Journal of Natural Disaster Science, Volume 28, Number 2, 2006, pp73-83

Dynamic behavior of masonry structures under pyroclastic flows

Junji KIYONOa, Robin J.S. SPENCEb and Tadayoshi NAKASHIMAca
Department of Urban Management, Kyoto Universityb
Department of Architecture, Cambridge UniversitycGraduate School of Contemporary Sociology, Aichi Shukutoku University(Received for 2 Feb., 2006 and in revised from 20 Jun., 2006)

ABSTRACT
Pyroclastic flow is a dangerous hazard for people and houses so buildings have to provide a measure of protection to the occupants. In order to improve the structural strength of buildings, we need to know the structural
behavior against the lateral pressure of the flow. In this study, dynamic behavior of unreinforced masonry structures affected by pyroclastic flows was analyzed using 2-dimensional (2D) Distinct Element Methods (DEM).
DEM is a numerical analysis technique, in which the positions of elements are calculated by systematically solving equations. The structure is modeled as an assembly of distinct elements connected by virtual springs and dashpots where elements come into contact. Masonry structures with simple structural elements; walls, floors, a roof,
and furniture were modeled. The strength of mortar was varied to check the effect of pyroclastic flow on the structural behavior under different conditions. Pressure acting on a wall due to pyroclastic flow was modeled as a simple time function of which the peak value was varied from 0.1 MPa to 10 MPa. A pressure model of which intensity changes with height was also treated. Tilting, lateral movement, collapse and swept away within several seconds are the typical collapse process of a weak masonry structure even when the lateral pressure is 1 KPa. The
collapse of the masonry structure is controlled by the relation between the overturning moment due to the lateralpressure and the resistant moments due to gravity and mortar joint strength.

1. INTRODUCTION
Pyroclastic flow is particularly dangerous because it can occur
with little warning, move at high speed and with enormous destructive power [Spence et al. 2004 (1)]. Historical eruptions of
Vesuvius occurred in 79, 472 and 1631. Surveys of various typesof building in the Vesuvian area determined the impact of pyroclastic flow [Spence et al. 2004 (2)]. A realistic model of the eruption has been constructed that handles the physical parameters of
the pyroclastic flow [Todesco et al. 2002]. Direct observations ofrecent volcanic eruptions such as Mt St Helens, Mt Unzen andSoufriere Hill have reinforced the information on such flows.
Pressures acting on specific faces of a building depend on thecharacteristics of the flow around the building. A typical scenarioof the invasion of pyroclastic flow begins with glazed openings,
ingress of ash, and the ignition of furniture. However, when a highlateral pressure acts on a building, the building itself could failthrough overloading of critical structural elements because theresistance of a tuff masonry wall of 600 mm and 400 mm thick are
10-13 KPa and 6.8-9 KPa, respectively [Spence et al. 2004 (2)].
Petrazzuoli et al. (2004) compiled the value of pressure acting
on a building based on the results of several researchers; a reinforced building begins to sustain damage at approximately 7 KPa,
and 35 KPa is the upper limit value of pressure for all buildings.
The pressure away from the vent for the 79-AD eruption of
Vesuvius was less than 10 KPa. The dynamic pressure of pyroclastic flow of Vesuvius at about 2 km distance was about 7-10

