Ž .Construction and Building Materials 14 2000 133]146

Improved assessment of mass concrete dams using acoustictravel time tomography. Part I } theory

Leonard J. Bonda,U, William F. Kepler b, Dan M. Frangopolc

aPacific Northwest National Laboratory, 902 Battelle Boule¨ard, Richland, WA 99352, USAbUS Bureau of Reclamation, D-8180, Den¨er Federal Center, Den¨er, CO 80225, USA

cDepartment of Ci il, En¨ironmental, and Architectural Engineering, CB-428, Uni ersity of Colorado, Boulder, CO 80309-0423, USA

Received 28 May 1999; received in revised form 24 September 1999; accepted 6 January 2000

Abstract

This is the first part of an investigation on improved assessment of mass concrete dams using Acoustic Travel TimeŽ .Tomography ATTT . It presents the concept and basic science for ATTT. ATTT combines aspects of ultrasonic measurements

previously used for material characterization, ultrasonic methods applied to test concrete and features of methods used in shallowseismic surveys. This sciencertechnology is integrated into a system that records travel time data and applies tomographysoftware. The resulting tomographs have the potential to provide cross-sectional images of the structure that can be used tolocate cracks, identify regions of structural damage, and other anomalies deep inside a massive concrete structure. Results frominitial laboratory and field studies obtained with a system that embodies the approach presented in this paper and which provides

Žproof-of-concept data, are presented in a companion paper Kepler WF, Bond LJ, Frangopol DM. Improved assessment of massconcrete dams using acoustic travel time tomography. Part II } applications. Constr Build Mater, 2000; Vol. 14, No. 3, pp.

.147]156 . Q 2000 Elsevier Science Ltd. All rights reserved.

Keywords: Non-destructive testing; Concrete; Dams; Tomography

1. Introduction

There is a compelling need to provide new andimproved measurement science and technology,together with appropriate methodologies, for the analy-sis, monitoring, protection and management of the

w xnation’s critical infrastructure 1,2 . Much of this criti-cal civil infrastructure, including mass concrete dams, israpidly approaching, or in some cases has alreadypassed its original design life. Such structures face the

U Corresponding author. Tel.: q1-509-375-4486; fax: q1-509-372-4583.

Ž .E-m ail addresses: leonard.bond@ pnl.gov L .J. B ond ,Ž .wkepler@ ibr8gw8o.usbr.gov W .F. K epler , frangopo@

Ž .spot.colorado.edu D.M. Frangopol

impact of age-related degradation and damage accumu-lation, which are to some extent both random anddeterministic. It is, therefore, necessary to providemeasurement and monitoring technology that is robust,reliable, low-cost, user-friendly, effective for wide area

w xcoverage and provides a record of the inspection 3 .The data from such testing is then employed in finiteelement analysis to provide estimates for remainingstrength, rate of degradation and remaining safe life.Assessments on the population of particular types andfamilies of structures, such as dams, are then also usedto identify and prioritize those where repair and otherremedial action is needed.

To meet the increasing need to inspect large struc-tures, various forms of acoustic tomography are nowbeing developed for applications that include sub-

0950-0618r00r$ - see front matter Q 2000 Elsevier Science Ltd. All rights reserved.Ž .PII: S 0 9 5 0 - 0 6 1 8 0 0 0 0 0 1 4 - 3

( )L.J. Bond et al. r Construction and Building Materials 14 2000 133]146134

w xsurface structures 4 and laboratory-scale feasibilityw xstudies 5,6 .

Ž .This paper Part I presents the concept and basicŽ .science for Acoustic Travel Time Tomography ATTT .

ATTT combines aspects of ultrasonic measurementsfor material characterization, ultrasonic methods ap-plied to test concrete, and shallow seismic surveys intoa system that records travel-time data and appliestomography software. The resulting tomographs havethe potential to provide cross-section images of thestructure that can be used to locate cracks, identifyregions of structural damage, and other anomalies deepinside a massive concrete structure. Results for initiallaboratory and field studies obtained with a system thatembodies the approach presented in this paper andwhich provides proof-of-concept data are presented in

w xa companion paper 7 .

2. Background

Ž .Acoustic Travel Time Tomography ATTT can beseen as a natural extension from earlier studies. It isdeveloped from concepts which had, however, onlypreviously been presented in a diffuse body ofknowledge that crossed the boundaries of several tradi-tional disciplines. For example, in geophysics the pathdependence of acoustic velocity and attenuation hasbeen studied in small samples, including at elevatedtemperatures and pressures. This approach has beenextended to suites of transducers, set as linear arrays,for example on the sides of westerly granite samplesw x8 , and for the analysis of cumulative damage in cycli-

w xcally loaded ceramic matrix composites 9 . In ATTT,arrival time data are collected using a suite of trans-ducers in the form of a sparse linear-array, and result-ing data, including source and receiver spatial coordi-nates, are processed using a software algorithm.

