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The clay soils of the city of Douala are constantly saturated with water, which permanently favors the hydrodynamic behavior of the soils (swelling or consolidation). This phenomenon can cause serious disturbances in the structure of buildings resulting in the appearance of cracks in structures (buildings, road bridge, viaduct, etc.). The foundation raft is a very important structure in the dimensioning of structures. Given the soil-structure interactions, its mechanical characteristics must be the subject of a special study linked to the building environment. In this article, we present a study of the mechanical behavior of a foundation raft anchored in a laminate floor. The aim is to highlight the influence of the mechanical properties of the foundation soil on the evolution of the mechanical behavior of the raft. The method used is a numerical simulation. A physical model taking into account a 5-storey building based in Douala in the Denver district is studied. The foundation on the raft foundation of this building follows an elastic constitutive law with Mazars damage, and rests on a laminated soil of plastic elastic model with Camclay plasticity criterion. The ground-raft and ground-ground interfaces are carried out with the finite elements joined to three nodes (JOI3), and obey the Coulomb model; it is an expansion joint model with Mohr-Coulomb type criterion and associated flow. The numerical resolution is carried out by the finite element method, and the numerical simulations via the Cast3M calculation code. The results from the simulations show that the mechanical characteristics of foundation soils, in this case the water content, the compactness, the state of consolidation, greatly influence the mechanical behavior of the foundation slab. There is indeed a significant settlement and a great deformation of the raft foundation when the water content of the soil layers increases, and when the states of consolidation and compactness are low. This article allows us to predict and control the evolution of the behavior of the ground-structure interface of a raft foundation and to adopt a new model appropriate for the sizing of civil engineering structures.

In Cameroon, the urbanization rate in 2010 was 52%, for a total population estimated at 19,648,287 inhabitants, with 17 towns of at least 100,000 inhabitants. The cities of Douala (economic capital) and Yaoundé (political capital) which in 2005 alone housed 21.3% of the total population and 43.7% of the urban population, totaled in 2010 more than 5 million inhabitants (approximately 23.5% of the total population of Cameroon) [

Soils, like all other materials, deform when loaded. In accordance with the general principles of soil mechanics, the deformations of saturated clay soils are linked to variations in the effective stresses, that is to say, to variations in the difference between the total stresses and the pressure of the pore water. Total stresses are created by the forces of gravity and by other loads applied to the surface of the soil (by embankments, shallow foundations, slabs, etc.) or inside the soil mass (deep foundations, tunnels), etc. [

The uncertainty on the mechanical properties of soils linked to the heterogeneity within the same layer, results in an uncertainty on the amplitude of settlements and their evolution over time. The calculations give an idea of the differential settlements that can be expected at a given time. They can lead to fairly long consolidation times, and it may be necessary to consider an acceleration of settlements either by pre-loading or by intensified drainage. In this study we considered the values from the soil report note then we carried out experimental verifications on the site in order to take soil samples for laboratory studies in order to verify the results of the geotechnical report (content of water, void index, particle size analysis). We then, using Terzaghi’s method [

The model chosen in (

Following a geotechnical survey campaign which took place on the study site of the project, we have recorded in

Depth (m) | shapes | Number of values | Thickness (m) | Average | standard deviation | Min (MPa) | Max (MPa) | Moy-0.5σ |
---|---|---|---|---|---|---|---|---|

0 to 3 | Grayish sandy clay | 3 | 3 | 0.97 | 0.55 | 0.44 | 1.55 | 0.70 |

3 to 5.5 | Gray, slightly sandy plasticclay | 2 | 2 | 1.81 | 0.76 | 1.28 | 2.35 | 1.43 |

5 to 10.50 | Gray sandy clay | 5 | 5.5 | 2.00 | 0.19 | 1.70 | 2.20 | 1.91 |

10.50 to 15 | Little sandy brown clay | 5 | 4.5 | 1.95 | 0.07 | 1.86 | 2.03 | 1.92 |

shapes | Roof/NL | Thickness (m) | Pl*(Mpa) | Em (Mpa) |
---|---|---|---|---|

Grayish sandy clay | 0 | 3 | 0.70 | 5.18 |

Gray, slightly sandy plastic clay | 3 | 2 | 1.43 | 20.41 |

Gray sandy clay | 5.5 | 5.5 | 1.91 | 22.48 |

Little sandy brown clay | 10.5 | 4.5 | 1.92 | 26.48 |

The verification of the bearing capacities and the calculation of the footing’s settlements are carried out using the values of the loads which will be exerted in the subsoil. In our case, we have the maximum load Cm = 31 MN, calculated on the basis of the load drops. These are shallow foundations, namely a general raft of dimensions 15.40 × 21 m. The results of verification of settlements by the pressuremeter method are as follows: Calculation method of settlements according to Terzaghi.

