WO2024258879A1 - 3d-printed earth formwork for reinforced concrete construction - Google Patents

Abstract

Embodiments utilize a method of making a mold (108a) of additive manufacturing material for use in producing a structural element for a structure. The mold (108a) includes an interior surface (502) having a geometry defined by the additive manufacturing material configured to constrain a composition of matter to be disposed within the geometry of the interior surface at least until the composition of matter sufficiently stabilizes with a shape, based on the geometry, toward becoming the structural element. The mold also includes an exterior surface (503) having a geometry defined by the additive manufacturing material, the geometry being a function of: (i) hydrostatic pressure expected to be exhibited as a combination of at least the composition of matter as constrained by the interior surface, and (ii) properties of the additive manufacturing material between the interior and exterior surfaces.

Description

3D-PRINTED EARTH FORMWORK FOR REINFORCED CONCRETE CONSTRUCTION

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of U.S. Provisional Application No. 63/507,725, filed on June 12, 2023, and entitled “3D Printed Earth Formwork For Reinforced Concrete Construction,” the entire disclosure of which is hereby incorporated herein by reference.

BACKGROUND

[0002] Locally sourced earthen materials are used for construction everywhere on Earth. Over 3.5 billion people live and work in earthen structures. However, earth as a resource for modern construction is often overlooked or underutilized. In modem construction practice, most projects begin with excavation and removal of many tons of soil to make way for foundations. That soil is typically treated as waste which can be costly to remove.

[0003] Since Roman times, formwork for concrete has predominately been produced from processed timber. Size and availability of timber and skilled labor to mill it into precise shapes have driven what could be built, leading to a common saying that a concrete building is “built twice,” first as a timber formwork structure, then as a cast concrete structure [8].

[0004] Today, more sophisticated reinforced concrete projects may use modular steel forms or even massive slip-forming molds for simple geometries, such as cooling towers or building cores. However, most housing and urban infrastructure construction still utilizes a system of flat timber boards or plywood held in place by wooden supports. Depending on the quality of formwork material and skill of the builders, the formwork material may be reused for more than one concrete pour. However, at the end of their lifecycle, formwork materials typically go to landfill [9].

[0005] For much of the world, timber, steel, and foam formwork are becoming increasingly costly as supplies of each material dwindle. As global efforts continue to push for reducing climate impact in the built environment, scalable technologies that offer both minimal carbon impact and high-speed construction are of paramount importance. [0006] As the rate of global, rapid urbanization continues to grow, researchers and practitioners in Architecture, Engineering, and Construction (AEC) are being pushed to explore automation to accelerate development of new housing and infrastructure [1]. At the same time, the construction industry is contributing 11% of global annual carbon emissions, a number projected to grow over the next 50 years. Eight percent of this impact is a direct effect of cement production for concrete, currently the world’s most ubiquitous building material [2]. To address the twofold challenge of rapid urbanization and the climate impact of growing cities, novel systems must be developed to minimize the use of concrete in new construction with globally scalable construction automation technologies.

SUMMARY

[0007] Embodiments disclosed herein present novel methods for 3D-printing earth as formwork for shaped, reinforced concrete building elements. Using additive manufacturing, soil, often considered waste on a construction site, is transformed into infinitely recyclable formwork for mass-customized, shape-optimized, structural elements readily deployable in industry.

[0008] An example embodiment is directed toward a mold of additive manufacturing material for use in producing a structural element for a structure. The mold includes an interior surface having an interior geometry defined by the additive manufacturing material configured to constrain a composition of matter to be disposed within a volume bounded by the interior surface at least until the composition of matter sufficiently stabilizes (i.e., stabilizes such that the mechanical properties of the materials resist the hydrostatic pressure of casting with no deflection) with a shape, based on the interior geometry, toward becoming the structural element. The mold further includes an exterior surface having an exterior geometry defined by the additive manufacturing material, the exterior geometry being a function of: (i) hydrostatic pressure expected to be exhibited as a combination of at least the composition of matter as constrained by the interior surface, and (ii) properties of the additive manufacturing material between the interior and exterior surfaces.

[0009] In an example embodiment, the additive manufacturing material includes an earthen material and a combination of least one of: a liquid, fiber, sand, or any combination thereof. For additive manufacturing material that includes fiber, the fiber is oriented in the additive manufacturing material within the mold perpendicular to a force of the hydrostatic pressure.

[0010] In an example embodiment, the additive manufacturing material is obtained from a site at which the mold is disposed and sifted to a specified size of granularity.

[0011] In an example embodiment, the mold is a first mold and at least a portion of the additive manufacturing material previously was previously within a second mold, and wherein the first mold may be deconstructed, and the additive manufacturing material may be reused for making at least one third mold.

[0012] In an example embodiment the additive manufacturing material is in a viscous state at the time the composition of matter is introduced within the interior surface.

[0013] In an example embodiment the interior surface is coated with a hydrophobic substance.

[0014] In an example embodiment the interior geometry is a materially efficient structural shape (i.e., a shape that utilizes less material the a conventionally constructed building element with the same use case, while meeting all the same structural load and building code requirements) that constrains the composition of matter to produce the structural element with less composition of matter than the structural element would use absent reduction by the mold.

[0015] In an example embodiment the exterior geometry defines a support structure providing for uniform conditions for drying the additive manufacturing material.

[0016] An example embodiment further includes rebar reinforcement placed within the volume bounded by the interior surface.

[0017] In an example embodiment the rebar reinforcement further includes at least one of the following: (i) a prefabricated rebar reinforcement spacing jig configured to physically locate the rebar at preferential locations within the volume; and (ii) a prefabricated rebar connection jig protruding through the exterior surface through a location, and producing a surface type configured to mate with another structural element, or any combination thereof. [0018] Another embodiment is directed toward a method of fabricating a mold of additive manufacturing material for use in producing a structural element for use in a structure. The method includes extruding an additive manufacturing material to define an interior surface having an interior geometry configured to constrain a composition of matter to be disposed within a volume bounded by the interior surface at least until the composition of matter sufficiently stabilizes within a shape, based on the interior geometry, toward becoming the structural element. The method includes extruding an additive manufacturing material to define an exterior surface having an exterior geometry, the exterior geometry being a function of (i) hydrostatic pressure expected to be produced as a combination of the composition of matter as constrained by the interior surface, and (ii) properties of the additive manufacturing material between the interior and exterior surfaces.

[0019] Another embodiment is directed toward computer-implemented method of 3D- printing a mold. The computer-implemented method includes generating instructions for a tool path for a 3D-printer configured to extrude an additive manufacturing material to define an interior surface with an interior geometry configured to constrain a composition of matter to be disposed within a volume bounded by the interior surface at least until the composition of matter sufficiently stabilizes with a shape of a structural element to be produced, based on the interior geometry, toward becoming the structural element. The computer-implemented method includes generating instructions for a tool path for a 3D-printer configured to extrude the additive manufacturing material to define an exterior surface with an exterior geometry, the exterior geometry being a function of: (i) hydrostatic pressure expected to be exhibited by the interior surface, and (ii) properties of the additive manufacturing material between the interior and exterior surfaces. The computer-implemented method also enables the instructions to be communicated to the 3D-printer to cause the 3D-printer to follow the instructions to 3D-print the mold.

[0020] In an example embodiment the tool path for a 3D-printer is based on a set of design parameters including at least one of: (i) a local building code requirement or restriction, (ii) a structural requirement of the structural element to be produced or a structure to be produced using more than one structural element, or any combination thereof.

[0021] Another embodiment is directed toward a computer-numerical-control (CNC) robot for use in producing a structural element for a structure. The robot includes an extrusion head, and a CNC robot controller configured to cause the extrusion head to extrude an additive manufacturing material having an interior geometry configured to constrain a composition of matter at least until the composition of matter sufficiently stabilizes with a shape, based on the geometry, toward becoming the structural element. The CNC robot controller is further configured cause the extrusion head to extrude an additive manufacturing material to form an exterior surface having an exterior geometry, the exterior geometry being a function of: (i) hydrostatic pressure expected to be exhibited by the composition of matter as constrained by the interior surface, and (ii) properties of the additive manufacturing material between the interior and exterior surfaces.

[0022] In an example embodiment the CNC robot is further configured to perform at least one of the following, prior to the controller’s causing the extrusion head to extrude the additive manufacturing material: (i) mapping a surface of a print area, or (ii) flattening the surface of the print area through use of the extrusion head, an auxiliary mechanical appendage, a modular attachment, or a subsystem communicatively coupled to the controller. [0023] In an example embodiment the CNC robot is further configured to perform dimensional validation of the interior geometry or the exterior geometry by at least one of: LiDar scanning, structured light scanning, touchpoint sensing, physical measurement through use of the extrusion head, an auxiliary mechanical appendage, a modular attachment, or a subsystem communicatively coupled to the controller.

