | S | K | K | K | |
---|---|---|---|---|---|---|---|

Stabilized materials | 0.75 | 15 | 0.03 | 1 | 1.4 | 1 | 1 |

For medium and high traffic roads (T > T3): A = 0.012.

For low traffic roads (T ≤ T3): A = 0.016.

### 3.4 Presentation of the results

^{3}, with the optimal water contents between 13.1 and 19%. The results of the CBR shear tests moulded at 95% Modified Proctor gave CBR values between 32 and 49; the elastic modulus (E

_{dyn}) obtained from simple compression tests varies between 927 and 2295 MPa. Meanwhile for the sub-grade materials we obtained dry densities ranging from 14.1 to 18.9 kN/m

^{3}with optimal water contents ranging from 11.7 to 29.7%. The CBR moulded at 95% Modified Proctor ranged between 6.5 and 19, the elastic modulus (E

_{dyn}) obtained from simple compression tests varies between 111 and 249. These results are summarized in Tables 8 and 9.

Identification tests parameters for burrow pit materials

Samples (%) | E1 | E2 | E3 | E4 | E5 | E6 | E7 |
---|---|---|---|---|---|---|---|

Water content ω | 23.3 | 23.5 | 23.3 | 23.0 | 16.8 | 15.2 | 15.1 |

Liquid limit LL | 64.0 | 77.0 | 64.0 | 69.0 | 61.0 | 56.0 | 52.0 |

Plastic limit PL | 39.0 | 56.0 | 39.0 | 47.0 | 41.0 | 38.0 | 37.0 |

Plasticity index PI | 25.0 | 21.0 | 25.0 | 22.0 | 20.0 | 18.0 | 15.0 |

Percentage fines content | 30.0 | 25.0 | 11.0 | 15.0 | 12.0 | 10.0 | 10.0 |

Identification tests parameters for sub-grade materials

Samples (%) | B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 | B9 |
---|---|---|---|---|---|---|---|---|---|

Water content ω | 15.2 | 23.9 | 24.8 | 27.3 | 27.1 | 29.5 | 44.9 | 15.9 | 23.9 |

Liquid limit LL | 66.4 | 78.9 | 64.1 | 65.3 | 70.8 | 62.3 | 64.0 | 54.1 | 56.8 |

Plastic limit PL | 39.1 | 43.5 | 44.1 | 35.2 | 51.6 | 32.6 | 36.4 | 28.5 | 32.3 |

Plasticity index PI | 27.3 | 35.4 | 20.0 | 30.1 | 19.2 | 29.7 | 27.6 | 25.6 | 24.5 |

Percentage fines content | 86.9 | 76.7 | 62.5 | 82.9 | 96.2 | 76.8 | 79.7 | 46.1 | 35.1 |

CBR and the elastic modulus (E_{dyn}) values of burrow material

Samples | E1 | E2 | E3 | E4 | E5 | E6 | E7 |
---|---|---|---|---|---|---|---|

CBR | 32 | 36 | 38 | 40 | 43 | 47 | 49 |

E | 927 | 999 | 1245 | 1299 | 1734 | 1842 | 2295 |

CBR and E_{dyn} Values for sub-grade soils

Samples | B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 | B9 |
---|---|---|---|---|---|---|---|---|---|

CBR | 13.5 | 11.2 | 6.5 | 11.3 | 11.2 | 11.3 | 11.2 | 19 | 14.4 |

E | 186 | 144 | 111 | 156 | 144 | 156 | 144 | 249 | 219 |

### 3.5 Pavement design

The determination of the constituents of the road layer and their characteristics (thickness, Young’s modulus, etc.) must enable the highway to support the traffic loadings within the expected lifespan of the road. This is carried out either empirically or by a more rational method. The empirical approach consists of the CBR method as well as the semi-empirical approach, which takes into account the observation of existing pavements, and sometimes the mechanical behavioral patterns of materials. A more rational method utilizes principles of continuum mechanics and strength of materials.

