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'0~" SOIL DYNAMICS
. AND" MACHINE '.. FOUNDATIONS By
Dr. SWAMI SARAN
Department of Civil Enginemng
University of Roorkee
Roorkee-247 667 (INDIA) ~ ~) j JW' .:r-.~
,J}j~-4-' \.-:. J:'" 4i~ \;S" .5357 :OJW 13!fi/3 11!2 :~Jt; 1999
iF Galgotia ublications
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pvt.ltd. 5,AnsarIRoad, Daryaganj,New Delhl-110 002
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Soil Dynamics ' and Machine rl( -5 - "- \:' ~"'~ ~.;
5; ~ "rz ~ ~1J . :,~--/ ";: ~,>' ,qqq ' Foundatio~s~, ' , i (' ~ \ .. .
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,'- , };~ i-~ "-)f>; ~",;'~~ First Edition 1999 ~ Reserved - 1999 No matter in full or part may be reproduced or transmitted in any form or by any means (exceptfor review
or criticism) without the written permission of the author and publishers. Though much care has been taken by the author and the publishers to make the book error (factual or
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that might have crept in at any stage. Published by .Suneel Galgotia for Galgotia Publications (P) Ltd.
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;." ..- "". , PREFACE During the last 25 years, considerable work in the area of soil dynamics and machine foundationshas been
reported.Courseson soil dynamicsandmachinefoundationsalreadyexistat graduatelevelin many institutions,
and its inclusion at undergraduate level is progressing fast.
The author is engaged in teaching the course on soil dynamicsand machine foundationsat gr'duate level
from last fLfteen
years. The text of this book has been developed mainlyout of my notes preparedfor teaching
the students.The consideration in developingthe text is its lucide presentationfor clear understandingof the
subject.The material has been arrangedlogicallyso that the reader can follow the developmentalsequenceof
the subject with relative ease. A number of solved examples have been included in each chapter. All the
formulae,charts and examples are given in SI units.
Some of the material included in this text book has been drawn from the works of other autors. Inspiteof
sincereefforts,somecontributionsmay nothavebeen acknowledged.The authorapologisesfor suchomissions.
The author wishes to express his appreciationto Km. Lata Juneja, Sri RaJeevGrover and Sri S. S. Gupta
for typing and drawing work. Thanks arealso due to the many collegues,friends and studentswho assistedin wittingof thisbook. . . The author would be failing in his duty it he does not aclaiowledge the support he received from his
family members who. encouraged him through the various stages. of study and writing.
The book is dedicated to author's Sonin law, (Late) Shri Akhil Gupta as a token of his love, affectionand
regards to him.
(Dr. Swami Saran) : 11~f1
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oS ;"'..., ,~'~:~~F~B .:'l~ CONTENTS .
PREFACE 1. INTRODUCTION
1.1 General
1.2
1.3
1.4 2. THEORY OF VIBRATIONS
2.1 General
2.2 Defmitions
2.3 Harmonic Motion
2.4 Vibrations of a Single Degree Freedom System
2.5 Vibration Isolation
2.6
2.7
2.8 3. Earthquake Loading
Equivalent Dynamic Load to an Actual Earthquake Load
Seismic Force for Pseudo-staticAnalysis
Illustrative Examples
References
Practice Problems Theory of Vibration Measuring Instruments
Vibration of Multiple Degree Freedom Systems
Undamped Dynamic VibrationAbsorbers
Illustrative Examples
Practice Problems WAVE PROP AGATION IN AN ELASTIC, HOMOGENEOUS.
. AND ISOTROPIC MEDIUM
3.1 General
3.2
Stress, Strain and Elastic Constants
3.3 Longitudinal Elastic Waves in a Rod oflnfmite Length
3.4 Torsional Vibration ora Rod of Infmite Length
3.5 End Conditions
3.6
3.7
3.8
3.9
3.10
3.11 Longitudinal Vibrations of Rods of Finite Length
Torsional Vibrations of Rods of Finite Length
Wave Propagation in an lnfmite, HomogeneousIsotropic, Elastic Medium
Wave Propagation in Elastic, Half Space
Geophysical Prospecting
Typical Values of CompressionWave and Shear Wave Velocities
Illustrative Examples
References.. . ;
'.