[0024] In an example embodiment the CNC robot further includes a modular attachment coupled to the extrusion head configured to perform, as a function of instructions by the controller, at least one of: (i) applying a physical force configured to settle the material, (ii) providing a guide for placement of, or assist in shaping of a rebar reinforcement, (iii) physically lifting the structural element once it has sufficiently stabilized, or any combination thereof.

[0025] In an example embodiment the controller is further configured to perform at least one of: (i) collecting data relating to the production of the structure, or (ii) transmitting data relating to the production of the structure to a server.

[0026] In an example embodiment the extrusion head is coupled to a multi-axis articulating arm that is one of: a 3 -axis articulating arm, or a 6-axis articulating arm.

BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The foregoing will be apparent from the following more particular description of example embodiments, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating embodiments.

[0028] FIG. 1 is a lifecycle diagram that illustrates how earthen material (“earth”) may be used as a reusable 3D-printable building material, according to an embodiment. [0029] FIG. 2 is a workflow diagram of a system for reusable building structures, according to an embodiment.

[0030] FIGs. 3 A - 3C are graphical representations illustrating design, optimization, and

3D-printing of a system for reusable building structures, according to an embodiment.

[0031] FIG. 4 is a close-up image of an earthen material being extruded from a 3D- printer configured to print the formwork for a mold, according to an embodiment.

[0032] FIG. 5 is an image of a 3D-printed earthen mold for use in producing a structural element of a building structure, according to an embodiment.

[0033] FIG. 6 is a set of three images, illustrating how a 3D-printed earthen mold may be reverted from its mold state and converted back to an extrudable mixture to produce new molds, according to an embodiment.

[0034] FIG. 7 is a graphical representation relating to design parameters and considerations for building a mold for producing a structural element to be used in producing a structure, according to an embodiment.

[0035] FIG. 8 is an image depicting how rebar may be placed within a mold to produce a structural element of a building structure, according to an embodiment.

[0036] FIG. 9 is an image depicting buttressing on the exterior surface of a mold to be used to make a structural component for a building structure, according to an embodiment.

[0037] FIG. 10 is an optimized design for a tilt-up frame embodiment.

[0038] FIG. 11 is a graphical representation depicting how the structural element optimized design varies according to certain design strategies.

[0039] FIGs. 12A and 12B are images illustrating what a tilt-up structural element may look like once the 3D-printed earthen mold has been removed.

[0040] FIG. 13 is a graphical representation illustrating a scanned cast of a structural element and a digital model of the 3D-printed earthen formwork for the same cast.

[0041] FIG. 14 is a simplified block diagram of a computer system in which embodiments may be implemented.

[0042] FIG. 15 is a simplified block diagram of a computer network environment in which embodiments may be implemented.

[0043] FIG. 16 illustrates an earthen formwork system support server environment in which embodiments may be implemented. DETAILED DESCRIPTION

[0044] A description of example embodiments follows.

[0045] Embodiments disclosed herein harness a capability of additive manufacturing to produce materially efficient, shape-optimized structural elements with low-carbon, infinitely recyclable formwork. Embodiments also outline an additive manufacturing formwork methodology applicable across a range of environments and fabrication typologies, including cast-in-place, tilt-up, and pre-fabrication. By making complex formwork more accessible, embodiments make it possible for designers and builders to choose low-carbon options that may previously have been prohibitively expensive and difficult to manufacture.

[0046] Concrete is one of the most widely used modern building materials. Concrete is inexpensive and strong, its components are globally accessible, and a broad spectrum of building typologies, single-story houses to 100-story skyscrapers can be constructed using the same basic building technologies. For many, concrete is a symbol of modernity and success. It is the material of the 21^st-century city. There is a strong likelihood that concrete usage will continue to increase steadily into the foreseeable future. Reducing the material’s climate impact can be coalesced into three basic strategies: (i) change the chemistry of concrete to reduce its carbon emissions, (ii) change how cement is manufactured, or (iii) use less concrete.

[0047] The first strategy is the subject of extensive research with promising but limited results in terms of CO2 savings relative to cost and accessibility [4]. Waste streams from steel manufacturing and other industrial processes can be used to offset some of the concrete’s cement content. However, those waste streams come from industries that are rapidly transforming to reduce their own carbon impact and minimize the very waste driving concrete emissions reductions. Secondly, transitioning cement production to electrochemical systems that utilize a renewable grid mix may cut a portion of emissions, but it is expensive and has not been demonstrated at scale [5]. The third option is seemingly simple and immediately actionable: utilize methods which use less concrete in new construction.

Research has shown that more than half the concrete in a typical building is structurally unnecessary and could be eliminated through shape optimization [6]. The challenge lies in fabrication. Reinforced concrete structures are typically made from consistent rectilinear sections to minimize the complexity of both formwork and reinforcement. Any added complexity in a concrete building can be closely correlated to increased cost and material waste [7]. Unique geometry requires unique formwork and highly skilled labor to fabricate it. As a result, improving the material efficiency of concrete buildings is primarily a challenge of efficiently producing complex formwork.

[0048] Establishing scalable, automated construction methods is a widespread challenge for the building industry. As other manufacturing processes, including automotive and tech, have moved forward with increasing levels of automation, construction has remained a largely manual process [18]. Concrete 3D-printing is growing as an industrialized method for automation in construction, primarily as formwork for more conventional, code-compliant, cast-in-place reinforced concrete structures. This technique can be seen in buildings produced around the world by researchers and construction companies. Studies have also shown the viability of 3D-printed mortar for shape-optimized spanning systems, including waffle slabs and post- tensioned, topology-optimized beams [20]. Recent studies have detailed the advances in 3D-printed cementitious formwork [21], illustrating the key differences between the existing typologies of large-scale additive manufacturing (powder bed and fused deposition).

[0049] As the technology has evolved over the past two decades, similar formwork research efforts have been made with other industrially processed, engineered materials, including thermoplastics, geopolymers, and ceramics. Each of these approaches presents different advantages ranging from high resolution, cantilevering geometry printed over the course of days in plastics [22] to low resolution, minimally cantilevering geometries printed in a matter of minutes using mortar and mineral composites [12]. Each of these studies has a recurring tradeoff between fabrication speed, resolution/geometric freedom and precision, and material performance. Embodiments described herein balance these tradeoffs, creating a system that can be deployed on-site or in a prefabrication context using waste soils already available on building sites.

[0050] In each of the previously mentioned systems, the integration of reinforcement and the afterlife of the formwork material are key sticking points. Finding methods for the use of standard reinforcement design made of readily available rebar sizes and commonly formed shapes facilitates the broader application of these formwork methods [25], [26]. The time required to build a sufficiently robust rebar cage may far exceed that required to produce formwork conventionally or with additive technologies. As such, standardized, prefabricated units are often employed in industry. To realize the potential of mass customization for material saving and design freedom, equal attention must be paid to formwork and reinforcement. For lost formwork strategies, reinforcing may need to be placed sequentially or in modular elements as printing proceeds, creating the potential for added complexity and an increase in the steel used, resulting in higher carbon impacts. Embodiments implemented herein explore multiple approaches to reinforcing and methods for the mass customization of bespoke rebar cages for integration with 3D-printed earth formwork.

[0051] For example, embodiments utilized herein provide for a prefabricated rebar reinforcement spacing jig configured to physically locate the rebar at preferential locations within the volume (i.e., locations which provide the greatest reinforcement benefit), or a prefabricated rebar connection jig protruding through the exterior surface at a location and producing a surface type configured to mate with another structural element. In these embodiments, rebar may be made of carbon steel, recycled steel, a composite material, an alloy, a mesh, or any other suitable structural reinforcement composition for the structural element. These locations may be moment locations for the structural element (i.e., a joint that allows a transfer of a bending forces between a column and a beam or any two members in a structure, i.e., locations of angular force within the overall structure being constructed). This results in lower complexity during construction, as well as the ability to adhere to bespoke rebar geometry suitable for the optimized structural element. Additional rebar placement details are described below, at least in reference to FIG. 8.

[0052] FIG. 1 illustrates a lifecycle diagram 100 of how earthen material (“earth”) may be used as a reusable 3D-printable building material, according to an embodiment. In embodiments, the system starts with using raw earth 101, which may typically be obtained from excavation performed at a construction site or from prior 3D-prints as recycled earth. In these embodiments, raw earth may include but is not limited to roughly 20% - 30% clay and 50% - 70% sand, no more than 10% coarse particles, and a starting water content of 4% - 10% water [45]. The raw earth 101 is left to dry for a period of time, which becomes dry earth 102, and is then sifted 103 to remove impurities from the earth. In some embodiments, straw 104 (i.e., dried stalks of plants such as cellulosic fibers) may be added to the earth to provide strength to the earth. A person of ordinary skill in the art should appreciate many different substances may be added to the earth in place of straw. Additionally, additional strengthening may be implemented through the use of strategically placed stones or concrete blocks placed and arranged to provide additional support to the mold.

