Numerical simulations of structures with geomaterial using Z-soil. Philippe Menétrey INGPHI SA Place St-François 2, CH-1003 Lausanne

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1 Numerical simulations of structures with geomaterial using Z-soil Philippe Menétrey INGPHI SA Place St-François 2, CH-1003 Lausanne Keywords: numerical analysis, retaining wall, stockade, anchorage plate, crack propagation in concrete Abstract The purpose of this contribution is to present some numerical simulations of structures using Z-soil. Three recent structures are considered; first, the strengthening of an existing stockade, then the new loading of a retaining wall and finally the crack propagation in a concrete anchorage plate. Theses cases are presented as well as the developed numerical models and the main results. The numerical analysis with Z-soil was useful for all these practical applications. First, it allows proving that the existing stockade has to be strengthened with a soil anchorage. Then, it shows that the new loading of the retaining wall creates little deflection and the safety against overturning is acceptable. Finally, the crack propagation in the concrete anchorage plate allows demonstrating that the chosen system was not safe enough. For all these applications, the sensitivity of the numerical analysis is investigated that allows showing that the type of the failure criterion modifies the safety factor against overturning of the stockade, the size of the finite element mesh influences the safety factor against overturning of the existing retaining wall and the flow rule influences the carrying load and the crack propagation in the concrete anchorage plate. Consequently, numerical simulations of structures with geomaterial have to be undertaken with great care. 1. Introduction Three different practical applications of the computer program Z-soil are considered here: The rehabilitation of an existing stockade 55

2 The new loading of an existing retaining wall The crack propagation in a concrete anchorage plate These applications are presented as well as the associated numerical model. It has to be mentioned, that these are practical applications and that efficiency of the computation is also one point to address. Therefore, finishing touches were not put to the finite element mesh demonstrating the requirement for practical applications of powerful type of finite element. Another preliminary remark concerns the safety factor. All the numerical simulations were performed using characteristic values of the soil and the load. The safety factor was addressed in a global manner at the end of the computation. Different safety factors for loading and resistance effects (required by the actual standards) are not suitable for numerical simulations of structures with geomaterial because the soil behaviour cannot be classified in loading or resistance effect. 2. Rehabilitation of a stockade An old stockade overhanging Montreux had to be rehabilitated. The stockade is composed of an old retaining wall made of stone and an overhanging concrete plate for the pavement of the road as illustrated in Fig. 1. The retaining wall shows some deflections and cracks. Furthermore, the concrete pavement has to be renewed. Fig. 1: view of the existing stockade The soil is composed of gravel with characteristics as presented in Tab. 1 and rock underneath which is not reached. The traffic load due is 5 kn/m 2. 56

3 Failure criterion γ E ν φ c ψ [kn/m 3 ] [kn/m 2 ] [ ] [kn/m 2 ] [ ] Gravel Mohr-Coulomb Tab. 1: material characteristics for the stockade model The first analyse was to investigate the existing stockade with the finite element mesh shown in Fig FE MESH t = 5.0 [day] Author : Philippe Menétrey Date : :51:16 File : C:\Zsoil\Collonge\publication\C actuel Title : Stockade: existing state Fig. 2: mesh of the existing stockade The stability analysis of the existing stockade was performed and it allows showing that the safety factor against overturning was very little as it only reaches 1.1. The failure mechanism is shown in Fig. 3 (left). The first strengthening method to be considered was to enlarge the foot of the wall. However, the failure mechanism was more important as it is included the wall above as shown in Fig. 3 (right). The resulting safety factor was slightly increased up to 1.2. Consequently, the only way to increase the stability of the stockade is to add soil anchorage. A little anchorage force of 400 kn/m allows increasing the safety factor. The obtained failure mechanism is presented in Fig. 4. It has to be mentioned that the failure criterion influences the stability analysis. Using a Mohr-Coulomb failure criterion (smooth version according to Menétrey and Willam [1]) the safety factor is 1.7. Using a Drucker-Prager failure criterion with plain strain adjustment leads to a reduced safety factor of 1.5 as illustrated in Fig