Practice Problems 1-12
I
3
6
9
12
12
12
13-66
13
14
15
18
32
36
39
48
53
64
êéóïïé
67
67
70
72
74
76
80
81
86
93
108
108
116
117 £i,., ~ viii 4. Soil Dynamics & Machine Foundations DYNAMIC SOIL PRO~ER~5.
4.1
General '-. ."' . 4.2
4.3
4.4 ëò LaboratoryTechinques
Field Tests
FactorsAffecting Shear Modulus, ElasticModulus and Elastic Constants
IllustrativeExamples
References
PracticeProblems ïèéóîíé
187
187
201
221
236 DYNANnCEARTHPRESSURE
ëò ï General ëòî Pseudo-static Methods 5.3 Displacement Analysis
Illustrative Examples
References 237 PracticeProblems 6. DYNAMIC BEARING CAPACITY OF SHALLOW FOUNDATIONS
6.1 Pseudo-static Analysis 6.3
6.4 7. General 6.2 Bearing Capacity of Footings
Dynamics Analysis
Illustrative Examples
References
Practice Problems LIQUEFACTION OF SOILS
7. 1
General
7.2
Definitions
7.3
7.4 --.118-186
118
118
147
163
174
182
184 Mechanism of Liquefaction
Laboratory Studies DynamicTriaxial Test
7.6
Cyclic Simple Shear Test
7.7
Comparisonof Cyclic Stress Causing Liquefactionunder Triaxial and
Simple Shear Conditions
7.8
StandardCurves and Correlations for Liquefaction
7.9
Evaluationof Zone of Liquefactionin Field
7.10 VibrationTable Studies
7.11 Field Blast Studies éòë 7.12 Evaluationof LiquefactionPotentialusing Standard Penetration Resistance 7.13 Factors Affecting Liquefaction - îíèóîéè
238
238
238 .
249
268
277
278
îéçóííç
279
2.79
281
283
288
296
300
301
306
309
314
319
323 Contents ix ' 324
326
332
336
339 7.14 AntiliquefactionMeasures
7.15 Studies on Use of Gravel Drains
IllustrativeExamples
References
Practice Problems 8. . GENERAL PRINCIPLES
8.1
General
8.2
8.3 Types of Machines and Foundations
General Requirements of Machine Foundation 8.4
8.5 Perimissible Amplitude
Allowable Soil Pressure 8.6
8.7 9. 340-351
340
340
347
348
349 Permissible Stresses of Concrete of Steel
Permissible Stresses of Timber
References FOUNDATIONS OF RECIPROCATING MACHINES
9.1 General
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9 10. . OF MACIDNE FOUNDATION DESIGN Modes of Vibrationof a Rigid FoundationBlock
Methods of Analysis
Linear Elastic Weightless Spring Method
Elastic Half-space Method
Effect of Footing Shape on Vibratory Response
Dynamic Response of Embedded Block Foundation
Soil Mass Participating in Vibrations
Design Procedure for a Block Foundation
Illustrative Examples
References
Practice Problems FOUNDATIONS OF IMPACT TYPE MACIDNES
10.1 General 349
350
351
íëîóìîî
352
~ 352
353
354
370
392
394
400
402
408
419 .
420 ìîíóììî
423 Design Procedure for a Hammer Foundation 426
432 Illustrative Examples
References
Practice Problems 436
442
442 10.2 DynamicAnalysis
10.3 11. . FOUNDATIONS OF ROTARY MACHINES
11.1 General
11.2 Special Considerations
11.3 Design Criteria ììíóìêð
443
444
445 ,{" '<~" .'.' , ", '",' ;;,' ..~ .'~ , INTRODUCTION 1.1 GENERAL
Geotechnical engineers frequently come across two types of problem in relation to the analysis and design of foundations namely (i) foundations subjected to static loads and (ii) foundations subjected to
dynamic loads. The characteristic feature of a static load is that for a given structure the load carried by
the foundation at any given time is constant in magnitude and direction ~.g. dead weight of the structure.
