# A Systemic Approach to Simulate the Construction Process of Self-Supporting Masonry Structures

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## Abstract

**:**

## 1. Introduction

## 2. Robotic Assistance in Masonry Structures: Combating Tensile Stress through Compression-Focused Design

## 3. Aim of the Paper

## 4. Construction Factors

#### 4.1. Construction Factors in Historical Self-Supporting Vaulting Technologies

#### 4.1.1. Geometrical Factors

#### 4.1.2. Mechanical Factors

#### 4.1.3. Construction Factors

#### 4.2. Technological Factors

#### 4.3. Temporal Factors

## 5. Simulation of the Construction Process

## 6. The Construction of the Voussoir Arch

#### 6.1. Case Study: Masonry Historical Arch

^{3}. The blocks placed on the abutments are arranged on a horizontal bed joint, as illustrated in Figure 4.

_{N}, k

_{S}, and the coefficient of Coulomb friction [41]. As described in [42], k

_{N}and k

_{S}are related, respectively, to the difficulty of pressing and slipping of the blocks with respect to each other. The values assumed within the simulation are k

_{N}= 3.7 × 10

^{9}N/m and k

_{S}= 3.7 × 10

^{8}N/m, with a friction angle of about 30°. The displacement recorded during the simulations of the construction sequence is illustrated in Figure 7 where vector displacements of each block along the construction process are illustrated. The set of sequential analyses was executed as described in Section 5, i.e., estimating the deformation and settlements considering the actual configurations of the previous building stages.

^{−4}. Further, a comparison is made with the traditional construction process, i.e., the stone arch is built using centering, as illustrated in Figure 8f. Here the maximum displacement recorded is about 0.45 mm, i.e., about 31% lower than the previous simulations. As expected, the construction sequence variation affects the structure’s state. The role of CFs is visible in the structural analysis and affects the state preeminently during the construction works, while they could be irrelevant once the structure is completed. The various examples presented with alterations applied to the CFs identify the significance of the CFs in the structural analysis and affect the state during construction.

#### 6.2. Case Study: Anatomy of Structure Masonry Historical Arch

^{−3}mm.

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CF | Construction Factor |

AEC | Architecture, Engineering, and Construction |

PVT | Pitched Vaulting Technique |

CTVT | Clay Tube Vaulting Technique |

TVT | Tile Vaulting Technique |

HVT | Herringbone Vaulting Technique |

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**Figure 1.**Masonry glass shell under construction using robotic arms. Reprinted with permission from Ref. [17].

**Figure 2.**Self-supporting vaulting techniques. (

**a**) Pitched vaults, different schemes to lay bricks. Drawing of A. Choisy [28]. (

**b**) Clay tube vault, detail of a section of the San Vitale dome (Ravenna, Italy), horizontal and vertical orientation of the tubes [27]. (

**c**) Process of construction of tile vault. From left to right: light-centering, construction sequence, and layering of the vault [29].

**Figure 4.**(

**a**) Masonry arch (Viterbo, Italy). (

**b**) Geometrical model of masonry arch construction analyzed. The structure rests on a horizontal foundation even though the street level is sloping, so all analyses were conducted considering a horizontal plane as the foundation (black line).

**Figure 5.**(

**a**) Workspaces of robots A, B, and C. (

**b**–

**i**) Construction stages. The three robots cooperate for the construction. During the different stages each robot works alternatively providing support or placing blocks. For example, in (

**d**) robots A and B support the arch and C places blocks, while in (

**e**) robots C and B support and A positions the stone.

**Figure 6.**(

**a**–

**c**) Lines of thrusts and domains of orientation of reactions of three different construction stages (

**a**–

**c**). Dashed lines represent the limit direction defined by friction angle. Domains change during construction due to the advancement of the lay of new blocks.

**Figure 8.**(

**a**) CF: friction angle. Failure mode due to slippage. (

**b**) CF: stereotomy, the variation of the shape of the two blocks at the arch spring leads to a different displacement field; see Figure 7c. (

**c**) Failure mode due to the absence of the lateral stone courses that aid in the contrast of the horizontal thrusts. (

**d**,

**e**) Alternative assembly sequence using only two robots. (

**f**) The construction of the arch that adopts the centering leads to different (smaller) displacements than that obtained in Figure 7f.

**Figure 9.**Domain of orientation of reactions. (

**a**) First construction stage of Phase I. (

**b**) Last construction stage of Phase I. The size of domains decreases with the advancement of construction, suggesting the identification of the most critical construction phases. Reprinted with permission from Ref. [17].

**Figure 10.**Construction stages of the central arch. (

**a**) Incomplete arch showing the position of the robotic support. Out-of-plane overturning phenomena occur leading to a displacement of about 1.80 mm. (

**b**,

**c**) Simulation of construction of the central arch. The robot arm gripping point lies in the plane of the arch. The color scale is associated with the displacement vectors of each node.

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**MDPI and ACS Style**

Paris, V.; Ruscica, G.; Olivieri, C.; Mirabella Roberti, G.
A Systemic Approach to Simulate the Construction Process of Self-Supporting Masonry Structures. *Sustainability* **2023**, *15*, 9596.
https://doi.org/10.3390/su15129596

**AMA Style**

Paris V, Ruscica G, Olivieri C, Mirabella Roberti G.
A Systemic Approach to Simulate the Construction Process of Self-Supporting Masonry Structures. *Sustainability*. 2023; 15(12):9596.
https://doi.org/10.3390/su15129596

**Chicago/Turabian Style**

Paris, Vittorio, Giuseppe Ruscica, Carlo Olivieri, and Giulio Mirabella Roberti.
2023. "A Systemic Approach to Simulate the Construction Process of Self-Supporting Masonry Structures" *Sustainability* 15, no. 12: 9596.
https://doi.org/10.3390/su15129596