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Dated March 30, 2007
The Metropolitan Museum of Art – MMA

1000 Fifth Avenue

New York, NY 10028-0198

Preliminary Results from

LDEO Test Vibration Measurements

in The American Wing,

The Metropolitan Museum of Art,

New York.


K. H. Jacob and J. Armbruster.

Lamont Doherty Earth Observatory

of Columbia University

PO Box 1000

Palisades NY 10964

Phone: (845) 365 8440

Fax (845) 365 8150
On Monday, March 12, 2007, during a day when the Metropolitan Museum of Art (MMA) was closed to the public, two teams from Columbia University measured vibrations inside the American Wing (AM) of the Museum. The sources for the vibrations were test rock excavations outside the glass curtain wall of the AM Courtyard (CY). The purpose of the tests was to simulate the effects of possible future rock excavations within the Courtyard, and their effects on structures and art objects in the courtyard and nearby galleries.
The two teams, from the Lamont-Doherty Earth Observatory (LDEO) and the Department of Civil Engineering (CE) used two different sets of instruments with two distinct objectives. The LDEO instruments were deployed largely on the museum floors and other reference locations; CE measured motions mainly on art displays and objects or architectural details to record their respective response to the floor motions.
The findings of this initial report are preliminary and focus on the LDEO floor (and some Bank Façade) measurements. Integration with the CE measurements on art objects and displays is still in progress. A final report with detailed documentation will be provided later.
Six basic instrument Set-Ups covered the LDEO Deployments:
1) W-E profile from the southern hallway of the Frank Lloyd Wright Room to the eastern wall of the Courtyard;

2) N-directed profile from the Tiffany Glass Gallery (west of the FLWR) through the entire length of the hallway to the north of it;

3) The Bank Façade together with the northern part of the West Balcony;

4) N-S directed Profile along the centerline of the northern 4/5 of the West Balcony;

5) SE-directed profile across the Courtyard to the Tiffany Columns at its south end; and

6) ESE-directed profile across the Courtyard towards the Tiffany Mosaic Fountain

All recordings were made to resolve useful frequencies typically between about 5 to 85 Hz, the frequency range where most of the structures and objects were expected to have their basic modal response.

Two types of hydraulic impact rock breakers (BRH 4000, delivering 1250 ft lbs; and a TRAMAC V46, with 7500 ft lbs) generated the ground vibrations. A total of 11 time windows (each approximately 4 minutes long) covered the 6 different instrument set-ups, using between 1 to 3 time windows per instrument set-up. Sometimes during each 4-minute window the operator had to reposition the hammer according to progress in breaking up the hard rock (Manhattan Schist). Repositioning takes typically less than 10 seconds, but introduces gaps and irregularities in the excitation of ground motions.


2.1 Variable Excitation of Induced Vibrations due to Variable Operating Conditions of the Hydraulic Rock Breakers and for Different Rock Conditions.
The peak acceleration produced by the smaller rock hammer (BRH 4000 - 1250 ft lbs) was on average a factor 2 to 3 smaller than the vibrations induced by the larger hammer (Tramac V46 – 7500 ft lbs). This is roughly consistent with the notion that the induced ground motions are approximately proportional to the square root of the delivered energy (√ (7500/1250) = √ 6 = 2.4).
However, variability of induced ground velocities (or accelerations) by the V46 itself is greater than a factor of 2, and much higher (2 to 3 orders of magnitude !) in the spectral frequency domain. Another variability lies in the proportion of energy delivered to the three different components of motion (vertical, and two horizontal directions).
This extreme variability depends on a number of physical processes:

(1) whether the hammer encounters jointed or dense rock;

(2) whether the hammer works near a vertical rock face or a horizontal rock surface;

(3) whether the hammer operates in a vertical or inclined strike direction;

(4) whether the hammer works at full hydraulic or reduced pressure and power delivery;

(5) the hardness of the encountered rock also determines the strike frequency. On very compact flat rock, the V46 slowed to about 4 strikes per second (producing very high amplitudes); it accelerated to about 12 strikes per second or more when it slipped on inclined surfaces or hit softer or jointed rock, and delivered lower induced ground motion amplitudes under these latter conditions.

