Structures under Shock & Impact VI, C.A. Brebbia & N. Jones … · manufacturer of the machine. The...

Evaluation of performance of machine

foundation under blast-induced excitation

M.H. El NaggarGeotechnical Research Centre, University of Western Ontario, Canada

Abstract

The planning of foundations for equipment sensitive to vibrations requires athorough dynamic investigation of the proposed location of the foundation withregard to the effect of already existing or additional vibration sources. This paperdiscusses the analyses performed for a power plant facility that is subjected toblasting-induced vibration from an adjacent quarry. To assess the level ofseismic excitation at the site due to blasting activities in the quarry, an extensiveground vibration-monitoring program was carried out. This program includedinitial blast monitoring of production blasts at the future turbine location, and thedevelopment of a final design acceleration time-history. The results of thevibration-monitoring program showed that the production blasts displayedextremely variable vibration characteristics and indicated the potential for anunacceptable response of the machine foundation. The ground accelerations dueto blasting were measured and recorded for three directions simultaneously:vertical and two orthogonal horizontal directions. The measurements with themost intense ground accelerations taken at the ground surface in the location ofthe future machine foundation were selected as the final design acceleration time-history. The proposed foundation option is a shallow foundation system thatconsists of a rigid reinforced concrete slab resting on a layer of engineered fillunderlain by the native bedrock. The analytical model used to calculate thedynamic characteristics of the foundation system is described. The availableapproaches for the analysis of the foundation's response to transient loads arediscussed. In this case, a Fourier analysis approach was used to predict theresponse of the foundation to the blasting-induced vibrations. The results of theanalysis showed that the proposed foundation system would performsatisfactorily.

Structures under Shock & Impact VI, C.A. Brebbia & N. Jones (Editors) © 2000 WIT Press, www.witpress.com, ISBN 1-85312-820-1

48 Structures Under Shock and Impact VI

1 Introduction

The design of foundations for vibrating equipment is significantly different fromthe design of foundations supporting static loads. Foundations for vibratingequipment must provide supports for the machinery and its attachments (ultimatelimit states design). In addition, they must provide adequate rigidity to hold themachinery in place with limited vibration amplitudes during normal operatingconditions (serviceability limit states). Because this high-speed equipment mustmeet very strict vibration criteria, the rigidity rather than the strength requirementoften governs its foundation design.

Foundations supporting large power generators, motors and compressors aresubjected to harmonic excitations during normal operation. These harmonicforces develop when the rotating parts of the machinery (rotors) with inevitableimbalances are put into a rotating motion. The design of the machine foundationrequires the calculation of the response of the foundation-machine system tothese forces as they represent the only source of vibration. In the case offoundations supporting highly sensitive devises and/or foundations supportingequipment in the vicinity of external sources of strong excitations, the vibrationdue to the external source must be considered. In this paper, a case study ispresented where ground transmitted excitation rather than the harmonic load dueto the normal operation of the machine governs the design.

2 Design criteria

The design of a machine foundation has to meet both static and dynamicrequirements for satisfactory performance. The static requirements include theability of the foundation to support the static (factored) weight of the machine-foundation system without failure in the supporting soil, and limiting thedeflection or settlement of the foundation to the specified tolerance. The dynamiccriteria require that: a) resonance should be avoided, i.e. the natural frequency ofthe machine-foundation system should not coincide with the operating frequencyof the machine (commonly, the natural frequency of the system is designed to beat least 1.2 times the operating frequency); and b) vibration amplitudes due to allsources of excitation should not exceed the permissible values that are set by themanufacturer of the machine.

The dynamic criteria usually govern the design because of the strict vibrationtolerances for the machines. The total response of the system should becalculated accounting for excitations from all sources.

3 Design approach

The main objective of the design is to limit the response amplitudes of thefoundation to the specified tolerance in all vibration modes. The tolerance is


Structures Under Shock and Impact 17 49

usually set by the machine manufacturer to ensure a satisfactory performance ofthe machine and minimum disturbance for people working in its immediatevicinity. The displacement of foundations subjected to dynamic loads depends onthe type and geometry of the foundation, the flexibility of the supporting groundand the type of dynamic loading.