[0053] Still referring to FIG. 1, continuing this example embodiment, water 105 is then added to the mixture and mixed 106 to create a viscous (i.e., having a low enough viscosity such that it may easily flow through the extrusion system of the implemented large scale extrusion based additive manufacturing process, but high enough such that it remains in place once extruded) earthen material capable of flowing through an extruder of a 3D-printer 108b. The mixture is then aged 107 before being able to be 3D-printed by the 3D-printer 108b into a 3D-printed formwork 108a for concrete and rebar placement. The formwork 108a with concrete and rebar within is then left to dry 109. Once the formwork 108a has been dried, it may be recycled 110 by being demolished 111 and then rehydrated 112 to convert it back into a mix 106. This process allows the earthen material to be used in an indefinite number of formworks. Further details relating to example embodiments are described below, at least in reference to FIG. 2.

[0054] FIG. 2 is a workflow diagram 200 for a method for fabricating a mold of additive manufacturing material for use in producing a structural element for use in a structure, according to an embodiment. The method begins by extruding at 201 an additive manufacturing material to define an interior surface having an interior geometry. In some embodiments, the interior surface is coated with a hydrophobic substance. The interior geometry and interior surface are configured to constrain a composition of matter (i.e., concrete) to be disposed within a volume bounded by the interior surface at least until the composition of matter sufficiently stabilizes (i.e., stabilizes such that the mechanical properties of the materials resist the hydrostatic pressure of casting with no deflection) within a shape, based on the interior geometry, toward becoming the structural element. In some embodiments, the geometry of the interior surface may be a materially efficient structural shape (i.e., a shape that utilizes less material the a conventionally constructed building element with the same use case, while meeting all the same structural load and building code requirements)that constrains the composition of matter to produce the structural element with less composition of matter than the structural element would use absent reduction by the mold. The additive manufacturing material may be an earthen material and may be obtained from a site at which the mold is disposed and sifted to a specified size of granularity. Further, the additive manufacturing material may include an earthen material and a combination of least one of: a liquid, fiber, sand, or any combination thereof. When the additive manufacturing material includes fiber, the fiber is oriented within the additive manufacturing material perpendicular to a force of the hydrostatic pressure. In addition, the additive manufacturing material may be in a viscous state at the time the composition of matter is introduced within the interior surface. Certain additives, such as sodium silicate, may reduce the water requirement to, for example, 5-40% water and 0 - 20% fiber. Further, rebar may be placed within the interior surface for additional support for the structural element. The rebar may include a prefabricated rebar reinforcement spacing jig configured to physically locate the rebar at preferential locations within the volume (i.e., locations which provide the greatest reinforcement benefit), and or a prefabricated rebar connection jig protruding through the exterior surface at a location and producing a surface type configured to mate with another structural element. These locations may be moment locations for the structural element. [0055] Still referring to FIG. 2, the method continues by extruding the additive manufacturing material to define an exterior surface having a geometry. The exterior geometry being a function of (i) hydrostatic pressure expected to be produced as a combination of the composition of matter as constrained by the interior surface, and (ii) properties of the additive manufacturing material between the interior and exterior surfaces. In some embodiments, the mold is a first mold and at least a portion of the additive manufacturing material previously composed at least a portion of at least one second mold, and the first mold may be deconstructed, and the additive manufacturing material may be reused for making at least one third mold.

[0056] In some embodiments, the geometry of the exterior surface may define a support structure for providing uniform conditions for drying the additive manufacturing material. The exterior surface geometry may include additional buttressing designed to provide additional support for withstanding hydrostatic pressure expected to be exhibited in the mold. For example, see at least the additional buttressing 504 of FIG. 5, described below.

[0057] Additive manufacturing (AM) is a flexible method of digital fabrication. In the embodiments disclosed herein, AM processes produce both finished building elements and temporary formwork for traditional reinforced concrete. Processing and mechanical parameters of the local soil being used are factored into early-stage design to leverage fully the construction potential of AM. The result is building elements that are materially efficient, highly performative, and produced with zero waste. To test and demonstrate material-aware earth 3D-printing for formwork, three implementations of the systems and methods described herein include but are not limited to: (i) cast-in-place, (ii) tilt-up, and (iii) pre-fab, also referred to as shaped.

[0058] Cast-in-place refers to an earth wall acting as lost formwork for a cast-in-place, curving frame poured after the printed earth reaches a dry state in about 72-96 hours. Tilt-up refers to a 2D-shape optimized portal frame cast on its side in an earth mold printed and reinforced with optimized buttressing to resist hydrostatic pressure on the mold in a partially dried state, reducing the time between printing and casting to about 12-24 hours. Pre-fab refers to a 3D-shape optimized beam cast in an earth mold printed to maintain even wall thickness throughout for rapid drying to allow casting within about 24-48 hours and 6-axis surfacing toolpaths for geometric accuracy to maximize material savings.

[0059] Each of these three implementations employs a novel material-driven computational design methodologies to minimize print time and concrete use. In each case, for consistency, the design process was driven by the California Building Code (but may be any other local, regional, or national code) structural design and concrete fabrication requirements, allowing for prototypes that could be used in multistory construction today. [0060] FIGs. 3A - 3C are graphical representations of three different ways 3D-printed formwork may be implemented. In FIG. 3 A, the tilt-up configuration 301 shows how a concrete structure may be constructed by a foundation 302 and titled upwards 90 degrees to be a standing concrete structure. By the foundation 302, an earthen 3D-printed base 303 is extruded from a suitable 3D-printer. A 3D-printed formwork 304 is printed on the base 303, and rebar 305 is added to the formwork 304. Concrete 306 is then poured, and once it has dried, the formwork is removed, and the concrete structure is tilted up 90 degrees.

[0061] Referring to FIG. 3B, the cast-in-place configuration 311 shows how a concrete structure may be constructed by being cast-in-place around a 3D-printed earthen formwork. A foundation 312 is laid, and a 3D-printed earthen formwork 313 is printed on top of the foundation 312. Rebar 314a-b is added within the formwork 313, and a 3D-printed earthen wall 315 is built on top of the formwork 313. Concrete 316 is then poured, and once it has dried, the formwork is removed, and the concrete structure remains.

[0062] Referring to FIG. 3C, the shaped configuration 321 shows how a concrete structure may be cast into any shape using 3D-printed earthen formwork. A roughing pass 322a-b is printed with a suitable 3D-printer. Next, a bridging pass 323 is printed within the shaped structure, followed by a finish pass 324. Rebar 325 is then added atop the finish pass 323, followed by a concrete pour 326. Once the concrete 326 has dried and the 3D-printed earthen formwork is removed, a shaped concrete structure remains.

[0063] A simple mixture of earth, water, and straw produces the raw earth material suitable for 3D-printing (See FIG. 1). An appropriate mixture for climate and printing needs is determined by adjusting the ratio of each component. Two earth sources are primarily used by embodiments disclosed herein: raw local earth, and that same earth recycled from prior 3D mud prints.

[0064] After excavation, raw earth is sifted to sort out particles greater than 1cm in diameter, a constraint defined by the pumping system (for example, a progressive cavity pump). Sifting is more easily enabled when the earth is dry, and if necessary, it can be spread into a thin layer to sun dry prior to sifting. Earth is passed through a sifting structure with an angled wire mesh and thus sorted to an appropriate particle size for pumping to the 3D- printing end effector. While a particular sifting method process is defined herein, any sifting method capable of separating particles having a size (e.g., diameter) greater than 1 cm may be used to separate such particles from raw earth. All such methods are envisioned and should be considered to be within the scope of this disclosure.

[0065] Once earth is sifted, it is weighed and mixed. For example, 100 kg of earth batches were mixed at a time during tesing. This was a feasible quantity to batch in a six- cubic-foot concrete mixer and transport via wheelbarrow. To reach a final mixture with 15%- 20% hydration, 20 kg of water (by weight) was added into the mixer, followed by 50 kg of the dry earth in 10 kg increments. Once the earth and water had homogenized (5-10 minutes mixing), 0.03 kg mulched straw with a maximum length of 10 cm was added. Once thoroughly incorporated, the remaining 50 kg of sifted earth was added to the mixture in batches of 10 kg at a time. The mud thickens with each addition of dry earth, and when mixing is completed, the mud body can flow but is still viscous and cohesive. In total, in some embodiments, each batch consists of 100 kg of dry sifted earth, 20 kg of water, and 0.03 kg of chopped straw.

