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New developments in the modeling and the design of geosynthetic reinforcements of platforms subjected to localized sinkholes

Laurent Briançon1, Pascal Villard2 and Bastien Chevalier2

1Conservatoire National des Arts et Métiers, 292 Rue Saint-Martin, 75141 Paris Cedex 03, France; PH 33 (0)1 58 80 87 58; FAX 33 (0)1 58 80 86 01, email : [email protected] 2Laboratoire 3S-R, Grenoble Universités, UJF, INP, CNRS, BP 53, 38041 Grenoble Cedex 09, France; PH 33 (0)4 56 52 86 28; FAX 33(0)4 76 82 70 43; email: [email protected]

ABSTRACT One of the techniques currently used to reinforce road and railway platforms in areas subjected to localized sinkholes is reinforcement by geosynthetic sheet. To improve the existing design methods, based on simple assumptions, a new approach has been developed, taking better into account the real behavior of this reinforcement, in particular the geosynthetic behavior in anchorage areas and the increase in stress at the edges of the cavity. A numerical study based on the coupling between the finite element method (FEM) and the discrete element method (DEM) was performed to validate the new analytical approach and verify the assumptions. Comparison of the results obtained by this new analytical method with measurements of a full-scale experiment and the results of numerical model confirmed the relevance of these new developments.

INTRODUCTION Construction of highways or railway lines requires detection campaigns to locate sinkholes in areas at risk. However, some cavities cannot be detected, or appear after construction of the structure (karstic cavities). A solution commonly adopted in areas at risk is to use reinforcement techniques; those with one or several geosynthetics are attractive because they are easy to implement and inexpensive.

Experimental and theoretical research into this topic has given rise to analytical design methods (British Standard BS 8006, 1995; Villard et al., 2000). Using simple assumptions, it is possible to predict vertical displacements of the geosynthetic sheet and surface settlement, knowing the stiffness of the geosynthetic and size of the cavity. It is generally assumed that the geosynthetic is fixed at the edge of the cavity.

To improve the usual design methods, a new approach has been developed (Briançon and Villard, 2008); it is based on the existing methods to describe behavior of the geosynthetic over the cavity (membrane effect) but takes into account the geosynthetic behavior in anchorage (friction and sliding) areas and the increase in stress at the edge of the cavity.

664GeoFlorida 2010: Advances in Analysis, Modeling & Design(GSP 199) © 2010 ASCE

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This new method could be applied to continuous sections of linear structures and to the specific cases of overlapping geotextiles where the boundaries conditions are different (Villard and Briançon, 2008).

To understand the behavior of this reinforcement and to take into account more relevant assumptions, a numerical study based on the coupling between the finite element method (FEM) and the discrete element method (DEM) was performed (Villard et al., 2009). Comparison of the results obtained by this new analytical method with measurements of a full-scale experiment and the results of numerical model confirmed the relevance of these new developments.

NEW DESIGN METHOD PROPOSED The new procedure uses mechanisms and assumptions proposed in the existing design methods and validated by full-scale experiments or laboratory tests: - The load q transmitted to the geosynthetic sheet results from the weight of the

collapsed area of soil above the cavity and from overload p applied to the fill soil surface. It is evaluated using the Terzaghi method (1943), considering that the soil immediately above the cavity tries to move in a vertical column between the adjacent masses of soil which have remained stable (Figure 1). The shear strength along the slip lines resists to the displacement of the active soil mass, reducing stresses on the geosynthetic sheet above the cavity and increasing vertical stresses at the edge of the cavity.

- Above the cavity, as particles rearrange, the apparent soil volume increases. This increase is linked to the nature, granular distribution, initial compactness and state of stresses applied to the material. The ratio between the new soil volume and the initial soil volume is called the expansion coefficient Ce. The expansion of soil may occur in cylindrical soil collapse (Figure 1).

- Due to their structure, geosynthetics have low bending rigidity and can therefore be strained only by tensile forces. When they are submitted to stresses that are perpendicular to their horizontal plane, they take the shape of a membrane (Giroud, 1995) so that the tensile forces guarantee the static equilibrium of the sheet (Figure 1).

Figure 1. Usual scheme of subsidence.

