Advances in Civil Engineering

Advances in Civil Engineering / 2020 / Article

Research Article | Open Access

Volume 2020 |Article ID 8877367 |

Zoa Ambassa, Jean Chills Amba, "Assessment of Stiffness and Strength Parameters for the Soft Soil Model of Clays of Cameroon", Advances in Civil Engineering, vol. 2020, Article ID 8877367, 16 pages, 2020.

Assessment of Stiffness and Strength Parameters for the Soft Soil Model of Clays of Cameroon

Academic Editor: Jia-wen Zhou
Received05 May 2020
Revised18 Aug 2020
Accepted31 Aug 2020
Published18 Sep 2020


This paper focuses on the advanced modelling of soft Cameroon clays for the global prediction of the behaviour of geotechnical structures. A comprehensive set of experimental data on Cameroon subsoils from the oedometer and triaxial tests are analyzed in this paper in order to determine the stiffness and strength parameters for the Soft Soil model. It is based on 71 soil samples taken from both sides of the construction sites of several major structures across the territory. At the first approach, the soil samples taken were analyzed in a geotechnical laboratory to obtain physical and mechanical identification parameters specific to each soil type. The results obtained reveal that the analyzed soils are generally compressible clays. In the second phase, the law of behaviour of the Soft Soil model was used to characterize these Cameroon soils. Its parameters were obtained after calibration of the results of the laboratory tests obtained in first approach. The results obtained in this article can be compared to the different models obtained on clays soils around the world. The parameters are of the same order of magnitude as other clays modelled around the world.

1. Introduction

1.1. Interest and Needs of Soils Modeling

In the practice of numerical modelling, not just any law of behaviour can be considered as an acceptable approximation of any real behaviour, even after calibration of the parameters. The soil has a stress-strain relationship that is nonlinear and irreversible from a certain threshold. For numerical modelling to provide a realistic estimate of behaviour, it must use advanced behavioural laws adapted to each type of soil. In the context of this article, we have dealt with several types of compressible soils with different mechanical behaviours. In this paper, an advanced law of behaviour called the Soft Soil model, which describes the behaviour of the compressible soils in a realistic way, will be highlighted. Present, several civil engineering and geotechnical works are under construction in Cameroon. The predictive evaluation of the behaviour (settlements, lift, and stability) of these infrastructures is often carried out by empirical methods or conventional analytical methods. These do not always take into account the realistic behaviour of the material or the overall behaviour of the work and impose simplifying assumptions of behaviour. From these shortcomings in the study of structures, it is important to determine the parameters of advanced soil models that are not currently available in Cameroon in order to effectively predict the behaviour of geotechnical structures considering successive phases of construction. This global approach involves defining a specific constitutive law for each soil type, determining its parameters using classical geotechnical laboratory data and modern numerical technics. The parameters of the advanced Soft Soil model will be determined from 71 soil samples taken from construction sites across Cameroon. These parameters will constitute a national database of exploitable compressible soil parameters that can be used in numerical modelling to predict the overall behaviour of geotechnical structures.

1.2. Literature Review on Compressible Soils

The analysis of the consolidation of clay for the prediction of the foundation settlement of a structure is of particular importance in geotechnics. The first rational approach to this problem, based on the principle of effective stress, was proposed by Terzaghi [1]. After this, an intensive research has been conducted in this area. A logical extension of Terzaghi’s one-dimensional consolidation theory to a 3D situation is due to the complete coupled porous-elastic formulation of Biot [2]. The two theories of Terzaghi and Biot postulate that soil behaviour is linearly elastic. For global problems, most researchers are turning to digital methods. Schiffman and Arya [3], using Terzaghi’s one-dimensional consolidation model (1D), conducted a research using the finite difference method and the finite element method. Desai proposed a nonlinear model for the soil and implemented this model in a finite element computation program to deal with the one-dimensional consolidation problem. Melanie’s model [4], developed at LCPC to represent the behaviour of natural clays by finite element calculations, is an anisotropic elastoplastic model with hardening, which allows the resolution of consolidation problems. It is derived from the modified Cam-Clay model. Soft soils, which are normally consolidated, are known for their very high compressibility [59]. It is obvious that creep is important for problems that show a significant primary settlement: this is the case of road construction, foundations, dikes on compressible soils, or dams where strong primary settlements are followed by creep settlements years later [8, 1012]. In other cases, dams or buildings may initially be based on over-consolidated soils; the primary settlements are then relatively small. In addition to foundation settlement problems, creep plays an important role in slope stability problems. Several natural slopes with a low safety factor often show continuous displacements due to creep under constant mechanical or hydraulic conditions [13, 14]. In recent years, several research studies have been carried out around the world to determine the advanced soil parameters for feeding advanced soils models implanted in geotechnical software for the calculation of geotechnical works in construction or in the process of being monitoring. This is the case with the stiffness and strength parameters for hardening and the Soft Soil model of soft and stiff Bangkok clays investigated by Adachi and Oka and Suched et al. [13, 15]. These authors conducted several series of isotropically consolidated drained and undrained compression tests at the Asian Institute of Technology on soil samples from Bangkok, and then exploited the results of these tests to obtain the advanced parameters of these soils for the advanced calculation of geotechnical works in Bangkok. Nallathamby and Minna [16] modelled and exploited the advanced parameters of soft anisotropic soils for their exploitation in the calculation of the experimental embankment of Murro in Finland. The results were compared with those measured during the test phase of the work. This Murro test embankment was constructed on a 23 m deep deposit of medium sensitive clay near the town of Seinäjoki in Western Finland. The embankment has been monitored for a long time, since it was built in 1993, and it has been subjected to several studies. The almost normally consolidated clay is overlain by a 1.6 m thick overconsolidated dry crust, and the underlying thick clay layer is almost normally consolidated and relatively homogeneous. The groundwater table is estimated to be at 0.8 m below the ground level. Murro clay is highly strain anisotropic and time dependent [16]. Many other studies have been investigated for clays [1719]. A large number of Cc −  (Cc is the compression index, and is the natural water content) correlations have been proposed by researchers for different soft clays around the world, but comparisons of these correlations and reasons for differences between them are rarely reported. The Cc −  relationships of marine soft clays from eight China’s coastal cities have been investigated by Gao and Chen [19]. It is found that the north coast clays have larger slope of the Cc −  relationships (about 0.02) than the south coast clays (about 0.008).