[0066] FIG. 4 shows a close-up image 400 of earthen material being extruded from a 3D- printer configured to print a mold for a structural element to be used in producing a structure, according to an embodiment. The earthen material 401 is extruded from the print head or extrusion head 402 of a computer-numerical-control (CNC) robot (not pictured) in layers 403 that eventually build up the mold. The earthen material 401 is wet as it is extruded, and once it has sufficiently stabilized, rebar and concrete (not shown) may then be added within the mold.

[0067] FIG. 5 shows an image 500 depicting a 3D-printed earthen mold for use in producing a structural element of a building structure, according to an embodiment. A CNC robot 501 configured to extrude an earthen material prints an interior surface 502 and an exterior surface 503 layer by layer until the desired height and shape of the mold is completed. The exterior surface 503 contains additional buttressing 504 designed to hold a hydrostatic pressure expected to be produced by the interior surface and the wet concrete to be poured within. Rebar 505 is placed within the interior surface of the mold to add strength to the structural element to be produced.

[0068] In some embodiments, the CNC robot may be a robot configured to extrude, via an extrusion head or similar attachment, the earthen material into a mold upon instruction from a robot controller. The robot controller may be configured to map the surface of a print area, flatten the surface of the print area through use of the extrusion head, an auxiliary mechanical appendage, a modular attachment, or a subsystem communicatively coupled to the controller. The extrusion head of the 3D-printer may take several forms ranging from an open pipe with swappable nozzle sizes, to an auger or pinch valve configured to calibrate the stop and start of earthen material flow. Further, the controller may perform dimensional validation of the interior geometry or the exterior geometry by at least one of: LiDar scanning, structured light scanning, touchpoint sensing, physical measurement, or any combination thereof. Further still, the CNC robot may comprise a modular attachment coupled to the extrusion head configured to perform, as a function of instructions by the controller, applying a physical force configured to settle the material, providing a guide for placement of, or assist in shaping of a rebar reinforcement, and or physically lifting the structural element once it has sufficiently stabilized. The extrusion head of the robot may be coupled to, for example, a 3-axis or a 6-axis articulating arm.

[0069] FIG. 6 shows three images, 601, 602, and 603 respectively, illustrating how a 3D- printed earthen mold may be reverted from its mold state (once the mold has been removed) back to an extrudable mixture to produce new molds. Once the structural element has sufficiently settled into a shape, the mold may be removed. The dry pieces of the removed mold 601 can then be collected. Then, the dry pieces 601 may be saturated with water, which is represented by the damp mold pieces 602. Further saturation, represented by a mixed and wet extrudable material 603 can then be reused to create further molds. Embodiments disclosed herein may take advantage of passive recycling method, i.e., leaving the dry pieces in water for one to three days so that it may be reconstituted, or an active recycling method, i.e., actively mixing the dry pieces with water so that it may be read to be reused within ten to fifteen minutes.

[0070] The processing of recycled (already printed) earth varies slightly because this material has already been sifted and modified with straw. Therefore, the mud does not need to be crushed and sifted; it can simply be rehydrated. If the mud to be recycled contains pieces of concrete from the casting process larger than a predefined threshold (e.g., a 1 cm particle size threshold which may correspond to a particle size acceptable by a pump configured to pump the additive material), it can be dried, crushed, and re-sifted. Recycled mud is more easily re-hydrated if the surface area is increased by breaking apart the dried chunks. Recycled 3D mud prints may be crushed, weighed, and added to a wheelbarrow using a sledgehammer. A ratio of 20% water by weight is then poured over the dried pieces of 3D-prints. A hoe or shovel may be helpful for mixing and turning the mud as it hydrates. The rehydrated chunks and straw can then be added to the concrete mixer or turned and combined with a shovel until the desired homogenous mixture is achieved. Leaving the rehydrated material for 12-48 hours facilitates the complete homogenization of the mix. However, it is entirely possible to print immediately after remixing a batch of the earth so long as the mixing is thorough. Larger scale equipment used in geotechnical engineering, such as sifting shake tables and higher volume concrete mixers, could be used to accelerate and scale the material processing workflow.

[0071] One advantage of additive manufacturing with the earth is the potential for not only producing formwork on-site but also integrating earth excavated during initial construction into the formwork’s earth mixture. Onsite fabrication of formwork with excavated earth may cut down on the transportation costs of structural elements and disposal of excavated earth and allow for real-time modification of formwork designs. For this approach to be effective, it may be helpful that local and site-specific environmental conditions, such as humidity, precipitation, and sun exposure, are taken into consideration and that soil is tested to evaluate how it will perform as formwork. Environmental conditions may impact the ratio of ingredients used in the mud mixture, printing time, and drying time. Slight workflow modifications, such as shade structures, additional water, or fans, may accommodate environmental fluctuations.

[0072] Earth for printing can be sourced directly from the construction site where the printed forms are needed. However, there may be significant variations from site to site depending on geography, depth of excavation, and geologic history. Some indicators that local earth is suitable for additive manufacturing are if there is existing earthen architecture in the region or if there is evidence of erosion and silty deposits nearby. The color and texture of the earth can be a good indication as well. There are simple onsite field tests and printingspecific tests for determining a material's cantilever and bridging potential, which can indicate if a site’s soil is adequate for earthen construction and formwork [36]. In these embodiments, raw earth may include but is not limited to roughly 20% - 30% clay and 50% - 70% sand, no more than 10% coarse particles, and a starting water content of 4% - 10% water [45]. Field tests for evaluation are adequate for 3D-printing formwork uses; however, further geotechnical, structural, and chemical laboratory tests may be done as well if the intention is to leave earthen formwork as part of the completed structure for structural, thermal, or aesthetic reasons. Further lab testing on the earth may include dry density, unconfmed compressive strength, particle size distribution, plastic limit, expansion index, and specific gravity.

[0073] Mold release agents may be helpful in removing the concrete from the earth molds and limiting water exchange. Various mold coatings were explored to minimize moisture exchange between printed earth and poured concrete, given the potential to reduce concrete strength and consistency. Test coatings included ceramic wax (for example, car wax), oil lubricants (for example, a sprayable penetrating oil), and spray-on rubber. 3D-printed earth cylinders with an interior dimension of 20cm diameter and 100cm height were printed and left to dry to a “leather hard state” (moisture content approximately 5%) before being coated with three layers of each material, leaving time for each coat to dry before the next is applied. Rubber coating was removed from the experiment because it limits the recyclability of the earth mixture, while wax does not. Three samples of wax-coated and uncoated cylinders were prepared, along with three control cylinders of the same dimension cast in plastic molds. Concrete was then cast in the cylinders, de -molded after one week, and load tested after one month. [0074] Load tests of the cast concrete cylinders did not indicate a significant difference between wax-coated and uncoated molds. A set of six cast concrete cylinders were then prepared, three from waxed earth molds and three from unwaxed molds. In unconfmed compression tests, no statistically significant difference was found in performance between the cylinders.

[0075] A computational design workflow may be implemented to allow the builder to factor in material, structural, and fabrication considerations from an early stage. The design software may use, for example, Rhino3D/ Grasshopper [37], the Design Space Explorer plugin [38], Python 3.8, and the Karamba 3D plugin [39] to integrate material properties and structural optimization to produce 2D and 3D shape-optimized concrete elements, including frames, beams, and foundations. The fabrication method to be used may be defined by the size of the building element and how it can be manufactured as quickly as possible; for example, instead of printing formwork for a frame to be cast in one piece standing vertically, the model is positioned on its side, and a tilt-up strategy is employed, reducing print time from days to minutes. As the designer works, the model may provide key metrics, including material usage in both final geometry and forms, as well as estimated fabrication time and stability of the mold during fabrication and under the hydrostatic pressure of casting, allowing for carbon-informed design exploration within the latent space of the shape optimization. Toolpaths for the finalized geometry may then be generated with the specified layer resolution. The toolpaths used in these embodiments are continuous in order to minimize print time, requiring careful consideration of print sequence.

[0076] FIG. 7 shows a graphical representation 700 relating to design parameters and considerations for building a mold for producing a structural element to be used in producing a structure, according to an embodiment. A user may input design parameters 701 into a design software to influence an optimized design. These design parameters 701 may be design constraints 702, such as a local building code, structural requirements, or programmatic needs. They may also be fabrication constraints 703, such as the machine and the material being used. In addition, the design parameters 701 may be an objective 704 of the structural element, such as material savings or carbon reduction. These design parameters are input into the software, which designs an optimized design 705 of the structural element. Then, the 3D-printing 706 of the mold may begin. [0077] Designing and fabricating additive earth formwork requires careful detailing.