To achieve the above objective, the design of a machine foundation involvesa trial-and-error procedure [1]. This procedure includes the following steps:

1. Estimate the dynamic loads: that includes the determination of theirmagnitudes and characteristics.

2. Establish the soil profile and evaluate the soil properties required for thedynamic analysis (Shear modulus, mass density, Poisson's ratio and materialdamping ratio).

3. Select the type and trial dimensions of the foundation based on experience andwith the manufacturer's input, establish the performance criteria.

4. Compute the dynamic response of the trial foundation (step 3) supported bythe given soil profile (step 2) due to the estimated load (step 1) and comparethe response with the performance criteria. If the response is not satisfactory,modify the dimensions of the foundation (step 3) and repeat the analysis untilsatisfactory design is achieved.

As can be noted from this procedure, the dynamic response analysis is themajor component in the design process. The analysis essentially involves thecalculation of the vibration characteristics of the machine-foundation-soil system(i.e. the natural frequencies and the vibration amplitudes due to all sources ofvibration). The complexity of the response analysis required depends on the typeof the foundation system. For flexible foundation systems (e.g tabletop or matfoundations), dynamic finite element analysis may be necessary. For rigidfoundations resting directly on the soil or supported by pile groups, simplifiedanalytical and/or numerical methods are commonly used in the analysis.

The response of soils and foundations to dynamic excitation is frequencydependent and thus is a function of the stiffness and damping parameters of thesoil and the foundation. Therefore, the evaluation of the appropriate stiffness anddamping parameters (impedance functions) for the foundation soil or pile/soilsystem is a key step in the analysis.

4 Foundation impedance functions

The basic mathematical model used in the dynamic analysis is a lumped masswith a spring and dashpot shown in Figure 1. If the mass, m, is free to move inonly one direction, e.g. vertical, it is said to have a single degree of freedom(SDF). The foundation block has six degrees of freedom, three translational andthree rotational. These are the displacements along the axes x, y and z androtation about the same axes.

The response of the mass depends on the nature of the soil reaction that ismodeled by both the spring and the dashpot. The spring represents the elasticityof the soil and is characterized by the stiffness constant k, which is defined as the


50

force that produces a unit compression (or extension) v of the spring in thepositive direction of the displacement of the mass. The dashpot representsdamping caused by energy dissipation. Damping is derived from two sources,energy dissipated through waves spreading away from the foundation (radiationdamping) and energy dissipated due to the imperfect elasticity of the soil(hysteretic or material damping). Two main foundation types are commonlyused, shallow foundations and deep foundations (piles).

A number of approaches are available to calculate the impedance functionsof both shallow and deep foundations. Most of these approaches are based on theassumption of elastic or viscoelastic soil continuum. The impedance function of afoundation system is a complex quantity, one that has a real part, KI, representingthe stiffness and an imaginary (out of phase) component, 2, representing thedamping. The impedance function of the foundation in each vibration mode canbe written as:

K = K,+;K, (1)

The impedance function can also be expressed using the stiffness constant, k(* 0» and the constant of equivalent viscous damping, c=Im(K/tt>)=K2/(£> where ® = frequency of loading in radians. For shallow foundations, theconstants k and c can be evaluated using the elastic half-space theory. Theprincipal advantages of this model are that it accounts for energy dissipationthrough elastic waves, provides for systematic analysis and describes soilproperties using basic constants such as shear modulus, material damping ratioand Poisson's ratio. The theory yields formulae and charts (see El Naggar [1]).For deep foundations, impedance functions can be calculated using thesuperposition approach described in El Naggar and Novak [2]. In this approach,the stiffness of individual piles is considered first, and the group effect isintroduced through the interaction factors approach. All the techniques used tocalculate the impedance functions for shallow footings and deep foundations areencoded in the computer program DYNA5 (Novak et al. [3]) that was used in thisstudy.

m m

+v

a- Actual system b- Basic model of SDFFigure 1 The basic mathematical model used in foundation dynamics

5 Evaluation of dynamic excitation

The type of response of a system depends on the nature of the loads applied. Theloads and responses resulting from them can be periodic, transient or random.