#### 3.5.1 Material characteristics and traffic

^{6}and 4 × 10

^{6}(depending on the vehicle count ratio) and an average sub-grade CBR of 12.2; we obtain a T3 traffic class and an S3 soil bearing class corresponding to a preliminary pavement structure shown on Table 10. Table 11 gives the choice of pavement materials and the corresponding thicknesses with respect to road traffic demands and sub-grade thickness in accordance with the CEBTP method.

Proposed preliminary pavement structure with pavement material

Pavement layers | Thickness (cm) | Nature of materials |
---|---|---|

Riding surface | 5 | Bituminous concrete |

Base | 20 | Lateritic gravel or natural gravel stabilized with cement |

Sub-base | 20 | Lateritic gravel or natural gravel 0/D |

Choice of pavement materials and corresponding thicknesses with respect to road traffic loadings and subgrade thickness in centimeters.

*Source*: Practical guide for pavement design for tropical countries T.2 BCEOM CEBTP

Trafic T | S | S | S | S | S | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

T | T | T | T | T | T | T | T | T | T | ||

R | Bituminous concrete | 5 | * | 5 | * | 5 | * | 5 | * | 5 | * |

B | Lateritic gravel | 20 | * | 20 | * | 20 | * | 20 | * | 25 | * |

F | Lateritic gravel | 40 | * | 30 | * | 20 | * | 15 | * | 0 | * |

R | Bituminous concrete | 5 | 7 | 5 | 7 | 5 | 7 | 5 | 7 | 5 | * |

B | Lateritic gravel or crushed natural gravel stabilized with cement | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | * |

F | Lateritic gravel or crushed natural gravel 0/D | 45 | 50 | 25 | 30 | 20 | 25 | 15 | 20 | 0 | * |

R | Bituminous concrete | 5 | 7 | 5 | 7 | 5 | 7 | 5 | 7 | 5 | 7 |

B | Crushed aggregate 0/d | 60 | 65 | 45 | 30 | 40 | 45 | 30 | 35 | 20 | 23 |

F | |||||||||||

R | Bituminous concrete | 5 | * | 5 | * | 5 | * | 5 | * | 5 | * |

B | Sandy clay stabilized with cement | 20 | * | 20 | * | 20 | * | 20 | * | 20 | * |

F | Sandy clay | 55 | * | 35 | * | 25 | * | 20 | * | 0 | * |

#### 3.5.2 Determination of the allowable stresses

_{t, perm}= 62.8 μdef; for the base layer (materials stabilized with hydraulic binders), we have the permissible horizontal stress σ

_{t, perm}= 0.427 MPa and for the sub-base layer (lateritic gravel or granular materials) the permissible vertical deformation ε

_{z, perm}= 487.3 μdéf. In the Alizée software, the bending tensile stresses and their corresponding deformations are negative, the vertical displacements are positive and are in the direction of gravity and their positive values are considered. Thus, the values of these design parameters obtained from the Alize simulation for the designed pavement are given in Table 12. From Table 12, we have ε

_{t}= − 4.5 μdef for the surface layer; σ

_{t}= − 0.118 MPa (base layer); ε

_{z}= 103.8μf corresponding to the sub-base layer.

Verification of pavement parameters from Alize software

Level of Calculationono | Epsilon T horizontal | Sigma T horizontal | Epsilon Z Vertical | Sigma Z vertical |
---|---|---|---|---|