2. Methodology

Generally, the perfectly linear elastic behaviour law with a Mohr–Coulomb- (MC-) type failure criterion is used in geotechnical engineering calculations. This law defines the behaviour of the soil based on 5 parameters: Young’s modulus (E), the angle of friction (φ), the cohesion (c), the dilatancy angle (ψ), and the Poisson ratio (). However, several studies [13, 2023] have shown that this model does not represent the nonlinearity of the actual behaviour of the soil and imposes that the module in loading is the same as that in unloading. In the case of a structure exposed to cyclic loadings, for example, case of foundations of industrial buildings receiving vibrating machinery, wave breaking on a dike, and traffic load, unloading areas play a predominant role in determining its behaviour. This simplification therefore has a consequence in the models for the prediction of the real behaviour of the structure in question. The choice of the realistic behaviour model for this study meets two requirements:(i)On the one hand, that of better representing the behaviour of compressible soils in Cameroon compared to the Mohr–Coulomb model(ii)On the other hand, that of identifying the parameters of the Soft Soil model from the results of triaxial or oedometric tests on the materials selected in several construction sites throughout the national territory

Several studies have shown that the dedicated Soft Soil (SSM) model for the realistic representation of the behaviour of compressible soils is implemented in several calculation codes [24]. It will be highlighted in 71 soil samples taken in the central, south, and Littoral regions of Cameroon. From the classical geotechnical laboratory results on soils, the parameters of this advanced model will be determined according to the relationships linking several geotechnical parameters presented in detail later in this article.

3. Formulation of the Soft Soil Model (SSM)

In this section, we start from the classical formulation of the Soft Soil Creep model (SSCM) to the determination of the parameters of the Soft Soil model. The Soft Soil model makes it possible to take into account the work hardening of the soft clays but not the secondary consolidation; this results in the evolution of the axial strain in an oedometric test as a function of time, after the end of the primary consolidation. This deformation evolves according to the logarithm of time (at least for observable time scales).

3.1. Generalization of the Differential Law for 3D Creep

The 3D model is a generalization of the 1D model. We will adopt the stress invariants for the pressure  = soct and the deviatoric stress . With soct and τoct being the normal octahedral stress and the octahedral shear stress, respectively, these invariants are used to define a new equivalent mean constraint called :where .

Figure 1 shows that the measured stress is the constant on the ellipses in the plane -q. Actually, we have the modified Cam-Clay model ellipses amended by Roscoe and Burland [25]. The soil parameter M represents the slope (of what is called critical state line as shown in Figure 1). Equation (1) is used for the deviatoric stress q:where φcv is the angle of critical friction or constant volume. Using the above definition of q, the equivalent pressure is constant over an ellipse and in the principal stress space. To extend the theory in 1D to the general case in 3D, we will now focus on the case of normal consolidation encountered in an oedometer. This value of M is a practical value calculated by default. Moreover, the finite element calculation code is used for the analysis of geotechnical structures: PLAXIS [24, 26] makes it possible to calculate an approximate value of (coefficient of resting land under normal consolidation conditions), which is the value of M calculated from equation (2). In general, the value of calculated by the program is greater than that calculated by Jacky’s formula . Otherwise, one could enter a value of to calculate the value of M by using Brinkgreve formula developed in the following PLAXIS calculation code [26]:

The load surfaces are ellipses with associated flow (increment of normal deformation at the ellipse) while for rupture, the flow is not associated (that is, why it is necessary to enter the dilatancy angle, possibly zero, which corresponds to the plastic flow at constant volume).

Under these conditions, we have , and from relation (1) we derive the following relations:where and is the generalized preconsolidation pressure, this parameter being proportional to the one-dimensional case. For a known value of , can be computed from σ′, and can also be calculated from .

Instead of the parameters A, B, and C of the one-dimensional model, we will now use the parameters κ and λ, defined by the following relations:where is the same Poisson’s ratio.

3.2. Formulation of Elastic Deformations in 3D

The 1D model can be extended to obtain the 3D model, but until now, this has not been performed for elastic deformations. In order to obtain a 3D model for elastic deformations, the elastic modulus Eur is defined as dependent on the stress [24] by

3.3. Parameters of the Soft Soil Model

As soon as the ultimate limit criterion f (σ′, c, φ) = 0 is reached, the instantaneous plastic strain speed develops in accordance with the flow law with  =  (σ′, ψ); the parameters of plastic flow of the material are as follows: c′ is the effective cohesion, φ′ is the Mohr–Coulomb friction angle, and ψ is the dilatancy angle. For fine and cohesive soils, the dilatancy angle is usually small and can therefore often be taken as zero. The Soft Soil model therefore requires the following hardware constants.(i)Break parameters as in the Mohr–Coulomb modelc: shear strength (kPa)φ: angle of shearing resistance (°)Ψ: angle of dilatance (°)(ii)Basic stiffness parametersλ: modified compression index used in the constitutive “Soft Soil” modelК: modified swelling unloading-reloading index in the constitutive “Soft Soil” model(iii)Advanced parameters: Poisson’s ratio in unloading/loading (by default,  = 0.15 for clay),: the ratio , the coefficient of lateral earth pressure in normally consolidated condition,M: soil parameter representing the slope (so-called critical state line).

