ctbuh.org/papers

Title:An Analysis Code and a Planning Tool Based on a Key Element Index forControlled Explosive Demolition

Author:Daigoro Isobe, Division of Engineering Mechanics and Energy, University ofTsukuba

Subjects:
Keywords:

Building Code
Demolition

Publication Date:

2014

Original Publication:

International Journal of High-Rise Buildings Volume 3 Number 4

Paper Type:

1. Book chapter/Part chapter
2. Journal paper
3. Conference proceeding
4. Unpublished conference paper
5. Magazine article
6. Unpublished© Council on Tall Buildings and Urban Habitat / Daigoro IsobeInternational Journal of High-Rise Buildings
December 2014, Vol 3, No 4, 243-254

International Journal of

High-Rise Buildingswww.ctbuh-korea.org/ijhrb/index.php

An Analysis Code and a Planning Tool Based on a Key Element
Index for Controlled Explosive Demolition
Daigoro Isobe†
Division of Engineering Mechanics and Energy, University of Tsukuba, Ibaraki 305-8573, Japan

Abstract
In this study, a demolition analysis code using the adaptively shifted integration (ASI)-Gauss technique, which describes
structural member fracture by shifting the numerical integration point to an appropriate position and simultaneously releasing
the sectional forces in the element, is developed. The code was verified and validated by comparing the predicted results withthose of several experiments. A demolition planning tool utilizing the concept of a key element index, which explicitly indicatesthe contribution of each structural column to the vertical load capacity of the structure, is also develped. Two methods of
selecting specific columns to efficiently 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 conducting collapse
analyses using the ASI-Gauss technique. The numerical results suggest that to achieve 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 should be selected when explosives are ignited in a sequence, with a final blast set on a column
with large index value.
Keywords: Controlled explosive demolition, Key element index, Collapse analysis, Finite element method, ASI-Gauss technique

1. Introduction
The technology used in the demolition of old or uninhabitable buildings has always been of major interest in
civil engineering and remains a challenge in engineering
practice. Because conventional demolition techniques thatuse a hydraulic concrete crusher, a concrete cutter or anonexplosive 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, it also posesa high risk of damage to neighboring buildings, especiallyin urban areas [1]. Furthermore, explosive demolition requires high levels of knowledge and experience [2,3],
which are very difficult for general engineers to master.
Although there are several explosive demolition companies currently working in the USA and Europe, the demolition technique has been only used in a few cases inJapan, which may or may not be due to the above reasons. To help familiarize Japanese construction companies
with explosive demolition methods, numerical assumptions
using computational analysis will be essential in ensuring
the success of this technique.
To date, only a few numerical codes have shown highperformance when modeling structurally discontinuous pro†

Corresponding author: Daigoro Isobe
Tel: +81-29-853-6191; Fax: +81-29-853-5207
E-mail: isobe@kz.tsukuba.ac.jp

blems; e.g., the distinct element method (DEM) [4] anddiscontinuous deformation analysis (DDA) [5] have beensuccessfully applied to model overall collapse phenomena [6-9]. The Applied Element Method (AEM) [10],which can predict crack initiation and propagation in thematerial and can also follow the total behavior from zeroloading to complete collapse, has also been applied toblast demolition analysis of structures. However, theabove-mentioned discrete numerical methods need many
assumptions on the models with less physical meanings,
and there are still no adequate numerical procedures available to accurately track the explosive demolition process,which includes coupled and complicated failure mechanisms of structural frame members.
The first objective of this study was to develop ananalysis code for explosive demolition that can explicitly
express member fracture and elemental contact in the demolition process. This code is based on the adaptively
shifted integration (ASI)-Gauss technique [11], which is a
modified version of the previously developed ASI technique [12,13] for the linear Timoshenko beam element
and computes highly accurate elastoplastic solutions evenwith the minimum number of elements per member. The
ASI-Gauss technique obtains an even higher accuracy,
particularly in the elastic range, by placing the numericalintegration points of the two consecutive elements toform an elastically deformed member so that stresses andstrains are evaluated at the Gaussian integration points ofthe two-element member. Moreover, the technique can be244