KPa, and at a 4-5 km distance they estimated it to be less than 1-2
KPa. Also they concluded that the r.c. structures (week aseismic
structure, acceleration design 0.04 G) provide collapse loads
greater than 3-5 KPa; The Horizontal Pressure Limit (HPL) of 1-2floor r.c. structures is more than 5 KPa; the non-engineered structures are vulnerable to pyroclastic flow action.
To reduce the number and type of casualties caused by structural damage due to pyroclastic flow, it is important to understandthe effect of pyroclastic flow on buildings. This study simulated
the collapse process of unreinforced masonry structures using
DEM [Cundall, 1974], to investigate the effects of the flow impact
on several types of masonry structures. When we consider the
potential injuries and casualties, overturning furniture also is an
important factor although it is affected by various external, indeterminate factors, such as the existence of stoppers, the flooring material, and the size of the furniture. In this study, we also made amodel in which furniture is placed on the floor. There are few simulation studies that trace the total dynamic behavior of the structure
including the interior from the beginning to its collapse. For example, Kiyono and Furukawa (2004) simulated the collapse process oftimber frame houses and assessed injury to humans in the house.
We focus on masonry structures and analyze the process thatcauses their collapse. The DEM approach is suitable for dynamic
analysis of masonry structures that are common worldwide. There
are many types of masonry buildings. The behavior of masonrybuildings depends on the construction method, the characteristicsof the materials, the age of construction and so on. We here deal

KEY WORDS: Masonry building, Dynamic behavior, Pyroclastic flow, Collapse simulation, Distinct element method

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with a concrete block unreinforced masonry structure as a typicalmasonry structure. By carrying out the house collapse simulation,
the relationship between the lateral pressure of pyroclastic flow andthe levels of damage occurring to structures can be obtained. This
relationship can then be used to take proper countermeasures topyroclastic flow, thereby reducing the number of casualties due tohouse collapse.
In this study, 2D simulations of the collapse of unreinforced
masonry structure were made. The force acting on a wall due topyroclastic flow was given and the dynamic behavior was calculated. Case studies by changing the number of stories, strength ofjoint mortar between concrete blocks, and existence of furniture
were considered. Pressure varying models were also used to investigate the effect of different densities of a stratified body on the
structure. The findings should aid in defining the relationshipbetween the degree of damage occurring to an unreinforced masonry structure and the pressure of pyroclastic flow.
2. METHOD
2.1 Equation of Motion
DEM, a numerical analysis method that computes the positionof individual elements by solving equations of motion step by step,
was used. All the elements are assumed to be rigid. Virtual
springs and dashpots in the normal and tangential directions are
generated when an element comes into contact with other elements,
and the contact force acts through these generated virtual springsand dashpots. By solving the equation of motion for each element
step by step, the behavior of all the elements in combination can betraced. The forces acting on an element are the external force (fx,fz) and the sum of the contact forces between elements (Fx, Fz, Mθ).
Accelerations of an element in a 2D case are calculated byx˙˙ = ( f x + Â Fx ) / m(1)z˙˙ = ( fz + Â Fz ) / m(2)q˙˙ = Â Mq / Iq(3)

in which m is the element's mass, Iθ is the inertia moments aroundthe center of the gravity.
Assuming that acceleration is constant for the short period Δt,
the velocity and displacement of each element can be calculated bymeans of the following difference scheme, and the total structural
behavior can be traced:Ï x˙t ¸ Ï x˙t -Dt ¸ Ï x˙˙t -Dt ¸
Ô Ô Ô
Ô Ô
Ô
Ì z˙t ˝ = Ì z˙t -Dt ˝ + Ì z˙˙t -Dt ˝ Dt
Ô ˙ Ô Ô ˙ Ô Ô ˙˙ ÔÓq t ˛ Óq t -Dt ˛ Óq t -Dt ˛(4)

Ï xt ¸ Ï xt -Dt ¸ Ï x˙t -Dt ¸
Ô
Ô Ô
Ô Ô Ô
Ì zt ˝ = Ì zt -Dt ˝ + Ì z˙t -Dt ˝ DtÔq Ô Ôq Ô Ô ˙ Ô
Ó t ˛ Ó t -Dt ˛ Óq t -Dt ˛(5)where Δt is the time interval of the computation.
2.2 Contact Judgment
When elements come into contact, the spring and dashpot are
generated in the calculation. The contact model for the 2D analysis, shown in Fig. 1, is the case in which the corner of a circularelement is in contact along their edges. In order to simplify the
judgment, the element was modeled by the use of 1/4-circle for its
corner. Judgment of contact is made by considering the collocation
between the two elements concerned.
2.3 Contact Force
The contact forces in the normal and tangential directions arecalculated by taking into account increments in the restoring anddamping forces in each time step [Kiyono et al., 2004].
3. PARAMETERS AND ANALYTICAL MODEL
3.1 Spring Constant, Damping Coefficient and Friction
Coefficient
In DEM, most of the force-displacement laws for elastic contact between two spherical elements in the normal direction are
based on the Hertz theory [Johnson, 1985]. Imagine that two
spherical elements, i and j, are in contact and subjected to a normal
contact force. Assume ri and rj are the radii of the two elements.
The Young's modulus for the elements are E i and E j and the
Poisson's ratios are νi and νj. The equivalent Young's modulus EisÊ 1-ni2 1-n j2 ˆE=Á+E j ˜¯Ë Ei-1