2.1. Prior art for ultrasonic and other non-destructi etesting methods of concrete

Ultrasonic measurements of material propertiesrmorphological conditions, including degradation and

w xdamage, have been investigated for many years 10 .There is even more literature describing the use of

Ž .ultrasound in non-destructive testing NDT , particu-larly applied to metals.

The testing of concrete using techniques that employultrasound has been undertaken both in the laboratory

w xand on-site since the 1950s 11]14 . The developmentof commercial and relatively inexpensive instruments in

Ž .the 1970s led to Ultrasonic Pulse Velocity UPV mea-surements being adopted as the basis for standard and

w xwidely used test techniques 15]17 . The basic configu-

Fig. 1. Basic ultrasonic transducer configurations employed in con-Ž . Ž .crete testing. Source 1 and receiver 2 .

rations used for such transmission measurements areshown in Fig. 1. This testing is almost exclusively limitedto time-of-flight measurements to give average propertydata for the path between the transmitter and thereceiving transducer. These approaches have now beendeveloped as a tool for the quantification of the initial

w xcure in concrete 18 , for the determination of materialw xproperties 10 , and for the assessment of various forms

w xof ‘damage’ and degradation 19,20 . There has alsobeen a significant effort to transition the NDT ofconcrete from the research laboratory into field appli-

w xcations 21 . These approaches all provide point-to-pointdata that are useful; however, the integration of thesedata to provide ‘images’ for the internal structure,including the location and types of anomalies, would bemore useful.

There are four broad categories of non-destructivetesting methods used for concrete that are in current

Ž . Ž .use: a methods which estimate strength; b methodsŽ .which estimate elastic properties; c methods which

locate and characterize voids and cracks within theŽ .structure; and d tests used to evaluate reinforcing

w xsteel 22 .Extensive reviews of the standard methods for test-

w xing concrete are in the literature 23,24 and this mate-rial is not repeated here.

( )L.J. Bond et al. r Construction and Building Materials 14 2000 133]146 135

w xA further review is provided by Kepler 25 . Stress]wave propagation techniques are the most commonnon-destructive testing procedures used to evaluate

w xcivil structures 26 . They are best suited for locatingvoids and delaminations in a structure, but can also beused to estimate the modulus of the concrete.

2.2. Tomography

Tomography is a technique for data processing thatprovides cross-sectional images from the analysis whichhas been under development in geophysics and medical

w ximaging for many years 27,28 . Tomography can beŽ .implemented in three basic forms: i parallel-scanning

and rotation } which is commonly used in medicalŽ .computerized tomography CT; ii two-sided transmis-

Ž .sion employing two linear arrays of sensors; and iiifour-sided transmission. The potential and limitationsof tomography have been reviewed by Santamarina and

w xGheshlaghi 29 .This approach has been implemented on a limited

w xbasis in NDT 30 . The application of many advancedultrasonic and tomographic testing methodologies hasbeen limited by the available technology, and it hasbeen considered by many to be impractical due to costand time constraints. These restrictions and limitationscan now be largely overcome.

The objective of a tomographic survey is to provide across-section that will show the internal structure andlocal properties of the material located between a set

w xof measuring points 28 . Such methods allow betteridentification of anomalous regions by performing aninversion of boundary measurements to determine thephysical properties within the body of the structure.

Travel time tomography is a method that uses infor-mation from acoustic wave transmission to construct amap of velocities through an interior slice of an objectw x27 . As the wave travels through the object beingstudied its travel time and hence velocity is affected bythe variations in the condition of the internal material.Regions of high or low modulus, density, and defectssuch as voids or cracks will affect the travel time.

Defects usually observed in concrete, such as cracks,have the greatest influence on the acoustic wave veloc-ity. If the concrete has no macro-defects and is crack-free, changes in elastic modulus have a much greatereffect on the wave velocity than does changes in thedensity. So, for defect-free section of concrete, varia-tion in the modulus is the parameter that controls the

w xstress wave propagation velocity 6 .In theory, the absolute value of the modulus of

elasticity can be calculated if the density is determinedand both the compressive wave and shear wave veloci-

Fig. 2. Typical relations between modulus of elasticity and pulsevelocity for concrete.

ties are measured. In practice, for a material such asconcrete, only compressive wave velocity is measured,since reliable detection of the shear wave arrival time

w xis not easy 31 . Poisson’s ratio for concrete can bew xassumed to be equal to 0.20"0.02 14 . This assump-

tion enables a tomogram based on only compressivewave velocities, and using an assumed constant Pois-son’s ratio, to show relative variations of elastic modu-lus through the concrete mass. Examples of typicalcorrelations between ultrasonic velocity in concreteand modulus of elasticity are shown in Fig. 2.

