Building pathologies caused by failure of Fundão Tailing Dam: A principal component analysis aproach

SILVA JUNIOR, LADIR ANTONIO DA; SANTOS, TATIANA B. DOS

doi:10.1590/0001-3765202320220458

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ENGINEERING SCIENCES • An. Acad. Bras. Ciênc. 95 (suppl 1) • 2023 • https://doi.org/10.1590/0001-3765202320220458 copy

Building pathologies caused by failure of Fundão Tailing Dam: A principal component analysis aproach

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

This article presents a study of the impacts caused by Fundão dam failure in buildings from Gesteira district, Barra Longa city, Brazil. The analyzed dataset was built using technical reports from surveys carried out in 152 buildings. Principal component analysis was capable of explain the interdependence of data variable and allowed conditions of understand the consequences and evidenced pathologies. Heavy vehicle traffic caused more damage (57% of buildings) to the studied buildings than the contact with the tailing mud (43% of buildings).

Key words
Heavy vehicle traffic; impacts; pathologies; tailing mud; unsupervised machine learning

Variable	Lable	Type
P1	Tailing reached to the building ground	Qualitative
P2	Heavy vehicle traffic	Qualitative
P3	Nature of building pathology is exogenous	Qualitative
P4	Risk level	Qualitative
P5	Building pathology worsen by the event	Qualitative
P6	Number of cracks caused by settlement	Quantitative
P7	Number of cracks caused by masonry expansion	Quantitative
P8	Number of cracks caused by thermal variations of the masonry	Quantitative
P9	Number of cracks caused by thermal variations of the floor system	Quantitative
P10	Number of cracks caused by floor system deflection	Quantitative
P11	Number of cracks caused by support deflection	Quantitative
P12	Number of cracks caused by superior beam deflection	Quantitative
P13	Number of cracks caused by structural deflection	Quantitative
P14	Number of horizontal cracks caused by overloading	Quantitative
P15	Number of vertical cracks caused by overloading	Quantitative
P16	Number of cracks caused by negative bending in the sills	Quantitative
P17	Number of cracks in openings (doors, windows, vents)	Quantitative
P18	Number of detachments	Quantitative
P19	Number of infiltrations	Quantitative

Variable	Rating 0	Rating 1	Rating 2	Rating 3
Tailing reached to the building ground – P1	No	Near	Lot	Building ground
Heavy vehicle traffic – P2	No	Yes
Nature of building pathology is exogenous – P3	No	Yes
Risk Level – P4	Minimum	Medium	Critical
Building pathologies worsen by the event - P5	No	Yes

ID	P1	P2	P3	P4	P5	P6	P8	P12	P14	P16	P17	P18	P19
1	2	1	1	0	1	3	0	0	0	0	0	0	0
2	3	1	1	0	1	1	0	0	0	0	0	0	0
3	2	1	1	1	1	14	10	0	0	6	8	6	0
4	2	1	1	0	1	3	7	4	0	0	1	0	0
5	2	1	1	0	1	1	4	0	0	0	0	0	0
6	0	1	0	0	1	0	0	0	7	0	0	0	1
7	0	1	1	1	1	1	14	0	0	0	8	15	0
8	0	1	0	2	1	12	0	0	1	1	0	0	0
9	0	1	0	2	1	0	0	0	2	0	0	0	0
10	0	1	0	0	1	0	0	0	1	0	0	2	0

Correlation value	Description
0.1 to 0.3	Weak linear correlation
0.3 to 0.5	Moderate linear correlation
0.5 to 0.7	Strong linear correlation
0.7 to 1.0	Very strong linear correlation

