Wednesday, January 21, 2015

R&D in Concrete Block Masonry

Manufactured concrete block represents a great success story of the 20th century.  An entire global industry has developed and evolved into a high state of efficiency and economy, all based on manufactured concrete block.  This technology thrives in virtually every country on earth: the traditional, rectangular concrete masonry unit (CMU) is produced inexpensively and with an engineering knowledge which is well understood and successfully put into practice by block producers globally.  The result is something we all tend to take for granted: high-strength, consistently dimensioned, inexpensive, rapidly produced CMU’s which are suitable for vertical walls in virtually any type of building, including residential, commercial, public buildings and infrastructure.  With such a successful model of production, distribution, assembly and availability already well established and in place, what –if any- new developments can research and development (R&D) add to this existing industry and practice?
My own work as a masonry designer has addressed this question for 25 years now.  I will attempt to summarize the areas of potential future growth, development and design which this robust industry has left essentially unfulfilled.  A look at current areas of research conducted by various segments of the scientific and engineering world indicate areas which stand to benefit and develop rapidly from the existing engineering practices of the concrete block industry.  The research and development proposed here hold the potential to transform the concrete block industry’s offerings into an entirely new realm of products which will provide better building systems at a lower cost on a global basis.  A modest effort in research and development will reap huge benefits for humanity; it will grow the concrete block industry and make superior, affordable, beautiful and holistic construction available for all.

One specific area of current research which has garnered significant attention from scientists, engineers, designers and practitioners is the idea of topological interlocking structures.  “Topological” refers to “Topology (from the Greek τόπος, "place", and λόγος, "study") [which] is the mathematical study of shapes and topological spaces. It is an area of mathematics concerned with the properties of space that are preserved under continuous deformations including stretching and bending, but not tearing or gluing. This includes such properties as connectedness continuity and boundary.  Topology developed as a field of study out of geometry and set theory, through analysis of such concepts as space, dimension, and transformation. Such ideas go back to Leibniz, who in the 17th century envisioned the geometria situs (Greek-Latin for "geometry of place") and analysis situs (Greek-Latin for "picking apart of place"). The term topology was introduced by Johann Benedict Listing in the 19th century, although it was not until the first decades of the 20th century that the idea of a topological Space was developed. By the middle of the 20th century, topology had become a major branch of mathematics” (taken from Wikipedia).
Currently, concrete block design and practice do not provide for topological construction.  The standard rectangular concrete block designs (with which we are so familiar) can only be used to create straight vertical walls and square corners.  A few designs allow for a slightly curving wall, which have found use mainly in retaining walls and landscaping applications.  Other novel designs allow for slight variations to the basic idea of a vertical wall, including corners which occur at 45 degrees and so on.  Current concrete block designs are far from providing a full expression of topology.  Curving walls –such as those provided by landscaping applications- only curve in one dimension, like a cylindrical surface, and do not allow curvature in two dimensions, like a spherical surface.  A form of concrete block known as “articulated block” (shown above and below) does some interesting work as an erosion-arresting embankment material.  Articulated block do not interlock in the plane being assembled; blocks can slide in and out of the assembly.   There are some great articulated block designs being developed though.

The design of CMU’s which allow for full topological expression provides the ability to use block to make roofs and complete curved structures (e.g. complete spheres, ovals, elliptical, catenary and other designs).  The design ability which can create a full expression of topology allows the use of high strength, affordable, rapidly produced building components which provide all the benefits of concrete block, including: fire resistance, termite resistance, rot resistance, building longevity, resale value, solidity, appearance, and the ability to withstand extreme weather events (hurricanes, tornadoes, typhoons, storm surges, tsunamis, etc.).    The creation of CMU designs which allow for full topological expression will create an entirely new architectural vocabulary for building with concrete block, and will create entirely new markets for concrete block.
If an interlocking aspect is included in the masonry unit then the topology in masonry is made particularly more effective.  One striking example (which has fueled much of the current research) is the failure of thermal tiles on the space shuttle Columbia.  Because they did not interlock, these topological tiles (designed to wrap around the shuttle: topologically) were free to move and dislodge themselves from their protective positions since they were held in place only by adhesive, leaving the shuttle vulnerable to catastrophic reentry into the earth’s atmosphere.  Researchers were quick to realize that if an interlocking aspect of each masonry unit (or tile) were incorporated, then the geometry of the individual masonry units would have helped keep them in their proper location (anchored by adjacent masonry units) and prevented them from being removed.  Furthermore, researchers have realized that topological interlocking masonry units (or tiles) would not suffer complete, systemic failure if one of these masonry units were damaged: the other adjacent and surrounding tiles would stay in place, even if one tile broke or was removed.  By including the interlocking feature into the masonry unit itself, a separate independent connector is not required.