For a tomographic reconstruction, the test area isfirst divided into a number of pixels, each of which isassumed to have its own ‘average’ velocity. The traveltime for a ‘ray’ between two points on the perimeter ofthe area is then the sum of the transit times acrosseach of the pixels which form the path. The simplestanalytical technique assumes that each incident stresswave travels in a straight line between the transmitterand receiver. The most frequently used method inengineering tomography is an iterative algorithm. Thisalgorithm gradually corrects the error between themeasured travel time and the estimated travel time foreach ray. This approximation is adequate for propaga-tion in uniform homogeneous materials. However, ifvelocities for adjacent regions vary by more than ap-proximately 20%, refraction and bending of the waves

w xbecomes significant 32 , and more complex algorithmsare required.

In geophysical seismology, curved ray techniquesw xwere developed to consider this effect 33 . The curved

ray method traces rays between the transmitter andreceiver using ray paths that may cause large shadowzones to occur. In these zones no rays travel.

As with any other analysis techniques, tomographyhas its strengths and weaknesses. The greater the num-ber of rays and source]receiver combinations, the more‘boundary data’ acquired and the better the resolution.

( )L.J. Bond et al. r Construction and Building Materials 14 2000 133]146136

However, the greater the number of rays more dataprocessing time and data storage space are required toperform the inversion. If the ray paths are not evenlydistributed, as is often the case for an item with com-plex geometry, the uneven distribution or coverage ofrays magnifies the complexity in the inversion. This cancause noise which may appear in the form of ‘ghosts’particularly in low information regions in the imagew x28 .

The critical elements that set the accuracy of atomograph are mesh coarseness, and the angle between

w xray paths 34 . The mesh formed by the ray paths mustbe tight enough so that the smallest critical defect islarger than the largest pixel within the mesh. In addi-tion, the larger the intersection angle between each raypath across each pixel, the greater the accuracy of thetomograph. Testing large dams is difficult because ac-cess to all of the surfaces is not always possible, and insome cases simply not practical. Fortunately, tech-niques have been developed that enable a tomographyto be formed using sparse arrays and limited anglesw x35 .

It is imperative to validate the results of a tomographw xwith known conditions 36 . This can be done mathe-

matically with a forward model: making a model of theassumed conditions, then applying theoretical compres-sive wave velocities to reach a similar solution as wasachieved in the field. A better method of validation isto compare the results of the tomograph with theknown conditions of the structure, and such data areusually obtained through a combination of visual in-spection and coring.

2.3. Re¨iew current dam testing and e¨aluationmethodologies

Concrete dams are cast in a series of horizontalmonoliths, and the joints or lift lines between theseblocks become a critical part of a dam safety analysis.A structural safety analysis of a large concrete dam is acomplex investigation using a very large number of

w xparameters 37 . The key parameters include: the mea-sured or assumed condition of the structure, the mate-rial properties of the concrete, and the assumed load-ing the structure has experienced. There is a degree ofuncertainty with all of the parameters, and therefore,with the results of the safety analysis.

When a safety analysis is performed, the designerinputs the assumed structural dimensions into a com-

Ž .puter program, usually employing a finite element FEw xcode 38 . The typical elastic properties used in an FE

analysis are shown in Table 1. The data used areusually ‘assumed’ or average material property values.A typical assumed loading sequence, which considersenvironmental and hydraulic loading, becomes inputfor the analysis program. The program will then returnthe expected range of future stress loading for theassumed loading spectrum applied to the structure. Ifthe calculated stresses are below the allowable valuesfor the concrete and lift-lines, as determined from atesting program, and allowing some required safetyfactor, then the structure is deemed to be ‘safe.’ Ifcalculations indicate that a structure will experiencestressrloading above the ‘safe’ level, remedial actionwill be taken. Such action can be in the form of

Table 1Parameters used as data in FE models

Parameter Range Accuracy

Geometric dimensions 100s feet 0.1 feetŽ . Ž .100 s m 30 mm

6 6 6Modulus of elasticity 4.0=10 "1.0=10 psi 0.1=10 psiŽ . Ž .27.6"7 GPa 0.7 GPa

Poisson’s ratio 0.20 0.01

Density 150"5 pcf 0.5 pcf3 3Ž . Ž .2400"80 kgrm 8.0 kgrm

Coefficient of thermal 5.0"1.0r8F 1.1r8FŽ . Ž .expansion 9.0"1.81r8C 0.18r8C

2 2Diffusivity 0.050"0.020 feet rh 0.002 feet rh2 2Ž . Ž .0.005"0.002 m rh 0.0002 m rh

Ž . Ž .Specific heat 0.24"0.02 Btur lb 8F 0.05 Btur lb 8Fw Ž .x w Ž .x1000"84 Jr kg 8K 210 Jr kg 8K

( )L.J. Bond et al. r Construction and Building Materials 14 2000 133]146 137

structural modifications or changes in expected loading,such as lowering the lake level.