and the relative radius of contact curvature, r, isFig. 1 Contact models of circular elements(6)

DYNAMIC BEHAVIOR OF MASONRY STRUCTURES UNDER PYROCLASTIC FLOWS

Ê 1 1ˆ
r=Á + ˜
Ë ri r j ¯

-1

(7)

According to the Hertz theory for the elastic contact of two spheresin the normal direction, the force-displacement relationship is[ en ] t =4
E r ◊n33(8)where, [en]t and n respectively are the normal contact force andcontact displacement at time t. This force-displacement relationship can be transformed into the differential equation[ en ] t = [ en ] t -Dt + 2E r ◊ n Dn

(9)where, Δn is the increment of contact displacement. The spring
constant in the normal direction at time t therefore is expressed as
K n = 2E r ◊ n(10)Because this study uses rectangular-parallelepiped elements, we
utilized the equivalent radius which has the same volume.
The spring constant in the tangential direction was defined as
Ks =Kn
2(1 + n )(11)

where ν is the Poisson's ratio for the timber frame.
As for the damping coefficient, critical damping was adopted
C n = 2 mK n

(12)

C s = 2 mK s

(13)where, m is the equivalent mass of two elements. When theirmasses are mi and mj,

Ê 1
1 ˆ
m=Á
+
˜
Ë mi m j ¯

75

-1

(14)

These parameters are calculated by the use of Young's modulus
and the Poisson's ratio [Architectural Institute of Japan, 1995]. The
density of a concrete block is the apparent density. The parameters
used are shown in Table 1.
The dynamic friction coefficient is determined by the field testof collapsed brick masonry houses that was performed during thedamage survey of the 2003 Bam Earthquake [Kiyono et al., 2005].
Although the measured friction was of baked bricks, we here used
this value ignoring the materials such as masonry, roof, concreteslab and furniture. The value of the static friction coefficient isassumed to be the same value for the dynamic friction.
3.2 Joint Parameters
In conventional DEM, connectivity between elements is notconsidered, the elements act independently as a discontinuum. The
masonry elements of a real building, however, are connected bymortar, and the structure acts as a continuum. The joint spring,which allows a structure to behave as a continuum until its joints
are broken, therefore is introduced.
Members of most masonry buildings are mortised together
with mortar. We assume the bonding of mortar is broken when thetension and shear forces exceed the threshold intensity.
The spring constants for a joint in the normal and tangential
direction were determined as follows. We varied the resistancestrengths for both directions as 1 Kgf×104/m2 (weak) and 0.1
Kgf×104/m2 (very weak) based on the field measurement [Kiyono
et al., 2005]. The total shear area, 0.20 m×1.0 m (unit depth)×2(top and bottom side of the block) = 0.40 m2, is obtained from Fig.
2. The shear intensity therefore is 0.4 m2×1 Kgf×104/m2 (0.1
Kgf×104/m2)×9.8 m/sec2=3.92×104 N (3.94×103 N). In thisstudy, joints are broken when the restoring force for the normal andtangential directions exceeds the joint intensity (in calculation, aTable 1. Density and elastic properties for concrete block, concrete and wood