4 e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e-01 t = 5.0 [day] Safety= 1.1 Author : Philippe Menétrey Date : :51:16 File : C:\Zsoil\Collonge\publication\C actuel Title : Stockade: existing state e-01 t = 5.0 [day] Safety= 1.2 Z_SOIL.PC 2003 v.6.24 Expert License No: v62D Company : ZACE Author : ZACE Date : :02:21 File : C:\Zsoil\Collonge\publication\C pied Title : Zsoil example e-01 Fig. 3: intensity of displacement for failure; (left) existing, (right) enlarged foot e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e-01 t = 5.0 [day] Safety= 1.5 Author : Philippe Menétrey Date : :58:14 File : C:\Zsoil\Collonge\publication\C anc4 dp Title : Stockade (Drucker-Prager) e-01 t = 5.0 [day] Safety= 1.7 Author : Philippe Menétrey Date : :49:28 File : C:\Zsoil\Collonge\publication\C anc4 mc Title : Stockade (Mohr-Coulomb) e-01 Fig. 4: failure mechanism of the stockade with soil anchorage (left) Mohr-Coulomb SF 1.7; (right) Drucker-Prager SF New loading on an existing retaining wall The so-called CEVA project plans a new railway line in Geneva for connecting the centre of city with Annemasse in France. Close to the Geneva station, this new railway line follows existing retaining walls. This wall had to be checked for these new railway loads. The retaining wall is made of concrete, which is modelled as an elastic-linear material. Other material characteristics are shown in Tab. 2. The mesh of the retaining wall is presented in Fig. 5. Failure criterion γ [kn/m 3 ] E [kn/m 2 ] ν φ [ ] c [kn/m 2 ] ψ [ ] Backfill (mat. 2) Drucker-Prager Silt (mat. 3) Drucker-Prager Gravel (mat. 4) Drucker-Prager Tab. 2: material characteristics for the existing retaining wall model 58

5 FE MESH t = 4.0 [day] Author : Philippe Menétrey Date : :09:15 File : C:\Zsoil\St-Gervais\StGervais2 Fig. 5: existing retaining wall under railway loads The deflection under service load of 30 kn/m 2 is presented in Fig. 6. It could be noted that the deflection is reaching 9 mm under the new railway line and the settlement of the wall was reaching 2 mm. The requirements to avoid overturning of the railway line are therefore controlled e-02 EXTR-U 1.072e e-03 EXTR-V 3.983e e-03 MAX-DISP 9.818e-03 [m] DEFORMED MESH t = 4.0 [day] Author : Philippe Menétrey Date : :09:15 File : C:\Zsoil\St-Gervais\StGervais2 Fig. 6: deflection of the existing retaining wall under railway loads A stability analysis was performed and the failure mechanism is illustrated in Fig. 7. This computation allow showing that the existing retaining wall under the new loading has a safety factor against overturning of about

6 e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e+00 EXTR-U 1.195e e-01 EXTR-V 5.352e e-01 MAX-DISP 9.604e-01 [m] t = 4.0 [day] Safety= 1.5 Author : Philippe Menétrey Date : :09:15 File : C:\Zsoil\St-Gervais\StGervais2 DISPL. VECTORS t-ref.= 4.0 [day] Safety-ref= 1.4 t = 4.0 [day] Safety= 1.5 Author : Philippe Menétrey Date : :09:15 File : C:\Zsoil\St-Gervais\StGervais2 Fig. 7: failure mechanism for a fine mesh SF 1.5 (left: intensity of displacement; right: increase of displacement vector) However, with a coarse mesh, the obtained safety factor was 1.7 as presented in Fig. 8 instead of the 1.5 obtained with the dense mesh. This demonstrates once more the influence of the mesh density. In this case, the difference is probably due to the thin layer of backfill (material 2) under the retaining wall e-01 EXTR-U 9.195e e-01 EXTR-V 1.452e e-01 MAX-DISP 3.371e-01 [m] t = 4.0 [day] Safety= 1.8 Author : Philippe Menétrey Date : :18:12 File : C:\Zsoil\St-Gervais\StGervais1 DISPL. VECTORS t-ref.= 4.0 [day] Safety-ref= 1.7 t = 4.0 [day] Safety= 1.8 Author : Philippe Menétrey Date : :18:12 File : C:\Zsoil\St-Gervais\StGervais1 Fig. 8: failure mechanism for a coarse mesh SF 1.5 (left) intensity of displacement; (right) increase of displacement vector) 4. Crack propagation in a concrete anchorage plate The erection procedure of bridge using hydraulic jack to slide the bridge deck requires anchorage structures that are particularly safe. The anchorage structure for the sliding of the Trient railway bridge is considered here. An overview of the concrete anchorage plate is presented in Fig. 9. The anchorage plate is analyzed with Z-soil in order to investigate the safety of concrete plate. A two-dimensional plain strain computation is performed with the mesh presented in Fig

