zhong_design of foundations for large dynamic equipment in a high seismic region_2013

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Design of Foundations for Large Dynamic Equipment in a High Seismic Region

Zhong (John) Liu, Ph.D., P.E., S.E.1

1

Kiewit Power Engineers Corp., 9401 Renner Blvd., Lenexa, KS, 66219; PH (913)-928-7467;email: [email protected]

ABSTRACT

Generally, foundations for large dynamic equipment are made of considerable amounts

concrete, thus they contribute to a significant percentage of a projects total concrete quantity.Designing these dynamic foundations requires a series of static and dynamic analyses to meet the

vibration requirement of the equipment and any seismic requirements of the local building codes.

This article researches and compares different modeling methods, and then proposes an efficientapproach for their design in high seismic regions.

For design optimization, two different types of foundations should be considered forthese areas: mats and piles. Liquefaction, downdrag on piles, bearing pressure, spring constants,

soil stratification, water table, soil types, bearing depth, and settlement, can all affect afoundation. Reviewing the geotech report and performing a cost/risk analysis with the contractor

should make it clear which type of foundation should be considered at a given locale. Engineers

should design these foundations using a finite element modeling software that can handledynamic loading. Modal analysis can be used to provide frequencies and displacement

amplitudes to verify vibration performance criteria based on ACI 351 and the manufactures

requirements. Modal analysis can also be used to analyze seismic response spectrum per SAPtime history analysis. In addition, a model based on static and quasi-static loads as required by

the applicable building code should be analyzed. The ability to combine these models into onecan help to solve these problems more quickly and efficiently.

A case study for a foundation of steam turbine generator is presented, in which, the

analysis features and design procedures used are described in detail. This may help designengineers understand the different advantages and results of finite element models, to pick the

best modeling option for any given situation.

Keywords: Dynamic Analysis, Seismic Analysis, Turbine Foundation, Pile Cap, DynamicEquipment, Gas Power Plant

INTRODUCTION

Due to economic, environmental and technological changes, natural gas power plants

have become more popular. In which, the foundation of large dynamic equipment such as a CTG

(Combustion Turbine Generator) or STG (Steam Turbine Generator) take major role among thestructures because of the amount of concrete required to support them. Traditionally, design

methods of turbine foundations have developed gradually from rule-of-thumb to scientific

engineering methods. Currently, ACI 351.3R-4 (Foundations for Dynamic Equipment) [1] and

manufactures requirements offer a design basis for dynamic analysis. Local building codes [2]offer seismic and other structural requirements that also need to be met. The following provides

1403Structures Congress 2013 ASCE 2013

Structures Congress 2013


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some basic knowledge, touches on what is required when designing large dynamic equipment in

seismic regions, as well as giving modeling tips.

FOUNDATIONS OF LARGE DYNAMIC EQUIPMENT

A gas power plant the dynamic equipment of a CTG or STG generally includes thefollowing: compressor, turbine, and generator. Per ACI 351.3R-4 two types of foundations are

acceptable for use; block-type and tabletop-type. The above mentioned code also lists

requirements for both. For gas turbines, block foundations are used; for steam turbines, thecondenser arrangement in the low pressure turbine area leads to a tabletop-type foundations

being required. Both block and tabletop foundations may be directly supported by underling soil

or by piles to reach deeper soil layers for sufficient load bearing capacity. These foundations maybe expanded to include nearby structures and equipment, isolated from surrounding structures by

a joint filled with elastic material, by vibration isolators, or springs from supporting structures.

The various options of foundations, manufacture requirements, and building code requirements,can lead to multiple complicated structural models all of which have both pros and cons.

Depending on the project a traditional procedure may be the best design methodology, as theyare proven and are typically simpler.

The dimensions of foundations generally start from rule-of thumb based on mass, shape,and thickness. For example, the foundation weight in the case of rotating machines should be at

least 3 times the total machine weight. For block foundations using piles or springs, this ratio can

be reduced to 2.5 times [1]. The pile cap mass should be 1.5 to 2.5 times and 2.5 to 4 times themass of the machine for centrifugal and reciprocating machines, respectively [3]. The basic

principle behind these values is that the foundation behaves as a rigid body that reduces the

vibrations of machine can impart into the soil below. Other factors such a soil properties, pilesize and spacing, anchorage requirements, and equipment layout also affect the sizing of the

foundation. Most importantly, the foundation needs to be designed per code and manufacturesrequirements. Being able to account for all these factors in the modeling phase is necessary.

