th

9 International Conference on
Shock & Impact Loads on Structures
Fukuoka, Japan, Nov. 16-18, 2011

BLAST DEMOLITION PLANNING TOOL USINGKEY ELEMENT INDEX
Daigoro Isobe* and Takuya Katsu†*

University of Tsukuba
1-1-1 Tennodai Tsukuba-shi, Ibaraki 305-8573, Japane-mail: <isobe@kz.tsukuba.ac.jp> webpage: http://www.kz.tsukuba.ac.jp/~isobe/

Keywords: Blast demolition, key element index, collapse analysis, ASI-Gauss technique

Abstract. The main objective of this study is to develop a demolition planning tool
for buildings based on a parameter called the key element index, which indicates thecontribution of a structural column to the vertical capacity of the structure. Two waysof selecting specific columns to demolish the whole structure are demonstrated:
selecting the columns from the largest index value and from the smallest index
value. The demolition results are confirmed numerically by carrying out collapse
analyses using the adaptively shifted integration (ASI)-Gauss technique, and thetendencies of the demolition modes to follow the key element index values are
estimated. The numerical results suggest that for a successful demolition, a group ofcolumns with the largest key element index values should be selected when
explosives are ignited in a simultaneous blast, whereas those with the smallest
values should be selected when explosives are ignited sequentially, with a final blast
set on a column with a large index value.
1

INTRODUCTION

The technology used in the demolition of old or uninhabitable buildings has always been of majorinterest in civil engineering and remains a challenge in engineering practice. Because conventional
demolition techniques that use a hydraulic concrete crusher, a concrete cutter or a nonexplosive
demolition agent are lengthy and costly, demolition techniques using controlled explosives are often
used to meet the heavy demand for demolition work. Although this method increases work efficiency,1
it also poses a high risk of damage to neighboring buildings, especially in urban areas . Furthermore,
2,3
blast demolition requires high levels of knowledge and experience , which are very difficult for
general engineers to master. Although there are several blast demolition companies currently working
in the USA and Europe, the demolition technique has been only used in a few cases in Japan, which
may or may not be due to the above reasons. To help familiarize Japanese construction companies
with blast demolition methods, numerical assumptions using computational analysis will be essential inensuring the success of this technique.
To date, only a few numerical codes have shown high performance when modeling structurally
4
discontinuous problems; e.g., the distinct element method (DEM) and discontinuous deformation
5
6,7,8,9analysis (DDA) have been successfully applied to model overall collapse phenomena. However,there are still no adequate numerical procedures available to accurately track the blast demolition
process, which includes coupled and complicated failure mechanisms of structural frame members.
10
Therefore, we applied the adaptively shifted integration (ASI)-Gauss technique to develop ananalysis code for blast demolition that can explicitly express member fracture and elemental contact in†Kubota, Co.
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Daigoro Isobe and Takuya Katsu

the demolition process. In this code, the accurate modeling of a fractured section in a member isenabled by shifting the numerical integration points in the finite elements and by reducing the sectional
forces of the elements immediately after the occurrence of the fractured section. It also yields highly
accurate solutions with small mesh subdivisions and requires little calculation time and a small amountof memory.
The main objective of this study, on the other hand, is to develop a demolition planning tool basedon a parameter called the key element index, which indicates the contribution of a structural column tothe vertical capacity of the structure. Two ways of selecting specific columns to demolish the whole
structure are demonstrated: selecting the columns from the largest index value and from the smallest
index value. The demolition results are confirmed numerically by carrying out collapse analyses using
the numerical code mentioned above, and the tendencies of the demolition modes to follow the key
element index values are estimated.
2

KEY ELEMENT INDEX

Due to variations in their span lengths and strengths, certain columns in a structure support morevertical loads than other columns and thus act as “key elements” in the structure. Several indexes
have been developed to evaluate the contribution of each column to the strength of a structure, i.e., to11
determine the key elements, such as the redundancy index by Frangopol and the sensitivity index by
12
Itoh et al. . These indexes are effective for identifying highly sensitive columns that support thevertical load; however, they equivalently identify those columns that only cause partial collapse and arethus not useful for demolition planning, where the major aim is the total collapse of a structure.
Therefore, we propose a new index, called the key element index, for estimating the contribution ofbase columns to the total collapse of the structure.
The key element index is calculated as follows. First, we perform a static pushdown analysis byequally applying incremental vertical loads at every structural joint in a modeled structure. Several
columns on the upper floors may yield in this process, but the vertical loads are neverthelesscontinuously applied in steps until one of the base columns yields. The total vertical load (including thefloor loads) applied to a column at the step when one of the base columns yields is defined as theultimate yield strength PG of the structure. The ultimate yield strength of the initial, undamaged
structure is denoted 0 PG, and the ultimate yield strength of a structure with one base column
eliminated is denoted 1 PG. The key element index KI of column m, for example, can be defined as theratio of the ultimate yield strengths of the present and the initial step. The index can thus be written as:
0
1 KIm = 0PG/1PG(1)