Earth, as a traditional building material, absorbs tolerance errors. As the material takes on a more significant role in modern construction and as concrete formwork, it may be useful to consider tolerance, margin of error, and installation of structural elements. Detailing differs for each case situation, but overarching considerations may include rebar clear cover that meets local building code, lifting points for modular cast elements, and the moment connections between the foundation, wall, and beam. In each case, some embodiments utilize higher resolution 3D-printed thermoplastic jigs. Printed clips (see FIG. 8) make it possible to hand-bend rebar approximately to shape and then additively improve the accuracy of the cage as each clip is connected, completing the cage. These elements may also be mass customized and deployed as needed to maintain clear cover or register a moment connection.

[0078] FIG. 8 shows an image 800 depicting how rebar may be placed within a mold to produce a structural element of a building structure, according to an embodiment. Rebar 801 is placed within the mold to provide strength and reinforcement to the concrete of the structural element. Prefabricated clips 802a-n make it possible to construct the rebar in an optimal fashion by taking any guess work out of the rebar placement. These clips 802a-n are prefabricated at a desired length and allow the rebar 801 to be placed at pre-defined distances from additional rebar within the mold. This ensures an optimal rebar placement prior to the concrete being poured.

[0079] In preparation for lifting and moving the cast-in-place interior and exterior surfaces of the mold, the earth print may be modified to create the negative space required in the foundation for direct lifting with a forklift. In some embodiments, plastic is laid down so the print can contract upon itself as it dries, and lifting straps are laid below the plastic. After the precast frame has cured, the straps may be used to lift and move the element to the site. [0080] Modular concrete elements rely on robust moment connections. These connection points are dictated by the digital model and are coordinated with footing and beam connections. For foundation connections, steel plates with holes for bolted connections may be welded to the rebar cage, producing moment connections compliant with a local building code, for example California building code [42, p. 19]. 3D-printed plastic plugs may be inserted into the bolt holes, preventing concrete from being cast in these zones so that bolts can be placed and tightened when the element was lifted into position. [0081] Hydrostatic pressure increases linearly with depth, leading to high lateral loads on formwork at the base of a wall or column. Baseline hydrostatic pressure tests were conducted for printed earth [28]. In the methodology of embodiments presented herein, buttressing is parametrically generated in response to a model of hydrostatic pressure after the shape optimization of a base geometry is completed. This technique is both computationally quick and may be applied across a wide range of geometric conditions, facilitating casting before the mold is dry. For hybrid, lost formwork earth/concrete structures, more bespoke consideration of hydrostatic pressure may be required. Tests up to three meters were conducted on cylinders of various moisture content samples from wet to dry printed earth with an interior diameter of 20cm, wall thickness of 40mm, and a 20mm layer height. Cylinders were chosen to provide a uniform loading condition in 360 degrees. Concrete with a density of 2.4g/cm³ was used, and five seconds of vibrating compaction with a vibratory rod was used after the concrete reached a depth of 10cm and again at 20cm to properly simulate larger scale casts. No deformation or failure was observed in all but the highest water content tests, indicating the material’s robustness as formwork.

[0082] The hydrostatic pressure test cylinders were loaded with wet concrete to a pressure of 0.11 mega pascal (MPa). Across three samples for each water content (5%, 10%, 15%, 20%), failure was only observed in the 15-20% water content cylinders. Below 10% water content (or a “leather hard” state by feel), the cylinders were not deformed; above 10% water content, local buckling was observed in a classic hoop stress failure, resulting in a split in the mold approximately 5 cm from the base of the cylinder. Frictional forces prevent the failure from occurring at the bottom of the mold, where pressure is highest. Given the initial results described herein and in [28], a larger-scale test was conducted on a single cylinder at 5% water content (the typical moisture level at which the test case studies were cast). The cylinder’s height was extended with three meters of plastic tubing. When fully loaded to a hydrostatic pressure of 0.17 MPa, no deformation was observed by fdling the tube with wet concrete.

[0083] The design workflow was reconfigured to assume the earth at casting moisture of 5% could resist 0.1 MPa of hydrostatic pressure. This assumption gives the model a minimum safety factor of 1.5 based on these tests and enables prediction of where buckling would occur, particularly in long, straight sections of the mold. [0084] FIG. 9 shows an image 900 depicting buttressing on the exterior surface of a mold to be used to make a structural component for a building structure, according to an embodiment. The exterior surface of the mold structure contains additional buttressing features 901 designed to support a hydrostatic pressure expected to be produced as a combination of the forces of the interior surface 902 and the poured concrete 903.

[0085] Within the scope of traditional additive manufacturing and for most of the printing paths outlined herein, a 3 -axis gantry system is sufficient. However, a 6-axis systems may achieve increasingly complex geometries, where the tool path is no longer relegated to planar, vertically-oriented configurations. Non-planar configurations may better conform to 3D surface conditions, provide more accurate surface reproduction, and limit undesirable surface finishes [41].

[0086] As desired geometry increases in size and with lower robotic mobility (fixed robotic arms), it may be useful to develop a robotic locomotion strategy for reachability and to avoid singularities within a print. Machine toolpaths exit the digital model with polar planar rotations to maximize the arm's reach and allow continuous printing through typically problematic quadrant-based singularities.

[0087] A toolpath may be placed within the robot cell’s given work area, sometimes spanning 360 degrees. Specific geometries may be better suited for such a configuration, for example, tilt-up frames that can wrap around a robot's mounting location. However, positioning is not always entirely sufficient, and instead, the robot axes should respond to the toolpath’s location at any given time. In the case of a long-spanning beam (>4m), where the entire cartesian X or Y axis of a robot is needed, singularities in the wrist (between axes four and six) may occur. However, such an event depends on work height and whether or not the robot’s configuration will render axis five at 0 degrees.

[0088] Alternatively, after a tool path is positioned, its position frames may be calculated and reoriented so that the X-axis points in the robot's direction in a polar fashion. Additional universal manual plane rotations varying from -20 to 20 degrees may improve printability. In such a case, the plane's Z-axes have not changed their vectors.

[0089] In some situations, the geometry to be cast may exceed the tolerance of the available build area. The ground plane may not be flat enough to maintain a submillimeter tolerance across a four-meter beam. As such, in some embodiments, a roughing raft pass is used to create a surface precisely parallel to the robot’s base plane. This may only require one pass over the build area, or in more extreme scenarios (printing on-site or in an environment where site preparation is not practical), an interpolated leveling strategy may be employed by building up increasing planar layers of material relative to a starting mesh conformal to the build surface. This may be achieved through 3D-scanning the site, projecting the base toolpath to the scan, and interpolating layers upward to a plane from the scan surface. In some embodiments, a single layer of material may be sufficient to rationalize a warehouse floor and provide a precise platform for printing.

[0090] Given that printing systems using minimally processed local materials may be time-consuming to calibrate for retraction, embodiments may employ continuous extrusion and may use strategic toolpathing algorithms (i.e., computer-implemented methods) to avoid the need for travel moves. This also may reduce the cost and complexity of both the extruder pump and pump control system, as no pinch valves or speed control integration is necessary. For print base surface rationalization, a model may use a simple linear parallel path or, in the case of more complex geometry, a reaction-diffusion space-filling curve. For roughing and finishing passes in 2D and 3D shaped molds, a square waveform of consistent frequency but variable amplitude may be used to tailor a continuous curve to produce an accurate surface. For 3D forms, a roughing pass may be printed in 2.5D (X and Y rotation fixed, Z moving) for high-speed printing, followed by a fully 3D finish pass normal to the model surface.

[0091] This cradle-to-grave model of embodiments utilized herein assumes that both the robotic arm and pump are operating at full power all the time and does not account for the circularity of the material. A conservative estimate of 0.006kgC02/kg indicates that, unlike other additive manufacturing processes, carbon impact may be driven by print time, not material quantity. The most considerable carbon impacts for a functional unit of printed earth may come from the power draw of the pumping system. Practically, however, limiting material usage correlates to minimizing print time; the shorter the print path, the less run time and material are required. Compared to other AM formwork methods using foam, mortar, thermoplastics, or even fired clay, the carbon impact is low enough that entirely different design considerations are possible. Material usage may not be a cost or carbon concern so long as overall fabrication time does not impede production. This opens up possibilities like using earth as support material and infill for 3D-shaped molds or as buttressing to resist hydrostatic pressure without incurring a significantly elevated carbon impact. [0092] To illustrate the generalizability of the these embodiments, three case studies were designed and fabricated for testing. Case Study One relates to a cast-in-place wall and frame system, Case Study Two relates to a 2D shape-optimized tilt-up portal frame, and Case Study Three relates to a 3D shape-optimized flanged beam.

