I 1 Coupling finite elements and discrete elements methods, application to reinforced embankment by piles and geosynthetics B. Le Hello, B. Chevalier, G. Combe, P. Villard Laboratoire Sols, Solides, Structures - Risques, Grenoble, Université Joseph Fourrier, Pôle International, France le_hello@geo.hmg.inpg.fr [email protected][email protected][email protected]ABSTRACT The design of geotechnical earth structures is, due to the use of new technologies and new materials, more and more sophisticated. This needs the development and the adaptation of the existing numerical models to take into account the specificity and the particularity of the behaviour of each component of the structure. A coupling between Finite Elements Method and Discrete Elements Method was done in order to clarify the mechanical behaviour of embankments soil reinforced by piles and geosynthetics. The coupling of the two numerical models allows us to keep the main advantages of each method: use of a continuous model defined by the macroscopic parameters to describe the fibrous structure of the geosynthetic sheet and its interaction with the soil, and use of a discrete model to describe the mechanisms of arching effect and transfer of load in the soil. First, load transfer mechanisms are underlined in applications to embankment built on subsiding trenches and over a network of piles. In a second part, applications to embankments built on compressible soil and reinforced by piles and geosynthetic sheets are presented. Results given are the displacements and the deformations of the structure, the tensile forces acting in the armed directions of the geosynthetic and the efficiencies of piles, geosynthetic and supporting soil. INTRODUCTION The upgrading of very soft soil areas (recent deposits and mud) requires innovating processes. Reinforcement with vertical piles is a ‘traditional’ process used to improve the bearing pressure of the very soft soil. A recent approach of this concept is the addition of a geosynthetic like reinforcement at the base of the embankment (Fig.1). The geosynthetic has to allow the transfer of the vertical load, due to the weight of the embankment, to the piles in order to minimise the applied load on the soft soil.
Transcript
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Coupling finite elements and discrete
elements methods, application to reinforced embankment by piles and
The design of geotechnical earth structures is, due to the use of new technologies and new materials, more and more sophisticated. This needs the development and the adaptation of the existing numerical models to take into account the specificity and the particularity of the behaviour of each component of the structure. A coupling between Finite Elements Method and Discrete Elements Method was done in order to clarify the mechanical behaviour of embankments soil reinforced by piles and geosynthetics. The coupling of the two numerical models allows us to keep the main advantages of each method: use of a continuous model defined by the macroscopic parameters to describe the fibrous structure of the geosynthetic sheet and its interaction with the soil, and use of a discrete model to describe the mechanisms of arching effect and transfer of load in the soil. First, load transfer mechanisms are underlined in applications to embankment built on subsiding trenches and over a network of piles. In a second part, applications to embankments built on compressible soil and reinforced by piles and geosynthetic sheets are presented. Results given are the displacements and the deformations of the structure, the tensile forces acting in the armed directions of the geosynthetic and the efficiencies of piles, geosynthetic and supporting soil.
INTRODUCTION
The upgrading of very soft soil areas (recent deposits and mud) requires innovating processes. Reinforcement with vertical piles is a ‘traditional’ process used to improve the bearing pressure of the very soft soil. A recent approach of this concept is the addition of a geosynthetic like reinforcement at the base of the embankment (Fig.1). The geosynthetic has to allow the transfer of the vertical load, due to the weight of the embankment, to the piles in order to minimise the applied load on the soft soil.
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The vertical load due to the weight of the embankment can be directly transferred to the piles by an arching effect or indirectly via the membrane effect of the geosynthetic. Loads transmitted to the piles are reported primarily to the bedrock or partially to the soft soil by friction. The main numerical difficulties correlated to the modelling of this type of structure result from: - the significant deformability of the structure needed to develop tensile force into the flexible reinforcement sheet, − the complex interaction between the soil, geosynthetic and piles at the interfaces, − the specific behaviour of materials constitutive of these reinforced earth structures (membrane behaviour of the geosynthetic, arching effect and transfer of load in the soil). The coupling between finite element and discrete element models is motivated by: − the need to use finite elements to describe the fibrous structure of the geosynthetic sheet (modelling by discrete elements does not allow to take into account particular directions of reinforcement and the non linear tensile behaviour of each fibre direction), − the need to use discrete elements to fit well the particular behaviour of granular soils: influence of the variation of porosity on the mechanical behaviour of the soil during the collapse of the embankment on the geosynthetic sheet, expansion, dilatancy, arching effect and representative transfer of load in the granular soil (shape and granular distribution of the particles of soil have experimentally and numerically a great influence on the mechanism of arching effect), − the need to take into account the interface behaviour. The major disadvantage of modelling both the soil and the geosynthetic by discrete elements lies in the restitution of the macroscopic behaviour of the interface which is tributary, at the same time, of the relative roughness of the particles of soil with the sheet (relative roughness being able to evolve during simulation if the geosynthetic sheets are very weak), and of the inter granular microscopic friction (the fitting between micro and macro properties being difficult to obtain in this case). The advantage to model the soil by discrete element and the sheet by finite element is that it is possible to define directly the interface behaviour by specific contact laws using the macroscopic friction angle (no fitting between micro and macro properties).