Daigoro Isobe | International Journal of High-Rise Buildings

used to express member fracture by shifting the numerical integration point to an appropriate position and simultaneously releasing the sectional forces in the element. The
numerical code was validated herein by comparing thenumerical results with a simple impact test and a simulated demolition experiment.
The second objective of this study was to develop ademolition planning tool based on a parameter called the
key element index, which indicates the contribution of astructural column to the vertical capacity of the structure.
Two ways of selecting specific columns to demolish thewhole structure are demonstrated: selecting the columns
from the largest index value and from the smallest index
value. The demolition results are confirmed numericallyby carrying out collapse analyses using the ASI-Gauss
technique, and the tendencies of the demolition modes tofollow the key element index values are estimated.
This paper is organized as follows. Section 2 introduces
the outline of the ASI-Gauss technique and the memberfracture and elemental-contact algorithms. In Section 3,
several examples are presented for the validation of thenumerical code. Section 4 presents the concept of the key
element index and the demolition planning tool developed
using the index values, followed by numerical examples.
Finally, Section 5 concludes the paper.

2. Numerical Methods for Collapse Analysis
The general concepts of the ASI-Gauss technique are
explained in this section. The algorithms concerning member fracture and elemental contact are then described.

2.1. The ASI-Gauss techniqueFig. 1 shows a linear Timoshenko beam element and its
physical equivalence to the rigid body-spring model(RBSM). As shown in the figure, the relationship between the locations of the numerical integration point andthe stress evaluation point where a plastic hinge is actually formed is expressed as [14]r = –s(1)

In the above equation, s is the location of the numericalintegration point, and r is the location where stresses andstrains are actually evaluated. We refer to r as the stressevaluation point hereinafter. The variables s and r are dimensionless quantities that take values between -1 and 1.
In both the ASI and ASI-Gauss techniques, the numerical integration point is shifted adaptively to form a plastic
hinge at exactly the point where a fully plastic section isformed. When the plastic hinge is determined to be unloaded, the corresponding numerical integration point isshifted back to its normal position. Here, the normal position indicates the location where the numerical integration point is placed when the element acts elastically. By
doing so, the plastic behavior of the element is simulated

Figure 1. Linear Timoshenko beam element and its physical equivalent.

appropriately, and a convergent solution is achieved with
only a small number of elements per member. However,in the ASI technique, the numerical integration point isplaced at the midpoint of the linear Timoshenko beam
element, which is considered to be optimal for one-point
integration, when the entire region of the element behaveselastically. When the number of elements per member isvery small, solutions in the elastic range are inaccurate
because one-point integration is used to evaluate the loworder displacement function of the beam element.
The main difference between the ASI and ASI-Gauss
techniques lies in the location of the normal position of
the numerical integration point. In the ASI-Gauss technique, two consecutive elements that form a member are
considered as a subset, and the numerical integration points of an elastically deformed member are placed so thatthe stress evaluation points coincide with the Gaussian
integration points of the member. This placement meansthat stresses and strains are evaluated at the Gaussian
integration points of elastically deformed members. Gaussian integration points are optimal for two-point integration, and the accuracy of bending deformation is mathematically guaranteed [15]. In this way, the ASI-Gauss technique has the advantages of two-point integration while
using one-point integration in the actual calculations.
Fig. 2 shows the differing locations of the numericalintegration points of elastically deformed elements in the
ASI and ASI-Gauss techniques. The elemental stiffness
matrix, generalized strain and sectional force increment
vectors in the elastic range for the ASI technique are
given by Eqs. (2), and those for the ASI-Gauss techniqueare given by Eqs. (3).
T[ K ] = L[ B (0 )] [ D(0 )] [ B(0) ](2a){∆ε (0)} = [ B(0)]{∆u}(2b)

An Analysis Code and a Planning Tool Based on a Key Element Index for Controlled Explosive Demolition

245

Figure 2. Locations of the numerical integration and stress evaluation points in the elastic range.

