Author Contributions
Conceptualization, V.S., R.V. and T.M.F.; methodology, S.M., H.L., V.S., R.V. and T.M.F.; software, H.L., S.M.; validation, S.M., H.L., V.S., T.M.F. and R.V.; investigation, S.M., H.L.; resources, R.V.; data curation, H.L., S.M.; writing—original draft preparation, S.M.; writing—review and editing, T.M.F., R.V., H.L., and V.S.; visualization, S.M., H.L.; supervision, V.S., R.V. and T.M.F.; project administration, R.V.; funding acquisition, R.V., V.S. and T.M.F. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Geographical distribution of adobe buildings in Portugal, as reported in the INE 2011 [
13].
Figure 1.
Geographical distribution of adobe buildings in Portugal, as reported in the INE 2011 [
13].
Figure 2.
Photographs of the main façades: (a) two-story (Building 2); (b) 2-story plus an attic (Building 3).
Figure 2.
Photographs of the main façades: (a) two-story (Building 2); (b) 2-story plus an attic (Building 3).
Figure 3.
Dimensions of Building 1 and details of the modeling in the LS-DYNA environment: (a) elevation view showing the front (main façade), (inset right) close-up of a lintel beam; (b) elevation view showing the symmetric left and right gable end walls; (c) plan view of the building and position of compression-only springs: (left inset) wall thickness detail (right inset) close-up view of a corner intersection, constraints, and interlocking.
Figure 3.
Dimensions of Building 1 and details of the modeling in the LS-DYNA environment: (a) elevation view showing the front (main façade), (inset right) close-up of a lintel beam; (b) elevation view showing the symmetric left and right gable end walls; (c) plan view of the building and position of compression-only springs: (left inset) wall thickness detail (right inset) close-up view of a corner intersection, constraints, and interlocking.
Figure 4.
Dimensions of Building 2 and details of the modeling in the LS-DYNA environment: (a) elevation view showing the front (main façade); (b) elevation view showing the left and right walls; (c) plan view of the building and position of compression-only springs (left inset) wall thickness detail.
Figure 4.
Dimensions of Building 2 and details of the modeling in the LS-DYNA environment: (a) elevation view showing the front (main façade); (b) elevation view showing the left and right walls; (c) plan view of the building and position of compression-only springs (left inset) wall thickness detail.
Figure 5.
Dimensions of Building 3 and details of the modeling in the LS-DYNA environment: (a) elevation view showing the front (main façade) and back (rear façade) showing the gable end walls; (b) elevation view showing the left and right walls; (c) plan view of the building and position of compression-only springs (left inset) wall thickness detail.
Figure 5.
Dimensions of Building 3 and details of the modeling in the LS-DYNA environment: (a) elevation view showing the front (main façade) and back (rear façade) showing the gable end walls; (b) elevation view showing the left and right walls; (c) plan view of the building and position of compression-only springs (left inset) wall thickness detail.
Figure 6.
Recreated single adobe double-T wall in the LS-DYNA environment (a) dimensions and detailing; (b) Top and isometric view of the in-plane mode of vibration with its corresponding matched frequency f = 23 Hz.
Figure 6.
Recreated single adobe double-T wall in the LS-DYNA environment (a) dimensions and detailing; (b) Top and isometric view of the in-plane mode of vibration with its corresponding matched frequency f = 23 Hz.
Figure 7.
Framework for vulnerability assessment of adobe buildings.
Figure 7.
Framework for vulnerability assessment of adobe buildings.
Figure 8.
Procedure utilizing the automated algorithms in LS-DYNA for pre-processing, processing, and post-processing of the building models.
Figure 8.
Procedure utilizing the automated algorithms in LS-DYNA for pre-processing, processing, and post-processing of the building models.
Figure 9.
Procedure utilizing the automated algorithms in LS-DYNA for pre-processing, processing, and post-processing of the building models.
Figure 9.
Procedure utilizing the automated algorithms in LS-DYNA for pre-processing, processing, and post-processing of the building models.
Figure 10.
Material models in LS-DYNA: (
a) Mixed-mode traction-separation law adapted from [
10]; (
b) assessment of projection distance for a free slave node adapted from [
43].
Figure 10.
Material models in LS-DYNA: (
a) Mixed-mode traction-separation law adapted from [
10]; (
b) assessment of projection distance for a free slave node adapted from [
43].
Figure 11.
Fundamental periods of vibration and the corresponding modes for translation in X-direction and Y-direction: (a,b) building 1; (c,d) building 2; (e,f) building 3.
Figure 11.
Fundamental periods of vibration and the corresponding modes for translation in X-direction and Y-direction: (a,b) building 1; (c,d) building 2; (e,f) building 3.
Figure 12.
Response spectra of the bi-directional components of the selected ground motion records: (a) horizontal component in X-direction; (b) horizontal component in Y-direction.
Figure 12.
Response spectra of the bi-directional components of the selected ground motion records: (a) horizontal component in X-direction; (b) horizontal component in Y-direction.
Figure 13.
Crack formation and volume loss shown at the end stage of the non-linear time history analyses sustained by buildings 1–3 for the 5 damage states: (a,d,g,j,m) building 1; (b,e,h,k,n) building 2; (c,f,i,l,o) building 3.
Figure 13.