3.4. Modified Swelling Index and Modified Compression Index

These parameters can be obtained from an isotropic compression test or an oedometric test. When the logarithm of the stress is plotted against the deformation, the curve can be approximated by two straight lines. The slope of the normal consolidation curve gives the modified compression index λ, and the slope of the discharge curve (or swelling) can be used to calculate the modified swelling index κ. It should be noted that there is a difference between the modified indices κ and λ and the original parameters of the Cam-Clay model, κ and λ. Relationship with the Cam-Clay model parametersand relationship with classic parameters

There is no exact relationship between the isotropic compression indices κ and κ and the one-dimensional swelling index because the ratio of horizontal to vertical stress changes during unidimensional discharge. For the approximation, it is assumed that the case of average stress during the discharge is a case of isotropic stress, that is, to say the horizontal and vertical stresses are equal.

This synthesis on the formulation of the Soft Soil model, an advanced behaviour model implemented in several computation codes, shows that it is a sufficiently simple model to be able to determine its parameters from a classical geotechnical study (triaxial and oedometric tests). In this model, there is no wedging parameter without a physical signification as often found in other models. The determination of its parameters can require optimization techniques. The user must focus on two choices: one is inherent to geotechnics in general, and the other is realistic digital simulation. The determination of the geotechnical parameters to be entered in a calculation code is not different from a choice of “manual” calculation parameters for a compaction calculation, for example. Some of the parameters are different in their expressions but always remain connected to classical geotechnical constants. The models of behaviour developed are distinguished mainly by the type of mechanical problem to be solved on the soil or on structures in soil, by the number and type of parameters that characterize them. The least “current” parameter is presumably the dilatancy. In fact, the choice of the model of behaviour depends on the problem posed, which model of behaviour is to be used for which geotechnical problem? This question is not so simple because there is no “universal” model capable of reproducing the behaviour of any type of the geotechnical work.

4. Mechanical Properties of Cameroon Soils

4.1. Geology Setting of Cameroon

The geological history of Cameroon begins with the Archaean era between 3.5 and 2.5 billion years (Ga) ago. Its different phases of development are illustrated by geological masses formed during successive orogenic cycles. It is characterized by formation of craton and mountain ranges and subsequent extension phases by the splitting of the continental crust. From the south to the north, we have (Figure 2) the following:(1)The Cameroonian southern domain consists of Pan-African metasedimentary units such as the Ntui-Betamba, Yaoundé, and Ayos-Mbalmayo-Benbis units. The layers were plunged onto the Archaean Congo Craton towards the south [27, 28] from this domain, which were affected by four stages of ductile deformation, corresponding to alternating phases of E-W to NW-SE contraction (D1, D3) and N-S to NE-SW extension D2 [27].(2)The Cameroonian central domain, broad area that extends between the fault of the Sanaga to the south and the Tibati-Banyo fault to the north. It consists of Archaean to Palaeoproterozoic high-grade gneisses intruded by widespread Pan-African syntectonic plutonic rocks of high-K calc-alkaline affinities [27]. Major setbacks in this area seem to have guided the implementation of plutonism having an orthogneissification with variable intensity. This area is subjected to an advanced general metamorphism where banking is composed of gneiss and amphibolite.(3)The Cameroonian northern domain is characterized by subordinate 830 Ma old metavolcanic rocks of tholeiitic and alkaline affinities associated with metasediments known as the Poli series. This domain is characterized by three stages of deformation: an early phase D1 is associated to the metamorphism with granulite facies, medium pressure [27]. A phase D2 dated 600–580 Ma is synchronous with an intense migmatization [27] and a granitization associated to a metamorphism with amphibolite facies (600°, 5–7 Kb) and greenschist facies (550°, 5 Kb). And a phase D3 is liable to the dextral setbacks E-W and drive folds N-S to E-W.

4.2. Nature of Investigated Materials

To do this, it was necessary to have on the one hand, enough experience (interesting the geological formations of the country), and on the other hand, results of tests carried out in geotechnical laboratory under perfectly controlled conditions on samples which were intact, taken from the sites of structures under construction. Data collection took place over a period of almost four years. It involves some 60 geotechnical studies (on seventy-one sites) of civil engineering and geotechnical works carried out by laboratories in various regions of the territory. The analyzed samples come mainly from the central, south, and Littoral Cameroon regions. We do not claim to have obtained an exhaustive sampling or quite representative of all types of soils likely to be encountered in Cameroon. However, the results obtained on residual soils (lateritic in the central and southern regions and alluvial in the Littoral region) indicate certain trends already allowing us to determine through the advanced modelling of soils, good parameters of the Soft Soil model. It should be noted that lateritic soils cover about 70% of the Cameroonian territory [28].

For example, Yaoundé, Cameroon’s capital, is made up of typical ferralitic soils at three levels, namely [28](i)A loose upper formation dominated by topsoil.(ii)A ferruginous, nodular, armored intermediate layer consisting of iron hydroxide and kaolinite clay accumulations from hydrolysis of rock minerals.(iii)At the lower horizon, the geological formations encountered are the grenatiferes gneiss with micas or biotite only, whose structure of the mother rock (Gneiss) is conserved in depth and more altered towards the surface. Minerals such as quartz, kaolinites, goethite, and hematite are encountered.

All these formations belong to the old metamorphic base. Each time depending on the type and scale of the project to be carried out, the cored holes, and reconnaissance wells on construction sites have revealed the pedological overview of the soils of the central Cameroon region. The different terrain profiles generally encountered reveal not only the possible combinations of the sequence of soil layers in the city of Yaoundé but also the nature of each layer. So, we find in the extent of the city: clays and lateritic reddish bass. Lateritic cuirasses are observed as well.

In the Littoral region, the sedimentary rocks form low lying and gently undulating hills along the western side of the Dibamba River. The strata have experienced tropical weathering, which has resulted in the development of a lateritic residual soil profile. This type of rock mass tropical leads to weathering profiles as presented by Fookes [29] and shown in Figure 3. The material viewed at site comprises weathering Grade 6, as seen in the trial pit photograph from site, with possibly weathering Grade 5 material encountered towards the base of deeper rotary boreholes. Below this material, the stratum may then transition more rapidly to weathered parent rock material. This transition was not identified in the deepest exploratory boreholes that went 30 m below the ground level. In the exploratory holes observed, there was no clear evidence for overlying transported material, so material may be weathered in situ. The following section presents the nature of the materials investigated in this paper.