THE NUMERICAL APPROACH
The numerical approach selected to allow the coupling between the discrete and finite elements, consist to insert in an existing discrete element code SDEC (Donzé & Magnier, 1995, 1997) the specific finite elements characteristic of the geosynthetic sheet behaviour. The behaviour of these finite elements is governed, like the discrete elements, by the Newton’s law of motion. The interaction behaviour between these two kinds of elements is given by specific contact law defined at each contact point. The assumptions which manage
Embankment
Soft soil
BedrockPiles
Geotextile
Arching effect
Load on the bedrock
Membrane effect of the geotextile
Figure 1. Reinforced embankment by piles and geosynthetics.
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the behaviour of each element and the numerical specificities linked to the coupling of the two methods are presented below.
The finite elements used to describe the membrane behaviour of the geosynthetic sheet
The finite elements included in the three dimensional discrete elements software are three nodes elements developed previously in a finite element procedure (Villard & Giraud, 1998) to simulate the behaviour of earth reinforced structures. These elements allow to take into account the fibrous structure of any type of geosynthetic (woven, non woven geosynthetic reinforced in specific directions or knitted geosynthetic) and to well describe the tensile and membrane behaviour of the sheet (due to their constitution, geosynthetic sheet has no rigidity in flexion). These numerical developments were validated by comparison with analytical solutions of the membrane effect obtained in simple cases (Villard et al., 2000) and with experimental results of laboratory tests or full-scale experiments (Gourc & Villard, 2000). The fundamental assumptions which lead to the establishment of the behaviour of a three nodes element are: − each element consists of a set of fibres with various orientations, initially forming a plane, − the intersection and the tangle of wire are such as it does not have to slip between the wire (presence of connection points between wire). It results that the behaviour of a fibre network is obtained by superposition of behaviours obtained in each fibre direction, − the tensile efforts in each direction of fibres are directed in the direction of fibres after deformation (great displacements), − the tensile stress supported by a set of fibres with the same direction is defined by the relation σ =Ε(ε) ∗ ε. E(ε) is the secant module of fibres (function of the density of fibres) and ε is the deformation of fibres in the direction considered. ε is defined by the relation ε=(l’-l)/l with respectively l the initial length and l’ the length after deformation of considered fibres. The modulus of elasticity in compression is very weak compared to the elastic modulus in traction (no compression in fibres), − there is no bending stress, − the deformations in each fibre directions are constant on an element, due to the use of linear interpolations functions for the definition of the three nodes elements. The fundamental equation characteristic of the behaviour of a three nodes finite element can be written as: {F}= [Ku]{u}+{Fu} (1) where {F} are the forces acting on the nodes of an element, {u} the nodal displacements of the element, [Ku] the elementary matrix of rigidity depending on the final position of the three nodes, and {Fu} a corrective vector force resulting from the large displacements formulation.
The discrete element model The discrete element software used is a three dimensional software (SDEC) based on a Newtonian approach which uses rigid bodies (Donzé & Magnier, 1995, 1997). The basis elements employed are spherical particles of various sizes which can interact together (two elements may be considered as interacting while not touching). The algorithm of calculation used consists in successively alternating the application of the Newton's second law of motion to the particles and a force-displacement law to the contacts. The equations of motion are integrated using an explicit centred finite difference algorithm involving a time step Δt.
