KNS4553 SOIL DYNAMICS

KANIRAJ SHENBAGA

UNIVERSITY MALAYSIA SARAWAK

By the end of this course, the students should be

able to design machine foundations complying with

design criteria, evaluate liquefaction potential of

saturated soil, suggest preventive measures,

evaluate lateral earth pressures during earthquakes,

and recommend vibration isolation measures.

Learning Objective 3

By the end of this course, the students should

be able to investigate contemporary practices

and issues on applications of soil dynamics in

machine foundations and earthquake

engineering and prepare technical reports of

the investigations.

Learning Objective 4

Machine Foundations

KNS4553 Soil Dynamics

Block foundation

A pedestal of concrete on which the machine rests.

Box or caisson foundation

A hollow concrete block which supports the machinery at the top.

Wall foundation

A pair of walls which support the machinery at the top slab.

Frame foundation

A frame work of columns, beams, and slabs. The machinery is

supported on the top deck slab.

Types of Machine Foundations

Block Foundation

http://mechanicaldatahelp.blogspot.com/2011/05/machine-foundations-ii.html

Based on operating speed:

Low to medium frequencies (< 500 rpm)

Medium to high frequencies (300 to 1000

rpm)

Very high frequencies (> 1000 rpm)

Types of Machines

1 rpm = 1 revolution per minute = 2π radians per minute

Reciprocating engines (50 to 250 rpm),

compressors, and large blowers:

Low to medium speed machines; Usually

supported on a block foundation

Diesel engines and gas engines:

Medium to high frequency machines

Machines Producing Periodical Forces

High speed internal combustion engines,

electric motors, and turbo generators:

Very high speed machines

Turbo generators are usually supported on

frame foundations, and others on block

foundation.

Machines Producing Periodical Forces

Electric Motor Support

http://www.bing.com/images/search?q=images+of+machine+foundations&view=detail&id=51A66497BBA89E6F0328D059EF7FC06D35167732&first=0&qpvt=images+of+machine+foundations&FORM=IDFRIR

Turbogenerator Foundation

http://www.bing.com/images/search?q=images+of+turbogenerator+frame+foundations&view=detail&id=56716CD0DE953A83499DDE5748D03F17FCB7D873&first=0&FORM=IDFRIR

Turbogenerator Foundation

http://www.coyne-et-bellier.fr/en/dun/sin/fiche_lavrion_industrie.html

Forge hammers and presses:

Usually supported on block foundation

For the construction of a large hammer

foundation see:

http://www.fluekiger.ch/american-

english/our-new-drop-forging-

hammer/index.html

Machines Producing Periodical Forces

Typical configurations of the mounting systems in hammer foundations: (a) one-mass foundation, (b, c), two-mass foundation with springs and dampers

http://origin-ars.els-cdn.com/content/image/1-s2.0-S0022460X03010198-gr1.gif

Direct spring support of a Forging Hammer http://www.gerb.com/en/arbeitsgebiete/arbeitsgebiete.php?ID=151

Loading diagram giving the magnitude and

position of static and dynamic loads exerted by

the machine on the foundation

Power and operating speed of machine

Details of grooves, openings, ducts, embedded

parts, etc., in the foundation

Soil data

Data for Machine Foundation Design

Design Requirements

KNS4553 Soil Dynamics

A machine foundation should satisfy two criteria:

a) Static load criteria

b) Dynamic load criteria

Design Criteria

a) The foundation should be properly located

(location criterion).

b) It must be safe against failure by rupture of soil

(bearing capacity criterion).

c) The foundation must not excessively (settlement

criterion).

Static Load Criteria

a) No resonance should occur.

Resonant frequency must be very large or very small compared to the operating speed of the machine.

b) The amplitude of motion (displacement or rotation) must be within permissible limits under service conditions.

Permissible limits: Prescribed by manufacturers of machine, Code provisions, Empirical guidelines (for preliminary design)

Dynamic Load Criteria

Richard’s Chart for Limiting

Amplitudes of Displacement

in Vertical Vibration

How to use the chart

• Determine the amplitude of

displacement.

• Locate the point on the chart.

• Evaluate the response of persons

to the vibration.

When response limits are defined simultaneously by

values of displacement, velocity, and acceleration,

the plot is called a response spectra for vibration

limits.

