I was the ‘builder’ for both of these small prototypes, and as a member of the BLOCK research group, I am presently taking on the project of constructibility for this stone pavilion.  My goal will be to translate between modes of digital fabrication (for vault research and prototype construction) and modes of masonry fabrication (in the construction of stone vaults) – to understand the cutting edge possibilities and limitations of the tools for each, and thus to streamline the greatest potentials of Thrust Network Analysis into the construction of full scale vaults.

In the coming posts, I will go into detail in these aforementioned fabrication analyses.  For the time being, however, allow me to first share the work of this latest vault iteration at “Einblicke”, from which we may extract a series of insights for development.

I:  Construction

II:  Shipping & Unpacking

III:  Assembly

IV:  Exhibition

- Lara

On September 24, 2009, the exhibition “Einblicke” opens, celebrating the new Institute of Technology in Architecture (ITA) at the Faculty of Architecture (D-ARCH) of the ETH Zurich. Philippe Block will be showing his research and projects introduction his BLOCK Research Group at ETH. The latest model of the Escobedo Vault will be featured at the exhibition, providing it arrives on time and in tact (i.e. in exactly 103 pieces) from the other side of the Atlantic.

More Info about the  exhibition.

This new cutting pattern is used for the  new 3D-printed model which has been printed and assembled by Lara. The tolerance issues, due to the 3D printing process, observed on the last model, only worsened due to the increased size of the model. We will have to look for more accurate 3D-printers in order to obtain realistic structural models of stone-cut vaults and to consider this approach as a feasible way to prototype complex vaulted assemblies. More about this soon…

Inspired by all the amazing stone work I saw on a visit to Palma de Mallorca, the capital of the Balearic Island Mallorca (Spain), I started paying attention to how the voussoirs of these vaults were cut. I did need inspiration to solve the problematic issue in the previous version of the vault, its cutting pattern.

Looking up at all the stunning stone vaults taught me a lot about Stereotomy (= The science or art of cutting solids into certain figures or sections, as arches, and the like; especially, the art of stonecutting –  http://www.thefreedictionary.com/Stereotomy). In the previous try, L-shaped pieces were avoided since it was thought that those would appear awkward. In fact, it can be seen on the previous image that these L-shape pieces allow to nicely turn the corner over a groin and visually (and structurally) tie the entire vault together.

This image shows how to nicely morph from a groin vault into an elliptical vault. The stereotomy language/logic shown in this curving, vaulted arcade gives an important clue how we could transition between the different recognizable parts of our vault.

Discussing the new evolutions with John Curry at Escobedo Construction’s office in Buda, TX.

Lara securely boxed in the model, just in time to take it with me on the flight to Austin.

Luckily, a little (referring to the size of the model) stone mason volunteered to make it happen: Lara Davis. After many hours of shaving off the faces and carefully checking the digital model, the vault was assembled upside-down in its cradle. Unfortunately, because of a lack of proper interlocking of the pieces, the vault could not be assembled without gluing the pieces together.

The main reason for making a scale model is to have an extra check on the stability of the vault and check effects which are not taken into consideration into the TNA: sliding failure under all loading cases for the chosen cutting pattern, possible collapse mechanisms due to support displacements, or sensibility of the vault under asymmetric live loads.

The challenge of the formwork is that it needs to be taken off after the vault has been assembled. Thanks to Katelyn for trying to make it work. At the end, it was chosen to make a cradle formwork to assemble the vault upside down. The idea was to then flip over the vault, pressing it against the supports on the base. The thrust and interlocking of the blocks should make this possible.

Download here Philippe Block’s PhD dissertation which describes the details of the methodology used to design this vault prototype:

THRUST NETWORK ANALYSIS: Exploring Three-dimensional Equilibrium.

TECHNOLOGY: FREE-FORM MASON
MIT’S JOHN OCHSENDORF REINFORCES MASONRY’S HISTORIC SIGNIFICANCE.

After the powder-base printer is done, we needed to excavate the model from the build tray. I felt like a true archeologist looking for a lost city, but there were also a few flash backs to happy times in the sandbox as a child.

After excavation, the brittle pieces need to cure in the oven and then want to be coated with a wax. Anyone fancies solving this 70 piece 3D puzzle?

Thanks to Chris, Patrick and Junno for helping with the 3D printing.

We now want to 3D print a scale model of this block assembly. Because we could only get one overnight printing session on the machine, we needed to fit the entire cut-up vault into one 3D printer batch (8in x 10in x 8in). This results in a scale model of approximately one foot squared. Things had to move fast to be ready to print, so no time left for nice packing… Enjoy my packing chaos!

Ready to print! The estimated printing time for our model was about 7 hours.

Because of the complex curvature of the inner surface (= the result from the form-finding process), this method does not necessarily create clean cut lines on the entire outer surface. In the convex parts of the vaults, this method renders clean voussoirs (= masonry units/blocks), but it becomes messy in the transitions to concave parts. The intersections therefore need to be cleaned up and interpreted in these areas to get satisfactory cut lines. Connecting the interior and exterior cut lines gives the vousoirs (c).

The cutting pattern is being informed by the force lines (black) and topo-lines (orange) of the target thrust surface (a). This results in a solution that reflects -and emphasizes- the structural logic of the vault, but also helps recognizing the different transitions in vault typologies of this design, going from a groin vault part, to a more domical cap or the flaring edges of an Isler-type ‘free-form’ vault.   

On the three-dimensional thrust surface, we are laying out possible approximate stone layouts (b). The average stone size is about 3 by 6 feet, with an average thickness of 1ft resulting in pretty heavy pieces of stone (about one ton each!). Cuts will be made perpendicular to this surface to avoid sliding and guarantee proper arch action.

The form-finding / design process is iterative. The internal force distribution is being manipulated / altered by playing around with the graphical reciprocal force diagrams. This provides a high level of control to ‘shape’ and fine-tune the three-dimensional solution. The updated internal force distribution at each step is then used as a measure for the thickness of the vault: the vault becomes thicker where more forces accumulate (that’s the logic / strategy we chose). This added thickness has to be accounted for in the loads applied in the nodes and the program runs again to find the updated equilibrium shape.

This piped solution gives a good idea of the sculptural qualities of the thickening along the main force lines in the network. These ribs will also help stiffen the vault, which becomes very important under asymmetric loading conditions.

The sketch model received a nice stone base, so it was ready for a serious photo shoot in the dusty stone fabrication mill.

The horizontal components of the branch forces can be measured directly from the force diagram.

The forces in the equilibrium network are here visualized by piping the branches proportional to the (square root of the) forces in them. This visualizes very well where forces need to be attracted in order to achieve this asymmetric vault.

By using this non-uniform offsetting strategy we achieve some interesting formal qualities such as the crater/volcano-like ridge around the oculus. In general, this thickening allows to read the structural better: the form follows the forces.

This is an initial step to suggest the thickness of the vault. Applying asymmetric loads will also influence the ultimate boundaries of the vault.

The 3-d physical model will be highly instrumental in figuring out the how to cut up the stone structure in masonry units.

Looks like a strange spider is taking over Escobedo’s main office… Notice the appropriate temporary base.

Would be pretty wicked looking!

 The vault features… description

The pavilion will be at the edge of a 40 ft ravine with an interesting undercut ledge in natural rock. What an amazing location!!  

The ‘local’ wildlife -game, bisons, longhorns, and z-donks (yes, a crossbred of zebra and donkey indeed!)- do not realize yet what original shelter they will be getting!

We set out to show the world that stone can be real sexy!

press release