While this idea of the beneficial nature of interlocking masonry units is illustrated by the Columbia tragedy, it holds great significance for the less exotic application of buildings here on terra firma.  To fully understand this, we will look at the current state-of-the-art for masonry engineering analysis.  Examining a masonry arch, the current engineering model makes 3 assumptions: 1. Masonry units have infinite compressive strength; 2. Masonry units have no tensile strength; 3. Masonry units never slide against each other (they remain in their fixed position).  We will concern ourselves here with the third assumption, the idea that masonry units in an arch (known as voussoirs) never move relative to one another.

In reality and in practice, voussoirs are known to move against each other in a masonry arch.  When this occurs, the arch can be significantly weakened and this movement of voussoirs can result in failure and collapse of the arch.  A catenary thrust line is an imaginary line of force which exists in the wall thickness of the arch.  Catenary (from Latin “catena” or chain) is the shape of a hanging chain or cable under gravity; if this shape of a hanging chain is inverted, then a catenary thrust line is generated.  As long as this imaginary thrust line does not touch or exit the arch wall thickness, the arch will remain standing and stable.  If the imaginary catenary thrust line touches or exits either the inner surface (intrados) or the outer surface (extrados) of the arch, then a hinge will form at that location.  Several hinges allow a mechanism for movement of the arch, resulting in a buckling or folding of the arch about these hinge locations, leading to failure and collapse of the arch.  However, if voussoirs possess an interlocking feature such that they are not free to move relative to any adjacent (interconnected) voussoirs, then the catenary thrust line will not touch or exit either the intrados or extrados of the arch due to movement.  Thus interlocking masonry units in an arch are fundamentally much stronger, more robust and more stable than masonry units which do not interlock.
The creation of an effective interlocking feature on a topological masonry unit produced on a standard conventional block machine is a very real challenge for the masonry designer.  Interlocking features are actually commonplace in standard (non-topological) blocks: the ‘top’ and ‘bottom’ of the concrete masonry unit can readily incorporate interlocking features.  A wide variety of designs is possible if the interlocking feature does not include topological arrangements, but the designer is still limited to building straight vertical walls.  In order to provide an interlocking feature for a topological masonry unit, the sides of the block must be used (not just the ‘top’ and ‘bottom’ of the block) as sites of interlock.  The difficulty here is that a block mold must be readily stripped from the block without any undercut, or draft, or negative angle.  In other words, an interlocking feature on a topological block will create undercuts: an interlocking topological block simply will not release from a mold.  This contradiction can be overcome by symmetry and design.

Another difficulty in creating an interlocking topological block on a block machine is the ability of the mold cavity to be filled completely, evenly and homogeneously.  If a section of the mold near the ‘bottom’ of the block has an overhanging feature (steel mold above it) then it will not fill as readily as an open cavity which allows the concrete mix to flow into it, unimpeded.  A section of mold cavity which has an overhanging feature will impede the flow of concrete into the cavity, resulting in segregation of aggregate.  This segregation of aggregate will typically result in a weakened section of the block where larger aggregate is prevented from filling as easily as in an open mold cavity.  Lack of larger aggregate in a filled mold section creates a weaker section of concrete as a result.