The calculation of the overall settlement Δh of a laminate floor by several compressible saturated layers is generally evaluated by:

Δ h = Δ h i + Δ h c + Δ h s + Δ h f (1)

■ Δhi: this is the immediate settlement, it depends on the overload (Δσ), the compressible soil thickness (h), a geometry factor of the medium I and the deformation modulus (E). This settlement occurs before any drainage has had time to take place. it is expressed by:

Δ h i = Δ σ E I (2)

■ Δhc: This is a primary consolidation settlement of zero lateral strain, linked to the drainage of the multilayer system where there is an effective initial stress ( σ ′ 0 ) uniformly overloaded by ( Δ σ ′ ). This relation is given by:

Δ h c = H C c 1 + e o log σ ′ 0 + Δ σ ′ σ ′ 0 (3)

■ Δhs: This is the secondary settlement at zero lateral strain, corresponding to a creep of the skeleton after dissipation of the pore overpressure.

■ Δhf: This is the settlement caused by the lateral movements of the soil.

Based on the calculations made, the final settlement is estimated at:

Δ h = Δ h i + Δ h c = 0.0263 cm

The chosen geometric model consists of a ribbed raft, anchored in a laminate floor made up of o, x, y. The following main assumptions are made:

- The soils are homogeneous and isotropic. The dimensions considered are 15.4 min width.

- The triangular finite elements with quadratic interpolation (tri6: triangle with 6 nodes and 2 degrees of freedom by node (Ux; Uy)) are used for the mesh of the base and the layers of soil. The resolution being partly carried out at the nodes of the mesh, this thus makes it possible to densify the nodes in the model and to approach the real solution as well as possible.

1) Mazars mechanical model for the raft foundation

The foundation raft has a model of elastic mechanical behavior with Mazars damage. The damage variable “D” constitutes an observable state variable for the material [

- Plastic or viscoplastic deformation:

ε p = ε + ε e (4)

- The variable of scalar nature, characterizing isotropic hardening

P = ∫ 0 t ( 2 3 ε ˙ p ( τ ) : ε ˙ p ( τ ) ) 1 / 2 d τ (5)

- The tensor variable of order 2 characterizing the kinematic hardening α In the space of constraints, the flow surface is represented by the function f

f = f ( σ , p , X , p ˙ , T ) (6)

Kuhn and Tucker [

- The point representative of the stress state σ ∗ must belong to the flow surface [

f = f ( σ ∗ , p , X , p ˙ , T ) (7)

- Throughout the flow, the point representative of the stress state must not be able to leave the surface:

d f ( σ * ) = d f d σ : d σ * + d f d p d p + d f d X : d X + d f d p ˙ d p ˙ + d f d T d T = 0 (8)

The charge/discharge criteria become:

· f < 0 is equivalent to the elastic behavior

· f = 0 and df = 0 is equivalent to plastic flow

· f = 0 and df < 0 is equivalent to the elastic discharge

2) Modified Camclay mechanical model for soil layers

The soil has an elastoplastic model of behavior with modified Camclay plasticity criterion. This model is based on the concepts of limit state and critical state; he postulates the existence of a limit state and critical state curve to describe the elastoplastic behavior of normally consolidated isotropic soils, under homogeneous stresses [

F ( σ ) = q 2 + M 2 ( P ′ 2 − P ′ P ′ c ) (9)

P ′ c the pre-consolidation pressure given from Khemissa, by Equations (10)-(12)

q = ( ( σ 1 − σ 2 ) 2 + ( σ 1 − σ 3 ) 2 + ( σ 2 − σ 3 ) 2 ) / 2 (10)

P ′ = t r a c e [ σ ¯ ] (11)

P ′ c = P ′ c 0 exp [ ( ( 1 + e i ) / ( λ − k ) ) ε v p ] (12)

e i represents the initial void index of the soil. P ′ c 0 is the initial pre-consolidation pressure, λ the slope of the loading curve for a normally consolidated state and k the slope of the unloading-reloading curve for an over-consolidated state.

ε v P is the plastic component of the strain. The slope of the critical state line M in the plane (p, q), or coefficient of friction is defined by Equation (13). M is determined by the triaxial compression test and defined by Equation (6).