The samples were collected “undisturbed” using a PVC 100 mm diameter corer and 300 mm in length Figure 4. The shear box used was 60 mm in width and 25 mm in height, which is recognizable as the small shear box apparatus to the British Standards Institution [3032]. These investigations were conducted under perfectly controlled conditions. The soils of the central, southern (Figure 5), and Littoral regions (Figure 3) of Cameroon are represented:(i)Either reddish lateritic clays (central and southern regions)(ii)Either sandy clays or clay sand from Douala (Littoral region)

The ranges of variation of the characteristics of these soils are defined in Table 1. Figure 5 presents test pits, the soils samples, triaxial shear cell, and oedometric cell used for this paper.

Parameters of laboratory testRange of variation

Plasticity index (P. I)12–41.1
Liquid limit (LL)26–83.6
Natural water content ()8.1–56
Soil unit weight (γ) (kN/m3)15.1–23.4
Submerged unit weight (γ′) (kN/m3)6.84–13.6
Shear strength (c) (kPa)0.7–159
Angle of shearing resistance (φ) (°)9.9–50.1
Angle of dilatance (Ψ) (°)0.0–20.1
Coefficient of permeability (k) (m/s)2.03 × 10−11–2.29 × 10−4
Coefficient of consolidation in the vertical direction () (m2/s)1.82 × 10−8–3.79 × 10−3
Void ratio (e)0.36–1.44
Initial void ratio (e0)0.28–1.64
Preconsolidation pressure () (kPa)8–140
Oedometric modulus (Eoed) (MPa)1.9–15.1
Young’s modulus (E) (MPa)1.36–9.41
Compression index (Cc) 0.05–0.42
Swelling index ()0.0–0.03

4.3. Identifications Parameters and Compressibility of Cameroon Soils

Tables 2 and 3 summarize the results of the identification, compressibility, and shear strength tests carried out on soil samples taken from 71 sites of projects under construction in Cameroon. According to the results of oedometric compressibility, soils tested in the laboratory are generally compressible. The statistical significance of these laboratory data is presented in Tables 2 and 3.

Soil samplesPhysical identification parameters
Type of soilϒd (kN/m3)ϒs (kN/m3)ϒh (kN/m3)ϒsat (kN/m3)ϒ′ (kN/m3)e

1Nodulated reddish clay16.226.919.920.1810.120.67
2Nodulated reddish clay16.62720.320.4510.430.63
3Nodulated reddish clay16.82620.220.3410.320.55
4Nodulated reddish clay1626.319.719.929.880.65
5Yellowish clay1726.920.620.6810.70.58
6Yellowish lateritic gravel17.927.221.1721.3211.320.52
7Yellowish clay17.126.920.2620.7410.760.57
8Brown clay16.726.720.220.4510.440.6
9Yellowish clay1827.220.8821.3811.390.51
10Altered rock in reddish lateritic clay13.327.616.518.488.51.07
11Altered rock in yellowish lateritic clay13.727.116.418.648.640.98
12Reddish lateritic clay12.627.215.117.977.961.16
13Reddish lateritic clay13.426.916.518.428.411.01
14Altered rock in reddish lateritic clay14.427.716.919.29.270.91
15Altered rock in Motley clay15.226.61719.499.490.75
16Altered rock in reddish clay152716.219.449.440.8
17Altered rock in Motley clay15.526.316.919.619.590.7
18Nodulated reddish clay17.12720.620.7710.760.58
19Nodulated reddish clay17.726.520.721.02110.5
20Nodulated reddish clay15.92719.920.01100.7
21Nodulated reddish clay16.927.520.620.7510.740.63
22Nodulated reddish clay1626.919.720.0510.060.68
23Nodulated reddish clay16.427.120.220.3510.360.65
24Nodulated reddish clay16.42820.520.5410.530.71
25Nodulated reddish clay1626.519.919.969.940.66
26Nodulated reddish clay16.726.520.220.410.380.59
27Yellowish clay12.326.816.317.717.671.19
28Motley clay12.426.816.217.777.781.16
29Reddish lateritic clay14.226.917.718.928.940.89
30Altered breastplate in reddish clay14.526.917.519.119.090.86
31Altered breastplate in Motley clay13.126.916.418.238.241.05
32Altered breastplate in reddish clay14.626.81819.159.180.83
33Altered breastplate in reddish clay13.12616.618.068.040.99
34Altered breastplate in yellowish clay12.526.116.117.717.741.08
35Reddish lateritic clay13.22616.
36Reddish clay gravel20.828.523.223.513.50.37
37Reddish clay gravel20.42822.923.1113.140.37
38Reddish clay gravel20.128.322.92312.980.41
39Reddish clay gravel20.928.523.423.5713.60.36
40Reddish clay gravel20.228.822.923.1913.150.43
41Altered rock in Motley clay13.226.415.618.28.240.99
42Altered rock in reddish clay13.12616.418.068.040.99
43Altered rock in reddish lateritic clay13.726.51718.538.510.94
44Altered rock in reddish lateritic clay13.526.916.118.488.451
45Motley clay13.926.416.418.638.630.9
46Yellowish sandy clay14.326.516.818.98.920.85
47Yellowish sandy clay14.126.316.518.748.720.87
48Yellowish clay1426.716.918.768.740.91
49Altered rock in yellowish clay12.926.815.318.098.081.08
50Motley lateritic clay14.226.817.918.98.890.89
51Altered rock in motley clay12.126.51617.537.51.2
52Brown clay12.926.416.218.0181.05
53Yellowish clay14.126.917.118.868.850.91
54Altered rock in reddish clay12.326.716.417.697.71.17
55Reddish lateritic clay13.726.816.718.598.570.96
56Motley lateritic clay1327.216.718.228.231.09
57Altered rock in reddish lateritic clay12.82716.618.068.061.11
58Altered rock in reddish lateritic clay1326.816.418.158.161.06
59Yellowish clayed sand15.825.718.4219.659.70.627
60Yellowish sandy clay15.625.818.2519.559.60.654
61Yellowish sandy clay15.325.618.6619.329.30.673
62Reddish clay14.126.61818.88.780.89
63Altered rock in Motley clay1326.716.618.138.111.06
64Altered rock in yellowish lateritic clay12.926.616.618.058.061.06
65Altered rock in Motley clay13.926.71718.698.430.98
66Reddish clay13.126.616.818.188.141.04
67Reddish soft clay12.226.716.617.637.631.19
68Altered rock in reddish clay12.526.617.517.87.791.13
69Altered rock in reddish clay1126.717.116.886.841.44
70Reddish clay13.126.917.418.238.221.056
71Reddish clay13.226.717.618.268.281.018
Average value14.8426.8418.1219.319.310.85
Variance of soils samples5.180.384.612.312.320.06
Standard deviation2.280.622.151.521.520.25
Confidence interval range12.5626.2215.9817.87.780.6
Maximum value20.928.823.423.5713.61.44
Minimum value1125.615.116.886.840.36
Median value14.126.817.118.868.850.89