Crack formation and volume loss shown at the end stage of the non-linear time history analyses sustained by buildings 1–3 for the 5 damage states: (a,d,g,j,m) building 1; (b,e,h,k,n) building 2; (c,f,i,l,o) building 3.
Figure 14.
A schematic of the fragility assessment procedure: (a) probability of exceedance for three IMLs given a damage threshold; (b) Fragility function for a given damage state.
Figure 14.
A schematic of the fragility assessment procedure: (a) probability of exceedance for three IMLs given a damage threshold; (b) Fragility function for a given damage state.
Figure 15.
Illustration of volume loss using Building 2 (adapted from Okada [
50]).
Figure 15.
Illustration of volume loss using Building 2 (adapted from Okada [
50]).
Figure 16.
Fragility and fatality vulnerability function for each of the building classes, respectively (a,b) 1-story; (c,d) 2-story; (e,f) 2-story plus an attic.
Figure 16.
Fragility and fatality vulnerability function for each of the building classes, respectively (a,b) 1-story; (c,d) 2-story; (e,f) 2-story plus an attic.
Table 1.
Building characteristics and dimensions.
Table 1.
Building characteristics and dimensions.
Building Characteristics | Building 1 | Building 2 | Building 3 |
---|
Total no. of stories | 1 | 2 | 2 + Attic |
Length (m) | X-direction | 6.30 | 10.80 | 8.20 |
Y-direction | 7.80 | 9.30 | 12.00 |
Area (m2) | 49.14 | 100.44 | 98.40 |
Height (m) | 1st Story | 2.85 | 3.30 | 2.40 |
2nd Story | - | 3.30 | 3.60 |
Attic | - | - | 3.00 |
Total height (m) | 2.85 | 6.60 | 9.00 |
Total no. of external walls | 4 | 4 | 4 |
External wall thickness (cm) | 30 | 60 | 40 |
Gable-end walls | Yes | No | Yes |
Lintel beams | Yes | Yes | Yes |
Total no. of window openings | 4 | 15 | 16 |
Total no. of door openings | 2 | 3 | 4 |
Total percentage of openings (%) | 10 | 20 | 15 |
Table 2.
Mechanical properties and input parameters of the numerical models.
Table 2.
Mechanical properties and input parameters of the numerical models.
Element | Mechanical Properties | Value | Units |
---|
SOLID elements | Young’s modulus | 0.74 | GPa |
Poison’s ratio | 0.30 | - |
Density | 1500 | kg/m3 |
Cohesive elements | Static coeff. of friction | 0.4 | - |
Dynamic coeff. of friction | 0.3 | - |
Scale factor for segment penalty stiffness | 1.0 | - |
Normal and shear failure stress | 0.05 | MPa |
Normal and shear energy release rate | 10, 30, 20 | N/m |
Normal (CN) and tangential stiffness | 0.74 | GPa |
Springs | Timber elasticity modulus | 7.00 | GPa |
Timber elasticity modulus (5%) | 4.70 | GPa |
Design compressive strength | 16.00 | MPa |
Design bending strength | 14.00 | MPa |
Table 3.
Numerical modeling characteristics.
Table 3.
Numerical modeling characteristics.
| Building 1 | Building 2 | Building 3 |
---|
Mesh size (cm) | 7.5 | 15 | 10 |
Block size (cm) | 15 | 30 | 20 |
No. of nodes | 141,408 | 123,156 | 300,654 |
No. of solid elements | 42,223 | 37,040 | 89,962 |
No. of parts | 5162 | 4433 | 10,932 |
Total volume of blocks composing the walls (m3) | 17.80 | 124.90 | 89.90 |
Roof | Spring-based | Spring-based | Spring-based |
Table 4.
EDPs and DSs and the corresponding damage thresholds.
Table 4.
EDPs and DSs and the corresponding damage thresholds.
EDPs | DSs | Damage Description | Threshold |
---|
Crack propagation ratio | DS 1 | Negligible to slight | 15% |
DS 2 | Moderate | 25% |
Volume loss ratio | DS 3 | Substantial to heavy | 10% |
DS 4 | Very heavy | 25% |
DS 5 | Destruction | 40% |
Table 5.
Fatality vulnerability parameters for adobe buildings.
Table 5.
Fatality vulnerability parameters for adobe buildings.
Building Class | θ * | β ** |
---|
1-story | 1.06 | 0.88 |
2-story | 0.45 | 0.75 |
2-story plus attic | 0.45 | 0.77 |
Table 6.
Fragility parameters for adobe buildings.
Table 6.
Fragility parameters for adobe buildings.
Building Class | IM | DS 1 | DS 2 | DS 3 | DS 4 | DS 5 |
---|
µ * | σ ** | µ | σ | µ | σ | µ | σ | µ | σ |
---|
1-story | PGA | −0.89 | 0.39 | −0.67 | 0.39 | −0.43 | 0.37 | −0.20 | 0.37 | −0.08 | 0.37 |
2-story | PGA | −1.38 | 0.43 | −1.00 | 0.43 | −0.38 | 0.50 | −0.05 | 0.50 | 0.12 | 0.50 |
2-story plus attic | PGA | −1.39 | 0.42 | −0.96 | 0.42 | −0.46 | 0.49 | −0.17 | 0.49 | −0.02 | 0.49 |