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Recent numerical developments allow jointing together several spherical particles to make clusters. These developments are necessary to obtain more realistic mechanical behaviour of soil. Interaction laws, locally defined, make it possible to restore a global macroscopic behaviour of the particles assembly. The granular distribution, initial porosity, shape of clusters and the methodology of setting up the particles have a great influence on the numerical material behaviour. The identification of the micro mechanical parameters of contact needed to reproduce the macro mechanical behaviour of the material is complex and need a fitting of the model. Generally, numerical simulations of triaxial tests are enough to identify the main mechanical parameters (elastic modulus, Poisson coefficient, cohesion, dilatancy and friction angles). The curves presented on figures 2 and 3 give, for a set of micro mechanical parameters, the macro mechanical answers of the discrete elements model. The numerical samples tested are constituted by approximately 6000 spherical particles of several sizes; each diameter of particles is randomly chosen between a range of d and 2d. The spherical particles are setting to an initial porosity by progressive enlargement. Numerical triaxial tests at several initial porosities are simulated (the minimal porosity obtained is 0.352). We can note (Fig.2 and Fig.3) that the discrete model allows to describe in a very satisfactory way, the mechanical behaviour of granular material (contractancy, dilatancy, characteristic state).
Figure 3. Numerical results of triaxial tests: volumetric stain versus axial strain for several porosities (σ3 =110 kPa).
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Coupling Finite elements / discrete elements The finite elements included in the discrete element code are similar to those previously described. A thickness e has been given to them to prevent the interpenetration of the soil particles in contact with the two faces of one element. The geosynthetic sheets are defined by three nodes elements jointed together. To guarantee the regularity and the continuity of the contact surface between the triangular elements and the soil particles during the deformation of the sheet, cylinders and spheres of diameter e are placed respectively at the side and on the nodes of each triangle (Fig .4). So and thanks to the continuous surface of con-tact, the frictional forces are preserved when a soil element moves from a sheet element to another (what is not the case when a soil element loses the contact and comes into contact with another soil element). Specific interaction laws are used to characterize the interface behaviour between the soil particles and the sheet elements. The main contact parameters are the normal rigidity, the tangential rigidity and the friction angle. Taking into account the absence of relative roughness between the sheet elements and the soil particles, the microscopic friction angle of contact correspond exactly to the macroscopic friction angle given by the model. The three nodes sheets elements are treated like deformable discrete elements. For this reason, the behaviour of each sheet element is governed by the Newton's second law of motion applied to each node. For each cycle of calculation, the relative position between the sheet elements and the particles of the soil (sphere or assembly of spheres) are considered. The interpenetration of the elements the ones between the others allows the determination of the contact forces supported by each element, and by the way, for the three nodes of the sheet elements via the interpolation functions defined by the finite element model. The behaviour law of each element (defined by equation 1) allows, knowing nodal displacements of the element, the determination of the nodal forces resulting from the sheet deformation. Knowing the forces applied to each soil elements or each node of the sheet elements, it is possible thanks to the New-ton's second law of motion to calculate its acceleration, its speed and the nodal displacement between two steps of successive times. Displacements of the elements the ones compared to the others initiate a new sequence of calculation. Simple applications, carried out to validate the new numerical developments, show the efficiency of the new formulation for static or dynamic applications. We can note that the results of applications using sheet elements are rigorously the same to those obtained with the initial finite element software.
Three nodes finite elements Soil
particles
Cylinders
spheres
Figure 4. Interaction between soil and sheet elements.
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UNDERSTANDING OF THE LOAD TRANSFER MECHANISMS AND ARCHING EFFECT
Description of the structure modelled The transfer of load and the arching effect are one of the major mechanisms governing the behaviour of embankments built over voids or over a network of piles. In order to understand the influence of these two mechanisms a numerical parametric study was carried out in the bi-dimensional case of embankments built over trenches and in the tri-dimensional case of embankments built over a network of piles. In these two cases one part of the load due to the weight of the embankment (W) is transmitted by an arching effect to fix points (piles) or stable areas (at the vicinity of the trench). The capacity of the embankment to develop load transfer mechanisms is defined by an efficacy Ea. The subsidence mechanism necessary to obtain load transfer is governed by the vertical displacement of a horizontal plate based at the bottom of the embankment. The geometry of the modelled embankments is given in Figure 5 and Figure 6. The height H varies from 0.5m to 2.0m. The lateral boundaries are perfectly rigid walls with a friction angle equal to 0°. The bottom boundary conditions used in order to simulate the cap piles or the edges of the trenches are assumed to be perfectly rigid walls having a friction angle of 30°. The moving horizontal plate is a perfectly rigid wall having a friction angle of 0°. The embankment is modelled by discrete elements (8000 particles per m3). The particles shape is given in Figure 7. The particles assemblies present a porosity of 0.36 and have an apparent density of 16kN.m3. The mechanical characteristics have been determined by modelling a triaxial test with a constant lateral stress of 16kPa. The friction angle of the granular material simulated is 39° and the young modulus is around 11 MPa..
