Soil Dynamics and Machine Foundations Swami Saran_1999 - '0~ SOIL DYNAMICS AND MACHINE FOUNDATIONS By Dr SWAMI SARAN Department of Civil Enginemng

Soil Dynamics and Machine Foundations Swami Saran_1999 -...

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Unformatted text preview: . óóóóóó '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 P pvt.ltd. 5,AnsarIRoad, Daryaganj,New Delhl-110 002 . '" . ... " ,I, ,. "'C',' ;. -,' c '. '0' , "~; , , ,~' >.~ .:;~;~"!'ij:~,;~i::>A~~;. .:j : ~ ,; ~ '.p', ,:'.. 11' :':"~~~:O~':i;~,~:~,,~~, .' ~ TA :. -<:: ",:::- 2/~ Or. Swami Saran Soil Dynamics ' and Machine rl( -5 - "- \:' ~"'~ ~.; 5; ~ "rz ~ ~1J . :,~--/ ";: ~,>' ,qqq ' Foundatio~s~, ' , i (' ~ \ .. . ... , . ,'- , };~ 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 printing) free. But neither the author nor the publisher takes any legal responsibility for any mistake that might have crept in at any stage. Published by .Suneel Galgotia for Galgotia Publications (P) Ltd. 5, Ansari Road, Darya Ganj, New Delhi-ll0 002. '"" ,';.. ". ::::..',.- , , ,.,. '0'," .. :. ',.' '" Laser Typeset by .. ADO Computer's 402 (RPS) DDA Flats Mansarover Park, Shahdara, Delhi-l 10 032. Ph : 2292708 . ".. . Prinled al Cambridge PrintingWorks,New Dclhi-llO028 . >. ;." ..- "". , 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 1.:;;-,0,...::, ':,':' "~iJ , ..; '.o..;oc;."" òò×溬þôòò¢ c ,'t...,: '. '-~~' ,.)~ , ".,.~ 1" i""" ,"",-:,,»"'" j J ~ .,~ ;"""""""',","_'"""~r""""',"""",,,.'o_-' ~'j.'W.,~", . ,',. ..;' f~ '.- .,-;'~ O#y t' . ~""'j 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 ~ ':', :,": þù ',' Site ß (,rou nd su rtace ..-,' :rr: -- "" " :' ',' ',.',:', Epic.entre '" . " , .,' .. e, /'fIIT.'" ,... """ 'y.. " .."" " ...'. .:=- ':,. ...',,' , / / . ,"","-' ,,'..'- "..-,".," : " ..'" I / I' / / I / I I , Foc.us ~ Epic.entric. distance E " ô ô.,'ù record I I " ,"/ / / / f..JfL ,o.~ // ' / 7 . f:/' c.' <C°f..J J ' .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 f'.'.H ... I",. ';1' ~, ®ãáåó¬ùÿþæáæ·ÄãþùÑãþù¢ù ~.>.\;..: ~! f.:.~;) I"troduction ' !,;,,; ~~~ j i:'.;,~,;:; n ~~f;; S ~\.h~ ",\1.J j " J.!, s 1.2.2 Magnitude. Magnitude of an earthquake ,.._" a measure of the size of an earthquake, -',", is based on the -.-". . ~"."""""", ,.,..,.._~,-,, ".. 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 ',<{' 15 \ ::.~: . 25-30 , ;. 45-50 . . , ' " r.'t ~y~~~~ ' , SoU DyIUlllfics & Mtrehille Foundations 6, c:./ " :J - 'c 5 0\ 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. , ," , - ". " .< ,.' > , . , . ' '. ".'/ <",,"' " , " ',:""".". .,.,:'~c'"':"..' .'",:,.' . ' , ", ,J1;' , . .:..I..; " "Or. ~- --'-" . . . ._.n . " .'. ~.~.,>..,.. ~. - -- t--. ~,--... -- -, .. 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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