High energy impact on embankments: a numerical discrete approach

Transcription

1 High energy impact on embankments: a numerical discrete approach J-P. Plassiard & F.V. Donzé Laboratoire Sols, Solides, Structures INPG, UJF, CNRS RNVO - Grenoble, France Frederic.Donze@hmg.inpg.fr and P. Plotto I.M.S.R.N, Montbonnot, France pierre.plotto@imsrn.com ABSTRACT A discrete elements model is used to simulate the behavior of reinforced soil embankments submitted to high energy impact due to rockfall. The results of the model are compared to experimental data obtained from impact tests on full scale embankments. The first results when using a simplified discrete element model show a good agreement between numerical and experimental data. Improvements of the numerical model are under way and should contribute to the formulation of design criteria for reinforced embankments against rockfall. INTRODUCTION Reinforced embankments are currently used for rockfall mitigation when classical rockfall barriers can not deal with high energy or repeated impacts. These protective structures are mainly located in mountainous area to protect highways, railways and inhabited zones. After dealing with trajectography studies to determine the best site to built it up, the embankment must be strong enough to stop the potentially dangerous falling rock and must be capable of remaining sufficiently preserved to give an efficient protection for later impacts. Until now, no clear dimensioning rules had been established. This lack of regulation may be linked to the fact that the technology used to design these structures is still evolving fast and specific studies must be carried out for each case. The present work is a first approach to study the behavior of a reinforced soil embankment with a numerical method based on a discrete element method. The choice of this method has been made because it allows an interesting description of the material during the impact process, in particular the flow of the granulate material when the dynamical loading induces an important degradation of structure (Hentz, 2004).

2 The numerical code used here, SDEC, for Spherical Discrete Elements Code (Donzé & Magnier, 1997) is based on a smooth contact discrete element approach. Some of the characteristics of this software are first presented. Then, the full scale experimental testing of reinforced embankments with impacting rock block driven by the Politcenico di Torino in partnership with Tenax co. (Peila et Al., 2002) is presented in details. Finally, the numerical configuration is presented and the results are discussed. DISCRETE MODELING Introduction The numerical model is based on the a discrete element method using spherical elements. The different components of the studied embankment, are represented by different sets of discrete elements which can have a randomly distributed size. These sets of discrete elements are identified by using different and adequate physical and mechanical properties. The main physical property used here concerns the mass : according to the density of the simulated material, the mass of each discrete element is determined depending on its size and the packing arrangement. The mechanical properties are partly controlled by the chosen interaction laws. Interaction laws : mechanical consideration When these interactions have a tensional strength, the interaction law is qualified as a link, otherwise, it is just a purely frictional contact. In all cases, the interaction between two spherical discrete elements implies both, a normal force and a shear force. The normal force is linear, with a stiffness constant which depends on the square of the radius of the smaller interacting element, thus introducing a virtual local contact surface which induces a scale independency of the elastic properties, i.e., the local elastic parameters are adjusted to the characteristic size of the discrete element in order to create a global stiffness insensitive to the size of the discrete element. This adjustment law has the following form, ab Sint 1+ α Kn = E0 (1) D ab, init β (1 + ν) + γ(1 αν) ab ab 1 αν K s = K n (2) 1+ ν ab ab where, is the normal stiffness and K, the tangent stiffness. S is the virtual local K n s D, 0 interaction surface, a b init the initial distance between the centers of spheres, E the global reference Young modulus of the elements, ν is the Poisson s ration and α and β, two adjustable parameters. Non linear behaviors are deduced from the chosen yield criteria. As written above, two types of interactions exist, either frictional or linking. The first one corresponds to Coulomb s frictional law. There is no resistance to traction and tangential forces and motion is allowed as soon as the following equation is verified. f ( F, F ) F tan( Φ ) F = 0 (3) n s s c n int 2

3 F and n Fs are the normal and shear forces acting on the interaction, while c is the residual friction angle. The second one is equivalent to the Mohr Coulomb criterion. When one of the following condition is verified, as the link is broken the resulting behavior is purely frictional, as the link nature has been broken. These criteria are more complex than the last one, with the presence of the cohesion C 0, the internal frictional angle Φi ant the resistance to tractiont. Fs tan( Φ i ) Fn SintC0 = 0 f ( Fn, Fs ) (4) SintT Fn = 0 Φ Other specific parameters are used in the code, such as local interaction softening or damping ratio. The first one defines the local behavior when the yield criterion is reached. By varying this value, the medium can exhibit natures varying from quasi-brittle to perfectly elasticplastic. Damping is a factor that acts directly on the components of Newton s second law of motion. This factor must be handled with care because the physical basis of the damping process during a dynamical loading is not always well defined. The restitution coefficient is needed if the total elastic energy is not returned when relaxation occurs. Iterative process A simulation corresponds to an iterative process with three distinct steps. The first one established the neighbor-list for possible new contact between discrete elements, then the forces acting on each elements are determined. Finally the resolution of Newton s second law of motion and temporal integrations using an explicit scheme gives the new position, velocity and acceleration of each discrete element. FULL SCALE EXPERIMENTAL TESTS Geogrid reinforced soil embankments subjected to high energy rock impact have been built and tested by TENAX, in collaboration with the Politecnico di Torino. One part of this project included the impact tests on two embankments on which the present study focuses. The first embankment was symmetric (Figure 1) and was 4.2 m high. The width of the crosssection measured 5 m at the bottom and 0.9 m at the top. The angle between the horizontal plan and the upstream face approximated 65. The embankment was made of seven superposed layers of 0.6 m each, which were compacted and reinforced with geotextile and geogrids. 3