Fig. 2 Model of block masonry

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small value of corresponding displacement, 0.01 m, is used), therefore the spring constant Ks is 3.92×106 N/m (3.92×105 N/m). The
normal intensity is calculated from Eq. (10). In 2D DEM, a mortar
joint is expressed by two joint springs. The spring constant for 2D
DEM is therefore half the Kn and Ks value.
We assumed that the damping coefficient for the joint is 0.0 inboth the normal and tangential directions because the damping
effect is already considered by the virtual dashpot mentioned in
2.2. Spring constants and damping coefficients for the structure andjoint are shown in Table 2.
3.3 Time Interval
The interval used for computation markedly affects the stability of the results. If it is too long, results will diverge. Cundall[1975] recommends the interval
Dt < 2 m / K n(15)

From the above equation, the limitation is Δt < 0.003 sec. We
chose to use an interval of Δt = 0.0001 sec.
3.4 Modeling of the Structure and Pressure(a) Structural model
The structure analyzed is an unreinforced masonry structure(Fig. 3) of 5.00 m width and 2.70 m height for each floor. The
wall is made of concrete blocks (see Fig. 2; 0.15 m×0.20 m) with
an apparent density of 1.50×103 Kg/m3 and the floor is made ofconcrete slabs of 2.40×103 Kg/m3. The roof and furniture ismade of wood and its density is that of cypress wood (0.34×103
Kg/m3), but the apparent weight, namely half of the total weight, isused for the furniture. The sample structure shown in Fig. 3 has
two masonry walls, two floors, and a roof. These elements aremodeled as rectangles. Calculations of the mass and moments ofinertia of these elements are based on the density mentioned above.
In conventional DEM, elements are affected only by the contact forces between them, joint elements not being considered.
Elements of real masonry buildings, however, are connected withmortar at the joints and behave as a continuum until the joints(mortar) break. Joint elements connecting different elements therefore were introduced.
(b) Analytical cases
We modeled four masonry structures as shown in Fig. 4,
which are one- and two-story masonry structures with and without
furniture on the floor. The dynamic behavior under pyroclastic
flow is strongly affected by the mortar strength. We supposed thisjoint strength to be 0 N/m2 (no mortar; only friction), 0.1×105
N/m2 (very weak mortar) and 1.0×105 N/m2 (weak mortar) in bothnormal and tangential directions. If all the joints are sufficiently
strong to endure pyroclastic flow, the structure will not collapse,
therefore, we here chose the weaker bonding resistance. When theexternal force exceeds this value, the joint spring is broken and noresistance force works on the surface except friction among the elements.
Table 3 shows the analytical cases considered. A, B, and C
correspond to the joint strengths; 0 N/m2, 0.1×105 N/m2, and 1.0×
105 N/m2, respectively. The front number of A, B, and C means the
Table 2. Spring constant, damping coefficient and friction coefficient

Table 3. Analytical cases of buildings under various conditions

Fig. 3 Structural modelDYNAMIC BEHAVIOR OF MASONRY STRUCTURES UNDER PYROCLASTIC FLOWS

77

Table 4. Resistances of buildings and elements for the Vesuvian area (Spence et al. [2004 (1)])

Fig. 4 Analytical cases of 1- and 2- story masonry buildings

number of stories. The number following A, B, and C expresses
the number of furniture in the structure.
(c) Lateral pressure of pyroclastic flow
Spence et al. [2004 (1)] determined the probable resistance ofbuilding elements to lateral pressure of pyroclastic flow (Table 4).
The table shows that the resistance of a masonry wall is about 6-26
KPa. In this study, we consider relatively weak unreinforced
masonry structures. Therefore the pressures acting on the masonrywall are assumed to be the four values of 0.1 KPa, 1 KPa, 5 KPa,
and 10 KPa.
In our 2D model, the height of one block masonry is 0.15 m,
so that the area for a unit depth becomes 0.15 m2. The force of 150
N acts on the surface of the block element. The weight of theblock for unit depth is, 0.15 m (height)×0.20 m (width)×unit
depth×1.5×103 Kg/m3 (density), or 45 Kg. If acceleration of 1 G(9.8 m/sec2) acts on the block element, the force is about 450 N.
From this relation, 0.1 KPa, 1 KPa, 5 KPa, and 10 KPa are approximately equivalent to the lateral forces of 0.03 G, 0.3 G, 1.5 G and
3 G , respectively.
Determination of the time function of lateral pressure is a crucial issue. The duration of dynamic pressure due to pyroclastic