Membrane effect

Soil expansion Cylindrical soil

collapse above the cavity

τ

Overload p

Load q


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New developments based on experimental results (Briançon et al., 2006) are proposed to improve the design method. The experiment was performed on an instrumented embankment (30 m long by 1 m wide) submitted to localized sinkhole. This experiment, used also for comparison with the numerical model, consisted of a granular layer of a thickness of 0.5 m resting on a geosynthetic sheet reinforced in the longitudinal direction. A 2 m long and 1 m wide cavity, filled with two balloons, was first implanted in the subsoil under the geosynthetic sheet, 2 m from one end of the embankment. The progressive emptying of the balloons then made it possible to reproduce the subsidence mechanism. The geosynthetic used was a non-woven needle punched geotextile reinforced by polyester yarns in the main production direction. The granular layer was made of coarse elements of diameters ranging from 0.02 to 0.04 m. The Geodetect System (Briançon et al., 2006) measured the strains in the geosynthetic reinforcement continuously during the experiment at many points. Manual measurements were taken during the experiment to obtain the surface settlements and vertical displacements of the sheet above the cavity.

From this experiment, it was noted that, in anchorage areas, the friction forces between the soil and the sheet equilibrate the horizontal tensile force (TA) induced in the geosynthetic sheet by the membrane effect at the edge of the cavity (Figure 2). The mobilization of this friction requires a relative displacement between the geosynthetic sheet and the adjoining soil. The friction at the soil / geosynthetic (soil/GSY) interfaces in the continuous sections of structures and at the geosynthetic / geosynthetic (GSY/GSY) interface in the overlapping areas are described by the Coulomb friction laws. The strain developed on the geosynthetic in these areas induces a displacement UA at point A.

Above the cavity, under the action of the load applied to it, the geosynthetic will become deformed so that the change in geometry becomes significant. At the edge of the cavity, due to friction between the curved sheet and the corner of soil, we can notice (Figure 2) a decrease in the tensile force in the geosynthetic according to the change in orientation of the sheet (TA < Tmax).

Figure 2. New mechanisms taken into account in design methods.

Mechanism at the edge of the cavity

Displacement of the sheet in anchorage

T max

TA ϕA A


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The new design method takes into account the mechanisms at the edge of the cavity and the mobilization of the friction in the anchorage areas for different boundary limits. With this method, the general procedure required to determine the mechanical properties of the reinforcement includes: - determining load q applied to the geosynthetics, depending on the overload and

the characteristics of the cover soil, - determining displacement of the geosynthetics, considering its membrane

behavior and its stretching in the anchorage areas, - determining soil settlement, depending on its physical properties.

Simplified formulas were obtained for the continuous sections (Briançon and

Villard, 2008) of linear constructions reinforced by a monodirectional geosynthetic sheet. In this case, boundary conditions allow the assumption that the anchorage lengths on either side of the cavity are long enough.

In the overlapping areas, the friction to be taken into account was not only the friction between the soil and geosynthetic, but also the one acting between the two-geotextile sheets. For this case, it is necessary to take into account the equations corresponding to an infinite sheet for one side of the cavity and equations corresponding to a sheet with free extremity for the other side.

A design abacus was proposed from the new approach (Briançon and Villard, 2008). This abacus gives the maximum tensile force, optimal overlapping length and surface settlement for a given geometry. The geosynthetic tensile force must be designed with equations drawn up for continuous sections and geosynthetic vertical displacement and surface settlement must be designed with equations drawn up for overlapping sections. In order to validate the assumptions proposed in the analytical approach, an original numerical study based on a coupling between the Finite Element Method (FEM) and the Discrete Element Method (DEM), was performed.

DESCRIPTION OF THE NUMERICAL MODEL The numerical model used is a specific three-dimensional code developed to describe the behavior of earth structures reinforced with geosynthetic sheets under large displacements.

The finite element model allows restoring the behavior of the geosynthetic sheet by the mean of triple-node triangular elements of low thickness (Villard and Giraud, 1998) jointed together. Using this model, the fibrous structure and the directions of reinforcement of the geosynthetic can be easily taken into account. So the membrane and tensile behaviors of various types of geosynthetics can be correctly modeled (no bending or compression in fibers).