Live loads such as weight of train on a bridge and assembly of peopl{in a building are also classified as
static load, The characteristic feature of a dynamic load is that it varies with time. Dynamic loads on
foundations and engineering structures may act due to earthquakes, bomb blasts, operation of machines,
pile driving, quarrying, fast moving'traffic, wind or sea waves action. The nature of each dynamic load is
different from another. Figure 1.1 shows the variation of dynamic load with time in some typical cases,
Purely dynamic loads do not occur in nature. Loads ar~ always combinations of static and dynamic loads.
Static loads are caused by the dead weight of the structure, while dynamic loads may be caused through
the sources mentioned above.
.
' 0-3 01
.. 0.1 c:
0 - 0
...
CII -v 0.1.
CIoJ v et 0.2 0-3 . I 0 I I I I I
~ I I I I I 10' I I I I L...t-I.
15 ," I I I . 20 I I I I I I I I 25 Timt. . 5
(a) A.f~el~r9gramof F;.L
Centro earthquake of May 18,1940NS component
Fig. 1,.1:.y,,-:i~J.ion
o(dyn_m'c load with time in some typical cases (...Contd.) '---'--"-- ,_. I I
30 _.
2 Soil Dynamics & Machine Foundations +
1:) Time 0
0 u E
d c
>- a Period of loading
T usually large
(b) Dynamic load due to steady state vibration U
d + 0 v E
d
C Time >- a ~.T.I
.' (c) Multiple impulse loading Vertical High frequency
predominates
(d) Trice ofvertical acceleration of ground due to pile driving
. Fig. 1.1: Variation of dynamic load with time in IOmetypical cases ¶ Jntroduttion ïôîùÛßÎÌØÏË·ÄÕÛÔÑßÜ×ÒÙ -, ".- Vibrations of earth's surface caused by waves coming from a source of disturbance inside the earth are
described as Earthquakes and are one of the ri1ostdestructive forces that nature unleashes on earth.
When, at any depth below tile gro~d surfa~e,the strain ene~gy'ac~~ulated due to deformations in earth
mass exceeds the resilience of the storing material, it gets release through rupture. The energy thus
released is propogated in the form of waves which impart energy to the media through which they pass
and vibrate the structures standing on the earth's..surface. The point inside the earth mass where slipping
or fracture begins is termed as focus and the point just above the focus on the earth's surface is termed as
epicentre. The position of the focus is determined,with the help of seismograph records (Fig: 1.2]'u:ti't'ising
the average velocities of different waves and time difference in reaching the waves at the ground surface.
Figure 1.3 explains the various terms in simple manner. ITrace 1 amplitude) Fig. 1.2. : A typical earthquake ~
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.Fig, 1.3 : Definitions of focus and epicentre "._.,~~""'- '=-'3"'",""""",'"""""'~,'.' ~"..",.c.,=.: "...""""~"",,...,,'.-,..,=,,====o,.- - -l.., 4- ' ~~ ~ Soil Dynamics cl Machine Fo"nd4tio.ns 1.2.1 Intensity. The severity of shaking of an earthquake as felt or ob!jervedthrough damage is'described
as intensity ata certain place on an arbitrary scale. For this purpose modified Mercalli scale is more
common in use. It is divided into 12 degrees of intensity as presented in Table!.L
Table 1.1 : Modified MereaIli Intensity Scale (Abridged}
Classof
Earthquakes Description
Not felt except by a very few under specially favourable circumstances. " Felt only by a few persons at rest, specially on upper floors of buildings; and delicately suspended objects may swing. fII Felt quite noticeably indoors, specially on upper floors of buildings but many people do not
recognize it as an earthquake; standing motor cars may rock slightly, and vibration may be felt
like the passing of a truck. IV During the day felt indoors by many, outdoors by a few; at night some awakened,dishes, windows, doors disturbed, walls make cracking sound, sensation like heavytruck striking the building; and standing motor car rocked noticeably. V Felt by nearly everyone; many awakened; some dishes, windows, etc. broken; a few instances of
cracked plasters; unstable objects overturned; disturbance of trees, poles and other tall objects noticed sometimes and pendulum clocks may stop. . VI Felt by all; many frightened and run outdoors; some heavy furniture moved; a few instances of
fallen plaster or damaged chimneys; damage slight. VII Everybodyruns outdoors, damagenegligible in buildings of good design and construction; slight
to moderate in well built ordinary structures; considerable in poorly built or badly designed
structures; some chimneys broken; noticed by persons driving motor cars. VIII Damage slight j!, spe~ially designed structures; considerable in' ordinary substantial buildings
with partial collapse; very heavy it) poorly built structures; panel walls thrown out of framed
structure; heavy furniture overturned; sand and mud ejected in small amounts; changes in well
water; and disturbs persons driving motor cars.