flow is three orders of magnitude larger than that after a nuclear
explosion (milliseconds) [Petrazzuoli et al. (2004)]. However, theduration time and its peak value depend on many factors; the typeof eruption, magnitude of the eruption, distance from the vent, andso on. The duration could also change from seconds to minutes.
Even if the duration of strong dynamic pressure continues for several tens of minutes, the collapse process of the house take only afew seconds. Although many models on dynamic pressure can beconsidered, we determined the time function of lateral pressure,p(t), as follows.
p (t ) = A (tt) exp(1 - )
tp
tp

(16)

in which A is the peak amplitude, and tp is the peak time of lateralpressure. In this study, we assumed the peak time, tp, to be 2 sec.
Upstream is defined as the right-hand side and the pressure acts on
the right wall, floor, and roof uniformly. The function, Eq.(16), isshown in Fig. 5.

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Fig. 5 Time function of lateral pressure assumed

4. RESULTS

4.1 Effect of Pressures, Stories, and Furniture
In this study, the factors of the number of stories (1-story and2-story), the joint (mortar) strengths (0 N/m2, 0.1×105 N/m2 and1.0×105 N/m2), and existence of furniture are varied for the four
lateral pressures (0.1 KPa, 1 KPa, 5 KPa, and 10 KPa). The duration time of the simulation is 10 sec but the figures used here are of
up to 3 sec because the building collapsed within 3 sec in mostcases. The value of the pressure at 3 sec is about 60% of its peakpressure at 2 sec.
In case of the lateral pressure of 0.1 KPa, the masonry structures in all cases do not collapse even though they showed a small
deformation regardless of the joint strength (Fig. 6) because the lateral force is about 30 gal which is not a large value when considering the action of an earthquake. For a larger pressure than 0.1 KPa,
structures in all cases collapsed and furniture overturned.
Fig. 7 shows the collapse modes for the lateral pressure of 1.0
KPa. Walls on both sides for a 1-story structure tilted simultaneously [Fig.7(a)]. For the 2-story structure, the behavior of the firststory is the same as for the 1-story structure [Fig. 7(b), (c) and (d)],however, the collapse of the second story is classified into two patterns; the second story collapsed in the upstream direction against
the first story for the joint strength of 0 and 0.1×105 N/m2. The
other pattern is that the second story maintained its original shape
before the collapse of the first story and crashed down after that forthe joint strength of 1.0×105 N/m2 (Fig. 8).
For the case of 5.0 KPa, both walls of a 1-story structure tilted
and the upstream wall with a roof was blown off in the direction of
the other wall (Fig. 9). In a 2-story structure, both walls of the firststory tilted the same as the 1-story (Figs. 10, 11 and 12), however,the behavior of the second story shows three types of collapse pattern according to the joint strength and the existence of furniture.
The first is that the wall on which the pressure does not act began
to collapse due to the force of inertia and another wall moved andcollided with it as shown in Fig. 10. The second pattern is that thewall of the second story is broken by the reaction force of furniture
as shown in Fig.11. The third is that the second story maintained
its original shape until the collapse of the first story because of
having relatively strong joints (1.0×105 N/m2 ). The upper story
moved downstream maintaining the inner space and collapsed after