Almost all large concrete dams are included in ascheduled examination program. This program at pre-sent usually consists of a visual examination as well assurvey monitoring, using surveying techniques to quan-tify deformation and possible movement. If the struc-ture begins to show signs of distress, then a morethorough examination is in order. This detailed evalua-tion includes a review of the history of the structure,extracting and testing core samples, and finite elementmodel-based structural analysis. Methods of conditionassessment that are employed are well documented by

w xthe American Concrete Institute 24 , and the USw xBureau of Reclamation 39]41 .

The most common method of concrete dam inspec-tion remains a visual inspection of the structure, usu-ally performed from adjacent viewing areas and frombelow the downstream face or in the internal galleriesw x42 . This is often complemented with limited data fromstrain gauges located within the dam, which is recorded

w xat best monthly 42 . When it becomes obvious fromvisual observations, or through increase in leakage, thatthere is significant degradation and the structure ispotentially at risk, core samples are taken. These coresamples provide local strength and modulus values, andcan be used to estimate the remaining strength acrosslift lines.

However, even an extensive coring program can onlysample a very small percentage, probably less than0.1% of the volume of a large dam. For these reasons,it is typical for a structural analysis, using a finiteelement or other analytical model, to employ materialdata that are the ‘assumed average material values’.Local potentially weak areas are not usually identifiedor data for such areas is not included in the analysis.

No other current method can locate and map cracks,and estimate both local and global strength within a

w xlarge concrete dam 43 . If dam assessment is to besignificantly refined, 100% coverage using improvedinspection is required to provide data for use in morerefined finite element analysis, which incorporates boththe structural features } lift lines } and local varia-tions in properties.

3. Inspection requirements

Concrete is as inhomogeneous as any modern build-ing material can be. It is a mixture of water, air,cement, sand and coarse aggregate. Natural and ac-ceptable discontinuities range from the size of thelargest coarse aggregate down to the microscopicallysmall partially hydrated cement particles. However, onthe macro scale it does behave as an isotropic ho-

mogenous material with bulk physical properties. Theconstruction techniques for large concrete dams, com-bined with nominal operational loading conditions, en-sure that most defects will be in horizontal planes

w xalong lift-lines 44 .For older dams, it is expected that ‘weak zones’ in

lift-lines will have developed into complete delamina-tions, particularly where there is erosion of fine parti-cles due to water seepage. The inspection problem thensimplifies to become one of detection and mapping the

Ž .area s of cracked or delaminated zones in lift-lines,which can be supplemented by any characterization of

Ž .the mechanical properties strength of the ‘lifts’ orblocks of concrete used for dam construction.

A crack having a minimum opening of 0.08 mmŽ . w x0.003 inches 45 will not pass stress waves. Because ofthe large mismatch in acoustic impedance betweenconcrete and air, these boundaries cause the stresswave to undergo almost total reflection. At aconcrete]water interface, the reflection coefficient is0.70, and most of the energy is reflected. The acousticresponse of a water-filled crack is almost the same asthat of an air-filled crack.

A flaw must have a dimension in the direction per-pendicular to the wave front that is greater than thewavelength. Flaws smaller than the wavelength will beinvisible to acoustic testing. For low frequency testingof concrete this could pose a problem, since the wave-length is approximately 0.4 m. However, for large con-crete dams that are over 10 m thick and hundreds ofmeters wide, a crack of 0.4 m in length is structurallyinsignificant.

It is known that all large concrete structures includ-ing dams have defects in the form of cracks and weakareas. The question becomes, what is the size of adefect that is considered to be ‘significant’? The con-cept of defect significance has been extensively studiedin ‘Damage Tolerance’ and ‘Retirement for Cause’w x46,47 . A significant defect can be considered as onethat is not large enough to cause a failure at its currentsize, but if not repaired and assuming some definedloading spectrum, will grow into a critical defect thatcan, at some future time, lead to failure. In the contextof the definition of inspection intervals it can also beconsidered as a defect that may grow to become sig-nificant or even cause failure before the next scheduledinspection.