Soil samplesPhysical identification oedometer parameters
Type of soilK (m/s)Wnat (%)LL (%)PI (%)Eoed (kPa)e0 (kPa)Cc

1Nodulated reddish clay6.90E − 0729.670.634.368000.74600.1310.007
2Nodulated reddish clay1.61E − 0824.465.432.596000.678500.080.006
3Nodulated reddish clay3.77E − 1024.354.423.8138000.652850.0670.0042
4Nodulated reddish clay8.44E − 1127.465.234.786000.675990.1010.005
5Yellowish clay2.05E − 072961.226.787000.7281150.1080.0066
6Yellowish lateritic gravel9.03E − 1019.460.626.987000.5751400.1280.0074
7Yellowish clay6.09E − 0923.199000.6251250.1040.0053
8Brown clay5.32E − 1026.7151000.651000.0640.0048
9Yellowish clay4.69E − 0920.90.551100.1440.005
10Altered rock in reddish lateritic clay4.64E − 0623.671.633.640001.24280.3290.0163
11Altered rock in yellowish lateritic clay2.61E − 072058.430.130000.97537.50.2510.0099
12Reddish lateritic clay2076.241.11.27190.180.02
13Reddish lateritic clay8.27E − 0823.175.839.3108000.955280.160.016
14Altered rock in reddish lateritic clay3.60E − 0617.276.936.827001.1360.2930.0164
15Altered rock in Motley clay3.60E − 061269.935.228001.07552.50.2720.0109
16Altered rock in reddish clay8.171.9320.98600.2260.0134
17Altered rock in Motley clay5.87E −
18Nodulated reddish clay2.03E − 1123623096000.62587.50.0570.0086
19Nodulated reddish clay1.07E − 0925663144000.6251250.190.0073
20Nodulated reddish clay1.77E − 08295325140000.625910.0530.0053
21Nodulated reddish clay1.15E − 09297133105000.6852.50.0690.001
22Nodulated reddish clay7.65E − 09276230133000.72287.50.0560.0096
23Nodulated reddish clay3.71E − 1027673178000.7122.50.0740.009
24Nodulated reddish clay3.24E − 1030.165300.69532.50.0790.0102
25Nodulated reddish clay9.27E − 11276836109000.635650.0580.014
26Nodulated reddish clay34673559000.652450.0930.0133
27Yellowish clay5.55E − 083366.932.928001.1332.50.2880.007
28Motley clay1.43E − 0730.570.431.827001.15630.3480.007
29Reddish lateritic clay2.19E − 0724.562.831.842000.825650.2150.0033
30Altered breastplate in reddish clay9.35E − 072152.124.559000.655550.1380.004
31Altered breastplate in Motley clay1.55E − 072583.640.122001.280.3010.0055
32Altered breastplate in reddish clay3.73E − 0722.96831.648000.68700.1850.0042
33Altered breastplate in reddish clay1.96E − 0726.980.240.551000.675850.2030.0066
34Altered breastplate in yellowish clay3.00E − 0728.463.927.527001.24500.4060.0121
35Reddish lateritic clay3.95E − 0723743728001.089.20.3350.0082
36Reddish clay gravel1.59E − 0817.7653522000.32867.50.1850.0063
37Reddish clay gravel3.41E − 0925.4612831000.3287.50.220.0063
38Reddish clay gravel2.27E − 1023.3583185000.365990.0860.0059
39Reddish clay gravel6.47E − 0918.4662964000.2751300.140.0068
40Reddish clay gravel3.04E − 1118582760000.44857.50.0730.0069
41Altered rock in Motley clay4.77E − 0717.869.936.636000.89310.2090.0093
42Altered rock in reddish clay3.14E − 0725.674.433.269000.79567.50.1240.0077
43Altered rock in reddish lateritic clay3.32E − 0624.466.43648000.972780.1640.0057
44Altered rock in reddish lateritic clay9.58E − 0719.668.936.638001.015800.2250.0087
45Motley clay1.31E − 0718.129.316.323000.8500.2790.0059
46Yellowish sandy clay2.02E − 0717.431.316.537000.72650.2050.0069
47Yellowish sandy clay1.20E − 0717.329.214.743000.7862.50.1770.0059
48Yellowish clay3.30E − 0720.873.337.750000.88950.230.0226
49Altered rock in yellowish clay1.72E − 0718.848.419.739000.951020.3670.0085
50Motley lateritic clay1.20E − 0723.368.829.983000.831030.160.0072
51Altered rock in Motley clay2.96E − 0732.753.81748001.311040.4140.015
52Brown clay2.95E − 0725.851.820.823000.8200.2830.0097
53Yellowish clay1.96E − 0721.151.422.819000.845290.3340.0093
54Altered rock in reddish clay8.62E − 0633.160.32744001.02700.190.0073
55Reddish lateritic clay1.10E − 07226633.548000.77857.50.1550.0064
56Motley lateritic clay3.10E − 0728.371.331.433001.2340.2520.0087
57Altered rock in reddish lateritic clay5.90E − 073056.225.132001.16400.2560.0136
58Altered rock in reddish lateritic clay2.16E − 072660.628.956001.0872.50.1710.0136
59Yellowish clayed sand2.29E − 0416.5650.0822.920.5501200.1590.004
60Yellowish sandy clay1.47E − 0516.9966.3330.160.6071000.290.005
61Yellowish sandy clay6.04E − 0621.9876.0334.560.628650.2090.005
62Reddish clay2873335863.31.4900.4230.021
63Altered rock in Motley clay2874274952.30.85102.50.3470.027
64Altered rock in yellowish lateritic clay2669194661.50.98600.3080.022
65Altered rock in Motley clay2526269938.30.84400.2550.017
66Reddish clay28542071230.99500.20.013
67Reddish soft clay3662174431.61.3777.50.3890.025
68Altered rock in reddish clay4053124614.81.3857.50.370.023
69Altered rock in reddish clay5674275534.11.64290.4060.015
70Reddish clay3362226717.781.41150.3950.015
71Reddish clay3358196252.671.1862.50.2360.017
Average value4.88E − 0624.7662.9729.085942.020.8666.380.210.01
Variance of soils samples9.03E − 1049.32132.9745.860.08993.870.010.00
Standard deviation3.00E − 057.0211.536.773219.580.2931.530.10.01
Confidence interval range−2.52E − 0517.7351.4422.312722.440.5734.850.110.00
3.49E − 0531.7874.535.859161.61.1597.90.320.02
Maximum value2.29E − 045683.641.1151001.641400.420.03
Minimum value2.03E − 118.1261219000.2880.050.00
Median value1.84E − 0724.565.330.054876.150.8630.20.01

