# Integrating Non-Destructive Testing, Laser Scanning, and Numerical Modeling for Damage Assessment: The Room of the Elements

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## Abstract

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## 1. Introduction

## 2. Case Study

## 3. Line-Of-Sight Methods for Documentation

## 4. Non-Destructive Evaluation

## 5. Mapping Existing Crack Patterns

## 6. Numerical Modeling

#### 6.1. Levels of Modeling and Analysis

#### 6.2. Theory and Background for Numerical Modeling

- i = block number
- $\ddot{{x}_{i}}$ = acceleration of the block centroid
- $\dot{{x}_{i}}$ = velocity of the block centroid
- $\alpha $ = the viscous (mass-proportional) damping constant
- ${F}_{i}$ = sum of forces acting on the block
- m = block mass
- ${g}_{i}$ gravitational acceleration vector, and

- $\dot{{\omega}_{i}}$ = angular acceleration about the principal axis
- ${\omega}_{i}$ = angular velocity about the principal axis
- ${M}_{i}$ = principal moment of inertia
- I = total torque

- s = surface enclosing the mass, m, which is concentrated at the grid point
- ${\sigma}_{ij}$ = zone stress tensor
- ${n}_{j}$ = unit outward normal from the surface

#### 6.3. Model Parameters

- ${\rho}_{simulated}$ = density of the simulated slender block $(kg/{m}^{3})$
- ${V}_{simulated}$ = volume of the simulated slender block $\left({m}^{3}\right)$
- ${\rho}_{true}$ = density of the true, adjacent masonry wall $(kg/{m}^{3})$
- ${V}_{true}$ = volume of the true, adjacent masonry wall $\left({m}^{3}\right)$

#### 6.4. Loading Conditions for the Numerical Model

## 7. Diagnosing Crack Patterns

## 8. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**High resolution images of cracks in the Room of the Elements: (

**A**) full illustration of western wall, (

**B**–

**F**) images of specific cracks on the western wall.

**Figure 5.**Map of existing cracks on the foundation wall. Red indicates cracking over 1 cm; yellow indicates cracking on the order of 1 mm; orange indicates cracking in between these two limits.

**Figure 6.**Input geometry for numerical modeling. (

**A**) wall with brick infill and middle settlement configuration (

**B**) wall with concrete infill and left side settlement configuration.

**Figure 7.**Settlement of the floor in the Room of the Elements; the west wall was analyzed in this work due to cracking.

**Figure 8.**Displacement magnitudes of the existing geometry under combinations of dead load and settlement for brick infill and concrete infill; text value (m) indicates magnitude of settlement, while L, R, and M indicate settlement of left, right, and middle part of the wall, respectively.

**Figure 9.**Crack widths of the existing geometry under combinations of dead load and settlement for brick infill and concrete infill; text value (m) indicates magnitude of settlement, while L, R, and M indicate settlement of left, right, and middle part of the wall, respectively.

**Figure 11.**Workflow for integrating line-of-site documentation, non-destructive evaluation, and numerical modeling for understanding the extent and origins of existing crack patterns.

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**MDPI and ACS Style**

Napolitano, R.; Hess, M.; Glisic, B.
Integrating Non-Destructive Testing, Laser Scanning, and Numerical Modeling for Damage Assessment: The Room of the Elements. *Heritage* **2019**, *2*, 151-168.
https://doi.org/10.3390/heritage2010012

**AMA Style**

Napolitano R, Hess M, Glisic B.
Integrating Non-Destructive Testing, Laser Scanning, and Numerical Modeling for Damage Assessment: The Room of the Elements. *Heritage*. 2019; 2(1):151-168.
https://doi.org/10.3390/heritage2010012

**Chicago/Turabian Style**

Napolitano, Rebecca, Michael Hess, and Branko Glisic.
2019. "Integrating Non-Destructive Testing, Laser Scanning, and Numerical Modeling for Damage Assessment: The Room of the Elements" *Heritage* 2, no. 1: 151-168.
https://doi.org/10.3390/heritage2010012