The key element index at the nth step is then:0n KIm = 0PG/nPG(2)

The index shown above indicates the contribution of the present column (or columns) to the strengthof the initial, undamaged structure and can be used for cases in which the columns are eliminatedsimultaneously. However, the sensitivity of columns may change momentarily for those cases when
the columns are eliminated sequentially within a certain interval. Therefore, the updated index, as

Figure 1: A 15-storey, three-span model
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Daigoro Isobe and Takuya Katsu

shown below, is used for those cases with a sequential blast.
n-1
n KIm = n-1PG/nPG(3)

In this case, the index can be defined as the ratio of the ultimate yield strengths of the present and theprevious step.
As an example, the key element index values were calculated for a 15-story, three-span model, as
shown in Fig. 1. Each span length is 6 m, and the height between each floor is 3.6 m. The material
used for the columns and beams is SN490B steel. We selected box-type section of 430 mm × 430
stmm × 13 mm × 13 mm on the 1 floor columns and H-type section of 331 mm × 825.7 mm × 18.4 mm
× 13.2 mm for the beams, with the sectional sizes becoming gradually thinner in the higher stories.
2
The floor load, in this case, is set to 400 kgf/m . The updated index values and the selection ofcolumns from the largest index value at each step are shown in Fig. 2. For example, the key element
index value KI for column No. 16 (in the upper right corner) can be calculated at the first step as:
0
1 KI16 = 0PG/1PG =1.693(4)1
2 KI16 = 1PG/2PG =1.012(5)

and at the second step as:

If the index values calculated for multiple columns are the same, the column at the left and lower sideis selected prior to the other columns; in this case, to direct the whole collapsing building toward thelower left side. As shown in the figure, the selected columns tend to bias to the intended demolition
direction if the columns are selected from the largest index value. Furthermore, the distribution of the

1.693

1.523

1.523

1.693

1.523

1.214

1.214

1.523

1.523

1.214

1.214

1.523

1.693

1.523

1.523

1.693

st

(a) 1 step
1.012

1.006

0.994

1.012

1.185

1.021

1.000

0.994

1.407

1.161

1.021

1.006

1st

1.407

1.185

1.012

nd

(b) 2 step
1.043

1.000

1.000

0.988

1.525

1.081

1.000

0.988

2nd

1.181

1.000

0.996

1st

1.470

1.048

1.000

rd

(c) 3 step
1.250

1.042

1.042

1.042

3rd

7th

9th

1.042

2nd

5th

8th

1.042

6th

1.250

1st

4th
th

(d) 10 step
Column of the largest index value
Column already chosen in the previous steps

Figure 2: Updated index values and the selection of columns from among those with the largest values
397Daigoro Isobe and Takuya Katsu

1.693

1.523

1.523

1.693

1.523

1.214

1.214

1.523

1.523

1.214

1.214

1.523

1.523

1.693

1.693

1.523

st

(a) 1 step
1.425

1.268

1.255

1.395

1.344

1.251

1.201

1.255

1.506

1st

1.251

1.268

1.344

1.425

1.620

1.506

nd

(b) 2 step
1.187

1.243

1.267

1.359

1.243

1.251

2nd

1.267

1.267

1st

1.251

1.243

1.243

1.187

1.359

1.267

rd

(c) 3 step
3rd

1.214

1.070

6th

1.681

7th

2nd

1.077

9th

1st

8th

1.133

1.214

4th

5th

1.719

th

(d) 10 step
Column of the smallest index value
Column already chosen in the previous steps

Figure 3: Updated index values and the selection of columns from among those with the smallest values
selected columns differs, as shown in Fig. 3, when the columns are selected from the smallest index
value. The selected columns tend to distribute the load, stabilizing the structure and preventing
instantaneous collapse.
3

BLAST DEMOLITION PLANNING USING THE INTEGRATED KEY ELEMENT INDEX VALUES

Several blast demolition analyses were performed using selected columns, as described in theprevious section. We summed the key element index values of the selected columns and plotted thecollapse modes for each case. Each procedure was performed on models with different floor loads.
Figure 4 shows the distribution of the integrated values of the key element index and the collapse
modes of the structure for a simultaneous blast, where nonupdated index values are used. TC in the
figures indicates total collapse, PC indicates partial collapse, and NC indicates no collapse. The
integrated value indicated by the black circle in Fig. 4(a), for example, is calculated as follows:
0
0
0
0
0
0
1 KI1 +2 KI5+3 KI9+4 KI2+5 KI6+6 KI3 = 1.693+2.382+3.633+4.284+5.979+7.863= 25.834(6)

Here, again, note that the lower right subscript in the key element index indicates the column number,the upper left subscript indicates the step number under consideration in the calculation of the ultimate
yield strength ratio, and the lower left subscript indicates the present step number. As shown in the
figures, there are certain requirements for the integrated values of the key element index to ensurethat the structure is partially or totally demolished. The region of total collapse is large when the398Integrated value of nonupdated key element index