5. Results and Discussion

In the previous sections, the parameters of identification, compression, and shear resistance were presented for the soils of Cameroon, including the transformation relations of the laboratory parameters to the parameters of the Soft Soil model for their use in a numerical calculation code. Table 3 and Figures 68 present the performed parameters of the Soft Soil advanced model determined for the 71 soil samples analyzed from the central, south, and Littoral regions of Cameroon. They were obtained from the raw soil mechanics laboratory results that were presented in Tables 2 and 3 and calibrated according to the relations (1–8) of the advanced model formulation, the Soft Soil model [25], presented in parts of this article. The statistical significance of these parameters of the Soft Soil model is presented in Table 4. The results obtained in this paper (clays of Littoral region, central region, and southern region) can be compared to the different models obtained on the clays soils around the world. The parameters are of the same order of magnitude as other clays modelled around the world (Table 5): Haney clay [33]; Osaka clay [34]; the Cubzac-les-Ponts clayey embankment [35, 36]; from the site of the dam of Flumet in the Isère in France [14]; and the site of Saint-Laurent des eaux [14], the Bangkok clays [12, 15], and the Murro test embankment clay in Western Finland [16] to name only those. The soft soils found in the African continent (tropical zone soils) [3739] have been considered for these comparison in this paper: the settlement of a railway embankment on PVD-improved Karakore soft soil in Ethiopia [39]; the rheology of mechanical properties of soft soil in Nigeria [37]; and various problem on soft clayed soils in South Africa [38]. The results of monitoring of the full scale experimental embankment on soft Douala clays (Littoral region) of Cameroon have been published recently in this domain in the Journal of Civil Engineering [40].

Soil samplesParameters of the Soft Soil model
c (kPa)φ (°)Ψ (°)M (kPa)

Average value36.7430.183.111.650.500.150.04810.004654.1612.51
Variance of soils samples794.9560.0224.
Standard deviation28.197.754.910.380.110.000.02080.002327.217.16
Confidence interval range8.5522.43−1.791.270.390.150.02730.002326.955.35
Maximum value159.0050.1020.102.670.830.150.09730.0114113.0334.50
Minimum value0.709.900.000.760.230.150.01360.00055.952.07
Median value29.6029.500.001.600.510.150.04820.004050.5511.11

ParametersSoft silty clays of EthiopiaHaney clayOsaka clayFlumet clay, FranceSaint-Laurent clay, FranceCubzac clay, FranceBangkok clayCentral region claySouthern region clayLittoral region clay

γ (kN/m3)17.31718.51814.5191717.6
c (kPa)001032023.148.818.9
φ (°)30363237192635.121.631
Ψ (°)0007005.101
k (m/s)3.15 × 10−91.16 × 10−101.16 × 10−910−710−85.00 × 10−83.78 × 10−92.61 × 10−73.32 × 10−6

In the context of projects of great importance whose works are subjected to complex loading (vertical and horizontal components and moments applied to the foundation, dynamics loads, and cyclic loads), the analytical calculation is no sufficient to predict the behaviour of such structures. It is therefore necessary to first performed advanced soil modelling according to the results of laboratory tests and then to carry out a numerical modelling of the structure taking into account the realistic behaviour of the materials, the soil-structure interaction, and the different staged construction. For compressible soils, the Soft Soil model used in numerical modelling offers safety and comfortable results, hence the importance of advanced soil modelling used in numerical modelling for the prediction of behaviour of geotechnical structures.