. IX Damage considerable in specially designed structures; well designed framed structures thrown
out of plumb; very heavy in substantial buildings with parti~1collapse; buildings shifted off
foundations; ground cracked conspicuously; and underground pipes broken. X Some well built wooden structure~ destroyed; most masonry and framed structures with foundations destroyed; ground badly cracked; rails bent; land-slides considerable from river banks and
steep slopes; shifted sand and mud; and water splashed over banks. XI Few, if any, masonry structures remain standing; bridge destroyed; broad fissures in ground,
underground pipe lines completely out of service; earth slumps and landslips in soft ground; and ~ rails bent greatly.
XII '- Total damage; waves seen on ground surface; lines of sight and , lever distorted; and objects thrown
'" upward into the air. , . 'H", .1
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J.!, s 1.2.2 Magnitude. Magnitude of an earthquake ,.._" a measure of the size of an earthquake, -',",
is
based on the
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amplitude of elastic waves it generates. Richter (1958) suggested the following relation.
M = loglOA -loglO Aa
. ...(1.1)
where
M = Magnitude of earthquake
A = Trace amplitude in mm (Fig. 1.2)
Aa = Distance correction (F:ig.1.4)
,.
A relationship between strain energy released py an earthquake and its magnitude is given by Richter
(1958) as follows
~ , loglo E = 11.4 + ,. ...(1.2) 1.5 M where E = Energy released in earthquake in Ergs
A comparison of the magnitude M of an earthquake with maximum i tensity of the Modified Mercalli Scale is given in Table 1.2.
, Table 1.2 : Comparison , of the Richter Scale Magnitude with the Modified Mercalli Scale Richter Scale Magnitude (AI) Maximum Intensity, Modified
Mercalli Scale 2 I, II 3 m 4 IV,V 5 VI, Vp
VII, VIII 6
7
" , ' .IX, ; 8 X XI The fault length, affected area and duration of earthquake also depend on the magnitude of earthquake (Housner, 1965; Housner, 1970). Table ,1.3 gives approximate idea about these.
" ' ' Table 1.3 : Fault Length, Affected Area,~nd Duration of.Eart~quake
Magnitude oj
Earthquake
(Richter scale) Fault Length" 5 1-2 6 , , 2-5 . (/en?) ,(km) 7 25-50 . 8 >250 Duration of
'Earthquake
(8) 20,000 i '5 '. Affected.
Area 60,000:,...,
;l J " : f,2()',000'
2 ,00 ,OO j
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0: E
.S 4 0 « .For near
earthquake 0\ ~ 3 For teleseism$
surface waves
with time:
period 20 s ' ..!.- c 0
.+:
v ~
I- 2 0
U ~
c 1 0 ..- 11\
.- 0 0 1 1000 100 10 Distance
. 10000 \ in km . Fig. 1.4: Distaoce corredio.o for magnitude determination 1.3 EQUIVALENT DYNAMIC LOAD TO AN ACTUAL EARTHQUAKE LOAD
Figure 1.1 (a) shows the variation of dynamic load wi+htime observed during El Centro earthquake. The
loading is not periodic and the.peaks in anY two cycles are different. For the analysis and design of
foundations such a random variation is converted into equivalent number of cycles of uniformly varying
load [Fig. 1.1 (b)]. It means that the structure-foundation-soil system subjected to Ns cycles of uniformly
varying load will suffer same deformations and stresses as by the actual earthquakes. Most of the analyses
and laboratory teSting are 'carried out using this concept.'
.