The discrete element model, based on the molecular dynamics approach (Cundall and Strack, 1979), is used to restore, by the mean of a set of particles interacting at contact points, the behavior of granular materials under large displacements. The algorithm of calculation used consists in successively alternating the application of Newton's second law of motion to the particles and force-displacement laws to the contacts. Using this type of model, it is possible to take into


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account complex mechanisms such as rolling, expansion, transfer of load, arching effect and collapses. The elementary particles are spheres jointed together to form clusters with various shapes in order to restore the behavior of natural soil. Interaction laws, defined at local scale, make it possible to reproduce the global macroscopic behavior of the particle assembly. The elastic behavior depends on two local contact parameters: normal stiffness and shear stiffness. The plastic behavior is restored using a frictional contact failure criterion characterized by a microscopic friction angle.

Specific interaction laws are used to describe the interface behavior between the soil particles and the triangular finite elements. The contact parameters are the normal contact stiffness necessary to guarantee no major interpenetration between the finite and discrete elements, tangential contact stiffness and the interface friction angle to define the frictional failure criterion.

In accordance with the algorithm of calculation, the displacements of finite and discrete elements are managed, knowing the contact forces acting to each element, by Newton's second law of motion applied between two steps of successive times. At each calculation step, the interacting contact forces are deduced from the updated overlaps between the elements and particles. The contact forces between two jointed finite elements are obtained using the basic relations characteristic of the mechanical behavior of the finite triangular elements knowing the stretching and displacement of each node. The numerical model can be used for quasi-static or dynamic applications. COMPARISON BETWEEN ANALYTICAL, EXPERIMENTAL AND NUMERICAL RESULTS The experiment used for the comparison is the one described before and reported in details in Briançon et al. (2006). Due to the symmetry, the numerical model was 10 m long by 0.5 m in width (Figure 3). The granular material was modeled with 10000 clusters (diameters ranging from 0.02 m to 0.04 m) made of two overlapping particles and maintained in position by rigid walls. The micro-parameters of contact were chosen in order to resituate the experimental behavior of the granular soil (peak friction angle of 44°).

Figure 3. View of the numerical model at the end of the numerical process.

2 m 2 m

6 m

0.5 m


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The rigid subsoil was modeled by a set of spherical particles of 0.04 m diameter for which only vertical displacement was allowed, and no rolling admitted. The vertical displacement of the subsoil particles was governed by an elastic layer of 0.5 m in height and with an elastic modulus of 250 MPa.

The geosynthetic sheet was modeled with 1360 triangular finite elements of thickness 0.005 m. The 2 m long part of the sheet was free; unlike the 6 m long part which was fixed at its extremity. The non-woven needle punched support was modeled by a set of 8 orientations of fibers uniformly distributed in a plan with an equivalent tensile rigidity of 25 kN/m. The polyester yarns were modeled by specific fibers oriented in the longitudinal direction with an equivalent tensile rigidity of 1100 kN/m. The friction angle between the geosynthetic sheet and the granular soil was 30°, while that between the subsoil and the geosynthetic sheet was 25°.

The numerical sample was first equilibrated under gravity using a horizontal plate over the cavity to prevent any vertical displacements. The activation of the subsidence mechanisms was obtained by removing the horizontal plate.

The mechanisms studied were the stretching and the sliding of the geosynthetic sheet in the anchorage, the vertical displacements of the geosynthetic sheet over the cavity and the expansion of the soil particles assembly.

The comparison of the numerical an analytical strain values in the

geosynthetic sheet (Figure 4) with those given by the Geodetect System shows that both the frictional behavior in the anchorage areas and the increase in strain (and tensile force) at the edges of the cavity are well taken into account.

The mean difference in strain results from the assumption of a uniform vertical load applied over the cavity, which is not completely satisfactory due to the large displacements and transfers of load occurring in the granular layer. In fact, large displacements of the granular assembly induce tangential forces that lead to an increase of strain in the part of the geosynthetic sheet located over the cavity, which is not taken into account in the actual design method.