6. Conclusion

In this paper, we determined the parameters of the advanced compressible soil model on 71 soil samples from various locations in the country. The parameters of the Soft Soil model determined now serve as a national database for compressible soils. These parameters can be used in projects to numerically predict the behaviour of geotechnical structures under construction or during operation. Present, the most efficient tool for predicting complex phenomena is modelling. It is therefore important to first determine the parameters of each model likely to describe the actual behaviour of the structure before using it in a computer code. The study meets national or even international needs, which is to have a database for exploitable soils for supplying calculation codes when carrying out major projects. More precise methods, such as numerical calculations, should be used when the soil-structure interaction has a dominant influence. Numerical methods have the capacity to take into account macroscopic heterogeneities of the soil (layers of different characteristics or heterogeneity); the same is true of the heterogeneity caused by different loading levels according to the points of the Massif, in the case of a soil with nonlinear behavior (variable rigidity). Numerical methods make it possible to take into account any loading geometry and the phasing construction or the progressive application of loading; they are also well suited to situations where it is necessary to study the interaction between neighboring structures, that is, to say where one is dealing with one or more structure-soil-structure interaction problems. The use of the Soft Soil model for compressible soils involves longer computation times, since the stiffness matrix of the material is decomposed in each step of the calculation. For the analyzed soils, which are compressible, the Soft Soil model correctly describes their behaviour and makes it possible to optimize the designing of the geotechnical structures, which are supported or support these compressible soils, thus demonstrating the importance of the advanced modelling of soils for predicting the behaviour of geotechnical structures. This study is a contribution to the advanced soil modelling of Cameroon; it will be extended to the case of rigid soils with the hardening soil model.

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

The authors confirm that there are no conflicts of interest associated with this publication.


The authors acknowledge particularly the GéoMécanique team of the Laboratoire 3SR at Grenoble, France, and Geotechnical’s Laboratories and Engineering’s Offices of Cameroon for the facilities and support to perform the experiments. They also thank the people who were involved in obtaining the results from this paper.