In a large concrete dam, the significance of a givensize or area of a ‘crack-like lift-line delamination’, is afunction of the dam geometry, the physical propertiesof the concrete, the loading conditions, the location ofthe defect, rate of defect growth and inspection inter-val, in particular the time interval to the next inspec-tion. For a typical double arch concrete dam, it can beassumed that a crack does not become significant in

( )L.J. Bond et al. r Construction and Building Materials 14 2000 133]146138

size until it extends at least half-way through the dam,and this will usually have a surface-braking length of

w xmany meters on the up-stream face 37 .Ž .With an assumed dam thickness of 6 m 20 feet , and

for a crack with a worst-case 2:1 aspect ratio, growingfrom the dam down-stream facersurface, the critical

Ž .crack could have a surface length of 6 m 20 feet ,Ž .penetration of 3 m 10 feet and crackrdelamination

2 Ž 2 .area of approximately 30 m 320 feet .In addition to the critical defect size, for any struc-

ture and inspection method, it is also necessary toŽ . Ždetermine a the limit of detection set by a combina-

. Ž .tion of the physics and instrumentation ; and b arequired detection capability, that can be achieved with

Ž .a quantified probability of detection POD . The analy-sis that combines the POD and the rates for defectgrowth is used to define a required inspection interval,in order to achieve a particular level of confidence forthe inspection.

The rate at which concrete dams deteriorate is justbeginning to be studied. Although each structure seemsto be unique, when the complete population of struc-tures is classified by age, construction techniques used,and durability issues, it does seem that trends can beseen. However, most dam safety programs review eachstructure on an individual basis at least once every 10

w xyears 39 , and every 5 years for ‘at-risk’ structures.Given the current understanding of the rates of degra-dation for concrete dams it is not unreasonable toassume that major changes to the stability of the struc-ture will take at least 10 years to occur, and the damoperators would like to be able to predict structuraldegradation at least that far into the future.

Current structural analysis models, which mostly em-w xploy finite element analysis 38 , treat the concrete

within a dam as a homogenous material, with no localanomalies or change in physical properties. If improvedanalysis and increasing confidence in structural in-tegrity is to be achieved it is clearly at least necessaryto be able to include the effects of structure, such aslift-lines, find all cracks, weak areas, or other anomalieswithin the structure that are larger than half the thick-ness of the dam. To meet the requirements for predic-tion of remaining safe life or interval during whichremedial action can be performed it is necessary, for acombination of political, funding and technical reasonsto make predictions that extend a minimum of 5 andpreferably 10 years into the future. For these reasonsthe ideal NDT tool would have a capabilityrlimit ofdetection such that there would be a high probability offinding and lift-line delamination greater than 1.5 m2

Ž 2 .16 feet . For a semi-circular crack this would corre-spond to a crack length on the free surface of approxi-

Ž .mately 2 m 6.6 feet and a depth of approximately 1 mŽ .3.3 feet . For an interior penny-shaped crack thiswould correspond to a circle with a diameter of approx-

Fig. 3. Schematic of a cross-section of a dam illustrating basic raysthat form the basis of ATTT.

Ž .imately 1.4 m 4.6 feet , however, such defects arehighly unlikely to occur.

4. Concept of Acoustic Travel Time Tomography( )ATTT

To meet the inspection requirements describedŽ .above, Acoustic Travel Time Tomography ATTT was

invented. ATTT is a novel testing procedure, and dataprocessing approach, which can characterize the physi-cal properties of the mass-concrete blocks, and map thecondition of lift-lines, in particular any cracks, within alarge concrete dam.

A two- or three-sided rectangular array of sourceand receiver locations is developed. This employs asparse linear-array of receivers and an impulse source.The tomographic array is deployed in a series of verti-cal planes located at a sequence of positions across thedam, as shown in schematic form in Fig. 3. In practicethis would be combined with a reduced coring programto provide both global evaluation and local strengthand modulus values within the dam.

A fundamental premise of ATTT is that the wave-Ž .lengths of the acoustic stress waves are long when

compared with the local structures and particles in thematerial through which they propagate. This impliesthat the bulk material can be assumed to be homoge-neous and that the velocity of sound is well behaved.

The wavelength]velocity relationship at a particularfrequency is given by:

Ž .cs fl 1

where c is velocity, f is frequency and l is the wave-length.

For an assumed wave velocity of 3000 mrs at 50 kHzŽ .the wavelength is 60 mm 2.4 inches and at 5 kHz the

Ž .wavelength is 0.6 m 24 inches . A 0.6 m wavelength islarge when compared with most aggregate sizes.

