25th Japan Conference on Earthquake Engineering, Tokyo, 1999.7.29-31

DYNAMIC CHARACTERISTICS OF LEANINGTOWER OF PISA USING MICROTREMOR- PRELIMINARY RESULTS Yutaka NAKAMURA1, E. Dilek GURLER2 ,1,2Dr. Eng.,

Jun SAITA33Research Engineer

1,2,3 System and Data Research Co., Ltd. (SDR Bldg., 3-25-3 Fujimidai, Kunitachi-shi, 186-0003 Tokyo)

ABSTRACT
Determining the dynamic characteristics in advance and increasing durability of ground andstructures beyond the presumed seismic force is a fundamental for preserving the historicalstructures. Main purpose of this study is to investigate the dynamic and other characteristicfeatures of Pisa tower and answer the questions such as in which frequency the tower vibrates andwhere is the center and direction of this movement? Microtremor method is applied for thispurpose. Rocking vibration frequency for entire structure is found as 0.98Hz in NS and 1.06Hzfor EW direction. Center of this movement in NS direction is located in rather southern site of thecentral axis, almost under the bottom of foundation. In EW side this depth is about 1.5m under thefoundation. Amplification is bigger in EW direction which shows tendency to move to thisdirection also. Ground bearing capacity is also calculated and it has been found that it changes
between 1kg/cm3 to 1.3 kg/cm3 for the vertical frequency changing between 2.2-2.5 Hz. From theresults, microtremor method is proved to be a useful tool for this kind of investigations, since iteasily gives needed information in a short period of time.
Key Words : Leaning tower of Pisa, Microtremor, Dynamic characteristics, H/V(QTS)
spectrum, Rocking vibration, Spring coefficient (kv).

1. Introduction
Preservation of monuments all around the world andincreasing their stability against destructive forces,
especially to the earthquakes is an important issue formany countries. It is well known that, degree ofdamage during earthquakes strongly depends on
dynamic characteristics of buildings as well as
amplification of seismic waves. Because of this, first it
is necessary to analyze their behaviors before
reinforcing or repairing them.
Since historical monuments are not suitable forsophisticated analysis, strategy for this should beselected carefully. Considering this, the dynamic
characteristics and response of the leaning tower of
Pisa are analyzed on the basis of microtremor
measurements, performed on the ground and upper
floors of the tower.
The leaning tower of Pisa, has been tilting since 12th
century . According to its history, tower has neverreally been straight. During its construction architects
and later engineers have attempted to stop the leaning
and lessen the angle. All these efforts had unintended
side effects, and caused disastrous problems than they
set to solve. Also many research on explaining theinfluences including soil condition of the ground andweather conditions have performed. However, the real
danger for the safety of the Pisa is the possibility ofearthquakes and there is no detailed study about the
dynamic structural behavior of the tower which will bedirectly related with its damage during theearthquakes.
Among the other time consuming and expensive
approaches, microtremor is the easiest and cheapest
way to understand the structural behaviors withoutcausing any harm to the structure. In a short period oftime it provides several information including naturalfrequency, amplification and vibration characteristics
of structures at different frequencies. Preliminary
analysis of the measurements resulted that rocking
vibration frequency is of 0.98Hz in NS and 1.06Hz in
EW direction. Center of this movement is almost
under the bottom of the foundation in NS direction
located at southern side of the tower and at 1.5m depth
at EW direction.

2. Information About the Leaning Tower of
Pisa
The 14.000 tones, 58m high eight-story leaning
tower of Pisa is one of the most original works of artof the European Middle-Age and there are lots ofuncertainties about the original architect. It was started
to built in the year of 1173 and completed at 1350.
After a short time of construction started, tower started
to incline toward the north. And nearly after 100 year,the building shifted again so that by 1272, it wasvisibly leaning to the south. It stands more than 800years daring to the gravity and today the top of thetower is about 5.227 meters off centers, tilting
southward. Tower has 19.6 meters diameter with afoundation depth little less than 3 meters. Under thetower the components of the earth are mainly soil, clay
and mud. The area where Pisa is located had been aport in medieval times and the soil is a spongy mixture.
The surface layer (about 10 m) which is an
accumulated fluvium from River Arno has compacted
unevenly making the tower tilted. Under this layer,
there is a resistant band known as Pancone marine clay
with fine sand and shells which is about 20 metersdeep. This is followed by a deep layer of sandboundary which is horizontal under most of Pisa,
except where it is under the tower. Layers of clay andsand alternate down to roughly 70 meters. The entire
area where the tower is built is gradually sinking.