[0093] In Case Study One, a cast-in-place hybrid earth and concrete wall was designed to illustrate the potential for in-situ casting of concrete frames in nonbearing earth walls. The wall consisted of a reinforced concrete footing cast into 3D-printed earth formwork, a 3D- printed earth wall, four reinforced concrete columns cast into the wall, and a reinforced concrete sill. The earth print could be removed from the sill but remains in place for the wall and foundations after casting. Code-compliant rebar cages are bent and tied by hand using 3D-printed plastic clips to ensure proper spacing and position, according to an embodiment. All thread rods with threaded couplings were integrated into the base of the column cages, allowing for the placement of the vertical column rebar sequentially in half-meter sections as the print progressed in height..

[0094] The fabrication of the hybrid earth wall was more time-consuming than the other case study geometries due to drying requirements between prints of vertical wall sections. After 30cm of printing, the material needs to lose at least 5% of its moisture content to facilitate the addition of another 30cm of wet earth without failing under its self- weight. Drying time is dependent on atmospheric conditions in the printing space; on hot, low humidity (18°-30°C) days, printing up to a meter in 3-4 printing sessions spaced three hours apart may be possible. On higher humidity and lower temperature days (8°-18°C), printing may be limited to 50-60cm with six hours between 2-3 printing sessions. In earlier experiments printed outdoors, wind was found to be a drying accelerant but also the cause of differential drying and resultant cracking.

[0095] In Case Study Two, a portal frame was designed using a 2D multi-objective shape optimization to minimize concrete while meeting design and code structural requirements. The 2D shape optimization approach taken here is a numerical method that does not accurately model concrete mechanics, instead treating the concrete as an elastic material. This is in contrast to Case Study Three, described below, in which a 3D-shape optimization model was used, taking into account the full mechanical behavior of reinforced concrete. The frame was fabricated on its side, a “tilt-up” casting strategy common in on site manufacturing of monolithic concrete walls for big-box stores and warehouses with sufficient staging areas. Here, the goal was to produce a materially efficient structural element, maximizing the working range of a single robot arm while keeping the fabrication time as low as possible. The formwork included a space-filling pattern on the ground plane, a printed extrusion of the frame’s 2D profile, and printed buttresses to manage the hydrostatic pressure of concrete during the casting process. The frame included steel plates for bolted connections at its base and connection points for beams along its top. Once cured, the 3D-printed formwork was removed, and the frame was tilted into its upright position. Of the three embodied methods tested, the tilt-up frame embodiment may be considered the most successful in that the ratio of material used in both the mold and the cast element was minimal, the rebar cage was conventional and straightforward to fabricate, and the final product was immediately ready for use as a structural component of a code compliant building. This was the fastest way to manufacture the structural element while also being the largest single cast.

[0096] The tilt-up frame was designed for an interior wall condition with a tributary area of 3m x 3m, or 9m². These loads were transferred to the frame as a distributed line load. In the computational model, the frame was treated as a 2D mesh, with 274 points along the top of the frame, which received the total live (1.9 kN/m2) and dead (12.94 kN/m2) loads. The frame was designed to have two fixed connections with the ground.

[0097] FIG. 10 shows an optimized design 1000 for a tilt-up frame embodiment. Dimensions lOOla-b are shown for the optimized design, as well as a lOkN vertical load 1002a being applied downward on the top of the structure, and a vertical load 902b being applied laterally to the structure. Included in the optimized design are parameterized control points 1003, as well as fixed control points 1004. Not all control points are individually identified for clarity. The control polygon 1005 is also shown, which represents a standard structural element without the optimization performed, this control polygon 1005 also represents the minimum coverage area for rebar covering 1006. The optimization output 1007 represents an optimized design for the structural element to support the applied loads 1002a- b. The final frame 1008 represents the suggested optimized frame shape for the structural element in this embodiment for this use case, the optimized design may vary depending on structural necessity and use case. The optimized design 1000 also shows a deflected shape 1009 of how the structure may fail.

[0098] FIG. 11 shows a graphical representation 1100 depicting how the structural element varies according to certain design strategies. Designed-to-code structural element 1101 represents a structural element design taking into consideration only the local building code. In this example, structural element 1101 has a volume of 0.491 m³, a weight of 1,179.8 kg, and an EC of 218.3 kgCO². Conventional formwork designed structural element 1002 represents a structural element that may be designed using conventional formwork. In this example, structural element 1102 has a volume of 0.276 m³, a weight of 663.2 kg, and an EC of 122.7 kgCO². Shape optimized structural element 1003 utilizes embodiments disclosed herein but does not account for the minimum rebar coverage. In this example, shape optimized structural element 1103 has a volume of 0.205 m³, a weight of 492.6 kg, and an EC of 91.1 kgCO², which is a notable reduction in EC from structural elements 1001 and 1102. Shape optimized structural element adjusted for rebar 1104 utilizes the same design strategies from structural element 1003, however since minimum rebar coverage was not met with structural element 1103, structural element 1104 has been adjusted to provide the minimum rebar coverage. In this example, shape optimized structural element 1004 has a volume of 0.237 m³, a weight of 569.5 kg, and an EC of 105.5 kgCO².

[0099] Live loads, dead loads of the overlying slab, and frame weight were integrated into the model for single, double, and three-story conditions. The cast frame had a volume of 0.237 m³ and a weight of 569.5 kg, based on an estimated concrete density of 2,400 kg/m³. Frame reinforcement totaled 28.65 m of #4 rebar and weighed 28.57 kg, based on an estimated steel weight of 1 kg/linear meter. Based on these values, the total weight of the tilt- up frame was approximately 675 kg or 6.62 kN. Additional levels were loaded at two points along the vertical columns of the frame. Lateral load was calculated by using 20% of the total weight of the frame (6.62 kN), which is 1.3 kN.

[00100] FIGs. 12A and 12B show images 1201 and 1210, respectively, illustrating what a tilt-up structural element may look like once the 3D-printed earthen mold has been removed. FIG. 12A shows 3D-printed plastic rebar chairs 1202a-n that are visible to illustrate the shaping of the rebar to match the overall optimization for the structural element. FIG. 12B shows the moment connection location 1211 at which a plastic insert was used during the concrete pouring process to accurately register the moment connections at the top of the frame. These plastic inserts are removed after the casting has been completed, though they allow for a smooth and flat moment connection point 1211.

[00101] The two objectives of optimization are reducing maximum displacement and the 2D mesh area of the frame. The mesh area was parameterized with eight fixed and 12 adjustable control points, xl, x4, x9, and xl2 are parameterized to move horizontally, while all other parameterized control points move vertically. Displacement was calculated from a Karamba 3D model, modeling the frame as a 2D shell with a constant thickness. The optimization objective was to decrease the mesh area in 2D while maintaining a design constrained by the maximum allowable displacement (4mm). A penalty was applied if the max displacement is met and the displacement value is multiplied by a factor of four, exaggerating the penalty to limit quickly the design space of acceptable options. This value was then added to the output mesh area, dramatically increasing the objective value and clearly designating a poor solution. Optimization was run using the DSE toolbox [38]. First, a global optimization was run, followed by a local optimization. The optimization result is then exported and adjusted based on fabrication constraints.

[00102] In Case Study Three, a four-meter, 3D-shaped beam was designed using Beam Shape Explorer (BSE) [24], a tool that optimizes a series of the sections along the beam within a set of fabrication constraints, accurately accounting for concrete mechanics, and then lofts the resultant sections into a complete beam. The resultant solid geometry was then translated into a printable mold design, which included a 3 -axis roughing pass and a 6-axis finishing pass. The roughing pass takes advantage of the maximum bridging distances possible within two layers of printed earth at 20 cm layer heights, creating space for airflow underneath the mold to allow for even drying and the reduction of print material, thus reducing print time. The finishing pass utilizes space-filling waveforms with a fixed frequency and variable amplitude to cover effectively the complex 3D surface of the optimized beam mold. The printing took place over two days, leaving the roughing pass overnight to dry slowly to an adequate strength for the finish pass.

[00103] The reinforcement cage consisted of one piece of #4 rebar bent to an optimal shape defined by the multi-objective structural analysis and a grid of steel wire in the flange to provide transverse and temperature reinforcement. It is possible to bend the single, 20- shaped bar accurately by chalking a template curve on the floor. This may be done by hand through measurement or by simply attaching a drawing tool to the available CNC/robot system in use for printing. The rebar was positioned using the edge of the printed mold to support temporary suspension points for the cage. Additionally, 3x3x3 cm concrete Dobie blocks were placed under the cage to maintain proper clear cover during casting. These blocks were cast in reusable 3D-printed PLA molds. While printing this case study was more complex than the 2D-shaped tilt-up frame, the reinforcement was more straightforward to manufacture and left less room for human error and compounding tolerance issues. The challenge of fabricating the 3D shape-optimized beam was manufacturing an accurate, doubly curved mold surface through space-fdling toolpath generation and 6-axis extrusion oriented normal to the surface.