Design optimization plays a very important role to reach an efficient economical structure, as the

dynamic and seismic behavior of structures may change significantly from its original roughpreliminary sizing.

The information presented below is based on data from three gas power plants located in

California and designed by Kiewit Power Engineers Co. All three sites contained liquefiable soil

layers which required pile cap structures for the CTG and the other large dynamic equipment.

DYNAMIC REQUIREMENT FOR TURBINE FOUNDATION

Turbine vendors generally provide following dynamic loads during operation:

(1)Normal Torques Loads (NTL) The magnitude of the normal torque dependsupon the rotational speed and power output of the rotating components ofequipment. Fluid loads on the turbine impose a net torque on the casing that is

opposite to the rotation of the rotor. This load is given as an equivalent moment

couple.(2)Normal Machine Unbalance Loads (NUB) - Which is a result from imbalance in

the equipment during cyclic movement as a result of defects due to material

imperfection, design tolerances etc. This force is applied radially outward at




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infinite points off the centerline of the shaft. The unbalanced force amplitude

may be estimated as followings:

= me

Where m = rotor mass, = machine operating speed (radian/sec), and e = rotor eccentricity. Thisresult should be multiplied by a service factor, generally greater than or equal to 2 [1]. For

industry criteria, such as ISO 1940 and ASA/ANSI S2.19, define balance quality in terms of aconstant e = Q. Q can be found in Table 3.1 of ACI 351 [1] based on balance quality guide.

There are also dynamic emergency loads such as:

(1) Loss of Rotor Blade (RBL) - Which is an emergency load associated with a breakageof one or more blades of the turbine rotor. If this is not provided by the manufacturer, it

may be assumed to be 6 times Normal Machine Unbalance Loads (NUB).

(2) Generator Accidental Torque (SCT) - This load occurs when there is a short circuit atthe generator terminals thereby inducing a severe loading condition.

As both of the above emergency loads have such a small likelihood of occurrence, the

design load factors for ultimate strength is taken as unity or 1.0.For a dynamic analysis of foundation, the unbalanced forcing function may be applied as

a harmonic load as:

sin(

Where F(t) = Value of the forcing function at any instant of time t; F 0= Peak value of forcing

function; =machine operating speed; and =Phase angle.

When a turbine has more than one rotor, each rotor may have a different phase angle. Thefoundation should be designed for the most unfavorable combination of these phase angles. The

severity of the resulting foundation vibration can then be estimated based on the human

sensitivity to vibration. The recommended requirements may contain a peak vibration velocity atany point of foundation and the peak acceleration at the attached points for the turbine generator

sections. ACI 351[1] provides the limiting or permissible amplitudes as Fig. 3.9 and Fig.3.11 of[1] based on operation speeds.

Due to the difficulty of dynamic analysis for harmonic load, the manufacturer may

provide a simplified method of dynamic requirements, for example, a combined requirement ofnatural frequency and overall stiffness of the foundation. The natural frequency of foundation

needs to avoid resonance with the operating equipment. The manufacture provided the following

requirements for the CTGs at the Marsh Landing Power Plant. (1) The frequencies of entirefoundation system and individual components must not occur within a range from 70% up to 130%

of operating seed 3600 RPM. (2) The minimum exclusion criteria must be satisfied for all

modes where mass participation of at least 90%. (3) At least the first five modes must be

checked. (4) The stiffness of the foundation must be capable of maintaining negligiblemisalignments between the driven and driving equipment components. The criteria above may

be stated as static deflections on supports and bearings of foundation for critical dynamic loads,

such as NUB and NTL.




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SEISMIC SITE CONDITIONS

Three power plants have different seismic design parameters in Table 1.