measurements. PIC includes two sensors, connection
cables, main body installed in a metal case whichcontains A/D converter, portable computer andamplifiers inside. At every measurement points, threecomponents (two horizontal and one vertical) of
microtremor on the ground are recorded. Samplinginterval is 1/100 sec and the length of each record is40.96 sec. Measurement was repeated three times ateach observation point. One set of PIC instrument
together with two sensors was set on the ground floor
while the other was moved from one floor to the other.
With this system, microtremors of the tower andground were recorded at the same time. Measurements
were performed at 1P, 2P, 3P, 4P, 5P and 6P levels oftower shown in Figure 2.

3. Measurement Points and Outline of
Measurement Conditions

Figure 1. Location of the tower and measurement points on
the ground surface. Spectrums at right upper and left lower
corner are QTS spectrums for ground surface points.

Figure 1. shows the area where the tower is locatedand position of the measurement points on the groundsurface. Also QTS spectrums for ground surface
measurements are included in this figure. Figure 2.
shows cross section of the tower in NS direction,
including measurement points on the structure andlocal geology under the tower. Rocking center depths
for each floor are pointed with x.
(1) Measurement: An instrument named Portable
Intelligent Collector (PIC) was used for microtremor

Figure 2. Cross section of tower in NS direction including
measurement points on tower and local geologicalconditions. Rocking center depths for each floor is marked
with x.

(2) Analysis: After measurements, Fourier spectrum
for each components and QTS spectrums arecalculated(Nakamura, 1989). From a spectral ratio ofhorizontal to vertical components QTS (Quasi
Transfer Spectrum), predominant frequency (f) andamplification factor (A) which represents dynamic
characteristics of the ground and spectral ratios
between each floor and ground floor were calculated.
This ratio provided the combined predominantfrequency and amplification factor of entire tower andground. Using a methodology introduced by

Nakamura et al.(1995) rocking and other vibration
frequencies, together with rocking vibrations center
depths are calculated for each floors.

4. Results
QTS spectrums of ground are given in Figure 1. It
can be followed that having an amplification factor of
1.2 G6 and G8 have no clear peak probably because of
the effects of structure of tower, as well as different
ground characteristics at these points. Natural
frequency is around 1.2 Hz at all the points.
Amplification is rather high at G3, G4, G13 and G14
having a value of about 1.7 at longitudinal (NS) andtransversal (EW) direction.

direction. These shows the rocking vibration frequencyof the tower. One reason of higher frequency in EW
direction thought to be the weight of 830 tons of leadthat is placed on the south of the tower. This weightcause a small amount of difference in inertial force in
NS direction that might cause just a negligible
difference in momentums which will almost have noeffect in frequencies. The only reason seems to be asofter ground characteristics in NS direction. Vibration
frequencies of the structure for the second and thirdmode are 6.3Hz and 14Hz, respectively. Figure 4,shows first mode vibration characteristics in NS and
EW directions. In EW direction, amplification ishigher than NS direction, this shows that tower has atendency to move in EW direction also. Especiallyfrom 5P level this difference become bigger. Thismight be because of change in floor characteristics
starting from this floor. Rocking center depth for eachfloor was also obtained from the spectrum ratio of thehorizontal movements measured by two sensor fixed at
the same floor .

Figure 3a. Spectral ratios in NS direction.

Figure 3a and 3b shows spectral ratios of 2P, 3P, 4P,
5P and 6P with 1P. This ratio provided the combined
predominant frequency and amplification factor ofentire tower together with ground. There are several
peaks showing the different modes of the structure in
longitudinal and transversal components. First mode
frequency is about 0.98Hz in NS and 1.06Hz for EW

Figure 3b. Spectral ratios in EW direction.