According to Seed and Idriss (1911), the average equivalent uniform acceleration is about 65 percent
of the maximum acceleration. The number of significant cycles, Ns depends on the magnitude of earthquake. They recommended the values ofNs as 10, 20 and 30 for earthquakes ofmagnitudes 1, 1.5 and 8
respectively.
Lee and Chan (1912) suggested the following procedure for ..converting the irregular stress-time
history to the equivalent number of cycles of cyclic shear stresses of maximum magnitude equal to
K 'tmax' ~ ~eing a constant less th~.1JP.ity : ': ~:"E,j~\ ; Introduction, ',;. ' 7 , H, (i) Let Fig. 1.5 shows ~}Yl'icalea~CJ.uakereco.rd.Divide the s;t;essrange (0 to 'tmaX> acceleration
or
range (0 to amax)into convenient number ofleveIs and note the mean stress or mean acceleration
within' each level as mentioned in column no. 2 of Table 1.4. Then the number of cycles with
peaks 'Yhichfall within each of these levels is counted and recorded. Note that because the actual
time history is not symmetric about the zero stress axis, the number of peaks on both sides are
counted and two peaks are equivalent to one cycle. For example, an earthquake record shown in
Fig. 1.5 has number of cycles in various ranges of acceleration levels as listed in Col. 3 of
Table 1.4.
Om ox :; + 0 . 12 . 1\ c: 1\ A J\'
V VVV 1\ 0
0 ~
e:.I A A 1\ A A VVVV" e:.I
U
u
<X 9mox,= . -0.12 I I I I I I 2 0 4 6 8 10 12 14 Time ( s ) . Fig. 1.5 :, A typical earthquake record
' a plot between stress ratio and conversion factor as sh!)wnin Fig. 1.6.
Conversion factor is defined as'the ratio of equivalentnumber of cycles for 0.65 'tmax equivalent
to
number of cycles for K . 'tmax'Referring to this curve (Fig. 1.6) determine the conversion factor
to each average stress level (Col. 4 of Table 1.4). (ii) Seed et al. (1975) gave (iii) Determine the equivalen~number of unifofm cycles,at a maximum stress level of 0.65 'tma.x y
b
multiplying the values listed in Cols. 3 and 4. 'These are listed in Col. 5.
,
,
. .
. t
, . ' ,', , , (iv) Determine the total.,number of equivalent stress ,cycles at .0..65'tmaxby adding the values listed in
Col. 5. ,
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8 Soil Dynamics & Machine Foundatioiis" Table 1.4 : Equivalent Cycles for Anticipated Eartbquake
Acceleration
level il/ Average and
level in percent of percent of (I) Number (2) 100- 80 Conversion of.
cycles factor (3) Equivalent
number of cycles
at 0.65 1"ma:c (4) - - .. (5) 90
70 5/2 = 2.5
3/2 = 1.5 2.6
1.2 1.8 7/2 = 3.5 0.20 0.70 40 - 20 50
30 5/2 = 2.5 negligible 0.0 20 - 00 10 >100 negligible 0.00 80 - 60
60 - 40 '65 Total numberof
cycles = 9,0 1.0
r> ' - 111 111 ..... 0.8 0.6: I... C
..... ,111 x 0.4 u I 0 lt5 0.2
0
10 3 Conversion 1 factor, 0-3
0'1
(Ns )0.65 Tmax. 0-03 0'01 ( ~S)k Tmax
Fig. 1.6 : Conversion factor versus shear stress ratio For getting the equivalent number of cycles for 0.75 'tmax'read the yalue of conversion factor (Fig.
1.6) corresponding to an ordinate value of 0.75. It comes out as 1.5. The value of equivalent number of
cycles obtained for 0.65 'tmaxas illustrated in Table 1.4 is divided by this conversion factor to obtain
equivalent number of cycles corresponding to 0.75 'tmax 9.0/1.5= 6.0 cycles.
i.e.
Seed and Idriss (1971) and Lee and Chan (1972) developed the above concepts specifically for liquefacti~mstudies. More details of these procedures have been.discussed in Chapter 7. - --""" "~. .. j' Introduction .. 9 1.4 SEISMIC FORCE FOR PSEUDO-STATIC ANALYSIS
For the purpose of determining seismic force, the country is classified into five z...

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