Table 1. Seismic Parameters of Three Gas Power Plants in California

Criteria Haynes WalnutCreek

MarshLanding

Site Class F (D*) D D

Occupancy Category III III III

Seismic Design Category F (D*) D D

Seismic Importance Factor, I 1.5 1.25 1.25

Site Coefficients Fa = NA

Fv = NA

Fa = 1.00

Fv = 1.50

Fa = 1.00

Fv = 1.50

Mapped Spectral Response

Accelerations

Ss = NA

S1 = NA

Ss = 1.94

S1 = 0.73

Ss = 1.5

S1= 0.516

Maximum Spectral ResponseAccelerations

SMS =1.32SM1 =1.09

SMS =1.94SM1 =1.10

SMS =1.5SM1= 0.774

Design Spectral ResponseAccelerations

SDS = 0.88SD1= 0.73

SDS =1.3SD1= 0.73

SDS = 1.0SD1= 0.516

Design Peak Ground Acceleration NA 0.52g 0.4g

Long-Period Transition Period (TL) NA 8 Sec 8 Sec

Note: * Use Site Class D for structure with natural period of vibration < 0.5 seconds per ASCE

Chapter 20.3.1.

The major seismic hazards are those hazards associated with earthquakes such as ground

shaking, ground rupture, liquefaction, differential compaction or seismic settlement, and otherphenomena. Liquefaction is a phenomenon whereby saturated, granular soils lose their inherent

shear strength due to excess pore water pressure build-up which normally occurs during the

repeated cyclic loading an earthquake produces. Liquefaction hazards includes loads manifestedin the form of buoyancy force during liquefaction, increases in lateral earth pressures due to

liquefaction, horizontal and vertical movements resulting from lateral spreading, and post-

earthquake settlement of the liquefied materials.To avoid liquefaction hazards, deep foundations were required for the dynamic equipment on

these three power plants. Precast prestressed concrete piles were used for Marsh Landing project,

while auger pressure grouted (APG) piles are used for Haynes and Walnut Creek projects. All

piles are required to penetrate through any soil layers that liquefaction can occur before the pile

is counted on to take any axial loading. The effects of liquefaction will impose additionaldowndrag loads on piles in a seismic event. This downdrag force is a result of settling of soil

layer(s) which is caused by the dissipating of built-up of pore water pressure in the liquefiablesoils during ground shaking. Downdrag is a negative skin friction between soil and pile, which

is an additional load on the pile that reduces the axial capacity of the pile. For example, the

maximum downdrag load is about 40 kips to 80 kips based on the anticipated range ofthicknesses of the potentially liquefiable soils at Haynes project site.




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Figure 1. Haynes Repowering Project

According to California Building Code, the foundation may be designed per equivalent

lateral force (ELF) procedure or response spectrum analysis. Per ELF, the base shear is:

W

In which, W is weight of equipment, and coefficient

I/R

Where, I and SDS can be found in Table (1) and R = modification factor =3 per Table15.4-2 of ASCE 7-05.

FINITE ELEMENT MODELING

Concrete foundations of large equipment generally are designed per linear elastic analysis,

since amplitudes and static deformations are normally small (the stiffness change due to cracksmay be ignored). For finite element design types, beam, shell (plate), and solid elements may all

be used. Beam elements are generally used for table foundations and piles; shell and solid

elements may be used to model pile caps, massive block foundations, and pedestals.Using solid elements has an advantage to the other types as its possible to more

accurately model variable section changes of foundation compared to shell elements. However,

as they have more degrees of freedom and typically more elements, the calculation time required

is increased. The results from solid elements are also more difficult (compared to shell elements)to convert accurately into moment, shear, and axial forces which are necessary in design a

concrete section based on ACI 318.




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Figure 2. Marsh Landing CTG Model

For Marsh Landing project, solid elements were used for modeling the CTG foundation.Haynes and Walnut Creek projects, however used shell elements to model their dynamic

foundations. The equipment was modeled as masses that are connected to the plate/foundation

element nodes by rigid rods. By contrast if shell or solid elements are used, the rigid rods may

be linked to any point in the element, not just the surface as in when using plates. Be aware thatwhen a rigid rod is used for this purpose it stiffens the foundation, which may or may not have an

effect on the design depending on the differences in stiffness between the foundation and the

equipment.Boundary conditions also play an important role in the modeling of foundation. For

example, in a static model of mat foundation, damping properties and subgrade of soil may be

sufficient to analyze loads including quasi-static dynamic and seismic loads. However, toachieve a more accurate interaction model between subsoil and foundation, a special boundary

element may be required. The ability to do this can be difficult to find in commercial software.

Using a pile-soil interaction model is more realistic when designing a pile cap, but doing this

requires additional geotechnical parameters and specialized software. In the design of pile cap,we did not consider pile-soil interaction, because some traditional pipe analysis software such as

Lpile is independent from finite element software such SAP, RISA, and STAAD. Traditionally,

there are several options for pile modeling as followings.