  1. K. Terzaghi, “Theoretical Soil Mechanics,” Wiley, New York City, NY, USA, 1943. View at: Google Scholar
  2. M. A. Biot, “General theory of three—dimensional consolidation,” Journal of Applied Physics, vol. 12, no. 2, pp. 155–164, 1941. View at: Publisher Site | Google Scholar
  3. R. L. Schiffman and S. K. Arya, “One-dimensional consolidation,” in Numerical Methods in Geotechnical Engineering, pp. 364–378, McGraw-Hill, New York City, NY, USA, 1977. View at: Google Scholar
  4. I. Lepidas and J. P. Magnan, “Fluage et Consolidation des Sols Argileux: Modélisation Numérique,” Laboratoire Central des Ponts et Chaussées, Paris, France, 1990. View at: Google Scholar
  5. O. Combarieu, F. Gestin, and M. Pioline, “Remblais sur sols améliorés par inclusions rigides: premier chantier,” Bulletin de Liaison des Laboratoires des Ponts et Chaussées, vol. 191, pp. 55–61, 1994. View at: Google Scholar
  6. O. Combarieu and A. Frossard, “Amélioration des sols des berges de la loire par inclusions rigides pour stabiliser les remblais d’accès d’un poste de quai,” in Proceedings 13th European Conference on Soil Mechanics and Geotechnical Engineering (XIII ECSMGE), pp. 625–630, Rotterdam, Netherlands, 2003. View at: Google Scholar
  7. O. Combarieu, “Remblais sur sol compressible et inclusions rigides: amélioration de l’approche de dimensionnement,” Revue Française de Géotechnique, vol. 74, pp. 42–50, 2007. View at: Google Scholar
  8. Q. A. Dinh, “Etude sur modèle physique des mécanismes de transfert de charge dans les sols renforcés par inclusion rigides,” application au dimensionnement, École des ponts ParisTech, Champs-sur-Marne, France, 2010, Ph.D. thesis. View at: Google Scholar
  9. M. Equihua-Angiano, P. Foray, and O. Calderon, “Estimation of undrained shear strength of soft soil obtained by cylinder vertical penetration,” in Proceedings of the 18th International Conference on Soil Mechanics and Geotechnical Engineering, pp. 2933–2936, Paris, France, 2013. View at: Google Scholar
  10. S. Baotang, S. Jingyu, and B. Nick, “An approximate nonlinear modified Mohr-Coulomb shear strength criterion with critical state for intact rocks,” Journal of Rock Mechanics and Geotechnical Engineering, vol. 10, no. 4, pp. 645–652, 2018. View at: Publisher Site | Google Scholar
  11. S. M. Ahmed, “Assessment of clay stiffness and strength parameters using index properties,” Journal of Rock Mechanics and Geotechnical Engineering, vol. 10, pp. 579–593, 2018. View at: Publisher Site | Google Scholar
  12. L. Chanaton, W. Suched, B. Dariusz, O. Arumugam, and G. Erwin, “Stiffness and strength parameters for hardening soil model of soft and stiff bangkok clays,” Soils and Foundations, vol. 52, no. 4, pp. 682–697, 2012. View at: Publisher Site | Google Scholar
  13. T. Adachi and F. Oka, “Constitutive equation for normally consolidated clays based on elasto-viscoplasticity,” Soils and Foundations, vol. 22, pp. 57–70, 1982. View at: Publisher Site | Google Scholar
  14. M. Husein, “Etude du comportement différé des sols et des ouvrages géotechniques,” Joseph Fourier University, Grenoble, France, 2001, Ph.D. thesis. View at: Google Scholar
  15. T. Suched, S. Supot, O. Chanaton, E. Oh, and A. Balasubramaniam, “Small strain stiffness and stiffness degradation curve of bangkok clays,” Soils and Foundations, vol. 53, no. 4, pp. 498–509, 2013. View at: Publisher Site | Google Scholar
  16. K. Nallathamby and P. Minna, “Modelling creep behaviour of anisotropic soft soils,” Computers and Geotechnics Journal, vol. 69, pp. 46–57, 2015. View at: Publisher Site | Google Scholar
  17. ASIRI, “Recommendations for the Design, Construction and Control of Rigid Inclusion Ground Improvements”, ASIRI, Colombo, Sri Lanka, 2012.
  18. M. N. Chehat, M. Hussien, M. Abdellaziz, Z. Chekired, and M. Harichane, “Stiffness-and damping-strain curves of sensitive champlain clays through experimental and analytical approaches,” Canadian Geotechnical Journal, vol. 56, no. 3, pp. 364–377, 2019. View at: Publisher Site | Google Scholar
  19. Z. Gao and D. Chen, “Compression index versus natural water content relationships for China’s coastal soft cays,” KSCE Journal of Civil Engineering, vol. 23, pp. 4611–4620, 2019. View at: Google Scholar
  20. P. A. Vermeer and H. P. Neher, “A soft soil model that accounts for creep,” Beyond 2000 in Computational Geotechnics, Balkema, Amsterdam, Netherlands, 1999. View at: Google Scholar
  21. D. F. E. Vermeer and P. G. Stolle, “From the classical theory of secondary compression to modern creep,” Journal of Computer Methods and Advances in Geomechanics, vol. 4, pp. 2469–2478, 1997. View at: Google Scholar
  22. D. Zoa, J. C. Ambassa, and J. C. Amba, “Modélisation et évaluation de la stabilité d’un talus renforcé par clouage industriel en utilisant la méthode c-phi reduction de Plaxis,” Afrique Science Journal, vol. 13, no. 1, pp. 381–399, 2017. View at: Google Scholar
  23. D. Zoa, C. F. Ambassa, R. Ossende Owona, and E. Medjo, “Modélisation avancée des sols et analyse de la stabilité du ravin de kotto à douala 5è au Cameroun,” Afrique Science Journal, vol. 13, no. 2, pp. 32–44, 2017. View at: Google Scholar
  24. PLAXIS, “Finite Element Code for Soil and Rock Analyses: Material Models Manual,” PLAXIS, Exton, PA, USA, 2018. View at: Google Scholar
  25. J. B. Roscoe and J. Burland, “On the generalized stress-strain behavior of wet clays,” Journal of Terramechanics, vol. 7, no. 2, 1970. View at: Google Scholar
  26. PLAXIS, “Finite Element Code for Soil and Rock Analyses: Reference Manual,” PLAXIS, Exton, PA, USA, 2012. View at: Google Scholar
  27. S. F. Toteu, W. R. Van Schmus, J. Penaye, and A. Michard, “New U-Pb and Sm-Nd data from north-central Cameroon and its bearing on the pre-pan-african history of central Africa,” Precambrian Research, vol. 108, no. 4, pp. 45–73, 2001. View at: Publisher Site | Google Scholar
  28. E. Mengue, H. Mroueh, L. Lancelot, and R. M. Eko, “Evaluation of the compressibility and compressive strength of a compacted cement treated laterite soil for road application,” International Journal of Geotechnical and Geological Engineering, vol. 31, no. 4, pp. 1–26, 2018. View at: Publisher Site | Google Scholar
  29. P. G. Fookes, “Tropical Residual Soils,” CRC Press, Boca Raton, FL, USA, 1997. View at: Google Scholar
  30. British Standards Institution, “Code of Practice for Site Investigations (+A2 : 2010) BS 5930:1999,” British Standards Institution, London, UK, 1999. View at: Google Scholar
  31. M. Das Braja, “Principles of Geotechnical Engineering,” Pws-Kent Publishing, Stamford, CT, USA, 7th edition, 2016. View at: Google Scholar
  32. Eurocode, “Calcul Géotechnique—Partie 2: Calcul Sur la Base D’essais de Laboratoire,” Eurocode, Brussels, Belgium, 1999. View at: Google Scholar
  33. Y. P. Vaid and R. G. Campanella, “Time dependent behaviour of undisturbed clay,” Journal of Geotechnical Engineering Division ASCE, vol. 2, pp. 693–709, 1977. View at: Google Scholar
  34. H. Sekiguchi, “Theory of undrained creep rupture of normally consolidated clay based on elasto-viscoplasticity,” Soils and Foundations, vol. 24, no. 1, pp. 129–147, 1984. View at: Publisher Site | Google Scholar
  35. A. I. Michali, “Méthode pour l’identification des paramètres d’une loi élastoplastique à partir d’essais de laboratoire et in-situ, modélisation numérique du tassement d’un remblai sur sol compressible,” Ecole Centrale des Arts et Manufactures, Gif-sur-Yvette, France, 1994, Ph.D. thesis. View at: Google Scholar
  36. J. P. Magnan, J. P. Breton, J. P. Rajot, and H. Tar, “Fluage des sols mous des remblais et des fondations superficielles,” in Proceedings of the 12th European Conference on Soil Mechanics and Geotechnical Engineering, pp. 1121–1126, Amsterdam, Netherlands, 1999. View at: Google Scholar
  37. K. Onyelowe, D. B. Van, C. Igboayaka, F. Orji, and H. Ugwuanyi, “Rheology of mechanical properties of soft soil and stabilization protocols in the developing countries-Nigeria,” Materials Science for Energy Technologies, vol. 2, pp. 8–14, 2018. View at: Publisher Site | Google Scholar
  38. G. Jones and P. Davies, “Problem soils in south Africa-state of the art/soft clays,” The Civil Engineer Journal in South Africa, vol. 27, no. 7, pp. 355–365, 1985. View at: Google Scholar
  39. J. J. Muhammed, P. W. Jayawickrama, A. Teferra, and M. A. Ozer, “Settlement of a railway embankment on PVD-improved karakore soft alluvial soil,” International Journal Engineering Science and Technology, vol. 4, no. 3, 2020. View at: Publisher Site | Google Scholar
  40. Z. Ambassa, J. C. Amba, and F. X. Mbelen, “Monitoring and numerical modeling of the full scale experimental embankment on soft douala clays of Cameroon,” International Journal of Civil Engineering and Technology, vol. 11, no. 7, 2020. View at: Google Scholar

Copyright © 2020 Zoa Ambassa and Jean Chills Amba. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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