It should be noted that a drilled channel about a foot wide and a few feet deep had been excavated about a week earlier. It separated the test hammering site form the building foundations. This channel presumably reduced somewhat the propagation of surface wave ground motions from the rock into the adjacent floor foundations of the building. If such channels are not maintained, or grossly vary in dimensions, they will deliver different ground motion levels into the foundations adjacent to the area of excavation.
The density of the rock tends to increase with depth of excavation. Therefore the efficiency of the hammer to produce larger ground motions can be expected to increase as the excavation progresses to greater depths.
2.2 Vibration Amplitudes.
General Observations. These observations refer only to the LDEO measurements. Amplitudes for the CE measurements on the art objects and displays may differ from those quoted here.

Base Station: The strongest floor motions at the LDEO base station nearest to the rock hammer (about 10 to 15 feet) did not exceed the following (all measurements are zero-to-peak amplitudes; RMS stands for Root Mean Square):
Peak Acceleration:

Vertical 0.9 %g

Peak Velocity:

Vertical 0.0077 inch/sec

N-S 0.0063 inch/sec

E-W 0.0075 inch/sec

RMS Velocity:

Vertical 0.0014 inch/sec

N-S 0.0015 inch/sec

E-W 0.0017 inch/sec

Maximum Observed Values during March 12 Tests (zero to peak velocities)

Vertical 0. 0142 inch/sec W-Balcony, Center 2nd Bay from N

N-S 0. 0068 inch/sec Tiff. Glass Gallery, W-Wall center

E-W 0. 0130 inch/sec AW CrtYrd, ‘Cafeteria’ area, center N

Table 1: “Hotspots” for RMS-Velocity Amplification relative to “Base Station” (#3):
LDEO Set-Up/Deployment Factor/Comp. Location Instr.# Distance* (ft)


1) FLWR/Courtyard: 1.3 V FLWR SW #1 H40ft

2) Tiffany Glass Glry/N-Hallway 2.2 V&N Hallway Steps #5 H85ft

3) Bank Façade 0.4 N-S Base of Façade #4 H75ft

1.2 N-S 2ndFl Ledge #5 H76+V20

1.0 N-S 3rdFl Cornice #6 H76+V45

Ratio Ledge/Base 3.0 N-S Bank Façade V20

Ratio Cornice/Base 2.5 N-S Bank Façade V45

4) N-S Profile, West Balcony ~2.0 V Bays 2-5 #2-6 V20+H20-60

5) SE-Prof.CY to Tiffany Columns 1.7V-2.1E CafetCntrN #1 H30ft

6) ESE-Prof.CY to Tiffany Fountain 1.2 N CafetCntrN #1 H30ft


* H for horizontal, V for vertical distance (in ft)

2.2 Attenuation with Distance vs. Local Amplifications and Modes.
A generally weak and very erratic decrease of amplitudes of floor velocities with distance form the source (rock hammer) is observed. Where it is noticeable it is proportional to r-0.5 or 1/√ r . This slow decay with distance tends to indicate that surface and guided waves dominate. This weak attenuation with distance is strongly masked and overwhelmed by local resonances and modal behavior, leading to strong local amplifications in peak or RMS amplitudes (Table 1), and is more prominent in modal spectral behavior (see below). The local amplifications and resonances overwhelm distance effects for potentially multiple reasons:
Fill thickness between the rock subsurface and floor slab may be variable, or the fill may have variable density. Thicker, less dense fill will amplify floor motions.
Hollow spaces, or in a few cases, the proximity of basement spaces below the floor levels at the S and E periphery of the Courtyard, and a stairwell into the basement in the hallway north of the Tiffany Glass Gallery, seem to cause localized amplifications.
The West Balcony floors clearly act as diaphragms subject to vertical motions (we assume the East-Balcony does as well, although no measurements were made).
Similarly the E-W running wall of the Bank Façade wall acts as a diaphragm, subject to motions in the N-S direction, with RMS (time domain, not spectral) amplifications factors of 2 to 3, relative to the motions at the base of the façade.

2.3 Spectra and Extreme Spectral Amplification:
The spectra are much more variable than the time-domain records. Some portions of the spectra are smooth, others appear highly peaked. Two distinct causes may be responsible for the peaks in the spectra. When the hammer operates in a higher frequency mode than 10 hits/sec, the spectra tend to be smooth below 10 Hz. In those instances attenuation of spectral amplitudes with distance is noticeable. If the hammer’s strike rate drops below 10 Hz, there are distinct peaks in the spectra between 5 and 10 Hz correlated to the strike frequency of the hammer (and higher harmonics). Many of the structures most prone to resonances (as already indicated by amplification factors in the time-domain; see Table 1), show very strong amplifications overall, and even more so at distinct resonance frequencies. This is especially the case for the vertical components on the W-Balcony; and the N-S component of the Bank Façade’s mid- and upper levels. Spectral amplifcation also occurs at miscellaneous locations on floors near the FLWR, Tiffany Glass Gallery hallways, and Courtyard floors. Spectral amplification is highly variable, generally stays between 10 and 100, but in several instances exceeds factors of 100, and in very few cases (W-Balcony vertical components) exceeds 1,000 !!