Surface (z = 0.000) | ||||

h = 0050 m 0.000 m | − 19.7 X-J | 0084 X-J | − 36.4 Z-J | 0658 Z-R |

E = 7200.0 MPa | ||||

µ = 0350 0.050 m | − 14.5 Y-R | 0162 Y-R | 64.5 Z-R | 0583 Z-R |

Joined (z = 0.050 m) | ||||

h = 0200 m 0.050 m | − 14.5 Y-R | 0085 Y-J | 219.9 Z-R | 0583 Z-R |

E = 2300.0 MPa | ||||

µ = 0250 0.250 m | − 57,1 Y-J | − 0118 Y-R | 75,1 Z-R | 0122 Z-R |

Joined (z = 0,250 m) | ||||

h = 0,20 m 0,250 m | − 57,1 Y-J | − 0048 Y-J | 103,8 Z-R | 0122 Z-R |

E = 1409.0 MPa | ||||

µ = 0350 0,450 m | − 85,0 Y-J | − 0154 Y-J | 93,8 Z-J | 0033 Z-J |

Joined (z = 0,250 m) | ||||

h infinite 0,450 m | − 85,0 Y-J | − 0002 Y-J | 203,8 Z-J | 0033 Z-J |

E = 163,0 MPa | ||||

µ = 0350 |

##### 3.5.2.1 Results interpretation and discussion

The subgrade materials (B1, B2, B3, B4, B5, B6, B7, B8 and B9) were described using the HRB criterion as A-7-5 soils based on their plasticity indices, the fine contents and group indices (19; 20; 12; 20; 16; 20; 19; 14; and 15). The A-7-5 materials are classified as fair to poor materials for roadworks. The Casagrande plasticity chart classifies them as inorganic clays of high plasticity. Meanwhile the lateritic (burrow) materials utilized for the sub-base (E1, E2, E3, E4, E5, E6 and E7), was classified as A-2 based on the HRB criterion with group indices between 0 and 6 which allows this material to fall under excellent to good materials for roadworks. In summary these soils can be described as compressible nodular silty sands.

The results of the CBR tests prepared at 95% Modified Proctor compaction on burrow materials gave indices between 32 and 49, while for the sub-grade soil, the CBR was between 6.5 and 19. These values made it possible to classify the soils within the S5 bearing class for the burrow materials, also class S2 and S3 for sub-grade materials using the Liautaud [12] criterion. Since the CBR of sub-grade soils are all greater than 5, it follows that the sub-grade soils do not need improvement. However to meet certain constructional exigencies the lateritic soils can be improved by mechanical stabilization using basalt gravels as given by Hyoumbi et al. [8]. It is interesting to note that though the study area is found in the Western Highlands of Cameroon, the CBR values obtained within the Mbu Barfochu area are lower than those obtained by Djuickouo [5], who obtained 98 for the lateritic gravels formed on the Maka basalts within Dschang. This low CBR values, could be attributed to the trachytic nature of bedrock, which is low in ferromagnesian elements. Concurrently, the geomorphology characterized by steep slopes within the study area could be the reason for the low level of induration of Mbu–Baforchu lateritic soils. Geotechnical literature is replete with information of correlation of CBR with other soil properties [21], [7], [22], [19], [23], [11] but very few current works give a correlation of CBR and elastic modulus E [18], [20], [3]. Therefore upon using the regression relation obtained between the CBR indices and the elastic modulus, we obtain E = 163 bars (sub-grade material) and E = 1409 bars (burrow material). Using the ALIZEE-LCPC software a simulation was carried out with inputs being the Poisson ratio and layer thickness. The results obtained were ε_{t} = −14.5 μdef, ε_{t, perm} = 62.8 μdef for the surface layer; σ_{t }= − 0.118 MPa with σ_{t, perm} = 0.427 MPa representing the permissible value for the base layer and ε_{z} = 103.8 μdef, ε_{z, perm} = 487.3 μdef for the sub-base layer. From these results, it is evident that the designed pavement structure presents good characteristics since all the calculated values are lower than the permissible values. In other words, the pavement structure will not undergo any structural distress within the design period i.e. (15 years). Though NOUROU-Dine [17] researched on recycled materials, he also obtained similar results where the parameters of the pavement layers were lower than the permissible values; with ε_{t} = 10.8 μdef; σ_{t} = 2.46 bars and ε_{z} = 226.8 μdef while the respective permissible stresses and deflections were ε_{t, perm} = 146.7 μdef; σ_{t, perm} = 4.43 bars and ε_{z, perm} = 544 μdef. The values of the allowable stresses and deflections are presented in the Alizée sheets in “Appendix” section.