Response Spectra

Point A corresponds to: Frequency = 10 cps Displacement = 10-4 inch Velocity ≈ 0.007 in/sec Acceleration = 10-3 g

A

B

Point B corresponds to: Frequency = ? cps Displacement = ? inch Velocity ≈ ? in/sec Acceleration = ? g

Note: Limits based on amplitude of quantity

Response Spectra for

Limiting Amplitudes

of Motion in Vertical

Vibration

Barkan’s Recommendations

Type of machine Permissible amplitude of

displacement, mm

Low speed machinery (500 rpm) 0.20 – 0.25

Hammer foundation 1.00 – 1.20

High speed machinery (a) 3000 rpm Vertical vibration Horizontal vibration (b) 1500 rpm Vertical vibration Horizontal vibration

0.02 – 0.03 0.04 – 0.05

0.04 – 0.06 0.07 – 0.09

Blake’s Recommendation

AA: Dangerous. Shut it down now

to avoid danger

A: Failure is near. Correct within

two days to avoid breakdown.

B: Faulty. correct it within 10 days

to save maintenance dollars.

C: Minor faults. Correction wastes

dollars.

D: No faults. Typical new

equipment

Note: Limits based on peak to peak value of quantity

Blake’s Service Factors

Service Factorsa

Single-stage centrifugal pump, electric motor, fan

1

Typical chemical processing equipment, Noncritical

1

Turbine, turbogenerator, centrifugal Compressor

1.6

Centrifuge, stiff-shaftb; multistage centrifugal pump

2

Miscellaneous equipment, characteristics Unknown

2

Centrifuge, shaft-suspended, on shaft near basket

0.5

Centrifuge, link-suspended, slung 0.3

Service Factor indicates the importance of a machine in the installation.

Example 1: A centrifuge has a 0.01 in (0.250 mm) amplitude at 750 rpm. The value of the service factor is 2. The effective vibration therefore is 2 X 0.01 = 0.02 in (0.50 mm). This point falls in Class A in the chart. The vibrations, therefore, are excessive, and failure is imminent unless the corrective steps are taken immediately.

Example 2: A link-suspended centrifuge operating at 1250 rpm that has 0.003 in (0.075mm) amplitude with the basket empty. The service factor is 0.3, and the effective vibration is 0.0009 in (0.0225mm). This point falls in class C and indicates only minor fault.

A machine operates at a circular frequency of 31.4

rad/s and causes its foundation to vibrate vertically

at an amplitude of displacement of 0.13 mm in steady

state vibration. Evaluate the response of persons to

the vibration using:

(a) Richart’s chart, and (b) response spectra.

Exercise 1

Barkan’s Recommendations

The foundation must be preferably placed above water level to reduce propagation of vibration.

The machine foundation should be placed at a lower level than the surrounding structures and be separated from adjacent structures.

The combined centre of gravity of machine and foundation, and the centroid of the base area should as for as possible lie in the same vertical line.

There must be scope to incorporate future corrections in the base area or mass of the foundation if it becomes necessary due to inadequate performance of the foundation.

Dynamic Analysis of Block Foundations

KNS4553 Soil Dynamics

Degrees of Freedom of Block Foundations

In general, 6 degrees of freedom

3 translational modes (Vertical, Longitudinal, Lateral)

3 rotational (Rocking, Pitching, Yawing)

For cylindrical foundations, only 4 degrees of freedom due to symmetry

2 translational modes (Vertical, Sliding/Horizontal)

2 rotational modes (Rocking, Torsional/Yawing)

Dynamic Analysis Approaches

Empirical and semi-empirical formulae

Soil-as-spring approach

Elastic half-space approach

Empirical and Semi-empirical Formulae

Formulae available for vertical vibration only.

Damping is neglected. Therefore, resonant frequency is equal to natural frequency. (Keep operating speed away from natural frequency.)

The formulae do not consider amplitude of displacement. Not possible to check whether within permissible limits.

Can be used for approximate preliminary calculations, not for final design.

Units as specified in the formulae should be used.

Converse Formula

𝒇𝒏 = 𝟑. 𝟏𝟑𝟖𝟒𝟎𝜸

𝑮𝟏. 𝟔𝟒 −

𝑷𝒅𝑾

+ 𝟎. 𝟓𝟓𝑮𝒓𝒐𝑾𝒗

fn = natural frequency, cps

= unit weight of soil, pcf

G = shear modulus of soil, psi

Pd = maximum dynamic load, lb

Wv = static weight of vibrator or machine, lb

ro = radius of foundation or of an equivalent circular area in the case of rectangular foundation, in

Alpan’s Formula

𝒇𝒏 =𝜶

𝑾𝑨𝟏/𝟒

fn = natural frequency, cpm

W = static weight of machine and foundation, kgf

A = contact area of foundation, m2

= a constant (3,900 for peat; 69,000 for plastic clay;

82,000 for sand; 111,000 for sandstone)

A foundation block and machine weigh 12,000 kgf.

The foundation has a base area of 10 m2. If the block

foundation rests on sand, make a preliminary

estimate of its natural frequency.

Exercise 2