0

0,4

0,8

1,2

1,6

2

-3 -2 -1 0 1 2 3 4 5 6

Numerical

Analytical

Experiment

Exp. (5 months later)

Longitudinal position from the middle of the cavity (m)

Stra

in (%

)

Figure 4. Comparison of the strains in the geosynthetic sheet.


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The arching effect, not very significant in the case studied (thickness embankment of 0.5 m) allows a good approximation of the vertical displacement of the geosynthetic sheet (Figure 5). For great values of the thickness embankment the assumption of Terzaghi was probably not well-adapted and needed new development.

Another analytical assumption, actually discussed is connected to the use of the

expansion coefficient Ce. The figure 6 shows clearly that the areas submitted to an increase of volume are located at the vicinity of the edge of the cavity. The part of the granular assembly sited over the geosynthetic sheet at the axis of the cavity is not submitted to shear strains that may induce an increase of volume. The fact that the expansion coefficient is not constant remains problematic because its value has a great influence for the prediction of the vertical surface settlement.

CONCLUSION To improve the design of geosynthetic reinforcements of platforms subjected to localized sinkholes, a new approach has been developed taking into account new mechanisms as the geosynthetic behavior in anchorage areas and the increase in stress at the edge of the cavity due to the membrane effect.

The comparison between numerical, analytical and experimental results shows that the numerical and the analytical models reproduces the main mechanisms

Figure 6. Areas submitted to an increase of volume.

NumericalAnalyticalExperiment

Vertical displacement (m)-0.25

Longitudinal position over the cavity (m)- 0.5 0 0.5 1 -1

-0.05

-0.2

-0.15

-0.1

Figure 5. Comparison of the vertical displacements of the geosynthetic sheet.


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involved during the subsidence of the reinforced embankment: membrane effect, stretching, friction, and sliding of the geosynthetic sheet in the anchorage areas, and the behavior of the granular soil layer under large displacements.

The main differences are due to the simplified assumptions used to develop the analytical design method: the vertical loads uniformly applied on the geosynthetic sheet, no frictional forces between granular soil and the part of the geosynthetic sheet located over the cavity and constant value of the expansion coefficient Ce.

Moreover, for the case studied the differences between the analytical, numerical and experimental results obtained are quite satisfactory.

To improve the analytical method proposed, new developments need to be considered to a better understanding of load transfer and expansion phenomenon in the case of high granular layer thickness or cohesive soil.

REFERENCES Briançon L., Nancey A., Robinet A. and Voet M. (2006). “Set up of a warning

system integrated inside a reinforced geotextile for the survey of railway”. Proceedings of the Eighth International Conference on Geosynthetics, “8th ICG”. Yokohama, Japan, 18-22 September 2006,857-860.

Briançon, L. and Villard, P. (2008). “Design of geosynthetic reinforcements of platforms subjected to localised sinkholes”. Geotextiles and Geomembranes, 26(5), 416-428.

British Standard BS 8006 (1995). “Code of practice for strengthened/reinforced soils and other fills”. British Standard Institution, London, 162p.

Cundall P.A. and Strack O.D.L. (1979). “A discrete numerical model for granular assemblies”. Geotechnique, 29(1), 47-65.

Giroud, J. P. (1995). “Determination of geosynthetic strain due to deflexion”. Geosynthetic International, 2(3), 635-641.

Terzaghi, K. (1943). Theoretical soil Mechanics. New York, Wiley. Villard P. and Briançon, L. (2008). “Design of geosynthetic reinforcements of

platforms subjected to localised sinkholes”. Canadian Geotechnical Journal, 45(2), 196-209.

Villard, P. and Giraud, H. (1998). “Three-Dimensional modelling of the behavior of geotextile sheets as membrane”. Textile Research Journal, 68, 797-806.

Villard, P., Gourc, J.P. and Giraud, H. (2000). “A geosynthetic reinforcement solution to prevent the formation of localised sinkholes”. Canadian Geotechnical Journal, 37(5), 987-999.

Villard P., Chevalier B., Le Hello B. and Combe G. (2009). “Coupling between finite and discrete element methods for the modelling of earth structures reinforced by geosynthetic”. Computers and Geotechnics, 36, 709-717.


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