Structures Under Shock and Impact VI 5 j

Rotating machines produce centrifugal periodic forces due to unbalanced rotors.An unbalanced mass ™e rotating with an eccentricity ^ and circular velocity co

produces a centrifugal force P=m^eco^ . In design situations, the manufacturer of

the machine should provide the excitation forces. Transient loading ischaracterized by a nonperiodic time history of limited duration. This type ofloading is represented either by an analytical expression or by a set of digitaldata. Two different types of loads are considered in this study. The first is aharmonic load due to the operation of the rotating equipment and is evaluatedbased on the machine data provided by the vendor. The second is a transient loadand results from blasting activities in a quarry operation.

To assess the level of seismic excitation at the site of the future foundationdue to blasting activities in the quarry, an extensive ground vibration-monitoringprogram has to be carried out. This program should include initial blastmonitoring of production blasts at the future turbine location, and thedevelopment of a final design acceleration time-history. The results of thevibration-monitoring program would show the pattern and vibrationcharacteristics of the production blasts (i.e. duration of blasts, intensity of theground vibration, and frequency content). The analysis of the results ofmonitoring would indicate if there was a potential for an unacceptable responsefrom machine foundation.

6 Response analysis

Foundations supporting large machines are usually composed of thick reinforcedconcrete blocks resting on the ground or supported by a group of piles. In bothcases, the foundation can be assumed to vibrate as a rigid body. The equation ofmotion for this rigid body in one direction (i.e. SDF similar to that shown in Fig.1) when subjected to a dynamic excitation is

mS + cS + kS = P(t) (2)where m is the mass of the system, c and k are the damping coefficient andstiffness constant of the foundation along the direction considered and P(t) is the

loading excitation; and S, S and 8 are the acceleration, velocity anddisplacement of the foundation. For harmonic loading (i.e. load due to normaloperation of the rotating machine), the harmonic response is given by

S(t)= . ** cosfrrt +</>) (3)

_ fi~\Cwhere co is the loading frequency and =tan~^ - - is the phase shift.

k-mcoFor blast loading, the excitation force, P(t), is given by {-mii(t) } where

u(t) is the absolute ground acceleration time history measured at the location ofthe future foundation In this case, there are two approaches to solve for the

response of the foundation. In the first approach, the Duhamel integral of u(t) isused to calculate the relative displacement of the foundation, i.e.



(4)

where

The response of the machine-foundation system is influenced by both itsnatural frequency and the frequency of loading. The transient loading due toblasting is transmitted to the foundation as a combination of seismic wavespropagating in the ground at different frequencies. Equation 4 implies that thestiffness and damping of the foundation are constant. However, the stiffness anddamping of the foundation system are frequency dependent and the use of Eq. 4to calculate the response may compromise the accuracy.

Alternatively, Fourier analysis can be used to calculate the response of thefoundation to the transient load. In this analysis, the load is represented by thesum of a series of harmonic components by subjecting the load time history to a

Fast Fourier Transform (FFT). In the FFT, the input function x(t) (i.e. -m ii(t)) is

given at an even number, N (the computation is particularly efficient if N is equalto a power of two), of equidistant points in the time domain as

x =x(t =tAO, * =0,1,2.. ..(N -1) (5)

in which A* is a constant increment of time. The digital Fourier transform pair isgiven by

yV-lr —V Y p -xkn'N (fa\*k ~Zj " lO&J

N-l%n =XX<?~' ^ (6b)

/t=0Equation 6a expresses x(t) as a series of harmonic components with complex

r ^ iamplitudes %n =X\ being Fourier transforms of **. The exponent can be

rewritten as i2 nk/N=i where the frequency of the %* component is

The number of frequency components is limited, and for N data points, N/2frequency components are obtained. Thus, increased accuracy can only beobtained by increasing the number of data points. The response of a SDF systemloaded by the harmonic component would be governed by

/M^ + c^ + M = %y^ (8)The response of the system can be related to the loading by

(0 = 77( )x/ (9)

where H(a>n) is a transfer function given by

(10)


Structures Under Shock and Impact VI 53

where |/f()| = modulus of the complex transfer function. The real part of the

response due to the harmonic component is then given by

(11)

The principle of superposition gives the total response as 8(f) = (0 .