{∆σ (0)} = [ D(0)]{∆ε (0)}T(2c)

[ K ] = L[ B ( sg ) ] [ D( rg ) ] [ B ( sg ) ](3a){∆ε (rg)} = [ B(sg)]{∆u}(3b){∆σ (rg)} = [ D(rg)]{∆ε (rg)}

(3c)

2
2
sg = 1 – ------ , rg = – 1 + -----(3d)33Here, {∆ε}, {∆σ} and {∆u} are the generalized strain
increment vector, generalized stress (sectional force) increment vector and nodal displacement increment vector,
respectively. [B] is the generalized strain-nodal displacement matrix, [D] is the stress-strain matrix and L is thelength of the element.
The plastic potential used in this study is expressed by:
M 2 M 2 N ⎞2f ≡ ⎛--------x-⎞ + ⎛--------y-⎞ + ⎛----- – 1 = fy – 1 = 0⎝Mx0⎠ ⎝My0⎠ ⎝N0⎠

(4)

Here, fy is the yield function, and Mx , My and N are thebending moments around the x- and y-axes and the axial
force, respectively. The terms with the subscript 0 are thevalues that result in a fully plastic section in an element

when acting independently on a cross-section. The validity of the ASI-Gauss technique in elastoplastic analyses
under static and dynamic loadings were confirmed byvarious numerical tests [11].

2.2. Member fracture algorithm
Fig. 3 shows the locations of the numerical integration
points for each stage in the ASI-Gauss technique. A plastic hinge is normally generated before it develops into amember fracture, and the formation of a plastic hinge is
described by shifting the numerical integration point to
the opposite end of the fully plastic section according to
Eq. (1). For example, if a fully plastic section first occurs
at the right end of an element (r = 1) as shown in the
figure, the numerical integration point is immediately shifted to the left end of the element (s = -1). Simultaneously,
the numerical integration point of the adjacent element
forming the same member is shifted back to its midpoint,
the location appropriate for one-point integration. Member fracture is expressed by reducing the sectional forcesof the element immediately after the occurrence of a fractured section on either end of the element. The released
force vector {F}, which operates on the element at thenext step if a fractured section first occurs at the right end

Figure 3. Locations of the numerical integration points for each stage in the ASI-Gauss technique.

246

Daigoro Isobe | International Journal of High-Rise Buildingsof an element (r = 1), is expressed by the following equation:T{F} = L[ B(–1)] {σ (1)}(5)

Similarly, if a fully plastic section or a fractured section
first occurs at the left end of the element (r = -1), thenumerical integration point is shifted to the right end of
the element (s = 1).
In this study, member fracture is determined using bending strains, shear strains and axial tensile strains that occur in the elements, as shown in the following equation:κκγxz------x- – 1 ≥ 0 or ------y- – 1 ≥ 0 or ------- – 1 ≥ 0 or
κx0
κy0
γxz0

(6)

εz
γyz
------- – 1 ≥ 0 or ⎛⎝------⎞⎠ – 1 ≥ 0
ε
γyz0
z0
where κx, κy, γxz, γyz, εz, κx0, κy0, γxz0, γyz0 and εz0 are thebending strains around the x- and y-axes, the shear strains
for the x- and y-axes, the axial tensile strain and thecritical values for these strains, respectively. The criticalstrain values used in the analysis were obtained from laboratory experiments using high strength joint bolts [16].
2.3. Elemental contact algorithm
A set of two elements in potential contact is first selected by evaluating the shortest distance between them using
the geometric relations of the four nodes (see Fig. 4(a)).
By examining the angles between the assumed contact
point M and two nodes, a final determination of contact
is made if the angles ∠MB1B2 and ∠MB2B1 are both acute(see Fig. 4(b)); the two elements will not come in contact
if one of the angles is obtuse (see Fig. 4(c)). Once they
are determined to be in contact, the elements are boundwith a total of four gap elements between the nodes (seeFigure 4. Elemental contact algorithm.

Fig. 4(d)). The sectional forces are delivered through thesegap elements to the connecting elements. To express contact release, the gap elements are automatically eliminatedat the time when the mean value of the deformation ofgap elements is reduced to a specified ratio.