the second floor crashed to the ground (Fig. 12). Fig. 13 shows thecollapse pattern for the lateral pressure of 10 KPa. The masonry
structure behavior is almost the same as the case of 5 KPa except
for the speed of the collapse process.
The time to collapse for each case is shown in Fig. 14.
Collapse here is defined as the state in which the roof reaches thefirst floor. From the figure, the larger the lateral pressure of the
pyroclastic flow, the shorter the time to collapse. The strength of
the joint is effective when the pressure is up to 1.0 KPa because thetime to collapse is extended. But we could not find the effectiveness in this case study when the pressure is larger than 1.0 KPa.
Fig. 15 shows the relation between the times to collapse for theroof of a 1-story structure and that for the floor of a two-story
structure. Here, 'time to collapse' for the 2-story structure is thetime when the second floor reaches the first floor. The time to collapse for the first story of a 2-story structure is almost the same as
the time for a 1-story structure. Total time to collapse for a 2-story
structure, therefore, becomes longer than that of a 1-story structure.
As a typical collapse process is followed by tilting, moving
laterally, collapsing and being swept away, there is insufficientspace for occupants to survive. Although the strength of the building is considerably weak in these case studies, the masonry structure collapse occurred within several seconds even when the lateralpressure was 1 KPa.
Summarizing the above discussions, the findings are- Structures do not collapse at a lateral pressure of 0.1 KPa,
even if the joint mortar strength is 0 N/m2.
- The collapse mode of the second story depends on the joint
strength. As the joint strength becomes stronger, the second story maintains its original shape.
- The collapse modes of a 1-story building and the second
story of a 2-story building are almost the same.
- The existence of furniture affects the collapse mode of thewall because the reaction force acts on the wall. However
the final conditions after collapsing are almost the same.
4.2 Lateral Pressure Varying with Height
A new model for an ash-cloud flow mechanism has been presented based on the detailed investigation of the 15 September
1991 pyroclastic flow at Unzen Volcano, Japan. Although several
investigators have proposed a stratified pyroclastic current model,
the new model for pyroclastic flows is composed of three parts; a

DYNAMIC BEHAVIOR OF MASONRY STRUCTURES UNDER PYROCLASTIC FLOWS

Fig. 6 Structural behavior at 3.0 sec (lateral pressure: 0.1 KPa, no joint)

Fig. 7 Structural behavior for different joint strength at 2.0 sec (lateral pressure: 1.0 KPa)

Fig. 8 Behavior of 2-story structure for the joint strength of 1.0×105 N/m2 (lateral pressure: 1.0 KPa)

Fig. 9 Behavior of 1-story structure for the joint strength of 0 N/m2 (lateral pressure: 5.0 KPa)

Fig. 10 Behavior of 2-story structure for the joint strength of 0 N/m2 (lateral pressure: 5.0 KPa)

Fig. 11 Behavior of 2-story structure with furniture for the joint strength of 0 N/m2 (lateral pressure: 5.0 KPa)

Fig. 12 Behavior of 2-story structure with furniture for the joint strength of 1.0×105 N/m2 (lateral pressure: 5.0 KPa)

Fig. 13 Behavior of 2-story structure with furniture for the joint strength of 0 N/m2 (lateral pressure: 10.0 KPa)

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J. KIYONO, R. J.S. SPENCE AND T. NAKASHIMA

Fig. 14 Time to collapse for each caseFig. 15 Comparison of times to collapse between roof of 1-story and floorof 2-story masonry structure

Fig. 16 Various types of lateral pressures (uniform, linear, parabolic and lobe)