[00104] Case Study Three revealed two challenges to these embodiments. First, rationalizing a 3D geometry into a mold toolpath containing 3- and 6-axis paths required careful tolerance calibration and simulation to ensure the 6-axis paths did not cause the printer nozzle to intersect or scrape elements of the roughing pass. Once integrated into the parametric design model, further adjustments for similar beam geometry were straightforward. However, these pathing issues may be different for any number of 3D geometries. The second challenge is surface finish. In the tilt-up frame case study, embodiments leverage the imprint of the print path on the cast concrete for its aesthetic and expressive quality; here, embodiments explore making a smooth casting surface. While areas of the resultant beam have only a subtle imprint of the finish pass, other regions with slight under-extrusion produced small holes in the mold surface, leading to seam lines in the concrete cast. This challenge may be addressed by smoothing the mold surface after printing either robotically or by hand. Each corner of the space-filling square wave making up the finish pass contains a 12.5mm radius fillet from the nozzle geometry, making small gaps in the surface inevitable. Programmed over extrusion may address this.

[00105] Each case study mold and resultant concrete geometry was scanned and measured wherever possible. Lost formwork casts were not extracted for measurement. Various strategies were employed, each with its own assumed accuracy and tradeoffs. The first strategy was LiDar scanning, the second strategy was structured light scanning, the third strategy was touchpoint measurements of the mold, the fourth strategy was measuring using a tape measure, and the fifth strategy was weighing cast parts when possible.

[00106] 3D-scanning at the scale of a four-meter object poses inherent accuracy issues, given that none of the geometry produced may be scanned from a single point. Systems, such as a total station, needed to conduct accurate and repeatable measurements of sub-millimeter dimensions on a full-scale geometry may be more expensive than the entire existing printing system combined. A 2mm dimensional accuracy goal is chosen to comply with conventional, stick-built structures in California. Ultimately, it was found that direct measurement of critical dimensions, such as relative moment connection position by hand and with a pointer on the robot arm, was the most relevant to constructing accurate building elements. The surface of the cast reflects the resolution of the printed mold, resulting in a ridged texture. Global measurement of excess material from these ridges or other inaccuracies in the mold is difficult to quantify without weighing the element.

[00107] FIG. 13 shows a graphical representation 1300 illustrating a scanned cast 1301 of a structural element and a digital model 1302 of the 3D-printed earthen formwork for the same cast. In the graphical representation 1300, it can be seen that the details 1303 on the face of the cast are a result of the 3D-printed earthen formwork infill 1204 on the bottom of the mold. In some embodiments, this infill can be intentionally shaped to provide a desired design. In addition, it can be seen that there is a small amount of excess material 1305 on some edges of the scanned cast. This is a result of thin pieces of concrete making its way into the negative space between the extruded layers of the interior surface.

[00108] An advantage of LiDar scanning is the ability to precisely adjust the resolution of a given geometry through manipulations of layer height and print orientation. In the case of the 3D-shaped beam, the flange surfaces were ultimately more accurate than the side walls of the beam because they may be printed normal to the original input geometry. Doing so in the vertical walls of the beam may be performed using a smoothing nozzle attachment due to limitations of reach and self-intersection. In these tests, inaccuracies primarily occur as a result of the following factors: irregular extrusion, print resolution, or differential drying.

[00109] Irregular extrusion may be a result of mix inconsistency. Print resolution is essentially a matter of layer height choice and print nozzle sophistication. Entirely smooth, singly curved print surfaces may be achieved through active troweling. Differential drying is a more complex problem to address [19]. Given the addition of straw to the mix and the likely alignment of clay platelets in the extrusion process, the material is fundamentally anisotropic. In other words, the fiber is oriented in the additive manufacturing material (the earthen mold) in a direction perpendicular to a force of hydrostatic pressure. Frictional forces between the print and the print surface also influence how a print changes during drying. In these tests, most of these concerns were addressed by simply casting when the print still retains 5-10% of its moisture, limiting measured shrinkage to under 1%. A shrinkage factor was built into the parametric mold pipeline. [00110] Embodiments disclosed herein present novel additive manufacturing methods for fabricating reinforced concrete structures with 3D-printed, locally sourced earth. The ability to print geometrically complex (or simple) molds at a super-meter scale with directly recyclable, truly zero-waste material opens extensive opportunities for architects and engineers working to lower the climate impact of new construction. Additionally, these embodiments offer new aesthetic potentials in overall form and surface consideration. The process may be calibrated to the resolution required in different building elements through adjustments to layer height and print orientation.

[00111] The materially informed computational design methods developed to produce the case embodiments provide a reproducible framework for a wide range of potential building applications. Hybrid earthen structures with integrated voids for cast-reinforced concrete elements and geometrically complex-shaped concrete elements may be manufactured. Tools for rationalizing large print surfaces make these methods accessible for on-site fabrication and in a prefabrication factory setting. The automated buttressing algorithm facilitates the production of typically unstable print geometries (long straight sections) and allows for stable casting without form ties. Methods for calibrating tolerance in key mold sections through printed inserts make it possible to register elements accurately with an otherwise low- resolution surface. Similarly, mass customized 3D-printed rebar clips allow conventional rebar fabrication techniques to be accurately applied to shaped concrete geometry, minimizing steel usage and simplifying the construction of code-compliant rebar cages. The combination of printing and reinforcement strategies enables flexible and rapid application of these embodiment’s methods to geometrically complex building elements.

[00112] The significance of these embodied methods lies in their direct and flexible applicability to existing structural design standards. By designing a method around how reinforced concrete buildings are constructed today, embodiments provide a framework for implementing impactful carbon and cost-saving designs that were previously inaccessible due to geometric complexity. The use of local soil, a widely available material, and reproducible computational methods that may be adapted to a given soil's mechanical properties make 3D- printing earth formwork feasible anywhere that a robotic printing system can be deployed. [00113] FIG. 14 is a simplified block diagram of a computer-based system 1400 that may be used to implement any embodiments described herein. The system 1400 comprises a bus 1401. The bus 1401 serves as an interconnect between the various components of the system 1400. Connected to the bus 1401 is an input/output device interface 1402 for connecting various input and output devices such as a keyboard, mouse, display, speakers, etc. to the system 1400. A central processing unit (CPU) 1406 is connected to the bus 1401 and provides for the execution of computer instructions implementing embodiments, e.g., optimized design of a structural element, generating instructions for a tool path for a 3D- printer, or a CNC robot controller configured to cause an extrusion head to construct the mold. Memory 1403 provides volatile storage for data used for carrying out computer instructions implementing embodiments described herein. Storage 1404 provides non-volatile storage for software instructions, such as an operating system (not shown) and embodiment configurations, etc. The system 1400 also comprises a network interface 1405 for connecting to any variety of networks known in the art, including wide area networks (WANs) and local area networks (LANs).

[00114] It should be understood that the example embodiments described herein may be implemented in many different ways. In some instances, the various methods and machines described herein may each be implemented by a physical, virtual, or hybrid general purpose computer, such as the computer system 1400, or a computer network environment such as the computer environment 1500, described herein below in relation to FIG. 15. The computer system 1400 may be transformed into the machines that execute the methods described herein, for example, by loading software instructions into either memory 1403 or non-volatile storage 1404 for execution by the CPU 1406. One of ordinary skill in the art should further understand that the system 1400 and its various components may be configured to carry out any embodiments or combination of embodiments described herein. Further, the system 1400 may implement the various embodiments described herein utilizing any combination of hardware, software, and firmware modules operatively coupled, internally, or externally, to the system 1400.

[00115] FIG. 15 illustrates a computer network environment 1500 in which an embodiment of the present invention may be implemented. In the computer network environment 1500, the server 1501 is linked through the communications network 1502 to the clients 1503a-n. The environment 1500 may be used to allow the clients 1503a-n, alone or in combination with the server 1501, to execute any of the methods described herein, for example optimized design of a structural element, generating instructions for a tool path for a 3D-printer, or a CNC robot controller configured to cause an extrusion head to construct the mold. For non-limiting example, computer network environment 1500 provides cloud computing embodiments, software as a service (SAAS) embodiments, and the like.

[00116] Embodiments or aspects thereof may be implemented in the form of hardware, firmware, or software. If implemented in software, the software may be stored on any nontransient computer readable medium that is configured to enable a processor to load the software or subsets of instructions thereof. The processor then executes the instructions and is configured to operate or cause an apparatus to operate in a manner as described herein.

[00117] Further, firmware, software, routines, or instructions may be described herein as performing certain actions and/or functions of the data processors. However, it should be appreciated that such descriptions contained herein are merely for convenience and that such actions in fact result from computing devices, processors, controllers, or other devices executing the firmware, software, routines, instructions, etc.