3. Validation of the Methods
To validate the numerical code, we performed a simple
impact test with two beams. As shown in Fig. 5, one of
the two aluminum beams was rigidly clamped at the bothends, whereas the other was silently dropped with an initial velocity of 0 m/s from the height of 400 mm above
the clamped beam. The planned contact point between thetwo beams is indicated in the figure. The impact and contact phenomenon were observed using a high-speed camera, as shown in Fig. 6(a), and the numerical results obtained using the code based on the ASI-Gauss technique areshown in Fig. 6(b). The two results agree very well, indicating that the contact algorithm implemented in the numerical code performed as intended to model the impact,
contact and bounce phenomena.
Next, the code was validated by comparing the obtained
results with an experiment performed in the laboratory
using an electromagnetic system to experimentally simulate the explosive demolition of a structure [17]. The mainfeatures of the experimental system are as follows: twoelectromagnetic devices (KANETEC, KE-4RA, max. attach force = 110 N, for beams; KE-4B, max. attach force= 400 N, for columns) are mounted on both sides of analuminum pipe, as shown in Fig. 7, and the members arejoined with steel connectors held by the magnetic field
generated by the electromagnetic devices. Power is supplied to these devices through a 4-pin connector jack anda telephone cord. The blast intervals and switching of themagnetic field are controlled by the blast interval con-

An Analysis Code and a Planning Tool Based on a Key Element Index for Controlled Explosive Demolition

247

Figure 5. Experimental and analytical conditions for the impact test with two aluminum beams.

Figure 6. Experimental and numerical results for impact and contact phenomena with two aluminum beams.

troller and power switches, which are connected to a PC
and a power supply. The magnetic fields of the devices at
each blast point are sequentially released by the PC tosimulate member fracture caused by an explosion. The
system can simulate the failure of beams by disconnecting the magnetic force between the beams and the columns. However, the column failure cannot be initiated in
the electromagnetic system as in the real conditions. The
failure of the columns are simulated, first by switching
off the electromagnetic field of the column member joints
and then, by composing a cantilever system with the up-

per beam. The purpose of this system is to pile up the demolition test results, easily and safely, to validate the proposed numerical code.
The properties and conditions used for the experimentand the analysis are as follows: each span length was 34
cm (for the beams) or 28 cm (for the columns), with 3 cm
× 3 cm box-type beams and 4 cm × 4 cm box-type columns, each with a Young’s modulus of 70 GPa and a Poisson ratio of 0.345 (aluminum); the critical values of thebending strains were 2.4×10-4 rad/mm (beams) and 3.1×
10-4 rad/mm (columns); and the tension strains were 2.7×

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Daigoro Isobe | International Journal of High-Rise Buildings

Figure 7. Outline of the simulated blast demolition experimental system.

Figure 8. Blast conditions for a six-story frame model.

10-4 (beams) and 3.0×10-4 (columns). A time increment of
0.1 ms was used for the analysis. Numerical damping wasapplied, however, structural damping was not considered.
A six-story frame model was constructed using the described devices. The blast conditions are shown in Fig. 8;
the blast points and the blast sequence were carefully selected to enable the floor sections to fold in sequentiallystarting at the upper floors so as to avoid the dispersal offragments over a wide area. Fig. 9 shows a comparison of

the experimental demolition modes and the numerical results. The expected demolition mode was observed in bothcases, and the results are in very good agreement.

4. Blast Demolition Planning Tool using the
Key Element Index
In this section, a blast demolition planning tool using
the concept of a key element index is first described. Sev-

An Analysis Code and a Planning Tool Based on a Key Element Index for Controlled Explosive Demolition

249

Figure 9. Comparison of demolition modes.

eral numerical analyses are then performed on a 15-story,
three-span framed structure using the demolition plansobtained with the planning tool to demonstrate its utility.