4 Figure 1. Cross-section of the real case (from Oggieri et Al., 2004). Geogrids are generally used to strengthen constructions laterally and correspond to a steel mesh-formwork. They are constituted of two connected grids inserted between the soil layers and one at the surface. A hook is then attached between the two section extremities in order to ensure the stability of the global construction (Figure 2). The geotextile used were produced by TENAX and tagged TT045, corresponding to a traction strength of 45 KN/m (TENAX Company, 2002). Figure 3 shows the maximum tension force for this kind of material used for the embankment. geotextile hook geogrid 0.52m 0.6m Figure 2. Organization of a soillayer and its reinforcements(from Oggeri et Al., 2004) m Figure 3. Traction tests for several TENAX geotextiles. L=TT045 (from Tenax Compagny, 2002). 4

5 Each soil-layer is confined in a sheet of geotextile but is not attached to the other one which means that the soil-layers are just superposed. The soil used as fill came from the test site. It has little cohesion and the given friction-angle corresponds to the value before compaction (see Table 1). It seems that this value has to be increased when speaking of the internal friction-angle. The compaction reaches a ratio of 91 per cent for the compacity, suggesting an increase of value to for the internal friction-angle. γ' E[kPa] ν φ' c [kpa] Table 1. Mechanical properties of the soil for the two embankments (Peila at Al., 2002). The second case that was studied corresponds to the same embankment, but without any geogrid in the impacted area, only geotextile. This edge of the surface is 2m large, which is a little more important than the impacting boulder-size. Figure 4. Construction of the embankment (from Oggeri et Al., 2004). NUMERICAL MODELING A simplified numerical model was first built up to simulate the first full scale experiment (Figure 4). This simplification was made in order to check the capability of the model to reproduce this specific impact process. This model used about discrete elements. The geogrids were represented by specific sets of elements and in this first approach, the presence of the geotextile was neglected. In order to ensure the stability of the structure, each layer was confined by a network of discrete elements representing the geogrids. The global geometry was kept as close as possible to the real case, thus each set of discrete elements representing soil layer was 0,6 m thick. In attempting to remain close to the real behavior, the mechanical properties of the lateral geogrids elements were weakened along the transition between two sets of soil-layers elements. Mechanical properties of each structure of this model were evaluated with respect to the real properties. The interactions between geogrids discrete element were chosen to be elastic-plastic. 5

6 The second numerical model was built in a more complex way (Figure 6). First of all, more than discrete elements were used. Here both geotextiles and geogrids were computed. Here, a geogrid discrete elements set corresponds to a horizontal separation between two soil layers and to the lateral part, as in the real case. With an increase in the number of discrete elements used, the size of the elements of the geotextiles, the geogrids and the soil can be refined, thus allowing to reach a thickness of 0,05 m for the reinforcing structure components. Moreover, the geotextile sheets are now modeled. Figure 5. Cross-section of the first model and impacting boulder The contact between the two geotextiles separating the two soil layers is computed as purely frictional. However, in order to limit the number of element of these structures, only the geogrids are simulated on the lateral extremities of the soil layer, and the discrete elements representing the geotextile are connected at their extremities to the geogrid discrete elements. Finally the boulder-apexes are cut in order to keep the exact geometry of the real impact boulder. Figure 6. Cross-section of the refined model after generation of randomly organization for the soil medium. 6

7 To approximate the mechanical behavior of the numerical model of embankment, several parametric tests were performed. Concerning the Geogrid elastic-plastic and the geotextile quasi-brittle behavior, the characteristic values were obtained by setting up uniaxial numerical tests. Soils parameters are more difficult to reach, and tri-axial test must be performed to evaluate the global behavior. COMPARISON BETWEEN EXPERIMENTAL AND NUMERICAL RESULTS Results of the full scale experimental tests After the reinforced structure was impacted, the boulder was contained and was moved to the back face after this test (Figure 7). After removing the block, a hole of a size equivalent to those of the boulder appears in the front face with an extreme depth of 0,91m. The back face is also deformed, but each layer seems to have reacted separately because displacements are not regular along the vertical direction. This independent layer-behavior seems to be created by the geotextiles which have resisted to the impact on the back face. There is also an important displacement of the top layer in the vertical direction. This phenomenon might be due to the lack of stresses in this direction. Figure 7. front and back faces of the reinforced embankment after the impact. The block was humanly moved to the back face (from Oggeri et Al., 2004). The kinematics of the boulder during the impact is deduced by a camera which gave access to the position every 0,025 s. In Figure 8 the position of the boulder is given. The topmost curve corresponds to the resulting displacement, while the lowermost and almost horizontal curve represents the horizontal component in the direction of impact. The third negative curve corresponds to the vertical component. The linear part of these curves for times lower than 0,025 s indicates that the impact has not occurred yet. On the contrary, the linear-like evolution for times exceeding 0,125 s shows that the dynamics solicitation between the boulder and the embankment is over. The impact phenomenon appears to last 0,1 s for this experimental test. 7