bottom turbulent current of high concentration (main body), a fluidization zone above the former, and an overlying, convecting,diluted cloud [Fujii et al. 1999].
In the previous calculations, we assumed that the lateral pressure of the flow is uniform against the whole wall under consideration. But a lower density part of the flow is overriding the higher
density main body. Therefore we assumed three other lateral pressure models in which the pressure varies with height, and compared the structural behavior. Fig. 16 shows the lateral pressure
models; uniform, linear, parabolic, and lobe model. The pressure
acting on the center of the wall is 1 KPa for the first three models.
The pressures of the top and the bottom of the structure are 0.5
KPa and 1.5 KPa for the linear model, and 0.25 KPa and 2.25 KPa
for the parabolic model. In the lobe model, pressure lower than 2m dramatically changes from upper 0.25 KPa to bottom 3 KPa.
The transition range of the height is from 1 m to 2 m. The joint
strength is 1.0×105 N/m2 for all structural models.
The structural behavior is shown in Fig. 17 (a), (b), (c) and(d), respectively. Compared with the uniform model [Fig. 17 (a)],the structure for the linear model [Fig. 17 (b)] maintains its original shape especially in the second floor because the upper part ofthe pressure is weaker than the lower part. But finally, the second
floor tilted and overturned in the downstream direction. As for theparabolic pressure model [Fig. 17 (c)], the pressure to the first floor
is so strong that the first floor is swept off. As the bottom pressure
is locally high in the lobe pressure model, there is insufficient overturning moment for the wall [Fig. 17 (d)].
Modes of the structural collapse considerably vary even when
the pressure distribution acting on the wall only slightly changes.

In order to perform detailed analysis of the masonry structures
according to the scenario, gathering quantitative data on the pressure distribution of pyroclastic flow is needed.
4.3 Critical Condition of Lateral Pressure
For clarity, we deal with a simple 1-story masonry structure
without furniture. We checked the structural behavior for every
0.1 increment of lateral pressure from the initial value of 0.1 KPa.
From these calculations, we defined the critical value of pressure as
the pressure at which the structure collapses when exceeded. Fig.
18 (a) shows critical lateral pressure obtained from dynamic simulations for three joint mortar strengths. The critical values for joint
strengths of 0 N/m2, 0.1×105 N/m2, and 1.0×105 N/m2 were 0.3
KPa, 0.3 KPa, and 0.7 KPa, respectively. In this study, shear andnormal joint strengths are extremely small (0 N/m2, 0.1×105 N/m2,
and 1.0×105 N/m2) because we here focused on the collapse mechanism of masonry structure.
Now we check whether the above-mentioned-critical values
calculated through the dynamic analyses can be explained from theviewpoint of static equilibrium.
We consider the case that the lateral pressure is 1 KPa andjoint mortar strength is 1.0×105 N/m2 (100 KPa). The equilibrium
subject to the moment around the edge is as follows. A wall ismade of concrete blocks with a thickness of w=0.2 m and a heightof h=2.7 m, as shown in Fig. 18 (b). The lateral force acting on thewall, FP, is 2,700 N (1 KPa×2.7m×unit depth), whereas normal
joint strength, FJ , is 20,000 N (100 KPa×0.2 m×unit depth). As
the density of the block is 1.5×103 Kg/m3, the total weight of thewall, FG, becomes about 8,000 N (1.5×103 Kg/m3×0.2 m×2.7

DYNAMIC BEHAVIOR OF MASONRY STRUCTURES UNDER PYROCLASTIC FLOWS

Fig. 17 Comparison of collapse modes for various types of lateral pressures (uniform, linear, parabolic and lobe)

Fig. 18 Critical lateral pressures (1-story structure) and collapse mechanism

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J. KIYONO, R. J.S. SPENCE AND T. NAKASHIMA