(1)Model the piles as short beams with length of fixed point based on interpreted frompile analysis. This method may be used for both static and dynamic analysis [6],however this type of analysis has difficulty in accurately modeling the stiffness of thepile. This is because the interaction between the stiffness of pile and soil may not be

reasonably simplified as just a single fixed end beam.(2)Model the piles as fixed support points. This method is generally used for a

traditional static analysis. The reactions calculated are based on free or fixed

conditions by finite elements and can be used for pile analysis by assuming the pile




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top is either a free head or a fixed headed pile condition. If the foundation was

supported on bedrock, this could be an acceptable methodology. If not, basing thedesign on this method could generate errors and be unsafe as it will not distribute the

loads to the piles correctly due to the foundations stiffness being inaccurate.

(3)Model the piles as elastic spring supports. This method may be used for both staticand dynamic analysis. The spring constants include vertical, horizontal, rocking,cross-stiffness, and torsion. For this type of analysis, cross-stiffness coefficients play

an important role because the piles behave like the columns in a moment frame, as the

lateral deflection of frame is related to the moments of columns. Before using thismethod verify that the software being used will support modeling a cross-stiffness

spring coefficient. For example RISA and STAAD do cannot, while both SAP 2000

and GTStrudl offer an advanced option to input a matrix of spring constants. ForSAP 2000, in a fixed coordinate system, the spring forces and moments Fx, Fy, Fz, Mx,

My, and Mzat a joint are given by:

z

y

x

z

y

x

z

y

x

z

y

x

r

r

r

u

u

u

rz

ryrzrysym

rxrzrxryrx

uzrzuzryuzrxuz

uyrzuyryuyrxuyuzuy

uxrzuxryuxrxuxuzuxuyux

M

M

M

F

F

F

.

Where ux, uy, uz, rx, ry, and rz are the joint displacements and rotations, and the terms ux,

uxuy, uy, are specified spring stiffness coefficients. For dynamic analysis of equipment inoperation, Novak and Howell [4] provided equations of spring constants. Pile analysis software,

such as Lpile can also provide spring constants for us to fill out this matrix.

Figure 3. The global axial system in SAP

For a fixed head condition in the global axial system of SAP, the spring constants of a circular

pile are defined as follows:

ux = uy = lateral stiffness (kip/in) = an applied lateral force on the top of pile divided byinduced deflection.

uz = Axial stiffness (kip/in) = EA/L*




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rx = ry = Lateral bending stiffness (kip-in/rad) = an applied moment force on the top of

pile divided by induced rotation on same direction.rz = Torsional stiffness (kip-in/rad) = GJ/L

uxry = -uxry = Cross-couple term (kip-in/in) = The induced shear divided by an applied

rotation on the top of pile.

All other constants in the matrix are zeros.Where: A = Cross-sectional area (in2); E = Youngs modulus (ksi); G = 0.4E; J = Torsional

moment of inertia; L = Length of pile (in); L* = L for a bearing pile, L/2 for a pile with a

constant skin friction, and L/3 for a pile with a linearly varying skin friction.

CASE STUDY

A simplified foundation based on GEs GEK-63383 steam turbine generator is used for

this analysis. GEs dynamic criteria include two types of analysis: Method A (evaluation of

natural frequencies) and Method B (forced vibration). In the case study, several models areincluded to help engineers to decide the proper model for their analysis. Following conclusions

are reached through the case study.(1)Different element models: Beam elements can create a very simple STG foundationmodel which be analyzed by hand calculations. Rigid links are used to model theconnection joints of beams. Shell (plate) and solid elements were also be used to

represent the table top, columns, and footing (Figures 4 to 8). Based on SAP analysis,

all finite element design methods provided very close first natural periods (Table 2). Inother words, engineer may choose the type of element without having a significant

impact on the accuracy of the calculation. This is only true as long as the foundation

behaves as a rigid mat.(2)Soil springs: Soil spring constant may be calculated per 4.2 of ACI 351.3. Soil springs

can be modeled as typical link elements for shell elements or nonlinear links.Nonlinear links can be modified per different spring conditions, such as a compression-

only spring vertically.