3. Inferences, Conclusions, Recommendations.
On average, the peak and RMS velocities measured by LDEO during the March 12 tests stay well below the damage threshold values given in the literature and vibration standards. A most often quoted threshold peak velocity of 0.1 inch/sec for potential damage to sensitive buildings and structures is, on average, about one order of magnitude higher than most of the velocities measured at distances ranging from about 10 to 100 feet from the source.
Several concerns exist, however:
(1) If the distance of the rock hammer from an object or structure is less than 10 feet, the motions should markedly increase, including from acoustically transmitted noise at frequencies well above 50 Hz. Therefore at these short distances (e.g. close to the Bank Façade, or Tiffany Columns, the hammer will have to be operated at a strongly reduced power; or a less powerful hammer should be used; or other excavation methods may be chosen that are not prone to produce strong vibrations at frequencies below 100 Hz.
(2) Since the rock may become denser and less jointed as excavation reaches deeper, there will be a tendency for the vibrations produced by the rock hammer to become more intense. A factor 2 to 4 is likely, although no direct confirmation from the March 12 test can verify this. Vibration amplitudes should increase with the second to third power of the shear wave velocity of the rock, provided the rock hammer stiffness is sufficiently high compared to the rock.
(3) Care must be taken that structures or objects with highly un-damped resonances in the range of 5 to 100 Hz are removed from the floors or sufficient damping is provided, to avoid damaging resonances at specific frequency bands. The West and East Balconies are candidates, and glass display cases and/or contents at these locations may be removed unless results from the CE measurements indicate that they are not sensitive to the highly amplified balcony floor motions at specific resonant frequencies. The Bank Facade resonances are also of concern, and a buffer distance of anywhere from 6 to 10 feet in which rock hammers delivering more than 1,000 ft lbs should not be used, certainly not without continually monitoring the vibration levels of the façade at critical locations.
(4) This report presents preliminary findings solely on the basis of the LDEO measurements on floors and reference sites. These findings may have to be modified once they are integrated with the observations, findings and inferences from the CE team based on the vibrations measured on art objects and displays and architectural details.
(5) A final report will document many of the pertinent LDEO-collected data, observations and, in a few instances, may come to different conclusions. But the essence of the findings and conclusions is not expected to change, at least as far as the floor and main-structure vibrations are concerned. A proposal for possible monitoring during the actual excavation phase will be provided after a review of this Preliminary and the Final Report by Museum staff and its Contractors.


Standards and Empirical Limits of Motion at the Threshold of Inflicting Damage.
The damage inflicted by vibratory motion depends on the amplitude and frequency content of the motions and on the nature and robustness of the object that is set in motion.

Art objects and their display cases are generally more sensitive than buildings. And aged brittle buildings can be more sensitive than modern flexible or plastically performing buildings. Here are some of the relations and findings from the published literature (PPV stands for peak-to-peak velocity; and hence, PV – peak velocity PV = 0.5 PPV):

Note: The frequency scale is logarithmic from 1hz (left) to 10hz (center) to 100hz (right)

USBM: U.S. Bureau of Mines (a now dismantled federal agency). It was concerned with the effects of mine blasting on nearby buildings and structures.

German DIN standard:

Swiss Standard (see category IV is for historic buildings):

Units commonly used for measuring motions, and their conversions are:

For displacement d:

1 inch = 2.54 cm = 25.4 mm

1 cm = 10 mm = 0.39 inch (or 1 mm = 0.039 inch)
For velocity v:
1 inch/s = 2.54 cm/s = 25.4 mm/s

1 cm/s = 0.39 inch/s = 10 mm/s (or 1mm/s = 0.039 inch/s)

For acceleration a:
1 inch/s2 = 2.54 cm/s2 = 25.4 mm/s2

1 cm/s2 = 0.39 inch/s2 = 10 mm/s2 (or 1mm/s2 = 0.039 inch/s2)

and, with another unit, the Earth’s gravitational acceleration g:
1g = 981 cm/s2 ~ 409 inch/s2

1 inch/s2 ~ 2.54 cm/s2 ~ 0.00244g

1 cm/s2 = 0.39 inch/s2 ~ 0.001g

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