##### 3.5.2.2 Comparison between the CEBTP method and the Alizée LCPC software

We note that the CEBTP method is based essentially on the thickness of the sub-grade soil and the nature of the traffic loading in a bid to size the various layers without giving information on use after commissioning. On the other hand, the Alizée software takes into account the mechanical characteristics (modulus of elasticity, Poisson ratio) of burrow materials (laterite and crushed gravel) and sub-grade; then on the nature of the interfaces of the layers. By combining these parameters with those resulting from the CEBTP method (layer thicknesses), the Alizée LCPC software gives the stresses and the deflections that the pavement section may be subjected to with time. However, the most significant limitations of the Alizée software relates to assumptions taken into consideration when inputting the data. The pavement layers and the soil materials are assumed homogeneous, elastic and isotropic. The dynamic elastic moduli of the wearing courses are not clearly defined and it is that which the software assumes which are utilized for design.

## 4 Conclusion

The objective of this work was to characterize the lateritic materials and determine a correlation between the Californian bearing ratio (CBR) with the modulus of elasticity (E_{dyn}) the around the Mbu–Baforchu area in a bid to dimension a second access highway to the city of Bamenda. The geotechnical characteristics of the lateritic subgrade with regards to the HRB criterion is A-7-5 soil with variable group indices between 12 and 20. The A-7-5 materials were classified as fair to poor materials for roadworks. While the burrow material is A-2 with variable, group indices between 0 and 6 and were classified as excellent to good materials for roadworks. The strength characteristics gives maximum dry densities that are between 16 and 17 kN/m^{3} for the burrow material with optimal moisture contents of between 13.1 and 19%. For the sub-grade material, the maximum dry densities are between 14.1 and 18.9 kN/m^{3} and optimal moisture contents between 11.7 and 29.7%. The CBR prepared at 95% Modified Proctor gave indices of 32 and 49 for the burrow materials while the sub-grade material had CBR’s of between 6.5 and 19. Studies of correlations made it possible to evaluate the values of the elastic modulus with respect to the CBR of the lateritic materials. A regression equation between the elastic modulus and CBR for the burrow material gave E_{dyn} = 155.8exp (0.0541CBR) with a regression coefficient of 0.9599 while that for the subgrade material was E_{dyn} = 69.064exp (0.0706CBR) with a regression coefficient of 0.9295. From these it was realized that the relation binding the modulus of elasticity to the CBR is not linear as the empirical relationships generally used in road design; these relationships do not always reflect reality. The pavement structure designed for consists of a bituminous cover of 5 cm, a base course of 20 cm and a sub-base course of 20 cm, which is capable of carrying a traffic loading of up to 3000 vehicles per day. The different simulations carried out with the ALIZE-LCPC software shows us that the choice of the Poisson ratio is as important as that of the modulus of elasticity. These simulations gave us values of the stresses and deflections lower than the permissible values. The values obtained were ε_{t} = − 14.5 μdef, ε_{t, perm} = 62.8 μdef for the riding surface; σ_{t} = − 0.118 MPa with σ_{t, perm} = 0.427 MPa representing the permissible value for the base layer and ε_{z} = 103.8 μdef, ε_{z, perm} = 487.3 μdef for the sub-base layer; which reassures us that the pavement structure is durable. We recommend further research in this area so as to create a database of geotechnical characteristics of lateritic pavement materials at the national and sub-regional levels for a much more thoughtful and rigorous pavement design and management procedure.

## Notes

### Funding

This project was funded personally by the authors.

### Compliance with the ethical standards

### Conflict of interest

The authors declare that there is no conflict of interest.

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