	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15	P16	P17	P18	P19
P1	11.00	-0.15	0.58	0.06	0.24	0.23	-0.14	0.06	-0.03	-0.10	0.05	0.13	0.16	0.17	-0.09	0.09	0.05	-0.08	0.11
P2	-0.15	11.00	-0.04	0.00	0.63	0.05	0.08	0.12	0.07	-0.13	0.06	0.00	0.07	-0.13	0.04	0.04	0.13	0.11	-0.11
P3	0.58	-0.04	11.00	0.12	0.21	0.48	-0.12	0.25	0.14	-0.09	-0.04	0.18	0.24	-0.02	-0.11	0.14	0.01	0.11	0.16
P4	0.06	0.00	0.12	11.00	0.08	0.44	-0.05	0.01	-0.06	-0.08	0.04	-0.07	-0.05	0.07	-0.11	0.06	0.12	0.29	-0.06
P5	0.24	0.63	0.21	0.08	11.00	0.14	0.02	0.06	0.06	-0.19	0.04	0.04	0.05	0.04	-0.01	0.03	0.05	0.09	-0.08
P6	0.23	0.05	0.48	0.44	0.14	11.00	-0.10	-0.01	0.00	-0.04	-0.07	0.01	-0.07	-0.04	-0.15	0.25	-0.03	0.17	-0.05
P7	-0.14	0.08	-0.12	-0.05	0.02	-0.10	11.00	-0.05	-0.03	-0.02	-0.03	-0.02	-0.03	-0.02	-0.07	-0.02	0.05	0.00	0.05
P8	0.06	0.12	0.25	0.01	0.06	-0.01	-0.05	11.00	0.01	-0.06	0.00	0.18	0.18	-0.06	-0.13	0.37	0.17	0.42	0.28
P9	-0.03	0.07	0.14	-0.06	0.06	0.00	-0.03	0.01	11.00	-0.02	-0.02	-0.02	-0.03	-0.02	-0.01	-0.02	0.04	-0.03	-0.03
P10	-0.10	-0.13	-0.09	-0.08	-0.19	-0.04	-0.02	-0.06	-0.02	11.00	-0.02	-0.02	-0.02	-0.06	-0.01	-0.08	-0.04	-0.05	0.05
P11	0.05	0.06	-0.04	0.04	0.04	-0.07	-0.03	0.00	-0.02	-0.02	11.00	-0.02	0.00	-0.02	-0.06	-0.01	-0.06	-0.03	-0.05
P12	0.13	0.00	0.18	-0.07	0.04	0.01	-0.02	0.18	-0.02	-0.02	-0.02	11.00	-0.02	-0.02	-0.05	-0.01	-0.04	-0.03	0.03
P13	0.16	0.07	0.24	-0.05	0.05	-0.07	-0.03	0.18	-0.03	-0.02	0.00	-0.02	11.00	0.08	0.08	0.01	0.16	0.04	-0.01
P14	0.17	-0.13	-0.02	0.07	0.04	-0.04	-0.02	-0.06	-0.02	-0.06	-0.02	-0.02	0.08	11.00	-0.05	0.13	-0.06	-0.04	0.17
P15	-0.09	0.04	-0.11	-0.11	-0.01	-0.15	-0.07	-0.13	-0.01	-0.01	-0.06	-0.05	0.08	-0.05	11.00	-0.10	-0.11	-0.14	-0.04

$χ^{2}$	df	$p value$
428.01	55	$3.57 \times 10^{- 59}$

	$P C_{1}$	$P C_{2}$	$P C_{3}$	$P C_{4}$	$P C_{5}$	$P C_{6}$
Proportion of explained variance	0.23	0.15	0.14	0.13	0.10	0.07
Cumulative proportion	0.23	0.38	0.52	0.65	0.75	0.82
	$P C_{7}$	$P C_{8}$	$P C_{9}$	$P C_{10}$	$P C_{11}$
Proportion of explained variance	0.06	0.04	0.03	0.02	0.02
Cumulative proportion	0.88	0.92	0.96	0.98	1.00

	Tailing reached to the building ground (P1)	Heavy vehicle traffic (P2)	Nature of building pathology is exogenous (P3)	Risk level (P4)	Building pathology worsen by the event (P5)
$PC_1<-2$	No	No	No	Minimum	No
$-2<PC_1<0$	No	Yes	No	Minimum	Yes
$0<PC_1<2$	Lot	Yes	Yes	Minimum	Yes
$PC_1>2$	Lot	Yes	Yes	Critical	Yes

ID	Tailing the building reached to ground (P1)	Heavy vehicle traffic (P2)	Nature of building pathology is exogenous (P3)	Risk level (P4)	Building pathology worsen by the event (P5)	Range of PC1
93	Building ground	Yes	Yes	Minimum	Yes	0<PC₁<2
90	Building ground	Yes	Yes	Minimum	Yes	0<PC₁<2
91	Building ground	Yes	Yes	Minimum	Yes	0<PC₁<2
142	Building ground	No	Yes	Minimum	Yes	0<PC₁<2
5	Building ground	Yes	No	Regular	Yes	0<PC₁<2
8	Building ground	Yes	Yes	Minimum	Yes	0<PC₁<2
21	Building ground	Yes	Yes	Minimum	Yes	0<PC₁<2
77	Building ground	No	No	Minimum	Yes	-2<PC₁<0
78	Building ground	Yes	No	Minimum	Yes	0<PC₁<2
2	Building ground	No	Yes	Minimum	Yes	0<PC₁<2
57	Building ground	No	Yes	Minimum	Yes	0<PC₁<2
66	Building ground	No	Yes	Minimum	Yes	0<PC₁<2
69	Building ground	No	No	Minimum	Yes	-2<PC₁<0
94	Building ground	Yes	Yes	Minimum	Yes	0<PC₁<2
95	Building ground	No	Yes	Minimum	Yes	0<PC₁<2