D
0.95D
Figure 7. Particle shape.
Figure 6: Geometry of the embankment built over network of piles
H
1.0m
0.4m
Figure 5: Geometry of an embankment built over a subsiding trench
H
1.0m
1.0m
0.5m
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Arching effect obtained for embankments over trenches Simulations were carried out for several height of embankment. The particles are setting to the initial porosity of 0.36 by progressive enlargement as describe previously. The vertical displacement of the moving plate induces progressively a change of the particles interaction and an increase of the vertical load on the fix areas (at the edge of the trench). The efficacy of the arching effect is defined by W/W1E Ba −= where WB is the resulting vertical force applied on the moving plate and W is the weight of the granular column of soil located over the trench. The efficacy and the top surface settlement versus the vertical displacement of the moving plate are given in figure 8.
On figure 8 we can note that the efficacy of the soil embankment is fully obtain for a small vertical displacement of the horizontal plate. Comparing the several curves obtained we note that the efficacy of the granular layer for the load transfer increase with the height of the granular layer. It seems to exist a critic height from which an additional layer of granular material does not influence greatly the efficacy of the embankment. This critic height may correspond to the appearance of an arch, i.e. H~1.5m (Figure 10, 11). The following Figures show three different ways to characterise the arch mechanism in the granular layer. On the Figure 9, a graph gives the vertical displacement of a particle sited at a height Z from the bottom of the embankment for two particles families (Figure 5): particles located above the fixed areas of the bottom boundary (curves on the left) and particles located above the moving plate (curves on the right). On Figure 9 we can note that the vertical displacements of the particles sited at a height greater than 1 m are rather the same for the two particles family. This condition of equal settlement can be used to consider an arch (the particles assembly over the limit of equal settlement move as a unique solid). In this case the height of the arch is approximately 1.0m.
Figure 8. Efficacy and top surface settlement of the embankment
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(c) (d)
(b) (a)
Figure 10: (embankment over trench) Particle displacement for a 0.12m displacement of the horizontal moving plate with (a) H=0.5m; (b) H=1.0m, (c) H=1.5m; (d) H=2.0m (dark red corresponds to a settlement value of 0.12m and dark blue to 0m)
The Figure 10 shows a section of the granular layer for displacement of the horizontal moving plate of 0.12m, the colour map corresponds to the value of the particle displacement (dark blue = no displacement; dark red = 0.12m displacement). The Figure 11 shows in the same sections as in Figure 10 the intensity of shear strain calculated on a Delaunay tessellation of the granular layer (Cundall, 1982). Both Figures 10 and 11 reveal a height of 1.0m for the arch.
Figure 9: (embankment over trench) determination of the top of the arching mechanism
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The arching mechanisms predicted by Terzaghi (Terzaghi, 1943) can easily be observed in the numerical modelling. The interpretation of the results in a local way allows underlining these mechanisms in a very accurate way.
Arching effect obtained for embankments over network of piles Similar simulations than those define previously were carried out for an embankment placed over a network of piles. In this case, the efficacy of the arching effect Ea is defined by: Ea=WP/WT where WP is the vertical force applied by the granular layer on the piles and WT is total weight of the granular layer.
(c) (d)
Figure 11: (embankment over trench) shear strain calculated on a Delaunay tessellation of the granular layer, size of the squares is representing the intensity of shear strain; the upper limit of the represented values is equal to 10 average shear strain value.
(a) (b)
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Figure 12 shows the increase of efficacy with the thickness of the granular layer until a limit of about 90%. A critic height seems to exist in the case of piled embankment too, but the mechanisms of load transfer is quiet different as in the previous application. The shapes of the curves showing the equal settlement plane (Figure 13) is quiet different. The layer located over this plane has the same behaviour than a single block sliding downward (Figure 14, 15). The ‘equal settlement plane’ occurs in this case for a Z-Axis position of 0.35-0.40m.