In addition to sections of mold being less than ideally filled due to overhanging mold parts, there is another problem where a section of mold cavity at the ‘top’ of the mold has an open space below it (at the ‘bottom’).  This will create an overhanging projection of block, which is unsupported from underneath (at the ‘bottom’).  These cantilevered features of block are prone to cracking and breaking, especially upon handling as the un-cured block leaves the block-making machine. 
How can a topological interlocking masonry unit be created in a manner that provides adequately filled mold cavities at the ‘bottom’ of the mold, while also not creating weak cantilevered sections at the ‘top’ of the mold?  This is a very interesting design challenge; one which I hope will attract the efforts and solutions of other designers.

Catenary thrust line analysis of masonry domes is another area of current research.  Computer models which digitally process the applied stress and the resulting strain as hinge mechanisms are used to develop visual models.  Catenary thrust line analysis is also used to digitally analyze a computer 3D model as a tool for designing buildings.
Biomimicry/Biological Design as a source of masonry design is ripe with potential.  “Nature’s masons” include single-celled radiolarian and foraminifera, coral, sea anemones, sea horses, turtles and tortoises, Thor’shero shrew, and an endless array of life’s other innovative design solutions.
Anisotropy in manufactured concrete block has not been fully utilized with current block designs.  Vertical block walls are made with the weaker axis of the block facing horizontally, to the outside.  It is possible to orient the block so that the high strength axis faces outside, resulting in a significantly stronger building.
Robotic assembly is still in its early stages regarding masonry, but real progress continues in this field.  Robots may play an important role in the future of masonry.  Robotic assembly may have an early adaptation for situations that might endanger a human mason, such as radiation or other hazardous materials.  Construction Robotics is one company that is currently successfully developing robotic masonry.

3D Printing is also in its early stages, but is expected to develop with time.  3D printing should find early use in masonry applications which require a unique masonry piece, such as at the intersection of two arches, or to allow conduit or openings, etc.   In this role it will be cost effective fairly soon.

Tuesday, October 14, 2014

3D Printing and Masonry: a Brave New World of Construction

Three dimensional printing, or 3D printing, has come a long way over the past decade or so.  This technology is growing rapidly, and holds the possibility of disrupting many conventional technologies and entire industries.  One of the conventional construction technologies facing competition from 3D printing is masonry.  Will 3D printing eventually phase out traditional masonry construction?  What are the relative benefits of each technology: masonry versus 3D printing?  How soon will the masonry industry be impacted by 3D printing?

Recent developments in the field of 3D printing include the use of concrete and concrete-like material to create objects.  These objects include both masonry-like units which are subsequently assembled into an integrated structure and also the monolithic entire structure itself, “assembled” as a whole 3D printed object.  At the forefront of this technological breakthrough are 3D printing methods such as those under development by BehrokhKhoshnevis, professor of Industrial & Systems Engineering and Civil & Environmental Engineering and Director of the Center for Rapid Automated Fabrication Technologies (CRAFT) at the University of Southern California.  Khoshnevis refers to this technology being applied to print entire buildings as “Contour Crafting.”  He and others in the field speak of very high-strength 3D printed concrete materials as being just on the horizon; material with a compressive strength of around 10,000 psi.  Currently manufactured concrete block has a minimal compressive strength of around 3,000 psi, although high-performance concretes (HPC’s) are currently available with strengths up to around 20,000 psi and higher.

The advantages of 3D printed concrete –as compared to conventional concrete- include: fairly rapid construction, the ability to make complex shapes and forms, freedom from the constraints of molding, and potentially very high strength.  These benefits may also eventually include the ability to 3D print very detailed and intricate structural features integrated into the building; including ventilation, plumbing, wiring, etc.  Other developers in the 3D printed structures include the principals of “Emerging Objects”, Ronald Rael (at University of California Berkeley) and Virginia SanFratello (at San Jose State).  Their work includes hollow, interlocking masonry like units which assemble in a manner similar to topological interlocking structures (as discussed earlier on this blog).  It holds the promise of potentially creating structural configurations suitable for seismic areas and the ability to withstand major earthquakes.

Still others are 3D printing entire homes, and appear to be close to commercialization.  Among these is a Chinese company, whose equipment is said to be capable of producing ten houses in one day.  It should be noted that these houses are not printed as a whole; they are printed in panels and these panels are then assembled.  There is also a Dutch company, Dus Architects, whose equipment is also capable of printing ‘chunks’ of house, which then must be assembled into a home.