Variables with positive coefficients	Variables with negative coefficients
Tailing reached to the building ground (P1)	Heavy vehicle traffic (P2)
Nature of building pathology is exogenous (P3)	Building pathologies worsen by the event (P5)
Risk level (P4) is exogenous (P3)	Number of cracks caused by thermal variations of the masonry (P8)
Number of cracks caused by settlement (P6)	Number of cracks caused by structural deflection (P13)
	Number of cracks caused by negative bending in the sills (P16)
	Number of cracks in openings (P17)
	Number of detachments (P18)

Equipament	Reference PPV at 25 ft. (in/sec)
Vibratory roller	0.210
Large bulldozer	0.089
Caisson drilling	0.089
Loaded trucks	0.076
Jackhammer	0.035
Small bulldozer	0.003
Crack-and-seat operations	2.4

Equipment	Reference PPV at 25 ft. (in/sec)
Vibratory roller	0.716
Large bulldozer	0.303
Loaded trucks	0.259
Small bulldozer	0.010

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[1] Correspondence to: Ladir Antonio da Silva Junior E-mail: ladir.jr@uemg.br

Structure and Condition	Transient	Continuous/Frequent
	Sources	Intermittent Sources
Extremely fragile historic buildings, ruins, ancient monuments	0.12	0.08
Fragile buildings	0.2	0.1
Historic and some old buildings	0.5	0.25
Older residential structures	0.5	0.3
New residential structures	1.0	0.5
Modern industrial/commercial buildings	2.0	0.5

ID	P1	P2	P3	P4	P5	P6	P8	P12	P14	P16	P17	P18	P19
1	2	1	1	0	1	3	0	0	0	0	0	0	0
2	3	1	1	0	1	1	0	0	0	0	0	0	0
3	2	1	1	1	1	14	10	0	0	6	8	6	0
4	2	1	1	0	1	3	7	4	0	0	1	0	0
5	2	1	1	0	1	1	4	0	0	0	0	0	0
6	0	1	0	0	1	0	0	0	7	0	0	0	1
7	0	1	1	1	1	1	14	0	0	0	8	15	0
8	0	1	0	2	1	12	0	0	1	1	0	0	0
9	0	1	0	2	1	0	0	0	2	0	0	0	0
10	0	1	0	0	1	0	0	0	1	0	0	2	0

ID	P1	P2	P3	P4	P5	P6	P8	P12	P14	P16	P17	P18	P19
1	2	1	1	0	1	3	0	0	0	0	0	0	0
2	3	1	1	0	1	1	0	0	0	0	0	0	0
3	2	1	1	1	1	14	10	0	0	6	8	6	0
4	2	1	1	0	1	3	7	4	0	0	1	0	0
5	2	1	1	0	1	1	4	0	0	0	0	0	0
6	0	1	0	0	1	0	0	0	7	0	0	0	1
7	0	1	1	1	1	1	14	0	0	0	8	15	0
8	0	1	0	2	1	12	0	0	1	1	0	0	0
9	0	1	0	2	1	0	0	0	2	0	0	0	0
10	0	1	0	0	1	0	0	0	1	0	0	2	0

ID	P1	P2	P3	P4	P5	P6	P8	P12	P14	P16	P17	P18	P19
1	2	1	1	0	1	3	0	0	0	0	0	0	0
2	3	1	1	0	1	1	0	0	0	0	0	0	0
3	2	1	1	1	1	14	10	0	0	6	8	6	0
4	2	1	1	0	1	3	7	4	0	0	1	0	0
5	2	1	1	0	1	1	4	0	0	0	0	0	0
6	0	1	0	0	1	0	0	0	7	0	0	0	1
7	0	1	1	1	1	1	14	0	0	0	8	15	0
8	0	1	0	2	1	12	0	0	1	1	0	0	0
9	0	1	0	2	1	0	0	0	2	0	0	0	0
10	0	1	0	0	1	0	0	0	1	0	0	2	0