Figure 13: (piled embankment modelling) determination of the top of the arching mechanism
Figure 12: Efficacy and top surface settlement versus displacement of the horizontal moving
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Figure 15: (piled embankment modelling) Shear strain calculated on a Delaunay tessellation of the granular layer, size of the squares is representing the intensity of shear strain; the upper limit of the represented values is equal to 10 average shear strain value.
(d) (c)
(b) (a)
Figure 14: (piled embankment modelling) Particle displacement for a 0.12m displacement of the horizontal moving plate with (a) H=0.5m; (b) H=1.0m, (c) H=1.5m; (d) H=2.0m (dark red corresponds to a settlement value of 0.12m and dark blue to 0m)
(d) (c)
(b) (a)
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In conclusion, the discrete element method allows reproducing well the transfer of load and the arching effect in a granular soil embankment. Complementary studies are actually developed in order to define the influence of the shape particles and the behaviour of the soil characteristic (friction and cohesion).
APPLICATIONS TO REINFORCED EMBANKMENTS
Description of the structure modelled The geometry of the applications treated is given in figure 5 (H = 1 m, s = 1.5 m and a = 0.6 m). For reasons of symmetry and to prevent long time of calculation, only one square mesh of the embankment will be modelled. The embankment is reinforced by a geosynthetic sheet armed in two orthogonal directions. The tensile rigidity J of the reinforcement, defined for a meter width (T=J ε), is in each direction 1000 kN/m. T, defined for a meter wide, is the tensile force acting in the armed direction and ε the corresponding strain. The soil embankment is assumed to be a granular material issue from 7055 spherical discrete elements (diameter ranging between 0.04 m and 0.08 m) positioned in space with a random distribution at porosity of 0.36. The macro mechanical behaviours of the assembly of particles are those given in figures 2 and 3. The corresponding friction angle of the granular material simulated is in this case 30° and the young modulus is around 60 MPa. The particle density is 29.5 kN/m3, so the apparent density of the granular soil embankment is 18.88 kN/m3. The geosynthetic sheet is modelled with 200 triangular finite elements. The angle of friction between the geosynthetic sheet and the soil particles is 25°. The compressible subsoil under the geosynthetic sheet is assume to be very soft and is modelled by the Winkler's Spring Model (1867). The rigidity of the spring is given by K=ES/D with E the oedometric modulus of the soft soil (depending of the simulation carried out, E=0 MPa or 0.5 MPa), D the thickness of the layer of the compressible soil (D=10 m) and S the surface of influence of each spring. The boundaries conditions are no vertical displacements of the nodes of the sheet over the pile caps and no horizontal displacements of the particles of soil at the edges of the model. The mechanism studied is the deformation of the geosynthetic sheet and the movement in the soil embankment due to the weight of the soil particles.
Pile
Compressible soil
H
s
a
Embankment
D
Geosynthetic
Figure 16. Geometry of the reinforced embankment.
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Numerical results The discrete elements approach coupling with the finite element model allows to determinate the interacting forces between each element, the displacements of the soil particles, the displacements of the nodes of the geosynthetic sheet and the tensile forces acting in each three nodes element in the two directions of reinforcement. The numerical simulations were carried out for comparison with E=0 MPa (Case A) and E=0.5 MPa (Case B). The deformations of the geosynthetic sheet and the displacements of any particles of soil, resulting from the application of the weight embankment, are given in figure 6. The numerical surface settlements obtained on the top of the embankment are reported in table 1 for points S1, S2 and S3 (Fig.6). We can note that the surface settlements are not uniform; the great values being obtained at the centre of the square mesh (point S3).
Table 1. Surface settlements at point S1, S2 and S3.
Point S1 (m)
Point S2 (m)
Point S3 (m)
Case A 0.014 0.023 0.040 Case B 0.011 0.019 0.034
The curves shown in figure 7 give the vertical displacements of the geosynthetic sheet for two cross sections: between the piles (View 1) and at the axis of the square mesh of piles (View 2). The results are given with or without the action of the sub grade soil (Case A and Case B). Due to the membrane effect, the vertical displacements at the centre of the square mesh are bigger than those between the piles. The action of the sub grade soil is important especially in the great displacement areas. By comparison (Tab.1 and Fig.7) we can note that the vertical displacements at the centre of the square mesh are more important than those obtained at the surface level. This is due to the disorganization of the soil particles during the collapse of the embankment on the sheet (expansion and dilatancy).