The advantages of 3D printing should appear as obvious, namely: the ability to create virtually any shape, without the limitations imposed by a block machine, or undercuts, or draft angles; the relatively rapid pace of fabrication; a choice of materials (including plastics, concrete, and composites); and the ease of producing an object from a 3D computer file.  It would seem that the 3D printing of homes is inevitable, and that masonry will soon become a lost art - and go the way of film photography, which has been replaced by digital photography.

A few critical factors appear as though masonry will remain in the construction industry for the foreseeable future.   First of all, buildings must begin with a foundation.  In climates with freezing winters the foundation must be placed 3 or four feet below grade, or below the extent of the frost line on the coldest days.  This is simply not possible with the state-of-the-art in 3D printing technology available now.  3D printing technology cannot create a foundation below grade, although it is likely to overcome this obstacle in the future.  Secondly, most 3D printing technologies simply produce panels, or pieces or chunks of a structure which must then be assembled; this basically describes masonry, and is not an improvement over masonry per se.   Those 3D printers which are capable of producing an entire integrated, complete finished structure require an extensive working platform on which to operate.  This platform requires extensive, expensive, detailed site preparation for the 3D printer; this negates many of the so-called benefits of 3D printing an entire structure (more expensive, difficult, and time consuming).  Another major impediment to 3D printing is the fact that the construction industry is an extremely conservative industry and is very slow to accept new technologies.  This fact is made more relevant by the fickle nature of the construction consumer: people want houses, homes and buildings to look like they’ve always looked.  The 3D printing approach to providing homes still has a very long way to go before it produces houses that look very much like every house produced everywhere.  This is not an arena for brave new ideas: homeowners want their homes to look like their neighbors’.  “Fitting in” in the aesthetic sense is probably much more important than efficiency, strength, environmental concerns, longevity, or any other factor about construction.  The appearance of the finished product cannot be overemphasized, and 3D printing has a long way to go here.  Finally, and perhaps most importantly, is the factor of cost.  While 3D printer advocates say that they are faster and less expensive than masonry, it is instructive to note that the concrete block manufacturing industry has developed to a state of high efficiency and economy.  An 8 inch x 8 inch x 16 inch rectangular concrete block is produced in around 2 seconds, and typically costs around $1.00 or so.  This is the benchmark to beat, and 3D printing is not anywhere close to this, despite the claims being made.  It appears as though concrete block will probably be around for a while yet.

3D printing holds great promise for the future of construction.  Those who assume that it will never affect their industry (designers, builders, blockmakers, masons, etc.) do so at their own extreme risk; they are likely to go the way of film photography, i.e., extinction.  Instead, it appears inevitable that 3D printing will have a huge transformative effect on construction in general and on masonry in particular.  It seems that masonry will –in all likelihood- always exist, but that it will be fundamentally transformed by 3D printing.  Masons can design their work and have custom blocks produced on-site, instantly and inexpensively.  Brunelleschi would have put 3D printing of masonry to spectacular use; he wouldn’t have had to carve shapes from turnips to show his masons how he wanted block made.  They would be made instantly, exactly as he envisioned them.  It seems that 3D printing could well add to the art, science and craft of masonry in the relatively near future.

Sunday, June 15, 2014

Fibonacci Masonry

Today I’m taking a look at an esoteric topic relative to masonry: the Fibonacci sequence, the golden mean and some of the resulting geometry.   I will attempt to describe some of my own thoughts on this topic which are not yet fully formed, but seem to hold some promise nonetheless.  I beg the reader’s indulgence if I am overly speculative, but this is the nature of this particular beast.  I hope that someone else out there may be able to add to my speculation and –perhaps- provide additional insight into this curious realm of mathematics and geometry.