[00118] FIG. 16 illustrates an earthen formwork system support server 1600 environment in which embodiments may be implemented. In some embodiments, the earthen formwork 3D-printer 1601, 1604, or 1607, or an operator of the same (not shown), may need to exchange information relating to the formwork with an external server 1610 for various construction needs. For example, the earthen formwork 3D-printer 1601 may send local data 1602, including but not limited to information relating to the earth to be used in the mold, or a request for the optimized design of the mold for the building structure, to the earth formwork system support server 1610. The earth formwork system support server 1610 may then perform a computation or procure the instructions relating to printing the optimized design and send the robot control instructions 1603 back to the 3D-printer 1601, thereby informing the 3D-printer 1601 how to proceed.

[00119] Additionally, for example, the earthen formwork 3D-printer 1602 may send information 1605 relating to the surface geometry of the print surface to the earth formwork system support server 1610. The earth formwork system support server 1610 may then provide robot control instructions 1606 relating to the best way for the 3D-printer 1602 to level the print surface. A variety of data may be sent to the earth formwork support server 1610. A user operating or overseeing the 3D-printer 1607 may choose to supply a variety of user input data 1608 to the earth formwork support server 1610, such as but not limited to the current weather, soil conditions, or peripheral machinery assisting the 3D-printer 1607. The support server 1610 may be capable of returning suggestions or information 1609 to the user or may provide robot control instructions based on the user input data 1608 to the 3D-printer 1607. Notably, the earth formwork system support server 1610 may be able to access a database 1611 that includes applicable local, state, or federal building codes or regulations and return that information to the 3D-printers.

[00120] It should be understood that the flow diagrams, block diagrams, and network diagrams may include more or fewer elements, be arranged differently, or be represented differently. But it further should be understood that certain implementations may dictate the block and network diagrams and the number of block and network diagrams illustrating the execution of the embodiments be implemented in a particular way.

[00121] Accordingly, further embodiments may also be implemented in a variety of computer architectures, physical, virtual, cloud computers, and/or some combination thereof, and thus, the data processors described herein are intended for purposes of illustration only and not as a limitation of the embodiments.

[00122] It should be understood that the subject matter defined in the appended claims is not necessarily limited to the specific implementations described above. The specific implementations described above are disclosed as examples only.

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[00169] The teachings of all patents, published applications and references cited herein are incorporated by reference in their entirety. [00170] While example embodiments have been particularly shown and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the embodiments encompassed by the appended claims.

Claims

CLAIMS What is claimed is:

1. A mold of additive manufacturing material for use in producing a structural element for use in a structure, the mold comprising: an interior surface having an interior geometry defined by the additive manufacturing material and configured to constrain a composition of matter to be disposed within a volume bounded by the interior surface at least until the composition of matter sufficiently stabilizes with a shape, based on the interior geometry, toward becoming the structural element; and an exterior surface having an exterior geometry defined by the additive manufacturing material, the exterior geometry being a function of: (i) hydrostatic pressure expected to be exhibited by the composition of matter as constrained by the interior surface, and (ii) properties of the additive manufacturing material between the interior and exterior surfaces.

2. The mold of claim 1, wherein the additive manufacturing material includes an earthen material and a combination of least one of: a liquid, fiber, or sand; and wherein: for additive manufacturing material that includes fiber, the fiber is oriented in the additive manufacturing material within the mold in a direction perpendicular to a force of the hydrostatic pressure.

3. The mold of claims 1 or 2, wherein the additive manufacturing material is (i) obtained from a site at which the mold is disposed and (ii) sifted to a specified size of granularity.

4. The mold of any of claims 1-3, wherein the mold is a first mold and wherein at least a portion of the additive manufacturing material was previously within a second mold, and wherein the first mold may be deconstructed and the additive manufacturing material may be reused for making at least one third mold.

5. The mold of any of claims 1-4, wherein the additive manufacturing material is in a viscous state at a time the composition of matter is introduced within the interior surface.

6. The mold of any of claims 1-5, wherein the interior surface is coated with a hydrophobic substance.

7. The mold of any of claims 1-6, wherein the interior geometry is a materially efficient structural shape that constrains the composition of matter to produce the structural element with less composition of matter than the structural element would use absent reduction by the mold.

8. The mold of any of claims 1-7, wherein the exterior geometry defines a support structure providing for uniform conditions for drying the additive manufacturing material.

9. The mold of any of claims 1-8, further comprising rebar reinforcement placed within the volume bounded by the interior surface.

10. The mold of claim 9, wherein the rebar reinforcement further comprises at least one of the following:

(i) a prefabricated rebar reinforcement spacing jig configured to physically locate the rebar at preferential locations within the volume; or

(ii) a prefabricated rebar connection jig protruding through the exterior surface through a location, and producing a surface type configured to mate with another structural element.

11. A method of fabricating a mold of additive manufacturing material for use in producing a structural element for a use in a structure, the method comprising: extruding an additive manufacturing material to define an interior surface having an interior geometry configured to constrain a composition of matter to be disposed within a volume bounded by the interior surface at least until the composition of matter sufficiently stabilizes within a shape, based on the interior geometry, toward becoming the structural element; and extruding the additive manufacturing material to define an exterior surface having an exterior geometry, the exterior geometry being a function of (i) hydrostatic pressure expected to be produced by the composition of matter as constrained by the interior surface, and (ii) properties of the additive manufacturing material between the interior and exterior surfaces.

12. A computer-implemented method of 3D-printing a mold, the method comprising: generating instructions for a tool path for a 3D-printer configured to extrude an additive manufacturing material to define an interior surface with an interior geometry configured to constrain a composition of matter to be disposed within a volume bounded by the interior surface at least until the composition of matter sufficiently stabilizes with a shape of a structural element to be produced, based on the interior geometry, toward becoming the structural element; generating instructions for a tool path for a 3D-printer configured to extrude the additive manufacturing material to define an exterior surface with an exterior geometry, the exterior geometry being a function of: (i) hydrostatic pressure expected to be exhibited by the interior surface, and (ii) properties of the additive manufacturing material between the interior and exterior surfaces; and enabling the instructions to be communicated to the 3D-printer to cause the 3D-printer to follow the instructions to 3D-print the mold.

13. The computer-implemented method of claim 12, wherein the tool path for the 3D- printer is based on a set of design parameters including at least one of: (i) a local building code requirement or restriction, (ii) a structural requirement of the structural element to be produced or a structure to be produced using more than one structural element.

14. A computer-numerical-control (CNC) robot for use in producing a structural element for a structure, the CNC robot comprising: an extrusion head; and a CNC robot controller configured to cause the extrusion head to extrude: an additive manufacturing material to form an interior surface having an interior geometry configured to constrain a composition of matter at least until the composition of matter sufficiently stabilizes with a shape, based on the interior geometry, toward becoming the structural element; and the additive manufacturing material to form an exterior surface having an exterior geometry, the exterior geometry being a function of: (i) hydrostatic pressure expected to be exhibited by the composition of matter as constrained by the interior surface, and (ii) properties of the additive manufacturing material between the interior and exterior surfaces.

15. The CNC robot of claim 14, wherein the controller is further configured to perform at least one of the following, prior to the controller’s causing the extrusion head to extrude the additive manufacturing material: (i) mapping a surface of a print area, or (ii) flattening the surface of the print area through use of the extrusion head, an auxiliary mechanical appendage, a modular attachment, or a subsystem communicatively coupled to the controller.

16. The CNC robot of claims 14 or 15, wherein the controller is further configured to perform dimensional validation of the interior geometry or the exterior geometry by at least one of: LiDar scanning, structured light scanning, touchpoint sensing, or physical measurement through use of the extrusion head, an auxiliary mechanical appendage, a modular attachment, or a subsystem communicatively coupled to the controller.

17. The CNC robot of any of claims 14-16, wherein the additive manufacturing material includes an earthen material and a combination of least one of: a liquid, fiber, or sand; and wherein: for material that includes fiber, the fiber is oriented in the additive manufacturing material within the geometry of the interior or exterior surface in a direction perpendicular to a force of the hydrostatic pressure.

18. The CNC robot of any of claims 14-17, further comprising a modular attachment coupled to the extrusion head configured to perform, as a function of instructions by the controller, at least one of: (i) applying a physical force configured to settle the material, (ii) providing a guide for placement of, or assist in shaping of a rebar reinforcement, (iii) physically lifting the structural element once it has sufficiently stabilized.

19. The CNC robot of any of claims 14-18, wherein the controller is further configured to perform at least one of: (i) collecting data relating to the production of the structure, (ii) transmitting data relating to the production of the structure to a server.

20. The CNC robot of any of claims 14-19, wherein the extrusion head is coupled to a multi-axis articulating arm that is one of: a 3-axis articulating arm, or a 6-axis articulating arm.