7 Case study

A power plant facility is to be constructed very close to a quarry operation. Theproposed facility houses two combustion turbine-generator units and a steamturbine-generator unit. Each unit will be supported by an independentfoundation. The blasting is expected to occur up to 8 m from the plant boundary.Blasts occur on average two times a week and last for about O.Ssec each time. Aninitial vibration monitoring program indicated a potential vibration problem dueto the blasting activities. The requirements of the facility dictate that thecombustion turbine must not be damaged during the blast. The standardoperational tolerances on foundation vibrations for the combustion turbinefoundation are limited to peak dynamic displacements of 0.0762 mm (0.003 in).The selected foundation option is a shallow foundation system that consists of areinforced concrete slab 1.8 m thick. The native soil beneath the concrete slabwill be excavated and removed to a depth of 6 m below the existing groundsurface. An engineered fill 4.2 m thick will be placed prior to the foundationbeing constructed. The engineered fill will consist of coarse sand whoseproperties (soil shear wave velocity and material damping ratio) are defined fromlaboratory tests.

To evaluate the blast-induced excitation, an extensive ground vibration-monitoring program was carried out. This program included initial blastmonitoring of production blasts at the future turbine location, and thedevelopment of a final design acceleration time-history. The results of thevibration-monitoring program showed that the production blasts displayedextremely variable vibration characteristics and indicated the potential for anunacceptable response from the machine foundation. The ground accelerationsdue to blasting were measured and recorded for three directions simultaneously:vertical as well as two orthogonal horizontal directions. The measurements withthe most intense ground accelerations, taken at the ground surface in the locationof the future machine foundation, were selected as the final design accelerationtime-history.

It is important to identify the frequency content of the forcing function as itinfluences the response of the foundation system. Figure 2 shows the groundacceleration-time history measured at the weathered rock in the location of thesubject foundation that was selected as the design acceleration time-history. Thisacceleration-time history was used to calculate the force-time histories that wouldbe experienced by the proposed foundation. Examining the variation of the forceFourier amplitudes with frequency revealed that the acceleration intensity andforce amplitudes were highest in the longitudinal direction and lowest in the



transverse direction. It was also noted that most of the energy is concentrated inthe frequency range 600-780rad/sec (95-125Hz) for the longitudinal direction and500-920rad/sec (80-150Hz) for the vertical direction.

As the forcing function covers a range of frequencies, the stiffness anddamping of the foundation system should be calculated over that range. Becauseof the uncertainty about the shear wave velocity, V$, of both the engineered fillafter construction and the bedrock, different soil profiles were considered in theanalysis. Two main profiles were considered: homogeneous haifspace with auniform shear wave velocity (Haifspace profile, commonly used in practice); anda layer underlain by a homogeneous haifspace (Composite Medium profile, thatis more representative of the actual soil profile). In the Composite Mediumprofile, the shear wave velocity of the layer is assumed to be uniform and lessthan the shear wave velocity of the haifspace. For both profiles considered, theshear wave velocity of the soil at the bottom of the foundation was assumed to beequal to 180, 240 or 300 m/sec. In the Composite Medium profile, the shearwave velocity of the haifspace was assumed to be equal to 300 or 360 m/sec. Thestiffness and damping of the foundation were calculated over the frequency rangeof interest. Comparing the vertical stiffness and damping from the two profiles, itwas noted that the Composite Medium yielded higher vertical stiffness values(almost double) and much smaller damping values than the Haifspace profile.Similar observations were made for the horizontal direction, especially fordamping. The effect of the increase of the shear wave velocity was to increasethe stiffness and damping of the foundation system.