4.1. Key element index
Due to variations in their span lengths and strengths,
certain columns in a structure support more vertical 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 astructure, i.e., to determine the key elements, such as theredundancy index by Frangopol [18] and the sensitivity
index by Ito et al. [19]. These indexes are effective for
identifying highly sensitive columns that support the ver-tical load; however, they equivalently identify those columns that only cause partial collapse and are thus not useful for demolition planning, where the major aim is thetotal collapse of a structure. Therefore, a new index called
the key element index for estimating the contribution ofbase columns to the total collapse of the structure is proposed.
The key element index is calculated as follows. First,
we perform a static pushdown analysis by equally applying incremental vertical loads at every structural joint ina modeled structure. Several columns on the upper floors
may yield in this process, but the vertical loads are nevertheless continuously applied in steps until one of thebase columns yields. The total vertical load (including the

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Daigoro Isobe | International Journal of High-Rise Buildings

floor loads) applied to a column at the step when one of
the base columns yields is defined as the ultimate yieldstrength PG of the structure. The ultimate yield strength of
the initial, undamaged structure is denoted 0 PG, and theultimate yield strength of a structure with one base column eliminated is denoted 1 PG. The key element index KIof column m, for example, can be defined as the ratio of
the ultimate yield strengths of the present and the initialstep. The index can thus be written as:
0
1K Im = 0 PG /1 PG

(7)

(8)

The index shown above indicates the contribution of thepresent column (or columns) to the strength of the initial,
undamaged structure and can be used for cases in which
the columns are eliminated simultaneously. However, thesensitivity of columns may change momentarily for thosecases when the columns are eliminated sequentially withina certain interval. Therefore, the updated index, as shown
below, is used for those cases with a sequential blast.
n–1
n K Im = n – 1 PG /n PG

0
1KI16 = 0 PG /1 PG = 1.693(10)

and at the second step as:
1
2KI16 = 1 PG /2 PG = 1.012

The key element index at the nth step is then:0nK Im = 0 PG /n PG

mm × 13.2 mm for the beams, with the sectional sizes becoming gradually thinner in the higher stories. The floorload, in this case, is set to 400 kgf/m2. The updated index
values and the selection of columns from the largest index
value at each step are shown in Fig. 11. For example, thekey element index value KI for column No. 16 (in the upper right corner) can be calculated at the first step as:(11)

In this paper, the column at the left and lower side isselected prior to the other columns, if the index values calculated for multiple columns are the same, to direct thewhole collapsing building toward the lower left side. As
shown in the figure, the selected columns tend to bias to(9)

In this case, the index can be defined as the ratio of theultimate yield strengths of the present and the previous
step.
As an example, the key element index values were calculated for a 15-story, three-span model, as shown in Fig.
10. Each span length is 6 m, and the height between eachfloor is 3.6 m. The material used for the columns andbeams is SN490B steel. We selected box-type section of
430 mm × 430 mm × 13 mm × 13 mm on the 1st floor columns and H-type section of 331 mm × 825.7 mm × 18.4

Figure 10. A 15-story, three-span model.

Figure 11. Updated index values and the selection of columns from among those with the largest values (column
at the left and lower side is selected prior to the other column if they show same KI values).

An Analysis Code and a Planning Tool Based on a Key Element Index for Controlled Explosive Demolition

251

the intended demolition direction if the columns are selected from the largest index value. Furthermore, the distribution of the selected columns differs, as shown in Fig.
12, 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.

collapse, PC indicates partial collapse, and NC indicatesno collapse. The integrated value indicated by the black
circle in Fig. 13(a), for example, is calculated as follows:

4.2. Blast demolition planning using the integrated
values of the key element index
Several blast demolition analyses were performed using
selected columns, as described in the previous section.
The key element index values of the selected columns are
summed and the collapse modes for each case are plotted.
Each procedure was performed on models with different
floor loads. Fig. 13 shows the distribution of the integrated
values of the key element index and the collapse modesof the structure for a simultaneous blast, where nonupdated index values are used. TC in the figures indicates total