Integrated value of nonupdated key element index

Daigoro Isobe and Takuya Katsu

100
80

PC
60
40

TC

20

NC
0

300 400 500 600 700 800 900 1000

Floor load [kgf/m2]

35
30

TC

PC

25
20
15
10

NC

5
0

300 400 500 600 700 800 900 1000

Floor load [kgf/m2](a) Selecting columns from the largest index value (b) Selecting columns from the smallest index value

9

TC

Integrated value of updated key element index

Integrated value of updated key element index

Figure 4: Key element index values and collapse behavior of the model(simultaneous blast, nonupdated index value)

PC

6

3

0

NC

300 400 500 600 700 800 900 1000

16
14

TC
PC

12
10
8
6
4

NC

2
0

300 400 500 600 700 800 900 1000

Floor load [kgf/m2]

2

Floor load [kgf/m ](a) Selecting columns from the largest index value (b) Selecting columns from the smallest index value
Figure 5: Key element index values and collapse behavior of the model(sequential blast, updated index value)columns with the largest index values are successively selected (see Fig. 4(a)), whereas the region isvery small when the columns with the smallest index values are selected (see Fig. 4(b)). To
accomplish total collapse, neither the integrated index values nor the floor load should be too large
because larger values tend to make the structure relatively stable in the collapse process.
Figure 5 shows the distribution of the integrated values of the key element index and the collapse
modes of the structure for sequential blast, where updated index values are used. The integrated
value indicated by the black circle in Fig. 5(a), for example, is calculated as follows:
0
1
2
3
4
5
6
1 KI1 +2 KI5+3 KI9+4 KI2+5 KI6+6 KI3+7 KI10 = 1.693+1.407+1.525+1.179+1.396+1.315+1.377= 9.892(7)

The same tendencies as observed in Fig. 4 can be seen here in the distribution of the index values
and the collapse modes. However, the region of total collapse becomes much smaller than insimultaneous blasting because the structure tends to become relatively stable during each blast
interval.
It is evident from Fig. 4 and Fig. 5 that there are several specific areas of integrated index values
that allow for successful demolition, especially when the columns are selected from the largest key
element index values. However, the sequential blast of columns from the largest index values causes
the whole structure to gradually collapse in sequence, which may, in practical terms, cut the explosive
trigger wires and/or make the whole demolition procedure quite unstable. Therefore, the selection ofcolumns with the largest index values may only be used in demolition by simultaneous blasting. In
contrast, the selection of columns with the smallest index values may be used to keep the structure
stable until the last moment in a demolition by sequential blasting. The structure may be completely

399

Daigoro Isobe and Takuya Katsu

7.6 s

0.2 s

11.7 s

17.0 sFigure 6: Demolition mode for the simultaneous blast case(six columns selected from the largest nonupdated index value)

9.0 s

14.0 s23.0 s35.0 sFigure 7: Demolition mode for the sequential blast case(nine columns selected from the smallest updated index values and three columns
from the large ones selected for the final blast)demolished by a final blast on a column (or columns) with a large index value, essentially traversing
the solid line in Fig. 5(b) in one step.
4

BLAST DEMOLITION ANALYSIS OF A FRAMED STRUCTURE USING THE OBTAINED PLAN

Two analyses using the plans of blast demolition obtained in the previous section were performedon the model shown in Fig. 1. Each analysis took 50 to 90 minutes on a personal computer (CPU: 2.0
GHz Xeon, 8GB RAM). Figure 6 shows the demolition mode for the simultaneous blast case, in which
the eliminated columns were selected from among those with the largest nonupdated index values.
Six columns altogether were selected, in this case, and the integrated value of the key element index
was 25.834 as calculated in Eq. (6). Figure 7 shows the demolition mode for the sequential blast case,in which the columns were selected for elimination from among those with the smallest updated index
values. To achieve a total collapse, the columns with the large index values at the final step wereselected for the final blast. In this case, nine columns from among those with the smallest index
values (with the integrated value of 10.552) were sequentially eliminated over an interval of one
second, and then, three columns with the large index values (with the integrated value of 4.614) were
simultaneously eliminated at the final blast. Please note that the integrated index value of the initialnine columns does not traverse the solid line in Fig. 5(b), however, the total value including the final
three columns, which is 15.166, slightly traverse the line. Although the timings of the collapse initiationand the collapse modes slightly differ in each case, both display a successful demolition pattern, withthe structure totally demolished to ground level and towards the intended direction.
5

CONCLUSIONSThe key element index and its integrated values, as demonstrated in this paper, may be used toquantitatively verify which columns should be eliminated to best achieve a total collapse. The

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Daigoro Isobe and Takuya Katsu

numerical results suggest that for a successful demolition, a group of columns with the largest key
element index values should be selected when explosives are ignited in a simultaneous blast,whereas those with the smallest values should be selected when explosives are ignited sequentially,
with a final blast set on a column with a large index value. However, further investigation should beundertaken to enable the precise planning of blast intervals and locations required to allow the whole
structure to collapse in its own wake, which is very important to lower the risk of damage toneighboring buildings.

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