In mathematics,  the Fibonacci numbers or Fibonacci sequence are the numbers in the following integer sequence:
1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots\;
or (often, in modern usage):
0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots\; 
By definition, the first two numbers in the Fibonacci sequence are 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two. (taken from Wikipedia)
The earliest occurrence of this numerical sequence is found in Indian mathematics, in the context of  Sanskrit prose structure.  In the oral tradition of Sanskrit, great emphasis was placed on how long syllables (L) mix with short (S) and counting the different patterns of L and S within a given fixed length results in the Fibonacci numbers; the number of patterns that are m short syllables long is the Fibonacci number Fm + 1.   This prose structure is first traced back to Pingala, at around 200 BC.  It was later more fully described by Virahanka, at around 700 AD: Variations of two earlier meters [is the variation]... For example, for [a meter of length] four, variations of meters of two [and] three being mixed, five happens. [works out examples 8, 13, 21]... In this way, the process should be followed in all mātrā-vṛttas [prosodic combinations]. (taken from Wikipedia)
For the past 4 years on this blog I have spent the month of April writing poems about masonry for National Poetry Writing Month (NaPoWriMo) after being dared to do so by a poet friend.  It might be interesting to attempt a poem about masonry using the Sanskrit tradition of employing a Fibonacci sequence relative to variations of meter.  I wander…
In the West, the Fibonacci sequence was first realized and articulated by Leonardo of Pisa (known as Fibonacci) who described it in his book Liber Abaci (1202 AD).  He described the numerical sequence bearing his name by describing the idealized growth of a rabbit population over time.
As the Fibonacci sequence gets longer and the numbers get larger, the ratio between 2 adjacent numbers in this sequence approaches the golden ratio, or golden mean.  This is mathematically expressed as:  \psi = \frac{1 - \sqrt{5}}{2} = 1 - \varphi = - {1 \over \varphi} \approx -0.61803\,39887\cdots
Put another way, the golden ratio itself is approximately 1.6180339887…
Geometrically, the golden ratio may be expressed as a rectangle, one side being equal to 1.0, the other side being equal to 1.6180339887…

This rectangle can be used to generate a Fibonacci spiral:

I recently used this relationship to create a series of “Fibonacci spiral bowls” from clay on my potter’s wheel.  This was a fun experiment, I may make some more and play with this form a bit more.

It occurred to me that it would be a simple thing to make a masonry Fibonacci spiral structure using my triangular blocks to build cylindrical sections of varying radii, just as I have done with bowls of different radii.  Such a structure could be aesthetically interesting, and it could perhaps create an interesting interior space.  It may also possess unique characteristics which may serve some functional purpose: perhaps acoustic, or wave attenuating, or even structurally stronger.  I would like to build a Fibonacci masonry spiral and see what it’s like.
I also built a curious sculpture which relates the golden rectangle to an icosahedron.  If 3 golden rectangles are assembled at right angles to each other (orthogonally: x,y and z axes) then the corners of these 3 rectangles describe the corners of an icosahedron.  These pictures describe it better than words.

Finally, I would like to create a series of rectangular masonry bricks which employ the golden ratio in a way which I have not seen done by others.  Each rectangular brick would possess the edge lengths of 0. 6180339887… (depth), 1.0 (width), and 1. 6180339887… (length).  I would like to create a whole series of these bricks, with many different sizes.  Each size would be scaled by the golden ratio; each would get larger (or smaller) by a factor of 1. 6180339887… or 0.6180339887…   It seems to me that these bricks could be arranged in some very interesting patterns.  It would be necessary to dry stack them in order to realize the curious geometric relationships, since mortar would change the geometric patterns between bricks.  I have done some crude hand sketches which illustrate the curious possibilities of such a modular series of rectangular bricks which employ the golden ratio, but I am not sharing this for now. I am curious what anyone else out there might come up with.  If you have any ideas, let’s share them!  Show me yours and I’ll show you mine. 

I made this bowl a few days later.  I tried to include helicity to the Fibonacci spiral; I used 8 bowls scaled by Fibonacci - the largest is 24 inches, 61 cm diameter.

I hope to hear from someone out there, let’s do Fibonacci masonry!

Thursday, May 1, 2014

The mollusk, the arch and conjugate shearing

I’ve written repeatedly on this blog about nature’s masons.  Nature is the ultimate inspiration for design;  evolution showcases many masonry techniques.

