A baked anode is a complex material, that results from the mixing and baking of different petrol coke grains, with different size distributions, with a pitch binder. A PFC2D model accounting for the microstructure of a baked anode, using the Bonded Particle Model (BPM) has been developed in our previous studies.

Itasca's role is :

• Develop a numerical method to measure electrical resistivity based on the existing contact network in the discrete sample. The relation takes into a account the porosity of the sample and its volume as well as contact properties such as the thermal resistance of pipes, their length and their orientation.
• Build a numerical method to calculate the permeability of the assembly based on the Kozeny Carman theory. 

Both approaches allow local measurements to be made and provide the ability to analyze the evolution of these properties during the simulation.
We conclude that:

• Modifying the volume fraction of material (in the range value tested) only slightly modifies the electrical resistance of the sample (±2%).
• Modifying the volume fraction of material and/or the pores/voids ratio does not change the permeability, since the grain distributions for all material are equal and porosity is randomly distributed in materials. The permeability of the medium will be influenced mainly by a difference in granulometry and porosities from one material to another.

Estimating settlements due to a complex excavation - Itasca Consultants SAS (France)

In the context of the Greater Paris works, the VINCI-SPIE group is currently building a future metro station underneath the CNIT centre in Paris, for the westward extension of the RER E (EOLE). The West Pre-Station is particularly complex due to its excavation phasing and the presence of many surrounding structures, including among others a tram and several foundations.

Given these constrains, a FLAC3D model has been developed to estimate the surface movements induced by the excavations, to validate the proposed work sequence and support system.

Four main structures are modelled: the Carpeaux gallery, the T2 stairway, the West twin-tube and the Pre-Station itself. Many neighbouring structures are taken into account: the CNIT car park, the existing foundations as well as the tramway (Fig. 1, 2).The mesh is generated using the automatic mesher Griddle (Fig. 2). The soil is modelled by using the "Plastic-Hardening" (PH) model, allowing for a realistic predictions of the pre-failure behaviour.Thick support liners are represented by volumetric elements, whereas other tunnel supports (shotcrete, bolts, hangers, struts, frames, umbrella vaults) and foundation piles by using structural elements. More than 40 main stages are simulated.

Settlement evolutions along the tram way are obtained. More than 80% of the final movements are developed during the top-down excavation of the Carpeaux gallery. The maximum settlement is located near a large niche excavated to connect the gallery top slab to the existing pile foundations (Fig. 3).

Settlement above the stairway tunnel is more than 1 cm and is primary due to a surrounding heavily loaded foundation raft.The excavation of the remaining structures, as well as the groundwater rising, has only a limited influence on surface displacements, estimated in less than 0.5 cm.

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