S2 S3
View 1
View 2
S1
1.5 m
Figure 17. Global view of the modelled embankment.
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In order to evaluate the mechanism of dilatancy, an expansion coefficient Ce was estimated and reported in table 2. Ce is defined as the ratio between the thickness of the soil embankment after the simulation and its initial thickness before simulation (H=1m). The expansion of the soil is correlated to the porosity of the soil. The differences of porosity obtained in different areas of the embankment justify the use of a discrete element model to characterize the behaviour of the soil embankment (the macroscopic behaviour of the discrete elements assembly depends directly of the porosity, Figures 2 and 3). Table 2. Expansion coefficient of the soil embankment.
Point S2 (m) Point S3 (m) Case A 1.059 1.1 Case B 1.045 1.068
The tensile forces acting in the armed directions of the geosynthetic in the two cross sections (View 1 and View 2) are given Figure 8. We can note that the presence of the sub grade soil induce a decrease of the tensile forces in the geosynthetic.
In order to estimate the influence of each component on the behaviour of the embankment we have reported in table 3 the following ratios:
-0,14
-0,12
-0,1
-0,08
-0,06
-0,04
-0,02
00 0,5 1 1,5position (m)
Case A, View 1Case A, View 2Case B, View 1Case B, View 2
Ver
tical
dis
plac
emen
t (m
)
Figure 18. Vertical displacements of the geosynthetic sheet.
0
5
10
15
20
0 0,5 1 1,5position (m)
Case A, View 1Case A, View 2Case B, View 1Case B, View 2
Tens
ile fo
rce
(KN
)
Figure 19. Tensile forces supported by the geosynthetic sheet.
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− the efficacy of the pile Ep : ratio between the vertical loads transmitted to the piles (by membrane and arching effects) and the weight of the soil embankment, − the efficacy of the geosynthetic Eg : ratio between the vertical loads transmitted to the geosynthetic by membrane effect and the weight of the soil embankment, − the efficacy of the supporting soil Es : ratio between the vertical loads transmitted to the supporting soil and the weight of the soil embankment, − the efficacy of the arching effect Ea : (Ea = Ep - Eg). Table 3. Efficacy of each component of the reinforced structure.
Ep Ea Eg Es Case A 100 % 66 % 34 % 0% Case B 88 % 67 % 21 % 12 %
We can note (Tab.3) that the parts of load transmitted by arching effect are in the two cases (Case A and Case B) very important (67 %). We can conclude that for the simulated soil (assembly of great particles and for the chosen geometry) there is an important mechanism of transfer of load and formation of an arch in the soil embankment.
CONCLUSION
This model, coupling finite element method and discrete element method, let us think that it is a good way to simulate the behaviour of an embankment reinforced by piles and geosynthetics. The coupling finite elements / discrete elements makes it possible, in this case, to use the advantages of each method: a continuous model to describe the fibrous structure of the geosynthetic sheet and its interaction with the soil, and a discrete model to describe the behaviour of the granular soil. As shown, the main interest of the coupling MEF/MED is to take into account the membrane behaviour of the sheet and the mechanism of transfer of load into the soil embankment. However, a particular attention must be paid to the determination of the micro-mechanical parameters of contact to insert into the model. Moreover, a specific procedure of calculation must be carried out to place the particles of soil at a given initial porosity. For a better understanding of the mechanisms involved in embankments built on soft soil and reinforced by piles and geosynthetic, additional modelling works need to be carried out. In particular, complementary studies are needed to confirm the first results obtained, using clusters (rigid assembly of particles), various granular distributions of particles, a great number of particles for modelling the soil, several geometries of networks of piles and various types of reinforcement. This work, performed for frictional granular soil, can be extending to cohesive material. The results of the numerical model will be confronted with experimental results obtained on full-scale instrumented experiments (Villard et al., 2004; Chew et al., 2004). These works can be concluding by the realization of design abacus or by the establishment of analytical design methods. The numerical study of load transfer in granular layer implemented in different configurations shows a great variety of mechanisms. The numerical modelling allows understanding the mechanisms in a local-scale as in a global scale. The influence of more parameters has been studied as for example the particle shape or grading, mechanical properties of the granular layer. This study has to be carried on: cohesive granular material, implementation of additional load… Confrontation of numerical, experimental results will be carried out.
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