Mollusks have recently been investigated by two researchers at MIT, graduate student Ling Li and Professor Christine Ortiz.  Their research findings were published in the journal ‘Nature Materials’ (March, 2014) and focused on the mollusk Placuna placenta

This mollusk’s shell exhibits very tough qualities (resistant to crack propagation) while simultaneously remaining optically transparent.  When subject to extreme focused stress -such as may be encountered by its predators- the calcite material of Placuna placenta’s shell demonstrated very efficient energy dissipation and the ability to localize deformation, limiting damage to the area directly impacted and preventing crack propagation.

The mollusk’s shell is comprised of around 99% calcite and around 1% organic material which bind the calcite crystals together.  This is somewhat similar to the sharp defensive spikes found in sea urchins (as discussed here) which are also made primarily of calcite with small amount of organic binder material present.  Pure calcite (without organic binder) is a brittle crystalline material which easily cracks.

The mechanism wherein the type of deformation in Placuna placenta shell occurs was studied by using an indentation apparatus consisting of a diamond tip which is forced into the mollusk shell.  The resulting damage to the indent region was then visually recorded using electron microscopy and diffraction techniques to characterize the resulting damage.

This research cleverly showed that the deformation (or strain) of the mollusk shell was a crystallographic ‘twinning’ response to the applied stress.  Crystal twinning occurs when two separate crystals share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals in a variety of specific configurations. A twin boundary or composition surface separates the two crystals.

Part of the crystal shifts its position in a predictable way, leaving two regions with the same orientation as before, but with one portion shifted relative to the other. This twinning process occurs all around the stressed region, helping to form a kind of boundary that keeps the damage from spreading outward (preventing crack propagation).

This twinning mechanism provides for conjugate shearing.   The conjugate shearing mechanism has significance in terms of a toughened structure and is better than a conventional masonry arch structural response to an applied stress of voussoirs forming hinges.

Conjugate shearing was initially employed by geologists as a term to describe shear fractures in rocks subject to compressive stress.  The context and scale of this geologic feature have kept it from being analyzed, utilized or realized in the context of microscopic analysis or in the context of masonry design and modular structural systems.   Similarly, it is apparent that biologists and engineers have failed to fully appreciate the conjugate shearing mechanism demonstrated by the Placuna placenta’s calcite shell structure in response to applied stresses such as the indentation tests done by researchers at MIT.

The force required to cause conjugate shearing to occur (in an architectural arch or in a mollusk shell) is much higher than the force required to create a hinging mechanism as occurs in a conventional masonry arch comprised of wedge-shaped voussoirs.  For example, Thor’s hero shrew’s spine is configured in such a manner that it is disposed to conjugate shearing instead of creating a hinging mechanism which leads to buckling and collapse of the spine.  An adult human can stand upon and be supported by the tiny Thor’s hero shrew’s spine without breaking the poor animal’s back.  Conversely, a common shrew does not have the interlocking triangular design of Thor’s hero shrew’s vertebrae; its spine would buckle and collapse in the hinging mechanism of a conventional masonry arch if an adult human stood on top of it: the back would simply and easily be broken (poor regular shrew).

The calcite shell of Placuna placenta and its unique crystallographic twinning response to applied stress is another of Nature’s exemplars of exquisite design which incorporates the structural response of conjugate shearing to create a toughened structure which will blunt and stop crack propagation in an otherwise brittle material. 

Monday, April 28, 2014

Oh Block, why interlock?

If a block in an arch can budge
then it just needs a nudge
for the arch to get weak
you’ll not hear a creak
or some warning snaps
before the collapse.
So what’s to be done?
How safe’s anyone?
If the blocks in an arch interlock
they can’t move, anchored block
no unnerving fragility
the arch itself is stability.

Sunday, April 27, 2014


I can’t think of a trade I’d trust
more than the trade you really must
believe in to actually do it right
trust a mason all day and night.

Saturday, April 26, 2014

Anchor bricks

Bricks made of clay
have holes or recesses
to anchor the mortar.
It’s the best way
for mortar impresses
itself in the border.