m×unit depth×9.8 m/sec2). House collapse is controlled by the
relation between the overturning moment due to the lateral pressure
and resistant moments due to gravity and mortar joint strength. In
the above case, the overturning moment, FP×h/2 (3,645 Nm), islarger than the resistant moment, (FG +FJ)×w/2 (2,800 Nm), sothat the house collapsed at 1 KPa lateral pressure. From this relationship, the critical pressure can be estimated as 0.76 KPa. In thecases in which the joint strengths are 0 N/m2, and 0.1×105 N/m2,
the critical values are 0.21 KPa and 0.27 KPa, respectively. They
are in good agreement with the results obtained by the dynamic
analyses shown in Fig. 18 (a). This means that the critical lateralpressure can be approximately estimated by using the static equilibrium equation.
5. DISCUSSION
We used the structural parameters for brick masonry obtained
from a field survey conducted in the earthquake area in Bam, Iran.
The resistance strength of joint mortar for the tangential and normal directions were defined as 1 Kgf×104/m2 (weak) and 0.1
Kgf×104/m2 (very weak) because the average value of the collapsed masonry structures in Bam was about 0.1 Kgf×104/m2(which is why defined very weak ) and the general value of theshear strength for joint mortar is about 10 Kgf×104/m2 [Mayorca
et al., 2004]. In the center of Bam city, 60-80% of simple masonry
structures were very heavily damaged or collapsed [Hisada et al.,2004]. The MSK intensity is estimated to be more than IX aroundthis area. This seismic intensity corresponds to more than 0.2 G[Mostafaei et al., 2004]. In this study, as mentioned in Section
3.4(c), 1 KPa corresponds to 0.3 G. All the cases in which a pressure of more than 1 KPa acts on the structure were completely collapsed. A seismic force of 0.2 G destroyed most of the simple
masonry in the actual field in Bam and a force of more than 0.3 G
due to pyroclastic flow destroyed all the structures in the simulation. Both results are coherent. Of course, more information on
the material parameters of masonry structures is needed to conduct
an accurate simulation, however, we can show the simulation procedure with which the collapse mechanism of masonry structure
due to pyroclastic flow can be traced.
The collapse pattern varies with mortar joint strength. If thestrength is sufficiently large, a building will resist pyroclastic flow.
But during the pyroclastic flow, people may not avoid injury only
by considering strengthening the building. Because other crucial
issues such as ingression of hot gas and ash into the house due toglazed openings have to be taken into account.
Although the structural strength is considerably weak in thecase studies considered here, the collapse occurred within several
seconds even when the lateral pressure is 1 KPa. Avoiding the collapse by structural strengthening is a crucial issue. However, useful disaster prevention countermeasures such as predicting volcanic
eruption, constructing an emergency alarm system, working out theevacuation plan, ensuring the evacuation route and so on are very
important.
Advanced studies are needed after gathering quantitative dataon the constructional material, age of construction, mortal joint
strength and pressure distribution of the pyroclastic flow in thespecified site, which should provide valuable information forimproving pyroclastic flow-resistant designs and evacuation fromthe flow.
6. CONCLUSIONS
We developed a simulation procedure with which the collapse
mechanism of an unreinforced masonry structure can be traced.
We used DEM to analyze 2D behavior of masonry structures.
Although the structures and materials are simplified, various collapse patterns were simulated. A structural joint model was introduced, and the effects of joint strength were investigated.
Structures do not collapse at the lateral pressure of 0.1 KPa,
even if the joint mortar strength is 0 N/m2. The collapse mode of
the second story depends on the joint strength. As the joint
strength becomes stronger, the second story maintains its original
shape. The collapse modes of a 1-story building and the second
story of a 2-story building are almost the same. The existence offurniture affects the collapse mode of the wall because the reaction
force acts on the wall. However the final conditions after collapsing are almost the same. As a typical collapse process for thestrong lateral pressure is followed by tilting, moving laterally, collapsing and being swept away, there is insufficient space for occupants to survive.
The collapse of a masonry house is controlled by the relation
between overturning moment due to the lateral pressure and resistant moments due to gravity and mortar joint strength. This suggests that the critical values calculated through the dynamic analyses can be explained from the viewpoint of static equilibrium.
This study only dealt with a 2D confined space, more detailed
analyses including glazing failure and an extension to 3D analysis
is required.
ACKNOWLEDGEMENTS
We are grateful to Dr. Aiko Furukawa, Kyushu University, forsupport and advice on the DEM program, to Prof. Yutaka Ohta,
Aichi Shukutoku University, for helpful comments on the calculation results, and to Dr. Guillermo Toyos and Ms. Keiko Saito in
Martin Center, Cambridge University, for useful discussions on
volcanic risk and pyroclastic flow.
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