7 Fig. 9: overview of the anchorage plate for sliding bridge The numerical simulation is performed using the concrete modelled developed by Menétrey et al. [2] and implemented in Z-soil. The model was developed to reproduce the different states of stress characterizing punching failure so that the triaxial failure criterion developed by Menétrey and Willam [1] was considered. The dilatancy observed experimentally is matched with a non-associated flow rule. The concrete cracking phenomenon is described with the smeared crack model using the strain-softening formulation. The fictitious crack model developed by Hillerborg et al. [3] is considered for which the reduction of the tensile stress σ t is controlled by the crack opening w along the line of an exponential decohesion process. The fracture energy defined as the amount of energy absorbed per unit area in opening the crack from zero to the crack rupture opening w r, which is invariant with the finite element size. The simulation of localized concrete failure requires the dependence on the finite element size that plays the role of localization limiter. The brittleness of failure and the state of stress are linked with a fictitious number of cracks FE MESH t = 3.1 [day] Author : Philippe Menétrey Date : :38:14 File : C:\Zsoil\Trient\publications\Trient8 hb10 Title : Anchorage plate: Flow Hoek-Brown 10 Fig. 10: mesh of the anchorage plate 61

8 t = 2.3 [day] Author : Philippe Menétrey Date : :38:14 File : C:\Zsoil\Trient\publications\Trient8 hb10 Title : Anchorage plate: Flow Hoek-Brown 10 t = 3.0 [day] Author : Philippe Menétrey Date : :38:14 File : C:\Zsoil\Trient\publications\Trient8 hb10 Title : Anchorage plate: Flow Hoek-Brown 10 t = 2.3 [day] Z_SOIL.PC 2003 v.6.24 Expert License No: v62D Company : ZACE Author : ZACE Date : :48:16 File : C:\Zsoil\Trient\publications\Trient8 hb20 Title : Zsoil example t = 2.6 [day] Z_SOIL.PC 2003 v.6.24 Expert License No: v62D Company : ZACE Author : ZACE Date : :48:16 File : C:\Zsoil\Trient\publications\Trient8 hb20 Title : Zsoil example t = 2.6 [day] Author : Philippe Menétrey Date : :38:14 File : C:\Zsoil\Trient\publications\Trient8 hb10 Title : Anchorage plate: Flow Hoek-Brown 10 t = 3.1 [day] Author : Philippe Menétrey Date : :38:14 File : C:\Zsoil\Trient\publications\Trient8 hb10 Title : Anchorage plate: Flow Hoek-Brown 10 The crack propagation in concrete is presented in Fig 11. The numerical simulations allow showing that the prestressed reinforcement increases the confinement and the carrying load. However, the chosen system was not safe enough as the failure load was approaching the service load. The anchorage plate system had to be modified. Fig. 11: crack propagation in the anchorage plate (plastic flow: Menétrey and Willam [1] with 10 at the compressive meridian) It has to be mentioned that the failure load was reaching 1634 kn/m with a plastic potential following the Menétrey and Willam [1] (denoted as Hoek and Brown (M- W) in Z-soil) with an angle of 10 at the compressive meridian. However, with an opening angle of 20 at the compressive meridian, the failure load was reduced up to 891 kn/m and the corresponding crack propagation is presented in Fig. 12. Load level not reached Load level not reached Fig. 12: crack propagation in the anchorage plate (plastic flow: Menétrey and Willam [1] with 20 at the compressive meridian) 5. Conclusion Three different practical applications of the computer program Z-soil were presented: the strengthening of a stockade, the loading of an existing retaining wall and the crack propagation in a concrete anchorage plate. All these examples allow showing the utility of the Z-soil computations. First, it allows proving that the existing stockade has to be reinforced with a soil anchorage. Then, it shows that the new loading of the retaining wall creates little deflection and the safety against overturning is acceptable. Finally, the crack propagation in the 62

9 concrete anchorage plate allows demonstrating that the chosen system was not safe enough. For all these applications, the sensitivity of the numerical analysis is investigated that allows showing peculiar behaviour. The type of failure criterion modifies the safety factor of the stockade, the size of the finite element mesh influences the safety factor of the existing retaining wall and the flow rule influences the load level and the crack propagation in the anchorage plate. Consequently, numerical simulations of structures with geomaterial have to be undertaken with great care. References [1] Ph. Menétrey and K.J. Willam, A triaxial failure criterion for concrete and ist generalisation, ACI Structural Journal, 92(3), pp , [2] Ph. Menétrey, R. Walther, Th. Zimmermann, K.J. Willam, and P.E. Regan. Simulation of punching failure in reinforced-concrete structures. Journal of Structural Engineering: Structural Division of the ASCE, 123(5) pp , [3] A. Hillerborg, M. Modeer, and P.E. Petersson. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite element. Cement and Concrete Research (US), 6, pp ,

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