M = 6 sin φ / ( 1 − sin φ ) (13)

φ is the internal friction angle of the soil. As described by Equation (14), M is the slope of the line representing the critical shear behavior of the soil, where the strains continue to develop without a change in stress state

q = M P ′ (14)

The elastic law associated with the Camclay model is characterized by the Young modulus E and the Poisson’s ratio υ (assumed constant). These parameters are taken into account by the voluminal compressibility modulus K and the shear modulus G, given by Equation (15) and Equation (16)

K = ( ( 1 + e i ) / k ) P ′ (15)

G = [ 3 ( 1 − 2 υ ) / 2 ( 1 + υ ) ] K (16)

3) Plastic model of Mohr Coulomb for the ground-raft and ground-ground interfaces

The zero-thickness element approach was used to model the joints of the ground-raft and soil-ground interfaces. This element follows the elastoplastic constitutive law, with Mohr-Coulomb plasticity criterion [

f ( σ n , τ ) = | τ | − σ n tg ϕ − c (17)

with c, ϕ , respectively the cohesion and the friction angle at the interface. σ n and τ the normal and shear stresses.

4) The values of parameters used to perform this simulation

The numerical simulations are carried out using the Castem software, by successively varying the pré-consolidation pressure, the soil compacity (through the void index), and the Young modulus (function of water content). The numerical input parameters used in

The values in

PARAMETRES | VALEUR | PARAMETRES | VALEUR |
---|---|---|---|

Initial void index | e_{i} = 0.38 | pre-consolidation pression | P ′ c = 2.5 Mpa |

Coefficient of friction | M = 1.18 | Elastic slope | k = 0.007 |

Cohesion | c = 1 Mpa | Plastic slope | λ = 0.04 |

Poisson’s ratio | υ = 0.3 | Shear modulus | G = 150 Mpa |

Young modulus | E = 390 Mpa |

PARAMETRES | VALEUR | PARAMETRES | VALEUR |
---|---|---|---|

interface normal stiffness | KN = 980 Mpa/m | Friction angle | ϕ = 30˚ |

interface shear stiffness | KS = 375 Mpa/m | Dilalancy angle | ψ = 30˚ |

Maximum tensile strength | FTRC = 980 Mpa/m |

PARAMETRES | VALEUR | PARAMETRES | VALEUR |
---|---|---|---|

Poisson’s ratio | υ = 0.25 | Correction for shear | 1.06 |

Young modulus | variable | Tensile strain threshold | KTR0 = 1E−4 |

Concrete in compression | BCOM = 1900 | Concrete in tension | BTRA = 17,000 |

Steel in compression | ACOM = 1.4 | Steel in tension | ATRA = 0.8 |

The mechanical blockings are applied to the geometries of the soils and the raft as illustrated by

The loading of the structure takes place on the ribs of the raft foundation, as shown in (

F i + 1 = F i + Δ F (18)

where F i is the force applied to the time index i, and ∆F is the force increment at each time index. F i + 1 the force applied to the time index i + 1.

A finite element calculation will be performed step by step using the Cast3m finite element code. The parametric study will be carried out by varying the mechanical parameters of the soil in turn (water content, compactness, consolidation). The results will be extracted with the nodes and elements of the mesh as illustrated by (

To highlight the influence of the physico-mechanical characteristics of the soil on the behavior of the raft, Figures 7-14 show the local stress-displacement

curves at the head of the central rib of the raft, and the overall force-displacement of the raft, respectively. These curves are qualitatively in agreement with the work of Niandou [

The evolutions of the graph in (

The evolutions in graphs of

The objective of this article was to make a numerical simulation of the mechanical behavior of a foundation raft anchored in a laminate soil. The goal is to highlight the influence of the mechanical properties of the foundation soil in relation to the evolution of the mechanical behavior of the foundation raft subject to hydrodynamic variations of the physical parameters of the soil in the city of Douala in Cameroon. It emerges from after the boundary conditions and the models taken into account in the formulation of the studied problem that, when saturated clays are subjected to loadings at high load rates, deformations occur. We can therefore note that this evolution of settlement in the soil depends on several parameters which interact according to their solicitations. For this, we were able to highlight the influence of its parameters and note that, the stress and the breaking force mobilized in the study increase when the initial pre-consolidation pressure is greater and the void index decreases when the breaking stress is greater and finally the stress and the breaking force mobilized therefore increase with the cohesion and the friction angle of the soil. The interest of the work lies in taking into account the dimensioning parameters of the foundations of solid structures. In terms of perspectives, we envision the demonstration of a structural soil relationship of saturated clay soil types as well as a characterization of the physical parameters of soils as a function of heavy loads.

The authors declare no conflicts of interest regarding the publication of this paper.

Hugues, T.M., Didier, F., Martial, N. and Blaise, N.B. (2020) Numerical Study of the Mechanical Behavior of a Foundation Raft under the Hydrodynamic Influence of the Mechanical Characteristics of Clay Soils. Engineering, 12, 766-780. https://doi.org/10.4236/eng.2020.1210054