7.1 Response of the foundation system to ground motion

The foundation was assumed to be rigid and to be embedded in the ground. Theinertial force due to the ground motion was used as the dynamic excitation force.This inertial force was calculated as the mass of the foundation and the supportedequipment multiplied by the measured ground acceleration. To account for theuncertainty regarding the damping, its value was halved and the response wascalculated with the reduced value for both the Haifspace and Composite Mediumprofiles. Inspection of the results revealed that the analysis for the CompositeMedium profile with V; = 240 m/sec and reduced damping yielded the highestresponse in the vertical direction. Therefore, only the results from this case arepresented. Figure 3 shows the frequency response at the centre of gravity (C.G.)of the foundation system with a maximum vertical displacement of 0.0737 mm(0.0029in).

7.2 Response of the foundation system to operating loads

The response of the foundation under the effect of the operating loads was alsoevaluated. The operating loads considered in the analysis include the normaltorque loads, normal unbalance load and the turbine thrust/exhaust load. Theresponse was evaluated at the C.G. of the foundation system as well as at thebearing of various machinery components using the Composite Medium profilesand V; = 180 m/sec and 240 m/sec. The analysis with V, = 240 m/sec with


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reduced damping yielded the highest response in the vertical direction.Therefore, only the results from this case are presented here.

Figure 4 shows the frequency response at the C.G. of the foundationsystem. It is noted from Figure 4 that the peak response in the horizontaldirections x and y occurred at a frequency of approximately 400rpm (6.67Hz) andthe peak response in the vertical direction occurred at a frequency ofapproximately 600rpm (lOHz). These frequencies represent the naturalfrequencies of the equipment-foundation system. These natural frequencies arewell below the operating speed of the turbine/generator (3600rpm). Therefore,there are no resonance conditions. The maximum vibration amplitude calculatedwas 0.01 mm (0.00042in) at the exhaust support.

7.3 Evaluation of the results

The maximum total combined responses to normal operating loads and blastloading in all translational directions were calculated from Figs. 3 and 4. Themaximum response occurred in the vertical direction and was equal to 0.0837mm (0.0033in). The vibration amplitudes obtained using the ground vibrationmeasurements are very close to the specified tolerance value of 0.0762 mm(0.003in) and the total vibration amplitudes (i.e. including the vibrationamplitudes due to normal machine operation) may exceed the specified tolerance.However, they represent satisfactory dynamic performance. The analysisassumed that the entire foundation would vibrate in phase under the effect of theground vibration introduced at the centre of the foundation. This assumptionoverestimated the vibration of this specific foundation by an order of 2 to 3 (thisis called the T effect). This effect depends on the wavelengths of the seismicwaves relative to the dimensions of the rigid foundation. It is expected that thiseffect will reduce the vibration amplitudes by about 50%. This means that themaximum vibration amplitude due to a blast similar to the final designacceleration time-history is expected to be less than 0.0381 mm (0.0015 in).

Figure 2 Final design acceleration time history, vertical direction


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8 References

Structures Under Shock and Impact VI

[1] El Naggar, M. H. Dynamics of Foundations. Chapter 12 in Geotechnical andGeoenvironmental Engineering Handbook, ed. R. K. Rowe, KluwerAcademic Publishers, 2000.

[2] El Naggar, M. H. & Novak, M. Effect of foundation nonlinearity on modalproperties of offshore towers. Journal of Geotechnical Engineering ASCE,121 (9), 660-668, 1995.

[3] Novak, M., El Naggar, M. H., Sheta, M., El-Hifnawy, L., El-Marsafawi, H.,and Ramadan, O., 1999. DYNA5 a computer program for calculation offoundation response to dynamic loads. Geotechnical Research Centre, TheUniversity of Western Ontario, London, Ontario.

TIME (SEC)

Figure 3 Foundation response to blast loading

500 1000 1500 2000 2500 3000 3500 4000 4500FREQUENCY ( RPM)

Figure 4 Frequency response of the foundation due to operating loads


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