( )L.J. Bond et al. r Construction and Building Materials 14 2000 133]146 139

In such a material the compression wave velocity is afunction of the density of the concrete, the modulus ofelasticity, and Poisson’s ratio:

Ž .E 1yn2 Ž .V s 2p Ž .Ž .r 1qn 1y2n

Ž .where Esmodulus of elasticity GPa , and typicallyŽ 6 2 .ranges from 27 to 35 GPa 4.0]5.0=10 lbfrinches ,

Ž .¨ s Poisson’s ratio mmrmm , typically 0.20"0.02, rŽ 3. 3 Žs density kgrm , typically 2350 kgrm 145

3.lbmrfeet .In good concrete, these properties have a very limited

range of variation, and relationships between velocityand strength have been determined. However, in de-graded or cracked concrete, the velocity drops signifi-

Ž .cantly. The attenuation dBrm , which is a function offrequency, is also a good indicator of condition and isknown to be sensitive to various types of degradationincluding micro-cracking.

To achieve the required penetration of energy ATTTemploys an impulse source that produces a low fre-quency sonic spreading hemi-spherical wavefield in ahalf-space as shown in Fig. 4. The structure of concreteis such that any higher frequency components arerapidly attenuated and the propagating waves do ex-hibit the effects of dispersion and elongation in themeasured pulse due to multiple scattering. For animpulse transmitted through a section of concrete themost distinct feature is the first arrival of the direct

Ž .compression wave longitudinal or P wave pulse. Whenthe geometric distance between the source and eachreceiver is known and the travel time for the compres-sion wave is measured, the average velocity can bedetermined. It is this arrival which forms the basis for

the individual data which are combined in ATTT. Theset of arrival-time data, together with the source andreceiver coordinates defined by the dam geometry, arethen processed using software tomographic inversiontechniques that forms cross-sectional images. Theimages show the presence and location of cracks, otheranomalies, and areas of low modulus within a largeconcrete structure. Anomalies identified in the tomo-grams can be used to guide a core extraction program.When the resulting data are combined with the testresults of a coring program, an entire large concretedam can be characterized, giving data for use in struc-tural analysis and response models.

The impact source provides a broad-band, high-en-ergy, pulse that includes low-frequency energy. De-pending on the size and shape of the structure, and themaximum size aggregate, non-destructive measure-ments are made in the frequency range from approxi-

w xmately 1 to 50 kHz 26 . To determine the time ofimpact, an accelerometer is attached to the source or areceiver placed immediately adjacent to the impactlocation, either of which can be used as a referenceand system trigger.

5. The physics of ATTT

ATTT is based on a combination of phenomenawhich can be described by theories that have beendeveloped for physical acoustics. A review of the funda-mental theories for elastic waves in solids has been

w xprovided by Pao 49 , and the use of elasticwave]material structure interaction theories in NDEmodeling have been reviewed by Thompson and Wadleyw x50 . Canonical problems in the geometrical theory of

Ž w x.Fig. 4. Waves for impulse source on a free surface after Graff, 1975 48 .

( )L.J. Bond et al. r Construction and Building Materials 14 2000 133]146140

diffraction include the diffraction of waves in two andthree dimensions by an edge or crack. It is this type offundamental interaction combined with propagation ofpulses from an impulse source within a scatteringmedium, all set within the constraints of the geometryof the structure that define the system encountered inATTT. This combination of phenomena can then be

Ž . Ž .described by: a a point impulse source; b wavefieldŽ .near-fieldrfar-field effects for point sources; c crack

Ž .interactionsrtime-of-flight ray-theory; and d attenua-tion-Rayleigh scattering in coarse materials.

5.1. A point impulse source

Stress waves can be generated by any mechanismcapable of producing a force impact that varies rapidlywith time. The important parameters that characterizethe impact are the duration of impact, the area of theimpact, and the force or loading of the impact. Therelationships between these parameters are described

w xby the Hertz theory of elastic impact 26 . Impactgenerated stress waves are composed of a wide dis-tribution of frequencies and amplitudes, which in turnare a function of the force and duration of the impactw x51 .

Analytical solutions have been developed for an im-pulse source on a half-space. When a point impulsestress loading is applied to a solid, the disturbancewhich is generated travels through the solid as a set ofstress waves as shown in Fig. 4. In a semi-infinite elasticsolid there are three primary modes of stress wave

Ž .propagation: compression longitudinal or P-waves ,Ž .shear S -waves, and surface or Rayleigh waves. The

particle motions for a compression and shear waves areparallel and perpendicular to the direction of travel,respectively. The Rayleigh wave travels along the sur-face of the solid and at the surface there is ellipticalparticle motion. The speeds of the three waves aredifferent, and they are all different functions of elasticmoduli, Poisson’s ratio and the density of the material.

The impact sources in ATTT generate waves below50 kHz, and the received waves have frequencies lessthan 10 kHz. Typically, concrete has a compressionalwave speed between 3000 and 4000 mrs, and at 10 kHzthis corresponds to a wavelength of approximately 0.4

Ž .m 16 inches .