Here, again, note that the lower right subscript in the key
element index indicates the column number, the upper leftsubscript indicates the step number under consideration in
the calculation of the ultimate yield strength ratio, and thelower 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 ensure thatthe structure is partially or totally demolished. The regionof total collapse is large when the columns with the largest
index values are successively selected (see Fig. 13(a)),
whereas the region is very small when the columns withthe smallest index values are selected (see Fig. 13(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 thecollapse process.
Fig. 14 shows the distribution of the integrated valuesof the key element index and the collapse modes of thestructure for sequential blast, where updated index values
are used. The integrated value indicated by the black circle in Fig. 14(a), for example, is calculated as follows:

0
0
0
0
0
0
1KI1 + 2KI5 + 3KI9 + 4KI2 + 5KI6 + 6K I3= 1.693 + 2.382 + 3.633 + 4.284 + 5.979 + 7.863= 25.834

(12)

0
1
1
3
4
6
1KI1 + 2KI5 + 3KI9 + 4KI2 + 5K I6 + 7KI10= 1.693 + 1.407 + 1.525 + 1.179 + 1.315 + 1.377= 9.892

Figure 12. Updated index values and the selection of columns from among those with the smallest values (column
at the left and lower side is selected prior to the other columns if they show same KI values).

(13)

The same tendencies as observed in Fig. 13 can be seen
here in the distribution of the index values and the collapse
modes. However, the region of total collapse becomesmuch smaller than in simultaneous blasting because thestructure tends to become relatively stable during each
blast interval.
It is evident from Figs. 13 and 14 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 procedurequite unstable. Therefore, the selection of columns withthe 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
demolished by a final blast on a column (or columns)
with a large index value, essentially traversing the solid

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Daigoro Isobe | International Journal of High-Rise Buildings

Figure 13. Key element index values and collapse behavior of the model (simultaneous blast, nonupdated index value).

Figure 14. Key element index values and collapse behavior of the model (sequential blast, updated index value).

line in Fig. 14(b) in one step.

4.3. Blast demolition analysis of a framed structureusing the obtained plan
Two analyses using the plans of blast demolition obtained in the previous section were performed on the model
shown in Fig. 10. Each analysis took 50 to 90 minutes ona personal computer (CPU: 2.0 GHz Xeon, 8GB RAM).
Fig. 15 shows the demolition mode for the simultaneous
blast case, in which the eliminated columns were selectedfrom 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. (12). Fig. 16 shows the demolition mode for the sequential blast case, in which thecolumns were selected for elimination from among thosewith the smallest updated index values. To achieve a totalcollapse, the columns with the large index values at the
final step were selected 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 valueof the initial nine columns does not traverse the solid line
in Fig. 14(b), however, the total value including the final
three columns, which is 15.166, slightly traverse the line.
Although the timings of the collapse initiation and thecollapse modes slightly differ in each case, both display
a successful demolition pattern, with the structure totallydemolished to ground level and towards the intended direction.

5. Conclusions
The numerical code using the ASI-Gauss technique described herein yields highly accurate solutions with small
mesh subdivisions and requires little calculation time anda small amount of memory. The shifting of the numericalAn Analysis Code and a Planning Tool Based on a Key Element Index for Controlled Explosive Demolition

253

Figure 15. Demolition mode for the simultaneous blast case (six columns selected from the largest nonupdated index
value).

Figure 16. 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).

integration points enables the accurate modeling of a fractured section in a member, which is the main reason why
the code can be effectively applied to demolition problems.
The key element index and its integrated values, as demonstrated in this paper, may be used to quantitatively
verify which columns should be eliminated to best achieve a total collapse. The numerical results suggest that fora 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 be undertaken to enable the precise
planning of blast intervals and locations required to allow
the whole structure to collapse in its own wake, which isvery important to lower the risk of damage to neighboringbuildings.

6. Acknowledgements
The author would like to express his appreciation forthe contributions to the continuous testing and refinementof the code by the former and present graduate students
in our laboratory: Kyaw Myo Lynn, Kazunori Shimizu,
Kensuke Imanishi, Masashi Eguchi, Zion Sasaki, Tomonobu Omuro, Naoki Katahira, Hitoshi Yokota, Tetsuya
Hisanaga, Le Thi Thai Thanh, Yuta Arakaki, Takuya
Katsu and Tomoya Ogino.

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