Although having a deeper rocking center is better,
center of rocking vibration found from presentmeasurement is quite shallow in NS direction(almostbottom of the foundation) located at the south ofcentral axis. In EW direction this center is about 1.5m.
Change of the location of the rocking depth in NS and
EW direction is given on Figure 6.
f=0.98Hz

f=1.06Hz

6P

Where Kv is ground bearing capacity, w=2πf. f is thevertical vibration frequency. W is the mass and g isgravity. By inserting the values for Pisa tower into thisformulation which are, W=14000+820(lead) tons,
A=294m2, g=980 , f=2.2-2.5Hz, we can find the value
for Kv changes between 1.0-1.3 kg/cm3 for 2.2Hz and2.5Hz vertical vibration frequencies, respectively. This
represents the bearing capacity of soft ground that Pisa
is located.
E5P
4P

Tower‑BaseMeasurement points

6F(4P)
7F(5P)
8F(6P)

4F(3P)

1F(Wall)

2F(2P)N

1F(1P)

3P2P

N

05m010 unit

S

1P5P

S

2P 4P
3P 6P

E

5P
4P
3P
2P6PW

Apparent rocking centers estimated from each EW measurements

Figure 4. 1st mode vibration characteristics and locationof rocking center depths in EW direction.

Apparent rocking centers estimated from each NS measurements

W05m

Figure 6. Bird eye view of floors showing rocking center
locations on NS and EW directions at different floors.

5. Concluding Remarks

Figure 5. Ratio of vertical movements for 5P level(5Peast/5Pwest)

Vertical vibration frequency for entire tower is also
checked from the ratio of vertical movement for thesame floors. Figure 5, shows an example for
5Peast/5Pwest ratio of vertical movements at 5P level.
Amplitude spectrum, coherency and phase of theserecords are given. A peak at 1Hz represents rocking
vibration. And a peak around 2 Hz appears at eachfloor shows a vertical vibration frequency for entire
tower. Clear identification of vertical vibration
frequency is quite important since it gives anopportunity to calculate spring coefficient kv that will
be helpful to calculate ground bearing capacity.
Normally investigation of this coefficient needs time
consuming and expensive experiments. On the other
hand, with the investigation of vertical vibration
frequency this can be easily calculated with thefollowing formulation.
Kv . gW .w 2= w 2 → Kv =WgKv = A . kv → kv =W .w 2
g .A

Dynamic characteristics of the Pisa tower are
investigated as follows;
1) Predominant frequency and amplification factorof the ground is f=1.2 Hz and A=1.7. 2) Rockingvibration frequency is 0.98Hz in NS direction and 1,06
Hz in EW direction. Center of this vibration is locatedat the south of center line almost under the bottom offoundation in NS direction. This depth is about 1.5m
in EW direction. 3) Vertical vibration frequency for
entire tower is 3Hz. 4) Bearing capacity has been
calculated as 1-1.3 kg/cm3 for the area that tower islocated. 5) It has been shown that it is possible toinvestigate the response characteristics and structural
damage of structures through the analysis ofmicrotremor records. In later analysis other vibration
frequencies are planned to be calculated from theseinformation.

6. Acknowledgement
We would like to express our sincere gratitude tomembers of Department of Earth Science, Genova
University for their help and accompany during ourmeasurements. And also to Dr. Paolo Heiniger for hiscooperation.

7.

References

1) Nakamura, Y. 1989, A Method for Dynamic Characteristics
Estimation of Subsurface using Microtremor on the Ground
Surface, Quarterly Report of RTRI, Vol. 30, No.1, Railway
Technical Research Institute.
2) Nakamura, Y., Hidaka, K., Sato, S., Tachibana, M., 1995,
Proposition of a Method for Pier Inspection Using Microtremor,
Quarterly Report of RTRI, Vol. 36, No.1, ISSN 0033-9008.