5.2. Wa¨efield near-fieldr far-field effects for point sources

The typical geometry of a high dam is a thin double-curved concrete wall. When an impact source is appliedto the top, front, or back of the structure the waves areconfined within the thin sheet. This type of wave-geom-etry interaction is similar to that which can be encoun-tered for acoustic emissions in a thin sheet and the

Fig. 5. Waves from an impulse source on a plate showing spreadingto plate wave transition.

wave]plate interactions need to be considered in twomain regimes: the near-field and the far-field.

In the plate, the compression waves from a surfaceimpact spread initially as a hemispherical wave, as

Ž w x.shown in Fig. 4 after Graff 48 . As the waves expandup and down the plate in the far-field they transitioninto plate modes at a distance equal to the platethickness, as shown in Fig. 5. In 3-D, the near-field thespreading function is spherical and in the far-field it iscylindrical.

These geometrical effects restrict the simplest formof ATTT to a region around the impact site of no more

Ž .than twice the plate structure thickness. If a verysparse array is employed, the potential exists to employthe platerLamb wavefields to inspect very large regionsof the dam where range is then limited by the combina-tion of spreading function and attenuation.

5.3. Crack interactionsr time-of-flight ray-theory

Experience has shown that an acoustic pulse will notŽpass through a crack with a width of 0.08 mm 0.003

. w xinches or larger 51 , in effect causing a shadow zonebeyond the crack. The only waves that will be receivedimmediately below a crack or delaminated lift-line willbe scattered pulses and tip-diffracted waves, both ofwhich will have clearly identifiable travel time delays

w xwhen compared with the expected direct pulse 48 .A number of studies have considered low frequency

Ž .long wavelength scattering of ultrasound by cracks. Avariety of analytical and numerical model tools areavailable to give insight into this type of scatteringsystem and a review of the earlier literature has been

w xprovided by Dean 52 . The diffraction of elastic wavesat various forms of stress concentrations and cracks

w xwas reviewed by Mow and Pao 53 . Time-of-flightinspection theory using Kirchoff ray theory, tip-diffrac-tion and mode-conversion, has been developed to sup-port several types of NDT for application to the thick

w xsteel sections encountered in the nuclear industry 54 .

( )L.J. Bond et al. r Construction and Building Materials 14 2000 133]146 141

Fig. 6. Direct and tip-diffracted ray paths.

The problems of crack detection in the presence of acoarse-grain stainless steel micro-structure has also

w xbeen considered 55 , and this has resulted in thedevelopment of several types of ray-theory based inver-

Žsions, including SAFT Synthetic Aperture Focusing.Techniques . To support various forms of NDT, includ-

ing interactions with cracks, using long wavelengthsŽ .low frequencies a body of theory has been developedw x56 . This body of work provides much of the ray-theorymethodology required by ATTT.

A simple geometrical ray-theory model was em-ployed to predict wave arrival times. An example of thisanalysis is shown in Fig. 6. Reference travel times arethen calculated using ray paths and assumed or averagematerial properties. The amplitude of a tip-diffractedwave, in particular in the presence of the attenuationdue to the inhomogeneous nature of concrete, is ex-tremely difficult to calculate, and the necessary theoret-ical analysis was outside the scope of this study.

5.4. Attenuation } Rayleigh scattering in coarse materials

Ultrasonic attenuation in a material depends on boththe size of particles set in the matrix and acousticimpedance contrast, between particles and matrix. Thesize scale is set by the drl ratio, where d is the size ofthe particles and l is the wavelength of the integratingwavefield. The strength of the scattering, including if afeature is treated as a single scatterer in a matrix or ifmultiple scattering is significant, is then set by theacoustic impedance contrast between the inclusion andthe matrix. Techniques have been developed and im-plemented to use ultrasonic attenuation and back-

w xscatter to measure grain size in metals 10,57 . Anexample of the theory and experimental data for ultra-sonic attenuation caused by Rayleigh scattering by

w xgraphite nodules in cast iron is given by Papadakis 58 .Since that time there have been numerous studies ofgrain size in various metals. The literature for attenua-tion in concrete is more limited.

Concrete acts as a low-pass mechanical filter. As thesound wave travels through concrete the higher fre-quencies are attenuated as they hit the aggregate]paste

w xinterfaces. Signal attenuation as high as 30 dBrm 59has been measured using the James V-Meter, operat-ing at frequencies of approximately 50 kHz. As a wavepropagates through a solid its amplitude decreases with

Žpath length due to attenuation scattering and absorp-. Ž .tion and divergence beam spreading . In the evalua-

tion of concrete, to achieve propagation over the re-quired distances, low frequency waves must be used toreduce the rate of attenuation of wave energy due to

w xscattering 60 . For detection, the size of the flaw mustbe approximately equal to or larger than the wave-length of the propagating wave.