8 Displacement (m) Time (s) Figure 8. Displacement versus time of the impacting boulder before, during and after the impact phase (from Oggeri et Al., 2004). The second full scale experimental test is equivalent to the first one, but without geogrids in the impacted zone (Figure 9). This test was performed to evaluate in a better way the influence of the geotextiles. The structure collapses however the block is stopped by the embankment. In the simulation point of view, this test was used to define the dissipative process that should be affected to the soil. Indeed, as the soil does not transmit the totality of the forces, a set of purely elastic spheres would not fit. By using this test as a first approach, a local damping coefficient is easier to define because the soil action should be more dominating as in the reinforced case. After having quantitatively scaled this coefficient, all the mechanical parameters were defined. Thus, the simulation with the reinforced embankment should contribute to the first step of validation. Figure 9. Side view after the impact of unreinforced embankment (from Peila et Al., 2002). Presentation of numerical results The first results presented here correspond to the coarse model. On Figure 10, the resulting displacement (the positive curve) but also the vertical and horizontal displacement components agree with the real data (Figure 8). The analysis of the acceleration curves from 8

9 the output shows that the impact phase last 0,08 s, which is very similar to the real value of 0,1 s. Displacement (m) Time (s) Figure 10. Displacement versus time of the impacting boulder before, during and after the impact phase for the coarse simulation. These numerical results show that the range of penetration of the boulder in the embankment is comparable to the one noted in the experimental case. However, the top layer in the numerical simulation shows a displacement in the vertical direction, which is not seen in the experiments. This happens because this first numerical approach of the structure does not allow the independent displacements of each layer. The perturbations on the back face are more or less uniform although the weakened zones of the geogrids have broken themselves (Figure 11). The effect of the present structure of geogrids allows diffusion of displacement in the major part of the embankment. Thus, this model can not represent correctly the effect of reinforcement, although duration and deep values of the impact have the same range of experimental values. This observation justifies the creation of the complex model that reproduces the independent behavior of each soil layer by decoupling the geogrid networks at the different layer interfaces. It is indeed very important to describe this type of displacement, as the geotextiles and the geogrids should have localized the deformation more. This needs to be the basic configuration for the reinforcing structures that should avoid the unrealistic ripping of the internal soil layers. However, simulations using this second numerical model are still under way. Figure 11. Front size and back size of the coarse model, with the bloc impacting the embankment. 9

10 CONCLUSION The first aim of this study is to understand the degradation process of classical embankment during an impact loading. Thus, depending on reinforcement configuration, it will contribute to the formulation of a design criterion. The simulations were performed with the discrete element code SDEC. Full scale experimental tests achieved in Trento (Italy) with boulders impacting reinforced and unreinforced embankments are used to validate the present approach. The first results show that a good quantitative agreement is observed for some data. However, the global behavior of the model is not relevant yet, justifying the creation of a new refined model. This second model takes into account more particularities than the first one. Mechanical parameters are established with simple tests, except to simulate the dynamical dissipation for the soil, which remains a complex problem to tackle but can be calibrate directly from the unreinforced full scale test. ACKNOWLEDGMENTS Thanks to IMS-RN company for its financial support. The authors would like to acknowledge D. Peila and C. Oggeri for fruitful discussions and providing experimental data, under agreement of P. Recalacati from TENAX company. REFERENCES Donzé F.V., & S.-A. Magnier, «Spherical Discrete Element Code» In: Discrete Element Project Report no. 2. GEOTOP, Université du Québec à Montréal, Hentz S., L. Daudeville & F. Donzé, Identification and validation of a discrete element model for concrete. Journal of Engineering Mechanics. 130, 6, Oggeri, C., Peila D & Recalcati P. Rilevati paramass. In Peila D. (ed.), Bonifica di versanti rocciosi per la protezione del territorio. Trento, Peila D., Oggeri C., Castiglia C., Recalcati P. & Rimoldi P. Testing and modeling geogrid reinforced soil embankments subjet to high energy rock impacts. In Delmas, Gourc & Girard (eds.) Geosynthetics 7 th ICG, Swets & Zeitlinger Tenax Compagny, Technical Agrément Certificate N. 580/02, Geogrid soil reinforcement and stabilisation system. TENAX SpA,

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