(3)How to model rotors of turbine: Per GE manual, rigid links should be used per Figures13 to 17 of [7]. A rigid link is a specification between two joints such that the

displacements at the slave joint will be the same displacements as the master plus rigid

rotation. In SAP 2000, rigid links consist of a link element with all directions of

movement and rotations fixed. The GE manual doesnt suggest modeling the rotoraxial as a rigid link as the displacement check of misalignment tolerance matrix verifies

whether the axial line of rotor is straight. If a rigid link is used to replace axial line,

there wont be any misalignment result, which is erroneous. To give a better visionalview of model, a very weak link element may be used to replace rotor axes, which

wont change the result.

(4)Forced vibration analysis: Foundation vibrates under harmonic dynamic loads frommachine. For each bearing, unbalanced forces are based on weight of rotors and

operating speeds (Table 3). To model direction change of harmonic dynamic loads, sine

and cosine functions are added in two perpendicular axes. By using time historyanalysis, foundation structure should be verified per followings: (a) At rated speed, the

peak vibration velocity in the direction of each principal axis of the foundation at the

turbine-generator machine baseline interfaces should be less than 0.06 inches/second.




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(b) At any speed up to 120% of rated turbine speed (with the unbalance force adjusted

for speed), the peak vibration velocity in the direction of each of the principal axis ofthe foundation at the turbine-generator machine baseline interfaces should be less than

0.15 inches/second.

(5)Response spectra analysis: Similar to harmonic dynamic load, seismic responseanalysis may be analyzed by using the time history of design option in SAP. Based onSection 12.9 of ASCE 7-05, code specified design spectra or site spectra (Figure 9) may

be used.

Figure 4. Beam Element Model w/o Footing

Figure 5. Shell Element Model w/o Footing




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Figure 6. Solid Element Model w/o Footing

Figure 7. Solid Element Model w/ Footing &SoilSprings

Figure 8. Shell Element Model w/ Footing & Soil Links




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TABLE 2. First Natural Periods of Models

Model Period (Sec)

Beam Element Model w/o Footing 0.24817

Shell Element Model w/o Footing 0.25680

Solid Element Model w/o Footing 0.27943Solid Element Model w/ Footing & Soil Springs 0.46847

Shell Element Model w/ Footing & Soil Links 0.37771

TABLE 3. Unbalance Forces (kips) per Turbine Speed Following GE Manual [7]

Turbine

Speed(RPM)

Generator Rotor

(weight 142 kips)for bearings #5 & #6

HP/IP Rotor


LP Rotor


1500 4.53 1.21 4.05

1800 6.53 1.75 5.84

3000 18.13 4.85 16.22

3600 26.11 6.99 23.36

4320 37.60 10.06 33.63

Notes: Unbalance Force Equation F = 1.419e-8*W*N2, W = the rotor weight (lbf); N= themachine design operating speed in rpm; F = total unbalance force (lbf).

Figure 9. Design Response Spectra in Geo-Report




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CONCLUSIONS

Designing large dynamic equipment foundations located in high seismic regions is based

on a multitude of factors. The dynamic requirements and seismic requirements based on site

conditions both play a very important role. For seismic regions where liquefaction of soil layers

is possible, using deep pile foundations is likely going to be the best approach. For finiteelement analysis, SAP 2000 may be used to create a model for static and dynamic analysis. The

option to input a matrix of spring stiffness coefficients, calculated from an Lpile analysis, is very

convenient for modeling piles and can give the best results. A forced vibration analysis canverify foundation how behave during operation. While, a spectrum analysis can be used to verify

the equivalent lateral force procedure required per California Building Code.

REFERENCES

1. ACI 351.3R-04, Foundations for Dynamic Equipment, Reported by ACI Committee 351, 2004.

2. California Building Code, 2010.3. Suresh C. Arya, Michael ONeil, George Pincus, Design of Structures and Foundations for

Vibrating Machines, Gulf Publishing Company, 1979.4. Joseph E. Bowles, Foundation Analysis and Design, Mcgraw-Hill, 1997.

5. Peter Nawrotzki, Gunter Huffmann, Timur Uzunoglu, Static and Dynamic Analysis of

Concrete Turbine Foundations, Structural Engineering International, Mar, 2008.6. Arkady Livshits, Dynamic Analysis and Structural Design of Turbine Generator

Foundations,European Built Environment CAE Conference, July, 2008.

7. GE Energy, Turbine Generator Foundations, Feb, 2012.8. GE Energy, Turbine Generator Foundations, Feb, 1998.


zhong_design of foundations for large dynamic equipment in a high seismic region_2013

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