If the wave length of the propagating wave is less

Fig. 7. Attenuation of ultrasound in concrete and mortar as a function of frequency.

( )L.J. Bond et al. r Construction and Building Materials 14 2000 133]146142

than the size of aggregate, there will be scattering ateach mortar]aggregate interface. However, use of lowfrequency waves reduces the sensitivity of the propagat-

w xing wave to detect small flaws 61 .ŽIn theory, the highest frequency shortest wave-

.length that can be expected to pass through any sig-nificant length of concrete has a wave length four times

Ž .the size of the maximum size aggregate MSA . Forexample if the maximum size aggregate in the concrete

Ž .is 25 mm 1 inches frequencies greater than approxi-mately 40 kHz will be rapidly attenuated, and in bulkmaterial this is found to be the case. Attenuation data,as a function of frequency, based on work by Berthelot

w xet al. 62 for mortar and 10 mm MSA concrete areshown in Fig. 7. To achieve an inspection range ofseveral meters, it is necessary to use frequencies as lowas 5 kHz.

6. Implementation and models for ATTT

An implementation of ATTT on a section of a typi-

cal structure uses an impact source and a sparse lineararray of receivers, are shown in schematic form in Fig.8. The corresponding set of ray-paths, used to analyzethe tomographic inversion are shown in Fig. 9. Thenecessary instrumentation system is shown in schematicform in Fig. 10. The receivers are set in vertical lines

Ž .with a separation of 1.5 m 5 feet . These arrays can beŽ .up to 90 m 300 feet long and are set in vertical lines

Ž .spaced every 3 m 10 feet across the dam. The exactsource and receiver positions can be determined usingeither conventional surveying techniques or photo-grammetry.

Lines of data taken at successive lateral positionsalong the dam are used to map the joint condition andcracked area of each lift-line, as shown in schematicform in Fig. 11. Once detected and located, the defec-tive zones in the lift-lines can then be characterizedusing receivers in an increasingly dense array to aug-ment the number of data points and hence, the resolu-tion.

The coarseness of the mesh of the structural analysismodel used for a dam safety evaluation will ultimately

Fig. 8. Example of source]receiver arrays.

( )L.J. Bond et al. r Construction and Building Materials 14 2000 133]146 143

Fig

.9.

Sche

mat

icsh

owin

gra

y]gr

idfo

rso

urce

]re

ceiv

ersy

stem

.

( )L.J. Bond et al. r Construction and Building Materials 14 2000 133]146144

Fig. 10. Schematic showing instrumentation for ATTT.

determine the required level of characterization andtherefore, number of data points required. Currentfinite element analysis techniques employ elements that

Ž .are typically approximately 15=15 m 50=50 feetrectangular elements one-half or one-third the thick-

w xness of the dam 59 . Obviously the denser the datapoint grid, the better the data but the more costly thetesting and modeling of the dam will be.

As discussed previously, it is a combination of factorsincluding the energy in the impulse source, the wavespreading and attenuation characteristics, the geometryand material properties, which limit the effective in-spection zone. Theoretical estimates for input energyrequirements in relation to receiver sensitivity can beintegrated with a geometric ray theory coverage analy-

w xsis using ‘Sonar Equations’ 63 . If a source with anŽintensity equivalent to 50 W is used giving a nominal

.signal level of 100 dB a practical detection limit forŽ .the receiver including a source follower will be en-

countered at approximately 3 mV. This gives a practicalsystem dynamic range of approximately 220 dB. For a

Fig. 11. Schematic for lines of data taken at successive lateral posi-tions along the dam.

known attenuation a maximum range can then beestimated.

Arrival time data and the relative spatial coordinatesof the impact source and receivers are measured. It isthese data which form the primary data in the tomo-

w xgraphic inversion scheme 64 .

7. Conclusions

At present, there is no method that provides anadequate detailed assessment of mass concrete struc-tures, such as dams. A novel tomographic inspectionmethodology has been proposed and the fundamentalphysics discussed. The inspections using ATTT havebeen shown to have the potential to give descriptionsof life-line cracks and also to identify variations inelastic moduli. A series of laboratory and field testshave been performed to investigate and quantify thecapabilities of ATTT, and these are presented in a

w xcompanion paper 7 .

Acknowledgements

This work was performed with the support of theBureau of Reclamation, Denver, Colorado. Specialthanks to Tim Samaras and Larry Brown of AppliedResearch Associates and to the Reclamation ClimbTeam of Kurt von Fay, Kurt Mitchell and D. ThomasJohnson for their help with data acquisition.

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